TSTP Solution File: SWW208+1 by nanoCoP---2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : nanoCoP---2.0
% Problem : SWW208+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : nanocop.sh %s %d
% Computer : n015.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 12:25:45 EDT 2023
% Result : Theorem 4.58s 5.52s
% Output : Proof 4.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SWW208+1 : TPTP v8.1.2. Released v5.2.0.
% 0.11/0.12 % Command : nanocop.sh %s %d
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu May 18 22:27:07 EDT 2023
% 0.12/0.33 % CPUTime :
% 4.58/5.52
% 4.58/5.52 /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 4.58/5.52 Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.58/5.52 %-----------------------------------------------------
% 4.58/5.52 ncf(matrix, plain, [(11725 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), v_r), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, hAPP(c_Complex_OIm, hAPP(v_s, hAPP(v_f____, hAPP(v_ga____, 11728 ^ [])))))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), v_r), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))], (810 ^ _415872) ^ [_440568, _440570, _440572, _440574] : [-(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_440574, _440570) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_440572, _440568)), _440574 = _440572, _440570 = _440568], (820 ^ _415872) ^ [_440899, _440901] : [_440901 = _440899, -(c_Complex_Oexpi(_440901) = c_Complex_Oexpi(_440899))], (826 ^ _415872) ^ [_441173, _441175, _441177, _441179, _441181, _441183] : [-(c_Power_Opower_Opower(_441183, _441179, _441175) = c_Power_Opower_Opower(_441181, _441177, _441173)), _441183 = _441181, _441179 = _441177, _441175 = _441173], (840 ^ _415872) ^ [_441661, _441663, _441665, _441667] : [-(c_Complex_Orcis(_441667, _441663) = c_Complex_Orcis(_441665, _441661)), _441667 = _441665, _441663 = _441661], (850 ^ _415872) ^ [_441992, _441994] : [_441994 = _441992, -(c_Transcendental_Oarccos(_441994) = c_Transcendental_Oarccos(_441992))], (856 ^ _415872) ^ [_442210, _442212] : [_442212 = _442210, -(c_RComplete_Onatceiling(_442212) = c_RComplete_Onatceiling(_442210))], (862 ^ _415872) ^ [_442456, _442458, _442460, _442462] : [-(c_Nat__Transfer_Otsub(_442462, _442458) = c_Nat__Transfer_Otsub(_442460, _442456)), _442462 = _442460, _442458 = _442456], (872 ^ _415872) ^ [_442787, _442789] : [_442789 = _442787, -(c_Transcendental_Osin(_442789) = c_Transcendental_Osin(_442787))], (878 ^ _415872) ^ [_443005, _443007] : [_443007 = _443005, -(c_Nat_OSuc(_443007) = c_Nat_OSuc(_443005))], (884 ^ _415872) ^ [_443223, _443225] : [_443225 = _443223, -(c_Complex_Ocomplex_Ocomplex__size(_443225) = c_Complex_Ocomplex_Ocomplex__size(_443223))], (890 ^ _415872) ^ [_443441, _443443] : [_443443 = _443441, -(c_Transcendental_Ocos(_443443) = c_Transcendental_Ocos(_443441))], (896 ^ _415872) ^ [_443659, _443661] : [_443661 = _443659, -(c_Complex_Oarg(_443661) = c_Complex_Oarg(_443659))], (902 ^ _415872) ^ [_443905, _443907, _443909, _443911] : [-(c_Nat_Osize__class_Osize(_443911, _443907) = c_Nat_Osize__class_Osize(_443909, _443905)), _443911 = _443909, _443907 = _443905], (912 ^ _415872) ^ [_444292, _444294, _444296, _444298, _444300, _444302] : [-(c_Complex_Ocomplex_Ocomplex__rec(_444302, _444298, _444294) = c_Complex_Ocomplex_Ocomplex__rec(_444300, _444296, _444292)), _444302 = _444300, _444298 = _444296, _444294 = _444292], (926 ^ _415872) ^ [_444808, _444810, _444812, _444814, _444816, _444818] : [-(c_Complex_Ocomplex_Ocomplex__case(_444818, _444814, _444810) = c_Complex_Ocomplex_Ocomplex__case(_444816, _444812, _444808)), _444818 = _444816, _444814 = _444812, _444810 = _444808], (940 ^ _415872) ^ [_445296, _445298, _445300, _445302] : [-(c_Complex_Ocomplex_OComplex(_445302, _445298) = c_Complex_Ocomplex_OComplex(_445300, _445296)), _445302 = _445300, _445298 = _445296], (950 ^ _415872) ^ [_445627, _445629] : [_445629 = _445627, -(c_RComplete_Onatfloor(_445629) = c_RComplete_Onatfloor(_445627))], (956 ^ _415872) ^ [_445873, _445875, _445877, _445879] : [-(c_Groups_Osgn__class_Osgn(_445879, _445875) = c_Groups_Osgn__class_Osgn(_445877, _445873)), _445879 = _445877, _445875 = _445873], (966 ^ _415872) ^ [_446232, _446234, _446236, _446238] : [-(c_RealVector_Onorm__class_Onorm(_446238, _446234) = c_RealVector_Onorm__class_Onorm(_446236, _446232)), _446238 = _446236, _446234 = _446232], (976 ^ _415872) ^ [_446563, _446565] : [_446565 = _446563, -(c_Power_Opower__class_Opower(_446565) = c_Power_Opower__class_Opower(_446563))], (982 ^ _415872) ^ [_446781, _446783] : [_446783 = _446781, -(c_Transcendental_Oln(_446783) = c_Transcendental_Oln(_446781))], (988 ^ _415872) ^ [_447027, _447029, _447031, _447033] : [-(c_RealDef_Oreal(_447033, _447029) = c_RealDef_Oreal(_447031, _447027)), _447033 = _447031, _447029 = _447027], (998 ^ _415872) ^ [_447414, _447416, _447418, _447420, _447422, _447424] : [-(c_Divides_Odiv__class_Odiv(_447424, _447420, _447416) = c_Divides_Odiv__class_Odiv(_447422, _447418, _447414)), _447424 = _447422, _447420 = _447418, _447416 = _447414], (1012 ^ _415872) ^ [_447874, _447876] : [_447876 = _447874, -(c_Groups_Otimes__class_Otimes(_447876) = c_Groups_Otimes__class_Otimes(_447874))], (1018 ^ _415872) ^ [_448092, _448094] : [_448094 = _448092, -(c_Rings_Oinverse__class_Odivide(_448094) = c_Rings_Oinverse__class_Odivide(_448092))], (1024 ^ _415872) ^ [_448310, _448312] : [_448312 = _448310, -(c_Complex_Ocis(_448312) = c_Complex_Ocis(_448310))], (1030 ^ _415872) ^ [_448584, _448586, _448588, _448590, _448592, _448594] : [-(c_Groups_Ominus__class_Ominus(_448594, _448590, _448586) = c_Groups_Ominus__class_Ominus(_448592, _448588, _448584)), _448594 = _448592, _448590 = _448588, _448586 = _448584], (1044 ^ _415872) ^ [_449072, _449074, _449076, _449078] : [-(tc_fun(_449078, _449074) = tc_fun(_449076, _449072)), _449078 = _449076, _449074 = _449072], (1054 ^ _415872) ^ [_449403, _449405] : [_449405 = _449403, -(tc_Polynomial_Opoly(_449405) = tc_Polynomial_Opoly(_449403))], (1060 ^ _415872) ^ [_449677, _449679, _449681, _449683, _449685, _449687] : [-(c_COMBK(_449687, _449683, _449679) = c_COMBK(_449685, _449681, _449677)), _449687 = _449685, _449683 = _449681, _449679 = _449677], (1074 ^ _415872) ^ [_450249, _450251, _450253, _450255, _450257, _450259, _450261, _450263, _450265, _450267] : [-(c_COMBB(_450267, _450263, _450259, _450255, _450251) = c_COMBB(_450265, _450261, _450257, _450253, _450249)), _450267 = _450265, _450263 = _450261, _450259 = _450257, _450255 = _450253, _450251 = _450249], (1096 ^ _415872) ^ [_451127, _451129, _451131, _451133, _451135, _451137, _451139, _451141, _451143, _451145] : [-(c_COMBC(_451145, _451141, _451137, _451133, _451129) = c_COMBC(_451143, _451139, _451135, _451131, _451127)), _451145 = _451143, _451141 = _451139, _451137 = _451135, _451133 = _451131, _451129 = _451127], (1118 ^ _415872) ^ [_452005, _452007, _452009, _452011, _452013, _452015, _452017, _452019, _452021, _452023] : [-(c_COMBS(_452023, _452019, _452015, _452011, _452007) = c_COMBS(_452021, _452017, _452013, _452009, _452005)), _452023 = _452021, _452019 = _452017, _452015 = _452013, _452011 = _452009, _452007 = _452005], (1140 ^ _415872) ^ [_452799, _452801, _452803, _452805] : [-(c_Orderings_Oord__class_Oless(_452805, _452801) = c_Orderings_Oord__class_Oless(_452803, _452799)), _452805 = _452803, _452801 = _452799], (1150 ^ _415872) ^ [_453130, _453132] : [_453132 = _453130, -(c_Groups_Ozero__class_Ozero(_453132) = c_Groups_Ozero__class_Ozero(_453130))], (1156 ^ _415872) ^ [_453376, _453378, _453380, _453382] : [-(c_Orderings_Oord__class_Oless__eq(_453382, _453378) = c_Orderings_Oord__class_Oless__eq(_453380, _453376)), _453382 = _453380, _453378 = _453376], (1166 ^ _415872) ^ [_453735, _453737, _453739, _453741] : [-(c_Groups_Oabs__class_Oabs(_453741, _453737) = c_Groups_Oabs__class_Oabs(_453739, _453735)), _453741 = _453739, _453737 = _453735], (1176 ^ _415872) ^ [_454094, _454096, _454098, _454100] : [-(hAPP(_454100, _454096) = hAPP(_454098, _454094)), _454100 = _454098, _454096 = _454094], (1186 ^ _415872) ^ [_454425, _454427] : [_454427 = _454425, -(c_Groups_Oplus__class_Oplus(_454427) = c_Groups_Oplus__class_Oplus(_454425))], (1192 ^ _415872) ^ [_454623, _454625] : [_454625 = _454623, -(c_Groups_Oone__class_Oone(_454625) = c_Groups_Oone__class_Oone(_454623))], (2 ^ _415872) ^ [_416016] : [-(_416016 = _416016)], (4 ^ _415872) ^ [_416123, _416125] : [_416125 = _416123, -(_416123 = _416125)], (10 ^ _415872) ^ [_416327, _416329, _416331] : [-(_416331 = _416327), _416331 = _416329, _416329 = _416327], (20 ^ _415872) ^ [_416668, _416670, _416672, _416674] : [-(c_SEQ_Odecseq(_416672, _416668)), c_SEQ_Odecseq(_416674, _416670), _416674 = _416672, _416670 = _416668], (34 ^ _415872) ^ [_417112, _417114, _417116, _417118] : [-(c_SEQ_Oincseq(_417116, _417112)), c_SEQ_Oincseq(_417118, _417114), _417118 = _417116, _417114 = _417112], (48 ^ _415872) ^ [_417528, _417530] : [-(c_SEQ_Osubseq(_417528)), _417530 = _417528, c_SEQ_Osubseq(_417530)], (58 ^ _415872) ^ [_417851, _417853, _417855, _417857] : [-(c_SEQ_Omonoseq(_417855, _417851)), c_SEQ_Omonoseq(_417857, _417853), _417857 = _417855, _417853 = _417851], (72 ^ _415872) ^ [_418295, _418297, _418299, _418301] : [-(c_SEQ_OBseq(_418299, _418295)), c_SEQ_OBseq(_418301, _418297), _418301 = _418299, _418297 = _418295], (86 ^ _415872) ^ [_418739, _418741, _418743, _418745] : [-(c_SEQ_Oconvergent(_418743, _418739)), c_SEQ_Oconvergent(_418745, _418741), _418745 = _418743, _418741 = _418739], (100 ^ _415872) ^ [_419155, _419157] : [-(class_Fields_Olinordered__field__inverse__zero(_419155)), _419157 = _419155, class_Fields_Olinordered__field__inverse__zero(_419157)], (110 ^ _415872) ^ [_419450, _419452] : [-(class_Fields_Olinordered__field(_419450)), _419452 = _419450, class_Fields_Olinordered__field(_419452)], (120 ^ _415872) ^ [_419745, _419747] : [-(class_RealVector_Oreal__normed__div__algebra(_419745)), _419747 = _419745, class_RealVector_Oreal__normed__div__algebra(_419747)], (130 ^ _415872) ^ [_420040, _420042] : [-(class_Rings_Odivision__ring__inverse__zero(_420040)), _420042 = _420040, class_Rings_Odivision__ring__inverse__zero(_420042)], (140 ^ _415872) ^ [_420335, _420337] : [-(class_RealVector_Oreal__normed__algebra__1(_420335)), _420337 = _420335, class_RealVector_Oreal__normed__algebra__1(_420337)], (150 ^ _415872) ^ [_420630, _420632] : [-(class_RealVector_Oreal__normed__algebra(_420630)), _420632 = _420630, class_RealVector_Oreal__normed__algebra(_420632)], (160 ^ _415872) ^ [_420925, _420927] : [-(class_RealVector_Oreal__normed__vector(_420925)), _420927 = _420925, class_RealVector_Oreal__normed__vector(_420927)], (170 ^ _415872) ^ [_421220, _421222] : [-(class_RealVector_Oreal__normed__field(_421220)), _421222 = _421220, class_RealVector_Oreal__normed__field(_421222)], (180 ^ _415872) ^ [_421515, _421517] : [-(class_Fields_Ofield__inverse__zero(_421515)), _421517 = _421515, class_Fields_Ofield__inverse__zero(_421517)], (190 ^ _415872) ^ [_421810, _421812] : [-(class_RealVector_Ometric__space(_421810)), _421812 = _421810, class_RealVector_Ometric__space(_421812)], (200 ^ _415872) ^ [_422105, _422107] : [-(class_RealVector_Oreal__field(_422105)), _422107 = _422105, class_RealVector_Oreal__field(_422107)], (210 ^ _415872) ^ [_422400, _422402] : [-(class_Rings_Odivision__ring(_422400)), _422402 = _422400, class_Rings_Odivision__ring(_422402)], (220 ^ _415872) ^ [_422695, _422697] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_422695)), _422697 = _422695, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_422697)], (230 ^ _415872) ^ [_422990, _422992] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_422990)), _422992 = _422990, class_Groups_Oordered__cancel__ab__semigroup__add(_422992)], (240 ^ _415872) ^ [_423285, _423287] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_423285)), _423287 = _423285, class_Groups_Oordered__ab__semigroup__add__imp__le(_423287)], (250 ^ _415872) ^ [_423580, _423582] : [-(class_Rings_Olinordered__comm__semiring__strict(_423580)), _423582 = _423580, class_Rings_Olinordered__comm__semiring__strict(_423582)], (260 ^ _415872) ^ [_423875, _423877] : [-(class_Rings_Olinordered__semiring__1__strict(_423875)), _423877 = _423875, class_Rings_Olinordered__semiring__1__strict(_423877)], (270 ^ _415872) ^ [_424170, _424172] : [-(class_Rings_Olinordered__semiring__strict(_424170)), _424172 = _424170, class_Rings_Olinordered__semiring__strict(_424172)], (280 ^ _415872) ^ [_424465, _424467] : [-(class_Groups_Oordered__ab__semigroup__add(_424465)), _424467 = _424465, class_Groups_Oordered__ab__semigroup__add(_424467)], (290 ^ _415872) ^ [_424760, _424762] : [-(class_Groups_Oordered__ab__group__add__abs(_424760)), _424762 = _424760, class_Groups_Oordered__ab__group__add__abs(_424762)], (300 ^ _415872) ^ [_425055, _425057] : [-(class_Groups_Oordered__comm__monoid__add(_425055)), _425057 = _425055, class_Groups_Oordered__comm__monoid__add(_425057)], (310 ^ _415872) ^ [_425350, _425352] : [-(class_Groups_Olinordered__ab__group__add(_425350)), _425352 = _425350, class_Groups_Olinordered__ab__group__add(_425352)], (320 ^ _415872) ^ [_425645, _425647] : [-(class_Groups_Ocancel__ab__semigroup__add(_425645)), _425647 = _425645, class_Groups_Ocancel__ab__semigroup__add(_425647)], (330 ^ _415872) ^ [_425940, _425942] : [-(class_Rings_Oring__1__no__zero__divisors(_425940)), _425942 = _425940, class_Rings_Oring__1__no__zero__divisors(_425942)], (340 ^ _415872) ^ [_426235, _426237] : [-(class_Rings_Oordered__cancel__semiring(_426235)), _426237 = _426235, class_Rings_Oordered__cancel__semiring(_426237)], (350 ^ _415872) ^ [_426530, _426532] : [-(class_Rings_Olinordered__ring__strict(_426530)), _426532 = _426530, class_Rings_Olinordered__ring__strict(_426532)], (360 ^ _415872) ^ [_426825, _426827] : [-(class_Rings_Oring__no__zero__divisors(_426825)), _426827 = _426825, class_Rings_Oring__no__zero__divisors(_426827)], (370 ^ _415872) ^ [_427120, _427122] : [-(class_Rings_Oordered__comm__semiring(_427120)), _427122 = _427120, class_Rings_Oordered__comm__semiring(_427122)], (380 ^ _415872) ^ [_427415, _427417] : [-(class_Rings_Olinordered__semiring__1(_427415)), _427417 = _427415, class_Rings_Olinordered__semiring__1(_427417)], (390 ^ _415872) ^ [_427710, _427712] : [-(class_Groups_Oordered__ab__group__add(_427710)), _427712 = _427710, class_Groups_Oordered__ab__group__add(_427712)], (400 ^ _415872) ^ [_428005, _428007] : [-(class_Groups_Ocancel__comm__monoid__add(_428005)), _428007 = _428005, class_Groups_Ocancel__comm__monoid__add(_428007)], (410 ^ _415872) ^ [_428300, _428302] : [-(class_Groups_Ocancel__semigroup__add(_428300)), _428302 = _428300, class_Groups_Ocancel__semigroup__add(_428302)], (420 ^ _415872) ^ [_428595, _428597] : [-(class_Rings_Olinordered__semiring(_428595)), _428597 = _428595, class_Rings_Olinordered__semiring(_428597)], (430 ^ _415872) ^ [_428890, _428892] : [-(class_Rings_Olinordered__semidom(_428890)), _428892 = _428890, class_Rings_Olinordered__semidom(_428892)], (440 ^ _415872) ^ [_429185, _429187] : [-(class_Groups_Oab__semigroup__mult(_429185)), _429187 = _429185, class_Groups_Oab__semigroup__mult(_429187)], (450 ^ _415872) ^ [_429480, _429482] : [-(class_Groups_Ocomm__monoid__mult(_429480)), _429482 = _429480, class_Groups_Ocomm__monoid__mult(_429482)], (460 ^ _415872) ^ [_429775, _429777] : [-(class_Groups_Oab__semigroup__add(_429775)), _429777 = _429775, class_Groups_Oab__semigroup__add(_429777)], (470 ^ _415872) ^ [_430070, _430072] : [-(class_Rings_Oordered__semiring(_430070)), _430072 = _430070, class_Rings_Oordered__semiring(_430072)], (480 ^ _415872) ^ [_430365, _430367] : [-(class_Rings_Oordered__ring__abs(_430365)), _430367 = _430365, class_Rings_Oordered__ring__abs(_430367)], (490 ^ _415872) ^ [_430660, _430662] : [-(class_Rings_Oidom(_430660)), _430662 = _430660, class_Rings_Oidom(_430662)], (500 ^ _415872) ^ [_430955, _430957] : [-(class_Rings_Ono__zero__divisors(_430955)), _430957 = _430955, class_Rings_Ono__zero__divisors(_430957)], (510 ^ _415872) ^ [_431250, _431252] : [-(class_Rings_Olinordered__ring(_431250)), _431252 = _431250, class_Rings_Olinordered__ring(_431252)], (520 ^ _415872) ^ [_431545, _431547] : [-(class_Fields_Ofield(_431545)), _431547 = _431545, class_Fields_Ofield(_431547)], (530 ^ _415872) ^ [_431840, _431842] : [-(class_Divides_Osemiring__div(_431840)), _431842 = _431840, class_Divides_Osemiring__div(_431842)], (540 ^ _415872) ^ [_432135, _432137] : [-(class_Rings_Ocomm__semiring(_432135)), _432137 = _432135, class_Rings_Ocomm__semiring(_432137)], (550 ^ _415872) ^ [_432430, _432432] : [-(class_Rings_Ozero__neq__one(_432430)), _432432 = _432430, class_Rings_Ozero__neq__one(_432432)], (560 ^ _415872) ^ [_432725, _432727] : [-(class_Rings_Oordered__ring(_432725)), _432727 = _432725, class_Rings_Oordered__ring(_432727)], (570 ^ _415872) ^ [_433020, _433022] : [-(class_Orderings_Opreorder(_433020)), _433022 = _433020, class_Orderings_Opreorder(_433022)], (580 ^ _415872) ^ [_433315, _433317] : [-(class_Orderings_Olinorder(_433315)), _433317 = _433315, class_Orderings_Olinorder(_433317)], (590 ^ _415872) ^ [_433610, _433612] : [-(class_Groups_Omonoid__mult(_433610)), _433612 = _433610, class_Groups_Omonoid__mult(_433612)], (600 ^ _415872) ^ [_433905, _433907] : [-(class_Groups_Ocomm__monoid__add(_433905)), _433907 = _433905, class_Groups_Ocomm__monoid__add(_433907)], (610 ^ _415872) ^ [_434200, _434202] : [-(class_Groups_Omonoid__add(_434200)), _434202 = _434200, class_Groups_Omonoid__add(_434202)], (620 ^ _415872) ^ [_434495, _434497] : [-(class_Rings_Osemiring__0(_434495)), _434497 = _434495, class_Rings_Osemiring__0(_434497)], (630 ^ _415872) ^ [_434790, _434792] : [-(class_Groups_Oab__group__add(_434790)), _434792 = _434790, class_Groups_Oab__group__add(_434792)], (640 ^ _415872) ^ [_435085, _435087] : [-(class_Groups_Ogroup__add(_435085)), _435087 = _435085, class_Groups_Ogroup__add(_435087)], (650 ^ _415872) ^ [_435380, _435382] : [-(class_Rings_Omult__zero(_435380)), _435382 = _435380, class_Rings_Omult__zero(_435382)], (660 ^ _415872) ^ [_435675, _435677] : [-(class_Orderings_Oorder(_435675)), _435677 = _435675, class_Orderings_Oorder(_435677)], (670 ^ _415872) ^ [_435970, _435972] : [-(class_Rings_Ocomm__semiring__0(_435970)), _435972 = _435970, class_Rings_Ocomm__semiring__0(_435972)], (680 ^ _415872) ^ [_436265, _436267] : [-(class_Rings_Osemiring(_436265)), _436267 = _436265, class_Rings_Osemiring(_436267)], (690 ^ _415872) ^ [_436560, _436562] : [-(class_Orderings_Oord(_436560)), _436562 = _436560, class_Orderings_Oord(_436562)], (700 ^ _415872) ^ [_436855, _436857] : [-(class_Rings_Olinordered__idom(_436855)), _436857 = _436855, class_Rings_Olinordered__idom(_436857)], (710 ^ _415872) ^ [_437150, _437152] : [-(class_Groups_Osgn__if(_437150)), _437152 = _437150, class_Groups_Osgn__if(_437152)], (720 ^ _415872) ^ [_437445, _437447] : [-(class_Rings_Ocomm__ring__1(_437445)), _437447 = _437445, class_Rings_Ocomm__ring__1(_437447)], (730 ^ _415872) ^ [_437740, _437742] : [-(class_Rings_Oring__1(_437740)), _437742 = _437740, class_Rings_Oring__1(_437742)], (740 ^ _415872) ^ [_438035, _438037] : [-(class_Power_Opower(_438035)), _438037 = _438035, class_Power_Opower(_438037)], (750 ^ _415872) ^ [_438330, _438332] : [-(class_Groups_Ozero(_438330)), _438332 = _438330, class_Groups_Ozero(_438332)], (760 ^ _415872) ^ [_438625, _438627] : [-(class_Rings_Ocomm__ring(_438625)), _438627 = _438625, class_Rings_Ocomm__ring(_438627)], (770 ^ _415872) ^ [_438920, _438922] : [-(class_Rings_Oring(_438920)), _438922 = _438920, class_Rings_Oring(_438922)], (780 ^ _415872) ^ [_439215, _439217] : [-(class_Rings_Ocomm__semiring__1(_439215)), _439217 = _439215, class_Rings_Ocomm__semiring__1(_439217)], (790 ^ _415872) ^ [_439510, _439512] : [-(class_Groups_Oone(_439510)), _439512 = _439510, class_Groups_Oone(_439512)], (800 ^ _415872) ^ [_439785, _439787] : [-(hBOOL(_439785)), _439787 = _439785, hBOOL(_439787)], (1198 ^ _415872) ^ [_455115, _455117] : [hAPP(_455115, 1199 ^ [_455115, _455117]) = hAPP(_455117, 1199 ^ [_455115, _455117]), -(_455115 = _455117)], (1205 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), v_r)))], (1207 ^ _415872) ^ [] : [-(c_SEQ_Osubseq(v_f____))], (1209 ^ _415872) ^ [_455484] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, hAPP(c_Complex_OIm, hAPP(v_s, _455484)))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), v_r), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))))], (1211 ^ _415872) ^ [] : [-(c_SEQ_Osubseq(v_ga____))], (1213 ^ _415872) ^ [_455629] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(v_s, _455629))), v_r)))], (1215 ^ _415872) ^ [_455718] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _455718)))))], (1217 ^ _415872) ^ [_455803] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _455803)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), _455803))], (1219 ^ _415872) ^ [_455910] : [class_Rings_Olinordered__semidom(_455910), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_455910, c_Groups_Ozero__class_Ozero(_455910)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_455910), c_Groups_Oone__class_Oone(_455910)), c_Groups_Oone__class_Oone(_455910)))))], (1225 ^ _415872) ^ [_456164, _456166, _456168] : [class_Groups_Oordered__comm__monoid__add(_456164), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_456164, c_Groups_Ozero__class_Ozero(_456164)), _456166)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_456164, c_Groups_Ozero__class_Ozero(_456164)), _456168)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_456164, c_Groups_Ozero__class_Ozero(_456164)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_456164), _456166), _456168))))], (1239 ^ _415872) ^ [_456636, _456638, _456640] : [class_Groups_Oordered__comm__monoid__add(_456636), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_456636, c_Groups_Ozero__class_Ozero(_456636)), _456638)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_456636, c_Groups_Ozero__class_Ozero(_456636)), _456640)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_456636, c_Groups_Ozero__class_Ozero(_456636)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_456636), _456638), _456640))))], (1253 ^ _415872) ^ [_457122, _457124, _457126, _457128] : [class_Groups_Oordered__comm__monoid__add(_457122), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_457122, c_Groups_Ozero__class_Ozero(_457122)), _457124)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_457122, _457126), _457128)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_457122, _457126), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_457122), _457124), _457128))))], (1267 ^ _415872) ^ [_457614, _457616, _457618, _457620] : [class_Groups_Oordered__comm__monoid__add(_457614), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_457614, c_Groups_Ozero__class_Ozero(_457614)), _457616)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_457614, _457618), _457620)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_457614, _457618), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_457614), _457616), _457620))))], (1281 ^ _415872) ^ [_458092, _458094, _458096] : [class_Groups_Oordered__comm__monoid__add(_458092), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_458092, _458094), c_Groups_Ozero__class_Ozero(_458092))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_458092, _458096), c_Groups_Ozero__class_Ozero(_458092))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_458092, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_458092), _458094), _458096)), c_Groups_Ozero__class_Ozero(_458092))))], (1295 ^ _415872) ^ [_458564, _458566, _458568] : [class_Groups_Oordered__comm__monoid__add(_458564), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_458564, _458566), c_Groups_Ozero__class_Ozero(_458564))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_458564, _458568), c_Groups_Ozero__class_Ozero(_458564))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_458564, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_458564), _458566), _458568)), c_Groups_Ozero__class_Ozero(_458564))))], (1309 ^ _415872) ^ [_459036, _459038, _459040] : [class_Groups_Oordered__ab__group__add__abs(_459036), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_459036, c_Groups_Oabs__class_Oabs(_459036, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_459036), _459038), _459040))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_459036), c_Groups_Oabs__class_Oabs(_459036, _459038)), c_Groups_Oabs__class_Oabs(_459036, _459040)))))], (1315 ^ _415872) ^ [_459310, _459312] : [class_Groups_Oordered__ab__group__add__abs(_459310), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_459310, c_Groups_Oabs__class_Oabs(_459310, _459312)), c_Groups_Ozero__class_Ozero(_459310)))], (1321 ^ _415872) ^ [_459539, _459541] : [class_Groups_Oordered__ab__group__add__abs(_459539), 1324 ^ _415872 : [(1325 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_459539, c_Groups_Ozero__class_Ozero(_459539)), c_Groups_Oabs__class_Oabs(_459539, _459541))), _459541 = c_Groups_Ozero__class_Ozero(_459539)], (1331 ^ _415872) ^ [] : [-(_459541 = c_Groups_Ozero__class_Ozero(_459539)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_459539, c_Groups_Ozero__class_Ozero(_459539)), c_Groups_Oabs__class_Oabs(_459539, _459541))))]]], (1337 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(v_s, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), v_r)))], (1339 ^ _415872) ^ [_460073, _460075] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _460073)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex), _460073), _460075))), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _460075)))))], (1341 ^ _415872) ^ [_460208, _460210] : [class_Groups_Ozero(_460208), 1344 ^ _415872 : [(1345 ^ _415872) ^ [] : [c_Groups_Ozero__class_Ozero(_460208) = _460210, -(_460210 = c_Groups_Ozero__class_Ozero(_460208))], (1351 ^ _415872) ^ [] : [_460210 = c_Groups_Ozero__class_Ozero(_460208), -(c_Groups_Ozero__class_Ozero(_460208) = _460210)]]], (1357 ^ _415872) ^ [_460692, _460694, _460696] : [class_Rings_Olinordered__idom(_460692), -(_460694 = _460696), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_460692, _460694), _460696))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_460692, _460696), _460694)))], (1371 ^ _415872) ^ [_461146, _461148, _461150, _461152] : [class_Groups_Ocancel__semigroup__add(_461146), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_461146), _461148), _461150) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_461146), _461152), _461150), -(_461148 = _461152)], (1381 ^ _415872) ^ [_461523, _461525, _461527, _461529] : [class_Groups_Ocancel__ab__semigroup__add(_461523), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_461523), _461525), _461527) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_461523), _461525), _461529), -(_461527 = _461529)], (1391 ^ _415872) ^ [_461900, _461902, _461904, _461906] : [class_Groups_Ocancel__semigroup__add(_461900), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_461900), _461902), _461904) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_461900), _461902), _461906), -(_461904 = _461906)], (1401 ^ _415872) ^ [_462277, _462279, _462281, _462283] : [class_Groups_Ocancel__semigroup__add(_462277), 1404 ^ _415872 : [(1405 ^ _415872) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_462277), _462279), _462281) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_462277), _462283), _462281), -(_462279 = _462283)], (1411 ^ _415872) ^ [] : [_462279 = _462283, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_462277), _462279), _462281) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_462277), _462283), _462281))]]], (1417 ^ _415872) ^ [_462843, _462845, _462847, _462849] : [class_Groups_Ocancel__semigroup__add(_462843), 1420 ^ _415872 : [(1421 ^ _415872) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_462843), _462845), _462847) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_462843), _462845), _462849), -(_462847 = _462849)], (1427 ^ _415872) ^ [] : [_462847 = _462849, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_462843), _462845), _462847) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_462843), _462845), _462849))]]], (1433 ^ _415872) ^ [_463409, _463411, _463413, _463415] : [class_Groups_Oab__semigroup__add(_463409), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_463409), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_463409), _463411), _463413)), _463415) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_463409), _463411), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_463409), _463413), _463415)))], (1439 ^ _415872) ^ [_463693, _463695] : [class_Groups_Oone(_463693), 1442 ^ _415872 : [(1443 ^ _415872) ^ [] : [c_Groups_Oone__class_Oone(_463693) = _463695, -(_463695 = c_Groups_Oone__class_Oone(_463693))], (1449 ^ _415872) ^ [] : [_463695 = c_Groups_Oone__class_Oone(_463693), -(c_Groups_Oone__class_Oone(_463693) = _463695)]]], (1455 ^ _415872) ^ [_464163, _464165] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _464163), _464165)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _464165), _464163)), -(_464163 = _464165)], (1465 ^ _415872) ^ [_464496, _464498, _464500] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _464496), _464498)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _464498), _464500)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _464496), _464500)))], (1475 ^ _415872) ^ [_464835, _464837] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _464835), _464837))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _464837), _464835)))], (1481 ^ _415872) ^ [_465037] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _465037), _465037)))], (1483 ^ _415872) ^ [_465149, _465151] : [class_Groups_Oordered__ab__group__add__abs(_465149), -(c_Groups_Oabs__class_Oabs(_465149, c_Groups_Oabs__class_Oabs(_465149, _465151)) = c_Groups_Oabs__class_Oabs(_465149, _465151))], (1489 ^ _415872) ^ [_465375, _465377] : [class_Groups_Ocomm__monoid__add(_465375), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_465375), _465377), c_Groups_Ozero__class_Ozero(_465375)) = _465377)], (1495 ^ _415872) ^ [_465603, _465605] : [class_Groups_Omonoid__add(_465603), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_465603), _465605), c_Groups_Ozero__class_Ozero(_465603)) = _465605)], (1501 ^ _415872) ^ [_465831, _465833] : [class_Groups_Olinordered__ab__group__add(_465831), 1504 ^ _415872 : [(1505 ^ _415872) ^ [] : [c_Groups_Ozero__class_Ozero(_465831) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_465831), _465833), _465833), -(_465833 = c_Groups_Ozero__class_Ozero(_465831))], (1511 ^ _415872) ^ [] : [_465833 = c_Groups_Ozero__class_Ozero(_465831), -(c_Groups_Ozero__class_Ozero(_465831) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_465831), _465833), _465833))]]], (1517 ^ _415872) ^ [_466325, _466327] : [class_Groups_Ocomm__monoid__add(_466325), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_466325), c_Groups_Ozero__class_Ozero(_466325)), _466327) = _466327)], (1523 ^ _415872) ^ [_466553, _466555] : [class_Groups_Omonoid__add(_466553), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_466553), c_Groups_Ozero__class_Ozero(_466553)), _466555) = _466555)], (1529 ^ _415872) ^ [_466809, _466811, _466813, _466815] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_466809), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_466809, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_466809), _466811), _466813)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_466809), _466811), _466815))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_466809, _466813), _466815)))], (1539 ^ _415872) ^ [_467206, _467208, _467210, _467212] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_467206), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_467206, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_467206), _467208), _467210)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_467206), _467212), _467210))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_467206, _467208), _467212)))], (1549 ^ _415872) ^ [_467617, _467619, _467621, _467623, _467625] : [class_Groups_Oordered__ab__semigroup__add(_467617), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_467617, _467619), _467621)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_467617, _467623), _467625)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_467617, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_467617), _467619), _467623)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_467617), _467621), _467625))))], (1563 ^ _415872) ^ [_468135, _468137, _468139, _468141] : [class_Groups_Oordered__ab__semigroup__add(_468135), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_468135, _468137), _468139)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_468135, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_468135), _468141), _468137)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_468135), _468141), _468139))))], (1573 ^ _415872) ^ [_468532, _468534, _468536, _468538] : [class_Groups_Oordered__ab__semigroup__add(_468532), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_468532, _468534), _468536)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_468532, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_468532), _468534), _468538)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_468532), _468536), _468538))))], (1583 ^ _415872) ^ [_468929, _468931, _468933, _468935] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_468929), 1586 ^ _415872 : [(1587 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_468929, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_468929), _468931), _468933)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_468929), _468931), _468935))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_468929, _468933), _468935)))], (1593 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_468929, _468933), _468935)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_468929, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_468929), _468931), _468933)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_468929), _468931), _468935))))]]], (1599 ^ _415872) ^ [_469525, _469527, _469529, _469531] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_469525), 1602 ^ _415872 : [(1603 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_469525, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_469525), _469527), _469529)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_469525), _469531), _469529))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_469525, _469527), _469531)))], (1609 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_469525, _469527), _469531)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_469525, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_469525), _469527), _469529)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_469525), _469531), _469529))))]]], (1615 ^ _415872) ^ [_470121, _470123, _470125, _470127] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_470121), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_470121, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_470121), _470123), _470125)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_470121), _470123), _470127))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_470121, _470125), _470127)))], (1625 ^ _415872) ^ [_470518, _470520, _470522, _470524] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_470518), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_470518, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_470518), _470520), _470522)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_470518), _470524), _470522))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_470518, _470520), _470524)))], (1635 ^ _415872) ^ [_470929, _470931, _470933, _470935, _470937] : [class_Groups_Oordered__cancel__ab__semigroup__add(_470929), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_470929, _470931), _470933)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_470929, _470935), _470937)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_470929, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_470929), _470931), _470935)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_470929), _470933), _470937))))], (1649 ^ _415872) ^ [_471447, _471449, _471451, _471453] : [class_Groups_Oordered__cancel__ab__semigroup__add(_471447), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_471447, _471449), _471451)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_471447, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_471447), _471453), _471449)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_471447), _471453), _471451))))], (1659 ^ _415872) ^ [_471844, _471846, _471848, _471850] : [class_Groups_Oordered__cancel__ab__semigroup__add(_471844), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_471844, _471846), _471848)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_471844, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_471844), _471846), _471850)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_471844), _471848), _471850))))], (1669 ^ _415872) ^ [_472241, _472243, _472245, _472247] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_472241), 1672 ^ _415872 : [(1673 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_472241, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_472241), _472243), _472245)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_472241), _472243), _472247))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_472241, _472245), _472247)))], (1679 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_472241, _472245), _472247)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_472241, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_472241), _472243), _472245)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_472241), _472243), _472247))))]]], (1685 ^ _415872) ^ [_472837, _472839, _472841, _472843] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_472837), 1688 ^ _415872 : [(1689 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_472837, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_472837), _472839), _472841)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_472837), _472843), _472841))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_472837, _472839), _472843)))], (1695 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_472837, _472839), _472843)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_472837, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_472837), _472839), _472841)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_472837), _472843), _472841))))]]], (1701 ^ _415872) ^ [_473391] : [class_Rings_Ozero__neq__one(_473391), c_Groups_Ozero__class_Ozero(_473391) = c_Groups_Oone__class_Oone(_473391)], (1707 ^ _415872) ^ [_473588] : [class_Rings_Ozero__neq__one(_473588), c_Groups_Oone__class_Oone(_473588) = c_Groups_Ozero__class_Ozero(_473588)], (1713 ^ _415872) ^ [_473799, _473801] : [class_Groups_Oordered__ab__group__add__abs(_473799), 1716 ^ _415872 : [(1717 ^ _415872) ^ [] : [c_Groups_Oabs__class_Oabs(_473799, _473801) = c_Groups_Ozero__class_Ozero(_473799), -(_473801 = c_Groups_Ozero__class_Ozero(_473799))], (1723 ^ _415872) ^ [] : [_473801 = c_Groups_Ozero__class_Ozero(_473799), -(c_Groups_Oabs__class_Oabs(_473799, _473801) = c_Groups_Ozero__class_Ozero(_473799))]]], (1729 ^ _415872) ^ [_474264] : [class_Groups_Oordered__ab__group__add__abs(_474264), -(c_Groups_Oabs__class_Oabs(_474264, c_Groups_Ozero__class_Ozero(_474264)) = c_Groups_Ozero__class_Ozero(_474264))], (1735 ^ _415872) ^ [_474494, _474496, _474498] : [class_Groups_Oordered__ab__group__add__abs(_474494), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_474494, c_Groups_Oabs__class_Oabs(_474494, _474496)), _474498)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_474494, _474496), _474498)))], (1745 ^ _415872) ^ [_474827, _474829] : [class_Groups_Oordered__ab__group__add__abs(_474827), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_474827, _474829), c_Groups_Oabs__class_Oabs(_474827, _474829))))], (1761 ^ _415872) ^ [_475352, _475354] : [1762 ^ _415872 : [(1763 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _475352), _475354))], (1765 ^ _415872) ^ [] : [_475352 = _475354]], -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _475352), _475354)))], (1751 ^ _415872) ^ [_475080, _475082] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _475080), _475082)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _475080), _475082))), -(_475080 = _475082)], (1769 ^ _415872) ^ [_475687, _475689] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _475687), _475689)), 1772 ^ _415872 : [(1773 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _475687), _475689)))], (1775 ^ _415872) ^ [] : [_475687 = _475689]]], (1777 ^ _415872) ^ [_475945, _475947] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _475945), _475947))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _475945), _475947)), -(_475945 = _475947)], (1787 ^ _415872) ^ [_476283, _476285, _476287] : [class_Groups_Oordered__ab__group__add__abs(_476283), -(c_Groups_Oabs__class_Oabs(_476283, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_476283), c_Groups_Oabs__class_Oabs(_476283, _476285)), c_Groups_Oabs__class_Oabs(_476283, _476287))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_476283), c_Groups_Oabs__class_Oabs(_476283, _476285)), c_Groups_Oabs__class_Oabs(_476283, _476287)))], (1793 ^ _415872) ^ [_476545] : [class_Rings_Olinordered__idom(_476545), -(c_Groups_Oabs__class_Oabs(_476545, c_Groups_Oone__class_Oone(_476545)) = c_Groups_Oone__class_Oone(_476545))], (1799 ^ _415872) ^ [] : [c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)], (1801 ^ _415872) ^ [_476827, _476829, _476831] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _476827), _476829)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), _476831), _476827)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), _476831), _476829))))], (1807 ^ _415872) ^ [_477101, _477103, _477105] : [class_Groups_Oordered__comm__monoid__add(_477101), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_477101, _477103), c_Groups_Ozero__class_Ozero(_477101))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_477101, _477105), c_Groups_Ozero__class_Ozero(_477101))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_477101, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_477101), _477103), _477105)), c_Groups_Ozero__class_Ozero(_477101))))], (1821 ^ _415872) ^ [_477587, _477589, _477591, _477593] : [class_Groups_Oordered__comm__monoid__add(_477587), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_477587, c_Groups_Ozero__class_Ozero(_477587)), _477589)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_477587, _477591), _477593)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_477587, _477591), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_477587), _477593), _477589))))], (1835 ^ _415872) ^ [_478079, _478081, _478083, _478085] : [class_Groups_Oordered__comm__monoid__add(_478079), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_478079, c_Groups_Ozero__class_Ozero(_478079)), _478081)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_478079, _478083), _478085)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_478079, _478083), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_478079), _478081), _478085))))], (1849 ^ _415872) ^ [_478557, _478559, _478561] : [class_Groups_Oordered__comm__monoid__add(_478557), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_478557, c_Groups_Ozero__class_Ozero(_478557)), _478559)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_478557, c_Groups_Ozero__class_Ozero(_478557)), _478561)), 1860 ^ _415872 : [(1861 ^ _415872) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_478557), _478559), _478561) = c_Groups_Ozero__class_Ozero(_478557), 1864 ^ _415872 : [(1865 ^ _415872) ^ [] : [-(_478559 = c_Groups_Ozero__class_Ozero(_478557))], (1867 ^ _415872) ^ [] : [-(_478561 = c_Groups_Ozero__class_Ozero(_478557))]]], (1869 ^ _415872) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_478557), _478559), _478561) = c_Groups_Ozero__class_Ozero(_478557)), _478559 = c_Groups_Ozero__class_Ozero(_478557), _478561 = c_Groups_Ozero__class_Ozero(_478557)]]], (1879 ^ _415872) ^ [_479465, _479467, _479469] : [class_Groups_Oordered__comm__monoid__add(_479465), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_479465, c_Groups_Ozero__class_Ozero(_479465)), _479467)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_479465, c_Groups_Ozero__class_Ozero(_479465)), _479469)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_479465, c_Groups_Ozero__class_Ozero(_479465)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_479465), _479467), _479469))))], (1893 ^ _415872) ^ [_479923, _479925] : [class_Groups_Olinordered__ab__group__add(_479923), 1896 ^ _415872 : [(1897 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_479923, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_479923), _479925), _479925)), c_Groups_Ozero__class_Ozero(_479923))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_479923, _479925), c_Groups_Ozero__class_Ozero(_479923))))], (1903 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_479923, _479925), c_Groups_Ozero__class_Ozero(_479923))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_479923, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_479923), _479925), _479925)), c_Groups_Ozero__class_Ozero(_479923))))]]], (1909 ^ _415872) ^ [_480447, _480449] : [class_Groups_Olinordered__ab__group__add(_480447), 1912 ^ _415872 : [(1913 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_480447, c_Groups_Ozero__class_Ozero(_480447)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_480447), _480449), _480449))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_480447, c_Groups_Ozero__class_Ozero(_480447)), _480449)))], (1919 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_480447, c_Groups_Ozero__class_Ozero(_480447)), _480449)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_480447, c_Groups_Ozero__class_Ozero(_480447)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_480447), _480449), _480449))))]]], (1925 ^ _415872) ^ [_480985, _480987, _480989] : [class_Groups_Oordered__comm__monoid__add(_480985), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_480985, _480987), c_Groups_Ozero__class_Ozero(_480985))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_480985, _480989), c_Groups_Ozero__class_Ozero(_480985))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_480985, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_480985), _480987), _480989)), c_Groups_Ozero__class_Ozero(_480985))))], (1939 ^ _415872) ^ [_481471, _481473, _481475, _481477] : [class_Rings_Olinordered__semidom(_481471), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_481471, c_Groups_Ozero__class_Ozero(_481471)), _481473)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_481471, _481475), _481477)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_481471, _481475), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_481471), _481473), _481477))))], (1953 ^ _415872) ^ [_481949, _481951, _481953] : [class_Groups_Oordered__comm__monoid__add(_481949), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_481949, c_Groups_Ozero__class_Ozero(_481949)), _481951)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_481949, c_Groups_Ozero__class_Ozero(_481949)), _481953)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_481949, c_Groups_Ozero__class_Ozero(_481949)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_481949), _481951), _481953))))], (1967 ^ _415872) ^ [_482407, _482409] : [class_Groups_Olinordered__ab__group__add(_482407), 1970 ^ _415872 : [(1971 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_482407, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_482407), _482409), _482409)), c_Groups_Ozero__class_Ozero(_482407))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_482407, _482409), c_Groups_Ozero__class_Ozero(_482407))))], (1977 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_482407, _482409), c_Groups_Ozero__class_Ozero(_482407))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_482407, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_482407), _482409), _482409)), c_Groups_Ozero__class_Ozero(_482407))))]]], (1983 ^ _415872) ^ [_482931, _482933] : [class_Groups_Olinordered__ab__group__add(_482931), 1986 ^ _415872 : [(1987 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_482931, c_Groups_Ozero__class_Ozero(_482931)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_482931), _482933), _482933))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_482931, c_Groups_Ozero__class_Ozero(_482931)), _482933)))], (1993 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_482931, c_Groups_Ozero__class_Ozero(_482931)), _482933)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_482931, c_Groups_Ozero__class_Ozero(_482931)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_482931), _482933), _482933))))]]], (1999 ^ _415872) ^ [_483497, _483499, _483501, _483503, _483505] : [class_Groups_Oordered__cancel__ab__semigroup__add(_483497), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_483497, _483499), _483501)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_483497, _483503), _483505)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_483497, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_483497), _483499), _483503)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_483497), _483501), _483505))))], (2013 ^ _415872) ^ [_484029, _484031, _484033, _484035, _484037] : [class_Groups_Oordered__cancel__ab__semigroup__add(_484029), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_484029, _484031), _484033)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_484029, _484035), _484037)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_484029, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_484029), _484031), _484035)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_484029), _484033), _484037))))], (2027 ^ _415872) ^ [_484505] : [class_Rings_Olinordered__semidom(_484505), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_484505, c_Groups_Ozero__class_Ozero(_484505)), c_Groups_Oone__class_Oone(_484505))))], (2033 ^ _415872) ^ [_484711] : [class_Rings_Olinordered__semidom(_484711), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_484711, c_Groups_Oone__class_Oone(_484711)), c_Groups_Ozero__class_Ozero(_484711)))], (2039 ^ _415872) ^ [_484918] : [class_Rings_Olinordered__semidom(_484918), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_484918, c_Groups_Ozero__class_Ozero(_484918)), c_Groups_Oone__class_Oone(_484918))))], (2045 ^ _415872) ^ [_485124] : [class_Rings_Olinordered__semidom(_485124), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_485124, c_Groups_Oone__class_Oone(_485124)), c_Groups_Ozero__class_Ozero(_485124)))], (2051 ^ _415872) ^ [_485345, _485347] : [class_Rings_Olinordered__semidom(_485345), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_485345, _485347), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_485345), _485347), c_Groups_Oone__class_Oone(_485345)))))], (2057 ^ _415872) ^ [_485583, _485585] : [class_Groups_Oordered__ab__group__add__abs(_485583), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_485583, c_Groups_Ozero__class_Ozero(_485583)), _485585)), -(c_Groups_Oabs__class_Oabs(_485583, _485585) = _485585)], (2067 ^ _415872) ^ [_485900, _485902] : [class_Groups_Oordered__ab__group__add__abs(_485900), 2070 ^ _415872 : [(2071 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_485900, c_Groups_Oabs__class_Oabs(_485900, _485902)), c_Groups_Ozero__class_Ozero(_485900))), -(_485902 = c_Groups_Ozero__class_Ozero(_485900))], (2077 ^ _415872) ^ [] : [_485902 = c_Groups_Ozero__class_Ozero(_485900), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_485900, c_Groups_Oabs__class_Oabs(_485900, _485902)), c_Groups_Ozero__class_Ozero(_485900))))]]], (2083 ^ _415872) ^ [_486394, _486396] : [class_Groups_Oordered__ab__group__add__abs(_486394), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_486394, c_Groups_Ozero__class_Ozero(_486394)), c_Groups_Oabs__class_Oabs(_486394, _486396))))], (2089 ^ _415872) ^ [_486622, _486624] : [class_Groups_Oordered__ab__group__add__abs(_486622), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_486622, c_Groups_Ozero__class_Ozero(_486622)), _486624)), -(c_Groups_Oabs__class_Oabs(_486622, _486624) = _486624)], (2099 ^ _415872) ^ [_486910] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, hAPP(c_Complex_OIm, _486910))), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _486910))))], (2101 ^ _415872) ^ [_487073, _487075, _487077, _487079, _487081] : [class_RealVector_Oreal__normed__vector(_487073), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_487073, _487075)), _487077)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_487073, _487079)), _487081)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_487073, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_487073), _487075), _487079))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), _487077), _487081))))], (2115 ^ _415872) ^ [_487591, _487593, _487595] : [class_RealVector_Oreal__normed__vector(_487591), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_487591, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_487591), _487593), _487595))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_487591, _487593)), c_RealVector_Onorm__class_Onorm(_487591, _487595)))))], (2121 ^ _415872) ^ [_487861, _487863] : [class_RealVector_Oreal__normed__vector(_487861), 2124 ^ _415872 : [(2125 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_RealVector_Onorm__class_Onorm(_487861, _487863))), _487863 = c_Groups_Ozero__class_Ozero(_487861)], (2131 ^ _415872) ^ [] : [-(_487863 = c_Groups_Ozero__class_Ozero(_487861)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_RealVector_Onorm__class_Onorm(_487861, _487863))))]]], (2137 ^ _415872) ^ [_488342, _488344] : [class_RealVector_Oreal__normed__vector(_488342), 2140 ^ _415872 : [(2141 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_488342, _488344)), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), -(_488344 = c_Groups_Ozero__class_Ozero(_488342))], (2147 ^ _415872) ^ [] : [_488344 = c_Groups_Ozero__class_Ozero(_488342), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_488342, _488344)), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))]]], (2153 ^ _415872) ^ [_488816] : [class_RealVector_Oreal__normed__algebra__1(_488816), -(c_RealVector_Onorm__class_Onorm(_488816, c_Groups_Oone__class_Oone(_488816)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (2159 ^ _415872) ^ [_489028, _489030] : [class_RealVector_Oreal__normed__vector(_489028), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_489028, _489030)), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (2165 ^ _415872) ^ [_489253, _489255] : [class_RealVector_Oreal__normed__vector(_489253), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_RealVector_Onorm__class_Onorm(_489253, _489255))))], (2171 ^ _415872) ^ [_489471, _489473] : [class_RealVector_Oreal__normed__vector(_489471), 2174 ^ _415872 : [(2175 ^ _415872) ^ [] : [c_RealVector_Onorm__class_Onorm(_489471, _489473) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_489473 = c_Groups_Ozero__class_Ozero(_489471))], (2181 ^ _415872) ^ [] : [_489473 = c_Groups_Ozero__class_Ozero(_489471), -(c_RealVector_Onorm__class_Onorm(_489471, _489473) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))]]], (2187 ^ _415872) ^ [_489930] : [class_RealVector_Oreal__normed__vector(_489930), -(c_RealVector_Onorm__class_Onorm(_489930, c_Groups_Ozero__class_Ozero(_489930)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (2193 ^ _415872) ^ [_490142, _490144] : [class_Rings_Olinordered__idom(_490142), 2196 ^ _415872 : [(2197 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_490142, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_490142), _490144), _490144)), c_Groups_Ozero__class_Ozero(_490142))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_490142, _490144), c_Groups_Ozero__class_Ozero(_490142))))], (2203 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_490142, _490144), c_Groups_Ozero__class_Ozero(_490142))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_490142, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_490142), _490144), _490144)), c_Groups_Ozero__class_Ozero(_490142))))]]], (2209 ^ _415872) ^ [_490666, _490668] : [class_Orderings_Opreorder(_490666), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_490666, _490668), _490668)))], (2215 ^ _415872) ^ [_490855] : [-(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, _490855) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _490855))], (2217 ^ _415872) ^ [_490996, _490998, _491000, _491002] : [class_Orderings_Oord(_490996), 2220 ^ _415872 : [(2221 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_490998, _490996), _491000), _491002)), 2224 ^ _415872 : [(2225 ^ _415872) ^ [_491267] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_490996, hAPP(_491000, _491267)), hAPP(_491002, _491267))))]]], (2227 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_490996, hAPP(_491000, 2228 ^ [_490996, _490998, _491000, _491002])), hAPP(_491002, 2228 ^ [_490996, _490998, _491000, _491002]))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_490998, _490996), _491000), _491002)))]]], (2234 ^ _415872) ^ [_491665, _491667, _491669] : [class_Orderings_Olinorder(_491665), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_491665, _491667), _491669))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_491665, _491669), _491667)))], (2244 ^ _415872) ^ [_492007, _492009, _492011] : [class_Orderings_Oorder(_492007), 2247 ^ _415872 : [(2248 ^ _415872) ^ [] : [_492009 = _492011, 2251 ^ _415872 : [(2252 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_492007, _492009), _492011)))], (2254 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_492007, _492011), _492009)))]]], (2256 ^ _415872) ^ [] : [-(_492009 = _492011), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_492007, _492009), _492011)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_492007, _492011), _492009))]]], (2266 ^ _415872) ^ [_492689, _492691, _492693] : [class_Orderings_Opreorder(_492689), _492691 = _492693, -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_492689, _492691), _492693)))], (2276 ^ _415872) ^ [_493048, _493050, _493052, _493054, _493056] : [class_Orderings_Oord(_493048), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_493050, _493048), _493052), _493054)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_493048, hAPP(_493052, _493056)), hAPP(_493054, _493056))))], (2286 ^ _415872) ^ [_493427, _493429, _493431] : [class_Orderings_Oorder(_493427), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_493427, _493429), _493431)), 2293 ^ _415872 : [(2294 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_493427, _493431), _493429)), -(_493431 = _493429)], (2300 ^ _415872) ^ [] : [_493431 = _493429, -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_493427, _493431), _493429)))]]], (2306 ^ _415872) ^ [_494047, _494049, _494051, _494053] : [class_Orderings_Oord(_494047), _494049 = _494051, hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_494047, _494051), _494053)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_494047, _494049), _494053)))], (2320 ^ _415872) ^ [_494509, _494511, _494513, _494515] : [class_Orderings_Oorder(_494509), _494511 = _494513, hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_494509, _494515), _494513)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_494509, _494515), _494511)))], (2334 ^ _415872) ^ [_494971, _494973, _494975, _494977] : [class_Orderings_Oord(_494971), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_494971, _494973), _494975)), _494975 = _494977, -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_494971, _494973), _494977)))], (2348 ^ _415872) ^ [_495433, _495435, _495437, _495439] : [class_Orderings_Oorder(_495433), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_495433, _495435), _495437)), _495435 = _495439, -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_495433, _495439), _495437)))], (2362 ^ _415872) ^ [_495881, _495883, _495885] : [class_Orderings_Oorder(_495881), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_495881, _495883), _495885)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_495881, _495885), _495883)), -(_495883 = _495885)], (2376 ^ _415872) ^ [_496329, _496331, _496333, _496335] : [class_Orderings_Opreorder(_496329), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_496329, _496331), _496333)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_496329, _496333), _496335)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_496329, _496331), _496335)))], (2390 ^ _415872) ^ [_496787, _496789, _496791] : [class_Orderings_Oorder(_496787), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_496787, _496789), _496791)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_496787, _496791), _496789)), -(_496791 = _496789)], (2404 ^ _415872) ^ [_497235, _497237, _497239, _497241] : [class_Orderings_Oorder(_497235), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_497235, _497237), _497239)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_497235, _497241), _497237)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_497235, _497241), _497239)))], (2418 ^ _415872) ^ [_497721, _497723, _497725, _497727, _497729] : [class_Orderings_Oord(_497721), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_497723, _497721), _497725), _497727)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_497721, hAPP(_497725, _497729)), hAPP(_497727, _497729))))], (2428 ^ _415872) ^ [_498100, _498102, _498104] : [class_Orderings_Olinorder(_498100), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_498100, _498102), _498104))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_498100, _498104), _498102)))], (2438 ^ _415872) ^ [_498430, _498432] : [class_Orderings_Opreorder(_498430), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_498430, _498432), _498432))], (2444 ^ _415872) ^ [_498663, _498665, _498667] : [class_Orderings_Olinorder(_498663), 2447 ^ _415872 : [(2458 ^ _415872) ^ [] : [2459 ^ _415872 : [(2460 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_498663, _498665), _498667))], (2462 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_498663, _498667), _498665))]], _498665 = _498667], (2448 ^ _415872) ^ [] : [-(_498665 = _498667), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_498663, _498665), _498667))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_498663, _498667), _498665)))]]], (2466 ^ _415872) ^ [_499347, _499349, _499351] : [class_Orderings_Olinorder(_499347), 2469 ^ _415872 : [(2480 ^ _415872) ^ [] : [2481 ^ _415872 : [(2482 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_499347, _499351), _499349))], (2484 ^ _415872) ^ [] : [_499349 = _499351]], hBOOL(hAPP(c_Orderings_Oord__class_Oless(_499347, _499349), _499351))], (2470 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_499347, _499349), _499351))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_499347, _499351), _499349))), -(_499349 = _499351)]]], (2488 ^ _415872) ^ [_500031, _500033, _500035] : [class_Orderings_Olinorder(_500031), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_500031, _500033), _500035))), -(_500033 = _500035), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_500031, _500035), _500033)))], (2502 ^ _415872) ^ [_500467, _500469, _500471] : [class_Orderings_Olinorder(_500467), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_500467, _500469), _500471))), 2509 ^ _415872 : [(2510 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_500467, _500471), _500469))), -(_500471 = _500469)], (2516 ^ _415872) ^ [] : [_500471 = _500469, hBOOL(hAPP(c_Orderings_Oord__class_Oless(_500467, _500471), _500469))]]], (2522 ^ _415872) ^ [_501078, _501080, _501082] : [class_Orderings_Olinorder(_501078), -(_501080 = _501082), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_501078, _501080), _501082))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_501078, _501082), _501080)))], (2536 ^ _415872) ^ [_501518, _501520, _501522] : [class_Orderings_Oorder(_501518), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_501518, _501520), _501522)), _501520 = _501522], (2546 ^ _415872) ^ [_501850, _501852, _501854] : [class_Orderings_Opreorder(_501850), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_501850, _501852), _501854)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_501850, _501854), _501852))], (2556 ^ _415872) ^ [_502192, _502194, _502196] : [class_Orderings_Opreorder(_502192), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_502192, _502194), _502196)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_502192, _502196), _502194))], (2566 ^ _415872) ^ [_502534, _502536, _502538] : [class_Orderings_Oorder(_502534), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_502534, _502536), _502538)), _502536 = _502538], (2576 ^ _415872) ^ [_502866, _502868, _502870] : [class_Orderings_Oorder(_502866), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_502866, _502868), _502870)), _502870 = _502868], (2586 ^ _415872) ^ [_503198, _503200, _503202] : [class_Orderings_Opreorder(_503198), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_503198, _503200), _503202)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_503198, _503202), _503200))], (2596 ^ _415872) ^ [_503540, _503542, _503544] : [class_Orderings_Oorder(_503540), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_503540, _503542), _503544)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_503540, _503544), _503542))], (2606 ^ _415872) ^ [_503896, _503898, _503900, _503902] : [class_Orderings_Oord(_503896), _503898 = _503900, hBOOL(hAPP(c_Orderings_Oord__class_Oless(_503896, _503900), _503902)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_503896, _503898), _503902)))], (2620 ^ _415872) ^ [_504358, _504360, _504362, _504364] : [class_Orderings_Oorder(_504358), _504360 = _504362, hBOOL(hAPP(c_Orderings_Oord__class_Oless(_504358, _504364), _504362)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_504358, _504364), _504360)))], (2634 ^ _415872) ^ [_504820, _504822, _504824, _504826] : [class_Orderings_Oord(_504820), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_504820, _504822), _504824)), _504824 = _504826, -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_504820, _504822), _504826)))], (2648 ^ _415872) ^ [_505282, _505284, _505286, _505288] : [class_Orderings_Oorder(_505282), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_505282, _505284), _505286)), _505284 = _505288, -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_505282, _505288), _505286)))], (2662 ^ _415872) ^ [_505744, _505746, _505748, _505750] : [class_Orderings_Opreorder(_505744), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_505744, _505746), _505748)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_505744, _505748), _505750)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_505744, _505746), _505750)))], (2676 ^ _415872) ^ [_506216, _506218, _506220, _506222] : [class_Orderings_Oorder(_506216), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_506216, _506218), _506220)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_506216, _506222), _506218)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_506216, _506222), _506220)))], (2690 ^ _415872) ^ [_506674, _506676, _506678] : [class_Orderings_Opreorder(_506674), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_506674, _506676), _506678)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_506674, _506678), _506676))], (2700 ^ _415872) ^ [_507016, _507018, _507020] : [class_Orderings_Olinorder(_507016), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_507016, _507018), _507020))), -(_507018 = _507020), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_507016, _507020), _507018)))], (2714 ^ _415872) ^ [_507456, _507458, _507460] : [class_Orderings_Olinorder(_507456), 2717 ^ _415872 : [(2718 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_507456, _507458), _507460))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_507456, _507460), _507458)))], (2724 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_507456, _507460), _507458)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_507456, _507458), _507460))]]], (2730 ^ _415872) ^ [_507976, _507978, _507980] : [class_Orderings_Olinorder(_507976), 2733 ^ _415872 : [(2734 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_507976, _507978), _507980))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_507976, _507980), _507978)))], (2740 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_507976, _507980), _507978)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_507976, _507978), _507980))]]], (2746 ^ _415872) ^ [_508496, _508498, _508500] : [class_Orderings_Olinorder(_508496), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_508496, _508498), _508500))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_508496, _508500), _508498)))], (2756 ^ _415872) ^ [_508838, _508840, _508842] : [class_Orderings_Oorder(_508838), 2759 ^ _415872 : [(2760 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_508838, _508840), _508842)), 2763 ^ _415872 : [(2764 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_508838, _508840), _508842)))], (2766 ^ _415872) ^ [] : [_508840 = _508842]]], (2768 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_508838, _508840), _508842))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_508838, _508840), _508842)), -(_508840 = _508842)]]], (2778 ^ _415872) ^ [_509522, _509524, _509526] : [class_Orderings_Opreorder(_509522), 2781 ^ _415872 : [(2782 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_509522, _509524), _509526)), 2785 ^ _415872 : [(2786 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_509522, _509524), _509526)))], (2788 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_509522, _509526), _509524))]]], (2790 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_509522, _509524), _509526))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_509522, _509524), _509526)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_509522, _509526), _509524)))]]], (2800 ^ _415872) ^ [_510221, _510223, _510225] : [class_Orderings_Oorder(_510221), 2803 ^ _415872 : [(2814 ^ _415872) ^ [] : [2815 ^ _415872 : [(2816 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_510221, _510223), _510225))], (2818 ^ _415872) ^ [] : [_510223 = _510225]], -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_510221, _510223), _510225)))], (2804 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_510221, _510223), _510225)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_510221, _510223), _510225))), -(_510223 = _510225)]]], (2822 ^ _415872) ^ [_510903, _510905, _510907] : [class_Orderings_Olinorder(_510903), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_510903, _510905), _510907))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_510903, _510907), _510905)))], (2832 ^ _415872) ^ [_511247, _511249, _511251] : [class_Orderings_Olinorder(_511247), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_511247, _511249), _511251))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_511247, _511251), _511249)))], (2842 ^ _415872) ^ [_511591, _511593, _511595] : [class_Orderings_Olinorder(_511591), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_511591, _511593), _511595))), 2849 ^ _415872 : [(2850 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_511591, _511593), _511595)), -(_511593 = _511595)], (2856 ^ _415872) ^ [] : [_511593 = _511595, -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_511591, _511593), _511595)))]]], (2862 ^ _415872) ^ [_512200, _512202, _512204] : [class_Orderings_Oorder(_512200), -(_512202 = _512204), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_512200, _512202), _512204)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_512200, _512202), _512204)))], (2876 ^ _415872) ^ [_512637, _512639, _512641] : [class_Orderings_Oorder(_512637), -(_512639 = _512641), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_512637, _512641), _512639)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_512637, _512641), _512639)))], (2890 ^ _415872) ^ [_513074, _513076, _513078] : [class_Orderings_Olinorder(_513074), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_513074, _513076), _513078)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_513074, _513078), _513076))], (2900 ^ _415872) ^ [_513416, _513418, _513420] : [class_Orderings_Opreorder(_513416), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_513416, _513418), _513420)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_513416, _513418), _513420)))], (2910 ^ _415872) ^ [_513757, _513759, _513761] : [class_Orderings_Olinorder(_513757), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_513757, _513759), _513761)), 2917 ^ _415872 : [(2918 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_513757, _513759), _513761))), -(_513759 = _513761)], (2924 ^ _415872) ^ [] : [_513759 = _513761, hBOOL(hAPP(c_Orderings_Oord__class_Oless(_513757, _513759), _513761))]]], (2930 ^ _415872) ^ [_514365, _514367, _514369] : [class_Orderings_Oorder(_514365), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_514365, _514367), _514369)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_514365, _514367), _514369))), -(_514367 = _514369)], (2944 ^ _415872) ^ [_514800, _514802, _514804] : [class_Orderings_Oorder(_514800), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_514800, _514802), _514804)), -(_514802 = _514804), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_514800, _514802), _514804)))], (2958 ^ _415872) ^ [_515237, _515239, _515241] : [class_Orderings_Oorder(_515237), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_515237, _515239), _515241)), -(_515241 = _515239), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_515237, _515239), _515241)))], (2972 ^ _415872) ^ [_515688, _515690, _515692, _515694] : [class_Orderings_Opreorder(_515688), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_515688, _515690), _515692)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_515688, _515692), _515694)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_515688, _515690), _515694)))], (2986 ^ _415872) ^ [_516160, _516162, _516164, _516166] : [class_Orderings_Oorder(_516160), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_516160, _516162), _516164)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_516160, _516166), _516162)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_516160, _516166), _516164)))], (3000 ^ _415872) ^ [_516632, _516634, _516636, _516638] : [class_Orderings_Opreorder(_516632), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_516632, _516634), _516636)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_516632, _516636), _516638)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_516632, _516634), _516638)))], (3014 ^ _415872) ^ [_517104, _517106, _517108, _517110] : [class_Orderings_Oorder(_517104), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_517104, _517106), _517108)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_517104, _517110), _517106)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_517104, _517110), _517108)))], (3028 ^ _415872) ^ [_517548, _517550] : [class_Groups_Olinordered__ab__group__add(_517548), 3031 ^ _415872 : [(3032 ^ _415872) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_517548), _517550), _517550) = c_Groups_Ozero__class_Ozero(_517548), -(_517550 = c_Groups_Ozero__class_Ozero(_517548))], (3038 ^ _415872) ^ [] : [_517550 = c_Groups_Ozero__class_Ozero(_517548), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_517548), _517550), _517550) = c_Groups_Ozero__class_Ozero(_517548))]]], (3044 ^ _415872) ^ [] : [-(hAPP(c_Complex_OIm, c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (3046 ^ _415872) ^ [] : [-(hAPP(c_Complex_OIm, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (3048 ^ _415872) ^ [_518148, _518150] : [class_RealVector_Oreal__normed__vector(_518148), -(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_518148, _518150)) = c_RealVector_Onorm__class_Onorm(_518148, _518150))], (3054 ^ _415872) ^ [_518359, _518361] : [-(hAPP(c_Complex_OIm, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex), _518359), _518361)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), hAPP(c_Complex_OIm, _518359)), hAPP(c_Complex_OIm, _518361)))], (3056 ^ _415872) ^ [_518460] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _518460)))], (3058 ^ _415872) ^ [_518539] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _518539), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (3060 ^ _415872) ^ [_518651, _518653] : [class_Rings_Ocomm__semiring__1(_518651), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_518651), c_Groups_Ozero__class_Ozero(_518651)), _518653) = _518653)], (3066 ^ _415872) ^ [_518879, _518881] : [class_Rings_Ocomm__semiring__1(_518879), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_518879), _518881), c_Groups_Ozero__class_Ozero(_518879)) = _518881)], (3072 ^ _415872) ^ [_519121, _519123, _519125] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_519121), 3075 ^ _415872 : [(3076 ^ _415872) ^ [] : [_519123 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_519121), _519123), _519125), -(_519125 = c_Groups_Ozero__class_Ozero(_519121))], (3082 ^ _415872) ^ [] : [_519125 = c_Groups_Ozero__class_Ozero(_519121), -(_519123 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_519121), _519123), _519125))]]], (3088 ^ _415872) ^ [_519625, _519627] : [class_RealVector_Oreal__normed__vector(_519625), 3091 ^ _415872 : [(3092 ^ _415872) ^ [] : [_519627 = c_Groups_Ozero__class_Ozero(_519625), -(c_RealVector_Onorm__class_Onorm(_519625, c_Groups_Osgn__class_Osgn(_519625, _519627)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (3098 ^ _415872) ^ [] : [-(_519627 = c_Groups_Ozero__class_Ozero(_519625)), -(c_RealVector_Onorm__class_Onorm(_519625, c_Groups_Osgn__class_Osgn(_519625, _519627)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))]]], (3104 ^ _415872) ^ [_520121, _520123] : [class_Groups_Ozero(_520121), 3107 ^ _415872 : [(3108 ^ _415872) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_520121, _520123) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_520123 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_520121)))], (3114 ^ _415872) ^ [] : [_520123 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_520121)), -(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_520121, _520123) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (3120 ^ _415872) ^ [_520656, _520658, _520660, _520662, _520664, _520666] : [class_Rings_Olinordered__semiring__1__strict(_520656), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_520656, _520658), _520660)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_520656, _520662), _520660)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_520656, c_Groups_Ozero__class_Ozero(_520656)), _520664)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_520656, c_Groups_Ozero__class_Ozero(_520656)), _520666)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_520656), _520664), _520666) = c_Groups_Oone__class_Oone(_520656), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_520656, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_520656), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_520656), _520664), _520658)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_520656), _520666), _520662))), _520660)))], (3146 ^ _415872) ^ [] : [-(c_SEQ_Omonoseq(tc_RealDef_Oreal, c_COMBB(tc_Complex_Ocomplex, tc_RealDef_Oreal, tc_Nat_Onat, c_Complex_OIm, c_COMBB(tc_Nat_Onat, tc_Complex_Ocomplex, tc_Nat_Onat, v_s, c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____, v_ga____)))))], (3148 ^ _415872) ^ [] : [-(c_SEQ_Omonoseq(tc_RealDef_Oreal, c_COMBB(tc_Complex_Ocomplex, tc_RealDef_Oreal, tc_Nat_Onat, c_Complex_ORe, c_COMBB(tc_Nat_Onat, tc_Complex_Ocomplex, tc_Nat_Onat, v_s, v_f____))))], (3150 ^ _415872) ^ [_521629, _521631] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _521629), _521631)), _521629))], (3152 ^ _415872) ^ [_521733, _521735] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _521733), _521735)), _521735))], (3154 ^ _415872) ^ [_521838, _521840] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _521838), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _521840), _521838))))], (3156 ^ _415872) ^ [_521943, _521945] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _521943), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _521943), _521945))))], (3158 ^ _415872) ^ [_522077, _522079, _522081] : [class_RealVector_Oreal__normed__div__algebra(_522077), -(c_RealVector_Onorm__class_Onorm(_522077, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_522077), _522079), _522081)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_522077, _522079)), c_RealVector_Onorm__class_Onorm(_522077, _522081)))], (3164 ^ _415872) ^ [_522366, _522368] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _522366), _522368)), -(_522368 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _522366), 3167 ^ [_522366, _522368]))], (3171 ^ _415872) ^ [_522613, _522615] : [3172 ^ _415872 : [(3173 ^ _415872) ^ [_522694] : [_522615 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _522613), _522694)]], -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _522613), _522615)))], (3177 ^ _415872) ^ [_522897, _522899, _522901, _522903] : [class_Orderings_Oord(_522897), 3180 ^ _415872 : [(3181 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_522899, _522897), _522901), _522903)), 3184 ^ _415872 : [(3185 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_522899, _522897), _522901), _522903)))], (3187 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_522899, _522897), _522903), _522901))]]], (3189 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_522899, _522897), _522901), _522903))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_522899, _522897), _522901), _522903)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_522899, _522897), _522903), _522901)))]]], (3199 ^ _415872) ^ [_523674, _523676, _523678] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _523674), _523676)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _523674), _523678))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _523676), _523678)))], (3205 ^ _415872) ^ [_523886, _523888, _523890] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _523888), _523890)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _523886), _523888)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _523886), _523890))))], (3211 ^ _415872) ^ [_524191, _524193, _524195] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _524191), _524193)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _524191), _524195))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _524193), _524195)))], (3217 ^ _415872) ^ [_524403, _524405, _524407] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _524405), _524407)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _524403), _524405)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _524403), _524407))))], (3223 ^ _415872) ^ [_524679, _524681, _524683] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _524679), _524681)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _524679), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _524681), _524683))))], (3229 ^ _415872) ^ [_524941, _524943, _524945] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _524941), _524943)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _524941), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _524945), _524943))))], (3235 ^ _415872) ^ [_525203, _525205, _525207] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _525203), _525205)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _525203), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _525205), _525207))))], (3241 ^ _415872) ^ [_525465, _525467, _525469] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _525465), _525467)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _525465), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _525469), _525467))))], (3247 ^ _415872) ^ [_525727, _525729, _525731] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _525727), _525729)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _525727), _525731)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _525729), _525731))))], (3253 ^ _415872) ^ [_526001, _526003, _526005] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _526001), _526003)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _526001), _526005)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _526003), _526005))))], (3259 ^ _415872) ^ [_526289, _526291, _526293, _526295] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _526289), _526291)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _526293), _526295)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _526289), _526293)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _526291), _526295))))], (3269 ^ _415872) ^ [_526690, _526692, _526694, _526696] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _526690), _526692)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _526694), _526696)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _526690), _526694)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _526692), _526696))))], (3279 ^ _415872) ^ [_527091, _527093, _527095, _527097] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _527091), _527093)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _527095), _527093) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _527091), _527097), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _527095), _527097)))], (3289 ^ _415872) ^ [_527468, _527470, _527472] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _527468), _527470)), _527472)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _527468), _527472)))], (3295 ^ _415872) ^ [_527730, _527732, _527734] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _527730), _527732)), _527734)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _527732), _527734)))], (3301 ^ _415872) ^ [_527992, _527994, _527996] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _527992), _527994)), _527996)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _527992), _527996)))], (3307 ^ _415872) ^ [_528254, _528256, _528258] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _528254), _528256)), _528258)), 3310 ^ _415872 : [(3311 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _528254), _528258)))], (3313 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _528256), _528258)))]]], (3315 ^ _415872) ^ [_528607, _528609, _528611] : [class_RealVector_Oreal__normed__div__algebra(_528607), -(c_Groups_Osgn__class_Osgn(_528607, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_528607), _528609), _528611)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_528607), c_Groups_Osgn__class_Osgn(_528607, _528609)), c_Groups_Osgn__class_Osgn(_528607, _528611)))], (3321 ^ _415872) ^ [_528885, _528887, _528889] : [class_Rings_Ocomm__semiring__1(_528885), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_528885), _528887), _528889) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_528885), _528889), _528887))], (3327 ^ _415872) ^ [_529159, _529161, _529163, _529165] : [class_Rings_Ocomm__semiring__1(_529159), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_529159), _529161), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_529159), _529163), _529165)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_529159), _529163), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_529159), _529161), _529165)))], (3333 ^ _415872) ^ [_529471, _529473, _529475, _529477] : [class_Rings_Ocomm__semiring__1(_529471), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_529471), _529473), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_529471), _529475), _529477)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_529471), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_529471), _529473), _529475)), _529477))], (3339 ^ _415872) ^ [_529783, _529785, _529787, _529789] : [class_Rings_Ocomm__semiring__1(_529783), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_529783), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_529783), _529785), _529787)), _529789) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_529783), _529785), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_529783), _529787), _529789)))], (3345 ^ _415872) ^ [_530095, _530097, _530099, _530101] : [class_Rings_Ocomm__semiring__1(_530095), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_530095), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_530095), _530097), _530099)), _530101) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_530095), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_530095), _530097), _530101)), _530099))], (3351 ^ _415872) ^ [_530421, _530423, _530425, _530427, _530429] : [class_Rings_Ocomm__semiring__1(_530421), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_530421), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_530421), _530423), _530425)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_530421), _530427), _530429)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_530421), _530423), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_530421), _530425), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_530421), _530427), _530429))))], (3357 ^ _415872) ^ [_530785, _530787, _530789, _530791, _530793] : [class_Rings_Ocomm__semiring__1(_530785), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_530785), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_530785), _530787), _530789)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_530785), _530791), _530793)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_530785), _530791), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_530785), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_530785), _530787), _530789)), _530793)))], (3363 ^ _415872) ^ [_531149, _531151, _531153, _531155, _531157] : [class_Rings_Ocomm__semiring__1(_531149), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_531149), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_531149), _531151), _531153)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_531149), _531155), _531157)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_531149), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_531149), _531151), _531155)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_531149), _531153), _531157)))], (3369 ^ _415872) ^ [_531485, _531487, _531489] : [3370 ^ _415872 : [(3371 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _531485), _531487)))], (3373 ^ _415872) ^ [] : [hBOOL(hAPP(hAPP(_531489, _531487), _531485))]], 3376 ^ _415872 : [(3377 ^ _415872) ^ [] : [-(_531485 = _531487)], (3379 ^ _415872) ^ [] : [hBOOL(hAPP(hAPP(_531489, _531487), _531485))]], 3382 ^ _415872 : [(3383 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _531487), _531485)))], (3385 ^ _415872) ^ [] : [hBOOL(hAPP(hAPP(_531489, _531487), _531485))]], -(hBOOL(hAPP(hAPP(_531489, _531487), _531485)))], (3389 ^ _415872) ^ [_532178, _532180] : [3390 ^ _415872 : [(3391 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _532178), _532180))], (3393 ^ _415872) ^ [] : [_532178 = _532180]], -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _532178), _532180)))], (3397 ^ _415872) ^ [_532510, _532512, _532514, _532516] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _532510), _532512)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _532514), _532516)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _532510), _532514)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _532512), _532516))))], (3407 ^ _415872) ^ [_532883, _532885] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _532883), _532885)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _532885), _532883)), -(_532883 = _532885)], (3417 ^ _415872) ^ [_533216, _533218, _533220] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _533216), _533218)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _533218), _533220)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _533216), _533220)))], (3427 ^ _415872) ^ [_533555, _533557] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _533555), _533557)), -(_533555 = _533557), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _533555), _533557)))], (3437 ^ _415872) ^ [_533891, _533893, _533895] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _533891), _533893)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _533895), _533891)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _533895), _533893))))], (3443 ^ _415872) ^ [_534165, _534167, _534169] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _534165), _534167)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _534165), _534169)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _534167), _534169))))], (3449 ^ _415872) ^ [_534425, _534427] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _534425), _534427)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _534425), _534427)))], (3455 ^ _415872) ^ [_534655, _534657] : [_534655 = _534657, -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _534655), _534657)))], (3461 ^ _415872) ^ [_534875, _534877] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _534875), _534877)), _534875 = _534877], (3467 ^ _415872) ^ [_535096, _535098] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _535096), _535098)), _535098 = _535096], (3473 ^ _415872) ^ [_535287] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _535287), _535287))], (3475 ^ _415872) ^ [_535399, _535401] : [-(_535399 = _535401), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _535399), _535401))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _535401), _535399)))], (3485 ^ _415872) ^ [_535752, _535754, _535756, _535758] : [class_Groups_Oab__semigroup__mult(_535752), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_535752), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_535752), _535754), _535756)), _535758) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_535752), _535754), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_535752), _535756), _535758)))], (3501 ^ _415872) ^ [_536337, _536339] : [3502 ^ _415872 : [(3503 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _536337), _536339))], (3505 ^ _415872) ^ [] : [_536337 = _536339]], -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _536337), _536339)))], (3491 ^ _415872) ^ [_536065, _536067] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _536065), _536067)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _536065), _536067))), -(_536065 = _536067)], (3509 ^ _415872) ^ [_536672, _536674] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _536672), _536674)), 3512 ^ _415872 : [(3513 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _536672), _536674)))], (3515 ^ _415872) ^ [] : [_536672 = _536674]]], (3517 ^ _415872) ^ [_536930, _536932] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _536930), _536932))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _536930), _536932)), -(_536930 = _536932)], (3527 ^ _415872) ^ [_537254, _537256] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _537254), _537256))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _537256), _537254)))], (3543 ^ _415872) ^ [_537789, _537791] : [3544 ^ _415872 : [(3545 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _537789), _537791))], (3547 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _537791), _537789))]], _537789 = _537791], (3533 ^ _415872) ^ [_537514, _537516] : [-(_537514 = _537516), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _537514), _537516))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _537516), _537514)))], (3551 ^ _415872) ^ [_538110, _538112, _538114] : [class_Rings_Olinordered__idom(_538110), -(c_Groups_Osgn__class_Osgn(_538110, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_538110), _538112), _538114)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_538110), c_Groups_Osgn__class_Osgn(_538110, _538112)), c_Groups_Osgn__class_Osgn(_538110, _538114)))], (3557 ^ _415872) ^ [_538374, _538376] : [class_Rings_Olinordered__idom(_538374), -(c_Groups_Osgn__class_Osgn(_538374, c_Groups_Osgn__class_Osgn(_538374, _538376)) = c_Groups_Osgn__class_Osgn(_538374, _538376))], (3563 ^ _415872) ^ [_538571] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _538571), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _538571), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _538571), _538571)))))], (3565 ^ _415872) ^ [_538666] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _538666), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _538666), _538666))))], (3567 ^ _415872) ^ [_538755] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _538755), _538755)))], (3569 ^ _415872) ^ [_538837] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _538837), _538837))], (3571 ^ _415872) ^ [_538949, _538951] : [class_Rings_Ocomm__semiring__1(_538949), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_538949), _538951), c_Groups_Ozero__class_Ozero(_538949)) = c_Groups_Ozero__class_Ozero(_538949))], (3577 ^ _415872) ^ [_539181, _539183] : [class_Rings_Ocomm__semiring__1(_539181), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_539181), c_Groups_Ozero__class_Ozero(_539181)), _539183) = c_Groups_Ozero__class_Ozero(_539181))], (3583 ^ _415872) ^ [_539455, _539457, _539459, _539461, _539463] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_539455), 3586 ^ _415872 : [(3597 ^ _415872) ^ [] : [3598 ^ _415872 : [(3599 ^ _415872) ^ [] : [_539457 = _539461], (3601 ^ _415872) ^ [] : [_539459 = _539463]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_539455), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_539455), _539457), _539459)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_539455), _539461), _539463)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_539455), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_539455), _539457), _539463)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_539455), _539461), _539459)))], (3587 ^ _415872) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_539455), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_539455), _539457), _539459)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_539455), _539461), _539463)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_539455), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_539455), _539457), _539463)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_539455), _539461), _539459)), -(_539457 = _539461), -(_539459 = _539463)]]], (3605 ^ _415872) ^ [_540309, _540311, _540313, _540315] : [class_Rings_Ocomm__semiring__1(_540309), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_540309), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_540309), _540311), _540313)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_540309), _540315), _540313)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_540309), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_540309), _540311), _540315)), _540313))], (3611 ^ _415872) ^ [_540637, _540639, _540641, _540643] : [class_Rings_Ocomm__semiring__1(_540637), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_540637), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_540637), _540639), _540641)), _540643) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_540637), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_540637), _540639), _540643)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_540637), _540641), _540643)))], (3617 ^ _415872) ^ [_540979, _540981, _540983, _540985, _540987] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_540979), 3620 ^ _415872 : [(3631 ^ _415872) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_540979), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_540979), _540981), _540985)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_540979), _540983), _540987)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_540979), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_540979), _540981), _540987)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_540979), _540983), _540985))), 3634 ^ _415872 : [(3635 ^ _415872) ^ [] : [_540981 = _540983], (3637 ^ _415872) ^ [] : [_540985 = _540987]]], (3621 ^ _415872) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_540979), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_540979), _540981), _540985)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_540979), _540983), _540987)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_540979), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_540979), _540981), _540987)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_540979), _540983), _540985)), -(_540981 = _540983), -(_540985 = _540987)]]], (3639 ^ _415872) ^ [_541839, _541841, _541843, _541845] : [class_Rings_Ocomm__semiring__1(_541839), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_541839), _541841), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_541839), _541843), _541845)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_541839), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_541839), _541841), _541843)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_541839), _541841), _541845)))], (3645 ^ _415872) ^ [_542139, _542141] : [class_Rings_Olinordered__idom(_542139), -(c_Groups_Oabs__class_Oabs(_542139, _542141) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_542139), _542141), c_Groups_Osgn__class_Osgn(_542139, _542141)))], (3651 ^ _415872) ^ [_542375, _542377] : [class_Rings_Olinordered__idom(_542375), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_542375), c_Groups_Osgn__class_Osgn(_542375, _542377)), c_Groups_Oabs__class_Oabs(_542375, _542377)) = _542377)], (3657 ^ _415872) ^ [_542611, _542613] : [class_Rings_Ocomm__semiring__1(_542611), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_542611), _542613), c_Groups_Oone__class_Oone(_542611)) = _542613)], (3663 ^ _415872) ^ [_542839, _542841] : [class_Rings_Ocomm__semiring__1(_542839), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_542839), c_Groups_Oone__class_Oone(_542839)), _542841) = _542841)], (3669 ^ _415872) ^ [_543067, _543069] : [_543067 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _543067), _543069), -(_543069 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_543067 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3679 ^ _415872) ^ [_543393, _543395, _543397] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _543393), _543395)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _543397)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _543397), _543393)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _543397), _543395))))], (3689 ^ _415872) ^ [_543764, _543766, _543768] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _543764), _543766)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _543768)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _543764), _543768)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _543766), _543768))))], (3709 ^ _415872) ^ [_544450, _544452, _544454] : [3710 ^ _415872 : [(3711 ^ _415872) ^ [] : [_544450 = _544454], (3713 ^ _415872) ^ [] : [_544452 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _544450), _544452) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _544454), _544452))], (3699 ^ _415872) ^ [_544164, _544166, _544168] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _544164), _544166) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _544168), _544166), -(_544164 = _544168), -(_544166 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3727 ^ _415872) ^ [_545097, _545099, _545101] : [3728 ^ _415872 : [(3729 ^ _415872) ^ [] : [_545099 = _545101], (3731 ^ _415872) ^ [] : [_545097 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _545097), _545099) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _545097), _545101))], (3717 ^ _415872) ^ [_544811, _544813, _544815] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _544811), _544813) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _544811), _544815), -(_544813 = _544815), -(_544811 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3745 ^ _415872) ^ [_545767, _545769, _545771] : [3746 ^ _415872 : [(3747 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _545769)))], (3749 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _545767), _545771))]], -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _545767), _545769)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _545771), _545769))))], (3735 ^ _415872) ^ [_545458, _545460, _545462] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _545458), _545460)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _545462), _545460))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _545460)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _545458), _545462)))], (3763 ^ _415872) ^ [_546462, _546464, _546466] : [3764 ^ _415872 : [(3765 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _546462)))], (3767 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _546464), _546466))]], -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _546462), _546464)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _546462), _546466))))], (3753 ^ _415872) ^ [_546153, _546155, _546157] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _546153), _546155)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _546153), _546157))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _546153)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _546155), _546157)))], (3771 ^ _415872) ^ [_546848, _546850, _546852] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _546848), _546850)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _546852), _546850))), 3774 ^ _415872 : [(3775 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _546850)))], (3777 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _546848), _546852)))]]], (3779 ^ _415872) ^ [_547141, _547143, _547145] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _547141), _547143)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _547145), _547143)))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _547143)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _547141), _547145))], (3789 ^ _415872) ^ [_547543, _547545, _547547] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _547543), _547545)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _547543), _547547))), 3792 ^ _415872 : [(3793 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _547543)))], (3795 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _547545), _547547)))]]], (3797 ^ _415872) ^ [_547836, _547838, _547840] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _547836), _547838)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _547836), _547840)))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _547836)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _547838), _547840))], (3817 ^ _415872) ^ [_548488, _548490] : [3818 ^ _415872 : [(3819 ^ _415872) ^ [] : [_548488 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (3821 ^ _415872) ^ [] : [_548490 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _548488), _548490) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3807 ^ _415872) ^ [_548224, _548226] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _548224), _548226) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_548224 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_548226 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3825 ^ _415872) ^ [_548757] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _548757), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3827 ^ _415872) ^ [_548899, _548901] : [hBOOL(hAPP(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), _548899), _548901))), 3830 ^ _415872 : [(3831 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _548899)))], (3833 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _548901)))]]], (3835 ^ _415872) ^ [_549160, _549162] : [-(hBOOL(hAPP(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), _549160), _549162)))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _549160)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _549162))], (3845 ^ _415872) ^ [_549456] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _549456) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3847 ^ _415872) ^ [_549580, _549582, _549584] : [class_RealVector_Oreal__normed__algebra(_549580), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_549580, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_549580), _549582), _549584))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_549580, _549582)), c_RealVector_Onorm__class_Onorm(_549580, _549584)))))], (3853 ^ _415872) ^ [_549892, _549894, _549896, _549898, _549900] : [class_RealVector_Oreal__normed__algebra(_549892), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_549892, _549894)), _549896)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_549892, _549898)), _549900)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_549892, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_549892), _549894), _549898))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _549896), _549900))))], (3867 ^ _415872) ^ [_550410, _550412, _550414] : [class_Rings_Ono__zero__divisors(_550410), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_550410), _550412), _550414) = c_Groups_Ozero__class_Ozero(_550410), -(_550412 = c_Groups_Ozero__class_Ozero(_550410)), -(_550414 = c_Groups_Ozero__class_Ozero(_550410))], (3881 ^ _415872) ^ [_550853, _550855, _550857] : [class_Rings_Ono__zero__divisors(_550853), -(_550855 = c_Groups_Ozero__class_Ozero(_550853)), -(_550857 = c_Groups_Ozero__class_Ozero(_550853)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_550853), _550855), _550857) = c_Groups_Ozero__class_Ozero(_550853)], (3895 ^ _415872) ^ [_551302, _551304, _551306] : [class_Rings_Oring__no__zero__divisors(_551302), 3898 ^ _415872 : [(3909 ^ _415872) ^ [] : [3910 ^ _415872 : [(3911 ^ _415872) ^ [] : [_551304 = c_Groups_Ozero__class_Ozero(_551302)], (3913 ^ _415872) ^ [] : [_551306 = c_Groups_Ozero__class_Ozero(_551302)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_551302), _551304), _551306) = c_Groups_Ozero__class_Ozero(_551302))], (3899 ^ _415872) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_551302), _551304), _551306) = c_Groups_Ozero__class_Ozero(_551302), -(_551304 = c_Groups_Ozero__class_Ozero(_551302)), -(_551306 = c_Groups_Ozero__class_Ozero(_551302))]]], (3917 ^ _415872) ^ [_551982, _551984] : [class_Rings_Omult__zero(_551982), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_551982), _551984), c_Groups_Ozero__class_Ozero(_551982)) = c_Groups_Ozero__class_Ozero(_551982))], (3923 ^ _415872) ^ [_552214, _552216] : [class_Rings_Omult__zero(_552214), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_552214), c_Groups_Ozero__class_Ozero(_552214)), _552216) = c_Groups_Ozero__class_Ozero(_552214))], (3929 ^ _415872) ^ [_552446, _552448] : [class_RealVector_Oreal__normed__algebra(_552446), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_552446), _552448), c_Groups_Ozero__class_Ozero(_552446)) = c_Groups_Ozero__class_Ozero(_552446))], (3935 ^ _415872) ^ [_552678, _552680] : [class_RealVector_Oreal__normed__algebra(_552678), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_552678), _552680), c_Groups_Ozero__class_Ozero(_552678)) = c_Groups_Ozero__class_Ozero(_552678))], (3941 ^ _415872) ^ [_552910, _552912] : [class_RealVector_Oreal__normed__algebra(_552910), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_552910), c_Groups_Ozero__class_Ozero(_552910)), _552912) = c_Groups_Ozero__class_Ozero(_552910))], (3947 ^ _415872) ^ [_553142, _553144] : [class_RealVector_Oreal__normed__algebra(_553142), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_553142), c_Groups_Ozero__class_Ozero(_553142)), _553144) = c_Groups_Ozero__class_Ozero(_553142))], (3953 ^ _415872) ^ [_553416, _553418, _553420, _553422, _553424] : [class_Rings_Osemiring(_553416), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_553416), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_553416), _553418), _553420)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_553416), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_553416), _553422), _553420)), _553424)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_553416), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_553416), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_553416), _553418), _553422)), _553420)), _553424))], (3959 ^ _415872) ^ [_553782, _553784, _553786, _553788] : [class_Rings_Ocomm__semiring(_553782), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_553782), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_553782), _553784), _553786)), _553788) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_553782), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_553782), _553784), _553788)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_553782), _553786), _553788)))], (3965 ^ _415872) ^ [_554110, _554112, _554114, _554116] : [class_RealVector_Oreal__normed__algebra(_554110), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_554110), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_554110), _554112), _554114)), _554116) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_554110), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_554110), _554112), _554116)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_554110), _554114), _554116)))], (3971 ^ _415872) ^ [_554438, _554440, _554442, _554444] : [class_RealVector_Oreal__normed__algebra(_554438), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_554438), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_554438), _554440), _554442)), _554444) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_554438), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_554438), _554440), _554444)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_554438), _554442), _554444)))], (3977 ^ _415872) ^ [_554766, _554768, _554770, _554772] : [class_RealVector_Oreal__normed__algebra(_554766), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_554766), _554768), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_554766), _554770), _554772)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_554766), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_554766), _554768), _554770)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_554766), _554768), _554772)))], (3983 ^ _415872) ^ [_555094, _555096, _555098, _555100] : [class_RealVector_Oreal__normed__algebra(_555094), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_555094), _555096), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_555094), _555098), _555100)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_555094), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_555094), _555096), _555098)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_555094), _555096), _555100)))], (3989 ^ _415872) ^ [_555394, _555396] : [class_Groups_Ocomm__monoid__mult(_555394), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_555394), _555396), c_Groups_Oone__class_Oone(_555394)) = _555396)], (3995 ^ _415872) ^ [_555622, _555624] : [class_Groups_Omonoid__mult(_555622), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_555622), _555624), c_Groups_Oone__class_Oone(_555622)) = _555624)], (4001 ^ _415872) ^ [_555850, _555852] : [class_Groups_Ocomm__monoid__mult(_555850), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_555850), c_Groups_Oone__class_Oone(_555850)), _555852) = _555852)], (4007 ^ _415872) ^ [_556078, _556080] : [class_Groups_Omonoid__mult(_556078), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_556078), c_Groups_Oone__class_Oone(_556078)), _556080) = _556080)], (4013 ^ _415872) ^ [_556320, _556322, _556324] : [-(_556320 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 4016 ^ _415872 : [(4017 ^ _415872) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _556320), _556322) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _556320), _556324), -(_556322 = _556324)], (4023 ^ _415872) ^ [] : [_556322 = _556324, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _556320), _556322) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _556320), _556324))]]], (4029 ^ _415872) ^ [_556849, _556851, _556853] : [-(_556849 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 4032 ^ _415872 : [(4033 ^ _415872) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _556851), _556849) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _556853), _556849), -(_556851 = _556853)], (4039 ^ _415872) ^ [] : [_556851 = _556853, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _556851), _556849) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _556853), _556849))]]], (4045 ^ _415872) ^ [_557364, _557366] : [class_Rings_Olinordered__idom(_557364), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_557364), c_Groups_Oabs__class_Oabs(_557364, _557366)), c_Groups_Oabs__class_Oabs(_557364, _557366)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_557364), _557366), _557366))], (4051 ^ _415872) ^ [_557630, _557632, _557634] : [class_Rings_Olinordered__idom(_557630), -(c_Groups_Oabs__class_Oabs(_557630, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_557630), _557632), _557634)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_557630), c_Groups_Oabs__class_Oabs(_557630, _557632)), c_Groups_Oabs__class_Oabs(_557630, _557634)))], (4057 ^ _415872) ^ [_557865] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _557865) = _557865)], (4059 ^ _415872) ^ [_557974, _557976, _557978] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), _557974), _557976)), _557978) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _557974), _557978)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _557976), _557978)))], (4061 ^ _415872) ^ [_558171, _558173, _558175, _558177, _558179, _558181] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_558171), -(_558173 = c_Groups_Ozero__class_Ozero(_558171)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_558171), _558175), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_558171), _558173), _558179)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_558171), _558177), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_558171), _558173), _558181)), _558175 = _558177, -(_558179 = _558181)], (4079 ^ _415872) ^ [_558807, _558809, _558811] : [class_Rings_Ocomm__semiring__1(_558807), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_558807), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_558807), _558809), _558811)), _558811) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_558807), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_558807), _558809), c_Groups_Oone__class_Oone(_558807))), _558811))], (4085 ^ _415872) ^ [_559103, _559105, _559107] : [class_Rings_Ocomm__semiring__1(_559103), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_559103), _559105), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_559103), _559107), _559105)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_559103), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_559103), _559107), c_Groups_Oone__class_Oone(_559103))), _559105))], (4091 ^ _415872) ^ [_559385, _559387] : [class_Rings_Ocomm__semiring__1(_559385), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_559385), _559387), _559387) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_559385), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_559385), c_Groups_Oone__class_Oone(_559385)), c_Groups_Oone__class_Oone(_559385))), _559387))], (4097 ^ _415872) ^ [_559649, _559651] : [class_Rings_Olinordered__idom(_559649), 4100 ^ _415872 : [(4101 ^ _415872) ^ [] : [c_Groups_Osgn__class_Osgn(_559649, _559651) = c_Groups_Ozero__class_Ozero(_559649), -(_559651 = c_Groups_Ozero__class_Ozero(_559649))], (4107 ^ _415872) ^ [] : [_559651 = c_Groups_Ozero__class_Ozero(_559649), -(c_Groups_Osgn__class_Osgn(_559649, _559651) = c_Groups_Ozero__class_Ozero(_559649))]]], (4113 ^ _415872) ^ [_560114] : [class_Groups_Osgn__if(_560114), -(c_Groups_Osgn__class_Osgn(_560114, c_Groups_Ozero__class_Ozero(_560114)) = c_Groups_Ozero__class_Ozero(_560114))], (4119 ^ _415872) ^ [_560330, _560332] : [class_RealVector_Oreal__normed__vector(_560330), 4122 ^ _415872 : [(4123 ^ _415872) ^ [] : [c_Groups_Osgn__class_Osgn(_560330, _560332) = c_Groups_Ozero__class_Ozero(_560330), -(_560332 = c_Groups_Ozero__class_Ozero(_560330))], (4129 ^ _415872) ^ [] : [_560332 = c_Groups_Ozero__class_Ozero(_560330), -(c_Groups_Osgn__class_Osgn(_560330, _560332) = c_Groups_Ozero__class_Ozero(_560330))]]], (4135 ^ _415872) ^ [_560795] : [class_RealVector_Oreal__normed__vector(_560795), -(c_Groups_Osgn__class_Osgn(_560795, c_Groups_Ozero__class_Ozero(_560795)) = c_Groups_Ozero__class_Ozero(_560795))], (4141 ^ _415872) ^ [_560997] : [class_RealVector_Oreal__normed__algebra__1(_560997), -(c_Groups_Osgn__class_Osgn(_560997, c_Groups_Oone__class_Oone(_560997)) = c_Groups_Oone__class_Oone(_560997))], (4147 ^ _415872) ^ [_561227, _561229, _561231] : [class_Rings_Oordered__cancel__semiring(_561227), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_561227, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_561227), _561229), _561231)), c_Groups_Ozero__class_Ozero(_561227)))), 4152 ^ _415872 : [(4153 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_561227, c_Groups_Ozero__class_Ozero(_561227)), _561229)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_561227, _561231), c_Groups_Ozero__class_Ozero(_561227)))], (4159 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_561227, _561229), c_Groups_Ozero__class_Ozero(_561227))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_561227, c_Groups_Ozero__class_Ozero(_561227)), _561231))]]], (4167 ^ _415872) ^ [_561896, _561898, _561900] : [class_Rings_Oordered__ring(_561896), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_561896, c_Groups_Ozero__class_Ozero(_561896)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_561896), _561898), _561900)))), 4172 ^ _415872 : [(4173 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_561896, c_Groups_Ozero__class_Ozero(_561896)), _561898)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_561896, c_Groups_Ozero__class_Ozero(_561896)), _561900))], (4179 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_561896, _561898), c_Groups_Ozero__class_Ozero(_561896))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_561896, _561900), c_Groups_Ozero__class_Ozero(_561896)))]]], (4187 ^ _415872) ^ [_562593, _562595, _562597, _562599, _562601] : [class_Rings_Oordered__semiring(_562593), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_562593, _562595), _562597)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_562593, _562599), _562601)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_562593, c_Groups_Ozero__class_Ozero(_562593)), _562597)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_562593, c_Groups_Ozero__class_Ozero(_562593)), _562599)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_562593, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_562593), _562595), _562599)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_562593), _562597), _562601))))], (4209 ^ _415872) ^ [_563355, _563357, _563359, _563361, _563363] : [class_Rings_Oordered__semiring(_563355), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_563355, _563357), _563359)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_563355, _563361), _563363)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_563355, c_Groups_Ozero__class_Ozero(_563355)), _563357)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_563355, c_Groups_Ozero__class_Ozero(_563355)), _563361)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_563355, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_563355), _563357), _563361)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_563355), _563359), _563363))))], (4231 ^ _415872) ^ [_564103, _564105, _564107, _564109] : [class_Rings_Oordered__ring(_564103), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_564103, _564105), _564107)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_564103, _564109), c_Groups_Ozero__class_Ozero(_564103))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_564103, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_564103), _564109), _564107)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_564103), _564109), _564105))))], (4245 ^ _415872) ^ [_564611, _564613, _564615, _564617] : [class_Rings_Oordered__ring(_564611), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_564611, _564613), _564615)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_564611, _564617), c_Groups_Ozero__class_Ozero(_564611))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_564611, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_564611), _564615), _564617)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_564611), _564613), _564617))))], (4259 ^ _415872) ^ [_565119, _565121, _565123, _565125] : [class_Rings_Oordered__comm__semiring(_565119), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_565119, _565121), _565123)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_565119, c_Groups_Ozero__class_Ozero(_565119)), _565125)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_565119, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_565119), _565125), _565121)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_565119), _565125), _565123))))], (4273 ^ _415872) ^ [_565627, _565629, _565631, _565633] : [class_Rings_Oordered__semiring(_565627), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_565627, _565629), _565631)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_565627, c_Groups_Ozero__class_Ozero(_565627)), _565633)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_565627, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_565627), _565633), _565629)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_565627), _565633), _565631))))], (4287 ^ _415872) ^ [_566135, _566137, _566139, _566141] : [class_Rings_Oordered__semiring(_566135), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_566135, _566137), _566139)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_566135, c_Groups_Ozero__class_Ozero(_566135)), _566141)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_566135, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_566135), _566137), _566141)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_566135), _566139), _566141))))], (4301 ^ _415872) ^ [_566629, _566631, _566633] : [class_Rings_Oordered__ring(_566629), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_566629, _566631), c_Groups_Ozero__class_Ozero(_566629))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_566629, _566633), c_Groups_Ozero__class_Ozero(_566629))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_566629, c_Groups_Ozero__class_Ozero(_566629)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_566629), _566631), _566633))))], (4315 ^ _415872) ^ [_567101, _567103, _567105] : [class_Rings_Oordered__cancel__semiring(_567101), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_567101, _567103), c_Groups_Ozero__class_Ozero(_567101))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_567101, c_Groups_Ozero__class_Ozero(_567101)), _567105)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_567101, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_567101), _567103), _567105)), c_Groups_Ozero__class_Ozero(_567101))))], (4329 ^ _415872) ^ [_567573, _567575, _567577] : [class_Rings_Oordered__cancel__semiring(_567573), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_567573, c_Groups_Ozero__class_Ozero(_567573)), _567575)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_567573, _567577), c_Groups_Ozero__class_Ozero(_567573))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_567573, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_567573), _567577), _567575)), c_Groups_Ozero__class_Ozero(_567573))))], (4343 ^ _415872) ^ [_568045, _568047, _568049] : [class_Rings_Oordered__cancel__semiring(_568045), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_568045, c_Groups_Ozero__class_Ozero(_568045)), _568047)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_568045, _568049), c_Groups_Ozero__class_Ozero(_568045))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_568045, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_568045), _568047), _568049)), c_Groups_Ozero__class_Ozero(_568045))))], (4357 ^ _415872) ^ [_568517, _568519, _568521] : [class_Rings_Oordered__cancel__semiring(_568517), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_568517, c_Groups_Ozero__class_Ozero(_568517)), _568519)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_568517, c_Groups_Ozero__class_Ozero(_568517)), _568521)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_568517, c_Groups_Ozero__class_Ozero(_568517)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_568517), _568519), _568521))))], (4371 ^ _415872) ^ [_568989, _568991, _568993] : [class_Rings_Olinordered__ring__strict(_568989), 4374 ^ _415872 : [(4375 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_568989, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_568989), _568991), _568993)), c_Groups_Ozero__class_Ozero(_568989))), 4380 ^ _415872 : [(4381 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_568989, c_Groups_Ozero__class_Ozero(_568989)), _568991)))], (4383 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_568989, _568993), c_Groups_Ozero__class_Ozero(_568989))))]], 4384 ^ _415872 : [(4385 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_568989, _568991), c_Groups_Ozero__class_Ozero(_568989))))], (4387 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_568989, c_Groups_Ozero__class_Ozero(_568989)), _568993)))]]], (4389 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_568989, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_568989), _568991), _568993)), c_Groups_Ozero__class_Ozero(_568989)))), 4390 ^ _415872 : [(4391 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_568989, c_Groups_Ozero__class_Ozero(_568989)), _568991)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_568989, _568993), c_Groups_Ozero__class_Ozero(_568989)))], (4397 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_568989, _568991), c_Groups_Ozero__class_Ozero(_568989))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_568989, c_Groups_Ozero__class_Ozero(_568989)), _568993))]]]]], (4405 ^ _415872) ^ [_570098, _570100, _570102] : [class_Rings_Olinordered__ring__strict(_570098), 4408 ^ _415872 : [(4409 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_570098, c_Groups_Ozero__class_Ozero(_570098)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_570098), _570100), _570102))), 4414 ^ _415872 : [(4415 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_570098, c_Groups_Ozero__class_Ozero(_570098)), _570100)))], (4417 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_570098, c_Groups_Ozero__class_Ozero(_570098)), _570102)))]], 4418 ^ _415872 : [(4419 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_570098, _570100), c_Groups_Ozero__class_Ozero(_570098))))], (4421 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_570098, _570102), c_Groups_Ozero__class_Ozero(_570098))))]]], (4423 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_570098, c_Groups_Ozero__class_Ozero(_570098)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_570098), _570100), _570102)))), 4424 ^ _415872 : [(4425 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_570098, c_Groups_Ozero__class_Ozero(_570098)), _570100)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_570098, c_Groups_Ozero__class_Ozero(_570098)), _570102))], (4431 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_570098, _570100), c_Groups_Ozero__class_Ozero(_570098))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_570098, _570102), c_Groups_Ozero__class_Ozero(_570098)))]]]]], (4439 ^ _415872) ^ [_571193, _571195] : [class_Rings_Olinordered__ring(_571193), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_571193, c_Groups_Ozero__class_Ozero(_571193)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_571193), _571195), _571195))))], (4445 ^ _415872) ^ [_571459, _571461, _571463, _571465] : [class_Rings_Olinordered__ring__strict(_571459), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_571459, _571461), _571463)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_571459, _571465), c_Groups_Ozero__class_Ozero(_571459))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_571459, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_571459), _571465), _571463)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_571459), _571465), _571461))))], (4459 ^ _415872) ^ [_571967, _571969, _571971, _571973] : [class_Rings_Olinordered__ring__strict(_571967), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_571967, _571969), _571971)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_571967, _571973), c_Groups_Ozero__class_Ozero(_571967))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_571967, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_571967), _571971), _571973)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_571967), _571969), _571973))))], (4473 ^ _415872) ^ [_572475, _572477, _572479, _572481] : [class_Rings_Olinordered__comm__semiring__strict(_572475), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_572475, _572477), _572479)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_572475, c_Groups_Ozero__class_Ozero(_572475)), _572481)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_572475, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_572475), _572481), _572477)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_572475), _572481), _572479))))], (4487 ^ _415872) ^ [_572983, _572985, _572987, _572989] : [class_Rings_Olinordered__semiring__strict(_572983), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_572983, _572985), _572987)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_572983, c_Groups_Ozero__class_Ozero(_572983)), _572989)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_572983, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_572983), _572989), _572985)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_572983), _572989), _572987))))], (4501 ^ _415872) ^ [_573491, _573493, _573495, _573497] : [class_Rings_Olinordered__semiring__strict(_573491), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_573491, _573493), _573495)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_573491, c_Groups_Ozero__class_Ozero(_573491)), _573497)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_573491, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_573491), _573493), _573497)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_573491), _573495), _573497))))], (4515 ^ _415872) ^ [_573985, _573987, _573989] : [class_Rings_Olinordered__ring__strict(_573985), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_573985, _573987), c_Groups_Ozero__class_Ozero(_573985))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_573985, _573989), c_Groups_Ozero__class_Ozero(_573985))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_573985, c_Groups_Ozero__class_Ozero(_573985)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_573985), _573987), _573989))))], (4529 ^ _415872) ^ [_574457, _574459, _574461] : [class_Rings_Olinordered__semiring__strict(_574457), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_574457, _574459), c_Groups_Ozero__class_Ozero(_574457))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_574457, c_Groups_Ozero__class_Ozero(_574457)), _574461)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_574457, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_574457), _574459), _574461)), c_Groups_Ozero__class_Ozero(_574457))))], (4543 ^ _415872) ^ [_574943, _574945, _574947, _574949] : [class_Rings_Olinordered__ring__strict(_574943), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_574943, _574945), c_Groups_Ozero__class_Ozero(_574943))), 4550 ^ _415872 : [(4551 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_574943, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_574943), _574945), _574947)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_574943), _574945), _574949))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_574943, _574949), _574947)))], (4557 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_574943, _574949), _574947)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_574943, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_574943), _574945), _574947)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_574943), _574945), _574949))))]]], (4563 ^ _415872) ^ [_575636, _575638, _575640] : [class_Rings_Olinordered__semiring__strict(_575636), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_575636, c_Groups_Ozero__class_Ozero(_575636)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_575636), _575638), _575640))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_575636, c_Groups_Ozero__class_Ozero(_575636)), _575640)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_575636, c_Groups_Ozero__class_Ozero(_575636)), _575638)))], (4577 ^ _415872) ^ [_576108, _576110, _576112] : [class_Rings_Olinordered__semiring__strict(_576108), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_576108, c_Groups_Ozero__class_Ozero(_576108)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_576108), _576110), _576112))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_576108, c_Groups_Ozero__class_Ozero(_576108)), _576110)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_576108, c_Groups_Ozero__class_Ozero(_576108)), _576112)))], (4591 ^ _415872) ^ [_576580, _576582, _576584] : [class_Rings_Olinordered__semiring__strict(_576580), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_576580, c_Groups_Ozero__class_Ozero(_576580)), _576582)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_576580, _576584), c_Groups_Ozero__class_Ozero(_576580))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_576580, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_576580), _576584), _576582)), c_Groups_Ozero__class_Ozero(_576580))))], (4605 ^ _415872) ^ [_577052, _577054, _577056] : [class_Rings_Olinordered__semiring__strict(_577052), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_577052, c_Groups_Ozero__class_Ozero(_577052)), _577054)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_577052, _577056), c_Groups_Ozero__class_Ozero(_577052))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_577052, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_577052), _577054), _577056)), c_Groups_Ozero__class_Ozero(_577052))))], (4619 ^ _415872) ^ [_577524, _577526, _577528] : [class_Rings_Olinordered__semiring__strict(_577524), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_577524, c_Groups_Ozero__class_Ozero(_577524)), _577526)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_577524, c_Groups_Ozero__class_Ozero(_577524)), _577528)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_577524, c_Groups_Ozero__class_Ozero(_577524)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_577524), _577526), _577528))))], (4633 ^ _415872) ^ [_578010, _578012, _578014, _578016] : [class_Rings_Olinordered__ring__strict(_578010), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_578010, c_Groups_Ozero__class_Ozero(_578010)), _578012)), 4640 ^ _415872 : [(4641 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_578010, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_578010), _578012), _578014)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_578010), _578012), _578016))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_578010, _578014), _578016)))], (4647 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_578010, _578014), _578016)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_578010, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_578010), _578012), _578014)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_578010), _578012), _578016))))]]], (4653 ^ _415872) ^ [_578717, _578719, _578721, _578723] : [class_Rings_Olinordered__ring__strict(_578717), 4656 ^ _415872 : [(4657 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_578717, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_578717), _578719), _578721)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_578717), _578719), _578723))), 4662 ^ _415872 : [(4663 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_578717, c_Groups_Ozero__class_Ozero(_578717)), _578719)))], (4665 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_578717, _578721), _578723)))]], 4666 ^ _415872 : [(4667 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_578717, _578719), c_Groups_Ozero__class_Ozero(_578717))))], (4669 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_578717, _578723), _578721)))]]], (4671 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_578717, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_578717), _578719), _578721)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_578717), _578719), _578723)))), 4672 ^ _415872 : [(4673 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_578717, c_Groups_Ozero__class_Ozero(_578717)), _578719)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_578717, _578721), _578723))], (4679 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_578717, _578719), c_Groups_Ozero__class_Ozero(_578717))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_578717, _578723), _578721))]]]]], (4687 ^ _415872) ^ [_579880, _579882, _579884, _579886] : [class_Rings_Olinordered__ring__strict(_579880), 4690 ^ _415872 : [(4691 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_579880, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_579880), _579882), _579884)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_579880), _579886), _579884))), 4696 ^ _415872 : [(4697 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_579880, c_Groups_Ozero__class_Ozero(_579880)), _579884)))], (4699 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_579880, _579882), _579886)))]], 4700 ^ _415872 : [(4701 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_579880, _579884), c_Groups_Ozero__class_Ozero(_579880))))], (4703 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_579880, _579886), _579882)))]]], (4705 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_579880, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_579880), _579882), _579884)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_579880), _579886), _579884)))), 4706 ^ _415872 : [(4707 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_579880, c_Groups_Ozero__class_Ozero(_579880)), _579884)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_579880, _579882), _579886))], (4713 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_579880, _579884), c_Groups_Ozero__class_Ozero(_579880))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_579880, _579886), _579882))]]]]], (4721 ^ _415872) ^ [_581015, _581017] : [class_Rings_Olinordered__ring(_581015), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_581015, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_581015), _581017), _581017)), c_Groups_Ozero__class_Ozero(_581015)))], (4727 ^ _415872) ^ [_581268, _581270, _581272] : [class_Rings_Olinordered__semidom(_581268), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_581268, c_Groups_Oone__class_Oone(_581268)), _581270)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_581268, c_Groups_Oone__class_Oone(_581268)), _581272)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_581268, c_Groups_Oone__class_Oone(_581268)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_581268), _581270), _581272))))], (4741 ^ _415872) ^ [_581768, _581770, _581772, _581774, _581776] : [class_Rings_Olinordered__idom(_581768), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_581768, c_Groups_Oabs__class_Oabs(_581768, _581770)), _581772)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_581768, c_Groups_Oabs__class_Oabs(_581768, _581774)), _581776)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_581768, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_581768), c_Groups_Oabs__class_Oabs(_581768, _581770)), c_Groups_Oabs__class_Oabs(_581768, _581774))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_581768), _581772), _581776))))], (4755 ^ _415872) ^ [_582296, _582298, _582300] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _582296)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _582298), _582300)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _582296), _582298)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _582296), _582300))))], (4765 ^ _415872) ^ [_582653, _582655] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _582653)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _582655)), -(hBOOL(hAPP(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), _582653), _582655))))], (4775 ^ _415872) ^ [_582990, _582992, _582994] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _582990)), 4778 ^ _415872 : [(4779 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _582992), _582990)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _582994), _582990))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _582992), _582994)))], (4785 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _582992), _582994)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _582992), _582990)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _582994), _582990))))]]], (4791 ^ _415872) ^ [_583565, _583567] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _583565), _583565)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _583567), _583567)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 4794 ^ _415872 : [(4795 ^ _415872) ^ [] : [-(_583565 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (4797 ^ _415872) ^ [] : [-(_583567 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))]]], (4799 ^ _415872) ^ [_583838, _583840] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _583838), _583838)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _583840), _583840)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _583838 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _583840 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)], (4809 ^ _415872) ^ [_584175, _584177] : [class_Rings_Olinordered__idom(_584175), 4812 ^ _415872 : [(4813 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_584175, c_Groups_Osgn__class_Osgn(_584175, _584177)), c_Groups_Ozero__class_Ozero(_584175))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_584175, _584177), c_Groups_Ozero__class_Ozero(_584175))))], (4819 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_584175, _584177), c_Groups_Ozero__class_Ozero(_584175))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_584175, c_Groups_Osgn__class_Osgn(_584175, _584177)), c_Groups_Ozero__class_Ozero(_584175))))]]], (4825 ^ _415872) ^ [_584684, _584686] : [class_Rings_Olinordered__idom(_584684), 4828 ^ _415872 : [(4829 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_584684, c_Groups_Ozero__class_Ozero(_584684)), c_Groups_Osgn__class_Osgn(_584684, _584686))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_584684, c_Groups_Ozero__class_Ozero(_584684)), _584686)))], (4835 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_584684, c_Groups_Ozero__class_Ozero(_584684)), _584686)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_584684, c_Groups_Ozero__class_Ozero(_584684)), c_Groups_Osgn__class_Osgn(_584684, _584686))))]]], (4841 ^ _415872) ^ [_585221, _585223, _585225, _585227] : [class_Rings_Olinordered__semiring__strict(_585221), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_585221, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_585221), _585223), _585225)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_585221), _585223), _585227))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_585221, c_Groups_Ozero__class_Ozero(_585221)), _585223)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_585221, _585225), _585227)))], (4855 ^ _415872) ^ [_585729, _585731, _585733, _585735] : [class_Rings_Olinordered__semiring__strict(_585729), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_585729, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_585729), _585731), _585733)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_585729), _585735), _585733))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_585729, c_Groups_Ozero__class_Ozero(_585729)), _585733)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_585729, _585731), _585735)))], (4869 ^ _415872) ^ [_586237, _586239, _586241, _586243] : [class_Rings_Olinordered__semiring__strict(_586237), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_586237, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_586237), _586239), _586241)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_586237), _586239), _586243))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_586237, c_Groups_Ozero__class_Ozero(_586237)), _586239)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_586237, _586241), _586243)))], (4883 ^ _415872) ^ [_586745, _586747, _586749, _586751] : [class_Rings_Olinordered__semiring(_586745), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_586745, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_586745), _586747), _586749)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_586745), _586747), _586751))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_586745, c_Groups_Ozero__class_Ozero(_586745)), _586747)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_586745, _586749), _586751)))], (4897 ^ _415872) ^ [_587253, _587255, _587257, _587259] : [class_Rings_Olinordered__semiring__strict(_587253), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_587253, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_587253), _587255), _587257)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_587253), _587259), _587257))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_587253, c_Groups_Ozero__class_Ozero(_587253)), _587257)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_587253, _587255), _587259)))], (4911 ^ _415872) ^ [_587761, _587763, _587765, _587767] : [class_Rings_Olinordered__semiring(_587761), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_587761, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_587761), _587763), _587765)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_587761), _587767), _587765))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_587761, c_Groups_Ozero__class_Ozero(_587761)), _587765)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_587761, _587763), _587767)))], (4925 ^ _415872) ^ [_588283, _588285, _588287, _588289, _588291] : [class_Rings_Olinordered__semiring__strict(_588283), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_588283, _588285), _588287)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_588283, _588289), _588291)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_588283, c_Groups_Ozero__class_Ozero(_588283)), _588285)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_588283, c_Groups_Ozero__class_Ozero(_588283)), _588289)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_588283, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_588283), _588285), _588289)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_588283), _588287), _588291))))], (4947 ^ _415872) ^ [_589045, _589047, _589049, _589051, _589053] : [class_Rings_Olinordered__semiring__strict(_589045), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_589045, _589047), _589049)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_589045, _589051), _589053)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_589045, c_Groups_Ozero__class_Ozero(_589045)), _589047)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_589045, c_Groups_Ozero__class_Ozero(_589045)), _589051)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_589045, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_589045), _589047), _589051)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_589045), _589049), _589053))))], (4969 ^ _415872) ^ [_589807, _589809, _589811, _589813, _589815] : [class_Rings_Olinordered__semiring__strict(_589807), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_589807, _589809), _589811)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_589807, _589813), _589815)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_589807, c_Groups_Ozero__class_Ozero(_589807)), _589809)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_589807, c_Groups_Ozero__class_Ozero(_589807)), _589813)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_589807, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_589807), _589809), _589813)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_589807), _589811), _589815))))], (4991 ^ _415872) ^ [_590569, _590571, _590573, _590575, _590577] : [class_Rings_Olinordered__semiring__strict(_590569), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_590569, _590571), _590573)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_590569, _590575), _590577)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_590569, c_Groups_Ozero__class_Ozero(_590569)), _590573)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_590569, c_Groups_Ozero__class_Ozero(_590569)), _590575)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_590569, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_590569), _590571), _590575)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_590569), _590573), _590577))))], (5013 ^ _415872) ^ [_591317, _591319, _591321, _591323] : [class_Rings_Olinordered__ring__strict(_591317), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_591317, _591319), c_Groups_Ozero__class_Ozero(_591317))), 5020 ^ _415872 : [(5021 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_591317, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_591317), _591319), _591321)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_591317), _591319), _591323))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_591317, _591323), _591321)))], (5027 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_591317, _591323), _591321)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_591317, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_591317), _591319), _591321)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_591317), _591319), _591323))))]]], (5033 ^ _415872) ^ [_592024, _592026, _592028, _592030] : [class_Rings_Olinordered__ring__strict(_592024), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_592024, c_Groups_Ozero__class_Ozero(_592024)), _592026)), 5040 ^ _415872 : [(5041 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_592024, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_592024), _592026), _592028)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_592024), _592026), _592030))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_592024, _592028), _592030)))], (5047 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_592024, _592028), _592030)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_592024, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_592024), _592026), _592028)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_592024), _592026), _592030))))]]], (5053 ^ _415872) ^ [_592717, _592719, _592721] : [class_Rings_Olinordered__idom(_592717), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_592717, c_Groups_Ozero__class_Ozero(_592717)), _592719)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_592717, c_Groups_Ozero__class_Ozero(_592717)), _592721)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_592717, _592721), c_Groups_Oone__class_Oone(_592717))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_592717, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_592717), _592721), _592719)), _592719)))], (5071 ^ _415872) ^ [_593292, _593294, _593296] : [class_Rings_Olinordered__idom(_593292), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_593292, c_Groups_Ozero__class_Ozero(_593292)), _593294)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_593292, c_Groups_Ozero__class_Ozero(_593292)), _593296)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_593292, _593296), c_Groups_Oone__class_Oone(_593292))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_593292, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_593292), _593294), _593296)), _593294)))], (5089 ^ _415872) ^ [_593867, _593869, _593871] : [class_Rings_Oordered__ring__abs(_593867), -(c_Groups_Oabs__class_Oabs(_593867, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_593867), _593869), _593871)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_593867), c_Groups_Oabs__class_Oabs(_593867, _593869)), c_Groups_Oabs__class_Oabs(_593867, _593871))), 5096 ^ _415872 : [(5097 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_593867, c_Groups_Ozero__class_Ozero(_593867)), _593869))], (5099 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_593867, _593869), c_Groups_Ozero__class_Ozero(_593867)))]], 5100 ^ _415872 : [(5101 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_593867, c_Groups_Ozero__class_Ozero(_593867)), _593871))], (5103 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_593867, _593871), c_Groups_Ozero__class_Ozero(_593867)))]]], (5107 ^ _415872) ^ [_594539, _594541, _594543] : [class_Rings_Olinordered__idom(_594539), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_594539, c_Groups_Ozero__class_Ozero(_594539)), _594541)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_594539), c_Groups_Oabs__class_Oabs(_594539, _594543)), _594541) = c_Groups_Oabs__class_Oabs(_594539, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_594539), _594543), _594541)))], (5117 ^ _415872) ^ [_594918, _594920, _594922] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _594918)), 5120 ^ _415872 : [(5121 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _594918), _594920)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _594918), _594922))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _594920), _594922)))], (5127 