%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWW225+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n029.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 12:25:47 EDT 2023

% Result   : Theorem 5.91s 6.57s
% Output   : Proof 5.91s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWW225+1 : TPTP v8.1.2. Released v5.2.0.
% 0.03/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n029.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 22:29:58 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 5.91/6.57  
% 5.91/6.57  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 5.91/6.57  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.91/6.57  %-----------------------------------------------------
% 5.91/6.57  ncf(matrix, plain, [(11954 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____))), hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Nat_OSuc(hAPP(v_f____, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____)))))], (802 ^ _543626) ^ [_568254, _568256, _568258, _568260, _568262, _568264, _568266, _568268] : [-(c_Nat_Osemiring__1__class_Oof__nat__aux(_568268, _568264, _568260, _568256) = c_Nat_Osemiring__1__class_Oof__nat__aux(_568266, _568262, _568258, _568254)), _568268 = _568266, _568264 = _568262, _568260 = _568258, _568256 = _568254], (820 ^ _543626) ^ [_568887, _568889, _568891, _568893] : [-(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_568893, _568889) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_568891, _568887)), _568893 = _568891, _568889 = _568887], (830 ^ _543626) ^ [_569218, _569220] : [_569220 = _569218, -(v_g____(_569220) = v_g____(_569218))], (836 ^ _543626) ^ [_569436, _569438] : [_569438 = _569436, -(c_RComplete_Onatceiling(_569438) = c_RComplete_Onatceiling(_569436))], (842 ^ _543626) ^ [_569654, _569656] : [_569656 = _569654, -(c_Int_Osucc(_569656) = c_Int_Osucc(_569654))], (848 ^ _543626) ^ [_569872, _569874] : [_569874 = _569872, -(c_Int_Opred(_569874) = c_Int_Opred(_569872))], (854 ^ _543626) ^ [_570118, _570120, _570122, _570124] : [-(c_Nat__Transfer_Otsub(_570124, _570120) = c_Nat__Transfer_Otsub(_570122, _570118)), _570124 = _570122, _570120 = _570118], (864 ^ _543626) ^ [_570449, _570451] : [_570451 = _570449, -(c_Complex_Oexpi(_570451) = c_Complex_Oexpi(_570449))], (870 ^ _543626) ^ [_570695, _570697, _570699, _570701] : [-(c_Int_Onumber__class_Onumber__of(_570701, _570697) = c_Int_Onumber__class_Onumber__of(_570699, _570695)), _570701 = _570699, _570697 = _570695], (880 ^ _543626) ^ [_571082, _571084, _571086, _571088, _571090, _571092] : [-(c_Power_Opower_Opower(_571092, _571088, _571084) = c_Power_Opower_Opower(_571090, _571086, _571082)), _571092 = _571090, _571088 = _571086, _571084 = _571082], (894 ^ _543626) ^ [_571542, _571544] : [_571544 = _571542, -(c_Nat_Osemiring__1__class_Oof__nat(_571544) = c_Nat_Osemiring__1__class_Oof__nat(_571542))], (900 ^ _543626) ^ [_571788, _571790, _571792, _571794] : [-(c_RealVector_Onorm__class_Onorm(_571794, _571790) = c_RealVector_Onorm__class_Onorm(_571792, _571788)), _571794 = _571792, _571790 = _571788], (910 ^ _543626) ^ [_572147, _572149, _572151, _572153] : [-(c_Groups_Oabs__class_Oabs(_572153, _572149) = c_Groups_Oabs__class_Oabs(_572151, _572147)), _572153 = _572151, _572149 = _572147], (920 ^ _543626) ^ [_572478, _572480] : [_572480 = _572478, -(c_Complex_Ocis(_572480) = c_Complex_Ocis(_572478))], (926 ^ _543626) ^ [_572752, _572754, _572756, _572758, _572760, _572762] : [-(c_Groups_Ominus__class_Ominus(_572762, _572758, _572754) = c_Groups_Ominus__class_Ominus(_572760, _572756, _572752)), _572762 = _572760, _572758 = _572756, _572754 = _572752], (940 ^ _543626) ^ [_573240, _573242, _573244, _573246] : [-(c_Complex_Orcis(_573246, _573242) = c_Complex_Orcis(_573244, _573240)), _573246 = _573244, _573242 = _573240], (950 ^ _543626) ^ [_573571, _573573] : [_573573 = _573571, -(c_Groups_Otimes__class_Otimes(_573573) = c_Groups_Otimes__class_Otimes(_573571))], (956 ^ _543626) ^ [_573789, _573791] : [_573791 = _573789, -(c_Groups_Oone__class_Oone(_573791) = c_Groups_Oone__class_Oone(_573789))], (962 ^ _543626) ^ [_574007, _574009] : [_574009 = _574007, -(c_RComplete_Onatfloor(_574009) = c_RComplete_Onatfloor(_574007))], (968 ^ _543626) ^ [_574281, _574283, _574285, _574287, _574289, _574291] : [-(c_Divides_Odiv__class_Odiv(_574291, _574287, _574283) = c_Divides_Odiv__class_Odiv(_574289, _574285, _574281)), _574291 = _574289, _574287 = _574285, _574283 = _574281], (982 ^ _543626) ^ [_574741, _574743] : [_574743 = _574741, -(c_Groups_Ozero__class_Ozero(_574743) = c_Groups_Ozero__class_Ozero(_574741))], (988 ^ _543626) ^ [_575015, _575017, _575019, _575021, _575023, _575025] : [-(c_Rings_Oinverse__class_Odivide(_575025, _575021, _575017) = c_Rings_Oinverse__class_Odivide(_575023, _575019, _575015)), _575025 = _575023, _575021 = _575019, _575017 = _575015], (1002 ^ _543626) ^ [_575475, _575477] : [_575477 = _575475, -(c_Power_Opower__class_Opower(_575477) = c_Power_Opower__class_Opower(_575475))], (1008 ^ _543626) ^ [_575721, _575723, _575725, _575727] : [-(tc_fun(_575727, _575723) = tc_fun(_575725, _575721)), _575727 = _575725, _575723 = _575721], (1018 ^ _543626) ^ [_576052, _576054] : [_576054 = _576052, -(tc_Polynomial_Opoly(_576054) = tc_Polynomial_Opoly(_576052))], (1024 ^ _543626) ^ [_576270, _576272] : [_576272 = _576270, -(c_RealDef_Oreal(_576272) = c_RealDef_Oreal(_576270))], (1030 ^ _543626) ^ [_576488, _576490] : [_576490 = _576488, -(c_Nat_OSuc(_576490) = c_Nat_OSuc(_576488))], (1036 ^ _543626) ^ [_576734, _576736, _576738, _576740] : [-(hAPP(_576740, _576736) = hAPP(_576738, _576734)), _576740 = _576738, _576736 = _576734], (1046 ^ _543626) ^ [_577101, _577103, _577105, _577107, _577109, _577111] : [-(c_Groups_Oplus__class_Oplus(_577111, _577107, _577103) = c_Groups_Oplus__class_Oplus(_577109, _577105, _577101)), _577111 = _577109, _577107 = _577105, _577103 = _577101], (2 ^ _543626) ^ [_543770] : [-(_543770 = _543770)], (4 ^ _543626) ^ [_543877, _543879] : [_543879 = _543877, -(_543877 = _543879)], (10 ^ _543626) ^ [_544081, _544083, _544085] : [-(_544085 = _544081), _544085 = _544083, _544083 = _544081], (20 ^ _543626) ^ [_544422, _544424, _544426, _544428] : [-(c_SEQ_Odecseq(_544426, _544422)), c_SEQ_Odecseq(_544428, _544424), _544428 = _544426, _544424 = _544422], (34 ^ _543626) ^ [_544866, _544868, _544870, _544872] : [-(c_SEQ_Oincseq(_544870, _544866)), c_SEQ_Oincseq(_544872, _544868), _544872 = _544870, _544868 = _544866], (48 ^ _543626) ^ [_545310, _545312, _545314, _545316] : [-(c_SEQ_Omonoseq(_545314, _545310)), c_SEQ_Omonoseq(_545316, _545312), _545316 = _545314, _545312 = _545310], (62 ^ _543626) ^ [_545726, _545728] : [-(c_SEQ_Osubseq(_545726)), _545728 = _545726, c_SEQ_Osubseq(_545728)], (72 ^ _543626) ^ [_546049, _546051, _546053, _546055] : [-(c_SEQ_OBseq(_546053, _546049)), c_SEQ_OBseq(_546055, _546051), _546055 = _546053, _546051 = _546049], (86 ^ _543626) ^ [_546465, _546467] : [-(c_Nat__Numeral_Oneg(_546465)), _546467 = _546465, c_Nat__Numeral_Oneg(_546467)], (96 ^ _543626) ^ [_546760, _546762] : [-(hBOOL(_546760)), _546762 = _546760, hBOOL(_546762)], (106 ^ _543626) ^ [_547111, _547113, _547115, _547117, _547119, _547121] : [-(c_Orderings_Oord__class_Oless(_547119, _547115, _547111)), c_Orderings_Oord__class_Oless(_547121, _547117, _547113), _547121 = _547119, _547117 = _547115, _547113 = _547111], (124 ^ _543626) ^ [_547664, _547666] : [-(class_RealVector_Oreal__normed__div__algebra(_547664)), _547666 = _547664, class_RealVector_Oreal__normed__div__algebra(_547666)], (134 ^ _543626) ^ [_547959, _547961] : [-(class_RealVector_Oreal__normed__algebra__1(_547959)), _547961 = _547959, class_RealVector_Oreal__normed__algebra__1(_547961)], (144 ^ _543626) ^ [_548254, _548256] : [-(class_RealVector_Oreal__normed__algebra(_548254)), _548256 = _548254, class_RealVector_Oreal__normed__algebra(_548256)], (154 ^ _543626) ^ [_548549, _548551] : [-(class_RealVector_Oreal__normed__vector(_548549)), _548551 = _548549, class_RealVector_Oreal__normed__vector(_548551)], (164 ^ _543626) ^ [_548844, _548846] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_548844)), _548846 = _548844, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_548846)], (174 ^ _543626) ^ [_549139, _549141] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_549139)), _549141 = _549139, class_Groups_Oordered__cancel__ab__semigroup__add(_549141)], (184 ^ _543626) ^ [_549434, _549436] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_549434)), _549436 = _549434, class_Groups_Oordered__ab__semigroup__add__imp__le(_549436)], (194 ^ _543626) ^ [_549729, _549731] : [-(class_Rings_Olinordered__comm__semiring__strict(_549729)), _549731 = _549729, class_Rings_Olinordered__comm__semiring__strict(_549731)], (204 ^ _543626) ^ [_550024, _550026] : [-(class_Rings_Olinordered__semiring__1__strict(_550024)), _550026 = _550024, class_Rings_Olinordered__semiring__1__strict(_550026)], (214 ^ _543626) ^ [_550319, _550321] : [-(class_Rings_Olinordered__semiring__strict(_550319)), _550321 = _550319, class_Rings_Olinordered__semiring__strict(_550321)], (224 ^ _543626) ^ [_550614, _550616] : [-(class_Groups_Oordered__ab__semigroup__add(_550614)), _550616 = _550614, class_Groups_Oordered__ab__semigroup__add(_550616)], (234 ^ _543626) ^ [_550909, _550911] : [-(class_Groups_Oordered__ab__group__add__abs(_550909)), _550911 = _550909, class_Groups_Oordered__ab__group__add__abs(_550911)], (244 ^ _543626) ^ [_551204, _551206] : [-(class_Groups_Oordered__comm__monoid__add(_551204)), _551206 = _551204, class_Groups_Oordered__comm__monoid__add(_551206)], (254 ^ _543626) ^ [_551499, _551501] : [-(class_Groups_Olinordered__ab__group__add(_551499)), _551501 = _551499, class_Groups_Olinordered__ab__group__add(_551501)], (264 ^ _543626) ^ [_551794, _551796] : [-(class_Groups_Ocancel__ab__semigroup__add(_551794)), _551796 = _551794, class_Groups_Ocancel__ab__semigroup__add(_551796)], (274 ^ _543626) ^ [_552089, _552091] : [-(class_Rings_Oring__1__no__zero__divisors(_552089)), _552091 = _552089, class_Rings_Oring__1__no__zero__divisors(_552091)], (284 ^ _543626) ^ [_552384, _552386] : [-(class_Rings_Oordered__cancel__semiring(_552384)), _552386 = _552384, class_Rings_Oordered__cancel__semiring(_552386)], (294 ^ _543626) ^ [_552679, _552681] : [-(class_Rings_Olinordered__ring__strict(_552679)), _552681 = _552679, class_Rings_Olinordered__ring__strict(_552681)], (304 ^ _543626) ^ [_552974, _552976] : [-(class_Rings_Oring__no__zero__divisors(_552974)), _552976 = _552974, class_Rings_Oring__no__zero__divisors(_552976)], (314 ^ _543626) ^ [_553269, _553271] : [-(class_Rings_Oordered__comm__semiring(_553269)), _553271 = _553269, class_Rings_Oordered__comm__semiring(_553271)], (324 ^ _543626) ^ [_553564, _553566] : [-(class_Rings_Olinordered__semiring__1(_553564)), _553566 = _553564, class_Rings_Olinordered__semiring__1(_553566)], (334 ^ _543626) ^ [_553859, _553861] : [-(class_Groups_Oordered__ab__group__add(_553859)), _553861 = _553859, class_Groups_Oordered__ab__group__add(_553861)], (344 ^ _543626) ^ [_554154, _554156] : [-(class_Groups_Ocancel__comm__monoid__add(_554154)), _554156 = _554154, class_Groups_Ocancel__comm__monoid__add(_554156)], (354 ^ _543626) ^ [_554449, _554451] : [-(class_Groups_Ocancel__semigroup__add(_554449)), _554451 = _554449, class_Groups_Ocancel__semigroup__add(_554451)], (364 ^ _543626) ^ [_554744, _554746] : [-(class_Rings_Olinordered__semiring(_554744)), _554746 = _554744, class_Rings_Olinordered__semiring(_554746)], (374 ^ _543626) ^ [_555039, _555041] : [-(class_Rings_Olinordered__semidom(_555039)), _555041 = _555039, class_Rings_Olinordered__semidom(_555041)], (384 ^ _543626) ^ [_555334, _555336] : [-(class_Groups_Oab__semigroup__mult(_555334)), _555336 = _555334, class_Groups_Oab__semigroup__mult(_555336)], (394 ^ _543626) ^ [_555629, _555631] : [-(class_Groups_Ocomm__monoid__mult(_555629)), _555631 = _555629, class_Groups_Ocomm__monoid__mult(_555631)], (404 ^ _543626) ^ [_555924, _555926] : [-(class_Groups_Oab__semigroup__add(_555924)), _555926 = _555924, class_Groups_Oab__semigroup__add(_555926)], (414 ^ _543626) ^ [_556219, _556221] : [-(class_Rings_Oordered__semiring(_556219)), _556221 = _556219, class_Rings_Oordered__semiring(_556221)], (424 ^ _543626) ^ [_556514, _556516] : [-(class_Rings_Oordered__ring__abs(_556514)), _556516 = _556514, class_Rings_Oordered__ring__abs(_556516)], (434 ^ _543626) ^ [_556809, _556811] : [-(class_Rings_Oidom(_556809)), _556811 = _556809, class_Rings_Oidom(_556811)], (444 ^ _543626) ^ [_557104, _557106] : [-(class_Rings_Ono__zero__divisors(_557104)), _557106 = _557104, class_Rings_Ono__zero__divisors(_557106)], (454 ^ _543626) ^ [_557399, _557401] : [-(class_Rings_Olinordered__ring(_557399)), _557401 = _557399, class_Rings_Olinordered__ring(_557401)], (464 ^ _543626) ^ [_557694, _557696] : [-(class_Fields_Ofield(_557694)), _557696 = _557694, class_Fields_Ofield(_557696)], (474 ^ _543626) ^ [_557989, _557991] : [-(class_Divides_Osemiring__div(_557989)), _557991 = _557989, class_Divides_Osemiring__div(_557991)], (484 ^ _543626) ^ [_558284, _558286] : [-(class_Rings_Ocomm__semiring(_558284)), _558286 = _558284, class_Rings_Ocomm__semiring(_558286)], (494 ^ _543626) ^ [_558579, _558581] : [-(class_Nat_Osemiring__char__0(_558579)), _558581 = _558579, class_Nat_Osemiring__char__0(_558581)], (504 ^ _543626) ^ [_558874, _558876] : [-(class_Rings_Ozero__neq__one(_558874)), _558876 = _558874, class_Rings_Ozero__neq__one(_558876)], (514 ^ _543626) ^ [_559169, _559171] : [-(class_Rings_Oordered__ring(_559169)), _559171 = _559169, class_Rings_Oordered__ring(_559171)], (524 ^ _543626) ^ [_559464, _559466] : [-(class_Orderings_Opreorder(_559464)), _559466 = _559464, class_Orderings_Opreorder(_559466)], (534 ^ _543626) ^ [_559759, _559761] : [-(class_Orderings_Olinorder(_559759)), _559761 = _559759, class_Orderings_Olinorder(_559761)], (544 ^ _543626) ^ [_560054, _560056] : [-(class_Groups_Omonoid__mult(_560054)), _560056 = _560054, class_Groups_Omonoid__mult(_560056)], (554 ^ _543626) ^ [_560349, _560351] : [-(class_Groups_Ocomm__monoid__add(_560349)), _560351 = _560349, class_Groups_Ocomm__monoid__add(_560351)], (564 ^ _543626) ^ [_560644, _560646] : [-(class_Groups_Omonoid__add(_560644)), _560646 = _560644, class_Groups_Omonoid__add(_560646)], (574 ^ _543626) ^ [_560939, _560941] : [-(class_Rings_Osemiring__1(_560939)), _560941 = _560939, class_Rings_Osemiring__1(_560941)], (584 ^ _543626) ^ [_561234, _561236] : [-(class_Rings_Osemiring__0(_561234)), _561236 = _561234, class_Rings_Osemiring__0(_561236)], (594 ^ _543626) ^ [_561529, _561531] : [-(class_Groups_Oab__group__add(_561529)), _561531 = _561529, class_Groups_Oab__group__add(_561531)], (604 ^ _543626) ^ [_561824, _561826] : [-(class_Groups_Ogroup__add(_561824)), _561826 = _561824, class_Groups_Ogroup__add(_561826)], (614 ^ _543626) ^ [_562119, _562121] : [-(class_Rings_Omult__zero(_562119)), _562121 = _562119, class_Rings_Omult__zero(_562121)], (624 ^ _543626) ^ [_562414, _562416] : [-(class_Orderings_Oorder(_562414)), _562416 = _562414, class_Orderings_Oorder(_562416)], (634 ^ _543626) ^ [_562709, _562711] : [-(class_Int_Oring__char__0(_562709)), _562711 = _562709, class_Int_Oring__char__0(_562711)], (644 ^ _543626) ^ [_563004, _563006] : [-(class_Int_Onumber__ring(_563004)), _563006 = _563004, class_Int_Onumber__ring(_563006)], (654 ^ _543626) ^ [_563299, _563301] : [-(class_Rings_Ocomm__semiring__0(_563299)), _563301 = _563299, class_Rings_Ocomm__semiring__0(_563301)], (664 ^ _543626) ^ [_563594, _563596] : [-(class_Rings_Osemiring(_563594)), _563596 = _563594, class_Rings_Osemiring(_563596)], (674 ^ _543626) ^ [_563889, _563891] : [-(class_Rings_Olinordered__idom(_563889)), _563891 = _563889, class_Rings_Olinordered__idom(_563891)], (684 ^ _543626) ^ [_564184, _564186] : [-(class_Orderings_Oord(_564184)), _564186 = _564184, class_Orderings_Oord(_564186)], (694 ^ _543626) ^ [_564479, _564481] : [-(class_Rings_Oring__1(_564479)), _564481 = _564479, class_Rings_Oring__1(_564481)], (704 ^ _543626) ^ [_564774, _564776] : [-(class_Power_Opower(_564774)), _564776 = _564774, class_Power_Opower(_564776)], (714 ^ _543626) ^ [_565069, _565071] : [-(class_Groups_Ozero(_565069)), _565071 = _565069, class_Groups_Ozero(_565071)], (724 ^ _543626) ^ [_565364, _565366] : [-(class_Rings_Ocomm__ring(_565364)), _565366 = _565364, class_Rings_Ocomm__ring(_565366)], (734 ^ _543626) ^ [_565659, _565661] : [-(class_Rings_Oring(_565659)), _565661 = _565659, class_Rings_Oring(_565661)], (744 ^ _543626) ^ [_565954, _565956] : [-(class_Rings_Ocomm__ring__1(_565954)), _565956 = _565954, class_Rings_Ocomm__ring__1(_565956)], (754 ^ _543626) ^ [_566249, _566251] : [-(class_Int_Onumber(_566249)), _566251 = _566249, class_Int_Onumber(_566251)], (764 ^ _543626) ^ [_566544, _566546] : [-(class_Rings_Ocomm__semiring__1(_566544)), _566546 = _566544, class_Rings_Ocomm__semiring__1(_566546)], (774 ^ _543626) ^ [_566839, _566841] : [-(class_Groups_Oone(_566839)), _566841 = _566839, class_Groups_Oone(_566841)], (784 ^ _543626) ^ [_567170, _567172, _567174, _567176, _567178, _567180] : [-(c_Orderings_Oord__class_Oless__eq(_567178, _567174, _567170)), c_Orderings_Oord__class_Oless__eq(_567180, _567176, _567172), _567180 = _567178, _567176 = _567174, _567172 = _567170], (1060 ^ _543626) ^ [_577735, _577737] : [hAPP(_577735, 1061 ^ [_577735, _577737]) = hAPP(_577737, 1061 ^ [_577735, _577737]), -(_577735 = _577737)], (1067 ^ _543626) ^ [] : [-(c_SEQ_Osubseq(v_f____))], (1069 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____), hAPP(v_f____, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____))))], (1071 ^ _543626) ^ [_578133, _578135] : [class_Orderings_Opreorder(_578133), -(c_Orderings_Oord__class_Oless__eq(_578133, _578135, _578135))], (1077 ^ _543626) ^ [_578328, _578330] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _578328, c_Nat_OSuc(_578330)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _578328, _578330)))], (1079 ^ _543626) ^ [_578434, _578436] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Nat_OSuc(_578434), _578436) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _578434, _578436)))], (1081 ^ _543626) ^ [_578540, _578542] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Nat_OSuc(_578540), _578542) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _578540, c_Nat_OSuc(_578542)))], (1083 ^ _543626) ^ [_578689, _578691, _578693, _578695] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_578689), 1086 ^ _543626 : [(1087 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_578689, c_Groups_Oplus__class_Oplus(_578689, _578691, _578693), c_Groups_Oplus__class_Oplus(_578689, _578695, _578693)), -(c_Orderings_Oord__class_Oless__eq(_578689, _578691, _578695))], (1093 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_578689, _578691, _578695), -(c_Orderings_Oord__class_Oless__eq(_578689, c_Groups_Oplus__class_Oplus(_578689, _578691, _578693), c_Groups_Oplus__class_Oplus(_578689, _578695, _578693)))]]], (1099 ^ _543626) ^ [_579237, _579239, _579241, _579243] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_579237), 1102 ^ _543626 : [(1103 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_579237, c_Groups_Oplus__class_Oplus(_579237, _579239, _579241), c_Groups_Oplus__class_Oplus(_579237, _579239, _579243)), -(c_Orderings_Oord__class_Oless__eq(_579237, _579241, _579243))], (1109 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_579237, _579241, _579243), -(c_Orderings_Oord__class_Oless__eq(_579237, c_Groups_Oplus__class_Oplus(_579237, _579239, _579241), c_Groups_Oplus__class_Oplus(_579237, _579239, _579243)))]]], (1115 ^ _543626) ^ [_579785, _579787, _579789, _579791] : [class_Groups_Oordered__ab__semigroup__add(_579785), c_Orderings_Oord__class_Oless__eq(_579785, _579787, _579789), -(c_Orderings_Oord__class_Oless__eq(_579785, c_Groups_Oplus__class_Oplus(_579785, _579787, _579791), c_Groups_Oplus__class_Oplus(_579785, _579789, _579791)))], (1125 ^ _543626) ^ [_580150, _580152, _580154, _580156] : [class_Groups_Oordered__ab__semigroup__add(_580150), c_Orderings_Oord__class_Oless__eq(_580150, _580152, _580154), -(c_Orderings_Oord__class_Oless__eq(_580150, c_Groups_Oplus__class_Oplus(_580150, _580156, _580152), c_Groups_Oplus__class_Oplus(_580150, _580156, _580154)))], (1135 ^ _543626) ^ [_580529, _580531, _580533, _580535, _580537] : [class_Groups_Oordered__ab__semigroup__add(_580529), c_Orderings_Oord__class_Oless__eq(_580529, _580531, _580533), c_Orderings_Oord__class_Oless__eq(_580529, _580535, _580537), -(c_Orderings_Oord__class_Oless__eq(_580529, c_Groups_Oplus__class_Oplus(_580529, _580531, _580535), c_Groups_Oplus__class_Oplus(_580529, _580533, _580537)))], (1149 ^ _543626) ^ [_581007, _581009, _581011, _581013] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_581007), c_Orderings_Oord__class_Oless__eq(_581007, c_Groups_Oplus__class_Oplus(_581007, _581009, _581011), c_Groups_Oplus__class_Oplus(_581007, _581013, _581011)), -(c_Orderings_Oord__class_Oless__eq(_581007, _581009, _581013))], (1159 ^ _543626) ^ [_581372, _581374, _581376, _581378] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_581372), c_Orderings_Oord__class_Oless__eq(_581372, c_Groups_Oplus__class_Oplus(_581372, _581374, _581376), c_Groups_Oplus__class_Oplus(_581372, _581374, _581378)), -(c_Orderings_Oord__class_Oless__eq(_581372, _581376, _581378))], (1169 ^ _543626) ^ [_581680] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _581680, _581680))], (1171 ^ _543626) ^ [_581788, _581790] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _581788, _581790)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _581790, _581788))], (1177 ^ _543626) ^ [_582003, _582005] : [_582003 = _582005, -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _582003, _582005))], (1183 ^ _543626) ^ [_582229, _582231, _582233] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _582229, _582231), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _582231, _582233), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _582229, _582233))], (1193 ^ _543626) ^ [_582544, _582546] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _582544, _582546), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _582546, _582544), -(_582544 = _582546)], (1203 ^ _543626) ^ [_582847, _582849] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_582847), _582849), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _582847, _582849))], (1209 ^ _543626) ^ [_583065, _583067] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _583065, c_Nat_OSuc(_583067)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _583065, _583067)), -(_583065 = c_Nat_OSuc(_583067))], (1219 ^ _543626) ^ [_583379, _583381] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _583379, _583381), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _583379, c_Nat_OSuc(_583381)))], (1225 ^ _543626) ^ [_583626, _583628] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_583626), c_Nat_OSuc(_583628)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _583626, _583628))], (1231 ^ _543626) ^ [_583800, _583802] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _583800, _583802), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_583800), c_Nat_OSuc(_583802)))], (1247 ^ _543626) ^ [_584317, _584319] : [1248 ^ _543626 : [(1249 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _584317, _584319)], (1251 ^ _543626) ^ [] : [_584317 = c_Nat_OSuc(_584319)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _584317, c_Nat_OSuc(_584319)))], (1237 ^ _543626) ^ [_584053, _584055] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _584053, c_Nat_OSuc(_584055)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _584053, _584055)), -(_584053 = c_Nat_OSuc(_584055))], (1255 ^ _543626) ^ [_584644, _584646] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _584644, _584646)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_584646), _584644))], (1261 ^ _543626) ^ [_584817, _584819] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_584819), _584817), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _584817, _584819)], (1267 ^ _543626) ^ [_585008] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_585008), _585008)], (1269 ^ _543626) ^ [_585132, _585134, _585136] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _585132, _585134), _585136), 1272 ^ _543626 : [(1273 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _585132, _585136))], (1275 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _585134, _585136))]]], (1277 ^ _543626) ^ [_585457, _585459, _585461] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _585457, _585459), _585461), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _585457, _585461))], (1283 ^ _543626) ^ [_585699, _585701, _585703] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _585699, _585701), _585703), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _585701, _585703))], (1289 ^ _543626) ^ [_585955, _585957, _585959, _585961] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _585955, _585957), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _585959, _585961), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _585955, _585959), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _585957, _585961)))], (1299 ^ _543626) ^ [_586310, _586312, _586314] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _586310, _586312), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _586310, _586314), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _586312, _586314)))], (1305 ^ _543626) ^ [_586560, _586562, _586564] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _586560, _586562), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _586560, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _586564, _586562)))], (1311 ^ _543626) ^ [_586802, _586804, _586806] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _586802, _586804), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _586802, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _586804, _586806)))], (1317 ^ _543626) ^ [_587073, _587075, _587077] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _587073, _587075), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _587073, _587077)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _587075, _587077))], (1323 ^ _543626) ^ [_587261, _587263, _587265] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _587263, _587265), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _587261, _587263), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _587261, _587265)))], (1329 ^ _543626) ^ [_587528, _587530] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _587528, _587530), -(_587530 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _587528, 1332 ^ [_587528, _587530]))], (1336 ^ _543626) ^ [_587761, _587763] : [1337 ^ _543626 : [(1338 ^ _543626) ^ [_587836] : [_587763 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _587761, _587836)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _587761, _587763))], (1342 ^ _543626) ^ [_587990, _587992] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _587990, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _587990, _587992)))], (1344 ^ _543626) ^ [_588089, _588091] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _588089, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _588091, _588089)))], (1346 ^ _543626) ^ [_588217, _588219, _588221] : [class_Orderings_Olinorder(_588217), -(c_Orderings_Oord__class_Oless__eq(_588217, _588219, _588221)), -(c_Orderings_Oord__class_Oless__eq(_588217, _588221, _588219))], (1356 ^ _543626) ^ [_588573, _588575, _588577, _588579, _588581] : [class_Orderings_Oord(_588573), c_Orderings_Oord__class_Oless__eq(tc_fun(_588575, _588573), _588577, _588579), -(c_Orderings_Oord__class_Oless__eq(_588573, hAPP(_588577, _588581), hAPP(_588579, _588581)))], (1366 ^ _543626) ^ [_588950, _588952, _588954, _588956] : [class_Orderings_Oorder(_588950), c_Orderings_Oord__class_Oless__eq(_588950, _588952, _588954), c_Orderings_Oord__class_Oless__eq(_588950, _588956, _588952), -(c_Orderings_Oord__class_Oless__eq(_588950, _588956, _588954))], (1380 ^ _543626) ^ [_589384, _589386, _589388] : [class_Orderings_Oorder(_589384), c_Orderings_Oord__class_Oless__eq(_589384, _589386, _589388), c_Orderings_Oord__class_Oless__eq(_589384, _589388, _589386), -(_589388 = _589386)], (1394 ^ _543626) ^ [_589816, _589818, _589820, _589822] : [class_Orderings_Opreorder(_589816), c_Orderings_Oord__class_Oless__eq(_589816, _589818, _589820), c_Orderings_Oord__class_Oless__eq(_589816, _589820, _589822), -(c_Orderings_Oord__class_Oless__eq(_589816, _589818, _589822))], (1408 ^ _543626) ^ [_590250, _590252, _590254] : [class_Orderings_Oorder(_590250), c_Orderings_Oord__class_Oless__eq(_590250, _590252, _590254), c_Orderings_Oord__class_Oless__eq(_590250, _590254, _590252), -(_590252 = _590254)], (1422 ^ _543626) ^ [_590682, _590684, _590686, _590688] : [class_Orderings_Oorder(_590682), c_Orderings_Oord__class_Oless__eq(_590682, _590684, _590686), _590684 = _590688, -(c_Orderings_Oord__class_Oless__eq(_590682, _590688, _590686))], (1436 ^ _543626) ^ [_591128, _591130, _591132, _591134] : [class_Orderings_Oord(_591128), c_Orderings_Oord__class_Oless__eq(_591128, _591130, _591132), _591132 = _591134, -(c_Orderings_Oord__class_Oless__eq(_591128, _591130, _591134))], (1450 ^ _543626) ^ [_591574, _591576, _591578, _591580] : [class_Orderings_Oorder(_591574), _591576 = _591578, c_Orderings_Oord__class_Oless__eq(_591574, _591580, _591578), -(c_Orderings_Oord__class_Oless__eq(_591574, _591580, _591576))], (1464 ^ _543626) ^ [_592020, _592022, _592024, _592026] : [class_Orderings_Oord(_592020), _592022 = _592024, c_Orderings_Oord__class_Oless__eq(_592020, _592024, _592026), -(c_Orderings_Oord__class_Oless__eq(_592020, _592022, _592026))], (1478 ^ _543626) ^ [_592452, _592454, _592456] : [class_Orderings_Oorder(_592452), c_Orderings_Oord__class_Oless__eq(_592452, _592454, _592456), 1485 ^ _543626 : [(1486 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_592452, _592456, _592454), -(_592456 = _592454)], (1492 ^ _543626) ^ [] : [_592456 = _592454, -(c_Orderings_Oord__class_Oless__eq(_592452, _592456, _592454))]]], (1498 ^ _543626) ^ [_593066, _593068, _593070, _593072, _593074] : [class_Orderings_Oord(_593066), c_Orderings_Oord__class_Oless__eq(tc_fun(_593068, _593066), _593070, _593072), -(c_Orderings_Oord__class_Oless__eq(_593066, hAPP(_593070, _593074), hAPP(_593072, _593074)))], (1508 ^ _543626) ^ [_593429, _593431, _593433] : [class_Orderings_Opreorder(_593429), _593431 = _593433, -(c_Orderings_Oord__class_Oless__eq(_593429, _593431, _593433))], (1518 ^ _543626) ^ [_593752, _593754, _593756] : [class_Orderings_Oorder(_593752), 1521 ^ _543626 : [(1522 ^ _543626) ^ [] : [_593754 = _593756, 1525 ^ _543626 : [(1526 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_593752, _593754, _593756))], (1528 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_593752, _593756, _593754))]]], (1530 ^ _543626) ^ [] : [-(_593754 = _593756), c_Orderings_Oord__class_Oless__eq(_593752, _593754, _593756), c_Orderings_Oord__class_Oless__eq(_593752, _593756, _593754)]]], (1540 ^ _543626) ^ [_594410, _594412, _594414] : [class_Orderings_Olinorder(_594410), -(c_Orderings_Oord__class_Oless__eq(_594410, _594412, _594414)), -(c_Orderings_Oord__class_Oless__eq(_594410, _594414, _594412))], (1550 ^ _543626) ^ [_594750, _594752, _594754, _594756] : [class_Orderings_Oord(_594750), 1553 ^ _543626 : [(1554 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_594752, _594750), _594754, _594756), 1557 ^ _543626 : [(1558 ^ _543626) ^ [_595009] : [-(c_Orderings_Oord__class_Oless__eq(_594750, hAPP(_594754, _595009), hAPP(_594756, _595009)))]]], (1560 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_594750, hAPP(_594754, 1561 ^ [_594750, _594752, _594754, _594756]), hAPP(_594756, 1561 ^ [_594750, _594752, _594754, _594756])), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_594752, _594750), _594754, _594756))]]], (1567 ^ _543626) ^ [_595405, _595407, _595409, _595411] : [class_Groups_Ocancel__semigroup__add(_595405), c_Groups_Oplus__class_Oplus(_595405, _595407, _595409) = c_Groups_Oplus__class_Oplus(_595405, _595411, _595409), -(_595407 = _595411)], (1577 ^ _543626) ^ [_595766, _595768, _595770, _595772] : [class_Groups_Ocancel__ab__semigroup__add(_595766), c_Groups_Oplus__class_Oplus(_595766, _595768, _595770) = c_Groups_Oplus__class_Oplus(_595766, _595768, _595772), -(_595770 = _595772)], (1587 ^ _543626) ^ [_596127, _596129, _596131, _596133] : [class_Groups_Ocancel__semigroup__add(_596127), c_Groups_Oplus__class_Oplus(_596127, _596129, _596131) = c_Groups_Oplus__class_Oplus(_596127, _596129, _596133), -(_596131 = _596133)], (1597 ^ _543626) ^ [_596488, _596490, _596492, _596494] : [class_Groups_Ocancel__semigroup__add(_596488), 1600 ^ _543626 : [(1601 ^ _543626) ^ [] : [c_Groups_Oplus__class_Oplus(_596488, _596490, _596492) = c_Groups_Oplus__class_Oplus(_596488, _596494, _596492), -(_596490 = _596494)], (1607 ^ _543626) ^ [] : [_596490 = _596494, -(c_Groups_Oplus__class_Oplus(_596488, _596490, _596492) = c_Groups_Oplus__class_Oplus(_596488, _596494, _596492))]]], (1613 ^ _543626) ^ [_597030, _597032, _597034, _597036] : [class_Groups_Ocancel__semigroup__add(_597030), 1616 ^ _543626 : [(1617 ^ _543626) ^ [] : [c_Groups_Oplus__class_Oplus(_597030, _597032, _597034) = c_Groups_Oplus__class_Oplus(_597030, _597032, _597036), -(_597034 = _597036)], (1623 ^ _543626) ^ [] : [_597034 = _597036, -(c_Groups_Oplus__class_Oplus(_597030, _597032, _597034) = c_Groups_Oplus__class_Oplus(_597030, _597032, _597036))]]], (1629 ^ _543626) ^ [_597572, _597574, _597576, _597578] : [class_Groups_Oab__semigroup__add(_597572), -(c_Groups_Oplus__class_Oplus(_597572, c_Groups_Oplus__class_Oplus(_597572, _597574, _597576), _597578) = c_Groups_Oplus__class_Oplus(_597572, _597574, c_Groups_Oplus__class_Oplus(_597572, _597576, _597578)))], (1635 ^ _543626) ^ [_597824, _597826] : [c_Nat_OSuc(_597824) = c_Nat_OSuc(_597826), -(_597824 = _597826)], (1641 ^ _543626) ^ [_598071, _598073] : [c_Nat_OSuc(_598071) = c_Nat_OSuc(_598073), -(_598071 = _598073)], (1647 ^ _543626) ^ [_598241, _598243] : [_598241 = _598243, -(c_Nat_OSuc(_598241) = c_Nat_OSuc(_598243))], (1653 ^ _543626) ^ [_598431] : [c_Nat_OSuc(_598431) = _598431], (1655 ^ _543626) ^ [_598510] : [_598510 = c_Nat_OSuc(_598510)], (1657 ^ _543626) ^ [_598662, _598664, _598666] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _598662, _598664) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _598666, _598664), -(_598662 = _598666)], (1663 ^ _543626) ^ [_598846, _598848, _598850] : [_598846 = _598850, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _598846, _598848) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _598850, _598848))], (1669 ^ _543626) ^ [_599123, _599125, _599127] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _599123, _599125) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _599123, _599127), -(_599125 = _599127)], (1675 ^ _543626) ^ [_599307, _599309, _599311] : [_599309 = _599311, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _599307, _599309) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _599307, _599311))], (1681 ^ _543626) ^ [_599540, _599542, _599544] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _599540, _599542), _599544) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _599540, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _599542, _599544)))], (1683 ^ _543626) ^ [_599666, _599668, _599670] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _599666, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _599668, _599670)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _599668, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _599666, _599670)))], (1685 ^ _543626) ^ [_599778, _599780] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _599778, _599780) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _599780, _599778))], (1687 ^ _543626) ^ [_599924, _599926] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _599924), hAPP(c_RealDef_Oreal(tc_Nat_Onat), _599926)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _599924, _599926))], (1693 ^ _543626) ^ [_600102, _600104] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _600102, _600104), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _600102), hAPP(c_RealDef_Oreal(tc_Nat_Onat), _600104)))], (1699 ^ _543626) ^ [_600330, _600332] : [c_SEQ_Osubseq(_600330), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _600332, hAPP(_600330, _600332)))], (1705 ^ _543626) ^ [_600531, _600533] : [-(hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _600531, _600533)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _600531), hAPP(c_RealDef_Oreal(tc_Nat_Onat), _600533)))], (1707 ^ _543626) ^ [_600671, _600673, _600675] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _600671, _600673), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _600671, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _600675, _600673)))], (1713 ^ _543626) ^ [_600913, _600915, _600917] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _600913, _600915), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _600913, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _600915, _600917)))], (1719 ^ _543626) ^ [_601170, _601172] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _601170, _601172), -(_601172 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _601170, 1722 ^ [_601170, _601172]))], (1726 ^ _543626) ^ [_601403, _601405] : [1727 ^ _543626 : [(1728 ^ _543626) ^ [_601478] : [_601405 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _601403, _601478)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _601403, _601405))], (1732 ^ _543626) ^ [_601675, _601677, _601679, _601681] : [class_Orderings_Oorder(_601675), c_Orderings_Oord__class_Oless__eq(_601675, hAPP(_601677, 1737 ^ [_601675, _601677, _601679, _601681]), hAPP(_601677, c_Nat_OSuc(1737 ^ [_601675, _601677, _601679, _601681]))), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _601679, _601681), -(c_Orderings_Oord__class_Oless__eq(_601675, hAPP(_601677, _601679), hAPP(_601677, _601681)))], (1747 ^ _543626) ^ [_602241, _602243] : [hAPP(c_RealDef_Oreal(tc_Nat_Onat), _602241) = hAPP(c_RealDef_Oreal(tc_Nat_Onat), _602243), -(_602241 = _602243)], (1753 ^ _543626) ^ [_602415, _602417] : [_602415 = _602417, -(hAPP(c_RealDef_Oreal(tc_Nat_Onat), _602415) = hAPP(c_RealDef_Oreal(tc_Nat_Onat), _602417))], (1759 ^ _543626) ^ [_602653, _602655, _602657] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _602653, _602655), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _602657, _602653), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _602657, _602655)))], (1765 ^ _543626) ^ [_602889, _602891] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _602889, _602891), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _602891, _602889), -(_602889 = _602891)], (1775 ^ _543626) ^ [_603206, _603208, _603210] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _603206, _603208), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _603208, _603210), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _603206, _603210))], (1785 ^ _543626) ^ [_603521, _603523] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _603521, _603523)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _603523, _603521))], (1791 ^ _543626) ^ [_603707] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _603707, _603707))], (1793 ^ _543626) ^ [_603815, _603817] : [class_Orderings_Oorder(_603815), 1796 ^ _543626 : [(1807 ^ _543626) ^ [] : [1810 ^ _543626 : [(1811 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, 1808 ^ [_603815, _603817], 1809 ^ [_603815, _603817]))], (1813 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_603815, hAPP(_603817, 1809 ^ [_603815, _603817]), hAPP(_603817, 1808 ^ [_603815, _603817]))]], -(c_SEQ_Odecseq(_603815, _603817))], (1797 ^ _543626) ^ [] : [c_SEQ_Odecseq(_603815, _603817), 1800 ^ _543626 : [(1801 ^ _543626) ^ [_604091, _604093] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _604093, _604091), -(c_Orderings_Oord__class_Oless__eq(_603815, hAPP(_603817, _604091), hAPP(_603817, _604093)))]]]]], (1817 ^ _543626) ^ [_604716, _604718] : [class_Orderings_Oorder(_604716), 1820 ^ _543626 : [(1831 ^ _543626) ^ [] : [1834 ^ _543626 : [(1835 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, 1832 ^ [_604716, _604718], 1833 ^ [_604716, _604718]))], (1837 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_604716, hAPP(_604718, 1832 ^ [_604716, _604718]), hAPP(_604718, 1833 ^ [_604716, _604718]))]], -(c_SEQ_Oincseq(_604716, _604718))], (1821 ^ _543626) ^ [] : [c_SEQ_Oincseq(_604716, _604718), 1824 ^ _543626 : [(1825 ^ _543626) ^ [_604992, _604994] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _604994, _604992), -(c_Orderings_Oord__class_Oless__eq(_604716, hAPP(_604718, _604994), hAPP(_604718, _604992)))]]]]], (1841 ^ _543626) ^ [_605617, _605619] : [class_Orderings_Oorder(_605617), 1844 ^ _543626 : [(1863 ^ _543626) ^ [] : [1866 ^ _543626 : [(1867 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, 1864 ^ [_605617, _605619], 1865 ^ [_605617, _605619]))], (1869 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_605617, hAPP(_605619, 1864 ^ [_605617, _605619]), hAPP(_605619, 1865 ^ [_605617, _605619]))], (1873 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, 1870 ^ [_605617, _605619], 1871 ^ [_605617, _605619]))], (1875 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_605617, hAPP(_605619, 1871 ^ [_605617, _605619]), hAPP(_605619, 1870 ^ [_605617, _605619]))]], -(c_SEQ_Omonoseq(_605617, _605619))], (1845 ^ _543626) ^ [] : [c_SEQ_Omonoseq(_605617, _605619), 1850 ^ _543626 : [(1851 ^ _543626) ^ [_605957, _605959] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _605959, _605957), -(c_Orderings_Oord__class_Oless__eq(_605617, hAPP(_605619, _605959), hAPP(_605619, _605957)))]], 1856 ^ _543626 : [(1857 ^ _543626) ^ [_606179, _606181] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _606181, _606179), -(c_Orderings_Oord__class_Oless__eq(_605617, hAPP(_605619, _606179), hAPP(_605619, _606181)))]]]]], (1879 ^ _543626) ^ [_607119, _607121] : [class_Orderings_Oorder(_607119), 1882 ^ _543626 : [(1893 ^ _543626) ^ [] : [1895 ^ _543626 : [(1896 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_607119, hAPP(_607121, 1894 ^ [_607119, _607121]), hAPP(_607121, c_Nat_OSuc(1894 ^ [_607119, _607121])))], (1899 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_607119, hAPP(_607121, c_Nat_OSuc(1897 ^ [_607119, _607121])), hAPP(_607121, 1897 ^ [_607119, _607121]))]], -(c_SEQ_Omonoseq(_607119, _607121))], (1883 ^ _543626) ^ [] : [c_SEQ_Omonoseq(_607119, _607121), 1888 ^ _543626 : [(1889 ^ _543626) ^ [_607410] : [-(c_Orderings_Oord__class_Oless__eq(_607119, hAPP(_607121, _607410), hAPP(_607121, c_Nat_OSuc(_607410))))]], 1890 ^ _543626 : [(1891 ^ _543626) ^ [_607481] : [-(c_Orderings_Oord__class_Oless__eq(_607119, hAPP(_607121, c_Nat_OSuc(_607481)), hAPP(_607121, _607481)))]]]]], (1903 ^ _543626) ^ [_607940] : [-(hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Nat_OSuc(_607940)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _607940), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (1905 ^ _543626) ^ [_608073, _608075, _608077] : [class_Rings_Ocomm__semiring__1(_608073), -(c_Groups_Oplus__class_Oplus(_608073, _608075, _608077) = c_Groups_Oplus__class_Oplus(_608073, _608077, _608075))], (1911 ^ _543626) ^ [_608331, _608333, _608335, _608337] : [class_Rings_Ocomm__semiring__1(_608331), -(c_Groups_Oplus__class_Oplus(_608331, _608333, c_Groups_Oplus__class_Oplus(_608331, _608335, _608337)) = c_Groups_Oplus__class_Oplus(_608331, _608335, c_Groups_Oplus__class_Oplus(_608331, _608333, _608337)))], (1917 ^ _543626) ^ [_608611, _608613, _608615, _608617] : [class_Rings_Ocomm__semiring__1(_608611), -(c_Groups_Oplus__class_Oplus(_608611, _608613, c_Groups_Oplus__class_Oplus(_608611, _608615, _608617)) = c_Groups_Oplus__class_Oplus(_608611, c_Groups_Oplus__class_Oplus(_608611, _608613, _608615), _608617))], (1923 ^ _543626) ^ [_608891, _608893, _608895, _608897] : [class_Rings_Ocomm__semiring__1(_608891), -(c_Groups_Oplus__class_Oplus(_608891, c_Groups_Oplus__class_Oplus(_608891, _608893, _608895), _608897) = c_Groups_Oplus__class_Oplus(_608891, _608893, c_Groups_Oplus__class_Oplus(_608891, _608895, _608897)))], (1929 ^ _543626) ^ [_609171, _609173, _609175, _609177] : [class_Rings_Ocomm__semiring__1(_609171), -(c_Groups_Oplus__class_Oplus(_609171, c_Groups_Oplus__class_Oplus(_609171, _609173, _609175), _609177) = c_Groups_Oplus__class_Oplus(_609171, c_Groups_Oplus__class_Oplus(_609171, _609173, _609177), _609175))], (1935 ^ _543626) ^ [_609423, _609425] : [class_Orderings_Oorder(_609423), c_SEQ_Oincseq(_609423, _609425), -(c_SEQ_Omonoseq(_609423, _609425))], (1945 ^ _543626) ^ [_609720, _609722] : [class_Orderings_Oorder(_609720), c_SEQ_Odecseq(_609720, _609722), -(c_SEQ_Omonoseq(_609720, _609722))], (1955 ^ _543626) ^ [_610017, _610019] : [class_Groups_Oone(_610017), 1958 ^ _543626 : [(1959 ^ _543626) ^ [] : [c_Groups_Oone__class_Oone(_610017) = _610019, -(_610019 = c_Groups_Oone__class_Oone(_610017))], (1965 ^ _543626) ^ [] : [_610019 = c_Groups_Oone__class_Oone(_610017), -(c_Groups_Oone__class_Oone(_610017) = _610019)]]], (1971 ^ _543626) ^ [_610529, _610531, _610533, _610535, _610537] : [class_Rings_Ocomm__semiring__1(_610529), -(c_Groups_Oplus__class_Oplus(_610529, c_Groups_Oplus__class_Oplus(_610529, _610531, _610533), c_Groups_Oplus__class_Oplus(_610529, _610535, _610537)) = c_Groups_Oplus__class_Oplus(_610529, c_Groups_Oplus__class_Oplus(_610529, _610531, _610535), c_Groups_Oplus__class_Oplus(_610529, _610533, _610537)))], (1977 ^ _543626) ^ [_610803, _610805] : [class_Orderings_Oorder(_610803), c_Orderings_Oord__class_Oless__eq(_610803, hAPP(_610805, 1982 ^ [_610803, _610805]), hAPP(_610805, c_Nat_OSuc(1982 ^ [_610803, _610805]))), -(c_SEQ_Oincseq(_610803, _610805))], (1988 ^ _543626) ^ [_611220, _611222] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _611220, _611222), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _611220), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _611222), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))], (1994 ^ _543626) ^ [_611406, _611408] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _611406), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _611408), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _611406, _611408))], (2000 ^ _543626) ^ [_611671, _611673] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _611671, _611673), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _611671), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), hAPP(c_RealDef_Oreal(tc_Nat_Onat), _611673)))], (2006 ^ _543626) ^ [_611857, _611859] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _611857), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), hAPP(c_RealDef_Oreal(tc_Nat_Onat), _611859)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _611857, _611859))], (2012 ^ _543626) ^ [_612093, _612095] : [class_Orderings_Oorder(_612093), 2019 ^ _543626 : [(2020 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, 2017 ^ [_612093, _612095], 2018 ^ [_612093, _612095]))], (2022 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_612093, hAPP(_612095, 2018 ^ [_612093, _612095]), hAPP(_612095, 2017 ^ [_612093, _612095]))]], -(c_SEQ_Omonoseq(_612093, _612095))], (2026 ^ _543626) ^ [_612656, _612658] : [class_Orderings_Oorder(_612656), 2033 ^ _543626 : [(2034 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, 2031 ^ [_612656, _612658], 2032 ^ [_612656, _612658]))], (2036 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_612656, hAPP(_612658, 2031 ^ [_612656, _612658]), hAPP(_612658, 2032 ^ [_612656, _612658]))]], -(c_SEQ_Omonoseq(_612656, _612658))], (2040 ^ _543626) ^ [_613219, _613221] : [class_Orderings_Oorder(_613219), c_Orderings_Oord__class_Oless__eq(_613219, hAPP(_613221, c_Nat_OSuc(2045 ^ [_613219, _613221])), hAPP(_613221, 2045 ^ [_613219, _613221])), -(c_SEQ_Omonoseq(_613219, _613221))], (2051 ^ _543626) ^ [_613607, _613609] : [class_Orderings_Oorder(_613607), c_Orderings_Oord__class_Oless__eq(_613607, hAPP(_613609, 2056 ^ [_613607, _613609]), hAPP(_613609, c_Nat_OSuc(2056 ^ [_613607, _613609]))), -(c_SEQ_Omonoseq(_613607, _613609))], (2062 ^ _543626) ^ [] : [-(hAPP(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))], (2064 ^ _543626) ^ [_614076, _614078, _614080, _614082] : [class_Rings_Osemiring__1(_614076), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_614076, _614078, c_Nat_OSuc(_614080), _614082) = c_Nat_Osemiring__1__class_Oof__nat__aux(_614076, _614078, _614080, hAPP(_614078, _614082)))], (2070 ^ _543626) ^ [_614340, _614342, _614344] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _614340, _614342), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _614342, _614340)), _614344) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_614342), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _614340, _614344)))], (2076 ^ _543626) ^ [_614568] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _614568, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2078 ^ _543626) ^ [_614647] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _614647, c_Nat_OSuc(_614647)))], (2080 ^ _543626) ^ [_614757, _614759] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _614757, _614759), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_614757), c_Nat_OSuc(_614759)))], (2086 ^ _543626) ^ [_614950] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _614950))], (2088 ^ _543626) ^ [_615029] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(_615029)))], (2090 ^ _543626) ^ [_615110] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_615110), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _615110)], (2092 ^ _543626) ^ [_615208, _615210] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _615208, c_Nat_OSuc(_615210)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _615208, c_Groups_Oone__class_Oone(tc_Nat_Onat)), _615210))], (2094 ^ _543626) ^ [_615317] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _615317), -(c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _615317, c_Groups_Oone__class_Oone(tc_Nat_Onat))) = _615317)], (2100 ^ _543626) ^ [_615521] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _615521), -(_615521 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _615521, c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (2106 ^ _543626) ^ [_615724, _615726] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _615724, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _615724, _615726)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2108 ^ _543626) ^ [_615870, _615872] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _615870, _615872) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _615870, _615872))], (2114 ^ _543626) ^ [_616042, _616044] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _616042, _616044), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _616042, _616044) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2120 ^ _543626) ^ [_616264, _616266] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _616264, _616266), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _616264, _616266) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2126 ^ _543626) ^ [_616499] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _616499), -(_616499 = c_Nat_OSuc(2129 ^ [_616499]))], (2133 ^ _543626) ^ [_616714] : [2134 ^ _543626 : [(2135 ^ _543626) ^ [_616785] : [_616714 = c_Nat_OSuc(_616785)]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _616714))], (2139 ^ _543626) ^ [_616963] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _616963, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_616963 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2145 ^ _543626) ^ [_617121] : [_617121 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _617121, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (2151 ^ _543626) ^ [_617358, _617360] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _617358, c_Nat_OSuc(_617360)), -(_617358 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 2159 ^ _543626 : [(2160 ^ _543626) ^ [] : [-(_617358 = c_Nat_OSuc(2158 ^ [_617358, _617360]))], (2162 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, 2158 ^ [_617358, _617360], _617360))]]], (2164 ^ _543626) ^ [_617770, _617772] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _617770, c_Nat_OSuc(_617772))), 2165 ^ _543626 : [(2166 ^ _543626) ^ [] : [_617770 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (2168 ^ _543626) ^ [_617939] : [_617770 = c_Nat_OSuc(_617939), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _617939, _617772)]]], (2176 ^ _543626) ^ [_618192] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _618192, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2178 ^ _543626) ^ [_618270] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _618270, _618270)], (2180 ^ _543626) ^ [_618378, _618380] : [class_Orderings_Opreorder(_618378), c_Orderings_Oord__class_Oless(_618378, _618380, _618380)], (2186 ^ _543626) ^ [_618604] : [-(_618604 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _618604))], (2192 ^ _543626) ^ [_618765] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _618765), _618765 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (2208 ^ _543626) ^ [_619262, _619264] : [2209 ^ _543626 : [(2210 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _619262, _619264)], (2212 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _619264, _619262)]], _619262 = _619264], (2198 ^ _543626) ^ [_619003, _619005] : [-(_619003 = _619005), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _619003, _619005)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _619005, _619003))], (2216 ^ _543626) ^ [_619567, _619569, _619571] : [class_Orderings_Olinorder(_619567), 2219 ^ _543626 : [(2230 ^ _543626) ^ [] : [2231 ^ _543626 : [(2232 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(_619567, _619569, _619571)], (2234 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(_619567, _619571, _619569)]], _619569 = _619571], (2220 ^ _543626) ^ [] : [-(_619569 = _619571), -(c_Orderings_Oord__class_Oless(_619567, _619569, _619571)), -(c_Orderings_Oord__class_Oless(_619567, _619571, _619569))]]], (2238 ^ _543626) ^ [_620227, _620229, _620231] : [class_Orderings_Olinorder(_620227), 2241 ^ _543626 : [(2252 ^ _543626) ^ [] : [2253 ^ _543626 : [(2254 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(_620227, _620231, _620229)], (2256 ^ _543626) ^ [] : [_620229 = _620231]], c_Orderings_Oord__class_Oless(_620227, _620229, _620231)], (2242 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(_620227, _620229, _620231)), -(c_Orderings_Oord__class_Oless(_620227, _620231, _620229)), -(_620229 = _620231)]]], (2260 ^ _543626) ^ [_620844] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _620844) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2262 ^ _543626) ^ [_620955, _620957] : [class_Groups_Ozero(_620955), 2265 ^ _543626 : [(2266 ^ _543626) ^ [] : [c_Groups_Ozero__class_Ozero(_620955) = _620957, -(_620957 = c_Groups_Ozero__class_Ozero(_620955))], (2272 ^ _543626) ^ [] : [_620957 = c_Groups_Ozero__class_Ozero(_620955), -(c_Groups_Ozero__class_Ozero(_620955) = _620957)]]], (2278 ^ _543626) ^ [_621454, _621456] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _621454, _621456)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _621456, _621454))], (2284 ^ _543626) ^ [_621628, _621630] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _621630, _621628), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _621628, _621630)))], (2290 ^ _543626) ^ [_621822] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _621822, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2292 ^ _543626) ^ [_621930, _621932] : [class_Groups_Ogroup__add(_621930), -(c_Groups_Ominus__class_Ominus(_621930, _621932, c_Groups_Ozero__class_Ozero(_621930)) = _621932)], (2298 ^ _543626) ^ [_622121] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _622121, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _622121)], (2300 ^ _543626) ^ [_622232, _622234] : [class_Groups_Ogroup__add(_622232), -(c_Groups_Ominus__class_Ominus(_622232, _622234, _622234) = c_Groups_Ozero__class_Ozero(_622232))], (2306 ^ _543626) ^ [_622423] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _622423, _622423) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2308 ^ _543626) ^ [_622548, _622550, _622552] : [class_Groups_Oab__group__add(_622548), 2311 ^ _543626 : [(2312 ^ _543626) ^ [] : [_622550 = _622552, -(c_Groups_Ominus__class_Ominus(_622548, _622550, _622552) = c_Groups_Ozero__class_Ozero(_622548))], (2318 ^ _543626) ^ [] : [c_Groups_Ominus__class_Ominus(_622548, _622550, _622552) = c_Groups_Ozero__class_Ozero(_622548), -(_622550 = _622552)]]], (2324 ^ _543626) ^ [_623054, _623056, _623058] : [class_Groups_Oordered__ab__group__add(_623054), 2327 ^ _543626 : [(2328 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(_623054, _623056, _623058), -(c_Orderings_Oord__class_Oless(_623054, c_Groups_Ominus__class_Ominus(_623054, _623056, _623058), c_Groups_Ozero__class_Ozero(_623054)))], (2334 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(_623054, c_Groups_Ominus__class_Ominus(_623054, _623056, _623058), c_Groups_Ozero__class_Ozero(_623054)), -(c_Orderings_Oord__class_Oless(_623054, _623056, _623058))]]], (2340 ^ _543626) ^ [_623566, _623568, _623570] : [class_Orderings_Olinorder(_623566), -(c_Orderings_Oord__class_Oless(_623566, _623568, _623570)), -(_623568 = _623570), -(c_Orderings_Oord__class_Oless(_623566, _623570, _623568))], (2354 ^ _543626) ^ [_623986, _623988, _623990] : [class_Groups_Ogroup__add(_623986), 2357 ^ _543626 : [(2358 ^ _543626) ^ [] : [c_Groups_Ominus__class_Ominus(_623986, _623988, _623990) = c_Groups_Ozero__class_Ozero(_623986), -(_623988 = _623990)], (2364 ^ _543626) ^ [] : [_623988 = _623990, -(c_Groups_Ominus__class_Ominus(_623986, _623988, _623990) = c_Groups_Ozero__class_Ozero(_623986))]]], (2370 ^ _543626) ^ [_624477, _624479, _624481] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _624477, _624479), _624481) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _624477, _624481), _624479))], (2372 ^ _543626) ^ [_624618, _624620, _624622] : [class_Rings_Osemiring__1(_624618), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_624618, _624620, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _624622) = _624622)], (2378 ^ _543626) ^ [_624856, _624858, _624860] : [class_Orderings_Olinorder(_624856), -(c_Orderings_Oord__class_Oless(_624856, _624858, _624860)), 2385 ^ _543626 : [(2386 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(_624856, _624860, _624858)), -(_624860 = _624858)], (2392 ^ _543626) ^ [] : [_624860 = _624858, c_Orderings_Oord__class_Oless(_624856, _624860, _624858)]]], (2398 ^ _543626) ^ [_625447, _625449, _625451] : [class_Orderings_Olinorder(_625447), -(_625449 = _625451), -(c_Orderings_Oord__class_Oless(_625447, _625449, _625451)), -(c_Orderings_Oord__class_Oless(_625447, _625451, _625449))], (2412 ^ _543626) ^ [_625857, _625859] : [-(_625857 = _625859), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _625857, _625859)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _625859, _625857))], (2422 ^ _543626) ^ [_626152] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _626152), -(c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _626152, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = _626152)], (2428 ^ _543626) ^ [_626370, _626372] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _626370), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _626370, c_Nat_OSuc(_626372)), _626370))], (2434 ^ _543626) ^ [_626596, _626598] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _626596), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _626598), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _626598, _626596), _626598))], (2444 ^ _543626) ^ [_626879] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _626879, _626879)], (2446 ^ _543626) ^ [_626987, _626989] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _626987, _626989), _626989 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (2452 ^ _543626) ^ [_627200, _627202] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _627200, _627202), _627202 = _627200], (2458 ^ _543626) ^ [_627413, _627415] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _627413, _627415), _627413 = _627415], (2464 ^ _543626) ^ [_627640, _627642, _627644] : [class_Orderings_Oorder(_627640), c_Orderings_Oord__class_Oless(_627640, _627642, _627644), _627642 = _627644], (2474 ^ _543626) ^ [_627964, _627966, _627968] : [class_Orderings_Opreorder(_627964), c_Orderings_Oord__class_Oless(_627964, _627966, _627968), c_Orderings_Oord__class_Oless(_627964, _627968, _627966)], (2484 ^ _543626) ^ [_628290, _628292, _628294] : [class_Orderings_Opreorder(_628290), c_Orderings_Oord__class_Oless(_628290, _628292, _628294), c_Orderings_Oord__class_Oless(_628290, _628294, _628292)], (2494 ^ _543626) ^ [_628616, _628618, _628620] : [class_Orderings_Oorder(_628616), c_Orderings_Oord__class_Oless(_628616, _628618, _628620), _628618 = _628620], (2504 ^ _543626) ^ [_628940, _628942, _628944] : [class_Orderings_Oorder(_628940), c_Orderings_Oord__class_Oless(_628940, _628942, _628944), _628944 = _628942], (2514 ^ _543626) ^ [_629264, _629266, _629268] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _629264, _629266), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _629264, _629268), _629266))], (2520 ^ _543626) ^ [_629506, _629508, _629510] : [class_Orderings_Opreorder(_629506), c_Orderings_Oord__class_Oless(_629506, _629508, _629510), c_Orderings_Oord__class_Oless(_629506, _629510, _629508)], (2530 ^ _543626) ^ [_629832, _629834, _629836] : [class_Orderings_Oorder(_629832), c_Orderings_Oord__class_Oless(_629832, _629834, _629836), c_Orderings_Oord__class_Oless(_629832, _629836, _629834)], (2540 ^ _543626) ^ [_630172, _630174, _630176, _630178] : [class_Orderings_Oord(_630172), _630174 = _630176, c_Orderings_Oord__class_Oless(_630172, _630176, _630178), -(c_Orderings_Oord__class_Oless(_630172, _630174, _630178))], (2554 ^ _543626) ^ [_630618, _630620, _630622, _630624] : [class_Orderings_Oorder(_630618), _630620 = _630622, c_Orderings_Oord__class_Oless(_630618, _630624, _630622), -(c_Orderings_Oord__class_Oless(_630618, _630624, _630620))], (2568 ^ _543626) ^ [_631064, _631066, _631068, _631070] : [class_Orderings_Oord(_631064), c_Orderings_Oord__class_Oless(_631064, _631066, _631068), _631068 = _631070, -(c_Orderings_Oord__class_Oless(_631064, _631066, _631070))], (2582 ^ _543626) ^ [_631510, _631512, _631514, _631516] : [class_Orderings_Oorder(_631510), c_Orderings_Oord__class_Oless(_631510, _631512, _631514), _631512 = _631516, -(c_Orderings_Oord__class_Oless(_631510, _631516, _631514))], (2596 ^ _543626) ^ [_631956, _631958, _631960, _631962] : [class_Orderings_Opreorder(_631956), c_Orderings_Oord__class_Oless(_631956, _631958, _631960), c_Orderings_Oord__class_Oless(_631956, _631960, _631962), -(c_Orderings_Oord__class_Oless(_631956, _631958, _631962))], (2610 ^ _543626) ^ [_632404, _632406, _632408, _632410] : [class_Orderings_Oorder(_632404), c_Orderings_Oord__class_Oless(_632404, _632406, _632408), c_Orderings_Oord__class_Oless(_632404, _632410, _632406), -(c_Orderings_Oord__class_Oless(_632404, _632410, _632408))], (2624 ^ _543626) ^ [_632838, _632840, _632842] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _632838, _632840), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _632838, _632842), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _632842, _632840), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _632842, _632838)))], (2634 ^ _543626) ^ [_633183, _633185, _633187] : [class_Orderings_Opreorder(_633183), c_Orderings_Oord__class_Oless(_633183, _633185, _633187), c_Orderings_Oord__class_Oless(_633183, _633187, _633185)], (2644 ^ _543626) ^ [_633495, _633497] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _633495, _633497) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _633497, _633495) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_633495 = _633497)], (2654 ^ _543626) ^ [_633852, _633854, _633856, _633858, _633860] : [class_Groups_Oab__group__add(_633852), c_Groups_Ominus__class_Ominus(_633852, _633854, _633856) = c_Groups_Ominus__class_Ominus(_633852, _633858, _633860), 2661 ^ _543626 : [(2662 ^ _543626) ^ [] : [_633854 = _633856, -(_633858 = _633860)], (2668 ^ _543626) ^ [] : [_633858 = _633860, -(_633854 = _633856)]]], (2674 ^ _543626) ^ [_634517, _634519, _634521, _634523, _634525] : [class_Groups_Oordered__ab__group__add(_634517), c_Groups_Ominus__class_Ominus(_634517, _634519, _634521) = c_Groups_Ominus__class_Ominus(_634517, _634523, _634525), 2681 ^ _543626 : [(2682 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(_634517, _634519, _634521), -(c_Orderings_Oord__class_Oless(_634517, _634523, _634525))], (2688 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(_634517, _634523, _634525), -(c_Orderings_Oord__class_Oless(_634517, _634519, _634521))]]], (2694 ^ _543626) ^ [_635132] : [-(_635132 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _635132))], (2700 ^ _543626) ^ [_635355, _635357, _635359] : [class_Orderings_Olinorder(_635355), -(c_Orderings_Oord__class_Oless(_635355, _635357, _635359)), -(_635357 = _635359), -(c_Orderings_Oord__class_Oless(_635355, _635359, _635357))], (2714 ^ _543626) ^ [_635779, _635781, _635783] : [2715 ^ _543626 : [(2716 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _635779, _635781))], (2718 ^ _543626) ^ [] : [hBOOL(hAPP(hAPP(_635783, _635781), _635779))]], 2721 ^ _543626 : [(2722 ^ _543626) ^ [] : [-(_635779 = _635781)], (2724 ^ _543626) ^ [] : [hBOOL(hAPP(hAPP(_635783, _635781), _635779))]], 2727 ^ _543626 : [(2728 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _635781, _635779))], (2730 ^ _543626) ^ [] : [hBOOL(hAPP(hAPP(_635783, _635781), _635779))]], -(hBOOL(hAPP(hAPP(_635783, _635781), _635779)))], (2734 ^ _543626) ^ [_636470, _636472, _636474] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _636470, _636472), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _636474, _636470), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _636470, _636474), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _636472, _636474)))], (2744 ^ _543626) ^ [_636815, _636817, _636819] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _636815, _636817), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _636815, _636819), 2751 ^ _543626 : [(2752 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _636817, _636815), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _636819, _636815)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _636817, _636819))], (2758 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _636817, _636819), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _636817, _636815), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _636819, _636815)))]]], (2764 ^ _543626) ^ [_637461, _637463, _637465] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _637461, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _637463, _637465)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _637461, _637465), _637463))], (2770 ^ _543626) ^ [_637649, _637651, _637653] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _637649, _637653), _637651), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _637649, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _637651, _637653)))], (2776 ^ _543626) ^ [_637887, _637889] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _637887, _637889)), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _637889, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _637887, _637889)) = _637887)], (2782 ^ _543626) ^ [_638118, _638120] : [class_Groups_Olinordered__ab__group__add(_638118), 2785 ^ _543626 : [(2786 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(_638118, c_Groups_Ozero__class_Ozero(_638118), c_Groups_Oplus__class_Oplus(_638118, _638120, _638120)), -(c_Orderings_Oord__class_Oless(_638118, c_Groups_Ozero__class_Ozero(_638118), _638120))], (2792 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(_638118, c_Groups_Ozero__class_Ozero(_638118), _638120), -(c_Orderings_Oord__class_Oless(_638118, c_Groups_Ozero__class_Ozero(_638118), c_Groups_Oplus__class_Oplus(_638118, _638120, _638120)))]]], (2798 ^ _543626) ^ [_638606, _638608] : [class_Groups_Olinordered__ab__group__add(_638606), 2801 ^ _543626 : [(2802 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(_638606, c_Groups_Oplus__class_Oplus(_638606, _638608, _638608), c_Groups_Ozero__class_Ozero(_638606)), -(c_Orderings_Oord__class_Oless(_638606, _638608, c_Groups_Ozero__class_Ozero(_638606)))], (2808 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(_638606, _638608, c_Groups_Ozero__class_Ozero(_638606)), -(c_Orderings_Oord__class_Oless(_638606, c_Groups_Oplus__class_Oplus(_638606, _638608, _638608), c_Groups_Ozero__class_Ozero(_638606)))]]], (2814 ^ _543626) ^ [_639108, _639110, _639112] : [class_Groups_Oordered__comm__monoid__add(_639108), c_Orderings_Oord__class_Oless(_639108, c_Groups_Ozero__class_Ozero(_639108), _639110), c_Orderings_Oord__class_Oless(_639108, c_Groups_Ozero__class_Ozero(_639108), _639112), -(c_Orderings_Oord__class_Oless(_639108, c_Groups_Ozero__class_Ozero(_639108), c_Groups_Oplus__class_Oplus(_639108, _639110, _639112)))], (2828 ^ _543626) ^ [_639548, _639550, _639552] : [class_Groups_Oordered__comm__monoid__add(_639548), c_Orderings_Oord__class_Oless(_639548, _639550, c_Groups_Ozero__class_Ozero(_639548)), c_Orderings_Oord__class_Oless(_639548, _639552, c_Groups_Ozero__class_Ozero(_639548)), -(c_Orderings_Oord__class_Oless(_639548, c_Groups_Oplus__class_Oplus(_639548, _639550, _639552), c_Groups_Ozero__class_Ozero(_639548)))], (2842 ^ _543626) ^ [_639959, _639961] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _639959, _639961), c_Nat_OSuc(_639959)))], (2844 ^ _543626) ^ [_640089, _640091, _640093] : [class_Groups_Oordered__ab__group__add(_640089), 2847 ^ _543626 : [(2848 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_640089, _640091, _640093), -(c_Orderings_Oord__class_Oless__eq(_640089, c_Groups_Ominus__class_Ominus(_640089, _640091, _640093), c_Groups_Ozero__class_Ozero(_640089)))], (2854 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_640089, c_Groups_Ominus__class_Ominus(_640089, _640091, _640093), c_Groups_Ozero__class_Ozero(_640089)), -(c_Orderings_Oord__class_Oless__eq(_640089, _640091, _640093))]]], (2876 ^ _543626) ^ [_641161, _641163, _641165] : [-(hBOOL(hAPP(_641161, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _641163, _641165)))), 2879 ^ _543626 : [(2880 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _641163, _641165))], (2882 ^ _543626) ^ [] : [hBOOL(hAPP(_641161, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 2884 ^ _543626 : [(2885 ^ _543626) ^ [] : [-(_641163 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _641165, 2883 ^ [_641161, _641163, _641165]))], (2887 ^ _543626) ^ [] : [hBOOL(hAPP(_641161, 2883 ^ [_641161, _641163, _641165]))]]], (2860 ^ _543626) ^ [_640630, _640632, _640634] : [hBOOL(hAPP(_640630, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _640632, _640634))), 2863 ^ _543626 : [(2864 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _640632, _640634), -(hBOOL(hAPP(_640630, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (2870 ^ _543626) ^ [_640962] : [_640632 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _640634, _640962), -(hBOOL(hAPP(_640630, _640962)))]]], (2907 ^ _543626) ^ [_642322, _642324, _642326] : [-(hBOOL(hAPP(_642322, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _642324, _642326)))), 2910 ^ _543626 : [(2911 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _642324, _642326))], (2913 ^ _543626) ^ [] : [hBOOL(hAPP(_642322, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 2915 ^ _543626 : [(2916 ^ _543626) ^ [] : [-(_642324 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _642326, 2914 ^ [_642322, _642324, _642326]))], (2918 ^ _543626) ^ [] : [hBOOL(hAPP(_642322, 2914 ^ [_642322, _642324, _642326]))]]], (2891 ^ _543626) ^ [_641783, _641785, _641787] : [hBOOL(hAPP(_641783, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _641785, _641787))), 2894 ^ _543626 : [(2895 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _641785, _641787), -(hBOOL(hAPP(_641783, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (2901 ^ _543626) ^ [_642121] : [_641785 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _641787, _642121), -(hBOOL(hAPP(_641783, _642121)))]]], (2922 ^ _543626) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (2924 ^ _543626) ^ [_642991, _642993] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _642991), hAPP(c_RealDef_Oreal(tc_Nat_Onat), _642993)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _642991, _642993))], (2930 ^ _543626) ^ [_643169, _643171] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _643169, _643171), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _643169), hAPP(c_RealDef_Oreal(tc_Nat_Onat), _643171)))], (2946 ^ _543626) ^ [_643692, _643694] : [2947 ^ _543626 : [(2948 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _643692)], (2950 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _643694)]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _643692, _643694)))], (2936 ^ _543626) ^ [_643426, _643428] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _643426, _643428)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _643426)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _643428))], (2954 ^ _543626) ^ [_644012, _644014] : [_644012 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _644012, _644014) = _644014)], (2960 ^ _543626) ^ [_644182, _644184] : [-(_644182 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _644182, _644184) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _644182, c_Groups_Oone__class_Oone(tc_Nat_Onat)), _644184)))], (2966 ^ _543626) ^ [_644439, _644441, _644443] : [class_Groups_Oordered__comm__monoid__add(_644439), c_Orderings_Oord__class_Oless(_644439, c_Groups_Ozero__class_Ozero(_644439), _644441), c_Orderings_Oord__class_Oless__eq(_644439, c_Groups_Ozero__class_Ozero(_644439), _644443), -(c_Orderings_Oord__class_Oless(_644439, c_Groups_Ozero__class_Ozero(_644439), c_Groups_Oplus__class_Oplus(_644439, _644441, _644443)))], (2980 ^ _543626) ^ [_644879, _644881, _644883] : [class_Groups_Oordered__comm__monoid__add(_644879), c_Orderings_Oord__class_Oless__eq(_644879, c_Groups_Ozero__class_Ozero(_644879), _644881), c_Orderings_Oord__class_Oless(_644879, c_Groups_Ozero__class_Ozero(_644879), _644883), -(c_Orderings_Oord__class_Oless(_644879, c_Groups_Ozero__class_Ozero(_644879), c_Groups_Oplus__class_Oplus(_644879, _644881, _644883)))], (2994 ^ _543626) ^ [_645333, _645335, _645337, _645339] : [class_Groups_Oordered__comm__monoid__add(_645333), c_Orderings_Oord__class_Oless(_645333, c_Groups_Ozero__class_Ozero(_645333), _645335), c_Orderings_Oord__class_Oless__eq(_645333, _645337, _645339), -(c_Orderings_Oord__class_Oless(_645333, _645337, c_Groups_Oplus__class_Oplus(_645333, _645335, _645339)))], (3008 ^ _543626) ^ [_645793, _645795, _645797, _645799] : [class_Groups_Oordered__comm__monoid__add(_645793), c_Orderings_Oord__class_Oless__eq(_645793, c_Groups_Ozero__class_Ozero(_645793), _645795), c_Orderings_Oord__class_Oless(_645793, _645797, _645799), -(c_Orderings_Oord__class_Oless(_645793, _645797, c_Groups_Oplus__class_Oplus(_645793, _645795, _645799)))], (3022 ^ _543626) ^ [_646239, _646241, _646243] : [class_Groups_Oordered__comm__monoid__add(_646239), c_Orderings_Oord__class_Oless(_646239, _646241, c_Groups_Ozero__class_Ozero(_646239)), c_Orderings_Oord__class_Oless__eq(_646239, _646243, c_Groups_Ozero__class_Ozero(_646239)), -(c_Orderings_Oord__class_Oless(_646239, c_Groups_Oplus__class_Oplus(_646239, _646241, _646243), c_Groups_Ozero__class_Ozero(_646239)))], (3036 ^ _543626) ^ [_646679, _646681, _646683] : [class_Groups_Oordered__comm__monoid__add(_646679), c_Orderings_Oord__class_Oless__eq(_646679, _646681, c_Groups_Ozero__class_Ozero(_646679)), c_Orderings_Oord__class_Oless(_646679, _646683, c_Groups_Ozero__class_Ozero(_646679)), -(c_Orderings_Oord__class_Oless(_646679, c_Groups_Oplus__class_Oplus(_646679, _646681, _646683), c_Groups_Ozero__class_Ozero(_646679)))], (3050 ^ _543626) ^ [_647147, _647149, _647151, _647153, _647155] : [class_Groups_Oordered__ab__group__add(_647147), c_Groups_Ominus__class_Ominus(_647147, _647149, _647151) = c_Groups_Ominus__class_Ominus(_647147, _647153, _647155), 3057 ^ _543626 : [(3058 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_647147, _647149, _647151), -(c_Orderings_Oord__class_Oless__eq(_647147, _647153, _647155))], (3064 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_647147, _647153, _647155), -(c_Orderings_Oord__class_Oless__eq(_647147, _647149, _647151))]]], (3070 ^ _543626) ^ [_647790, _647792, _647794] : [class_Groups_Ogroup__add(_647790), -(c_Groups_Oplus__class_Oplus(_647790, c_Groups_Ominus__class_Ominus(_647790, _647792, _647794), _647794) = _647792)], (3076 ^ _543626) ^ [_648034, _648036, _648038] : [class_Groups_Ogroup__add(_648034), -(c_Groups_Ominus__class_Ominus(_648034, c_Groups_Oplus__class_Oplus(_648034, _648036, _648038), _648038) = _648036)], (3082 ^ _543626) ^ [_648278, _648280, _648282] : [class_Orderings_Olinorder(_648278), 3085 ^ _543626 : [(3086 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(_648278, _648280, _648282)), -(c_Orderings_Oord__class_Oless__eq(_648278, _648282, _648280))], (3092 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_648278, _648282, _648280), c_Orderings_Oord__class_Oless(_648278, _648280, _648282)]]], (3098 ^ _543626) ^ [_648774, _648776, _648778] : [class_Orderings_Olinorder(_648774), 3101 ^ _543626 : [(3102 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_648774, _648776, _648778)), -(c_Orderings_Oord__class_Oless(_648774, _648778, _648776))], (3108 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(_648774, _648778, _648776), c_Orderings_Oord__class_Oless__eq(_648774, _648776, _648778)]]], (3114 ^ _543626) ^ [_649270, _649272, _649274] : [class_Orderings_Olinorder(_649270), -(c_Orderings_Oord__class_Oless__eq(_649270, _649272, _649274)), -(c_Orderings_Oord__class_Oless(_649270, _649274, _649272))], (3124 ^ _543626) ^ [_649596, _649598, _649600] : [class_Orderings_Oorder(_649596), 3127 ^ _543626 : [(3128 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(_649596, _649598, _649600), 3131 ^ _543626 : [(3132 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_649596, _649598, _649600))], (3134 ^ _543626) ^ [] : [_649598 = _649600]]], (3136 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(_649596, _649598, _649600)), c_Orderings_Oord__class_Oless__eq(_649596, _649598, _649600), -(_649598 = _649600)]]], (3146 ^ _543626) ^ [_650256, _650258, _650260] : [class_Orderings_Opreorder(_650256), 3149 ^ _543626 : [(3150 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(_650256, _650258, _650260), 3153 ^ _543626 : [(3154 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_650256, _650258, _650260))], (3156 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_650256, _650260, _650258)]]], (3158 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(_650256, _650258, _650260)), c_Orderings_Oord__class_Oless__eq(_650256, _650258, _650260), -(c_Orderings_Oord__class_Oless__eq(_650256, _650260, _650258))]]], (3168 ^ _543626) ^ [_650919, _650921, _650923] : [class_Orderings_Oorder(_650919), 3171 ^ _543626 : [(3182 ^ _543626) ^ [] : [3183 ^ _543626 : [(3184 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(_650919, _650921, _650923)], (3186 ^ _543626) ^ [] : [_650921 = _650923]], -(c_Orderings_Oord__class_Oless__eq(_650919, _650921, _650923))], (3172 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_650919, _650921, _650923), -(c_Orderings_Oord__class_Oless(_650919, _650921, _650923)), -(_650921 = _650923)]]], (3190 ^ _543626) ^ [_651577, _651579, _651581] : [class_Orderings_Olinorder(_651577), -(c_Orderings_Oord__class_Oless(_651577, _651579, _651581)), -(c_Orderings_Oord__class_Oless__eq(_651577, _651581, _651579))], (3200 ^ _543626) ^ [_651905, _651907, _651909] : [class_Orderings_Olinorder(_651905), -(c_Orderings_Oord__class_Oless__eq(_651905, _651907, _651909)), -(c_Orderings_Oord__class_Oless(_651905, _651909, _651907))], (3210 ^ _543626) ^ [_652233, _652235, _652237] : [class_Orderings_Olinorder(_652233), -(c_Orderings_Oord__class_Oless(_652233, _652235, _652237)), 3217 ^ _543626 : [(3218 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_652233, _652235, _652237), -(_652235 = _652237)], (3224 ^ _543626) ^ [] : [_652235 = _652237, -(c_Orderings_Oord__class_Oless__eq(_652233, _652235, _652237))]]], (3230 ^ _543626) ^ [_652822, _652824, _652826] : [class_Orderings_Oorder(_652822), -(_652824 = _652826), c_Orderings_Oord__class_Oless__eq(_652822, _652824, _652826), -(c_Orderings_Oord__class_Oless(_652822, _652824, _652826))], (3244 ^ _543626) ^ [_653243, _653245, _653247] : [class_Orderings_Oorder(_653243), -(_653245 = _653247), c_Orderings_Oord__class_Oless__eq(_653243, _653247, _653245), -(c_Orderings_Oord__class_Oless(_653243, _653247, _653245))], (3258 ^ _543626) ^ [_653664, _653666, _653668] : [class_Orderings_Olinorder(_653664), c_Orderings_Oord__class_Oless__eq(_653664, _653666, _653668), c_Orderings_Oord__class_Oless(_653664, _653668, _653666)], (3268 ^ _543626) ^ [_653990, _653992, _653994] : [class_Orderings_Opreorder(_653990), c_Orderings_Oord__class_Oless(_653990, _653992, _653994), -(c_Orderings_Oord__class_Oless__eq(_653990, _653992, _653994))], (3278 ^ _543626) ^ [_654315, _654317, _654319] : [class_Orderings_Olinorder(_654315), c_Orderings_Oord__class_Oless__eq(_654315, _654317, _654319), 3285 ^ _543626 : [(3286 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(_654315, _654317, _654319)), -(_654317 = _654319)], (3292 ^ _543626) ^ [] : [_654317 = _654319, c_Orderings_Oord__class_Oless(_654315, _654317, _654319)]]], (3298 ^ _543626) ^ [_654903, _654905, _654907] : [class_Orderings_Oorder(_654903), c_Orderings_Oord__class_Oless__eq(_654903, _654905, _654907), -(c_Orderings_Oord__class_Oless(_654903, _654905, _654907)), -(_654905 = _654907)], (3312 ^ _543626) ^ [_655322, _655324, _655326] : [class_Orderings_Oorder(_655322), c_Orderings_Oord__class_Oless__eq(_655322, _655324, _655326), -(_655324 = _655326), -(c_Orderings_Oord__class_Oless(_655322, _655324, _655326))], (3326 ^ _543626) ^ [_655743, _655745, _655747] : [class_Orderings_Oorder(_655743), c_Orderings_Oord__class_Oless__eq(_655743, _655745, _655747), -(_655747 = _655745), -(c_Orderings_Oord__class_Oless(_655743, _655745, _655747))], (3340 ^ _543626) ^ [_656178, _656180, _656182, _656184] : [class_Orderings_Opreorder(_656178), c_Orderings_Oord__class_Oless(_656178, _656180, _656182), c_Orderings_Oord__class_Oless__eq(_656178, _656182, _656184), -(c_Orderings_Oord__class_Oless(_656178, _656180, _656184))], (3354 ^ _543626) ^ [_656626, _656628, _656630, _656632] : [class_Orderings_Oorder(_656626), c_Orderings_Oord__class_Oless(_656626, _656628, _656630), c_Orderings_Oord__class_Oless__eq(_656626, _656632, _656628), -(c_Orderings_Oord__class_Oless(_656626, _656632, _656630))], (3368 ^ _543626) ^ [_657074, _657076, _657078, _657080] : [class_Orderings_Opreorder(_657074), c_Orderings_Oord__class_Oless__eq(_657074, _657076, _657078), c_Orderings_Oord__class_Oless(_657074, _657078, _657080), -(c_Orderings_Oord__class_Oless(_657074, _657076, _657080))], (3382 ^ _543626) ^ [_657522, _657524, _657526, _657528] : [class_Orderings_Oorder(_657522), c_Orderings_Oord__class_Oless__eq(_657522, _657524, _657526), c_Orderings_Oord__class_Oless(_657522, _657528, _657524), -(c_Orderings_Oord__class_Oless(_657522, _657528, _657526))], (3396 ^ _543626) ^ [_657970, _657972, _657974, _657976] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_657970), 3399 ^ _543626 : [(3400 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(_657970, c_Groups_Oplus__class_Oplus(_657970, _657972, _657974), c_Groups_Oplus__class_Oplus(_657970, _657976, _657974)), -(c_Orderings_Oord__class_Oless(_657970, _657972, _657976))], (3406 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(_657970, _657972, _657976), -(c_Orderings_Oord__class_Oless(_657970, c_Groups_Oplus__class_Oplus(_657970, _657972, _657974), c_Groups_Oplus__class_Oplus(_657970, _657976, _657974)))]]], (3412 ^ _543626) ^ [_658518, _658520, _658522, _658524] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_658518), 3415 ^ _543626 : [(3416 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(_658518, c_Groups_Oplus__class_Oplus(_658518, _658520, _658522), c_Groups_Oplus__class_Oplus(_658518, _658520, _658524)), -(c_Orderings_Oord__class_Oless(_658518, _658522, _658524))], (3422 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(_658518, _658522, _658524), -(c_Orderings_Oord__class_Oless(_658518, c_Groups_Oplus__class_Oplus(_658518, _658520, _658522), c_Groups_Oplus__class_Oplus(_658518, _658520, _658524)))]]], (3428 ^ _543626) ^ [_659066, _659068, _659070, _659072] : [class_Groups_Oordered__cancel__ab__semigroup__add(_659066), c_Orderings_Oord__class_Oless(_659066, _659068, _659070), -(c_Orderings_Oord__class_Oless(_659066, c_Groups_Oplus__class_Oplus(_659066, _659068, _659072), c_Groups_Oplus__class_Oplus(_659066, _659070, _659072)))], (3438 ^ _543626) ^ [_659431, _659433, _659435, _659437] : [class_Groups_Oordered__cancel__ab__semigroup__add(_659431), c_Orderings_Oord__class_Oless(_659431, _659433, _659435), -(c_Orderings_Oord__class_Oless(_659431, c_Groups_Oplus__class_Oplus(_659431, _659437, _659433), c_Groups_Oplus__class_Oplus(_659431, _659437, _659435)))], (3448 ^ _543626) ^ [_659810, _659812, _659814, _659816, _659818] : [class_Groups_Oordered__cancel__ab__semigroup__add(_659810), c_Orderings_Oord__class_Oless(_659810, _659812, _659814), c_Orderings_Oord__class_Oless(_659810, _659816, _659818), -(c_Orderings_Oord__class_Oless(_659810, c_Groups_Oplus__class_Oplus(_659810, _659812, _659816), c_Groups_Oplus__class_Oplus(_659810, _659814, _659818)))], (3462 ^ _543626) ^ [_660288, _660290, _660292, _660294] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_660288), c_Orderings_Oord__class_Oless(_660288, c_Groups_Oplus__class_Oplus(_660288, _660290, _660292), c_Groups_Oplus__class_Oplus(_660288, _660294, _660292)), -(c_Orderings_Oord__class_Oless(_660288, _660290, _660294))], (3472 ^ _543626) ^ [_660653, _660655, _660657, _660659] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_660653), c_Orderings_Oord__class_Oless(_660653, c_Groups_Oplus__class_Oplus(_660653, _660655, _660657), c_Groups_Oplus__class_Oplus(_660653, _660655, _660659)), -(c_Orderings_Oord__class_Oless(_660653, _660657, _660659))], (3482 ^ _543626) ^ [_660975, _660977] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_660975), c_Nat_OSuc(_660977)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _660975, _660977))], (3484 ^ _543626) ^ [_661095, _661097, _661099] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_661095), _661097), c_Nat_OSuc(_661099)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _661095, _661097), _661099))], (3486 ^ _543626) ^ [_661211, _661213] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _661211, _661213), _661213) = _661211)], (3488 ^ _543626) ^ [_661313, _661315] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _661313, _661315), _661313) = _661315)], (3490 ^ _543626) ^ [_661429, _661431, _661433] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _661429, _661431), _661433) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _661429, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _661431, _661433)))], (3492 ^ _543626) ^ [_661555, _661557, _661559] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _661555, _661557), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _661555, _661559)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _661557, _661559))], (3494 ^ _543626) ^ [_661681, _661683, _661685] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _661681, _661683), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _661685, _661683)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _661681, _661685))], (3496 ^ _543626) ^ [_661822, _661824, _661826] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _661822, _661824), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _661822, _661826), 3503 ^ _543626 : [(3504 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _661824, _661822), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _661826, _661822)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _661824, _661826))], (3510 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _661824, _661826), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _661824, _661822), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _661826, _661822)))]]], (3516 ^ _543626) ^ [_662439, _662441, _662443] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _662439, _662441), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _662439, _662443), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _662441, _662439), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _662443, _662439)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _662441, _662443))], (3526 ^ _543626) ^ [_662798, _662800, _662802] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _662798, _662800), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _662798, _662802), 3533 ^ _543626 : [(3534 ^ _543626) ^ [] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _662800, _662798) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _662802, _662798), -(_662800 = _662802)], (3540 ^ _543626) ^ [] : [_662800 = _662802, -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _662800, _662798) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _662802, _662798))]]], (3546 ^ _543626) ^ [_663395, _663397] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _663395, _663397), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _663397, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _663397, _663395)) = _663395)], (3552 ^ _543626) ^ [_663637, _663639, _663641] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _663637, _663639), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _663637, _663641), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _663639, _663641)))], (3558 ^ _543626) ^ [_663887, _663889, _663891] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _663887, _663889), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _663891, _663889), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _663891, _663887)))], (3564 ^ _543626) ^ [_664108, _664110] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _664108, _664110), _664108))], (3566 ^ _543626) ^ [_664251, _664253] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _664251, _664253)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _664253, c_Nat_OSuc(_664251)))], (3572 ^ _543626) ^ [_664424, _664426] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _664426, c_Nat_OSuc(_664424)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _664424, _664426)], (3588 ^ _543626) ^ [_664934, _664936] : [3589 ^ _543626 : [(3590 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _664934, _664936)], (3592 ^ _543626) ^ [] : [_664934 = _664936]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _664934, c_Nat_OSuc(_664936)))], (3578 ^ _543626) ^ [_664674, _664676] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _664674, c_Nat_OSuc(_664676)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _664674, _664676)), -(_664674 = _664676)], (3596 ^ _543626) ^ [_665257, _665259] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_665257), c_Nat_OSuc(_665259)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _665257, _665259))], (3602 ^ _543626) ^ [_665431, _665433] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _665431, _665433), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_665431), c_Nat_OSuc(_665433)))], (3608 ^ _543626) ^ [_665655, _665657] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _665655, _665657)), 3611 ^ _543626 : [(3612 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _665655, c_Nat_OSuc(_665657)), -(_665655 = _665657)], (3618 ^ _543626) ^ [] : [_665655 = _665657, -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _665655, c_Nat_OSuc(_665657)))]]], (3624 ^ _543626) ^ [_666129, _666131] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _666129, _666131)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _666129, c_Nat_OSuc(_666131)), -(_666131 = _666129)], (3634 ^ _543626) ^ [_666439, _666441] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _666439, _666441), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _666439, c_Nat_OSuc(_666441)))], (3640 ^ _543626) ^ [_666657, _666659] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _666657, _666659), -(c_Nat_OSuc(_666657) = _666659), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_666657), _666659))], (3650 ^ _543626) ^ [_666985, _666987, _666989] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _666985, _666987), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _666987, _666989), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_666985), _666989))], (3660 ^ _543626) ^ [_667304, _667306] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _667304, c_Nat_OSuc(_667306)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _667304, _667306)), -(_667304 = _667306)], (3670 ^ _543626) ^ [_667614, _667616] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_667614), _667616), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _667614, _667616))], (3676 ^ _543626) ^ [_667832, _667834] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_667832), c_Nat_OSuc(_667834)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _667832, _667834))], (3682 ^ _543626) ^ [_668083, _668085] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _668083, _668085), 3685 ^ _543626 : [(3686 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _668083, _668085))], (3688 ^ _543626) ^ [] : [_668083 = _668085]]], (3690 ^ _543626) ^ [_668325, _668327] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _668325, _668327)), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _668325, _668327), -(_668325 = _668327)], (3710 ^ _543626) ^ [_668918, _668920] : [3711 ^ _543626 : [(3712 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _668918, _668920)], (3714 ^ _543626) ^ [] : [_668918 = _668920]], -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _668918, _668920))], (3700 ^ _543626) ^ [_668662, _668664] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _668662, _668664), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _668662, _668664)), -(_668662 = _668664)], (3718 ^ _543626) ^ [_669222, _669224, _669226] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _669222, _669224), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _669222, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _669224, _669226)))], (3724 ^ _543626) ^ [_669464, _669466, _669468] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _669464, _669466), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _669464, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _669468, _669466)))], (3730 ^ _543626) ^ [_669676, _669678] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _669676, _669678), _669676)], (3732 ^ _543626) ^ [_669774, _669776] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _669774, _669776), _669776)], (3734 ^ _543626) ^ [_669931, _669933, _669935] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _669931, _669933), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _669931, _669935)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _669933, _669935))], (3740 ^ _543626) ^ [_670119, _670121, _670123] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _670121, _670123), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _670119, _670121), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _670119, _670123)))], (3746 ^ _543626) ^ [_670371, _670373, _670375] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _670371, _670373), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _670371, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _670373, _670375)))], (3752 ^ _543626) ^ [_670613, _670615, _670617] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _670613, _670615), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _670613, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _670617, _670615)))], (3758 ^ _543626) ^ [_670855, _670857, _670859] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _670855, _670857), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _670855, _670859), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _670857, _670859)))], (3764 ^ _543626) ^ [_671119, _671121, _671123, _671125] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _671119, _671121), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _671123, _671125), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _671119, _671123), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _671121, _671125)))], (3774 ^ _543626) ^ [_671488, _671490, _671492, _671494] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _671488, _671490), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _671492, _671490) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _671488, _671494), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _671492, _671494))], (3784 ^ _543626) ^ [_671841, _671843, _671845] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _671841, _671843), _671845), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _671841, _671845))], (3790 ^ _543626) ^ [_672069, _672071] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _672069, _672071), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _672069, _672071))], (3796 ^ _543626) ^ [_672283, _672285] : [3797 ^ _543626 : [(3798 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _672283, _672285)], (3800 ^ _543626) ^ [] : [_672283 = _672285]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _672283, _672285))], (3804 ^ _543626) ^ [_672571, _672573] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _672571, _672573), -(_672571 = _672573), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _672571, _672573))], (3814 ^ _543626) ^ [_672877, _672879] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _672877, _672879), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _672877, _672879))], (3830 ^ _543626) ^ [_673376, _673378] : [3831 ^ _543626 : [(3832 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _673376, _673378)], (3834 ^ _543626) ^ [] : [_673376 = _673378]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _673376, _673378))], (3820 ^ _543626) ^ [_673120, _673122] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _673120, _673122), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _673120, _673122)), -(_673120 = _673122)], (3838 ^ _543626) ^ [_673695, _673697] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _673695, _673697), 3841 ^ _543626 : [(3842 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _673695, _673697))], (3844 ^ _543626) ^ [] : [_673695 = _673697]]], (3846 ^ _543626) ^ [_673937, _673939] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _673937, _673939)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _673937, _673939), -(_673937 = _673939)], (3856 ^ _543626) ^ [_674245, _674247] : [class_Groups_Omonoid__add(_674245), -(c_Groups_Oplus__class_Oplus(_674245, c_Groups_Ozero__class_Ozero(_674245), _674247) = _674247)], (3862 ^ _543626) ^ [_674465, _674467] : [class_Groups_Ocomm__monoid__add(_674465), -(c_Groups_Oplus__class_Oplus(_674465, c_Groups_Ozero__class_Ozero(_674465), _674467) = _674467)], (3868 ^ _543626) ^ [_674685, _674687] : [class_Groups_Olinordered__ab__group__add(_674685), 3871 ^ _543626 : [(3872 ^ _543626) ^ [] : [c_Groups_Ozero__class_Ozero(_674685) = c_Groups_Oplus__class_Oplus(_674685, _674687, _674687), -(_674687 = c_Groups_Ozero__class_Ozero(_674685))], (3878 ^ _543626) ^ [] : [_674687 = c_Groups_Ozero__class_Ozero(_674685), -(c_Groups_Ozero__class_Ozero(_674685) = c_Groups_Oplus__class_Oplus(_674685, _674687, _674687))]]], (3884 ^ _543626) ^ [_675167, _675169] : [class_Groups_Omonoid__add(_675167), -(c_Groups_Oplus__class_Oplus(_675167, _675169, c_Groups_Ozero__class_Ozero(_675167)) = _675169)], (3890 ^ _543626) ^ [_675387, _675389] : [class_Groups_Ocomm__monoid__add(_675387), -(c_Groups_Oplus__class_Oplus(_675387, _675389, c_Groups_Ozero__class_Ozero(_675387)) = _675389)], (3896 ^ _543626) ^ [_675607, _675609] : [class_Rings_Ocomm__semiring__1(_675607), -(c_Groups_Oplus__class_Oplus(_675607, c_Groups_Ozero__class_Ozero(_675607), _675609) = _675609)], (3902 ^ _543626) ^ [_675827, _675829] : [class_Rings_Ocomm__semiring__1(_675827), -(c_Groups_Oplus__class_Oplus(_675827, _675829, c_Groups_Ozero__class_Ozero(_675827)) = _675829)], (3908 ^ _543626) ^ [_676061, _676063, _676065] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_676061), 3911 ^ _543626 : [(3912 ^ _543626) ^ [] : [_676063 = c_Groups_Oplus__class_Oplus(_676061, _676063, _676065), -(_676065 = c_Groups_Ozero__class_Ozero(_676061))], (3918 ^ _543626) ^ [] : [_676065 = c_Groups_Ozero__class_Ozero(_676061), -(_676063 = c_Groups_Oplus__class_Oplus(_676061, _676063, _676065))]]], (3924 ^ _543626) ^ [_676523] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_676523)], (3926 ^ _543626) ^ [_676602] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_676602)], (3928 ^ _543626) ^ [_676681] : [c_Nat_OSuc(_676681) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (3930 ^ _543626) ^ [_676760] : [c_Nat_OSuc(_676760) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (3932 ^ _543626) ^ [_676839] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_676839)], (3934 ^ _543626) ^ [_676918] : [c_Nat_OSuc(_676918) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (3936 ^ _543626) ^ [_676998] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _676998) = _676998)], (3938 ^ _543626) ^ [_677080] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _677080, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _677080)], (3940 ^ _543626) ^ [_677220, _677222] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _677220, _677222) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 3943 ^ _543626 : [(3944 ^ _543626) ^ [] : [-(_677220 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3946 ^ _543626) ^ [] : [-(_677222 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (3948 ^ _543626) ^ [_677465, _677467] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _677465, _677467) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _677465 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _677467 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (3958 ^ _543626) ^ [_677774, _677776] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _677774, _677776) = _677774, -(_677776 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3964 ^ _543626) ^ [_678007] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _678007, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_678007 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3970 ^ _543626) ^ [_678165] : [_678165 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _678165, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (3976 ^ _543626) ^ [_678344] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _678344))], (3988 ^ _543626) ^ [_678816] : [3991 ^ _543626 : [(3992 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, 3989 ^ [_678816], 3990 ^ [_678816]))], (3994 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(_678816, 3989 ^ [_678816]), hAPP(_678816, 3990 ^ [_678816]))]], -(c_SEQ_Osubseq(_678816))], (3978 ^ _543626) ^ [_678467] : [c_SEQ_Osubseq(_678467), 3981 ^ _543626 : [(3982 ^ _543626) ^ [_678625, _678627] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _678627, _678625), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(_678467, _678627), hAPP(_678467, _678625)))]]], (3998 ^ _543626) ^ [_679306, _679308, _679310, _679312, _679314] : [class_Groups_Oordered__cancel__ab__semigroup__add(_679306), c_Orderings_Oord__class_Oless(_679306, _679308, _679310), c_Orderings_Oord__class_Oless__eq(_679306, _679312, _679314), -(c_Orderings_Oord__class_Oless(_679306, c_Groups_Oplus__class_Oplus(_679306, _679308, _679312), c_Groups_Oplus__class_Oplus(_679306, _679310, _679314)))], (4012 ^ _543626) ^ [_679798, _679800, _679802, _679804, _679806] : [class_Groups_Oordered__cancel__ab__semigroup__add(_679798), c_Orderings_Oord__class_Oless__eq(_679798, _679800, _679802), c_Orderings_Oord__class_Oless(_679798, _679804, _679806), -(c_Orderings_Oord__class_Oless(_679798, c_Groups_Oplus__class_Oplus(_679798, _679800, _679804), c_Groups_Oplus__class_Oplus(_679798, _679802, _679806)))], (4026 ^ _543626) ^ [_680248, _680250] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _680248, _680250), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_680250), _680248) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _680250, _680248)))], (4032 ^ _543626) ^ [_680498, _680500, _680502] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _680498, _680500), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _680500, _680502), _680498) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _680500, _680498), _680502))], (4038 ^ _543626) ^ [_680762, _680764, _680766] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _680762, _680764), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _680764, _680762), _680766) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _680764, _680766), _680762))], (4044 ^ _543626) ^ [_681026, _681028, _681030] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _681026, _681028), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _681030, _681028), _681026) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _681030, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _681028, _681026)))], (4050 ^ _543626) ^ [_681290, _681292, _681294] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _681290, _681292), 4053 ^ _543626 : [(4054 ^ _543626) ^ [] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _681292, _681290) = _681294, -(_681292 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _681294, _681290))], (4060 ^ _543626) ^ [] : [_681292 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _681294, _681290), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _681292, _681290) = _681294)]]], (4066 ^ _543626) ^ [_681792, _681794] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _681792, _681794), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _681794, _681792), _681792) = _681794)], (4072 ^ _543626) ^ [_682034, _682036, _682038] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _682034, _682036), 4075 ^ _543626 : [(4076 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _682038, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _682036, _682034)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _682038, _682034), _682036))], (4082 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _682038, _682034), _682036), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _682038, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _682036, _682034)))]]], (4088 ^ _543626) ^ [_682556, _682558, _682560] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _682556, _682558), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _682560, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _682558, _682556)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _682560, _682558), _682556))], (4094 ^ _543626) ^ [_682806, _682808] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _682806, _682808), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _682806, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _682808, _682806)) = _682808)], (4100 ^ _543626) ^ [_683048, _683050, _683052] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _683048, _683050), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _683052, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _683050, _683052), _683048)))], (4106 ^ _543626) ^ [_683327, _683329, _683331] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _683327, _683329), _683331), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _683327, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _683331, _683329)))], (4112 ^ _543626) ^ [_683515, _683517, _683519] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _683515, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _683519, _683517)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _683515, _683517), _683519))], (4118 ^ _543626) ^ [_683767, _683769, _683771] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _683767, _683769), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _683771, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _683769, _683767)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _683771, _683767), _683769))], (4124 ^ _543626) ^ [_684002, _684004] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _684002, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _684002, _684004))))], (4126 ^ _543626) ^ [_684103, _684105] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _684103, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _684105, _684103))))], (4128 ^ _543626) ^ [_684248, _684250] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _684248, _684250), -(_684250 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _684248, 4131 ^ [_684248, _684250])))], (4135 ^ _543626) ^ [_684487, _684489] : [4136 ^ _543626 : [(4137 ^ _543626) ^ [_684564] : [_684489 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _684487, _684564))]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _684487, _684489))], (4141 ^ _543626) ^ [_684735, _684737] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_684735), _684737), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _684735, _684737))], (4147 ^ _543626) ^ [_684953, _684955] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _684953, _684955), 4150 ^ _543626 : [(4151 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _684955, c_Nat_OSuc(_684953)), -(_684955 = _684953)], (4157 ^ _543626) ^ [] : [_684955 = _684953, -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _684955, c_Nat_OSuc(_684953)))]]], (4163 ^ _543626) ^ [_685424, _685426] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _685424, _685426), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_685424), _685426))], (4169 ^ _543626) ^ [_685642, _685644] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _685642, _685644), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _685642, c_Nat_OSuc(_685644)))], (4175 ^ _543626) ^ [_685889, _685891] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_685889), _685891), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _685889, _685891))], (4181 ^ _543626) ^ [_686059, _686061] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _686059, _686061), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_686059), _686061))], (4187 ^ _543626) ^ [_686308, _686310] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _686308, c_Nat_OSuc(_686310)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _686308, _686310))], (4193 ^ _543626) ^ [_686478, _686480] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _686478, _686480), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _686478, c_Nat_OSuc(_686480)))], (4199 ^ _543626) ^ [_686727, _686729] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _686727, _686729), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_686727), _686729))], (4205 ^ _543626) ^ [_686897, _686899] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_686897), _686899), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _686897, _686899))], (4211 ^ _543626) ^ [_687117, _687119] : [class_Groups_Olinordered__ab__group__add(_687117), 4214 ^ _543626 : [(4215 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_687117, c_Groups_Ozero__class_Ozero(_687117), c_Groups_Oplus__class_Oplus(_687117, _687119, _687119)), -(c_Orderings_Oord__class_Oless__eq(_687117, c_Groups_Ozero__class_Ozero(_687117), _687119))], (4221 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_687117, c_Groups_Ozero__class_Ozero(_687117), _687119), -(c_Orderings_Oord__class_Oless__eq(_687117, c_Groups_Ozero__class_Ozero(_687117), c_Groups_Oplus__class_Oplus(_687117, _687119, _687119)))]]], (4227 ^ _543626) ^ [_687605, _687607] : [class_Groups_Olinordered__ab__group__add(_687605), 4230 ^ _543626 : [(4231 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_687605, c_Groups_Oplus__class_Oplus(_687605, _687607, _687607), c_Groups_Ozero__class_Ozero(_687605)), -(c_Orderings_Oord__class_Oless__eq(_687605, _687607, c_Groups_Ozero__class_Ozero(_687605)))], (4237 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_687605, _687607, c_Groups_Ozero__class_Ozero(_687605)), -(c_Orderings_Oord__class_Oless__eq(_687605, c_Groups_Oplus__class_Oplus(_687605, _687607, _687607), c_Groups_Ozero__class_Ozero(_687605)))]]], (4243 ^ _543626) ^ [_688107, _688109, _688111] : [class_Groups_Oordered__comm__monoid__add(_688107), c_Orderings_Oord__class_Oless__eq(_688107, c_Groups_Ozero__class_Ozero(_688107), _688109), c_Orderings_Oord__class_Oless__eq(_688107, c_Groups_Ozero__class_Ozero(_688107), _688111), -(c_Orderings_Oord__class_Oless__eq(_688107, c_Groups_Ozero__class_Ozero(_688107), c_Groups_Oplus__class_Oplus(_688107, _688109, _688111)))], (4257 ^ _543626) ^ [_688547, _688549, _688551] : [class_Groups_Oordered__comm__monoid__add(_688547), c_Orderings_Oord__class_Oless__eq(_688547, c_Groups_Ozero__class_Ozero(_688547), _688549), c_Orderings_Oord__class_Oless__eq(_688547, c_Groups_Ozero__class_Ozero(_688547), _688551), 4268 ^ _543626 : [(4269 ^ _543626) ^ [] : [c_Groups_Oplus__class_Oplus(_688547, _688549, _688551) = c_Groups_Ozero__class_Ozero(_688547), 4272 ^ _543626 : [(4273 ^ _543626) ^ [] : [-(_688549 = c_Groups_Ozero__class_Ozero(_688547))], (4275 ^ _543626) ^ [] : [-(_688551 = c_Groups_Ozero__class_Ozero(_688547))]]], (4277 ^ _543626) ^ [] : [-(c_Groups_Oplus__class_Oplus(_688547, _688549, _688551) = c_Groups_Ozero__class_Ozero(_688547)), _688549 = c_Groups_Ozero__class_Ozero(_688547), _688551 = c_Groups_Ozero__class_Ozero(_688547)]]], (4287 ^ _543626) ^ [_689441, _689443, _689445, _689447] : [class_Groups_Oordered__comm__monoid__add(_689441), c_Orderings_Oord__class_Oless__eq(_689441, c_Groups_Ozero__class_Ozero(_689441), _689443), c_Orderings_Oord__class_Oless__eq(_689441, _689445, _689447), -(c_Orderings_Oord__class_Oless__eq(_689441, _689445, c_Groups_Oplus__class_Oplus(_689441, _689443, _689447)))], (4301 ^ _543626) ^ [_689901, _689903, _689905, _689907] : [class_Groups_Oordered__comm__monoid__add(_689901), c_Orderings_Oord__class_Oless__eq(_689901, c_Groups_Ozero__class_Ozero(_689901), _689903), c_Orderings_Oord__class_Oless__eq(_689901, _689905, _689907), -(c_Orderings_Oord__class_Oless__eq(_689901, _689905, c_Groups_Oplus__class_Oplus(_689901, _689907, _689903)))], (4315 ^ _543626) ^ [_690347, _690349, _690351] : [class_Groups_Oordered__comm__monoid__add(_690347), c_Orderings_Oord__class_Oless__eq(_690347, _690349, c_Groups_Ozero__class_Ozero(_690347)), c_Orderings_Oord__class_Oless__eq(_690347, _690351, c_Groups_Ozero__class_Ozero(_690347)), -(c_Orderings_Oord__class_Oless__eq(_690347, c_Groups_Oplus__class_Oplus(_690347, _690349, _690351), c_Groups_Ozero__class_Ozero(_690347)))], (4329 ^ _543626) ^ [_690744] : [-(c_Nat_OSuc(_690744) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _690744))], (4331 ^ _543626) ^ [_690828] : [-(c_Nat_OSuc(_690828) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _690828, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (4333 ^ _543626) ^ [] : [-(hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (4335 ^ _543626) ^ [_691023, _691025] : [c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _691023, _691025), 4340 ^ _543626 : [(4341 ^ _543626) ^ [] : [-(_691023 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (4343 ^ _543626) ^ [] : [-(_691025 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 4344 ^ _543626 : [(4345 ^ _543626) ^ [] : [-(_691023 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4347 ^ _543626) ^ [] : [-(_691025 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (4349 ^ _543626) ^ [_691433, _691435] : [-(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _691433, _691435)), 4350 ^ _543626 : [(4351 ^ _543626) ^ [] : [_691433 