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _594920), _594922)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _594918), _594920)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _594918), _594922))))]]], (5133 ^ _415872) ^ [_595478, _595480, _595482] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _595478)), 5136 ^ _415872 : [(5137 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _595480), _595478)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _595482), _595478))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _595480), _595482)))], (5143 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _595480), _595482)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _595480), _595478)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _595482), _595478))))]]], (5149 ^ _415872) ^ [_596066, _596068, _596070, _596072, _596074] : [class_Rings_Ocomm__semiring__1(_596066), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_596066), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_596066), _596068), _596070)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_596066), _596072), _596074)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_596066), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_596066), _596068), _596072)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_596066), _596070), _596074)))], (5155 ^ _415872) ^ [_596416, _596418, _596420, _596422] : [class_Rings_Ocomm__semiring__1(_596416), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_596416), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_596416), _596418), _596420)), _596422) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_596416), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_596416), _596418), _596422)), _596420))], (5161 ^ _415872) ^ [_596728, _596730, _596732, _596734] : [class_Rings_Ocomm__semiring__1(_596728), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_596728), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_596728), _596730), _596732)), _596734) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_596728), _596730), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_596728), _596732), _596734)))], (5167 ^ _415872) ^ [_597040, _597042, _597044, _597046] : [class_Rings_Ocomm__semiring__1(_597040), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_597040), _597042), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_597040), _597044), _597046)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_597040), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_597040), _597042), _597044)), _597046))], (5173 ^ _415872) ^ [_597352, _597354, _597356, _597358] : [class_Rings_Ocomm__semiring__1(_597352), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_597352), _597354), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_597352), _597356), _597358)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_597352), _597356), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_597352), _597354), _597358)))], (5179 ^ _415872) ^ [_597650, _597652, _597654] : [class_Rings_Ocomm__semiring__1(_597650), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_597650), _597652), _597654) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_597650), _597654), _597652))], (5185 ^ _415872) ^ [_597882] : [-(_597882 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _597882)))], (5191 ^ _415872) ^ [_598093, _598095] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _598093), _598095) = _598093, -(_598095 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5197 ^ _415872) ^ [_598315, _598317] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _598315), _598317)), _598317 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5203 ^ _415872) ^ [_598565, _598567] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _598565), _598567) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 5206 ^ _415872 : [(5207 ^ _415872) ^ [] : [-(_598565 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5209 ^ _415872) ^ [] : [-(_598567 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (5211 ^ _415872) ^ [_598814, _598816] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _598814), _598816) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _598814 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _598816 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5221 ^ _415872) ^ [_599142] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _599142), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_599142 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5227 ^ _415872) ^ [_599308] : [_599308 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _599308), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (5233 ^ _415872) ^ [_599495] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _599495), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _599495)], (5235 ^ _415872) ^ [_599578] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _599578), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (5247 ^ _415872) ^ [_599995, _599997] : [5248 ^ _415872 : [(5249 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _599995))], (5251 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _599997))]], -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _599995), _599997))))], (5237 ^ _415872) ^ [_599719, _599721] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _599719), _599721))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _599719))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _599721)))], (5255 ^ _415872) ^ [_600276] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _600276) = _600276)], (5257 ^ _415872) ^ [_600357] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _600357)))], (5259 ^ _415872) ^ [_600481] : [-(_600481 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _600481)))], (5265 ^ _415872) ^ [_600644] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _600644)), _600644 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5271 ^ _415872) ^ [_600825] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _600825), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (5273 ^ _415872) ^ [_600923] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _600923)), -(c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, _600923) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (5279 ^ _415872) ^ [_601137, _601139] : [class_Rings_Olinordered__idom(_601137), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_601137, c_Groups_Ozero__class_Ozero(_601137)), _601139)), -(c_Groups_Osgn__class_Osgn(_601137, _601139) = c_Groups_Oone__class_Oone(_601137))], (5289 ^ _415872) ^ [_601458, _601460] : [class_Rings_Olinordered__idom(_601458), 5292 ^ _415872 : [(5293 ^ _415872) ^ [] : [c_Groups_Osgn__class_Osgn(_601458, _601460) = c_Groups_Oone__class_Oone(_601458), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_601458, c_Groups_Ozero__class_Ozero(_601458)), _601460)))], (5299 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_601458, c_Groups_Ozero__class_Ozero(_601458)), _601460)), -(c_Groups_Osgn__class_Osgn(_601458, _601460) = c_Groups_Oone__class_Oone(_601458))]]], (5305 ^ _415872) ^ [_602008, _602010, _602012, _602014, _602016, _602018] : [class_Rings_Olinordered__semiring__1(_602008), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_602008, _602010), _602012)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_602008, _602014), _602012)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_602008, c_Groups_Ozero__class_Ozero(_602008)), _602016)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_602008, c_Groups_Ozero__class_Ozero(_602008)), _602018)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_602008), _602016), _602018) = c_Groups_Oone__class_Oone(_602008), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_602008, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_602008), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_602008), _602016), _602010)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_602008), _602018), _602014))), _602012)))], (5332 ^ _415872) ^ [] : [-(c_SEQ_Osubseq(5330 ^ []))], (5334 ^ _415872) ^ [] : [-(c_SEQ_Omonoseq(tc_RealDef_Oreal, c_COMBB(tc_Complex_Ocomplex, tc_RealDef_Oreal, tc_Nat_Onat, c_Complex_OIm, c_COMBB(tc_Nat_Onat, tc_Complex_Ocomplex, tc_Nat_Onat, v_s, c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____, 5330 ^ [])))))], (5336 ^ _415872) ^ [_603089, _603091, _603093, _603095] : [class_RealVector_Oreal__normed__vector(_603089), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _603091), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_603089, _603093)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _603091), c_RealVector_Onorm__class_Onorm(_603089, _603095)))), -(_603093 = c_Groups_Ozero__class_Ozero(_603089))], (5350 ^ _415872) ^ [_603565, _603567, _603569] : [class_Rings_Olinordered__ring__strict(_603565), 5353 ^ _415872 : [(5364 ^ _415872) ^ [] : [5365 ^ _415872 : [(5366 ^ _415872) ^ [] : [-(_603567 = c_Groups_Ozero__class_Ozero(_603565))], (5368 ^ _415872) ^ [] : [-(_603569 = c_Groups_Ozero__class_Ozero(_603565))]], -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_603565, c_Groups_Ozero__class_Ozero(_603565)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_603565), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_603565), _603567), _603567)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_603565), _603569), _603569)))))], (5354 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_603565, c_Groups_Ozero__class_Ozero(_603565)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_603565), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_603565), _603567), _603567)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_603565), _603569), _603569)))), _603567 = c_Groups_Ozero__class_Ozero(_603565), _603569 = c_Groups_Ozero__class_Ozero(_603565)]]], (5372 ^ _415872) ^ [_604326, _604328, _604330] : [class_Rings_Olinordered__ring(_604326), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_604326, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_604326), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_604326), _604328), _604328)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_604326), _604330), _604330))), c_Groups_Ozero__class_Ozero(_604326)))], (5378 ^ _415872) ^ [_604617, _604619, _604621] : [class_Rings_Olinordered__ring__strict(_604617), 5381 ^ _415872 : [(5382 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_604617, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_604617), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_604617), _604619), _604619)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_604617), _604621), _604621))), c_Groups_Ozero__class_Ozero(_604617))), 5385 ^ _415872 : [(5386 ^ _415872) ^ [] : [-(_604619 = c_Groups_Ozero__class_Ozero(_604617))], (5388 ^ _415872) ^ [] : [-(_604621 = c_Groups_Ozero__class_Ozero(_604617))]]], (5390 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_604617, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_604617), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_604617), _604619), _604619)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_604617), _604621), _604621))), c_Groups_Ozero__class_Ozero(_604617)))), _604619 = c_Groups_Ozero__class_Ozero(_604617), _604621 = c_Groups_Ozero__class_Ozero(_604617)]]], (5400 ^ _415872) ^ [_605374, _605376, _605378] : [class_Rings_Olinordered__ring(_605374), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_605374, c_Groups_Ozero__class_Ozero(_605374)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_605374), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_605374), _605376), _605376)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_605374), _605378), _605378)))))], (5406 ^ _415872) ^ [_605650, _605652] : [class_Orderings_Oorder(_605650), 5409 ^ _415872 : [(5428 ^ _415872) ^ [] : [5431 ^ _415872 : [(5432 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, 5429 ^ [_605650, _605652]), 5430 ^ [_605650, _605652])))], (5434 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_605650, hAPP(_605652, 5429 ^ [_605650, _605652])), hAPP(_605652, 5430 ^ [_605650, _605652])))], (5438 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, 5435 ^ [_605650, _605652]), 5436 ^ [_605650, _605652])))], (5440 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_605650, hAPP(_605652, 5436 ^ [_605650, _605652])), hAPP(_605652, 5435 ^ [_605650, _605652])))]], -(c_SEQ_Omonoseq(_605650, _605652))], (5410 ^ _415872) ^ [] : [c_SEQ_Omonoseq(_605650, _605652), 5415 ^ _415872 : [(5416 ^ _415872) ^ [_606006, _606008] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _606008), _606006)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_605650, hAPP(_605652, _606008)), hAPP(_605652, _606006))))]], 5421 ^ _415872 : [(5422 ^ _415872) ^ [_606244, _606246] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _606246), _606244)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_605650, hAPP(_605652, _606244)), hAPP(_605652, _606246))))]]]]], (5444 ^ _415872) ^ [_607262, _607264, _607266] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _607262), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _607264)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _607262), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _607266)))), -(_607264 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (5454 ^ _415872) ^ [_607600, _607602] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _607600), _607602) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _607602), _607600))], (5456 ^ _415872) ^ [_607720, _607722, _607724] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _607720), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _607722), _607724)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _607722), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _607720), _607724)))], (5458 ^ _415872) ^ [_607854, _607856, _607858] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _607854), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _607856), _607858)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _607854), _607856)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _607854), _607858)))], (5460 ^ _415872) ^ [_607994, _607996, _607998] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _607994), _607996)), _607998) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _607994), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _607996), _607998)))], (5462 ^ _415872) ^ [_608128, _608130, _608132] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _608128), _608130)), _608132) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _608128), _608132)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _608130), _608132)))], (5464 ^ _415872) ^ [_608312, _608314, _608316] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _608312), _608314) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _608312), _608316), -(_608314 = _608316)], (5470 ^ _415872) ^ [_608504, _608506, _608508] : [_608506 = _608508, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _608504), _608506) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _608504), _608508))], (5476 ^ _415872) ^ [_608789, _608791, _608793] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _608789), _608791) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _608793), _608791), -(_608789 = _608793)], (5482 ^ _415872) ^ [_608981, _608983, _608985] : [_608981 = _608985, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _608981), _608983) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _608985), _608983))], (5488 ^ _415872) ^ [_609208, _609210] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _609208), _609210) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _609210), _609208))], (5490 ^ _415872) ^ [_609328, _609330, _609332] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _609328), _609330)), _609332) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _609328), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _609330), _609332)))], (5492 ^ _415872) ^ [_609462, _609464, _609466] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _609462), _609464)), _609466) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _609462), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _609464), _609466)))], (5494 ^ _415872) ^ [_609626, _609628] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _609626), _609628) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 5497 ^ _415872 : [(5498 ^ _415872) ^ [] : [-(_609626 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (5500 ^ _415872) ^ [] : [-(_609628 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (5502 ^ _415872) ^ [_609875, _609877] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _609875), _609877) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _609875 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _609877 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (5512 ^ _415872) ^ [_610173, _610175] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _610173), _610175) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _610175), _610173))], (5514 ^ _415872) ^ [_610265] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _610265), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _610265)], (5516 ^ _415872) ^ [_610407, _610409] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _610407), _610409), 5519 ^ _415872 : [(5520 ^ _415872) ^ [] : [-(_610407 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (5522 ^ _415872) ^ [] : [-(_610409 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (5524 ^ _415872) ^ [_610656, _610658] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _610656), _610658)), _610656 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _610658 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (5534 ^ _415872) ^ [_610940] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _610940) = _610940)], (5536 ^ _415872) ^ [_611079, _611081] : [_611079 = _611081, 5539 ^ _415872 : [(5540 ^ _415872) ^ [] : [-(hAPP(c_Complex_ORe, _611079) = hAPP(c_Complex_ORe, _611081))], (5542 ^ _415872) ^ [] : [-(hAPP(c_Complex_OIm, _611079) = hAPP(c_Complex_OIm, _611081))]]], (5544 ^ _415872) ^ [_611340, _611342] : [-(_611340 = _611342), hAPP(c_Complex_ORe, _611340) = hAPP(c_Complex_ORe, _611342), hAPP(c_Complex_OIm, _611340) = hAPP(c_Complex_OIm, _611342)], (5554 ^ _415872) ^ [_611665, _611667] : [hAPP(c_Complex_ORe, _611665) = hAPP(c_Complex_ORe, _611667), hAPP(c_Complex_OIm, _611665) = hAPP(c_Complex_OIm, _611667), -(_611665 = _611667)], (5564 ^ _415872) ^ [_611973, _611975] : [-(hAPP(c_Complex_OIm, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), _611973), _611975)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(c_Complex_ORe, _611973)), hAPP(c_Complex_OIm, _611975))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(c_Complex_OIm, _611973)), hAPP(c_Complex_ORe, _611975))))], (5566 ^ _415872) ^ [_612092] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(c_Complex_ORe, _612092)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _612092))))], (5568 ^ _415872) ^ [] : [-(hAPP(c_Complex_ORe, c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (5570 ^ _415872) ^ [_612248, _612250] : [-(hAPP(c_Complex_ORe, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex), _612248), _612250)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), hAPP(c_Complex_ORe, _612248)), hAPP(c_Complex_ORe, _612250)))], (5572 ^ _415872) ^ [] : [-(hAPP(c_Complex_ORe, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (5574 ^ _415872) ^ [_612402] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, hAPP(c_Complex_ORe, _612402))), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _612402))))], (5576 ^ _415872) ^ [_612552, _612554] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _612552), _612554)), -(_612554 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _612552), 5579 ^ [_612552, _612554]))], (5583 ^ _415872) ^ [_612799, _612801] : [5584 ^ _415872 : [(5585 ^ _415872) ^ [_612880] : [_612801 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _612799), _612880)]], -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _612799), _612801)))], (5599 ^ _415872) ^ [_613443] : [5602 ^ _415872 : [(5603 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, 5600 ^ [_613443]), 5601 ^ [_613443])))], (5605 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(_613443, 5600 ^ [_613443])), hAPP(_613443, 5601 ^ [_613443])))]], -(c_SEQ_Osubseq(_613443))], (5589 ^ _415872) ^ [_613070] : [c_SEQ_Osubseq(_613070), 5592 ^ _415872 : [(5593 ^ _415872) ^ [_613236, _613238] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _613238), _613236)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(_613070, _613238)), hAPP(_613070, _613236))))]]], (5609 ^ _415872) ^ [_613923, _613925] : [c_SEQ_Osubseq(_613923), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _613925), hAPP(_613923, _613925))))], (5615 ^ _415872) ^ [_614161, _614163, _614165] : [class_Rings_Olinordered__ring__strict(_614161), 5618 ^ _415872 : [(5619 ^ _415872) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_614161), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_614161), _614163), _614163)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_614161), _614165), _614165)) = c_Groups_Ozero__class_Ozero(_614161), 5622 ^ _415872 : [(5623 ^ _415872) ^ [] : [-(_614163 = c_Groups_Ozero__class_Ozero(_614161))], (5625 ^ _415872) ^ [] : [-(_614165 = c_Groups_Ozero__class_Ozero(_614161))]]], (5627 ^ _415872) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_614161), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_614161), _614163), _614163)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_614161), _614165), _614165)) = c_Groups_Ozero__class_Ozero(_614161)), _614163 = c_Groups_Ozero__class_Ozero(_614161), _614165 = c_Groups_Ozero__class_Ozero(_614161)]]], (5637 ^ _415872) ^ [] : [-(c_SEQ_Oconvergent(tc_RealDef_Oreal, c_COMBB(tc_Complex_Ocomplex, tc_RealDef_Oreal, tc_Nat_Onat, c_Complex_ORe, c_COMBB(tc_Nat_Onat, tc_Complex_Ocomplex, tc_Nat_Onat, v_s, v_f____))))], (5639 ^ _415872) ^ [_614956, _614958, _614960] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _614956)), 5642 ^ _415872 : [(5643 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _614956), _614958)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _614956), _614960))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _614958), _614960)))], (5649 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _614958), _614960)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _614956), _614958)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _614956), _614960))))]]], (5655 ^ _415872) ^ [_615517] : [-(hBOOL(hAPP(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), _615517), _615517)))), -(_615517 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (5661 ^ _415872) ^ [_615692] : [_615692 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), hBOOL(hAPP(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), _615692), _615692)))], (5667 ^ _415872) ^ [_615929, _615931, _615933] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _615929)), 5670 ^ _415872 : [(5671 ^ _415872) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _615929), _615931) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _615929), _615933), -(_615931 = _615933)], (5677 ^ _415872) ^ [] : [_615931 = _615933, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _615929), _615931) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _615929), _615933))]]], (5683 ^ _415872) ^ [_616459, _616461, _616463] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _616459)), 5686 ^ _415872 : [(5687 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _616459), _616461)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _616459), _616463))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _616461), _616463)))], (5693 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _616461), _616463)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _616459), _616461)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _616459), _616463))))]]], (5699 ^ _415872) ^ [_617005, _617007] : [class_RealVector_Ometric__space(_617005), -(c_SEQ_Oconvergent(_617005, c_COMBK(_617005, tc_Nat_Onat, _617007)))], (5705 ^ _415872) ^ [_617235, _617237, _617239] : [class_RealVector_Oreal__normed__algebra(_617235), c_SEQ_Oconvergent(_617235, _617237), -(c_SEQ_Oconvergent(_617235, c_COMBB(_617235, _617235, tc_Nat_Onat, hAPP(c_Groups_Otimes__class_Otimes(_617235), _617239), _617237)))], (5715 ^ _415872) ^ [_617578, _617580, _617582] : [class_RealVector_Oreal__normed__algebra(_617578), c_SEQ_Oconvergent(_617578, _617580), -(c_SEQ_Oconvergent(_617578, c_COMBC(tc_Nat_Onat, _617578, _617578, c_COMBB(_617578, tc_fun(_617578, _617578), tc_Nat_Onat, c_Groups_Otimes__class_Otimes(_617578), _617580), _617582)))], (5725 ^ _415872) ^ [_617933, _617935, _617937] : [class_RealVector_Oreal__normed__algebra(_617933), c_SEQ_Oconvergent(_617933, _617935), c_SEQ_Oconvergent(_617933, _617937), -(c_SEQ_Oconvergent(_617933, c_COMBS(tc_Nat_Onat, _617933, _617933, c_COMBB(_617933, tc_fun(_617933, _617933), tc_Nat_Onat, c_Groups_Otimes__class_Otimes(_617933), _617935), _617937)))], (5739 ^ _415872) ^ [_618381, _618383, _618385] : [class_RealVector_Oreal__normed__vector(_618381), c_SEQ_Oconvergent(_618381, _618383), c_SEQ_Oconvergent(_618381, _618385), -(c_SEQ_Oconvergent(_618381, c_COMBS(tc_Nat_Onat, _618381, _618381, c_COMBB(_618381, tc_fun(_618381, _618381), tc_Nat_Onat, c_Groups_Oplus__class_Oplus(_618381), _618383), _618385)))], (5763 ^ _415872) ^ [_619144, _619146, _619148] : [5764 ^ _415872 : [(5765 ^ _415872) ^ [] : [_619144 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5767 ^ _415872) ^ [] : [_619146 = _619148]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _619144), _619146) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _619144), _619148))], (5753 ^ _415872) ^ [_618858, _618860, _618862] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _618858), _618860) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _618858), _618862), -(_618858 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_618860 = _618862)], (5771 ^ _415872) ^ [_619475, _619477, _619479, _619481] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _619475), _619477)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _619479), _619477)), _619481)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _619475), _619479)), _619477)), _619481))], (5774 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 5772 ^ [])))], (5776 ^ _415872) ^ [_619724] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, hAPP(c_Complex_OIm, _619724))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _619724)), 5772 ^ []))))], (5779 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 5777 ^ [])))], (5781 ^ _415872) ^ [_619947] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, hAPP(c_Complex_ORe, _619947))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _619947)), 5777 ^ []))))], (5784 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 5782 ^ [])))], (5786 ^ _415872) ^ [_620170] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, hAPP(c_Complex_OIm, _620170))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _620170)), 5782 ^ []))))], (5789 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 5787 ^ [])))], (5791 ^ _415872) ^ [_620393] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, hAPP(c_Complex_ORe, _620393))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _620393)), 5787 ^ []))))], (5793 ^ _415872) ^ [_620522, _620524] : [class_RealVector_Oreal__normed__algebra(_620522), 5797 ^ _415872 : [(5798 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 5796 ^ [_620522, _620524])))], (5800 ^ _415872) ^ [_620832] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_620522, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_620522), _620832), _620524))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_620522, _620832)), 5796 ^ [_620522, _620524]))))]]], (5802 ^ _415872) ^ [_620968] : [c_SEQ_Oconvergent(tc_Complex_Ocomplex, _620968), -(c_SEQ_Oconvergent(tc_RealDef_Oreal, c_COMBB(tc_Complex_Ocomplex, tc_RealDef_Oreal, tc_Nat_Onat, c_Complex_ORe, _620968)))], (5808 ^ _415872) ^ [_621170] : [c_SEQ_Oconvergent(tc_Complex_Ocomplex, _621170), -(c_SEQ_Oconvergent(tc_RealDef_Oreal, c_COMBB(tc_Complex_Ocomplex, tc_RealDef_Oreal, tc_Nat_Onat, c_Complex_OIm, _621170)))], (5814 ^ _415872) ^ [_621372] : [class_RealVector_Oreal__normed__algebra(_621372), 5818 ^ _415872 : [(5819 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 5817 ^ [_621372])))], (5821 ^ _415872) ^ [_621712, _621714] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_621372, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_621372), _621714), _621712))), 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(_621372, _621714)), c_RealVector_Onorm__class_Onorm(_621372, _621712))), 5817 ^ [_621372]))))]]], (5823 ^ _415872) ^ [_621869, _621871] : [class_RealVector_Oreal__normed__algebra(_621869), 5827 ^ _415872 : [(5828 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 5826 ^ [_621869, _621871])))], (5830 ^ _415872) ^ [_622179] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_621869, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_621869), _621871), _622179))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_621869, _622179)), 5826 ^ [_621869, _621871]))))]]], (5832 ^ _415872) ^ [_622343, _622345, _622347] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _622343), _622345)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _622343), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _622347), _622345))))], (5838 ^ _415872) ^ [_622605, _622607, _622609] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _622605), _622607)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _622605), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _622607), _622609))))], (5844 ^ _415872) ^ [_622853, _622855] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _622853), _622855)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _622853), _622855)))], (5850 ^ _415872) ^ [_623097, _623099, _623101] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _623097), _623099)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _623097), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _623099), _623101))))], (5856 ^ _415872) ^ [_623359, _623361, _623363] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _623359), _623361)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _623359), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _623363), _623361))))], (5863 ^ _415872) ^ [_623640] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, hAPP(c_Complex_OIm, _623640))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _623640)), 5861 ^ []))))], (5866 ^ _415872) ^ [_623800] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, hAPP(c_Complex_ORe, _623800))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _623800)), 5864 ^ []))))], (5868 ^ _415872) ^ [_623927, _623929] : [class_Orderings_Oorder(_623927), 5871 ^ _415872 : [(5882 ^ _415872) ^ [] : [5885 ^ _415872 : [(5886 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, 5883 ^ [_623927, _623929]), 5884 ^ [_623927, _623929])))], (5888 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_623927, hAPP(_623929, 5884 ^ [_623927, _623929])), hAPP(_623929, 5883 ^ [_623927, _623929])))]], -(c_SEQ_Odecseq(_623927, _623929))], (5872 ^ _415872) ^ [] : [c_SEQ_Odecseq(_623927, _623929), 5875 ^ _415872 : [(5876 ^ _415872) ^ [_624211, _624213] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _624213), _624211)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_623927, hAPP(_623929, _624211)), hAPP(_623929, _624213))))]]]]], (5892 ^ _415872) ^ [_624876, _624878] : [-(hBOOL(hAPP(_624876, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_624876, _624878)), 5900 ^ _415872 : [(5901 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, 5899 ^ [_624876, _624878]), _624878)))], (5909 ^ _415872) ^ [] : [-(hBOOL(hAPP(_624876, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 5899 ^ [_624876, _624878]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (5903 ^ _415872) ^ [_625336] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _625336), 5899 ^ [_624876, _624878])), hBOOL(hAPP(_624876, _625336))]]], (5911 ^ _415872) ^ [_625645] : [class_RealVector_Oreal__normed__algebra(_625645), 5915 ^ _415872 : [(5916 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 5914 ^ [_625645])))], (5918 ^ _415872) ^ [_625985, _625987] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_625645, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_625645), _625987), _625985))), 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(_625645, _625987)), c_RealVector_Onorm__class_Onorm(_625645, _625985))), 5914 ^ [_625645]))))]]], (5920 ^ _415872) ^ [_626142, _626144] : [class_Orderings_Oorder(_626142), c_SEQ_Odecseq(_626142, _626144), -(c_SEQ_Omonoseq(_626142, _626144))], (5930 ^ _415872) ^ [_626439, _626441] : [class_RealVector_Oreal__normed__algebra(_626439), 5934 ^ _415872 : [(5935 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 5933 ^ [_626439, _626441])))], (5937 ^ _415872) ^ [_626749] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_626439, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_626439), _626749), _626441))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_626439, _626749)), 5933 ^ [_626439, _626441]))))]]], (5939 ^ _415872) ^ [_626899, _626901] : [class_RealVector_Oreal__normed__algebra(_626899), 5943 ^ _415872 : [(5944 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 5942 ^ [_626899, _626901])))], (5946 ^ _415872) ^ [_627209] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_626899, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_626899), _626901), _627209))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_626899, _627209)), 5942 ^ [_626899, _626901]))))]]], (5948 ^ _415872) ^ [_627359, _627361] : [class_RealVector_Oreal__normed__vector(_627359), 5951 ^ _415872 : [(5952 ^ _415872) ^ [] : [c_SEQ_OBseq(_627359, _627361), 5956 ^ _415872 : [(5957 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 5955 ^ [_627359, _627361])))], (5959 ^ _415872) ^ [_627755] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_627359, hAPP(_627361, _627755))), 5955 ^ [_627359, _627361])))]]], (5961 ^ _415872) ^ [] : [-(c_SEQ_OBseq(_627359, _627361)), 5962 ^ _415872 : [(5963 ^ _415872) ^ [_627891] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _627891)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_627359, hAPP(_627361, 5966 ^ [_627359, _627361, _627891]))), _627891))]]]]], (5972 ^ _415872) ^ [_628268, _628270] : [class_Orderings_Oorder(_628268), 5975 ^ _415872 : [(5986 ^ _415872) ^ [] : [5989 ^ _415872 : [(5990 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, 5987 ^ [_628268, _628270]), 5988 ^ [_628268, _628270])))], (5992 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_628268, hAPP(_628270, 5987 ^ [_628268, _628270])), hAPP(_628270, 5988 ^ [_628268, _628270])))]], -(c_SEQ_Oincseq(_628268, _628270))], (5976 ^ _415872) ^ [] : [c_SEQ_Oincseq(_628268, _628270), 5979 ^ _415872 : [(5980 ^ _415872) ^ [_628552, _628554] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _628554), _628552)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_628268, hAPP(_628270, _628554)), hAPP(_628270, _628552))))]]]]], (5996 ^ _415872) ^ [_629231, _629233, _629235] : [class_RealVector_Oreal__normed__vector(_629231), c_SEQ_OBseq(_629231, c_COMBB(tc_Nat_Onat, _629231, tc_Nat_Onat, _629233, c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _629235))), -(c_SEQ_OBseq(_629231, _629233))], (6006 ^ _415872) ^ [_629576, _629578, _629580] : [class_RealVector_Oreal__normed__vector(_629576), c_SEQ_OBseq(_629576, _629578), -(c_SEQ_OBseq(_629576, c_COMBB(tc_Nat_Onat, _629576, tc_Nat_Onat, _629578, c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _629580))))], (6016 ^ _415872) ^ [_629893] : [c_SEQ_OBseq(tc_RealDef_Oreal, _629893), c_SEQ_Omonoseq(tc_RealDef_Oreal, _629893), -(c_SEQ_Oconvergent(tc_RealDef_Oreal, _629893))], (6026 ^ _415872) ^ [_630182, _630184] : [class_Orderings_Oorder(_630182), c_SEQ_Oincseq(_630182, _630184), -(c_SEQ_Omonoseq(_630182, _630184))], (6036 ^ _415872) ^ [_630493, _630495, _630497] : [class_RealVector_Oreal__normed__vector(_630493), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _630495)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_630493, hAPP(_630497, 6045 ^ [_630493, _630495, _630497]))), _630495)), -(c_SEQ_OBseq(_630493, _630497))], (6051 ^ _415872) ^ [_630993, _630995] : [class_RealVector_Oreal__normed__vector(_630993), c_SEQ_OBseq(_630993, _630995), 6059 ^ _415872 : [(6060 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 6058 ^ [_630993, _630995])))], (6062 ^ _415872) ^ [_631360] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_630993, hAPP(_630995, _631360))), 6058 ^ [_630993, _630995])))]]], (6064 ^ _415872) ^ [] : [-(c_Complex_Oexpi(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))], (6066 ^ _415872) ^ [_631539] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _631539)), -(c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), _631539), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_RComplete_Onatceiling(_631539)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (6072 ^ _415872) ^ [] : [-(c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6074 ^ _415872) ^ [_631803] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_RComplete_Onatceiling(_631803))))], (6076 ^ _415872) ^ [_631914, _631916] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _631914), _631916)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_631914)), c_RComplete_Onatceiling(_631916))))], (6082 ^ _415872) ^ [] : [-(c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (6084 ^ _415872) ^ [_632191] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _632191), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), -(c_RComplete_Onatceiling(_632191) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6090 ^ _415872) ^ [_632424] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_632424)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _632424), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))], (6096 ^ _415872) ^ [_632604] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _632604), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_632604)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (6102 ^ _415872) ^ [_632819, _632821] : [-(c_Complex_Oexpi(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex), _632819), _632821)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Complex_Oexpi(_632819)), c_Complex_Oexpi(_632821)))], (6104 ^ _415872) ^ [_632932] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _632932)), -(c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), _632932), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_RComplete_Onatfloor(_632932)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (6110 ^ _415872) ^ [_633172, _633174] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _633172)), _633174)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _633174), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _633172)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))), -(c_RComplete_Onatceiling(_633174) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _633172), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (6120 ^ _415872) ^ [_633531, _633533] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _633531)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _633533)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_RComplete_Onatfloor(_633531)), c_RComplete_Onatfloor(_633533))), c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _633531), _633533)))))], (6130 ^ _415872) ^ [_633870] : [c_SEQ_OBseq(tc_RealDef_Oreal, _633870), 6137 ^ _415872 : [(6138 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, 6135 ^ [_633870]), 6136 ^ [_633870])))], (6140 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(_633870, 6135 ^ [_633870])), hAPP(_633870, 6136 ^ [_633870])))]], -(c_SEQ_Oconvergent(tc_RealDef_Oreal, _633870))], (6144 ^ _415872) ^ [_634406] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_RealDef_Oreal(tc_Nat_Onat, _634406))))], (6146 ^ _415872) ^ [_634489] : [-(c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat, _634489)) = _634489)], (6148 ^ _415872) ^ [_634572] : [-(c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat, _634572)) = _634572)], (6150 ^ _415872) ^ [_634684, _634686] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _634684)), _634686)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _634684), c_RComplete_Onatfloor(_634686))))], (6156 ^ _415872) ^ [_634910] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _634910)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatfloor(_634910))), _634910)))], (6162 ^ _415872) ^ [_635167, _635169] : [c_RealDef_Oreal(tc_Nat_Onat, _635167) = c_RealDef_Oreal(tc_Nat_Onat, _635169), -(_635167 = _635169)], (6168 ^ _415872) ^ [_635341, _635343] : [_635341 = _635343, -(c_RealDef_Oreal(tc_Nat_Onat, _635341) = c_RealDef_Oreal(tc_Nat_Onat, _635343))], (6174 ^ _415872) ^ [_635536] : [-(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _635536)) = c_RealDef_Oreal(tc_Nat_Onat, _635536))], (6176 ^ _415872) ^ [_635652, _635654] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _635652)), 6179 ^ _415872 : [(6180 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _635654), c_RComplete_Onatfloor(_635652))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _635654)), _635652)))], (6186 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _635654)), _635652)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _635654), c_RComplete_Onatfloor(_635652))))]]], (6192 ^ _415872) ^ [_636132] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _636132), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatfloor(_636132))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))))], (6194 ^ _415872) ^ [] : [-(c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (6196 ^ _415872) ^ [_636323] : [c_RealDef_Oreal(tc_Nat_Onat, _636323) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_636323 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6202 ^ _415872) ^ [_636485] : [_636485 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_RealDef_Oreal(tc_Nat_Onat, _636485) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (6208 ^ _415872) ^ [_636667] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _636667)), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (6210 ^ _415872) ^ [_636811, _636813] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _636811)), c_RealDef_Oreal(tc_Nat_Onat, _636813))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _636811), _636813)))], (6216 ^ _415872) ^ [_637005, _637007] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _637005), _637007)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _637005)), c_RealDef_Oreal(tc_Nat_Onat, _637007))))], (6222 ^ _415872) ^ [_637278, _637280] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _637278)), c_RealDef_Oreal(tc_Nat_Onat, _637280))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _637278), _637280)))], (6228 ^ _415872) ^ [_637472, _637474] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _637472), _637474)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _637472)), c_RealDef_Oreal(tc_Nat_Onat, _637474))))], (6234 ^ _415872) ^ [_637716, _637718] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _637716)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _637716), c_RealDef_Oreal(tc_Nat_Onat, _637718))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_RComplete_Onatfloor(_637716)), _637718)))], (6244 ^ _415872) ^ [_638034, _638036] : [-(c_RealDef_Oreal(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _638034), _638036)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _638034)), c_RealDef_Oreal(tc_Nat_Onat, _638036)))], (6246 ^ _415872) ^ [_638149, _638151] : [-(c_RealDef_Oreal(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _638149), _638151)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _638149)), c_RealDef_Oreal(tc_Nat_Onat, _638151)))], (6248 ^ _415872) ^ [_638279, _638281] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _638279)), -(c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), _638279), c_RealDef_Oreal(tc_Nat_Onat, _638281))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_RComplete_Onatfloor(_638279)), _638281))], (6254 ^ _415872) ^ [_638531, _638533] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_RComplete_Onatfloor(_638531)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _638533)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _638531), c_RealDef_Oreal(tc_Nat_Onat, _638533))))], (6260 ^ _415872) ^ [] : [-(c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (6262 ^ _415872) ^ [_638836, _638838] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _638836)), _638838)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _638838), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _638836)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))), -(c_RComplete_Onatfloor(_638838) = _638836)], (6272 ^ _415872) ^ [_639154] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _639154), c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatceiling(_639154)))))], (6274 ^ _415872) ^ [] : [-(c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6276 ^ _415872) ^ [_639295] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_RComplete_Onatfloor(_639295))))], (6278 ^ _415872) ^ [_639406, _639408] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _639406), _639408)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatfloor(_639406)), c_RComplete_Onatfloor(_639408))))], (6284 ^ _415872) ^ [] : [-(c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (6286 ^ _415872) ^ [_639712] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _639712)), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), -(_639712 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6292 ^ _415872) ^ [_639884] : [_639884 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _639884)), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))], (6298 ^ _415872) ^ [_640106, _640108] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _640106), c_RealDef_Oreal(tc_Nat_Onat, _640108))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_640106)), _640108)))], (6304 ^ _415872) ^ [_640332] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _640332), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), -(c_RComplete_Onatfloor(_640332) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6310 ^ _415872) ^ [_640565] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_RealDef_Oreal(tc_Nat_Onat, _640565))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _640565)))], (6316 ^ _415872) ^ [_640735] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _640735)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_RealDef_Oreal(tc_Nat_Onat, _640735))))], (6322 ^ _415872) ^ [_640984, _640986] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _640984), _640986)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _640984)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), c_RealDef_Oreal(tc_Nat_Onat, _640986))))], (6328 ^ _415872) ^ [_641190, _641192] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _641190)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), c_RealDef_Oreal(tc_Nat_Onat, _641192))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _641190), _641192)))], (6334 ^ _415872) ^ [_641475, _641477] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _641475), _641477)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _641475)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _641477)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))))], (6340 ^ _415872) ^ [_641681, _641683] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _641681)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _641683)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _641681), _641683)))], (6346 ^ _415872) ^ [_641937, _641939] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _641937)), 6349 ^ _415872 : [(6350 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_641937)), _641939)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _641937), c_RealDef_Oreal(tc_Nat_Onat, _641939))))], (6356 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _641937), c_RealDef_Oreal(tc_Nat_Onat, _641939))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_641937)), _641939)))]]], (6362 ^ _415872) ^ [_642461] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat)), c_RComplete_Onatfloor(_642461))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _642461)))], (6368 ^ _415872) ^ [_642629] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _642629)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat)), c_RComplete_Onatfloor(_642629))))], (6374 ^ _415872) ^ [_642847, _642849] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _642847)), -(c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), _642847), c_RealDef_Oreal(tc_Nat_Onat, _642849))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_RComplete_Onatceiling(_642847)), _642849))], (6380 ^ _415872) ^ [_643099, _643101] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _643099)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _643101)), _643099)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), _643099), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), _643101))))], (6386 ^ _415872) ^ [_643405, _643407, _643409, _643411] : [class_RealVector_Oreal__normed__vector(_643405), 6392 ^ _415872 : [(6393 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _643407), 6391 ^ [_643405, _643407, _643409, _643411])))], (6395 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_643405, hAPP(_643409, 6391 ^ [_643405, _643407, _643409, _643411]))), _643411))]], -(c_SEQ_OBseq(_643405, _643409))], (6399 ^ _415872) ^ [_643935, _643937] : [class_RealVector_Oreal__normed__vector(_643935), 6402 ^ _415872 : [(6415 ^ _415872) ^ [] : [6417 ^ _415872 : [(6418 ^ _415872) ^ [_644706] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_643935, hAPP(_643937, 6416 ^ [_643935, _643937, _644706]))), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(_644706))))]], 6420 ^ _415872 : [(6421 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 6419 ^ [_643935, _643937])))], (6423 ^ _415872) ^ [_644937] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_643935, hAPP(_643937, _644937))), 6419 ^ [_643935, _643937])))]]], (6403 ^ _415872) ^ [] : [6412 ^ _415872 : [(6413 ^ _415872) ^ [_644519] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_643935, hAPP(_643937, _644519))), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(6411 ^ [_643935, _643937])))))]], 6404 ^ _415872 : [(6405 ^ _415872) ^ [_644183] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _644183)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_643935, hAPP(_643937, 6408 ^ [_643935, _643937, _644183]))), _644183))]]]]], (6425 ^ _415872) ^ [_645081, _645083] : [class_RealVector_Oreal__normed__vector(_645081), 6428 ^ _415872 : [(6441 ^ _415872) ^ [] : [6443 ^ _415872 : [(6444 ^ _415872) ^ [_645852] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_645081, hAPP(_645083, 6442 ^ [_645081, _645083, _645852]))), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(_645852))))]], 6446 ^ _415872 : [(6447 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 6445 ^ [_645081, _645083])))], (6449 ^ _415872) ^ [_646083] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_645081, hAPP(_645083, _646083))), 6445 ^ [_645081, _645083])))]]], (6429 ^ _415872) ^ [] : [6438 ^ _415872 : [(6439 ^ _415872) ^ [_645665] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_645081, hAPP(_645083, _645665))), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(6437 ^ [_645081, _645083])))))]], 6430 ^ _415872 : [(6431 ^ _415872) ^ [_645329] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _645329)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_645081, hAPP(_645083, 6434 ^ [_645081, _645083, _645329]))), _645329))]]]]], (6451 ^ _415872) ^ [_646198] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _646198), c_Nat_OSuc(_646198))))], (6453 ^ _415872) ^ [_646312, _646314] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _646312), _646314)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_646312)), c_Nat_OSuc(_646314))))], (6459 ^ _415872) ^ [_646521] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Nat_OSuc(_646521))))], (6461 ^ _415872) ^ [_646646, _646648, _646650] : [class_Rings_Olinordered__semidom(_646646), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_646646, c_Groups_Ozero__class_Ozero(_646646)), _646648)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_646646, _646648), c_Groups_Oone__class_Oone(_646646))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_646646, hAPP(hAPP(c_Power_Opower__class_Opower(_646646), _646648), c_Nat_OSuc(_646650))), _646648)))], (6475 ^ _415872) ^ [_647118, _647120, _647122] : [class_Rings_Ocomm__semiring__1(_647118), -(hAPP(hAPP(c_Power_Opower__class_Opower(_647118), _647120), c_Nat_OSuc(_647122)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_647118), _647120), hAPP(hAPP(c_Power_Opower__class_Opower(_647118), _647120), _647122)))], (6481 ^ _415872) ^ [_647398, _647400, _647402] : [class_Rings_Ocomm__semiring__1(_647398), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_647398), _647400), hAPP(hAPP(c_Power_Opower__class_Opower(_647398), _647400), _647402)) = hAPP(hAPP(c_Power_Opower__class_Opower(_647398), _647400), c_Nat_OSuc(_647402)))], (6487 ^ _415872) ^ [_647678, _647680, _647682] : [class_Rings_Ocomm__semiring__1(_647678), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_647678), hAPP(hAPP(c_Power_Opower__class_Opower(_647678), _647680), _647682)), _647680) = hAPP(hAPP(c_Power_Opower__class_Opower(_647678), _647680), c_Nat_OSuc(_647682)))], (6493 ^ _415872) ^ [_647972, _647974, _647976, _647978] : [class_Rings_Ocomm__semiring__1(_647972), -(hAPP(hAPP(c_Power_Opower__class_Opower(_647972), hAPP(hAPP(c_Power_Opower__class_Opower(_647972), _647974), _647976)), _647978) = hAPP(hAPP(c_Power_Opower__class_Opower(_647972), _647974), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _647976), _647978)))], (6499 ^ _415872) ^ [_648280, _648282, _648284, _648286] : [class_Rings_Ocomm__semiring__1(_648280), -(hAPP(hAPP(c_Power_Opower__class_Opower(_648280), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_648280), _648282), _648284)), _648286) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_648280), hAPP(hAPP(c_Power_Opower__class_Opower(_648280), _648282), _648286)), hAPP(hAPP(c_Power_Opower__class_Opower(_648280), _648284), _648286)))], (6505 ^ _415872) ^ [_648580, _648582] : [class_Rings_Ocomm__semiring__1(_648580), -(hAPP(hAPP(c_Power_Opower__class_Opower(_648580), _648582), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _648582)], (6511 ^ _415872) ^ [_648804, _648806] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_648804)), c_Nat_OSuc(_648806))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _648804), _648806)))], (6517 ^ _415872) ^ [_649042, _649044] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_649042)), _649044)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _649042), _649044)))], (6523 ^ _415872) ^ [_649276, _649278] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _649276), c_Nat_OSuc(_649278))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _649276), _649278))), -(_649276 = _649278)], (6533 ^ _415872) ^ [_649616, _649618, _649620] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _649616), _649618)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _649618), _649620)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_649616)), _649620)))], (6543 ^ _415872) ^ [_649959, _649961] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _649959), _649961)), -(c_Nat_OSuc(_649959) = _649961), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_649959)), _649961)))], (6553 ^ _415872) ^ [_650289, _650291] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _650289), _650291)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _650289), c_Nat_OSuc(_650291))))], (6559 ^ _415872) ^ [_650523, _650525] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _650523), _650525))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _650523), c_Nat_OSuc(_650525))), -(_650525 = _650523)], (6569 ^ _415872) ^ [_650849, _650851] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _650849), _650851))), 6572 ^ _415872 : [(6573 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _650849), c_Nat_OSuc(_650851))), -(_650849 = _650851)], (6579 ^ _415872) ^ [] : [_650849 = _650851, -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _650849), c_Nat_OSuc(_650851))))]]], (6585 ^ _415872) ^ [_651372, _651374] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_651372)), c_Nat_OSuc(_651374))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _651372), _651374)))], (6591 ^ _415872) ^ [_651562, _651564] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _651562), _651564)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_651562)), c_Nat_OSuc(_651564))))], (6607 ^ _415872) ^ [_652107, _652109] : [6608 ^ _415872 : [(6609 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _652107), _652109))], (6611 ^ _415872) ^ [] : [_652107 = _652109]], -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _652107), c_Nat_OSuc(_652109))))], (6597 ^ _415872) ^ [_651831, _651833] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _651831), c_Nat_OSuc(_651833))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _651831), _651833))), -(_651831 = _651833)], (6615 ^ _415872) ^ [_652446, _652448] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _652446), _652448))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _652448), c_Nat_OSuc(_652446))))], (6621 ^ _415872) ^ [_652635, _652637] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _652637), c_Nat_OSuc(_652635))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _652635), _652637))], (6627 ^ _415872) ^ [_652857, _652859] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Nat_OSuc(_652857)), _652859) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _652857), c_Nat_OSuc(_652859)))], (6629 ^ _415872) ^ [_652967, _652969] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Nat_OSuc(_652967)), _652969) = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _652967), _652969)))], (6631 ^ _415872) ^ [_653077, _653079] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _653077), c_Nat_OSuc(_653079)) = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _653077), _653079)))], (6633 ^ _415872) ^ [_653202, _653204] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_653202)), _653204)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _653202), _653204)))], (6639 ^ _415872) ^ [_653436, _653438] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _653436), c_Nat_OSuc(_653438))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _653436), _653438))), -(_653436 = c_Nat_OSuc(_653438))], (6649 ^ _415872) ^ [_653766, _653768] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _653766), _653768)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _653766), c_Nat_OSuc(_653768))))], (6655 ^ _415872) ^ [_654029, _654031] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_654029)), c_Nat_OSuc(_654031))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _654029), _654031)))], (6661 ^ _415872) ^ [_654219, _654221] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _654219), _654221)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_654219)), c_Nat_OSuc(_654221))))], (6677 ^ _415872) ^ [_654768, _654770] : [6678 ^ _415872 : [(6679 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _654768), _654770))], (6681 ^ _415872) ^ [] : [_654768 = c_Nat_OSuc(_654770)]], -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _654768), c_Nat_OSuc(_654770))))], (6667 ^ _415872) ^ [_654488, _654490] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _654488), c_Nat_OSuc(_654490))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _654488), _654490))), -(_654488 = c_Nat_OSuc(_654490))], (6685 ^ _415872) ^ [_655111, _655113] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _655111), _655113))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_655113)), _655111)))], (6691 ^ _415872) ^ [_655300, _655302] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_655302)), _655300)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _655300), _655302))], (6697 ^ _415872) ^ [_655507] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_655507)), _655507))], (6699 ^ _415872) ^ [_655664, _655666, _655668] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_655664)), _655666) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_655664)), _655668), -(_655666 = _655668)], (6705 ^ _415872) ^ [_655864, _655866, _655868] : [_655866 = _655868, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_655864)), _655866) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_655864)), _655868))], (6711 ^ _415872) ^ [_656128, _656130, _656132] : [class_RealVector_Oreal__normed__div__algebra(_656128), -(c_RealVector_Onorm__class_Onorm(_656128, hAPP(hAPP(c_Power_Opower__class_Opower(_656128), _656130), _656132)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_656128, _656130)), _656132))], (6717 ^ _415872) ^ [_656352] : [_656352 = c_Nat_OSuc(_656352)], (6719 ^ _415872) ^ [_656431] : [c_Nat_OSuc(_656431) = _656431], (6721 ^ _415872) ^ [_656569, _656571] : [c_Nat_OSuc(_656569) = c_Nat_OSuc(_656571), -(_656569 = _656571)], (6727 ^ _415872) ^ [_656739, _656741] : [_656739 = _656741, -(c_Nat_OSuc(_656739) = c_Nat_OSuc(_656741))], (6733 ^ _415872) ^ [_656959, _656961] : [c_Nat_OSuc(_656959) = c_Nat_OSuc(_656961), -(_656959 = _656961)], (6739 ^ _415872) ^ [_657147] : [c_Nat_OSuc(_657147) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (6741 ^ _415872) ^ [_657226] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_657226)], (6743 ^ _415872) ^ [_657305] : [c_Nat_OSuc(_657305) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (6745 ^ _415872) ^ [_657384] : [c_Nat_OSuc(_657384) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (6747 ^ _415872) ^ [_657463] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_657463)], (6749 ^ _415872) ^ [_657542] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_657542)], (6751 ^ _415872) ^ [_657665, _657667, _657669] : [class_RealVector_Oreal__normed__algebra__1(_657665), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_657665, hAPP(hAPP(c_Power_Opower__class_Opower(_657665), _657667), _657669))), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_657665, _657667)), _657669))))], (6757 ^ _415872) ^ [_657929, _657931] : [class_Rings_Ocomm__semiring__1(_657929), -(hAPP(hAPP(c_Power_Opower__class_Opower(_657929), _657931), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_657929))], (6763 ^ _415872) ^ [_658185, _658187, _658189, _658191] : [class_Rings_Ocomm__semiring__1(_658185), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_658185), hAPP(hAPP(c_Power_Opower__class_Opower(_658185), _658187), _658189)), hAPP(hAPP(c_Power_Opower__class_Opower(_658185), _658187), _658191)) = hAPP(hAPP(c_Power_Opower__class_Opower(_658185), _658187), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _658189), _658191)))], (6769 ^ _415872) ^ [_658496] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _658496)), -(_658496 = c_Nat_OSuc(6772 ^ [_658496]))], (6776 ^ _415872) ^ [_658713] : [6777 ^ _415872 : [(6778 ^ _415872) ^ [_658785] : [_658713 = c_Nat_OSuc(_658785)]], -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _658713)))], (6782 ^ _415872) ^ [_658964] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _658964), c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_658964 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6788 ^ _415872) ^ [_659130] : [_659130 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _659130), c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (6794 ^ _415872) ^ [_659375, _659377] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _659375), c_Nat_OSuc(_659377))), -(_659375 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 6802 ^ _415872 : [(6803 ^ _415872) ^ [] : [-(_659375 = c_Nat_OSuc(6801 ^ [_659375, _659377]))], (6805 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, 6801 ^ [_659375, _659377]), _659377)))]]], (6807 ^ _415872) ^ [_659807, _659809] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _659807), c_Nat_OSuc(_659809)))), 6808 ^ _415872 : [(6809 ^ _415872) ^ [] : [_659807 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (6811 ^ _415872) ^ [_659984] : [_659807 = c_Nat_OSuc(_659984), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _659984), _659809))]]], (6819 ^ _415872) ^ [_660308, _660310] : [c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _660308), _660310), 6824 ^ _415872 : [(6825 ^ _415872) ^ [] : [-(_660308 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (6827 ^ _415872) ^ [] : [-(_660310 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 6828 ^ _415872 : [(6829 ^ _415872) ^ [] : [-(_660308 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6831 ^ _415872) ^ [] : [-(_660310 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (6833 ^ _415872) ^ [_660722, _660724] : [-(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _660722), _660724)), 6834 ^ _415872 : [(6835 ^ _415872) ^ [] : [_660722 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _660724 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (6841 ^ _415872) ^ [] : [_660722 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _660724 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (6849 ^ _415872) ^ [_661227, _661229] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _661227), _661229) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 6854 ^ _415872 : [(6855 ^ _415872) ^ [] : [-(_661227 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (6857 ^ _415872) ^ [] : [-(_661229 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 6858 ^ _415872 : [(6859 ^ _415872) ^ [] : [-(_661227 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6861 ^ _415872) ^ [] : [-(_661229 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (6863 ^ _415872) ^ [_661641, _661643] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _661641), _661643) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 6864 ^ _415872 : [(6865 ^ _415872) ^ [] : [_661641 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _661643 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (6871 ^ _415872) ^ [] : [_661641 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _661643 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (6879 ^ _415872) ^ [_662146, _662148] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _662146), _662148) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 6882 ^ _415872 : [(6883 ^ _415872) ^ [] : [-(_662146 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (6885 ^ _415872) ^ [] : [-(_662148 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (6887 ^ _415872) ^ [_662395, _662397] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _662395), _662397) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _662395 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _662397 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6897 ^ _415872) ^ [_662737, _662739] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _662737), _662739)), -(_662739 = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _662737), 6900 ^ [_662737, _662739])))], (6904 ^ _415872) ^ [_662990, _662992] : [6905 ^ _415872 : [(6906 ^ _415872) ^ [_663073] : [_662992 = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _662990), _663073))]], -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _662990), _662992)))], (6910 ^ _415872) ^ [_663235, _663237] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _663235), c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _663237), _663235)))))], (6912 ^ _415872) ^ [_663342, _663344] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _663342), c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _663342), _663344)))))], (6914 ^ _415872) ^ [_663493, _663495] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _663493), _663495)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_663493)), _663495)))], (6920 ^ _415872) ^ [_663679, _663681] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_663679)), _663681)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _663679), _663681)))], (6926 ^ _415872) ^ [_663944, _663946] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _663944), c_Nat_OSuc(_663946))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _663944), _663946)))], (6932 ^ _415872) ^ [_664130, _664132] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _664130), _664132)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _664130), c_Nat_OSuc(_664132))))], (6938 ^ _415872) ^ [_664395, _664397] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_664395)), _664397)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _664395), _664397)))], (6944 ^ _415872) ^ [_664581, _664583] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _664581), _664583)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_664581)), _664583)))], (6950 ^ _415872) ^ [_664817, _664819] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _664817), _664819)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _664817), c_Nat_OSuc(_664819))))], (6956 ^ _415872) ^ [_665051, _665053] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _665051), _665053)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_665051)), _665053)))], (6962 ^ _415872) ^ [_665285, _665287] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _665285), _665287)), 6965 ^ _415872 : [(6966 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _665287), c_Nat_OSuc(_665285))), -(_665287 = _665285)], (6972 ^ _415872) ^ [] : [_665287 = _665285, -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _665287), c_Nat_OSuc(_665285))))]]], (6978 ^ _415872) ^ [_665776, _665778] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_665776)), _665778)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _665776), _665778)))], (6984 ^ _415872) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (6986 ^ _415872) ^ [_666106, _666108, _666110] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_666106)), _666108)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_666106)), _666110))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _666108), _666110)))], (6992 ^ _415872) ^ [_666326, _666328, _666330] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _666328), _666330)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_666326)), _666328)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_666326)), _666330))))], (6998 ^ _415872) ^ [_666581, _666583] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _666581), c_Nat_OSuc(_666583)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _666581), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _666581), _666583)))], (7000 ^ _415872) ^ [_666695, _666697] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_666695)), _666697) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _666697), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _666695), _666697)))], (7002 ^ _415872) ^ [_666867, _666869, _666871] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_666867)), _666869)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_666867)), _666871))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _666869), _666871)))], (7008 ^ _415872) ^ [_667087, _667089, _667091] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _667089), _667091)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_667087)), _667089)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_667087)), _667091))))], (7014 ^ _415872) ^ [_667328] : [-(c_Nat_OSuc(_667328) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _667328))], (7016 ^ _415872) ^ [_667411] : [-(c_Nat_OSuc(_667411) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _667411), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (7018 ^ _415872) ^ [_667526, _667528] : [class_Orderings_Oorder(_667526), 7021 ^ _415872 : [(7032 ^ _415872) ^ [] : [7034 ^ _415872 : [(7035 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_667526, hAPP(_667528, 7033 ^ [_667526, _667528])), hAPP(_667528, c_Nat_OSuc(7033 ^ [_667526, _667528]))))], (7038 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_667526, hAPP(_667528, c_Nat_OSuc(7036 ^ [_667526, _667528]))), hAPP(_667528, 7036 ^ [_667526, _667528])))]], -(c_SEQ_Omonoseq(_667526, _667528))], (7022 ^ _415872) ^ [] : [c_SEQ_Omonoseq(_667526, _667528), 7027 ^ _415872 : [(7028 ^ _415872) ^ [_667825] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_667526, hAPP(_667528, _667825)), hAPP(_667528, c_Nat_OSuc(_667825)))))]], 7029 ^ _415872 : [(7030 ^ _415872) ^ [_667900] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_667526, hAPP(_667528, c_Nat_OSuc(_667900))), hAPP(_667528, _667900))))]]]]], (7042 ^ _415872) ^ [_668423] : [c_SEQ_Osubseq(_668423), 7045 ^ _415872 : [(7046 ^ _415872) ^ [_668546] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(_668423, _668546)), hAPP(_668423, c_Nat_OSuc(_668546)))))]]], (7048 ^ _415872) ^ [_668625] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(_668625, 7049 ^ [_668625])), hAPP(_668625, c_Nat_OSuc(7049 ^ [_668625])))), -(c_SEQ_Osubseq(_668625))], (7055 ^ _415872) ^ [_668895] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _668895) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_668895)))], (7057 ^ _415872) ^ [_669010, _669012] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _669010)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _669012)), -(hBOOL(hAPP(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), _669012), _669010))))], (7067 ^ _415872) ^ [_669333, _669335] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _669333)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _669335)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _669333), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _669333), _669335))))], (7077 ^ _415872) ^ [_669662, _669664] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _669662)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _669664)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _669662), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _669664), _669662))))], (7087 ^ _415872) ^ [_670020, _670022] : [hBOOL(hAPP(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), _670020), _670022))), 7090 ^ _415872 : [(7091 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _670020)))], (7093 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _670022)))]]], (7095 ^ _415872) ^ [_670281, _670283] : [-(hBOOL(hAPP(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), _670281), _670283)))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _670281)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _670283))], (7105 ^ _415872) ^ [_670577] : [-(hBOOL(hAPP(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(_670577)))))], (7107 ^ _415872) ^ [] : [-(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))], (7109 ^ _415872) ^ [_670715] : [-(c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(_670715)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _670715)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (7111 ^ _415872) ^ [_670836, _670838] : [class_RealVector_Oreal__normed__vector(_670836), 7114 ^ _415872 : [(7115 ^ _415872) ^ [] : [c_SEQ_OBseq(_670836, _670838), 7119 ^ _415872 : [(7120 ^ _415872) ^ [_671151] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_670836, hAPP(_670838, _671151))), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(7118 ^ [_670836, _670838])))))]]], (7122 ^ _415872) ^ [] : [7124 ^ _415872 : [(7125 ^ _415872) ^ [_671337] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_670836, hAPP(_670838, 7123 ^ [_670836, _670838, _671337]))), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(_671337))))]], -(c_SEQ_OBseq(_670836, _670838))]]], (7129 ^ _415872) ^ [_671531, _671533] : [class_RealVector_Oreal__normed__vector(_671531), 7132 ^ _415872 : [(7133 ^ _415872) ^ [] : [c_SEQ_OBseq(_671531, _671533), 7137 ^ _415872 : [(7138 ^ _415872) ^ [_671846] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_671531, hAPP(_671533, _671846))), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(7136 ^ [_671531, _671533])))))]]], (7140 ^ _415872) ^ [] : [7142 ^ _415872 : [(7143 ^ _415872) ^ [_672032] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_671531, hAPP(_671533, 7141 ^ [_671531, _671533, _672032]))), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(_672032))))]], -(c_SEQ_OBseq(_671531, _671533))]]], (7147 ^ _415872) ^ [_672212] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _672212)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _672212), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_SEQ_Omonoseq(tc_RealDef_Oreal, hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _672212)))], (7157 ^ _415872) ^ [_672507] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _672507)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _672507), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_SEQ_Oconvergent(tc_RealDef_Oreal, hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _672507)))], (7167 ^ _415872) ^ [_672802] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _672802)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _672802), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_SEQ_OBseq(tc_RealDef_Oreal, hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _672802)))], (7177 ^ _415872) ^ [_673139, _673141, _673143, _673145] : [class_Rings_Olinordered__semidom(_673139), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_673139, _673141), _673143)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_673139, c_Groups_Ozero__class_Ozero(_673139)), _673141)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _673145)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_673139, hAPP(hAPP(c_Power_Opower__class_Opower(_673139), _673141), _673145)), hAPP(hAPP(c_Power_Opower__class_Opower(_673139), _673143), _673145))))], (7195 ^ _415872) ^ [_673734, _673736, _673738] : [class_Rings_Olinordered__semidom(_673734), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_673734, c_Groups_Oone__class_Oone(_673734)), _673736)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _673738)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_673734, c_Groups_Oone__class_Oone(_673734)), hAPP(hAPP(c_Power_Opower__class_Opower(_673734), _673736), _673738))))], (7209 ^ _415872) ^ [_674210, _674212, _674214, _674216] : [class_Rings_Olinordered__semidom(_674210), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_674210, c_Groups_Oone__class_Oone(_674210)), _674212)), 7216 ^ _415872 : [(7217 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_674210, hAPP(hAPP(c_Power_Opower__class_Opower(_674210), _674212), _674214)), hAPP(hAPP(c_Power_Opower__class_Opower(_674210), _674212), _674216))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _674214), _674216)))], (7223 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _674214), _674216)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_674210, hAPP(hAPP(c_Power_Opower__class_Opower(_674210), _674212), _674214)), hAPP(hAPP(c_Power_Opower__class_Opower(_674210), _674212), _674216))))]]], (7229 ^ _415872) ^ [_674917, _674919, _674921, _674923] : [class_Rings_Olinordered__semidom(_674917), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_674917, c_Groups_Oone__class_Oone(_674917)), _674919)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_674917, hAPP(hAPP(c_Power_Opower__class_Opower(_674917), _674919), _674921)), hAPP(hAPP(c_Power_Opower__class_Opower(_674917), _674919), _674923))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _674921), _674923)))], (7243 ^ _415872) ^ [_675396, _675398, _675400] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _675396), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _675398), _675400)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _675396), _675398)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _675396), _675400)))], (7245 ^ _415872) ^ [_675536, _675538, _675540] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _675536), _675538)), _675540) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _675536), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _675538), _675540)))], (7247 ^ _415872) ^ [_675642] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _675642) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (7259 ^ _415872) ^ [_676045, _676047] : [7260 ^ _415872 : [(7261 ^ _415872) ^ [] : [_676047 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (7263 ^ _415872) ^ [] : [_676045 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _676045), _676047) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (7249 ^ _415872) ^ [_675781, _675783] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _675781), _675783) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_675783 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_675781 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (7277 ^ _415872) ^ [_676647, _676649] : [7278 ^ _415872 : [(7279 ^ _415872) ^ [] : [-(_676647 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (7281 ^ _415872) ^ [] : [_676649 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), c_Groups_Oabs__class_Oabs(tc_Int_Oint, _676647)), _676649))))], (7267 ^ _415872) ^ [_676372, _676374] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), c_Groups_Oabs__class_Oabs(tc_Int_Oint, _676372)), _676374))), _676372 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_676374 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7285 ^ _415872) ^ [_676972, _676974, _676976] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _676972)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _676972), _676974)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _676972), _676976))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _676974), _676976)))], (7305 ^ _415872) ^ [_677630, _677632] : [7306 ^ _415872 : [(7307 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _677630))], (7309 ^ _415872) ^ [] : [_677632 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hBOOL(hAPP(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), _677630), _677632))))], (7295 ^ _415872) ^ [_677358, _677360] : [hBOOL(hAPP(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), _677358), _677360))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _677358))), -(_677360 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7313 ^ _415872) ^ [_677936, _677938] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _677936)), -(hBOOL(hAPP(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), _677936), _677938))))], (7319 ^ _415872) ^ [_678151, _678153] : [-(c_RealDef_Oreal(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _678151), _678153)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _678151)), _678153))], (7321 ^ _415872) ^ [_678263, _678265] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _678263)), _678265) = c_RealDef_Oreal(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _678263), _678265)))], (7323 ^ _415872) ^ [_678390, _678392] : [_678390 = c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatfloor(_678390)), -(c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _678390), _678392)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_RComplete_Onatfloor(_678390)), _678392))], (7329 ^ _415872) ^ [_678656, _678658, _678660] : [class_Rings_Oring__1__no__zero__divisors(_678656), -(_678658 = c_Groups_Ozero__class_Ozero(_678656)), hAPP(hAPP(c_Power_Opower__class_Opower(_678656), _678658), _678660) = c_Groups_Ozero__class_Ozero(_678656)], (7339 ^ _415872) ^ [_679019, _679021, _679023, _679025] : [class_Groups_Ocomm__monoid__mult(_679019), -(hAPP(hAPP(c_Power_Opower__class_Opower(_679019), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_679019), _679021), _679023)), _679025) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_679019), hAPP(hAPP(c_Power_Opower__class_Opower(_679019), _679021), _679025)), hAPP(hAPP(c_Power_Opower__class_Opower(_679019), _679023), _679025)))], (7345 ^ _415872) ^ [_679333, _679335, _679337] : [class_Groups_Omonoid__mult(_679333), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_679333), hAPP(hAPP(c_Power_Opower__class_Opower(_679333), _679335), _679337)), _679335) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_679333), _679335), hAPP(hAPP(c_Power_Opower__class_Opower(_679333), _679335), _679337)))], (7351 ^ _415872) ^ [_679611, _679613] : [class_Groups_Omonoid__mult(_679611), -(hAPP(hAPP(c_Power_Opower__class_Opower(_679611), c_Groups_Oone__class_Oone(_679611)), _679613) = c_Groups_Oone__class_Oone(_679611))], (7357 ^ _415872) ^ [_679857, _679859, _679861] : [class_Rings_Olinordered__idom(_679857), -(c_Groups_Oabs__class_Oabs(_679857, hAPP(hAPP(c_Power_Opower__class_Opower(_679857), _679859), _679861)) = hAPP(hAPP(c_Power_Opower__class_Opower(_679857), c_Groups_Oabs__class_Oabs(_679857, _679859)), _679861))], (7363 ^ _415872) ^ [_680143, _680145, _680147, _680149] : [class_Groups_Omonoid__mult(_680143), -(hAPP(hAPP(c_Power_Opower__class_Opower(_680143), _680145), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _680147), _680149)) = hAPP(hAPP(c_Power_Opower__class_Opower(_680143), hAPP(hAPP(c_Power_Opower__class_Opower(_680143), _680145), _680147)), _680149))], (7369 ^ _415872) ^ [_680423, _680425] : [class_Groups_Omonoid__mult(_680423), -(hAPP(hAPP(c_Power_Opower__class_Opower(_680423), _680425), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _680425)], (7375 ^ _415872) ^ [_680661, _680663, _680665] : [class_Rings_Olinordered__semidom(_680661), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_680661, c_Groups_Ozero__class_Ozero(_680661)), _680663)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_680661, c_Groups_Ozero__class_Ozero(_680661)), hAPP(hAPP(c_Power_Opower__class_Opower(_680661), _680663), _680665))))], (7385 ^ _415872) ^ [_681040, _681042, _681044, _681046] : [class_Rings_Olinordered__semidom(_681040), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_681040, _681042), _681044)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_681040, c_Groups_Ozero__class_Ozero(_681040)), _681042)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_681040, hAPP(hAPP(c_Power_Opower__class_Opower(_681040), _681042), _681046)), hAPP(hAPP(c_Power_Opower__class_Opower(_681040), _681044), _681046))))], (7399 ^ _415872) ^ [_681534, _681536, _681538] : [class_Rings_Olinordered__semidom(_681534), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_681534, c_Groups_Ozero__class_Ozero(_681534)), _681536)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_681534, c_Groups_Ozero__class_Ozero(_681534)), hAPP(hAPP(c_Power_Opower__class_Opower(_681534), _681536), _681538))))], (7409 ^ _415872) ^ [_681899, _681901, _681903] : [class_Rings_Olinordered__semidom(_681899), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_681899, c_Groups_Oone__class_Oone(_681899)), _681901)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_681899, c_Groups_Oone__class_Oone(_681899)), hAPP(hAPP(c_Power_Opower__class_Opower(_681899), _681901), _681903))))], (7419 ^ _415872) ^ [_682264, _682266, _682268] : [class_Power_Opower(_682264), class_Rings_Omult__zero(_682264), class_Rings_Ono__zero__divisors(_682264), class_Rings_Ozero__neq__one(_682264), 7434 ^ _415872 : [(7435 ^ _415872) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_682264), _682266), _682268) = c_Groups_Ozero__class_Ozero(_682264), 7438 ^ _415872 : [(7439 ^ _415872) ^ [] : [-(_682266 = c_Groups_Ozero__class_Ozero(_682264))], (7441 ^ _415872) ^ [] : [_682268 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (7443 ^ _415872) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_682264), _682266), _682268) = c_Groups_Ozero__class_Ozero(_682264)), _682266 = c_Groups_Ozero__class_Ozero(_682264), -(_682268 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (7453 ^ _415872) ^ [_683247, _683249, _683251, _683253] : [class_Rings_Olinordered__semidom(_683247), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_683247, c_Groups_Oone__class_Oone(_683247)), _683249)), 7460 ^ _415872 : [(7461 ^ _415872) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_683247), _683249), _683251) = hAPP(hAPP(c_Power_Opower__class_Opower(_683247), _683249), _683253), -(_683251 = _683253)], (7467 ^ _415872) ^ [] : [_683251 = _683253, -(hAPP(hAPP(c_Power_Opower__class_Opower(_683247), _683249), _683251) = hAPP(hAPP(c_Power_Opower__class_Opower(_683247), _683249), _683253))]]], (7473 ^ _415872) ^ [_683896, _683898] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_683896), c_Groups_Ozero__class_Ozero(_683896)), c_Nat_OSuc(_683898)) = c_Groups_Ozero__class_Ozero(_683896)), class_Power_Opower(_683896), class_Rings_Osemiring__0(_683896)], (7483 ^ _415872) ^ [_684233, _684235, _684237] : [class_Groups_Omonoid__mult(_684233), -(hAPP(hAPP(c_Power_Opower__class_Opower(_684233), _684235), c_Nat_OSuc(_684237)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_684233), hAPP(hAPP(c_Power_Opower__class_Opower(_684233), _684235), _684237)), _684235))], (7489 ^ _415872) ^ [_684513, _684515, _684517] : [class_Power_Opower(_684513), -(hAPP(hAPP(c_Power_Opower__class_Opower(_684513), _684515), c_Nat_OSuc(_684517)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_684513), _684515), hAPP(hAPP(c_Power_Opower__class_Opower(_684513), _684515), _684517)))], (7495 ^ _415872) ^ [_684779, _684781] : [class_Power_Opower(_684779), -(hAPP(hAPP(c_Power_Opower__class_Opower(_684779), _684781), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_684779))], (7501 ^ _415872) ^ [_685035, _685037, _685039, _685041] : [class_Groups_Omonoid__mult(_685035), -(hAPP(hAPP(c_Power_Opower__class_Opower(_685035), _685037), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _685039), _685041)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_685035), hAPP(hAPP(c_Power_Opower__class_Opower(_685035), _685037), _685039)), hAPP(hAPP(c_Power_Opower__class_Opower(_685035), _685037), _685041)))], (7507 ^ _415872) ^ [_685359, _685361, _685363, _685365] : [class_Rings_Olinordered__semidom(_685359), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_685359, hAPP(hAPP(c_Power_Opower__class_Opower(_685359), _685361), _685363)), hAPP(hAPP(c_Power_Opower__class_Opower(_685359), _685365), _685363))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_685359, c_Groups_Ozero__class_Ozero(_685359)), _685365)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_685359, _685361), _685365)))], (7521 ^ _415872) ^ [_685867, _685869, _685871, _685873] : [class_Rings_Olinordered__semidom(_685867), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_685867, hAPP(hAPP(c_Power_Opower__class_Opower(_685867), _685869), c_Nat_OSuc(_685871))), hAPP(hAPP(c_Power_Opower__class_Opower(_685867), _685873), c_Nat_OSuc(_685871)))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_685867, c_Groups_Ozero__class_Ozero(_685867)), _685873)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_685867, _685869), _685873)))], (7535 ^ _415872) ^ [_686383, _686385, _686387, _686389] : [class_Rings_Olinordered__semidom(_686383), hAPP(hAPP(c_Power_Opower__class_Opower(_686383), _686385), c_Nat_OSuc(_686387)) = hAPP(hAPP(c_Power_Opower__class_Opower(_686383), _686389), c_Nat_OSuc(_686387)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_686383, c_Groups_Ozero__class_Ozero(_686383)), _686385)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_686383, c_Groups_Ozero__class_Ozero(_686383)), _686389)), -(_686385 = _686389)], (7553 ^ _415872) ^ [_686976, _686978, _686980] : [class_Rings_Olinordered__semidom(_686976), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_686976, c_Groups_Oone__class_Oone(_686976)), _686978)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_686976, hAPP(hAPP(c_Power_Opower__class_Opower(_686976), _686978), _686980)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_686976), _686978), hAPP(hAPP(c_Power_Opower__class_Opower(_686976), _686978), _686980)))))], (7563 ^ _415872) ^ [_687369, _687371, _687373] : [class_Rings_Olinordered__semidom(_687369), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_687369, c_Groups_Oone__class_Oone(_687369)), _687371)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_687369, c_Groups_Oone__class_Oone(_687369)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_687369), _687371), hAPP(hAPP(c_Power_Opower__class_Opower(_687369), _687371), _687373)))))], (7573 ^ _415872) ^ [_687736, _687738] : [class_Power_Opower(_687736), class_Rings_Osemiring__0(_687736), 7580 ^ _415872 : [(7581 ^ _415872) ^ [] : [_687738 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_687736), c_Groups_Ozero__class_Ozero(_687736)), _687738) = c_Groups_Oone__class_Oone(_687736))], (7587 ^ _415872) ^ [] : [-(_687738 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_687736), c_Groups_Ozero__class_Ozero(_687736)), _687738) = c_Groups_Ozero__class_Ozero(_687736))]]], (7593 ^ _415872) ^ [_688351, _688353, _688355] : [class_Rings_Olinordered__idom(_688351), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_688351, c_Groups_Ozero__class_Ozero(_688351)), hAPP(hAPP(c_Power_Opower__class_Opower(_688351), c_Groups_Oabs__class_Oabs(_688351, _688353)), _688355))))], (7599 ^ _415872) ^ [_688615, _688617, _688619] : [class_Rings_Olinordered__semidom(_688615), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_688615, c_Groups_Oone__class_Oone(_688615)), _688617)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_688615, c_Groups_Oone__class_Oone(_688615)), hAPP(hAPP(c_Power_Opower__class_Opower(_688615), _688617), c_Nat_OSuc(_688619)))))], (7609 ^ _415872) ^ [_688998, _689000, _689002, _689004] : [class_Rings_Olinordered__semidom(_688998), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _689000), _689002)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_688998, c_Groups_Oone__class_Oone(_688998)), _689004)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_688998, hAPP(hAPP(c_Power_Opower__class_Opower(_688998), _689004), _689000)), hAPP(hAPP(c_Power_Opower__class_Opower(_688998), _689004), _689002))))], (7623 ^ _415872) ^ [_689506, _689508, _689510, _689512] : [class_Rings_Olinordered__semidom(_689506), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_689506, c_Groups_Oone__class_Oone(_689506)), _689508)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_689506, hAPP(hAPP(c_Power_Opower__class_Opower(_689506), _689508), _689510)), hAPP(hAPP(c_Power_Opower__class_Opower(_689506), _689508), _689512))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _689510), _689512)))], (7637 ^ _415872) ^ [_690014, _690016, _690018, _690020] : [class_Rings_Olinordered__semidom(_690014), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_690014, c_Groups_Oone__class_Oone(_690014)), _690016)), 7644 ^ _415872 : [(7645 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_690014, hAPP(hAPP(c_Power_Opower__class_Opower(_690014), _690016), _690018)), hAPP(hAPP(c_Power_Opower__class_Opower(_690014), _690016), _690020))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _690018), _690020)))], (7651 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _690018), _690020)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_690014, hAPP(hAPP(c_Power_Opower__class_Opower(_690014), _690016), _690018)), hAPP(hAPP(c_Power_Opower__class_Opower(_690014), _690016), _690020))))]]], (7657 ^ _415872) ^ [_690721, _690723, _690725, _690727] : [class_Rings_Olinordered__semidom(_690721), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _690723), _690725)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_690721, c_Groups_Oone__class_Oone(_690721)), _690727)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_690721, hAPP(hAPP(c_Power_Opower__class_Opower(_690721), _690727), _690723)), hAPP(hAPP(c_Power_Opower__class_Opower(_690721), _690727), _690725))))], (7671 ^ _415872) ^ [_691215, _691217, _691219] : [class_Rings_Olinordered__semidom(_691215), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_691215, c_Groups_Ozero__class_Ozero(_691215)), _691217)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_691215, _691217), c_Groups_Oone__class_Oone(_691215))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_691215, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_691215), _691217), hAPP(hAPP(c_Power_Opower__class_Opower(_691215), _691217), _691219))), hAPP(hAPP(c_Power_Opower__class_Opower(_691215), _691217), _691219))))], (7685 ^ _415872) ^ [_691715, _691717, _691719] : [class_Rings_Olinordered__semidom(_691715), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_691715, c_Groups_Ozero__class_Ozero(_691715)), _691717)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_691715, _691717), c_Groups_Oone__class_Oone(_691715))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_691715, hAPP(hAPP(c_Power_Opower__class_Opower(_691715), _691717), c_Nat_OSuc(_691719))), c_Groups_Oone__class_Oone(_691715))))], (7699 ^ _415872) ^ [_692205, _692207, _692209, _692211] : [class_Rings_Olinordered__semidom(_692205), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _692207), _692209)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_692205, c_Groups_Ozero__class_Ozero(_692205)), _692211)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_692205, _692211), c_Groups_Oone__class_Oone(_692205))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_692205, hAPP(hAPP(c_Power_Opower__class_Opower(_692205), _692211), _692209)), hAPP(hAPP(c_Power_Opower__class_Opower(_692205), _692211), _692207))))], (7717 ^ _415872) ^ [_692824, _692826, _692828, _692830] : [class_Rings_Olinordered__semidom(_692824), hAPP(hAPP(c_Power_Opower__class_Opower(_692824), _692826), _692828) = hAPP(hAPP(c_Power_Opower__class_Opower(_692824), _692830), _692828), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_692824, c_Groups_Ozero__class_Ozero(_692824)), _692826)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_692824, c_Groups_Ozero__class_Ozero(_692824)), _692830)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _692828)), -(_692826 = _692830)], (7739 ^ _415872) ^ [_693524, _693526, _693528, _693530] : [class_Rings_Olinordered__semidom(_693524), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _693526), _693528)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_693524, c_Groups_Ozero__class_Ozero(_693524)), _693530)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_693524, _693530), c_Groups_Oone__class_Oone(_693524))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_693524, hAPP(hAPP(c_Power_Opower__class_Opower(_693524), _693530), _693528)), hAPP(hAPP(c_Power_Opower__class_Opower(_693524), _693530), _693526))))], (7757 ^ _415872) ^ [_694115, _694117] : [-(_694115 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), -(_694117 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(hAPP(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), _694115), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), 7764 ^ [_694115, _694117]), _694117))))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))], (7768 ^ _415872) ^ [_694532] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _694532), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))), -(_694532 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_694532 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (7778 ^ _415872) ^ [_694818] : [class_Power_Opower(_694818), -(c_Power_Opower__class_Opower(_694818) = c_Power_Opower_Opower(_694818, c_Groups_Oone__class_Oone(_694818), c_Groups_Otimes__class_Otimes(_694818)))], (7784 ^ _415872) ^ [_695025, _695027] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), c_Groups_Oabs__class_Oabs(tc_Int_Oint, _695025)), _695027))))], (7786 ^ _415872) ^ [_695116] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _695116) = _695116)], (7788 ^ _415872) ^ [_695197] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _695197), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _695197)], (7790 ^ _415872) ^ [_695309, _695311, _695313] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _695309), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _695311), _695313)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _695309), _695311)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _695309), _695313)))], (7792 ^ _415872) ^ [_695449, _695451, _695453] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _695449), _695451)), _695453) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _695449), _695453)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _695451), _695453)))], (7794 ^ _415872) ^ [_695590, _695592] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _695590)), 7797 ^ _415872 : [(7798 ^ _415872) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _695590), _695592) = c_Groups_Oone__class_Oone(tc_Int_Oint), 7801 ^ _415872 : [(7802 ^ _415872) ^ [] : [-(_695590 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (7804 ^ _415872) ^ [] : [-(_695592 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (7806 ^ _415872) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _695590), _695592) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _695590 = c_Groups_Oone__class_Oone(tc_Int_Oint), _695592 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (7816 ^ _415872) ^ [_696244, _696246, _696248] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _696244), _696246)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _696248)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _696248), _696244)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _696248), _696246))))], (7826 ^ _415872) ^ [_696601, _696603] : [c_Groups_Oabs__class_Oabs(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _696601), _696603)) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(c_Groups_Oabs__class_Oabs(tc_Int_Oint, _696601) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (7832 ^ _415872) ^ [_696834, _696836, _696838] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _696834), _696836)), _696838) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _696834), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _696836), _696838)))], (7834 ^ _415872) ^ [_696954, _696956] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _696954), _696956) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _696956), _696954))], (7836 ^ _415872) ^ [_697103, _697105, _697107, _697109] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _697103), _697105)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _697107), _697109)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _697103), _697107)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _697105), _697109))))], (7846 ^ _415872) ^ [_697490, _697492, _697494] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _697490), _697492)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _697490), _697494)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _697492), _697494))))], (7852 ^ _415872) ^ [_697750, _697752] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _697750), _697752)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _697750), c_Groups_Oone__class_Oone(tc_Int_Oint))), _697752)))], (7858 ^ _415872) ^ [_697978] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _697978)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _697978))))], (7864 ^ _415872) ^ [_698211] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _698211)), _698211)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _698211), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (7870 ^ _415872) ^ [_698405] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _698405), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _698405)), _698405)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (7876 ^ _415872) ^ [_698678, _698680] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _698678), c_Groups_Oone__class_Oone(tc_Int_Oint))), _698680)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _698678), _698680)))], (7882 ^ _415872) ^ [_698872, _698874] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _698872), _698874)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _698872), c_Groups_Oone__class_Oone(tc_Int_Oint))), _698874)))], (7888 ^ _415872) ^ [_699131] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oabs__class_Oabs(tc_Int_Oint, _699131)), c_Groups_Oone__class_Oone(tc_Int_Oint))), -(_699131 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (7894 ^ _415872) ^ [_699303] : [_699303 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oabs__class_Oabs(tc_Int_Oint, _699303)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (7910 ^ _415872) ^ [_699838, _699840] : [7911 ^ _415872 : [(7912 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _699838), _699840))], (7914 ^ _415872) ^ [] : [_699838 = _699840]], -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _699838), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _699840), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (7900 ^ _415872) ^ [_699554, _699556] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _699554), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _699556), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _699554), _699556))), -(_699554 = _699556)], (7918 ^ _415872) ^ [_700185, _700187] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _700185), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _700187), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _700185), _700187)))], (7924 ^ _415872) ^ [_700379, _700381] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _700379), _700381)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _700379), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _700381), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (7930 ^ _415872) ^ [_700623, _700625] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _700623), _700625))), -(_700623 = _700625), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _700625), _700623)))], (7940 ^ _415872) ^ [_700973, _700975] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _700973), _700975)), 7943 ^ _415872 : [(7944 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _700973), _700975)))], (7946 ^ _415872) ^ [] : [_700973 = _700975]]], (7948 ^ _415872) ^ [_701231, _701233] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _701231), _701233))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _701231), _701233)), -(_701231 = _701233)], (7958 ^ _415872) ^ [_701526] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _701526), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _701526)], (7960 ^ _415872) ^ [_701654] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint)), _701654)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _701654)))], (7966 ^ _415872) ^ [_701818] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _701818)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint)), _701818)))], (7972 ^ _415872) ^ [_702003] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _702003) = _702003)], (7974 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (7976 ^ _415872) ^ [_702136] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _702136)), _702136) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (7978 ^ _415872) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (7980 ^ _415872) ^ [_702317, _702319, _702321, _702323] : [-(hAPP(hAPP(c_Power_Opower_Opower(_702317, _702319, _702321), _702323), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _702319)], (7982 ^ _415872) ^ [_702467, _702469, _702471, _702473, _702475] : [-(hAPP(hAPP(c_Power_Opower_Opower(_702467, _702469, _702471), _702473), c_Nat_OSuc(_702475)) = hAPP(hAPP(_702471, _702473), hAPP(hAPP(c_Power_Opower_Opower(_702467, _702469, _702471), _702473), _702475)))], (7994 ^ _415872) ^ [_702911, _702913] : [7995 ^ _415872 : [(7996 ^ _415872) ^ [] : [_702913 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (7998 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _702911))]], -(hBOOL(hAPP(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), _702911), _702913))))], (7984 ^ _415872) ^ [_702639, _702641] : [hBOOL(hAPP(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), _702639), _702641))), -(_702641 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _702639)))], (8002 ^ _415872) ^ [_703231, _703233, _703235] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _703231)), _703231 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _703233), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _703231), _703235)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _703233)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _703235), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (8016 ^ _415872) ^ [_703689, _703691, _703693] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _703689)), _703689 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _703691), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _703689), _703693)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _703691), _703689)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint)), _703693)))], (8030 ^ _415872) ^ [_704147, _704149, _704151] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _704147), _704149)), _704151))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _704151), _704147)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _704147)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _704149)))], (8044 ^ _415872) ^ [_704609, _704611, _704613] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _704609), _704611)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _704613), _704609)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _704613), _704611))))], (8050 ^ _415872) ^ [_704868, _704870, _704872] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _704868), _704870)), _704872) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _704868), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _704870), _704872)))], (8052 ^ _415872) ^ [_705002, _705004, _705006] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _705002), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _705004), _705006)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _705004), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _705002), _705006)))], (8054 ^ _415872) ^ [_705122, _705124] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _705122), _705124) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _705124), _705122))], (8056 ^ _415872) ^ [_705243, _705245] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _705243), _705245)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _705245), _705243)), -(_705243 = _705245)], (8066 ^ _415872) ^ [_705576, _705578, _705580] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _705576), _705578)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _705578), _705580)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _705576), _705580)))], (8076 ^ _415872) ^ [_705915, _705917] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _705915), _705917))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _705917), _705915)))], (8082 ^ _415872) ^ [_706117] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _706117), _706117)))], (8084 ^ _415872) ^ [_706285, _706287, _706289, _706291, _706293, _706295] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _706285), _706287)), _706289) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _706291), _706293)), _706295), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _706291), _706293)), _706295)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _706289), _706285)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _706295)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _706291)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _706291), _706285)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _706293), _706287)))], (8110 ^ _415872) ^ [_707206, _707208, _707210, _707212, _707214] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _707206), _707208)), _707210)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _707206), _707212)), _707214))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _707214), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _707206), _707214)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _707206), _707210)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _707212), _707208)))], (8128 ^ _415872) ^ [_707891, _707893, _707895, _707897, _707899, _707901] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _707891), _707893)), _707895) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _707897), _707899)), _707901), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _707897), _707899)), _707901))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _707901), _707897)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _707895)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _707897)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _707897), _707891)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _707893), _707899)))], (8154 ^ _415872) ^ [_708806, _708808, _708810, _708812, _708814] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _708806), _708808)), _708810)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _708806), _708812)), _708814))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _708810)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _708810), _708806)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _708814), _708806)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _708808), _708812)))], (8172 ^ _415872) ^ [_709443, _709445, _709447] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _709443), _709445)), _709447)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _709447)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _709443)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _709445), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (8186 ^ _415872) ^ [_709897, _709899] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _709897)), -(hBOOL(hAPP(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), _709897), _709899))))], (8192 ^ _415872) ^ [_710127, _710129] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _710127)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _710129)), -(hBOOL(hAPP(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), _710127), _710129))))], (8202 ^ _415872) ^ [_710450, _710452] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _710450)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _710452)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _710450), _710452))))], (8212 ^ _415872) ^ [] : [-(hBOOL(hAPP(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))))], (8214 ^ _415872) ^ [] : [-(hBOOL(hAPP(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))))], (8216 ^ _415872) ^ [_710878, _710880, _710882] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Complex_Orcis(_710878, _710880)), _710882) = c_Complex_Orcis(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _710878), _710882), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _710882)), _710880)))], (8218 ^ _415872) ^ [_711002] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _711002)), 8222 ^ _415872 : [(8223 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, 8221 ^ [_711002])), _711002)))], (8225 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _711002), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(8221 ^ [_711002])))))]]], (8227 ^ _415872) ^ [_711399, _711401] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _711399)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _711401)), 8235 ^ _415872 : [(8236 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 8234 ^ [_711399, _711401])))], (8238 ^ _415872) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), 8234 ^ [_711399, _711401]), _711399) = _711401)], (8240 ^ _415872) ^ [_711912] : [-(_711912 = 8234 ^ [_711399, _711401]), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _711912)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _711912), _711399) = _711401]]], (8250 ^ _415872) ^ [_712253, _712255] : [-(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Complex_Orcis(_712253, _712255)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _712253))], (8252 ^ _415872) ^ [_712342] : [-(c_Complex_Orcis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _712342) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))], (8254 ^ _415872) ^ [_712465, _712467, _712469, _712471] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Complex_Orcis(_712465, _712467)), c_Complex_Orcis(_712469, _712471)) = c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _712465), _712469), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), _712467), _712471)))], (8256 ^ _415872) ^ [_712605, _712607] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _712605)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _712607)), 8264 ^ _415872 : [(8265 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 8263 ^ [_712605, _712607])))], (8267 ^ _415872) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), 8263 ^ [_712605, _712607]), _712605) = _712607)]]], (8269 ^ _415872) ^ [_713066, _713068] : [-(c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(_713066))), _713068)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Complex_Ocis(_713068)), c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _713066)), _713068))))], (8271 ^ _415872) ^ [_713207, _713209] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _713207)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _713209)), 8279 ^ _415872 : [(8280 ^ _415872) ^ [] : [-(hBOOL(hAPP(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, 8278 ^ [_713207, _713209])), _713207)), _713209)))], (8282 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _713209), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(8278 ^ [_713207, _713209]))), _713207))))]]], (8284 ^ _415872) ^ [_713734, _713736] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Complex_Ocis(_713734)), c_Complex_Ocis(_713736)) = c_Complex_Ocis(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), _713734), _713736)))], (8286 ^ _415872) ^ [] : [-(c_Complex_Ocis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))], (8288 ^ _415872) ^ [_713885] : [-(c_Complex_Ocis(_713885) = c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _713885))], (8290 ^ _415872) ^ [_713982, _713984] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Complex_Ocis(_713982)), _713984) = c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _713984)), _713982)))], (8292 ^ _415872) ^ [_714110, _714112] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _714110)), -(c_Transcendental_Oln(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _714110), _714112)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _714112)), c_Transcendental_Oln(_714110)))], (8298 ^ _415872) ^ [_714347, _714349] : [-(c_Transcendental_Ocos(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _714347)), _714349)) = hAPP(c_Complex_ORe, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Complex_Ocis(_714349)), _714347)))], (8300 ^ _415872) ^ [_714463, _714465] : [-(c_Transcendental_Osin(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _714463)), _714465)) = hAPP(c_Complex_OIm, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Complex_Ocis(_714465)), _714463)))], (8302 ^ _415872) ^ [_714579, _714581] : [-(c_Transcendental_Osin(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), _714579), _714581)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Transcendental_Osin(_714579)), c_Transcendental_Ocos(_714581))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Transcendental_Ocos(_714579)), c_Transcendental_Osin(_714581))))], (8304 ^ _415872) ^ [_714693] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Transcendental_Ocos(_714693)), c_Transcendental_Ocos(_714693))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Transcendental_Osin(_714693)), c_Transcendental_Osin(_714693))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (8306 ^ _415872) ^ [_714812] : [c_Transcendental_Osin(_714812) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Transcendental_Ocos(_714812)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (8312 ^ _415872) ^ [_715016] : [c_Transcendental_Ocos(_715016) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal), -(c_Transcendental_Osin(_715016) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (8318 ^ _415872) ^ [] : [-(c_Transcendental_Ocos(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (8320 ^ _415872) ^ [_715252] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Transcendental_Ocos(_715252)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))], (8322 ^ _415872) ^ [_715337] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Transcendental_Osin(_715337)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))], (8324 ^ _415872) ^ [] : [-(c_Transcendental_Osin(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (8326 ^ _415872) ^ [_715475] : [-(hAPP(c_Complex_OIm, c_Complex_Ocis(_715475)) = c_Transcendental_Osin(_715475))], (8328 ^ _415872) ^ [_715560] : [-(hAPP(c_Complex_ORe, c_Complex_Ocis(_715560)) = c_Transcendental_Ocos(_715560))], (8330 ^ _415872) ^ [_715674, _715676] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _715674)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _715676)), 8337 ^ _415872 : [(8338 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Transcendental_Oln(_715674)), c_Transcendental_Oln(_715676))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _715674), _715676)))], (8344 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _715674), _715676)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Transcendental_Oln(_715674)), c_Transcendental_Oln(_715676))))]]], (8350 ^ _415872) ^ [_716273, _716275] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _716273)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _716275)), 8357 ^ _415872 : [(8358 ^ _415872) ^ [] : [c_Transcendental_Oln(_716273) = c_Transcendental_Oln(_716275), -(_716273 = _716275)], (8364 ^ _415872) ^ [] : [_716273 = _716275, -(c_Transcendental_Oln(_716273) = c_Transcendental_Oln(_716275))]]], (8370 ^ _415872) ^ [_716828] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _716828)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Transcendental_Oln(_716828)), _716828)))], (8376 ^ _415872) ^ [] : [-(c_Transcendental_Oln(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (8378 ^ _415872) ^ [_717074] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Transcendental_Osin(_717074))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))], (8380 ^ _415872) ^ [_717162] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Transcendental_Ocos(_717162))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))], (8382 ^ _415872) ^ [_717264, _717266] : [-(hAPP(c_Complex_OIm, c_Complex_Orcis(_717264, _717266)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _717264), c_Transcendental_Osin(_717266)))], (8384 ^ _415872) ^ [_717372, _717374] : [-(hAPP(c_Complex_ORe, c_Complex_Orcis(_717372, _717374)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _717372), c_Transcendental_Ocos(_717374)))], (8386 ^ _415872) ^ [_717495, _717497] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _717495)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _717497)), 8393 ^ _415872 : [(8394 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Transcendental_Oln(_717495)), c_Transcendental_Oln(_717497))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _717495), _717497)))], (8400 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _717495), _717497)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Transcendental_Oln(_717495)), c_Transcendental_Oln(_717497))))]]], (8406 ^ _415872) ^ [_718080] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _718080)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_Transcendental_Oln(_718080))))], (8412 ^ _415872) ^ [_718282] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_Transcendental_Oln(_718282))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _718282)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _718282)))], (8422 ^ _415872) ^ [_718573] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _718573)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _718573), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Transcendental_Oln(_718573)), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))], (8432 ^ _415872) ^ [_718876] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _718876)), 8435 ^ _415872 : [(8436 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Transcendental_Oln(_718876)), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _718876), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))], (8442 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _718876), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Transcendental_Oln(_718876)), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))]]], (8448 ^ _415872) ^ [_719346] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _719346)), 8451 ^ _415872 : [(8452 ^ _415872) ^ [] : [c_Transcendental_Oln(_719346) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_719346 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (8458 ^ _415872) ^ [] : [_719346 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal), -(c_Transcendental_Oln(_719346) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))]]], (8464 ^ _415872) ^ [_719786] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _719786)), 8467 ^ _415872 : [(8468 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_Transcendental_Oln(_719786))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _719786)))], (8474 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _719786)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_Transcendental_Oln(_719786))))]]], (8480 ^ _415872) ^ [_720238] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _720238)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_Transcendental_Oln(_720238))))], (8486 ^ _415872) ^ [_720440] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_Transcendental_Oln(_720440))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _720440)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _720440)))], (8496 ^ _415872) ^ [_720731] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _720731)), 8499 ^ _415872 : [(8500 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_Transcendental_Oln(_720731))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _720731)))], (8506 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _720731)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_Transcendental_Oln(_720731))))]]], (8512 ^ _415872) ^ [_721197, _721199] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _721197)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _721199)), -(c_Transcendental_Oln(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _721197), _721199)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), c_Transcendental_Oln(_721197)), c_Transcendental_Oln(_721199)))], (8522 ^ _415872) ^ [_721526] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _721526)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Transcendental_Oln(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _721526))), _721526)))], (8528 ^ _415872) ^ [_721740] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _721740)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_Transcendental_Ocos(c_Transcendental_Oarccos(_721740)) = _721740)], (8534 ^ _415872) ^ [_721954] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _721954)), 8538 ^ _415872 : [(8539 ^ _415872) ^ [_722146] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _722146), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, 8537 ^ [_721954, _722146])), _721954))))]]], (8541 ^ _415872) ^ [_722281, _722283] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _722281)), 8545 ^ _415872 : [(8546 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 8544 ^ [_722281, _722283])))], (8548 ^ _415872) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), 8544 ^ [_722281, _722283]), c_Nat_OSuc(_722283)) = _722281)]]], (8550 ^ _415872) ^ [_722670, _722672] : [class_RealVector_Oreal__normed__algebra(_722670), 8554 ^ _415872 : [(8555 ^ _415872) ^ [_722889] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_722670, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_722670), _722889), _722672))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_722670, _722889)), 8553 ^ [_722670, _722672]))))]]], (8557 ^ _415872) ^ [_723037, _723039] : [class_RealVector_Oreal__normed__algebra(_723037), 8561 ^ _415872 : [(8562 ^ _415872) ^ [_723256] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_723037, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_723037), _723039), _723256))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_723037, _723256)), 8560 ^ [_723037, _723039]))))]]], (8564 ^ _415872) ^ [_723390] : [class_RealVector_Oreal__normed__algebra(_723390), 8568 ^ _415872 : [(8569 ^ _415872) ^ [_723643, _723645] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_723390, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_723390), _723645), _723643))), 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(_723390, _723645)), c_RealVector_Onorm__class_Onorm(_723390, _723643))), 8567 ^ [_723390]))))]]], (8571 ^ _415872) ^ [_723812, _723814, _723816] : [class_Groups_Omonoid__mult(_723812), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _723814)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_723812), hAPP(hAPP(c_Power_Opower__class_Opower(_723812), _723816), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _723814, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _723816) = hAPP(hAPP(c_Power_Opower__class_Opower(_723812), _723816), _723814))], (8581 ^ _415872) ^ [_724150] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_724150), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _724150)], (8583 ^ _415872) ^ [_724248, _724250] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _724248, c_Nat_OSuc(_724250)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _724248, c_Groups_Oone__class_Oone(tc_Nat_Onat)), _724250))], (8585 ^ _415872) ^ [_724385, _724387, _724389] : [class_RealVector_Oreal__normed__vector(_724385), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_724385, _724387), c_RealVector_Onorm__class_Onorm(_724385, _724389)))), c_RealVector_Onorm__class_Onorm(_724385, c_Groups_Ominus__class_Ominus(_724385, _724387, _724389)))))], (8591 ^ _415872) ^ [_724663, _724665, _724667] : [class_Groups_Oordered__ab__group__add(_724663), 8594 ^ _415872 : [(8595 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_724663, _724665), _724667)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_724663, c_Groups_Ominus__class_Ominus(_724663, _724665, _724667)), c_Groups_Ozero__class_Ozero(_724663))))], (8601 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_724663, c_Groups_Ominus__class_Ominus(_724663, _724665, _724667)), c_Groups_Ozero__class_Ozero(_724663))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_724663, _724665), _724667)))]]], (8607 ^ _415872) ^ [_725199, _725201, _725203] : [class_RealVector_Oreal__normed__vector(_725199), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_725199, _725201), c_RealVector_Onorm__class_Onorm(_725199, _725203))), c_RealVector_Onorm__class_Onorm(_725199, c_Groups_Ominus__class_Ominus(_725199, _725201, _725203)))))], (8613 ^ _415872) ^ [_725499, _725501, _725503, _725505, _725507] : [class_Groups_Oordered__ab__group__add(_725499), c_Groups_Ominus__class_Ominus(_725499, _725501, _725503) = c_Groups_Ominus__class_Ominus(_725499, _725505, _725507), 8620 ^ _415872 : [(8621 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_725499, _725501), _725503)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_725499, _725505), _725507)))], (8627 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_725499, _725505), _725507)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_725499, _725501), _725503)))]]], (8633 ^ _415872) ^ [_726166, _726168, _726170] : [class_Groups_Ogroup__add(_726166), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_726166), c_Groups_Ominus__class_Ominus(_726166, _726168, _726170)), _726170) = _726168)], (8639 ^ _415872) ^ [_726418, _726420, _726422] : [class_Groups_Ogroup__add(_726418), -(c_Groups_Ominus__class_Ominus(_726418, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_726418), _726420), _726422), _726422) = _726420)], (8645 ^ _415872) ^ [_726641, _726643] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _726641, _726643)), _726641)))], (8647 ^ _415872) ^ [_726773, _726775, _726777] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _726773), _726775)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _726777, _726775)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _726777, _726773))))], (8653 ^ _415872) ^ [_727039, _727041, _727043] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _727039), _727041)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _727039, _727043)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _727041, _727043))))], (8659 ^ _415872) ^ [_727291, _727293] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _727291), _727293)), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _727293, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _727293, _727291)) = _727291)], (8665 ^ _415872) ^ [_727541, _727543, _727545] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _727541), _727543)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _727541), _727545)), 8672 ^ _415872 : [(8673 ^ _415872) ^ [] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _727543, _727541) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _727545, _727541), -(_727543 = _727545)], (8679 ^ _415872) ^ [] : [_727543 = _727545, -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _727543, _727541) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _727545, _727541))]]], (8685 ^ _415872) ^ [_728168, _728170, _728172] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _728168), _728170)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _728168), _728172)), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _728170, _728168), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _728172, _728168)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _728170, _728172))], (8695 ^ _415872) ^ [_728543, _728545, _728547] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _728543), _728545)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _728543), _728547)), 8702 ^ _415872 : [(8703 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _728545, _728543)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _728547, _728543))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _728545), _728547)))], (8709 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _728545), _728547)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _728545, _728543)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _728547, _728543))))]]], (8715 ^ _415872) ^ [_729171, _729173] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _729171), _729173), _729173) = _729171)], (8717 ^ _415872) ^ [_729275, _729277] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _729275), _729277), _729275) = _729277)], (8719 ^ _415872) ^ [_729393, _729395, _729397] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _729393, _729395), _729397) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _729393, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _729395), _729397)))], (8721 ^ _415872) ^ [_729521, _729523, _729525] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _729521), _729523), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _729521), _729525)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _729523, _729525))], (8723 ^ _415872) ^ [_729651, _729653, _729655] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _729651), _729653), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _729655), _729653)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _729651, _729655))], (8725 ^ _415872) ^ [_729796, _729798, _729800] : [class_Groups_Oordered__ab__group__add(_729796), 8728 ^ _415872 : [(8729 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_729796, _729798), _729800)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_729796, c_Groups_Ominus__class_Ominus(_729796, _729798, _729800)), c_Groups_Ozero__class_Ozero(_729796))))], (8735 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_729796, c_Groups_Ominus__class_Ominus(_729796, _729798, _729800)), c_Groups_Ozero__class_Ozero(_729796))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_729796, _729798), _729800)))]]], (8741 ^ _415872) ^ [_730360, _730362, _730364, _730366, _730368] : [class_RealVector_Oreal__normed__algebra(_730360), -(c_Groups_Ominus__class_Ominus(_730360, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_730360), _730362), _730364), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_730360), _730366), _730368)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_730360), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_730360), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_730360), c_Groups_Ominus__class_Ominus(_730360, _730362, _730366)), c_Groups_Ominus__class_Ominus(_730360, _730364, _730368))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_730360), c_Groups_Ominus__class_Ominus(_730360, _730362, _730366)), _730368))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_730360), _730366), c_Groups_Ominus__class_Ominus(_730360, _730364, _730368))))], (8747 ^ _415872) ^ [_730794, _730796, _730798, _730800, _730802, _730804] : [class_Rings_Oring(_730794), 8750 ^ _415872 : [(8751 ^ _415872) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_730794), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_730794), _730796), _730798)), _730800) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_730794), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_730794), _730802), _730798)), _730804), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_730794), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_730794), c_Groups_Ominus__class_Ominus(_730794, _730796, _730802)), _730798)), _730800) = _730804)], (8757 ^ _415872) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_730794), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_730794), c_Groups_Ominus__class_Ominus(_730794, _730796, _730802)), _730798)), _730800) = _730804, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_730794), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_730794), _730796), _730798)), _730800) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_730794), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_730794), _730802), _730798)), _730804))]]], (8763 ^ _415872) ^ [_731528, _731530, _731532, _731534, _731536, _731538] : [class_Rings_Oring(_731528), 8766 ^ _415872 : [(8767 ^ _415872) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_731528), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_731528), _731530), _731532)), _731534) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_731528), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_731528), _731536), _731532)), _731538), -(_731534 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_731528), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_731528), c_Groups_Ominus__class_Ominus(_731528, _731536, _731530)), _731532)), _731538))], (8773 ^ _415872) ^ [] : [_731534 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_731528), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_731528), c_Groups_Ominus__class_Ominus(_731528, _731536, _731530)), _731532)), _731538), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_731528), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_731528), _731530), _731532)), _731534) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_731528), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_731528), _731536), _731532)), _731538))]]], (8779 ^ _415872) ^ [_732248, _732250, _732252, _732254, _732256] : [class_Rings_Oring(_732248), -(c_Groups_Ominus__class_Ominus(_732248, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_732248), _732250), _732252), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_732248), _732254), _732256)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_732248), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_732248), _732250), c_Groups_Ominus__class_Ominus(_732248, _732252, _732256))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_732248), c_Groups_Ominus__class_Ominus(_732248, _732250, _732254)), _732256)))], (8785 ^ _415872) ^ [_732592, _732594, _732596] : [class_Groups_Oordered__ab__group__add__abs(_732592), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_732592, c_Groups_Ominus__class_Ominus(_732592, c_Groups_Oabs__class_Oabs(_732592, _732594), c_Groups_Oabs__class_Oabs(_732592, _732596))), c_Groups_Oabs__class_Oabs(_732592, c_Groups_Ominus__class_Ominus(_732592, _732596, _732594)))))], (8791 ^ _415872) ^ [_732864, _732866, _732868] : [class_Groups_Oordered__ab__group__add__abs(_732864), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_732864, c_Groups_Ominus__class_Ominus(_732864, c_Groups_Oabs__class_Oabs(_732864, _732866), c_Groups_Oabs__class_Oabs(_732864, _732868))), c_Groups_Oabs__class_Oabs(_732864, c_Groups_Ominus__class_Ominus(_732864, _732866, _732868)))))], (8797 ^ _415872) ^ [_733136, _733138, _733140] : [class_Groups_Oordered__ab__group__add__abs(_733136), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_733136, c_Groups_Oabs__class_Oabs(_733136, c_Groups_Ominus__class_Ominus(_733136, c_Groups_Oabs__class_Oabs(_733136, _733138), c_Groups_Oabs__class_Oabs(_733136, _733140)))), c_Groups_Oabs__class_Oabs(_733136, c_Groups_Ominus__class_Ominus(_733136, _733138, _733140)))))], (8803 ^ _415872) ^ [_733399, _733401, _733403] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _733399, _733401), _733403) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _733399, _733403), _733401))], (8805 ^ _415872) ^ [_733568, _733570, _733572, _733574, _733576] : [class_Groups_Oab__group__add(_733568), c_Groups_Ominus__class_Ominus(_733568, _733570, _733572) = c_Groups_Ominus__class_Ominus(_733568, _733574, _733576), 8812 ^ _415872 : [(8813 ^ _415872) ^ [] : [_733570 = _733572, -(_733574 = _733576)], (8819 ^ _415872) ^ [] : [_733574 = _733576, -(_733570 = _733572)]]], (8825 ^ _415872) ^ [_734205, _734207, _734209] : [class_RealVector_Oreal__normed__vector(_734205), -(c_RealVector_Onorm__class_Onorm(_734205, c_Groups_Ominus__class_Ominus(_734205, _734207, _734209)) = c_RealVector_Onorm__class_Onorm(_734205, c_Groups_Ominus__class_Ominus(_734205, _734209, _734207)))], (8831 ^ _415872) ^ [_734446, _734448, _734450] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_734446), _734448), c_Nat_OSuc(_734450)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _734446, _734448), _734450))], (8833 ^ _415872) ^ [_734562, _734564] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_734562), c_Nat_OSuc(_734564)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _734562, _734564))], (8835 ^ _415872) ^ [_734683, _734685] : [class_Groups_Ogroup__add(_734683), -(c_Groups_Ominus__class_Ominus(_734683, _734685, c_Groups_Ozero__class_Ozero(_734683)) = _734685)], (8841 ^ _415872) ^ [_734903, _734905] : [class_Groups_Ogroup__add(_734903), -(c_Groups_Ominus__class_Ominus(_734903, _734905, _734905) = c_Groups_Ozero__class_Ozero(_734903))], (8847 ^ _415872) ^ [_735137, _735139, _735141] : [class_Groups_Oab__group__add(_735137), 8850 ^ _415872 : [(8851 ^ _415872) ^ [] : [_735139 = _735141, -(c_Groups_Ominus__class_Ominus(_735137, _735139, _735141) = c_Groups_Ozero__class_Ozero(_735137))], (8857 ^ _415872) ^ [] : [c_Groups_Ominus__class_Ominus(_735137, _735139, _735141) = c_Groups_Ozero__class_Ozero(_735137), -(_735139 = _735141)]]], (8863 ^ _415872) ^ [_735643, _735645, _735647] : [class_Groups_Ogroup__add(_735643), 8866 ^ _415872 : [(8867 ^ _415872) ^ [] : [c_Groups_Ominus__class_Ominus(_735643, _735645, _735647) = c_Groups_Ozero__class_Ozero(_735643), -(_735645 = _735647)], (8873 ^ _415872) ^ [] : [_735645 = _735647, -(c_Groups_Ominus__class_Ominus(_735643, _735645, _735647) = c_Groups_Ozero__class_Ozero(_735643))]]], (8879 ^ _415872) ^ [_736177, _736179, _736181, _736183, _736185] : [class_Groups_Oordered__ab__group__add(_736177), c_Groups_Ominus__class_Ominus(_736177, _736179, _736181) = c_Groups_Ominus__class_Ominus(_736177, _736183, _736185), 8886 ^ _415872 : [(8887 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_736177, _736179), _736181)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_736177, _736183), _736185)))], (8893 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_736177, _736183), _736185)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_736177, _736179), _736181)))]]], (8899 ^ _415872) ^ [_736801] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _736801) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8901 ^ _415872) ^ [_736883] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _736883, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _736883)], (8903 ^ _415872) ^ [_736965] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _736965, _736965) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8905 ^ _415872) ^ [_737076, _737078] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _737076, _737078) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _737078, _737076) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_737076 = _737078)], (8915 ^ _415872) ^ [_737405, _737407, _737409] : [class_Groups_Oordered__ab__group__add__abs(_737405), -(c_Groups_Oabs__class_Oabs(_737405, c_Groups_Ominus__class_Ominus(_737405, _737407, _737409)) = c_Groups_Oabs__class_Oabs(_737405, c_Groups_Ominus__class_Ominus(_737405, _737409, _737407)))], (8921 ^ _415872) ^ [_737661, _737663, _737665] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _737661), _737663)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _737661, _737665)), _737663)))], (8927 ^ _415872) ^ [_737919, _737921, _737923] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _737919), _737921)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _737919), _737923)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _737923, _737921)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _737923, _737919))))], (8937 ^ _415872) ^ [_738273, _738275, _738277] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _738273), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _738275, _738277)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _738273), _738275), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _738273), _738277)))], (8939 ^ _415872) ^ [_738409, _738411, _738413] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _738409, _738411)), _738413) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _738409), _738413), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _738411), _738413)))], (8941 ^ _415872) ^ [_738574, _738576, _738578, _738580] : [class_RealVector_Oreal__normed__algebra(_738574), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_738574), c_Groups_Ominus__class_Ominus(_738574, _738576, _738578)), _738580) = c_Groups_Ominus__class_Ominus(_738574, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_738574), _738576), _738580), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_738574), _738578), _738580)))], (8947 ^ _415872) ^ [_738886, _738888, _738890, _738892] : [class_RealVector_Oreal__normed__algebra(_738886), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_738886), c_Groups_Ominus__class_Ominus(_738886, _738888, _738890)), _738892) = c_Groups_Ominus__class_Ominus(_738886, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_738886), _738888), _738892), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_738886), _738890), _738892)))], (8953 ^ _415872) ^ [_739198, _739200, _739202, _739204] : [class_RealVector_Oreal__normed__algebra(_739198), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_739198), _739200), c_Groups_Ominus__class_Ominus(_739198, _739202, _739204)) = c_Groups_Ominus__class_Ominus(_739198, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_739198), _739200), _739202), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_739198), _739200), _739204)))], (8959 ^ _415872) ^ [_739510, _739512, _739514, _739516] : [class_RealVector_Oreal__normed__algebra(_739510), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_739510), _739512), c_Groups_Ominus__class_Ominus(_739510, _739514, _739516)) = c_Groups_Ominus__class_Ominus(_739510, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_739510), _739512), _739514), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_739510), _739512), _739516)))], (8965 ^ _415872) ^ [_739808, _739810, _739812] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _739808), _739810)), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _739812, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _739810, _739808)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _739812), _739808), _739810))], (8971 ^ _415872) ^ [_740113, _740115, _740117] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _740113, _740115)), _740117)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _740113), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _740117), _740115))))], (8977 ^ _415872) ^ [_740321, _740323, _740325] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _740321), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _740325), _740323))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _740321, _740323)), _740325)))], (8983 ^ _415872) ^ [_740593, _740595, _740597] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _740593), _740595)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _740597), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _740595), _740597), _740593))))], (8989 ^ _415872) ^ [_740849, _740851] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _740849), _740851)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _740849), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _740851, _740849)) = _740851)], (8995 ^ _415872) ^ [_741103, _741105, _741107] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _741103), _741105)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _741107), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _741105, _741103)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _741107), _741105), _741103))], (9001 ^ _415872) ^ [_741383, _741385, _741387] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _741383), _741385)), 9004 ^ _415872 : [(9005 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _741387), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _741385, _741383))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _741387), _741383)), _741385)))], (9011 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _741387), _741383)), _741385)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _741387), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _741385, _741383))))]]], (9017 ^ _415872) ^ [_741929, _741931] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _741929), _741931)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _741931, _741929)), _741929) = _741931)], (9023 ^ _415872) ^ [_742183, _742185, _742187] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _742183), _742185)), 9026 ^ _415872 : [(9027 ^ _415872) ^ [] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _742185, _742183) = _742187, -(_742185 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _742187), _742183))], (9033 ^ _415872) ^ [] : [_742185 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _742187), _742183), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _742185, _742183) = _742187)]]], (9039 ^ _415872) ^ [_742713, _742715, _742717] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _742713), _742715)), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _742717), _742715), _742713) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _742717), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _742715, _742713)))], (9045 ^ _415872) ^ [_742993, _742995, _742997] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _742993), _742995)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _742995, _742993)), _742997) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _742995), _742997), _742993))], (9051 ^ _415872) ^ [_743273, _743275, _743277] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _743273), _743275)), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _743275), _743277), _743273) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _743275, _743273)), _743277))], (9057 ^ _415872) ^ [_743553, _743555, _743557] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _743553), _743555)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _743553), _743557)), 9064 ^ _415872 : [(9065 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _743555, _743553)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _743557, _743553))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _743555), _743557)))], (9071 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _743555), _743557)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _743555, _743553)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _743557, _743553))))]]], (9077 ^ _415872) ^ [_744210, _744212, _744214] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _744210), _744212)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _744214), _744210)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _744210, _744214)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _744212, _744214))))], (9087 ^ _415872) ^ [_744608, _744610, _744612] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _744608), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _744610, _744612))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _744608), _744612)), _744610)))], (9093 ^ _415872) ^ [_744816, _744818, _744820] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _744816), _744820)), _744818)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _744816), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _744818, _744820))))], (9099 ^ _415872) ^ [_745074, _745076] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _745074), _745076))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _745076), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _745074, _745076)) = _745074)], (9105 ^ _415872) ^ [_745317, _745319] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _745317), _745319)), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_745319), _745317) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _745319, _745317)))], (9111 ^ _415872) ^ [_745561, _745563] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _745561), _745563)), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _745561, _745563) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9117 ^ _415872) ^ [_745818, _745820] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _745818, _745820) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _745818), _745820)))], (9123 ^ _415872) ^ [_745998, _746000] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _745998), _746000)), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _745998, _746000) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9129 ^ _415872) ^ [_746213, _746215] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _746213, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _746213), _746215)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9131 ^ _415872) ^ [_746317, _746319] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _746317, _746319)), c_Nat_OSuc(_746317))))], (9133 ^ _415872) ^ [_746437, _746439] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _746437)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _746439)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _746439, _746437)), _746439)))], (9143 ^ _415872) ^ [_746791, _746793] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _746791, _746793))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _746793), _746791)))], (9149 ^ _415872) ^ [_746975, _746977] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _746977), _746975)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _746975, _746977))))], (9155 ^ _415872) ^ [_747265, _747267, _747269, _747271, _747273, _747275] : [class_Rings_Oordered__ring(_747265), 9158 ^ _415872 : [(9159 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_747265, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_747265), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_747265), _747267), _747269)), _747271)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_747265), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_747265), _747273), _747269)), _747275))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_747265, _747271), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_747265), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_747265), c_Groups_Ominus__class_Ominus(_747265, _747273, _747267)), _747269)), _747275))))], (9165 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_747265, _747271), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_747265), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_747265), c_Groups_Ominus__class_Ominus(_747265, _747273, _747267)), _747269)), _747275))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_747265, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_747265), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_747265), _747267), _747269)), _747271)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_747265), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_747265), _747273), _747269)), _747275))))]]], (9171 ^ _415872) ^ [_748029, _748031, _748033, _748035, _748037, _748039] : [class_Rings_Oordered__ring(_748029), 9174 ^ _415872 : [(9175 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_748029, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_748029), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_748029), _748031), _748033)), _748035)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_748029), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_748029), _748037), _748033)), _748039))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_748029, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_748029), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_748029), c_Groups_Ominus__class_Ominus(_748029, _748031, _748037)), _748033)), _748035)), _748039)))], (9181 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_748029, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_748029), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_748029), c_Groups_Ominus__class_Ominus(_748029, _748031, _748037)), _748033)), _748035)), _748039)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_748029, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_748029), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_748029), _748031), _748033)), _748035)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_748029), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_748029), _748037), _748033)), _748039))))]]], (9187 ^ _415872) ^ [_748793, _748795, _748797, _748799, _748801, _748803] : [class_Rings_Oordered__ring(_748793), 9190 ^ _415872 : [(9191 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_748793, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_748793), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_748793), _748795), _748797)), _748799)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_748793), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_748793), _748801), _748797)), _748803))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_748793, _748799), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_748793), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_748793), c_Groups_Ominus__class_Ominus(_748793, _748801, _748795)), _748797)), _748803))))], (9197 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_748793, _748799), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_748793), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_748793), c_Groups_Ominus__class_Ominus(_748793, _748801, _748795)), _748797)), _748803))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_748793, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_748793), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_748793), _748795), _748797)), _748799)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_748793), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_748793), _748801), _748797)), _748803))))]]], (9203 ^ _415872) ^ [_749557, _749559, _749561, _749563, _749565, _749567] : [class_Rings_Oordered__ring(_749557), 9206 ^ _415872 : [(9207 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_749557, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_749557), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_749557), _749559), _749561)), _749563)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_749557), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_749557), _749565), _749561)), _749567))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_749557, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_749557), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_749557), c_Groups_Ominus__class_Ominus(_749557, _749559, _749565)), _749561)), _749563)), _749567)))], (9213 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_749557, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_749557), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_749557), c_Groups_Ominus__class_Ominus(_749557, _749559, _749565)), _749561)), _749563)), _749567)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_749557, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_749557), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_749557), _749559), _749561)), _749563)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_749557), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_749557), _749565), _749561)), _749567))))]]], (9219 ^ _415872) ^ [_750265, _750267] : [class_Rings_Oring__1(_750265), -(c_Groups_Ominus__class_Ominus(_750265, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_750265), _750267), _750267), c_Groups_Oone__class_Oone(_750265)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_750265), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_750265), _750267), c_Groups_Oone__class_Oone(_750265))), c_Groups_Ominus__class_Ominus(_750265, _750267, c_Groups_Oone__class_Oone(_750265))))], (9225 ^ _415872) ^ [_750563, _750565, _750567] : [class_Groups_Oordered__ab__group__add__abs(_750563), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_750563, c_Groups_Oabs__class_Oabs(_750563, c_Groups_Ominus__class_Ominus(_750563, _750565, _750567))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_750563), c_Groups_Oabs__class_Oabs(_750563, _750565)), c_Groups_Oabs__class_Oabs(_750563, _750567)))))], (9231 ^ _415872) ^ [_750871, _750873, _750875, _750877, _750879] : [class_Groups_Oordered__ab__group__add__abs(_750871), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_750871, c_Groups_Oabs__class_Oabs(_750871, c_Groups_Ominus__class_Ominus(_750871, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_750871), _750873), _750875), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_750871), _750877), _750879)))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_750871), c_Groups_Oabs__class_Oabs(_750871, c_Groups_Ominus__class_Ominus(_750871, _750873, _750877))), c_Groups_Oabs__class_Oabs(_750871, c_Groups_Ominus__class_Ominus(_750871, _750875, _750879))))))], (9237 ^ _415872) ^ [_751225, _751227, _751229, _751231] : [class_Rings_Olinordered__idom(_751225), 9240 ^ _415872 : [(9241 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_751225, c_Groups_Oabs__class_Oabs(_751225, c_Groups_Ominus__class_Ominus(_751225, _751227, _751229))), _751231)), 9244 ^ _415872 : [(9245 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_751225, c_Groups_Ominus__class_Ominus(_751225, _751229, _751231)), _751227)))], (9247 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_751225, _751227), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_751225), _751229), _751231))))]]], (9249 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_751225, c_Groups_Oabs__class_Oabs(_751225, c_Groups_Ominus__class_Ominus(_751225, _751227, _751229))), _751231))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_751225, c_Groups_Ominus__class_Ominus(_751225, _751229, _751231)), _751227)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_751225, _751227), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_751225), _751229), _751231)))]]], (9259 ^ _415872) ^ [_752001, _752003, _752005] : [class_RealVector_Oreal__normed__vector(_752001), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_752001, c_Groups_Ominus__class_Ominus(_752001, _752003, _752005))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_752001, _752003)), c_RealVector_Onorm__class_Onorm(_752001, _752005)))))], (9265 ^ _415872) ^ [_752249] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _752249)), -(c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _752249, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = _752249)], (9271 ^ _415872) ^ [_752469, _752471] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _752469)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _752469, c_Nat_OSuc(_752471))), _752469)))], (9293 ^ _415872) ^ [_753301, _753303, _753305] : [-(hBOOL(hAPP(_753301, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _753303, _753305)))), 9296 ^ _415872 : [(9297 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _753303), _753305)))], (9299 ^ _415872) ^ [] : [hBOOL(hAPP(_753301, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 9301 ^ _415872 : [(9302 ^ _415872) ^ [] : [-(_753303 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _753305), 9300 ^ [_753301, _753303, _753305]))], (9304 ^ _415872) ^ [] : [hBOOL(hAPP(_753301, 9300 ^ [_753301, _753303, _753305]))]]], (9277 ^ _415872) ^ [_752748, _752750, _752752] : [hBOOL(hAPP(_752748, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _752750, _752752))), 9280 ^ _415872 : [(9281 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _752750), _752752)), -(hBOOL(hAPP(_752748, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (9287 ^ _415872) ^ [_753096] : [_752750 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _752752), _753096), -(hBOOL(hAPP(_752748, _753096)))]]], (9324 ^ _415872) ^ [_754490, _754492, _754494] : [-(hBOOL(hAPP(_754490, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _754492, _754494)))), 9327 ^ _415872 : [(9328 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _754492), _754494)))], (9330 ^ _415872) ^ [] : [hBOOL(hAPP(_754490, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 9332 ^ _415872 : [(9333 ^ _415872) ^ [] : [-(_754492 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _754494), 9331 ^ [_754490, _754492, _754494]))], (9335 ^ _415872) ^ [] : [hBOOL(hAPP(_754490, 9331 ^ [_754490, _754492, _754494]))]]], (9308 ^ _415872) ^ [_753945, _753947, _753949] : [hBOOL(hAPP(_753945, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _753947, _753949))), 9311 ^ _415872 : [(9312 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _753947), _753949)), -(hBOOL(hAPP(_753945, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (9318 ^ _415872) ^ [_754287] : [_753947 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _753949), _754287), -(hBOOL(hAPP(_753945, _754287)))]]], (9339 ^ _415872) ^ [_755097, _755099, _755101] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _755097), _755099)), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _755099, _755097)), _755101) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_755099), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _755097), _755101)))], (9345 ^ _415872) ^ [_755381, _755383, _755385] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _755381), _755383)), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _755385, c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _755383, _755381))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _755385), _755381), c_Nat_OSuc(_755383)))], (9351 ^ _415872) ^ [_755693, _755695, _755697, _755699, _755701] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _755693), _755695)), 9354 ^ _415872 : [(9355 ^ _415872) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _755693), _755697)), _755699) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _755695), _755697)), _755701), -(_755699 = hAPP(hAPP(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, _755695, _755693)), _755697)), _755701))], (9361 ^ _415872) ^ [] : [_755699 = hAPP(hAPP(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, _755695, _755693)), _755697)), _755701), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _755693), _755697)), _755699) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _755695), _755697)), _755701))]]], (9367 ^ _415872) ^ [_756373, _756375, _756377, _756379, _756381] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _756373), _756375)), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _756373), _756377)), _756379), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _756375), _756377)), _756381)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _756379, hAPP(hAPP(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, _756375, _756373)), _756377)), _756381)))], (9373 ^ _415872) ^ [_756749, _756751, _756753, _756755, _756757] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _756749), _756751)), 9376 ^ _415872 : [(9377 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _756749), _756753)), _756755)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _756751), _756753)), _756757))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _756755), hAPP(hAPP(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, _756751, _756749)), _756753)), _756757))))], (9383 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _756755), hAPP(hAPP(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, _756751, _756749)), _756753)), _756757))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _756749), _756753)), _756755)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _756751), _756753)), _756757))))]]], (9389 ^ _415872) ^ [_757459, _757461, _757463, _757465, _757467] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _757459), _757461)), 9392 ^ _415872 : [(9393 ^ _415872) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _757461), _757463)), _757465) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _757459), _757463)), _757467), -(hAPP(hAPP(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, _757461, _757459)), _757463)), _757465) = _757467)], (9399 ^ _415872) ^ [] : [hAPP(hAPP(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, _757461, _757459)), _757463)), _757465) = _757467, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _757461), _757463)), _757465) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _757459), _757463)), _757467))]]], (9405 ^ _415872) ^ [_758139, _758141, _758143, _758145, _758147] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _758139), _758141)), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _758141), _758143)), _758145), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _758139), _758143)), _758147)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(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, _758141, _758139)), _758143)), _758145), _758147))], (9411 ^ _415872) ^ [_758515, _758517, _758519, _758521, _758523] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _758515), _758517)), 9414 ^ _415872 : [(9415 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _758517), _758519)), _758521)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _758515), _758519)), _758523))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(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, _758517, _758515)), _758519)), _758521)), _758523)))], (9421 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(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, _758517, _758515)), _758519)), _758521)), _758523)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _758517), _758519)), _758521)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _758515), _758519)), _758523))))]]], (9427 ^ _415872) ^ [_759225, _759227, _759229, _759231, _759233] : [class_RealVector_Oreal__normed__vector(_759225), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_759225, c_Groups_Ominus__class_Ominus(_759225, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_759225), _759227), _759229), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_759225), _759231), _759233)))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_759225, c_Groups_Ominus__class_Ominus(_759225, _759227, _759231))), c_RealVector_Onorm__class_Onorm(_759225, c_Groups_Ominus__class_Ominus(_759225, _759229, _759233))))))], (9433 ^ _415872) ^ [_759575, _759577, _759579, _759581] : [class_Groups_Omonoid__mult(_759575), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _759577), _759579)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_759575), _759581), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_759579), _759577)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_759575), hAPP(hAPP(c_Power_Opower__class_Opower(_759575), _759581), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _759579, _759577))), _759581))], (9443 ^ _415872) ^ [_759956] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _759956)), -(_759956 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _759956, c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (9449 ^ _415872) ^ [_760162] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _760162)), -(c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _760162, c_Groups_Oone__class_Oone(tc_Nat_Onat))) = _760162)], (9455 ^ _415872) ^ [_760402, _760404] : [_760402 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _760402), _760404) = _760404)], (9461 ^ _415872) ^ [_760576, _760578] : [-(_760576 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _760576), _760578) = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _760576, c_Groups_Oone__class_Oone(tc_Nat_Onat))), _760578)))], (9467 ^ _415872) ^ [_760869, _760871, _760873, _760875, _760877] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _760869), _760871)), 9470 ^ _415872 : [(9471 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _760871), _760873)), _760875)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _760869), _760873)), _760877))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(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, _760871, _760869)), _760873)), _760875)), _760877)))], (9477 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(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, _760871, _760869)), _760873)), _760875)), _760877)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _760871), _760873)), _760875)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _760869), _760873)), _760877))))]]], (9483 ^ _415872) ^ [_761579, _761581, _761583, _761585, _761587] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _761579), _761581)), 9486 ^ _415872 : [(9487 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _761579), _761583)), _761585)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _761581), _761583)), _761587))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _761585), hAPP(hAPP(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, _761581, _761579)), _761583)), _761587))))], (9493 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _761585), hAPP(hAPP(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, _761581, _761579)), _761583)), _761587))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _761579), _761583)), _761585)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _761581), _761583)), _761587))))]]], (9499 ^ _415872) ^ [_762267, _762269] : [_762267 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _762267), _762269) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9505 ^ _415872) ^ [_762441, _762443] : [-(_762441 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _762441), _762443) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _762443), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _762441, c_Groups_Oone__class_Oone(tc_Nat_Onat))), _762443)))], (9511 ^ _415872) ^ [_762720, _762722] : [_762720 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _762722), _762720) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (9517 ^ _415872) ^ [_762894, _762896] : [-(_762894 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _762896), _762894) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _762896), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _762896), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _762894, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (9523 ^ _415872) ^ [_763167, _763169, _763171] : [class_Rings_Ocomm__ring__1(_763167), -(c_Groups_Ominus__class_Ominus(_763167, hAPP(hAPP(c_Power_Opower__class_Opower(_763167), _763169), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(hAPP(c_Power_Opower__class_Opower(_763167), _763171), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_763167), c_Groups_Ominus__class_Ominus(_763167, _763169, _763171)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_763167), _763169), _763171)))], (9529 ^ _415872) ^ [_763475, _763477, _763479] : [class_Power_Opower(_763475), 9532 ^ _415872 : [(9533 ^ _415872) ^ [] : [_763477 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_763475), _763479), _763477) = c_Groups_Oone__class_Oone(_763475))], (9539 ^ _415872) ^ [] : [-(_763477 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_763475), _763479), _763477) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_763475), _763479), hAPP(hAPP(c_Power_Opower__class_Opower(_763475), _763479), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _763477, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (9545 ^ _415872) ^ [_764017] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _764017)), 9549 ^ _415872 : [(9550 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, 9548 ^ [_764017], c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _764017)))], (9552 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _764017), c_RealDef_Oreal(tc_Nat_Onat, 9548 ^ [_764017]))))]]], (9554 ^ _415872) ^ [_764448, _764450, _764452, _764454] : [class_RealVector_Oreal__normed__vector(_764448), class_Orderings_Oord(_764450), 9564 ^ _415872 : [(9565 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_764450, _764452), 9563 ^ [_764448, _764450, _764452, _764454])))], (9567 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_764448, c_Groups_Ominus__class_Ominus(_764448, hAPP(_764454, _764452), hAPP(_764454, 9563 ^ [_764448, _764450, _764452, _764454])))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))]], 9568 ^ _415872 : [(9569 ^ _415872) ^ [_765037] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_764450, _764452), _765037)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_764448, hAPP(_764454, _765037))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), c_RealVector_Onorm__class_Onorm(_764448, hAPP(_764454, _764452))))))]]], (9575 ^ _415872) ^ [_765364, _765366] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _765364), _765366)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _765364, _765366)), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))], (9581 ^ _415872) ^ [_765554, _765556] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _765554, _765556)), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _765554), _765556)))], (9587 ^ _415872) ^ [_765779, _765781] : [-(hAPP(c_Complex_OIm, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, _765779, _765781)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, hAPP(c_Complex_OIm, _765779), hAPP(c_Complex_OIm, _765781)))], (9589 ^ _415872) ^ [_765890, _765892] : [-(hAPP(c_Complex_ORe, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, _765890, _765892)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, hAPP(c_Complex_ORe, _765890), hAPP(c_Complex_ORe, _765892)))], (9591 ^ _415872) ^ [_766015, _766017, _766019] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _766015), c_Groups_Ominus__class_Ominus(tc_Int_Oint, _766017, _766019)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _766015), _766017), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _766015), _766019)))], (9593 ^ _415872) ^ [_766151, _766153, _766155] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Ominus__class_Ominus(tc_Int_Oint, _766151, _766153)), _766155) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _766151), _766155), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _766153), _766155)))], (9595 ^ _415872) ^ [_766317, _766319] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _766317), _766319)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _766317, _766319)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (9601 ^ _415872) ^ [_766507, _766509] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _766507, _766509)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _766507), _766509)))], (9607 ^ _415872) ^ [_766761, _766763, _766765] : [class_RealVector_Oreal__normed__vector(_766761), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_766761, _766763), c_RealVector_Onorm__class_Onorm(_766761, _766765))), c_RealVector_Onorm__class_Onorm(_766761, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_766761), _766763), _766765)))))], (9613 ^ _415872) ^ [_767012, _767014] : [-(hBOOL(hAPP(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, _767012, _767014))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, hAPP(c_Complex_ORe, _767012), hAPP(c_Complex_ORe, _767014)))), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, hAPP(c_Complex_OIm, _767012), hAPP(c_Complex_OIm, _767014)))))))], (9615 ^ _415872) ^ [_767194, _767196] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _767194), c_Groups_Ominus__class_Ominus(tc_Int_Oint, _767196, c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _767194), _767196)))], (9621 ^ _415872) ^ [_767384, _767386] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _767384), _767386)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _767384), c_Groups_Ominus__class_Ominus(tc_Int_Oint, _767386, c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (9627 ^ _415872) ^ [_767624, _767626] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _767624), _767626)), -(c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _767626, _767624)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _767626), c_RealDef_Oreal(tc_Nat_Onat, _767624)))], (9633 ^ _415872) ^ [_767863, _767865] : [-(c_Transcendental_Osin(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _767863, _767865)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Transcendental_Osin(_767863)), c_Transcendental_Ocos(_767865)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Transcendental_Ocos(_767863)), c_Transcendental_Osin(_767865))))], (9635 ^ _415872) ^ [_767987, _767989] : [-(c_Transcendental_Osin(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _767987, _767989)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Transcendental_Ocos(_767989)), c_Transcendental_Osin(_767987)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Transcendental_Osin(_767989)), c_Transcendental_Ocos(_767987))))], (9637 ^ _415872) ^ [_768111, _768113] : [-(hBOOL(hAPP(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, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex), _768111), _768113)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _768111))), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _768113))))], (9639 ^ _415872) ^ [_768229, _768231] : [-(c_Transcendental_Ocos(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), _768229), _768231)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Transcendental_Ocos(_768229)), c_Transcendental_Ocos(_768231)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Transcendental_Osin(_768229)), c_Transcendental_Osin(_768231))))], (9641 ^ _415872) ^ [_768355, _768357] : [-(c_Transcendental_Ocos(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _768355, _768357)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Transcendental_Ocos(_768355)), c_Transcendental_Ocos(_768357))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Transcendental_Osin(_768355)), c_Transcendental_Osin(_768357))))], (9643 ^ _415872) ^ [_768481, _768483] : [-(c_Transcendental_Ocos(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _768481, _768483)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Transcendental_Ocos(_768483)), c_Transcendental_Ocos(_768481))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Transcendental_Osin(_768483)), c_Transcendental_Osin(_768481))))], (9645 ^ _415872) ^ [_768622, _768624] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _768622)), _768624)), -(c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _768624, c_RealDef_Oreal(tc_Nat_Onat, _768622))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_RComplete_Onatfloor(_768624), _768622))], (9651 ^ _415872) ^ [_768849] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _768849, c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatfloor(_768849)))))], (9653 ^ _415872) ^ [_768970, _768972] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _768970)), _768972)), -(c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _768972, c_RealDef_Oreal(tc_Nat_Onat, _768970))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_RComplete_Onatceiling(_768972), _768970))], (9659 ^ _415872) ^ [_769211, _769213] : [-(hAPP(c_Complex_ORe, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), _769211), _769213)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(c_Complex_ORe, _769211)), hAPP(c_Complex_ORe, _769213)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(c_Complex_OIm, _769211)), hAPP(c_Complex_OIm, _769213))))], (9661 ^ _415872) ^ [_769371, _769373, _769375] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _769371)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _769373, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oabs__class_Oabs(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _769373, _769375))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _769371))), _769375)))], (9667 ^ _415872) ^ [_769661, _769663, _769665] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _769661)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _769663), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _769665), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oabs__class_Oabs(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _769665, _769663))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _769661)))))], (9673 ^ _415872) ^ [_769927] : [c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _769927) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex), _769927), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, _769927, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex), _769927), c_Complex_Oii))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, _769927, c_Complex_Oii))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))], (9691 ^ _415872) ^ [_770519, _770521] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _770519), _770521)), -(c_Nat__Transfer_Otsub(_770521, _770519) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, _770521, _770519))], (9697 ^ _415872) ^ [_770705, _770707] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _770705), _770707))), -(c_Nat__Transfer_Otsub(_770707, _770705) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (9703 ^ _415872) ^ [] : [-(hAPP(c_Complex_ORe, c_Complex_Oii) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (9705 ^ _415872) ^ [] : [c_Complex_Oii = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)], (9707 ^ _415872) ^ [] : [c_Complex_Oii = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)], (9709 ^ _415872) ^ [] : [-(hAPP(c_Complex_OIm, c_Complex_Oii) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (9711 ^ _415872) ^ [_771146, _771148] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _771146)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _771148)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Nat__Transfer_Otsub(_771146, _771148))))], (9721 ^ _415872) ^ [_771463, _771465] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _771463), _771465)), -(c_Nat__Transfer_Otsub(_771465, _771463) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, _771465, _771463))], (9727 ^ _415872) ^ [_771697, _771699] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _771697)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _771699)), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _771699), _771697), _771699) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _771699), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _771697, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (9737 ^ _415872) ^ [_772086, _772088, _772090, _772092, _772094] : [class_Groups_Oab__group__add(_772086), -(c_Groups_Ominus__class_Ominus(_772086, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_772086), _772088), _772090), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_772086), _772092), _772094)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_772086), c_Groups_Ominus__class_Ominus(_772086, _772088, _772092)), c_Groups_Ominus__class_Ominus(_772086, _772090, _772094)))], (9743 ^ _415872) ^ [_772384, _772386] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _772384)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint)), _772386)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _772384, _772386)), _772384)))], (9753 ^ _415872) ^ [_772723, _772725, _772727] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _772723)), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _772725, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _772727), _772723)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _772725, _772727), _772723))], (9759 ^ _415872) ^ [_773007, _773009, _773011, _773013] : [class_Divides_Osemiring__div(_773007), 9762 ^ _415872 : [(9763 ^ _415872) ^ [] : [_773009 = c_Groups_Ozero__class_Ozero(_773007), -(c_Divides_Odiv__class_Odiv(_773007, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_773007), _773009), _773011), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_773007), _773009), _773013)) = c_Groups_Ozero__class_Ozero(_773007))], (9769 ^ _415872) ^ [] : [-(_773009 = c_Groups_Ozero__class_Ozero(_773007)), -(c_Divides_Odiv__class_Odiv(_773007, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_773007), _773009), _773011), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_773007), _773009), _773013)) = c_Divides_Odiv__class_Odiv(_773007, _773011, _773013))]]], (9775 ^ _415872) ^ [_773617, _773619, _773621] : [class_Divides_Osemiring__div(_773617), -(_773619 = c_Groups_Ozero__class_Ozero(_773617)), -(c_Divides_Odiv__class_Odiv(_773617, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_773617), _773621), _773619), _773619) = _773621)], (9785 ^ _415872) ^ [_773969, _773971, _773973] : [class_Divides_Osemiring__div(_773969), -(_773971 = c_Groups_Ozero__class_Ozero(_773969)), -(c_Divides_Odiv__class_Odiv(_773969, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_773969), _773971), _773973), _773971) = _773973)], (9795 ^ _415872) ^ [_774335, _774337, _774339, _774341] : [class_Divides_Osemiring__div(_774335), -(_774337 = c_Groups_Ozero__class_Ozero(_774335)), -(c_Divides_Odiv__class_Odiv(_774335, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_774335), _774339), _774337), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_774335), _774341), _774337)) = c_Divides_Odiv__class_Odiv(_774335, _774339, _774341))], (9805 ^ _415872) ^ [_774735, _774737, _774739, _774741] : [class_Divides_Osemiring__div(_774735), -(_774737 = c_Groups_Ozero__class_Ozero(_774735)), -(c_Divides_Odiv__class_Odiv(_774735, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_774735), _774737), _774739), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_774735), _774737), _774741)) = c_Divides_Odiv__class_Odiv(_774735, _774739, _774741))], (9815 ^ _415872) ^ [_775107, _775109] : [class_Divides_Osemiring__div(_775107), -(_775109 = c_Groups_Ozero__class_Ozero(_775107)), -(c_Divides_Odiv__class_Odiv(_775107, _775109, _775109) = c_Groups_Oone__class_Oone(_775107))], (9825 ^ _415872) ^ [_775394] : [-(c_Divides_Odiv__class_Odiv(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _775394) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (9827 ^ _415872) ^ [_775505, _775507] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _775505)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _775507)), -(hBOOL(hAPP(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, _775505, _775507))))], (9837 ^ _415872) ^ [_775824, _775826] : [class_Divides_Osemiring__div(_775824), -(c_Divides_Odiv__class_Odiv(_775824, _775826, c_Groups_Ozero__class_Ozero(_775824)) = c_Groups_Ozero__class_Ozero(_775824))], (9843 ^ _415872) ^ [_776048, _776050] : [class_Divides_Osemiring__div(_776048), -(c_Divides_Odiv__class_Odiv(_776048, c_Groups_Ozero__class_Ozero(_776048), _776050) = c_Groups_Ozero__class_Ozero(_776048))], (9849 ^ _415872) ^ [_776272, _776274] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _776272), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _776274)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _776272, _776274)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (9859 ^ _415872) ^ [_776603, _776605] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _776603), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 9862 ^ _415872 : [(9863 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _776605, _776603)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _776605)))], (9869 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _776605)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _776605, _776603)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (9875 ^ _415872) ^ [_777106, _777108] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _777106)), 9878 ^ _415872 : [(9879 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _777108, _777106)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _777108), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (9885 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _777108), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _777108, _777106)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (9891 ^ _415872) ^ [_777598] : [-(_777598 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _777598, _777598) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (9897 ^ _415872) ^ [_777813, _777815] : [class_Divides_Osemiring__div(_777813), -(c_Divides_Odiv__class_Odiv(_777813, _777815, c_Groups_Oone__class_Oone(_777813)) = _777815)], (9903 ^ _415872) ^ [_778047, _778049, _778051] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _778047), _778049)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _778051), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _778049, _778051)), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _778047, _778051))))], (9913 ^ _415872) ^ [_778416, _778418, _778420] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _778416), _778418)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _778420)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _778416, _778420)), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _778418, _778420))))], (9923 ^ _415872) ^ [_778765, _778767] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _778765), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _778767), _778765)), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _778765, _778767) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (9933 ^ _415872) ^ [_779106, _779108, _779110] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _779106), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _779108)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _779108), _779110)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _779106, _779108)), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _779106, _779110))))], (9947 ^ _415872) ^ [_779558, _779560] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _779558), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _779560)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _779558, _779560)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (9957 ^ _415872) ^ [_779889, _779891] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _779889), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 9960 ^ _415872 : [(9961 ^ _415872) ^ [] : [hBOOL(hAPP(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, _779891, _779889))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _779891), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (9967 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _779891), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(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, _779891, _779889))))]]], (9973 ^ _415872) ^ [_780392, _780394] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _780392)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _780392), _780394)), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _780392, _780394) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (9983 ^ _415872) ^ [_780713, _780715] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _780713)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _780715), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _780713, _780715)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (9993 ^ _415872) ^ [_781058, _781060, _781062] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _781058)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _781060)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _781060), _781062)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _781058, _781062)), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _781058, _781060))))], (10007 ^ _415872) ^ [_781504, _781506] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _781504)), 10010 ^ _415872 : [(10011 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _781504, _781506))), 10014 ^ _415872 : [(10015 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _781506), _781504)))], (10017 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _781506)))]]], (10019 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _781504, _781506)))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _781506), _781504)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _781506))]]], (10029 ^ _415872) ^ [_782165, _782167] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _782165)), 10032 ^ _415872 : [(10033 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _782167, _782165))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _782165), _782167)))], (10039 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _782165), _782167)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _782167, _782165))))]]], (10045 ^ _415872) ^ [_782662, _782664] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _782662)), 10048 ^ _415872 : [(10049 ^ _415872) ^ [] : [hBOOL(hAPP(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, _782664, _782662))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _782664)))], (10055 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _782664)), -(hBOOL(hAPP(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, _782664, _782662))))]]], (10061 ^ _415872) ^ [_783179, _783181] : [c_Divides_Odiv__class_Odiv(tc_Int_Oint, _783179, _783181) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_783181 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 10070 ^ _415872 : [(10071 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _783179)))], (10073 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _783179), _783181)))]], 10074 ^ _415872 : [(10075 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _783179), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (10077 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _783181), _783179)))]]], (10079 ^ _415872) ^ [_783713, _783715] : [-(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _783713, _783715) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 10080 ^ _415872 : [(10081 ^ _415872) ^ [] : [_783715 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (10083 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _783713)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _783713), _783715))], (10089 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _783713), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _783715), _783713))]]], (10097 ^ _415872) ^ [_784320, _784322, _784324, _784326] : [class_Divides_Osemiring__div(_784320), -(_784322 = c_Groups_Ozero__class_Ozero(_784320)), -(c_Divides_Odiv__class_Odiv(_784320, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_784320), _784324), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_784320), _784322), _784326)), _784322) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_784320), _784326), c_Divides_Odiv__class_Odiv(_784320, _784324, _784322)))], (10107 ^ _415872) ^ [_784736, _784738, _784740, _784742] : [class_Divides_Osemiring__div(_784736), -(_784738 = c_Groups_Ozero__class_Ozero(_784736)), -(c_Divides_Odiv__class_Odiv(_784736, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_784736), _784740), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_784736), _784742), _784738)), _784738) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_784736), _784742), c_Divides_Odiv__class_Odiv(_784736, _784740, _784738)))], (10117 ^ _415872) ^ [_785138, _785140, _785142] : [class_Divides_Osemiring__div(_785138), -(_785140 = c_Groups_Ozero__class_Ozero(_785138)), -(c_Divides_Odiv__class_Odiv(_785138, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_785138), _785142), _785140), _785140) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_785138), c_Divides_Odiv__class_Odiv(_785138, _785142, _785140)), c_Groups_Oone__class_Oone(_785138)))], (10127 ^ _415872) ^ [_785518, _785520, _785522] : [class_Divides_Osemiring__div(_785518), -(_785520 = c_Groups_Ozero__class_Ozero(_785518)), -(c_Divides_Odiv__class_Odiv(_785518, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_785518), _785520), _785522), _785520) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_785518), c_Divides_Odiv__class_Odiv(_785518, _785522, _785520)), c_Groups_Oone__class_Oone(_785518)))], (10183 ^ _415872) ^ [_787625, _787627, _787629] : [-(hBOOL(hAPP(_787625, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _787627, _787629)))), 10186 ^ _415872 : [(10187 ^ _415872) ^ [] : [-(_787629 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (10189 ^ _415872) ^ [] : [hBOOL(hAPP(_787625, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], 10192 ^ _415872 : [(10193 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _787629)))], (10197 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 10195 ^ [_787625, _787627, _787629])))], (10199 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, 10195 ^ [_787625, _787627, _787629]), _787629)))], (10201 ^ _415872) ^ [] : [-(_787627 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _787629), 10194 ^ [_787625, _787627, _787629])), 10195 ^ [_787625, _787627, _787629]))], (10203 ^ _415872) ^ [] : [hBOOL(hAPP(_787625, 10194 ^ [_787625, _787627, _787629]))]], 10204 ^ _415872 : [(10205 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _787629), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (10209 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _787629), 10207 ^ [_787625, _787627, _787629])))], (10211 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, 10207 ^ [_787625, _787627, _787629]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (10213 ^ _415872) ^ [] : [-(_787627 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _787629), 10206 ^ [_787625, _787627, _787629])), 10207 ^ [_787625, _787627, _787629]))], (10215 ^ _415872) ^ [] : [hBOOL(hAPP(_787625, 10206 ^ [_787625, _787627, _787629]))]]], (10137 ^ _415872) ^ [_785927, _785929, _785931] : [hBOOL(hAPP(_785927, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _785929, _785931))), 10140 ^ _415872 : [(10141 ^ _415872) ^ [] : [_785931 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_785927, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (10147 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _785931)), 10150 ^ _415872 : [(10151 ^ _415872) ^ [_786471] : [-(hBOOL(hAPP(_785927, _786471))), 10152 ^ _415872 : [(10153 ^ _415872) ^ [_786600] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _786600)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _786600), _785931)), _785929 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _785931), _786471)), _786600)]]]]], (10165 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _785931), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 10168 ^ _415872 : [(10169 ^ _415872) ^ [_787090] : [-(hBOOL(hAPP(_785927, _787090))), 10170 ^ _415872 : [(10171 ^ _415872) ^ [_787222] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _785931), _787222)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _787222), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _785929 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _785931), _787090)), _787222)]]]]]]], (10219 ^ _415872) ^ [_789352, _789354, _789356, _789358] : [_789352 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _789354), _789356)), _789358), -(_789354 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _789352, _789354) = _789356), 10226 ^ _415872 : [(10227 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _789354)))], (10229 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _789358)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _789358), _789354))]], 10234 ^ _415872 : [(10235 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _789354))], (10237 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _789354), _789358)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _789358), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (10249 ^ _415872) ^ [_790282, _790284] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), _790282), _790284) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(c_Complex_ORe, _790282)), hAPP(c_Complex_ORe, _790284)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(c_Complex_OIm, _790282)), hAPP(c_Complex_OIm, _790284))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(c_Complex_ORe, _790282)), hAPP(c_Complex_OIm, _790284))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(c_Complex_OIm, _790282)), hAPP(c_Complex_ORe, _790284)))))], (10251 ^ _415872) ^ [_790472, _790474, _790476] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _790472), _790474)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _790474), _790476)), 10259 ^ _415872 : [(10260 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 10258 ^ [_790472, _790474, _790476])))], (10262 ^ _415872) ^ [_790938] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _790474, _790938))), 10258 ^ [_790472, _790474, _790476])), 10265 ^ _415872 : [(10266 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _790472), _790938)))], (10268 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _790938), _790476)))]]]]], (10270 ^ _415872) ^ [_791317, _791319, _791321] : [-(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _791317, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _791319), _791321)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _791317, _791319), _791321))], (10272 ^ _415872) ^ [_791446, _791448] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _791446), _791448)), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _791446, _791448) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10278 ^ _415872) ^ [_791645] : [-(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _791645, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = _791645)], (10280 ^ _415872) ^ [_791741, _791743] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _791741, _791743)), _791741)))], (10282 ^ _415872) ^ [_791873, _791875, _791877] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _791873), _791875)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _791873, _791877)), c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _791875, _791877))))], (10288 ^ _415872) ^ [_792159, _792161, _792163] : [_792159 = 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), _792159), _792161), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _792159), _792163)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10294 ^ _415872) ^ [_792359, _792361, _792363] : [-(_792359 = 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), _792359), _792361), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _792359), _792363)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _792361, _792363))], (10300 ^ _415872) ^ [_792620, _792622] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat)), _792620)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _792622)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _792622, _792620)), _792622)))], (10310 ^ _415872) ^ [_792945, _792947] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _792945)), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _792947), _792945), _792945) = _792947)], (10316 ^ _415872) ^ [_793179, _793181] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _793179)), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _793179), _793181), _793179) = _793181)], (10322 ^ _415872) ^ [_793427, _793429, _793431] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _793427)), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _793427), _793429), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _793427), _793431)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _793429, _793431))], (10328 ^ _415872) ^ [_793701, _793703, _793705] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _793701)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _793701), _793703)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _793705, _793703)), c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _793705, _793701))))], (10338 ^ _415872) ^ [_794063, _794065, _794067, _794069] : [-(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, c_Complex_Ocomplex_OComplex(_794063, _794065), c_Complex_Ocomplex_OComplex(_794067, _794069)) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _794063, _794067), c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _794065, _794069)))], (10340 ^ _415872) ^ [_794168] : [-(c_Complex_Ocomplex_OComplex(hAPP(c_Complex_ORe, _794168), hAPP(c_Complex_OIm, _794168)) = _794168)], (10342 ^ _415872) ^ [_794341, _794343, _794345, _794347] : [c_Complex_Ocomplex_OComplex(_794341, _794343) = c_Complex_Ocomplex_OComplex(_794345, _794347), 10345 ^ _415872 : [(10346 ^ _415872) ^ [] : [-(_794341 = _794345)], (10348 ^ _415872) ^ [] : [-(_794343 = _794347)]]], (10350 ^ _415872) ^ [_794606, _794608, _794610, _794612] : [-(c_Complex_Ocomplex_OComplex(_794606, _794608) = c_Complex_Ocomplex_OComplex(_794610, _794612)), _794606 = _794610, _794608 = _794612], (10360 ^ _415872) ^ [_794924, _794926] : [-(hAPP(c_Complex_OIm, c_Complex_Ocomplex_OComplex(_794924, _794926)) = _794926)], (10362 ^ _415872) ^ [_795024, _795026] : [-(hAPP(c_Complex_ORe, c_Complex_Ocomplex_OComplex(_795024, _795026)) = _795024)], (10364 ^ _415872) ^ [_795152, _795154, _795156, _795158] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex), c_Complex_Ocomplex_OComplex(_795152, _795154)), c_Complex_Ocomplex_OComplex(_795156, _795158)) = c_Complex_Ocomplex_OComplex(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), _795152), _795156), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), _795154), _795158)))], (10366 ^ _415872) ^ [_795321, _795323] : [c_Complex_Ocomplex_OComplex(_795321, _795323) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), 10369 ^ _415872 : [(10370 ^ _415872) ^ [] : [-(_795321 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (10372 ^ _415872) ^ [] : [-(_795323 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))]]], (10374 ^ _415872) ^ [_795564, _795566] : [-(c_Complex_Ocomplex_OComplex(_795564, _795566) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), _795564 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _795566 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)], (10384 ^ _415872) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (10386 ^ _415872) ^ [_795953, _795955] : [c_Complex_Ocomplex_OComplex(_795953, _795955) = c_Complex_Oii, 10389 ^ _415872 : [(10390 ^ _415872) ^ [] : [-(_795953 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (10392 ^ _415872) ^ [] : [-(_795955 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))]]], (10394 ^ _415872) ^ [_796196, _796198] : [-(c_Complex_Ocomplex_OComplex(_796196, _796198) = c_Complex_Oii), _796196 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _796198 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)], (10404 ^ _415872) ^ [] : [-(c_Complex_Oii = c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (10406 ^ _415872) ^ [_796585, _796587] : [c_Complex_Ocomplex_OComplex(_796585, _796587) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), 10409 ^ _415872 : [(10410 ^ _415872) ^ [] : [-(_796585 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (10412 ^ _415872) ^ [] : [-(_796587 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))]]], (10414 ^ _415872) ^ [_796828, _796830] : [-(c_Complex_Ocomplex_OComplex(_796828, _796830) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), _796828 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _796830 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)], (10424 ^ _415872) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Groups_Oone__class_Oone(tc_RealDef_Oreal), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (10426 ^ _415872) ^ [_797159] : [-(c_Complex_Ocis(_797159) = c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(_797159), c_Transcendental_Osin(_797159)))], (10428 ^ _415872) ^ [_797275, _797277] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _797275)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _797277), _797275))), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _797277, _797275) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _797277, _797275), _797275)))], (10438 ^ _415872) ^ [_797619, _797621] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _797619)), 10441 ^ _415872 : [(10442 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _797621), _797619)), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _797621, _797619) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10448 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _797621), _797619))), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _797621, _797619) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _797621, _797619), _797619)))]]], (10478 ^ _415872) ^ [_798985, _798987, _798989] : [-(hBOOL(hAPP(_798985, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _798987, _798989)))), 10481 ^ _415872 : [(10482 ^ _415872) ^ [] : [-(_798989 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10484 ^ _415872) ^ [] : [hBOOL(hAPP(_798985, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 10485 ^ _415872 : [(10486 ^ _415872) ^ [] : [_798989 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10490 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, 10488 ^ [_798985, _798987, _798989]), _798989)))], (10492 ^ _415872) ^ [] : [-(_798987 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _798989), 10487 ^ [_798985, _798987, _798989])), 10488 ^ [_798985, _798987, _798989]))], (10494 ^ _415872) ^ [] : [hBOOL(hAPP(_798985, 10487 ^ [_798985, _798987, _798989]))]]], (10454 ^ _415872) ^ [_798188, _798190, _798192] : [hBOOL(hAPP(_798188, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _798190, _798192))), 10457 ^ _415872 : [(10458 ^ _415872) ^ [] : [_798192 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_798188, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (10464 ^ _415872) ^ [] : [-(_798192 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 10467 ^ _415872 : [(10468 ^ _415872) ^ [_798648, _798650] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _798648), _798192)), _798190 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _798192), _798650)), _798648), -(hBOOL(hAPP(_798188, _798650)))]]]]], (10498 ^ _415872) ^ [_799899, _799901, _799903, _799905] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Complex_Ocomplex_OComplex(_799899, _799901)), c_Complex_Ocomplex_OComplex(_799903, _799905)) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _799899), _799903), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _799901), _799905)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _799899), _799905)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _799901), _799903))))], (10500 ^ _415872) ^ [_800032] : [-(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(_800032), c_Transcendental_Osin(_800032))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (10502 ^ _415872) ^ [_800134, _800136] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex), _800134), _800136) = c_Complex_Ocomplex_OComplex(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), hAPP(c_Complex_ORe, _800134)), hAPP(c_Complex_ORe, _800136)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), hAPP(c_Complex_OIm, _800134)), hAPP(c_Complex_OIm, _800136))))], (10504 ^ _415872) ^ [_800319, _800321, _800323] : [hBOOL(hAPP(_800319, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _800321, _800323))), 10509 ^ _415872 : [(10510 ^ _415872) ^ [] : [-(_800323 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10512 ^ _415872) ^ [] : [-(hBOOL(hAPP(_800319, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]], 10514 ^ _415872 : [(10515 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _800323), 10513 ^ [_800319, _800321, _800323])), _800321)))], (10517 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _800321), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _800323), c_Nat_OSuc(10513 ^ [_800319, _800321, _800323])))))], (10519 ^ _415872) ^ [] : [-(hBOOL(hAPP(_800319, 10513 ^ [_800319, _800321, _800323])))]]], (10521 ^ _415872) ^ [_800998, _801000, _801002] : [-(hBOOL(hAPP(_800998, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _801000, _801002)))), 10522 ^ _415872 : [(10523 ^ _415872) ^ [] : [_801002 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hBOOL(hAPP(_800998, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10529 ^ _415872) ^ [_801300] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _801002), _801300)), _801000)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _801000), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _801002), c_Nat_OSuc(_801300)))), hBOOL(hAPP(_800998, _801300))]]], (10541 ^ _415872) ^ [_801753, _801755, _801757] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _801753)), 10544 ^ _415872 : [(10555 ^ _415872) ^ [] : [_801755 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _801757, _801753), 10558 ^ _415872 : [(10559 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _801753), _801755)), _801757)))], (10561 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _801757), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _801753), c_Nat_OSuc(_801755)))))]]], (10545 ^ _415872) ^ [] : [-(_801755 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _801757, _801753)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _801753), _801755)), _801757)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _801757), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _801753), c_Nat_OSuc(_801755))))]]], (10563 ^ _415872) ^ [_802481, _802483] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _802481)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _802481), _802483)), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _802483, _802481) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _802483, _802481), _802481)))], (10573 ^ _415872) ^ [_802807, _802809] : [-(c_Complex_Ocomplex_Ocomplex__size(c_Complex_Ocomplex_OComplex(_802807, _802809)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10575 ^ _415872) ^ [_802907] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _802907)), -(c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _802907))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (10581 ^ _415872) ^ [_803115] : [-(_803115 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _803115))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (10587 ^ _415872) ^ [_803322] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _803322), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), -(c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _803322))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (10593 ^ _415872) ^ [_803535, _803537] : [-(c_Nat_Osize__class_Osize(tc_Complex_Ocomplex, c_Complex_Ocomplex_OComplex(_803535, _803537)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10595 ^ _415872) ^ [_803663, _803665, _803667, _803669] : [-(c_Complex_Ocomplex_Ocomplex__rec(_803663, _803665, c_Complex_Ocomplex_OComplex(_803667, _803669)) = hAPP(hAPP(_803665, _803667), _803669))], (10597 ^ _415872) ^ [_803802, _803804, _803806, _803808] : [-(c_Complex_Ocomplex_Ocomplex__case(_803802, _803804, c_Complex_Ocomplex_OComplex(_803806, _803808)) = hAPP(hAPP(_803804, _803806), _803808))], (10599 ^ _415872) ^ [_803928, _803930] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _803928)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _803930)), -(c_RComplete_Onatfloor(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal), _803928), c_RealDef_Oreal(tc_Nat_Onat, _803930))) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, c_RComplete_Onatfloor(_803928), _803930))], (10609 ^ _415872) ^ [_804240] : [-(c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, _804240) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal), _804240), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _804240)))], (10611 ^ _415872) ^ [_804387, _804389, _804391, _804393] : [class_RealVector_Oreal__normed__field(_804387), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_804387), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_804387), _804389), _804391)), _804393) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_804387), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_804387), _804389), _804393)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_804387), _804391), _804393)))], (10617 ^ _415872) ^ [_804715, _804717, _804719, _804721] : [class_Rings_Odivision__ring(_804715), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_804715), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_804715), _804717), _804719)), _804721) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_804715), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_804715), _804717), _804721)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_804715), _804719), _804721)))], (10623 ^ _415872) ^ [_805015, _805017] : [class_Rings_Odivision__ring(_805015), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_805015), _805017), c_Groups_Oone__class_Oone(_805015)) = _805017)], (10629 ^ _415872) ^ [_805257, _805259, _805261] : [class_Rings_Odivision__ring(_805257), -(_805259 = c_Groups_Ozero__class_Ozero(_805257)), 10636 ^ _415872 : [(10637 ^ _415872) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_805257), _805261), _805259) = c_Groups_Oone__class_Oone(_805257), -(_805261 = _805259)], (10643 ^ _415872) ^ [] : [_805261 = _805259, -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_805257), _805261), _805259) = c_Groups_Oone__class_Oone(_805257))]]], (10649 ^ _415872) ^ [_805861, _805863] : [class_Rings_Odivision__ring(_805861), -(_805863 = c_Groups_Ozero__class_Ozero(_805861)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_805861), _805863), _805863) = c_Groups_Oone__class_Oone(_805861))], (10659 ^ _415872) ^ [_806185, _806187] : [class_Rings_Odivision__ring__inverse__zero(_806185), 10662 ^ _415872 : [(10663 ^ _415872) ^ [] : [_806187 = c_Groups_Ozero__class_Ozero(_806185), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_806185), _806187), _806187) = c_Groups_Ozero__class_Ozero(_806185))], (10669 ^ _415872) ^ [] : [-(_806187 = c_Groups_Ozero__class_Ozero(_806185)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_806185), _806187), _806187) = c_Groups_Oone__class_Oone(_806185))]]], (10675 ^ _415872) ^ [_806725, _806727, _806729, _806731] : [class_Fields_Ofield(_806725), -(_806727 = c_Groups_Ozero__class_Ozero(_806725)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_806725), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_806725), _806729), _806727)), _806731) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_806725), hAPP(hAPP(c_Power_Opower__class_Opower(_806725), _806729), _806731)), hAPP(hAPP(c_Power_Opower__class_Opower(_806725), _806727), _806731)))], (10685 ^ _415872) ^ [_807143, _807145, _807147] : [class_Fields_Ofield__inverse__zero(_807143), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_807143), c_Groups_Oone__class_Oone(_807143)), hAPP(hAPP(c_Power_Opower__class_Opower(_807143), _807145), _807147)) = hAPP(hAPP(c_Power_Opower__class_Opower(_807143), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_807143), c_Groups_Oone__class_Oone(_807143)), _807145)), _807147))], (10691 ^ _415872) ^ [_807443, _807445, _807447] : [class_RealVector_Oreal__normed__field(_807443), c_SEQ_Oconvergent(_807443, _807445), -(c_SEQ_Oconvergent(_807443, c_COMBC(tc_Nat_Onat, _807443, _807443, c_COMBB(_807443, tc_fun(_807443, _807443), tc_Nat_Onat, c_Rings_Oinverse__class_Odivide(_807443), _807445), _807447)))], (10701 ^ _415872) ^ [_807798, _807800, _807802] : [-(c_RealVector_Onorm__class_Onorm(_807798, hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_807798), _807800), _807802)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_807798, _807800)), c_RealVector_Onorm__class_Onorm(_807798, _807802))), class_Fields_Ofield__inverse__zero(_807798), class_RealVector_Oreal__normed__field(_807798)], (10711 ^ _415872) ^ [_808177, _808179, _808181, _808183] : [class_Rings_Odivision__ring(_808177), -(_808179 = c_Groups_Ozero__class_Ozero(_808177)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_808177), _808181), _808179) = _808183, -(_808181 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_808177), _808183), _808179))], (10725 ^ _415872) ^ [_808658, _808660, _808662, _808664] : [class_Rings_Odivision__ring(_808658), -(_808660 = c_Groups_Ozero__class_Ozero(_808658)), _808662 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_808658), _808664), _808660), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_808658), _808662), _808660) = _808664)], (10739 ^ _415872) ^ [_809139, _809141, _809143, _809145] : [class_Rings_Odivision__ring(_809139), -(_809141 = c_Groups_Ozero__class_Ozero(_809139)), 10746 ^ _415872 : [(10747 ^ _415872) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_809139), _809143), _809141) = _809145, -(_809143 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_809139), _809145), _809141))], (10753 ^ _415872) ^ [] : [_809143 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_809139), _809145), _809141), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_809139), _809143), _809141) = _809145)]]], (10759 ^ _415872) ^ [_809809, _809811, _809813, _809815] : [class_Rings_Odivision__ring(_809809), -(_809811 = c_Groups_Ozero__class_Ozero(_809809)), 10766 ^ _415872 : [(10767 ^ _415872) ^ [] : [_809813 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_809809), _809815), _809811), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_809809), _809813), _809811) = _809815)], (10773 ^ _415872) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_809809), _809813), _809811) = _809815, -(_809813 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_809809), _809815), _809811))]]], (10779 ^ _415872) ^ [_810465, _810467, _810469] : [class_RealVector_Oreal__normed__field(_810465), -(_810467 = c_Groups_Ozero__class_Ozero(_810465)), -(c_RealVector_Onorm__class_Onorm(_810465, hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_810465), _810469), _810467)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_810465, _810469)), c_RealVector_Onorm__class_Onorm(_810465, _810467)))], (10789 ^ _415872) ^ [_810825, _810827] : [class_RealVector_Oreal__normed__field(_810825), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_810825), c_Groups_Ozero__class_Ozero(_810825)), _810827) = c_Groups_Ozero__class_Ozero(_810825))], (10795 ^ _415872) ^ [_811057, _811059] : [class_Rings_Odivision__ring(_811057), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_811057), c_Groups_Ozero__class_Ozero(_811057)), _811059) = c_Groups_Ozero__class_Ozero(_811057))], (10801 ^ _415872) ^ [_811289, _811291] : [class_Rings_Odivision__ring__inverse__zero(_811289), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_811289), _811291), c_Groups_Ozero__class_Ozero(_811289)) = c_Groups_Ozero__class_Ozero(_811289))], (10807 ^ _415872) ^ [_811549, _811551, _811553, _811555] : [class_Rings_Odivision__ring(_811549), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_811549), _811551), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_811549), _811553), _811555)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_811549), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_811549), _811551), _811553)), _811555))], (10813 ^ _415872) ^ [_811818, _811820] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _811818), _811820)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _811818), _811818)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal), _811820), _811818))], (10815 ^ _415872) ^ [_811979, _811981, _811983, _811985] : [class_Fields_Ofield__inverse__zero(_811979), -(hAPP(hAPP(c_Power_Opower__class_Opower(_811979), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_811979), _811981), _811983)), _811985) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_811979), hAPP(hAPP(c_Power_Opower__class_Opower(_811979), _811981), _811985)), hAPP(hAPP(c_Power_Opower__class_Opower(_811979), _811983), _811985)))], (10837 ^ _415872) ^ [_812769, _812771] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal), _812769), _812771)))), 10840 ^ _415872 : [(10841 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _812769), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (10843 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _812771))]], 10844 ^ _415872 : [(10845 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _812769))], (10847 ^ _415872) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _812771), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))]]], (10821 ^ _415872) ^ [_812308, _812310] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal), _812308), _812310))), 10824 ^ _415872 : [(10825 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _812308), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _812310)))], (10831 ^ _415872) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _812308))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _812310), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))]]], (10851 ^ _415872) ^ [_813233] : [-(hAPP(c_Complex_OIm, c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex, _813233)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal), hAPP(c_Complex_OIm, _813233)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _813233)))], (10853 ^ _415872) ^ [_813329] : [-(hAPP(c_Complex_ORe, c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex, _813329)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal), hAPP(c_Complex_ORe, _813329)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _813329)))], (10855 ^ _415872) ^ [_813482, _813484, _813486, _813488] : [class_RealVector_Oreal__normed__field(_813482), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_813482), c_Groups_Ominus__class_Ominus(_813482, _813484, _813486)), _813488) = c_Groups_Ominus__class_Ominus(_813482, hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_813482), _813484), _813488), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_813482), _813486), _813488)))], (10861 ^ _415872) ^ [_813794, _813796, _813798, _813800] : [class_Rings_Odivision__ring(_813794), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_813794), c_Groups_Ominus__class_Ominus(_813794, _813796, _813798)), _813800) = c_Groups_Ominus__class_Ominus(_813794, hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_813794), _813796), _813800), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_813794), _813798), _813800)))], (10867 ^ _415872) ^ [_814134, _814136, _814138, _814140, _814142, _814144] : [class_RealVector_Oreal__field(_814134), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_814134), c_Groups_Ominus__class_Ominus(_814134, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_814134), _814136), _814138), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_814134), _814140), _814142))), _814144) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_814134), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_814134), _814136), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_814134), c_Groups_Ominus__class_Ominus(_814134, _814138, _814142)), _814144))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_814134), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_814134), c_Groups_Ominus__class_Ominus(_814134, _814136, _814140)), _814144)), _814142)))], (10873 ^ _415872) ^ [_814517, _814519, _814521] : [-(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, hAPP(_814517, _814519), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal), c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, hAPP(_814517, _814521), hAPP(_814517, _814519))), c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _814521, _814519))), _814519)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, hAPP(_814517, _814521), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal), c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, hAPP(_814517, _814521), hAPP(_814517, _814519))), c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _814521, _814519))), _814521)))], (10875 ^ _415872) ^ [_814679, _814681] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _814679, _814681))), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _814679)), c_RealDef_Oreal(tc_Nat_Onat, _814681)))))], (10877 ^ _415872) ^ [_814840, _814842, _814844, _814846] : [class_Fields_Ofield(_814840), -(_814842 = c_Groups_Ozero__class_Ozero(_814840)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _814844), _814846)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_814840), _814842), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _814846, _814844)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_814840), hAPP(hAPP(c_Power_Opower__class_Opower(_814840), _814842), _814846)), hAPP(hAPP(c_Power_Opower__class_Opower(_814840), _814842), _814844)))], (10891 ^ _415872) ^ [_815343, _815345] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _815343)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _815345)), -(c_Transcendental_Oln(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal), _815343), _815345)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_Transcendental_Oln(_815343), c_Transcendental_Oln(_815345)))], (10901 ^ _415872) ^ [_815667, _815669] : [-(hBOOL(hAPP(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, hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _815667)), c_RealDef_Oreal(tc_Nat_Onat, _815669)), c_RealDef_Oreal(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _815667, _815669))))))], (10903 ^ _415872) ^ [_815786, _815788] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _815786)), c_RealDef_Oreal(tc_Nat_Onat, _815788)), c_RealDef_Oreal(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _815786, _815788)))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))], (10905 ^ _415872) ^ [_815951, _815953, _815955, _815957] : [class_Fields_Olinordered__field__inverse__zero(_815951), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_815951, _815953), _815955)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_815951, _815957), c_Groups_Ozero__class_Ozero(_815951))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_815951, c_Groups_Ozero__class_Ozero(_815951)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_815951), _815953), _815955))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_815951, hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_815951), _815957), _815953)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_815951), _815957), _815955))))], (10923 ^ _415872) ^ [_816586, _816588, _816590, _816592] : [class_Fields_Olinordered__field(_816586), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_816586, _816588), _816590)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_816586, c_Groups_Ozero__class_Ozero(_816586)), _816592)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_816586, c_Groups_Ozero__class_Ozero(_816586)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_816586), _816590), _816588))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_816586, hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_816586), _816592), _816590)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_816586), _816592), _816588))))], (10941 ^ _415872) ^ [_817178, _817180] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex), c_Complex_Ocis(_817178)), c_Complex_Ocis(_817180)) = c_Complex_Ocis(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _817178, _817180)))], (10943 ^ _415872) ^ [_817289] : [class_Rings_Oidom(_817289), -(class_Rings_Oidom(tc_Polynomial_Opoly(_817289)))], (10949 ^ _415872) ^ [_817479] : [class_Groups_Ocancel__comm__monoid__add(_817479), -(class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(_817479)))], (10955 ^ _415872) ^ [_817669] : [class_Rings_Ocomm__semiring__0(_817669), -(class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(_817669)))], (10961 ^ _415872) ^ [_817859] : [class_Rings_Ocomm__ring(_817859), -(class_Rings_Ocomm__ring(tc_Polynomial_Opoly(_817859)))], (10967 ^ _415872) ^ [] : [-(class_Rings_Oidom(tc_Complex_Ocomplex))], (10969 ^ _415872) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex))], (10971 ^ _415872) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex))], (10973 ^ _415872) ^ [] : [-(class_Rings_Ocomm__ring(tc_Complex_Ocomplex))], (10975 ^ _415872) ^ [] : [-(class_Rings_Oidom(tc_RealDef_Oreal))], (10977 ^ _415872) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal))], (10979 ^ _415872) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal))], (10981 ^ _415872) ^ [] : [-(class_Rings_Ocomm__ring(tc_RealDef_Oreal))], (10983 ^ _415872) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat))], (10985 ^ _415872) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Nat_Onat))], (10987 ^ _415872) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (10989 ^ _415872) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint))], (10991 ^ _415872) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Int_Oint))], (10993 ^ _415872) ^ [] : [-(class_Rings_Ocomm__ring(tc_Int_Oint))], (10995 ^ _415872) ^ [_818805, _818807] : [class_Orderings_Opreorder(_818805), -(class_Orderings_Opreorder(tc_fun(_818807, _818805)))], (11001 ^ _415872) ^ [_819017, _819019] : [class_Orderings_Oorder(_819017), -(class_Orderings_Oorder(tc_fun(_819019, _819017)))], (11007 ^ _415872) ^ [_819229, _819231] : [class_Orderings_Oord(_819229), -(class_Orderings_Oord(tc_fun(_819231, _819229)))], (11013 ^ _415872) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (11015 ^ _415872) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (11017 ^ _415872) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (11019 ^ _415872) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (11021 ^ _415872) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (11023 ^ _415872) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (11025 ^ _415872) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (11027 ^ _415872) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))], (11029 ^ _415872) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (11031 ^ _415872) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (11033 ^ _415872) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (11035 ^ _415872) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (11037 ^ _415872) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (11039 ^ _415872) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (11041 ^ _415872) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (11043 ^ _415872) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (11045 ^ _415872) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (11047 ^ _415872) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (11049 ^ _415872) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (11051 ^ _415872) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (11053 ^ _415872) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (11055 ^ _415872) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (11057 ^ _415872) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (11059 ^ _415872) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (11061 ^ _415872) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (11063 ^ _415872) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_Int_Oint))], (11065 ^ _415872) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (11067 ^ _415872) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (11069 ^ _415872) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (11071 ^ _415872) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (11073 ^ _415872) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (11075 ^ _415872) ^ [] : [-(class_Divides_Osemiring__div(tc_Int_Oint))], (11077 ^ _415872) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (11079 ^ _415872) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (11081 ^ _415872) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (11083 ^ _415872) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (11085 ^ _415872) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (11087 ^ _415872) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (11089 ^ _415872) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (11091 ^ _415872) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (11093 ^ _415872) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (11095 ^ _415872) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (11097 ^ _415872) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (11099 ^ _415872) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (11101 ^ _415872) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (11103 ^ _415872) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (11105 ^ _415872) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (11107 ^ _415872) ^ [] : [-(class_Groups_Osgn__if(tc_Int_Oint))], (11109 ^ _415872) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (11111 ^ _415872) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (11113 ^ _415872) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (11115 ^ _415872) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (11117 ^ _415872) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (11119 ^ _415872) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (11121 ^ _415872) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (11123 ^ _415872) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (11125 ^ _415872) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (11127 ^ _415872) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (11129 ^ _415872) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (11131 ^ _415872) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (11133 ^ _415872) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (11135 ^ _415872) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (11137 ^ _415872) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (11139 ^ _415872) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (11141 ^ _415872) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (11143 ^ _415872) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (11145 ^ _415872) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (11147 ^ _415872) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (11149 ^ _415872) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (11151 ^ _415872) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (11153 ^ _415872) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (11155 ^ _415872) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (11157 ^ _415872) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (11159 ^ _415872) ^ [] : [-(class_Divides_Osemiring__div(tc_Nat_Onat))], (11161 ^ _415872) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (11163 ^ _415872) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (11165 ^ _415872) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (11167 ^ _415872) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (11169 ^ _415872) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (11171 ^ _415872) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (11173 ^ _415872) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (11175 ^ _415872) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (11177 ^ _415872) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (11179 ^ _415872) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (11181 ^ _415872) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (11183 ^ _415872) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (11185 ^ _415872) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (11187 ^ _415872) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (11189 ^ _415872) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (11191 ^ _415872) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (11193 ^ _415872) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (11195 ^ _415872) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal))], (11197 ^ _415872) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal))], (11199 ^ _415872) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal))], (11201 ^ _415872) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal))], (11203 ^ _415872) ^ [] : [-(class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal))], (11205 ^ _415872) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal))], (11207 ^ _415872) ^ [] : [-(class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal))], (11209 ^ _415872) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal))], (11211 ^ _415872) ^ [] : [-(class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal))], (11213 ^ _415872) ^ [] : [-(class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal))], (11215 ^ _415872) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal))], (11217 ^ _415872) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal))], (11219 ^ _415872) ^ [] : [-(class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal))], (11221 ^ _415872) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal))], (11223 ^ _415872) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal))], (11225 ^ _415872) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal))], (11227 ^ _415872) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal))], (11229 ^ _415872) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal))], (11231 ^ _415872) ^ [] : [-(class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal))], (11233 ^ _415872) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal))], (11235 ^ _415872) ^ [] : [-(class_RealVector_Oreal__normed__field(tc_RealDef_Oreal))], (11237 ^ _415872) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal))], (11239 ^ _415872) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal))], (11241 ^ _415872) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal))], (11243 ^ _415872) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal))], (11245 ^ _415872) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal))], (11247 ^ _415872) ^ [] : [-(class_Rings_Olinordered__semiring(tc_RealDef_Oreal))], (11249 ^ _415872) ^ [] : [-(class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal))], (11251 ^ _415872) ^ [] : [-(class_Rings_Olinordered__semidom(tc_RealDef_Oreal))], (11253 ^ _415872) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal))], (11255 ^ _415872) ^ [] : [-(class_RealVector_Ometric__space(tc_RealDef_Oreal))], (11257 ^ _415872) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal))], (11259 ^ _415872) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_RealDef_Oreal))], (11261 ^ _415872) ^ [] : [-(class_Fields_Olinordered__field(tc_RealDef_Oreal))], (11263 ^ _415872) ^ [] : [-(class_Rings_Oordered__semiring(tc_RealDef_Oreal))], (11265 ^ _415872) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_RealDef_Oreal))], (11267 ^ _415872) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_RealDef_Oreal))], (11269 ^ _415872) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal))], (11271 ^ _415872) ^ [] : [-(class_Rings_Olinordered__ring(tc_RealDef_Oreal))], (11273 ^ _415872) ^ [] : [-(class_Rings_Olinordered__idom(tc_RealDef_Oreal))], (11275 ^ _415872) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal))], (11277 ^ _415872) ^ [] : [-(class_RealVector_Oreal__field(tc_RealDef_Oreal))], (11279 ^ _415872) ^ [] : [-(class_Rings_Odivision__ring(tc_RealDef_Oreal))], (11281 ^ _415872) ^ [] : [-(class_Rings_Ocomm__semiring(tc_RealDef_Oreal))], (11283 ^ _415872) ^ [] : [-(class_Groups_Oab__group__add(tc_RealDef_Oreal))], (11285 ^ _415872) ^ [] : [-(class_Rings_Ozero__neq__one(tc_RealDef_Oreal))], (11287 ^ _415872) ^ [] : [-(class_Rings_Oordered__ring(tc_RealDef_Oreal))], (11289 ^ _415872) ^ [] : [-(class_Orderings_Opreorder(tc_RealDef_Oreal))], (11291 ^ _415872) ^ [] : [-(class_Orderings_Olinorder(tc_RealDef_Oreal))], (11293 ^ _415872) ^ [] : [-(class_Groups_Omonoid__mult(tc_RealDef_Oreal))], (11295 ^ _415872) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_RealDef_Oreal))], (11297 ^ _415872) ^ [] : [-(class_Groups_Omonoid__add(tc_RealDef_Oreal))], (11299 ^ _415872) ^ [] : [-(class_Rings_Osemiring__0(tc_RealDef_Oreal))], (11301 ^ _415872) ^ [] : [-(class_Groups_Ogroup__add(tc_RealDef_Oreal))], (11303 ^ _415872) ^ [] : [-(class_Rings_Omult__zero(tc_RealDef_Oreal))], (11305 ^ _415872) ^ [] : [-(class_Orderings_Oorder(tc_RealDef_Oreal))], (11307 ^ _415872) ^ [] : [-(class_Rings_Osemiring(tc_RealDef_Oreal))], (11309 ^ _415872) ^ [] : [-(class_Orderings_Oord(tc_RealDef_Oreal))], (11311 ^ _415872) ^ [] : [-(class_Groups_Osgn__if(tc_RealDef_Oreal))], (11313 ^ _415872) ^ [] : [-(class_Rings_Oring__1(tc_RealDef_Oreal))], (11315 ^ _415872) ^ [] : [-(class_Fields_Ofield(tc_RealDef_Oreal))], (11317 ^ _415872) ^ [] : [-(class_Power_Opower(tc_RealDef_Oreal))], (11319 ^ _415872) ^ [] : [-(class_Groups_Ozero(tc_RealDef_Oreal))], (11321 ^ _415872) ^ [] : [-(class_Rings_Oring(tc_RealDef_Oreal))], (11323 ^ _415872) ^ [] : [-(class_Groups_Oone(tc_RealDef_Oreal))], (11325 ^ _415872) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex))], (11327 ^ _415872) ^ [] : [-(class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex))], (11329 ^ _415872) ^ [] : [-(class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex))], (11331 ^ _415872) ^ [] : [-(class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex))], (11333 ^ _415872) ^ [] : [-(class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex))], (11335 ^ _415872) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex))], (11337 ^ _415872) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex))], (11339 ^ _415872) ^ [] : [-(class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex))], (11341 ^ _415872) ^ [] : [-(class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex))], (11343 ^ _415872) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex))], (11345 ^ _415872) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex))], (11347 ^ _415872) ^ [] : [-(class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex))], (11349 ^ _415872) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex))], (11351 ^ _415872) ^ [] : [-(class_RealVector_Ometric__space(tc_Complex_Ocomplex))], (11353 ^ _415872) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex))], (11355 ^ _415872) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex))], (11357 ^ _415872) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex))], (11359 ^ _415872) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex))], (11361 ^ _415872) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex))], (11363 ^ _415872) ^ [] : [-(class_RealVector_Oreal__field(tc_Complex_Ocomplex))], (11365 ^ _415872) ^ [] : [-(class_Rings_Odivision__ring(tc_Complex_Ocomplex))], (11367 ^ _415872) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Complex_Ocomplex))], (11369 ^ _415872) ^ [] : [-(class_Groups_Oab__group__add(tc_Complex_Ocomplex))], (11371 ^ _415872) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Complex_Ocomplex))], (11373 ^ _415872) ^ [] : [-(class_Groups_Omonoid__mult(tc_Complex_Ocomplex))], (11375 ^ _415872) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex))], (11377 ^ _415872) ^ [] : [-(class_Groups_Omonoid__add(tc_Complex_Ocomplex))], (11379 ^ _415872) ^ [] : [-(class_Rings_Osemiring__0(tc_Complex_Ocomplex))], (11381 ^ _415872) ^ [] : [-(class_Groups_Ogroup__add(tc_Complex_Ocomplex))], (11383 ^ _415872) ^ [] : [-(class_Rings_Omult__zero(tc_Complex_Ocomplex))], (11385 ^ _415872) ^ [] : [-(class_Rings_Osemiring(tc_Complex_Ocomplex))], (11387 ^ _415872) ^ [] : [-(class_Rings_Oring__1(tc_Complex_Ocomplex))], (11389 ^ _415872) ^ [] : [-(class_Fields_Ofield(tc_Complex_Ocomplex))], (11391 ^ _415872) ^ [] : [-(class_Power_Opower(tc_Complex_Ocomplex))], (11393 ^ _415872) ^ [] : [-(class_Groups_Ozero(tc_Complex_Ocomplex))], (11395 ^ _415872) ^ [] : [-(class_Rings_Oring(tc_Complex_Ocomplex))], (11397 ^ _415872) ^ [] : [-(class_Groups_Oone(tc_Complex_Ocomplex))], (11399 ^ _415872) ^ [_829656] : [class_Rings_Oidom(_829656), -(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(_829656)))], (11405 ^ _415872) ^ [_829846] : [class_Rings_Olinordered__idom(_829846), -(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(_829846)))], (11411 ^ _415872) ^ [_830036] : [class_Rings_Olinordered__idom(_830036), -(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(_830036)))], (11417 ^ _415872) ^ [_830226] : [class_Rings_Olinordered__idom(_830226), -(class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(_830226)))], (11423 ^ _415872) ^ [_830416] : [class_Rings_Olinordered__idom(_830416), -(class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(_830416)))], (11429 ^ _415872) ^ [_830606] : [class_Rings_Olinordered__idom(_830606), -(class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(_830606)))], (11435 ^ _415872) ^ [_830796] : [class_Rings_Olinordered__idom(_830796), -(class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(_830796)))], (11441 ^ _415872) ^ [_830986] : [class_Rings_Olinordered__idom(_830986), -(class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(_830986)))], (11447 ^ _415872) ^ [_831176] : [class_Rings_Olinordered__idom(_831176), -(class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(_831176)))], (11453 ^ _415872) ^ [_831366] : [class_Rings_Olinordered__idom(_831366), -(class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(_831366)))], (11459 ^ _415872) ^ [_831556] : [class_Groups_Ocancel__comm__monoid__add(_831556), -(class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(_831556)))], (11465 ^ _415872) ^ [_831746] : [class_Rings_Oidom(_831746), -(class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(_831746)))], (11471 ^ _415872) ^ [_831936] : [class_Rings_Olinordered__idom(_831936), -(class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(_831936)))], (11477 ^ _415872) ^ [_832126] : [class_Rings_Olinordered__idom(_832126), -(class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(_832126)))], (11483 ^ _415872) ^ [_832316] : [class_Rings_Oidom(_832316), -(class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(_832316)))], (11489 ^ _415872) ^ [_832506] : [class_Rings_Olinordered__idom(_832506), -(class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(_832506)))], (11495 ^ _415872) ^ [_832696] : [class_Rings_Olinordered__idom(_832696), -(class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(_832696)))], (11501 ^ _415872) ^ [_832886] : [class_Rings_Olinordered__idom(_832886), -(class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(_832886)))], (11507 ^ _415872) ^ [_833076] : [class_Groups_Ocancel__comm__monoid__add(_833076), -(class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(_833076)))], (11513 ^ _415872) ^ [_833266] : [class_Rings_Olinordered__idom(_833266), -(class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(_833266)))], (11519 ^ _415872) ^ [_833456] : [class_Rings_Olinordered__idom(_833456), -(class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(_833456)))], (11525 ^ _415872) ^ [_833646] : [class_Rings_Ocomm__semiring__0(_833646), -(class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(_833646)))], (11531 ^ _415872) ^ [_833836] : [class_Rings_Ocomm__semiring__1(_833836), -(class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(_833836)))], (11537 ^ _415872) ^ [_834026] : [class_Groups_Ocomm__monoid__add(_834026), -(class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(_834026)))], (11543 ^ _415872) ^ [_834216] : [class_Rings_Olinordered__idom(_834216), -(class_Rings_Oordered__semiring(tc_Polynomial_Opoly(_834216)))], (11549 ^ _415872) ^ [_834406] : [class_Rings_Olinordered__idom(_834406), -(class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(_834406)))], (11555 ^ _415872) ^ [_834596] : [class_Rings_Oidom(_834596), -(class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(_834596)))], (11561 ^ _415872) ^ [_834786] : [class_Groups_Ocomm__monoid__add(_834786), -(class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(_834786)))], (11567 ^ _415872) ^ [_834976] : [class_Rings_Olinordered__idom(_834976), -(class_Rings_Olinordered__ring(tc_Polynomial_Opoly(_834976)))], (11573 ^ _415872) ^ [_835166] : [class_Rings_Olinordered__idom(_835166), -(class_Rings_Olinordered__idom(tc_Polynomial_Opoly(_835166)))], (11579 ^ _415872) ^ [_835356] : [class_Rings_Ocomm__semiring__1(_835356), -(class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(_835356)))], (11585 ^ _415872) ^ [_835546] : [class_Fields_Ofield(_835546), -(class_Divides_Osemiring__div(tc_Polynomial_Opoly(_835546)))], (11591 ^ _415872) ^ [_835736] : [class_Rings_Ocomm__semiring__0(_835736), -(class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(_835736)))], (11597 ^ _415872) ^ [_835926] : [class_Groups_Oab__group__add(_835926), -(class_Groups_Oab__group__add(tc_Polynomial_Opoly(_835926)))], (11603 ^ _415872) ^ [_836116] : [class_Rings_Ocomm__semiring__1(_836116), -(class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(_836116)))], (11609 ^ _415872) ^ [_836306] : [class_Rings_Olinordered__idom(_836306), -(class_Rings_Oordered__ring(tc_Polynomial_Opoly(_836306)))], (11615 ^ _415872) ^ [_836496] : [class_Rings_Olinordered__idom(_836496), -(class_Orderings_Opreorder(tc_Polynomial_Opoly(_836496)))], (11621 ^ _415872) ^ [_836686] : [class_Rings_Olinordered__idom(_836686), -(class_Orderings_Olinorder(tc_Polynomial_Opoly(_836686)))], (11627 ^ _415872) ^ [_836876] : [class_Rings_Ocomm__semiring__1(_836876), -(class_Groups_Omonoid__mult(tc_Polynomial_Opoly(_836876)))], (11633 ^ _415872) ^ [_837066] : [class_Rings_Ocomm__ring__1(_837066), -(class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(_837066)))], (11639 ^ _415872) ^ [_837256] : [class_Groups_Ocomm__monoid__add(_837256), -(class_Groups_Omonoid__add(tc_Polynomial_Opoly(_837256)))], (11645 ^ _415872) ^ [_837446] : [class_Rings_Ocomm__semiring__0(_837446), -(class_Rings_Osemiring__0(tc_Polynomial_Opoly(_837446)))], (11651 ^ _415872) ^ [_837636] : [class_Groups_Oab__group__add(_837636), -(class_Groups_Ogroup__add(tc_Polynomial_Opoly(_837636)))], (11657 ^ _415872) ^ [_837826] : [class_Rings_Ocomm__semiring__0(_837826), -(class_Rings_Omult__zero(tc_Polynomial_Opoly(_837826)))], (11663 ^ _415872) ^ [_838016] : [class_Rings_Olinordered__idom(_838016), -(class_Orderings_Oorder(tc_Polynomial_Opoly(_838016)))], (11669 ^ _415872) ^ [_838206] : [class_Rings_Ocomm__semiring__0(_838206), -(class_Rings_Osemiring(tc_Polynomial_Opoly(_838206)))], (11675 ^ _415872) ^ [_838396] : [class_Rings_Olinordered__idom(_838396), -(class_Orderings_Oord(tc_Polynomial_Opoly(_838396)))], (11681 ^ _415872) ^ [_838586] : [class_Rings_Olinordered__idom(_838586), -(class_Groups_Osgn__if(tc_Polynomial_Opoly(_838586)))], (11687 ^ _415872) ^ [_838776] : [class_Rings_Ocomm__ring__1(_838776), -(class_Rings_Oring__1(tc_Polynomial_Opoly(_838776)))], (11693 ^ _415872) ^ [_838966] : [class_Rings_Ocomm__semiring__1(_838966), -(class_Power_Opower(tc_Polynomial_Opoly(_838966)))], (11699 ^ _415872) ^ [_839156] : [class_Groups_Ozero(_839156), -(class_Groups_Ozero(tc_Polynomial_Opoly(_839156)))], (11705 ^ _415872) ^ [_839346] : [class_Rings_Ocomm__ring(_839346), -(class_Rings_Oring(tc_Polynomial_Opoly(_839346)))], (11717 ^ _415872) ^ [_839753, _839755, _839757, _839759] : [-(hAPP(c_COMBK(_839753, _839755, _839757), _839759) = _839757)], (11719 ^ _415872) ^ [_839914, _839916, _839918, _839920, _839922, _839924] : [-(hAPP(c_COMBB(_839914, _839916, _839918, _839920, _839922), _839924) = hAPP(_839920, hAPP(_839922, _839924)))], (11721 ^ _415872) ^ [_840087, _840089, _840091, _840093, _840095, _840097] : [-(hAPP(c_COMBC(_840087, _840089, _840091, _840093, _840095), _840097) = hAPP(hAPP(_840093, _840097), _840095))], (11723 ^ _415872) ^ [_840240, _840242, _840244, _840246, _840248, _840250] : [-(hAPP(c_COMBS(_840240, _840242, _840244, _840246, _840248), _840250) = hAPP(hAPP(_840246, _840250), hAPP(_840248, _840250)))], (11711 ^ _415872) ^ [_839536] : [class_Rings_Ocomm__semiring__1(_839536), -(class_Groups_Oone(tc_Polynomial_Opoly(_839536)))]], input).
% 4.58/5.53 ncf('1',plain,[hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), v_r), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, hAPP(c_Complex_OIm, hAPP(v_s, hAPP(v_f____, hAPP(v_ga____, 11728 ^ [])))))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), v_r), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))],start(11725 ^ 0)).
% 4.58/5.53 ncf('1.1',plain,[-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), v_r), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))), class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), v_r)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))],extension(1239 ^ 1,bind([[_456636, _456638, _456640], [tc_RealDef_Oreal, v_r, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)]]))).
% 4.58/5.53 ncf('1.1.1',plain,[-(class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal))],extension(11221 ^ 2)).
% 4.58/5.53 ncf('1.1.2',plain,[-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), v_r)))],extension(1205 ^ 2)).
% 4.58/5.53 ncf('1.1.3',plain,[-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))), class_Rings_Olinordered__semidom(tc_RealDef_Oreal)],extension(2039 ^ 2,bind([[_484918], [tc_RealDef_Oreal]]))).
% 4.58/5.53 ncf('1.1.3.1',plain,[-(class_Rings_Olinordered__semidom(tc_RealDef_Oreal))],extension(11251 ^ 3)).
% 4.58/5.53 ncf('1.2',plain,[-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, hAPP(c_Complex_OIm, hAPP(v_s, hAPP(v_f____, hAPP(v_ga____, 11728 ^ [])))))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), v_r), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))))],extension(1209 ^ 1,bind([[_455484], [hAPP(v_f____, hAPP(v_ga____, 11728 ^ []))]]))).
% 4.58/5.53 %-----------------------------------------------------
% 4.58/5.53 End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------