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _691435 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (4357 ^ _543626) ^ [] : [_691433 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _691435 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (4365 ^ _543626) ^ [_691934, _691936] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _691934, _691936) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 4370 ^ _543626 : [(4371 ^ _543626) ^ [] : [-(_691934 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (4373 ^ _543626) ^ [] : [-(_691936 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 4374 ^ _543626 : [(4375 ^ _543626) ^ [] : [-(_691934 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4377 ^ _543626) ^ [] : [-(_691936 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (4379 ^ _543626) ^ [_692344, _692346] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _692344, _692346) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 4380 ^ _543626 : [(4381 ^ _543626) ^ [] : [_692344 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _692346 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (4387 ^ _543626) ^ [] : [_692344 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _692346 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (4395 ^ _543626) ^ [_692831] : [c_SEQ_Osubseq(_692831), 4398 ^ _543626 : [(4399 ^ _543626) ^ [_692950] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(_692831, _692950), hAPP(_692831, c_Nat_OSuc(_692950))))]]], (4401 ^ _543626) ^ [_693025] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(_693025, 4402 ^ [_693025]), hAPP(_693025, c_Nat_OSuc(4402 ^ [_693025]))), -(c_SEQ_Osubseq(_693025))], (4408 ^ _543626) ^ [_693326, _693328, _693330] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _693326, _693328), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _693330, c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _693328, _693326))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _693330, _693326), c_Nat_OSuc(_693328)))], (4414 ^ _543626) ^ [_693570] : [class_Rings_Olinordered__semidom(_693570), -(c_Orderings_Oord__class_Oless(_693570, c_Groups_Ozero__class_Ozero(_693570), c_Groups_Oplus__class_Oplus(_693570, c_Groups_Oone__class_Oone(_693570), c_Groups_Oone__class_Oone(_693570))))], (4420 ^ _543626) ^ [_693780] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _693780, c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_693780 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_693780 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (4430 ^ _543626) ^ [_694072, _694074] : [class_Rings_Olinordered__semidom(_694072), -(c_Orderings_Oord__class_Oless(_694072, _694074, c_Groups_Oplus__class_Oplus(_694072, _694074, c_Groups_Oone__class_Oone(_694072))))], (4436 ^ _543626) ^ [_694280] : [class_Rings_Olinordered__semidom(_694280), c_Orderings_Oord__class_Oless(_694280, c_Groups_Oone__class_Oone(_694280), c_Groups_Ozero__class_Ozero(_694280))], (4442 ^ _543626) ^ [_694479] : [class_Rings_Olinordered__semidom(_694479), -(c_Orderings_Oord__class_Oless(_694479, c_Groups_Ozero__class_Ozero(_694479), c_Groups_Oone__class_Oone(_694479)))], (4448 ^ _543626) ^ [_694677] : [class_Rings_Olinordered__semidom(_694677), -(c_Orderings_Oord__class_Oless__eq(_694677, c_Groups_Ozero__class_Ozero(_694677), c_Groups_Oone__class_Oone(_694677)))], (4454 ^ _543626) ^ [_694875] : [class_Rings_Olinordered__semidom(_694875), c_Orderings_Oord__class_Oless__eq(_694875, c_Groups_Oone__class_Oone(_694875), c_Groups_Ozero__class_Ozero(_694875))], (4460 ^ _543626) ^ [_695116, _695118, _695120, _695122] : [class_Rings_Olinordered__semidom(_695116), c_Orderings_Oord__class_Oless(_695116, c_Groups_Ozero__class_Ozero(_695116), _695118), c_Orderings_Oord__class_Oless(_695116, _695120, _695122), -(c_Orderings_Oord__class_Oless(_695116, _695120, c_Groups_Oplus__class_Oplus(_695116, _695118, _695122)))], (4474 ^ _543626) ^ [_695548, _695550] : [class_Rings_Olinordered__idom(_695548), 4477 ^ _543626 : [(4478 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(_695548, c_Groups_Oplus__class_Oplus(_695548, _695550, _695550), c_Groups_Ozero__class_Ozero(_695548)), -(c_Orderings_Oord__class_Oless(_695548, _695550, c_Groups_Ozero__class_Ozero(_695548)))], (4484 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(_695548, _695550, c_Groups_Ozero__class_Ozero(_695548)), -(c_Orderings_Oord__class_Oless(_695548, c_Groups_Oplus__class_Oplus(_695548, _695550, _695550), c_Groups_Ozero__class_Ozero(_695548)))]]], (4490 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), v_d____))], (4492 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), v_r))], (4494 ^ _543626) ^ [_696113] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), hAPP(c_RealDef_Oreal(tc_Nat_Onat), _696113)))], (4496 ^ _543626) ^ [_696253, _696255] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _696253, _696255), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _696253, _696255), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (4502 ^ _543626) ^ [_696427, _696429] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _696427, _696429), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _696427, _696429))], (4508 ^ _543626) ^ [_696679, _696681, _696683, _696685] : [class_Orderings_Oord(_696679), 4511 ^ _543626 : [(4512 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_fun(_696681, _696679), _696683, _696685), 4515 ^ _543626 : [(4516 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_fun(_696681, _696679), _696683, _696685))], (4518 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_696681, _696679), _696685, _696683)]]], (4520 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_fun(_696681, _696679), _696683, _696685)), c_Orderings_Oord__class_Oless__eq(tc_fun(_696681, _696679), _696683, _696685), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_696681, _696679), _696685, _696683))]]], (4530 ^ _543626) ^ [] : [c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)], (4532 ^ _543626) ^ [] : [-(hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (4534 ^ _543626) ^ [_697497] : [hAPP(c_RealDef_Oreal(tc_Nat_Onat), _697497) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_697497 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4540 ^ _543626) ^ [_697659] : [_697659 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_RealDef_Oreal(tc_Nat_Onat), _697659) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (4546 ^ _543626) ^ [_697841] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _697841), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (4548 ^ _543626) ^ [_697952, _697954] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _697952, _697954), -(hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _697954, _697952)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _697954), hAPP(c_RealDef_Oreal(tc_Nat_Onat), _697952)))], (4554 ^ _543626) ^ [_698212, _698214, _698216] : [class_Rings_Olinordered__idom(_698212), -(_698214 = _698216), -(c_Orderings_Oord__class_Oless(_698212, _698214, _698216)), -(c_Orderings_Oord__class_Oless(_698212, _698216, _698214))], (4568 ^ _543626) ^ [_698637] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _698637), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(_698637 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4574 ^ _543626) ^ [_698801] : [_698801 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _698801), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (4580 ^ _543626) ^ [_698986] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Nat_OSuc(_698986))))], (4582 ^ _543626) ^ [_699114] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), hAPP(c_RealDef_Oreal(tc_Nat_Onat), _699114)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _699114))], (4588 ^ _543626) ^ [_699280] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _699280), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), hAPP(c_RealDef_Oreal(tc_Nat_Onat), _699280)))], (4594 ^ _543626) ^ [_699496, _699498] : [class_Groups_Olinordered__ab__group__add(_699496), 4597 ^ _543626 : [(4598 ^ _543626) ^ [] : [c_Groups_Oplus__class_Oplus(_699496, _699498, _699498) = c_Groups_Ozero__class_Ozero(_699496), -(_699498 = c_Groups_Ozero__class_Ozero(_699496))], (4604 ^ _543626) ^ [] : [_699498 = c_Groups_Ozero__class_Ozero(_699496), -(c_Groups_Oplus__class_Oplus(_699496, _699498, _699498) = c_Groups_Ozero__class_Ozero(_699496))]]], (4610 ^ _543626) ^ [_699964] : [class_Rings_Ozero__neq__one(_699964), c_Groups_Oone__class_Oone(_699964) = c_Groups_Ozero__class_Ozero(_699964)], (4616 ^ _543626) ^ [_700161] : [class_Rings_Ozero__neq__one(_700161), c_Groups_Ozero__class_Ozero(_700161) = c_Groups_Oone__class_Oone(_700161)], (4622 ^ _543626) ^ [_700386, _700388, _700390] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _700386, _700388), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _700388, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _700386, _700390)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _700388, _700386)), _700390))], (4632 ^ _543626) ^ [_700765, _700767, _700769, _700771, _700773] : [class_Groups_Oab__group__add(_700765), -(c_Groups_Ominus__class_Ominus(_700765, c_Groups_Oplus__class_Oplus(_700765, _700767, _700769), c_Groups_Oplus__class_Oplus(_700765, _700771, _700773)) = c_Groups_Oplus__class_Oplus(_700765, c_Groups_Ominus__class_Ominus(_700765, _700767, _700771), c_Groups_Ominus__class_Ominus(_700765, _700769, _700773)))], (4638 ^ _543626) ^ [_701039, _701041] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _701039), _701041), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _701041, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _701039), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_RComplete_Onatceiling(_701041) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _701039, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (4648 ^ _543626) ^ [_701374, _701376] : [-(hBOOL(hAPP(_701374, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_701374, _701376)), 4656 ^ _543626 : [(4657 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, 4655 ^ [_701374, _701376], _701376))], (4665 ^ _543626) ^ [] : [-(hBOOL(hAPP(_701374, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, 4655 ^ [_701374, _701376], c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (4659 ^ _543626) ^ [_701810] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _701810, 4655 ^ [_701374, _701376]), hBOOL(hAPP(_701374, _701810))]]], (4667 ^ _543626) ^ [_702109] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _702109)), -(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _702109) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _702109), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (4673 ^ _543626) ^ [_702345, _702347] : [class_Groups_Ozero(_702345), 4676 ^ _543626 : [(4677 ^ _543626) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_702345, _702347) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_702347 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_702345)))], (4683 ^ _543626) ^ [] : [_702347 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_702345)), -(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_702345, _702347) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (4689 ^ _543626) ^ [_702810] : [class_Rings_Olinordered__idom(_702810), -(c_Groups_Oabs__class_Oabs(_702810, c_Groups_Oone__class_Oone(_702810)) = c_Groups_Oone__class_Oone(_702810))], (4695 ^ _543626) ^ [] : [-(c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4697 ^ _543626) ^ [_703093, _703095, _703097] : [class_Int_Onumber(_703093), 4700 ^ _543626 : [(4701 ^ _543626) ^ [] : [c_Int_Onumber__class_Onumber__of(_703093, _703095) = _703097, -(_703097 = c_Int_Onumber__class_Onumber__of(_703093, _703095))], (4707 ^ _543626) ^ [] : [_703097 = c_Int_Onumber__class_Onumber__of(_703093, _703095), -(c_Int_Onumber__class_Onumber__of(_703093, _703095) = _703097)]]], (4713 ^ _543626) ^ [_703599, _703601, _703603] : [class_Int_Onumber__ring(_703599), class_Int_Oring__char__0(_703599), 4720 ^ _543626 : [(4721 ^ _543626) ^ [] : [c_Int_Onumber__class_Onumber__of(_703599, _703601) = c_Int_Onumber__class_Onumber__of(_703599, _703603), -(_703601 = _703603)], (4727 ^ _543626) ^ [] : [_703601 = _703603, -(c_Int_Onumber__class_Onumber__of(_703599, _703601) = c_Int_Onumber__class_Onumber__of(_703599, _703603))]]], (4733 ^ _543626) ^ [_704155] : [-(c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat), _704155)) = _704155)], (4735 ^ _543626) ^ [_704267, _704269] : [class_Groups_Oordered__ab__group__add__abs(_704267), 4738 ^ _543626 : [(4739 ^ _543626) ^ [] : [c_Groups_Oabs__class_Oabs(_704267, _704269) = c_Groups_Ozero__class_Ozero(_704267), -(_704269 = c_Groups_Ozero__class_Ozero(_704267))], (4745 ^ _543626) ^ [] : [_704269 = c_Groups_Ozero__class_Ozero(_704267), -(c_Groups_Oabs__class_Oabs(_704267, _704269) = c_Groups_Ozero__class_Ozero(_704267))]]], (4751 ^ _543626) ^ [_704732] : [class_Groups_Oordered__ab__group__add__abs(_704732), -(c_Groups_Oabs__class_Oabs(_704732, c_Groups_Ozero__class_Ozero(_704732)) = c_Groups_Ozero__class_Ozero(_704732))], (4757 ^ _543626) ^ [_704962, _704964, _704966] : [class_Groups_Oordered__ab__group__add__abs(_704962), c_Orderings_Oord__class_Oless__eq(_704962, c_Groups_Oabs__class_Oabs(_704962, _704964), _704966), -(c_Orderings_Oord__class_Oless__eq(_704962, _704964, _704966))], (4767 ^ _543626) ^ [_705279, _705281] : [class_Groups_Oordered__ab__group__add__abs(_705279), -(c_Orderings_Oord__class_Oless__eq(_705279, _705281, c_Groups_Oabs__class_Oabs(_705279, _705281)))], (4773 ^ _543626) ^ [_705509, _705511, _705513] : [class_Groups_Oordered__ab__group__add__abs(_705509), -(c_Groups_Oabs__class_Oabs(_705509, c_Groups_Oplus__class_Oplus(_705509, c_Groups_Oabs__class_Oabs(_705509, _705511), c_Groups_Oabs__class_Oabs(_705509, _705513))) = c_Groups_Oplus__class_Oplus(_705509, c_Groups_Oabs__class_Oabs(_705509, _705511), c_Groups_Oabs__class_Oabs(_705509, _705513)))], (4779 ^ _543626) ^ [_705783, _705785, _705787] : [class_Groups_Oordered__ab__group__add__abs(_705783), -(c_Groups_Oabs__class_Oabs(_705783, c_Groups_Ominus__class_Ominus(_705783, _705785, _705787)) = c_Groups_Oabs__class_Oabs(_705783, c_Groups_Ominus__class_Ominus(_705783, _705787, _705785)))], (4785 ^ _543626) ^ [_706025, _706027] : [class_Groups_Oordered__ab__group__add__abs(_706025), -(c_Groups_Oabs__class_Oabs(_706025, c_Groups_Oabs__class_Oabs(_706025, _706027)) = c_Groups_Oabs__class_Oabs(_706025, _706027))], (4791 ^ _543626) ^ [_706265, _706267, _706269] : [class_Int_Onumber__ring(_706265), class_Rings_Olinordered__idom(_706265), 4798 ^ _543626 : [(4799 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_706265, c_Int_Onumber__class_Onumber__of(_706265, _706267), c_Int_Onumber__class_Onumber__of(_706265, _706269)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _706267, _706269))], (4805 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _706267, _706269), -(c_Orderings_Oord__class_Oless__eq(_706265, c_Int_Onumber__class_Onumber__of(_706265, _706267), c_Int_Onumber__class_Onumber__of(_706265, _706269)))]]], (4811 ^ _543626) ^ [_706870, _706872, _706874] : [class_Int_Onumber__ring(_706870), class_Rings_Olinordered__idom(_706870), 4818 ^ _543626 : [(4819 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(_706870, c_Int_Onumber__class_Onumber__of(_706870, _706872), c_Int_Onumber__class_Onumber__of(_706870, _706874)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _706872, _706874))], (4825 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _706872, _706874), -(c_Orderings_Oord__class_Oless(_706870, c_Int_Onumber__class_Onumber__of(_706870, _706872), c_Int_Onumber__class_Onumber__of(_706870, _706874)))]]], (4831 ^ _543626) ^ [_707489, _707491, _707493, _707495] : [class_Int_Onumber__ring(_707489), -(c_Groups_Oplus__class_Oplus(_707489, c_Int_Onumber__class_Onumber__of(_707489, _707491), c_Groups_Oplus__class_Oplus(_707489, c_Int_Onumber__class_Onumber__of(_707489, _707493), _707495)) = c_Groups_Oplus__class_Oplus(_707489, c_Int_Onumber__class_Onumber__of(_707489, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _707491, _707493)), _707495))], (4837 ^ _543626) ^ [_707773, _707775, _707777] : [class_Int_Onumber__ring(_707773), -(c_Groups_Oplus__class_Oplus(_707773, c_Int_Onumber__class_Onumber__of(_707773, _707775), c_Int_Onumber__class_Onumber__of(_707773, _707777)) = c_Int_Onumber__class_Onumber__of(_707773, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _707775, _707777)))], (4843 ^ _543626) ^ [_708035, _708037, _708039] : [class_Int_Onumber__ring(_708035), -(c_Int_Onumber__class_Onumber__of(_708035, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _708037, _708039)) = c_Groups_Oplus__class_Oplus(_708035, c_Int_Onumber__class_Onumber__of(_708035, _708037), c_Int_Onumber__class_Onumber__of(_708035, _708039)))], (4849 ^ _543626) ^ [_708297, _708299, _708301] : [class_Int_Onumber__ring(_708297), -(c_Int_Onumber__class_Onumber__of(_708297, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _708299, _708301)) = c_Groups_Ominus__class_Ominus(_708297, c_Int_Onumber__class_Onumber__of(_708297, _708299), c_Int_Onumber__class_Onumber__of(_708297, _708301)))], (4855 ^ _543626) ^ [_708516] : [-(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _708516)) = hAPP(c_RealDef_Oreal(tc_Nat_Onat), _708516))], (4857 ^ _543626) ^ [_708618] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _708618, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_RComplete_Onatceiling(_708618) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4863 ^ _543626) ^ [_708799] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_RComplete_Onatceiling(_708799)))], (4865 ^ _543626) ^ [_708909, _708911] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _708909, _708911), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_708909), c_RComplete_Onatceiling(_708911)))], (4871 ^ _543626) ^ [_709102] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _709102, hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_RComplete_Onatceiling(_709102))))], (4873 ^ _543626) ^ [] : [-(c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (4875 ^ _543626) ^ [_709268, _709270] : [class_Groups_Oordered__ab__group__add__abs(_709268), -(c_Orderings_Oord__class_Oless__eq(_709268, c_Groups_Ozero__class_Ozero(_709268), c_Groups_Oabs__class_Oabs(_709268, _709270)))], (4881 ^ _543626) ^ [_709488, _709490] : [class_Groups_Oordered__ab__group__add__abs(_709488), 4884 ^ _543626 : [(4885 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_709488, c_Groups_Oabs__class_Oabs(_709488, _709490), c_Groups_Ozero__class_Ozero(_709488)), -(_709490 = c_Groups_Ozero__class_Ozero(_709488))], (4891 ^ _543626) ^ [] : [_709490 = c_Groups_Ozero__class_Ozero(_709488), -(c_Orderings_Oord__class_Oless__eq(_709488, c_Groups_Oabs__class_Oabs(_709488, _709490), c_Groups_Ozero__class_Ozero(_709488)))]]], (4897 ^ _543626) ^ [_709970, _709972] : [class_Groups_Oordered__ab__group__add__abs(_709970), c_Orderings_Oord__class_Oless__eq(_709970, c_Groups_Ozero__class_Ozero(_709970), _709972), -(c_Groups_Oabs__class_Oabs(_709970, _709972) = _709972)], (4907 ^ _543626) ^ [_710279, _710281] : [class_Groups_Oordered__ab__group__add__abs(_710279), c_Orderings_Oord__class_Oless(_710279, c_Groups_Oabs__class_Oabs(_710279, _710281), c_Groups_Ozero__class_Ozero(_710279))], (4913 ^ _543626) ^ [_710500, _710502] : [class_Groups_Oordered__ab__group__add__abs(_710500), 4916 ^ _543626 : [(4917 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(_710500, c_Groups_Ozero__class_Ozero(_710500), c_Groups_Oabs__class_Oabs(_710500, _710502)), _710502 = c_Groups_Ozero__class_Ozero(_710500)], (4923 ^ _543626) ^ [] : [-(_710502 = c_Groups_Ozero__class_Ozero(_710500)), -(c_Orderings_Oord__class_Oless(_710500, c_Groups_Ozero__class_Ozero(_710500), c_Groups_Oabs__class_Oabs(_710500, _710502)))]]], (4929 ^ _543626) ^ [_710984, _710986] : [class_Groups_Oordered__ab__group__add__abs(_710984), c_Orderings_Oord__class_Oless(_710984, c_Groups_Ozero__class_Ozero(_710984), _710986), -(c_Groups_Oabs__class_Oabs(_710984, _710986) = _710986)], (4939 ^ _543626) ^ [_711307, _711309, _711311] : [class_Groups_Oordered__ab__group__add__abs(_711307), -(c_Orderings_Oord__class_Oless__eq(_711307, c_Groups_Oabs__class_Oabs(_711307, c_Groups_Oplus__class_Oplus(_711307, _711309, _711311)), c_Groups_Oplus__class_Oplus(_711307, c_Groups_Oabs__class_Oabs(_711307, _711309), c_Groups_Oabs__class_Oabs(_711307, _711311))))], (4945 ^ _543626) ^ [_711571, _711573, _711575] : [class_Groups_Oordered__ab__group__add__abs(_711571), -(c_Orderings_Oord__class_Oless__eq(_711571, c_Groups_Oabs__class_Oabs(_711571, c_Groups_Ominus__class_Ominus(_711571, c_Groups_Oabs__class_Oabs(_711571, _711573), c_Groups_Oabs__class_Oabs(_711571, _711575))), c_Groups_Oabs__class_Oabs(_711571, c_Groups_Ominus__class_Ominus(_711571, _711573, _711575))))], (4951 ^ _543626) ^ [_711841, _711843, _711845] : [class_Groups_Oordered__ab__group__add__abs(_711841), -(c_Orderings_Oord__class_Oless__eq(_711841, c_Groups_Ominus__class_Ominus(_711841, c_Groups_Oabs__class_Oabs(_711841, _711843), c_Groups_Oabs__class_Oabs(_711841, _711845)), c_Groups_Oabs__class_Oabs(_711841, c_Groups_Ominus__class_Ominus(_711841, _711843, _711845))))], (4957 ^ _543626) ^ [_712105, _712107, _712109] : [class_Groups_Oordered__ab__group__add__abs(_712105), -(c_Orderings_Oord__class_Oless__eq(_712105, c_Groups_Ominus__class_Ominus(_712105, c_Groups_Oabs__class_Oabs(_712105, _712107), c_Groups_Oabs__class_Oabs(_712105, _712109)), c_Groups_Oabs__class_Oabs(_712105, c_Groups_Ominus__class_Ominus(_712105, _712109, _712107))))], (4963 ^ _543626) ^ [_712383, _712385, _712387, _712389] : [class_Rings_Olinordered__idom(_712383), 4966 ^ _543626 : [(4967 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(_712383, c_Groups_Oabs__class_Oabs(_712383, c_Groups_Ominus__class_Ominus(_712383, _712385, _712387)), _712389), 4970 ^ _543626 : [(4971 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(_712383, c_Groups_Ominus__class_Ominus(_712383, _712387, _712389), _712385))], (4973 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(_712383, _712385, c_Groups_Oplus__class_Oplus(_712383, _712387, _712389)))]]], (4975 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(_712383, c_Groups_Oabs__class_Oabs(_712383, c_Groups_Ominus__class_Ominus(_712383, _712385, _712387)), _712389)), c_Orderings_Oord__class_Oless(_712383, c_Groups_Ominus__class_Ominus(_712383, _712387, _712389), _712385), c_Orderings_Oord__class_Oless(_712383, _712385, c_Groups_Oplus__class_Oplus(_712383, _712387, _712389))]]], (4985 ^ _543626) ^ [_713111, _713113, _713115] : [class_Int_Onumber(_713111), class_Orderings_Olinorder(_713111), 4992 ^ _543626 : [(4993 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_713111, c_Int_Onumber__class_Onumber__of(_713111, _713113), c_Int_Onumber__class_Onumber__of(_713111, _713115)), c_Orderings_Oord__class_Oless(_713111, c_Int_Onumber__class_Onumber__of(_713111, _713115), c_Int_Onumber__class_Onumber__of(_713111, _713113))], (4999 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(_713111, c_Int_Onumber__class_Onumber__of(_713111, _713115), c_Int_Onumber__class_Onumber__of(_713111, _713113))), -(c_Orderings_Oord__class_Oless__eq(_713111, c_Int_Onumber__class_Onumber__of(_713111, _713113), c_Int_Onumber__class_Onumber__of(_713111, _713115)))]]], (5005 ^ _543626) ^ [_713750, _713752, _713754, _713756] : [class_Int_Onumber__ring(_713750), -(c_Groups_Oplus__class_Oplus(_713750, c_Int_Onumber__class_Onumber__of(_713750, _713752), c_Groups_Ominus__class_Ominus(_713750, c_Int_Onumber__class_Onumber__of(_713750, _713754), _713756)) = c_Groups_Ominus__class_Ominus(_713750, c_Int_Onumber__class_Onumber__of(_713750, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _713752, _713754)), _713756))], (5011 ^ _543626) ^ [_714020, _714022] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _714020, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _714022)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_714020), _714022))], (5017 ^ _543626) ^ [_714244, _714246] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _714244), 5020 ^ _543626 : [(5021 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_714244), _714246), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _714244, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _714246)))], (5027 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _714244, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _714246)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_714244), _714246))]]], (5033 ^ _543626) ^ [_714727, _714729] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _714727), _714729), -(c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _714729, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _714727))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_RComplete_Onatceiling(_714729), _714727))], (5039 ^ _543626) ^ [_714989, _714991, _714993] : [class_Groups_Oordered__ab__group__add__abs(_714989), -(c_Orderings_Oord__class_Oless__eq(_714989, c_Groups_Oabs__class_Oabs(_714989, c_Groups_Ominus__class_Ominus(_714989, _714991, _714993)), c_Groups_Oplus__class_Oplus(_714989, c_Groups_Oabs__class_Oabs(_714989, _714991), c_Groups_Oabs__class_Oabs(_714989, _714993))))], (5045 ^ _543626) ^ [_715281, _715283, _715285, _715287, _715289] : [class_Groups_Oordered__ab__group__add__abs(_715281), -(c_Orderings_Oord__class_Oless__eq(_715281, c_Groups_Oabs__class_Oabs(_715281, c_Groups_Ominus__class_Ominus(_715281, c_Groups_Oplus__class_Oplus(_715281, _715283, _715285), c_Groups_Oplus__class_Oplus(_715281, _715287, _715289))), c_Groups_Oplus__class_Oplus(_715281, c_Groups_Oabs__class_Oabs(_715281, c_Groups_Ominus__class_Ominus(_715281, _715283, _715287)), c_Groups_Oabs__class_Oabs(_715281, c_Groups_Ominus__class_Ominus(_715281, _715285, _715289)))))], (5051 ^ _543626) ^ [_715545] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _715545), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _715545)], (5053 ^ _543626) ^ [_715631] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _715631))))], (5055 ^ _543626) ^ [_715761] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_715761), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _715761, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (5061 ^ _543626) ^ [_715925] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _715925, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_715925), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (5067 ^ _543626) ^ [_716139, _716141] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _716139), -(c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _716139, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _716141))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatceiling(_716139), _716141))], (5073 ^ _543626) ^ [_716367] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _716367), -(c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _716367, c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatceiling(_716367), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (5079 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____), v_r))], (5081 ^ _543626) ^ [_716636] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _716636), 5085 ^ _543626 : [(5086 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, 5084 ^ [_716636], c_Groups_Oone__class_Oone(tc_Nat_Onat))), _716636))], (5088 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _716636, hAPP(c_RealDef_Oreal(tc_Nat_Onat), 5084 ^ [_716636])))]]], (5090 ^ _543626) ^ [_716999] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _716999), -(c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _716999, c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatfloor(_716999), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (5096 ^ _543626) ^ [_717243, _717245, _717247] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _717243, _717245), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _717245, _717247), 5104 ^ _543626 : [(5105 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 5103 ^ [_717243, _717245, _717247]))], (5107 ^ _543626) ^ [_717666] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _717245, _717666)), 5103 ^ [_717243, _717245, _717247]), 5110 ^ _543626 : [(5111 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _717243, _717666))], (5113 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _717666, _717247))]]]]], (5115 ^ _543626) ^ [_718008] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _718008), 5119 ^ _543626 : [(5120 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), 5118 ^ [_718008]), _718008))], (5122 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _718008, hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Nat_OSuc(5118 ^ [_718008]))))]]], (5124 ^ _543626) ^ [_718350] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_g____(_718350)), v_r))], (5126 ^ _543626) ^ [_718433] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _718433), _718433) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (5128 ^ _543626) ^ [_718563] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _718563), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _718563))], (5134 ^ _543626) ^ [_718723] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _718723), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _718723))], (5140 ^ _543626) ^ [_718962, _718964] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _718962, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _718964, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _718962, _718964))], (5146 ^ _543626) ^ [_719136, _719138] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _719136, _719138), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _719136, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _719138, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (5152 ^ _543626) ^ [_719389, _719391] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _719389, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _719391, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _719389, _719391))], (5158 ^ _543626) ^ [_719563, _719565] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _719563, _719565), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _719563, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _719565, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (5174 ^ _543626) ^ [_720080, _720082] : [5175 ^ _543626 : [(5176 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _720080, _720082)], (5178 ^ _543626) ^ [] : [_720080 = _720082]], -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _720080, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _720082, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (5164 ^ _543626) ^ [_719816, _719818] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _719816, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _719818, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _719816, _719818)), -(_719816 = _719818)], (5182 ^ _543626) ^ [_720407, _720409] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _720407, c_Groups_Oone__class_Oone(tc_Int_Oint)), _720409), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _720407, _720409))], (5188 ^ _543626) ^ [_720581, _720583] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _720581, _720583), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _720581, c_Groups_Oone__class_Oone(tc_Int_Oint)), _720583))], (5194 ^ _543626) ^ [_720820] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _720820), _720820), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _720820, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (5200 ^ _543626) ^ [_720996] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _720996, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _720996), _720996), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (5206 ^ _543626) ^ [_721208] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _721208), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _721208)))], (5212 ^ _543626) ^ [_721424, _721426] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _721424, _721426), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _721424, c_Groups_Oone__class_Oone(tc_Int_Oint)), _721426))], (5218 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (5220 ^ _543626) ^ [_721714] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oabs__class_Oabs(tc_Int_Oint, _721714), c_Groups_Oone__class_Oone(tc_Int_Oint)), -(_721714 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (5226 ^ _543626) ^ [_721878] : [_721878 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oabs__class_Oabs(tc_Int_Oint, _721878), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (5232 ^ _543626) ^ [_722121, _722123] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Int_Onumber__class_Onumber__of(tc_Int_Oint, _722121), c_Int_Onumber__class_Onumber__of(tc_Int_Oint, _722123)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _722121, _722123))], (5238 ^ _543626) ^ [_722299, _722301] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _722299, _722301), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Int_Onumber__class_Onumber__of(tc_Int_Oint, _722299), c_Int_Onumber__class_Onumber__of(tc_Int_Oint, _722301)))], (5244 ^ _543626) ^ [_722527, _722529] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _722527, _722529)), -(_722527 = _722529), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _722529, _722527))], (5254 ^ _543626) ^ [_722861, _722863] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _722861, _722863), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _722861, _722863), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (5260 ^ _543626) ^ [_723035, _723037] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _723035, _723037), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _723035, _723037))], (5266 ^ _543626) ^ [_723287, _723289, _723291, _723293] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _723287, _723289), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _723291, _723293), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _723287, _723291), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _723289, _723293)))], (5276 ^ _543626) ^ [_723642, _723644, _723646] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _723642, _723644), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _723642, _723646), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _723644, _723646)))], (5282 ^ _543626) ^ [_723907, _723909] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _723907, _723909), 5285 ^ _543626 : [(5286 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _723907, _723909))], (5288 ^ _543626) ^ [] : [_723907 = _723909]]], (5290 ^ _543626) ^ [_724149, _724151] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _724149, _724151)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _724149, _724151), -(_724149 = _724151)], (5300 ^ _543626) ^ [_724428] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _724428, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _724428)], (5302 ^ _543626) ^ [_724510] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _724510) = _724510)], (5304 ^ _543626) ^ [_724606, _724608] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Int_Onumber__class_Onumber__of(tc_Int_Oint, _724606), c_Int_Onumber__class_Onumber__of(tc_Int_Oint, _724608)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _724606, _724608)))], (5306 ^ _543626) ^ [_724761, _724763] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Int_Onumber__class_Onumber__of(tc_Int_Oint, _724761), c_Int_Onumber__class_Onumber__of(tc_Int_Oint, _724763)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _724761, _724763))], (5312 ^ _543626) ^ [_724939, _724941] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _724939, _724941), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Int_Onumber__class_Onumber__of(tc_Int_Oint, _724939), c_Int_Onumber__class_Onumber__of(tc_Int_Oint, _724941)))], (5318 ^ _543626) ^ [_725138] : [-(c_RComplete_Onatfloor(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, _725138)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _725138))], (5320 ^ _543626) ^ [_725253, _725255] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _725253, _725255), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _725255, _725253), -(_725253 = _725255)], (5330 ^ _543626) ^ [_725570, _725572, _725574] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _725570, _725572), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _725572, _725574), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _725570, _725574))], (5340 ^ _543626) ^ [_725899, _725901, _725903] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _725899, _725901), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _725903, _725899), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _725903, _725901)))], (5346 ^ _543626) ^ [_726134, _726136, _726138] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _726134, _726136), _726138) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _726134, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _726136, _726138)))], (5348 ^ _543626) ^ [_726260, _726262, _726264] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _726260, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _726262, _726264)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _726262, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _726260, _726264)))], (5350 ^ _543626) ^ [_726387, _726389] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _726387, _726389)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _726389, _726387))], (5356 ^ _543626) ^ [_726587, _726589] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _726587, _726589) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _726589, _726587))], (5358 ^ _543626) ^ [_726675] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _726675, _726675))], (5360 ^ _543626) ^ [_726754] : [-(c_RComplete_Onatfloor(hAPP(c_RealDef_Oreal(tc_Nat_Onat), _726754)) = _726754)], (5362 ^ _543626) ^ [_726851, _726853] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _726851), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, _726851, _726853)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _726853))))], (5364 ^ _543626) ^ [_726949] : [-(c_RComplete_Onatceiling(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, _726949)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _726949))], (5366 ^ _543626) ^ [] : [-(c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5368 ^ _543626) ^ [_727088] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_RComplete_Onatfloor(_727088)))], (5370 ^ _543626) ^ [_727198, _727200] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _727198, _727200), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatfloor(_727198), c_RComplete_Onatfloor(_727200)))], (5376 ^ _543626) ^ [] : [-(c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (5378 ^ _543626) ^ [_727459] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _727459, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_RComplete_Onatfloor(_727459) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5384 ^ _543626) ^ [_727655] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _727655), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_RComplete_Onatfloor(_727655)), _727655))], (5390 ^ _543626) ^ [_727873, _727875] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _727873), _727875), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _727873, c_RComplete_Onatfloor(_727875)))], (5396 ^ _543626) ^ [_728097, _728099] : [class_RealVector_Oreal__normed__vector(_728097), 5399 ^ _543626 : [(5412 ^ _543626) ^ [] : [5414 ^ _543626 : [(5415 ^ _543626) ^ [_728833] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_728097, hAPP(_728099, 5413 ^ [_728097, _728099, _728833])), hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Nat_OSuc(_728833)))]], 5417 ^ _543626 : [(5418 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 5416 ^ [_728097, _728099]))], (5420 ^ _543626) ^ [_729054] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_728097, hAPP(_728099, _729054)), 5416 ^ [_728097, _728099]))]]], (5400 ^ _543626) ^ [] : [5409 ^ _543626 : [(5410 ^ _543626) ^ [_728654] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_728097, hAPP(_728099, _728654)), hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Nat_OSuc(5408 ^ [_728097, _728099]))))]], 5401 ^ _543626 : [(5402 ^ _543626) ^ [_728336] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _728336), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_728097, hAPP(_728099, 5405 ^ [_728097, _728099, _728336])), _728336)]]]]], (5422 ^ _543626) ^ [_729194, _729196] : [class_RealVector_Oreal__normed__vector(_729194), 5425 ^ _543626 : [(5438 ^ _543626) ^ [] : [5440 ^ _543626 : [(5441 ^ _543626) ^ [_729930] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_729194, hAPP(_729196, 5439 ^ [_729194, _729196, _729930])), hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Nat_OSuc(_729930)))]], 5443 ^ _543626 : [(5444 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 5442 ^ [_729194, _729196]))], (5446 ^ _543626) ^ [_730151] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_729194, hAPP(_729196, _730151)), 5442 ^ [_729194, _729196]))]]], (5426 ^ _543626) ^ [] : [5435 ^ _543626 : [(5436 ^ _543626) ^ [_729751] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_729194, hAPP(_729196, _729751)), hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Nat_OSuc(5434 ^ [_729194, _729196]))))]], 5427 ^ _543626 : [(5428 ^ _543626) ^ [_729433] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _729433), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_729194, hAPP(_729196, 5431 ^ [_729194, _729196, _729433])), _729433)]]]]], (5448 ^ _543626) ^ [_730291, _730293] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _730291), 5451 ^ _543626 : [(5452 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _730293, c_RComplete_Onatfloor(_730291)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _730293), _730291))], (5458 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _730293), _730291), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _730293, c_RComplete_Onatfloor(_730291)))]]], (5464 ^ _543626) ^ [_730789] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), c_RComplete_Onatfloor(_730789)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _730789))], (5470 ^ _543626) ^ [_730953] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _730953), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), c_RComplete_Onatfloor(_730953)))], (5476 ^ _543626) ^ [_731138] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _731138, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_RComplete_Onatfloor(_731138)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))], (5478 ^ _543626) ^ [_731255, _731257] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _731255), _731257), -(c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _731257, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _731255))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_RComplete_Onatfloor(_731257), _731255))], (5484 ^ _543626) ^ [_731474] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _731474, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_RComplete_Onatfloor(_731474))))], (5486 ^ _543626) ^ [_731591, _731593] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _731591), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _731591, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _731593)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_RComplete_Onatfloor(_731591), _731593))], (5496 ^ _543626) ^ [_731906, _731908] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _731906), -(c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _731906, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _731908))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatfloor(_731906), _731908))], (5502 ^ _543626) ^ [_732148, _732150] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatfloor(_732148), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _732150), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _732148, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _732150)))], (5508 ^ _543626) ^ [_732380, _732382] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _732380), _732382), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _732382, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _732380), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_RComplete_Onatfloor(_732382) = _732380)], (5518 ^ _543626) ^ [_732721, _732723, _732725] : [class_RealVector_Oreal__normed__vector(_732721), -(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(_732721, _732723), c_RealVector_Onorm__class_Onorm(_732721, _732725))), c_RealVector_Onorm__class_Onorm(_732721, c_Groups_Ominus__class_Ominus(_732721, _732723, _732725))))], (5524 ^ _543626) ^ [_733019, _733021, _733023, _733025, _733027] : [class_RealVector_Oreal__normed__vector(_733019), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_733019, c_Groups_Ominus__class_Ominus(_733019, c_Groups_Oplus__class_Oplus(_733019, _733021, _733023), c_Groups_Oplus__class_Oplus(_733019, _733025, _733027))), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_733019, c_Groups_Ominus__class_Ominus(_733019, _733021, _733025)), c_RealVector_Onorm__class_Onorm(_733019, c_Groups_Ominus__class_Ominus(_733019, _733023, _733027)))))], (5530 ^ _543626) ^ [_733327, _733329, _733331] : [class_RealVector_Oreal__normed__vector(_733327), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_733327, _733329), c_RealVector_Onorm__class_Onorm(_733327, _733331)), c_RealVector_Onorm__class_Onorm(_733327, c_Groups_Ominus__class_Ominus(_733327, _733329, _733331))))], (5536 ^ _543626) ^ [_733591, _733593, _733595] : [class_RealVector_Oreal__normed__vector(_733591), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_733591, _733593), c_RealVector_Onorm__class_Onorm(_733591, _733595)), c_RealVector_Onorm__class_Onorm(_733591, c_Groups_Oplus__class_Oplus(_733591, _733593, _733595))))], (5542 ^ _543626) ^ [_733855, _733857, _733859] : [class_RealVector_Oreal__normed__vector(_733855), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_733855, c_Groups_Ominus__class_Ominus(_733855, _733857, _733859)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_733855, _733857), c_RealVector_Onorm__class_Onorm(_733855, _733859))))], (5548 ^ _543626) ^ [_734091] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, v_N1____, _734091), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_g____(hAPP(v_f____, _734091)), v_z____)), v_d____))], (5554 ^ _543626) ^ [_734294] : [-(c_Int_Onumber__class_Onumber__of(tc_Int_Oint, _734294) = _734294)], (5556 ^ _543626) ^ [_734375] : [-(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, _734375) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _734375))], (5558 ^ _543626) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (5560 ^ _543626) ^ [_734554, _734556, _734558] : [class_RealVector_Oreal__normed__vector(_734554), -(c_RealVector_Onorm__class_Onorm(_734554, c_Groups_Ominus__class_Ominus(_734554, _734556, _734558)) = c_RealVector_Onorm__class_Onorm(_734554, c_Groups_Ominus__class_Ominus(_734554, _734558, _734556)))], (5566 ^ _543626) ^ [_734796, _734798] : [class_RealVector_Oreal__normed__vector(_734796), -(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_734796, _734798)) = c_RealVector_Onorm__class_Onorm(_734796, _734798))], (5572 ^ _543626) ^ [_735022, _735024] : [class_RealVector_Oreal__normed__vector(_735022), 5575 ^ _543626 : [(5576 ^ _543626) ^ [] : [c_RealVector_Onorm__class_Onorm(_735022, _735024) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_735024 = c_Groups_Ozero__class_Ozero(_735022))], (5582 ^ _543626) ^ [] : [_735024 = c_Groups_Ozero__class_Ozero(_735022), -(c_RealVector_Onorm__class_Onorm(_735022, _735024) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))]]], (5588 ^ _543626) ^ [_735481] : [class_RealVector_Oreal__normed__vector(_735481), -(c_RealVector_Onorm__class_Onorm(_735481, c_Groups_Ozero__class_Ozero(_735481)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (5594 ^ _543626) ^ [_735693, _735695] : [class_RealVector_Oreal__normed__vector(_735693), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_735693, _735695)))], (5600 ^ _543626) ^ [_735909, _735911] : [class_RealVector_Oreal__normed__vector(_735909), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_735909, _735911), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (5606 ^ _543626) ^ [_736112] : [class_RealVector_Oreal__normed__algebra__1(_736112), -(c_RealVector_Onorm__class_Onorm(_736112, c_Groups_Oone__class_Oone(_736112)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (5612 ^ _543626) ^ [_736324, _736326] : [-(c_RealVector_Onorm__class_Onorm(_736324, c_Int_Onumber__class_Onumber__of(_736324, _736326)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, _736326))), class_Int_Onumber__ring(_736324), class_RealVector_Oreal__normed__algebra__1(_736324)], (5622 ^ _543626) ^ [_736643, _736645] : [class_RealVector_Oreal__normed__vector(_736643), 5625 ^ _543626 : [(5626 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_736643, _736645), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(_736645 = c_Groups_Ozero__class_Ozero(_736643))], (5632 ^ _543626) ^ [] : [_736645 = c_Groups_Ozero__class_Ozero(_736643), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_736643, _736645), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))]]], (5638 ^ _543626) ^ [_737119, _737121] : [class_RealVector_Oreal__normed__vector(_737119), 5641 ^ _543626 : [(5642 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_737119, _737121)), _737121 = c_Groups_Ozero__class_Ozero(_737119)], (5648 ^ _543626) ^ [] : [-(_737121 = c_Groups_Ozero__class_Ozero(_737119)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_737119, _737121)))]]], (5654 ^ _543626) ^ [_737611, _737613, _737615] : [class_RealVector_Oreal__normed__vector(_737611), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_737611, c_Groups_Oplus__class_Oplus(_737611, _737613, _737615)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_737611, _737613), c_RealVector_Onorm__class_Onorm(_737611, _737615))))], (5660 ^ _543626) ^ [_737903, _737905, _737907, _737909, _737911] : [class_RealVector_Oreal__normed__vector(_737903), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_737903, _737905), _737907), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_737903, _737909), _737911), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_737903, c_Groups_Oplus__class_Oplus(_737903, _737905, _737909)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _737907, _737911)))], (5674 ^ _543626) ^ [_738356, _738358] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, _738356, _738358)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _738356)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _738358)))], (5676 ^ _543626) ^ [_738483, _738485] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _738483), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _738485), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _738483, _738485)))], (5686 ^ _543626) ^ [] : [-(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)))], (5688 ^ _543626) ^ [_738835] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _738835), 5692 ^ _543626 : [(5693 ^ _543626) ^ [_739055] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, 5691 ^ [_738835], _739055), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_g____(hAPP(v_f____, _739055)), v_z____)), _738835))]]], (5699 ^ _543626) ^ [] : [-(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)))], (5702 ^ _543626) ^ [_739411] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, 5700 ^ [], _739411), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_g____(hAPP(v_f____, _739411)), v_z____)), v_d____))], (5709 ^ _543626) ^ [_739693] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, 5707 ^ [], _739693), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, v_g____(hAPP(v_f____, _739693)), v_z____)), v_d____))], (5715 ^ _543626) ^ [_739925, _739927] : [-(c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint, _739925))), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _739927), -(c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _739927, c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, _739925))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatceiling(_739927), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _739925)))], (5725 ^ _543626) ^ [_740269, _740271] : [-(c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint, _740269))), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _740271), -(c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _740271, c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, _740269))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatfloor(_740271), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _740269)))], (5735 ^ _543626) ^ [] : [c_Nat__Numeral_Oneg(c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (5737 ^ _543626) ^ [] : [c_Nat__Numeral_Oneg(c_Groups_Oone__class_Oone(tc_Int_Oint))], (5739 ^ _543626) ^ [_740732] : [-(c_Nat__Numeral_Oneg(_740732)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _740732))], (5745 ^ _543626) ^ [_740891] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _740891), c_Nat__Numeral_Oneg(_740891)], (5751 ^ _543626) ^ [_741113] : [c_Nat__Numeral_Oneg(_741113), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _741113, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (5757 ^ _543626) ^ [_741269] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _741269, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Nat__Numeral_Oneg(_741269))], (5763 ^ _543626) ^ [_741461] : [c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint, _741461)), -(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _741461) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5795 ^ _543626) ^ [_742420, _742422] : [-(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _742420) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _742422)), 5798 ^ _543626 : [(5799 ^ _543626) ^ [] : [-(c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint, _742420)))], (5801 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Int_Onumber__class_Onumber__of(tc_Int_Oint, _742422), c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], 5802 ^ _543626 : [(5803 ^ _543626) ^ [] : [c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint, _742420))], (5805 ^ _543626) ^ [] : [5806 ^ _543626 : [(5807 ^ _543626) ^ [] : [-(c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint, _742422)))], (5809 ^ _543626) ^ [] : [c_Int_Onumber__class_Onumber__of(tc_Int_Oint, _742420) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], 5810 ^ _543626 : [(5811 ^ _543626) ^ [] : [c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint, _742422))], (5813 ^ _543626) ^ [] : [_742420 = _742422]]]]], (5769 ^ _543626) ^ [_741704, _741706] : [c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _741704) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _741706), 5772 ^ _543626 : [(5773 ^ _543626) ^ [] : [c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint, _741704)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Int_Onumber__class_Onumber__of(tc_Int_Oint, _741706), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (5779 ^ _543626) ^ [] : [-(c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint, _741704))), 5782 ^ _543626 : [(5783 ^ _543626) ^ [] : [c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint, _741706)), -(c_Int_Onumber__class_Onumber__of(tc_Int_Oint, _741704) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (5789 ^ _543626) ^ [] : [-(c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint, _741706))), -(_741704 = _741706)]]]]], (5817 ^ _543626) ^ [_743188, _743190, _743192] : [c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint, _743188)), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _743188), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _743190), _743192)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _743190), _743192))], (5823 ^ _543626) ^ [_743402, _743404, _743406] : [-(c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint, _743402))), 5826 ^ _543626 : [(5827 ^ _543626) ^ [] : [c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint, _743404)), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _743402), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _743404), _743406)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _743402), _743406))], (5833 ^ _543626) ^ [] : [-(c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint, _743404))), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _743402), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _743404), _743406)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _743402, _743404)), _743406))]]], (5839 ^ _543626) ^ [_743999] : [c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint, _743999)), -(hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _743999)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (5845 ^ _543626) ^ [_744171] : [-(c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint, _744171))), -(hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _744171)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, _744171))], (5851 ^ _543626) ^ [_744402, _744404] : [-(c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint, _744402))), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _744404), 5858 ^ _543626 : [(5859 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _744402), c_RComplete_Onatfloor(_744404)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, _744402), _744404))], (5865 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, _744402), _744404), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _744402), c_RComplete_Onatfloor(_744404)))]]], (5871 ^ _543626) ^ [_744990, _744992] : [-(c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint, _744990))), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _744992), 5878 ^ _543626 : [(5879 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_744992), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _744990)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _744992, c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, _744990)))], (5885 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _744992, c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal, _744990)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_744992), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _744990)))]]], (5891 ^ _543626) ^ [_745598, _745600] : [c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint, _745598)), -(c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _745598), _745600)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _745600))], (5897 ^ _543626) ^ [_745790, _745792] : [-(c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint, _745790))), -(c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _745790), _745792)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Int_Osucc(_745790)), _745792))], (5903 ^ _543626) ^ [_746051] : [c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint, _746051)), -(c_Nat_OSuc(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _746051)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (5909 ^ _543626) ^ [_746221] : [-(c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint, _746221))), -(c_Nat_OSuc(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _746221)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Int_Osucc(_746221)))], (5915 ^ _543626) ^ [_746482, _746484, _746486, _746488] : [class_RealVector_Oreal__normed__vector(_746482), class_Orderings_Oord(_746484), 5925 ^ _543626 : [(5926 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_746484, _746486, 5924 ^ [_746482, _746484, _746486, _746488]))], (5928 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_746482, c_Groups_Ominus__class_Ominus(_746482, hAPP(_746488, _746486), hAPP(_746488, 5924 ^ [_746482, _746484, _746486, _746488]))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))]], 5929 ^ _543626 : [(5930 ^ _543626) ^ [_747040] : [c_Orderings_Oord__class_Oless__eq(_746484, _746486, _747040), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_746482, hAPP(_746488, _747040)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_746482, hAPP(_746488, _746486)))))]]], (5936 ^ _543626) ^ [_747310] : [c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _747310) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, _747310, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, _747310, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, _747310, c_Complex_Oii)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, _747310, c_Complex_Oii)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (5954 ^ _543626) ^ [] : [c_Complex_Oii = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)], (5956 ^ _543626) ^ [] : [c_Complex_Oii = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)], (5958 ^ _543626) ^ [_747916] : [c_Complex_Oii = c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex, _747916)], (5960 ^ _543626) ^ [_747997] : [-(c_Int_Osucc(_747997) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _747997, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (5962 ^ _543626) ^ [_748110, _748112] : [class_Int_Onumber__ring(_748110), -(c_Int_Onumber__class_Onumber__of(_748110, c_Int_Osucc(_748112)) = c_Groups_Oplus__class_Oplus(_748110, c_Groups_Oone__class_Oone(_748110), c_Int_Onumber__class_Onumber__of(_748110, _748112)))], (5968 ^ _543626) ^ [_748366, _748368] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _748366, _748368), -(c_Nat__Transfer_Otsub(_748368, _748366) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, _748368, _748366))], (5974 ^ _543626) ^ [_748544, _748546] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _748544, _748546)), -(c_Nat__Transfer_Otsub(_748546, _748544) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (5980 ^ _543626) ^ [_748767, _748769] : [class_RealVector_Oreal__normed__vector(_748767), 5983 ^ _543626 : [(5984 ^ _543626) ^ [] : [c_SEQ_OBseq(_748767, _748769), 5988 ^ _543626 : [(5989 ^ _543626) ^ [_749074] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_748767, hAPP(_748769, _749074)), hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Nat_OSuc(5987 ^ [_748767, _748769]))))]]], (5991 ^ _543626) ^ [] : [5993 ^ _543626 : [(5994 ^ _543626) ^ [_749252] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_748767, hAPP(_748769, 5992 ^ [_748767, _748769, _749252])), hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Nat_OSuc(_749252)))]], -(c_SEQ_OBseq(_748767, _748769))]]], (5998 ^ _543626) ^ [_749442, _749444] : [class_RealVector_Oreal__normed__vector(_749442), 6001 ^ _543626 : [(6002 ^ _543626) ^ [] : [c_SEQ_OBseq(_749442, _749444), 6006 ^ _543626 : [(6007 ^ _543626) ^ [_749749] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_749442, hAPP(_749444, _749749)), hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Nat_OSuc(6005 ^ [_749442, _749444]))))]]], (6009 ^ _543626) ^ [] : [6011 ^ _543626 : [(6012 ^ _543626) ^ [_749927] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_749442, hAPP(_749444, 6010 ^ [_749442, _749444, _749927])), hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Nat_OSuc(_749927)))]], -(c_SEQ_OBseq(_749442, _749444))]]], (6016 ^ _543626) ^ [_750117, _750119] : [class_RealVector_Oreal__normed__vector(_750117), 6019 ^ _543626 : [(6020 ^ _543626) ^ [] : [c_SEQ_OBseq(_750117, _750119), 6024 ^ _543626 : [(6025 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 6023 ^ [_750117, _750119]))], (6027 ^ _543626) ^ [_750502] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_750117, hAPP(_750119, _750502)), 6023 ^ [_750117, _750119]))]]], (6029 ^ _543626) ^ [] : [-(c_SEQ_OBseq(_750117, _750119)), 6030 ^ _543626 : [(6031 ^ _543626) ^ [_750634] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _750634), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_750117, hAPP(_750119, 6034 ^ [_750117, _750119, _750634])), _750634)]]]]], (6040 ^ _543626) ^ [_750997, _750999] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _750997), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _750999), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Nat__Transfer_Otsub(_750997, _750999)))], (6050 ^ _543626) ^ [_751308, _751310] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _751308, _751310), -(c_Nat__Transfer_Otsub(_751310, _751308) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, _751310, _751308))], (6056 ^ _543626) ^ [_751534, _751536] : [class_RealVector_Oreal__normed__vector(_751534), c_SEQ_OBseq(_751534, _751536), 6064 ^ _543626 : [(6065 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 6063 ^ [_751534, _751536]))], (6067 ^ _543626) ^ [_751890] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_751534, hAPP(_751536, _751890)), 6063 ^ [_751534, _751536]))]]], (6069 ^ _543626) ^ [_752040, _752042, _752044] : [class_RealVector_Oreal__normed__vector(_752040), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _752042), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_752040, hAPP(_752044, 6078 ^ [_752040, _752042, _752044])), _752042), -(c_SEQ_OBseq(_752040, _752044))], (6084 ^ _543626) ^ [_752532] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _752532, c_Int_OPls), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _752532)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (6090 ^ _543626) ^ [_752704] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _752704, c_Int_OPls)), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _752704)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Int_Osucc(_752704)))], (6096 ^ _543626) ^ [_752945] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _752945, c_Int_OPls), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _752945), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (6102 ^ _543626) ^ [_753117] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _753117, c_Int_OPls)), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _753117), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Int_Osucc(_753117)))], (6108 ^ _543626) ^ [] : [-(c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (6110 ^ _543626) ^ [_753376] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Int_OPls, _753376) = _753376)], (6112 ^ _543626) ^ [_753458] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _753458, c_Int_OPls) = _753458)], (6114 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Int_OPls, c_Int_OPls))], (6116 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Int_OPls, c_Int_OPls)], (6118 ^ _543626) ^ [_753645] : [-(c_Groups_Ominus__class_Ominus(tc_Int_Oint, _753645, c_Int_OPls) = _753645)], (6120 ^ _543626) ^ [_753742] : [class_Int_Onumber__ring(_753742), -(c_Int_Onumber__class_Onumber__of(_753742, c_Int_OPls) = c_Groups_Ozero__class_Ozero(_753742))], (6126 ^ _543626) ^ [_753940] : [class_Int_Onumber__ring(_753940), -(c_Groups_Ozero__class_Ozero(_753940) = c_Int_Onumber__class_Onumber__of(_753940, c_Int_OPls))], (6132 ^ _543626) ^ [_754152, _754154] : [class_Int_Onumber__ring(_754152), -(c_Groups_Oplus__class_Oplus(_754152, c_Int_Onumber__class_Onumber__of(_754152, c_Int_OPls), _754154) = _754154)], (6138 ^ _543626) ^ [_754374, _754376] : [class_Int_Onumber__ring(_754374), -(c_Groups_Oplus__class_Oplus(_754374, _754376, c_Int_Onumber__class_Onumber__of(_754374, c_Int_OPls)) = _754376)], (6144 ^ _543626) ^ [] : [-(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6146 ^ _543626) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Int_OPls))], (6148 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Int_OPls, c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (6150 ^ _543626) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint, c_Int_OPls))], (6152 ^ _543626) ^ [] : [c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint, c_Int_OPls))], (6154 ^ _543626) ^ [_754874] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _754874), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _754874, c_Int_OPls))], (6160 ^ _543626) ^ [_755038] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _755038, c_Int_OPls), -(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _755038))], (6166 ^ _543626) ^ [_755267] : [c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _755267) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _755267, c_Int_OPls))], (6172 ^ _543626) ^ [_755431] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _755431, c_Int_OPls), -(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _755431) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6178 ^ _543626) ^ [_755674, _755676] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _755674), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _755676)), 6181 ^ _543626 : [(6188 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _755674, _755676))], (6182 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _755674, _755676), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Int_OPls, _755676))]]], (6190 ^ _543626) ^ [_756020, _756022] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _756020), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _756022))), 6193 ^ _543626 : [(6194 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _756020, _756022))], (6196 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Int_OPls, _756022)]], c_Orderings_Oord__class_Oless(tc_Int_Oint, _756020, _756022)], (6212 ^ _543626) ^ [_756717, _756719] : [6213 ^ _543626 : [(6214 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _756717, _756719)], (6216 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _756717, c_Int_OPls)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _756717), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _756719)))], (6202 ^ _543626) ^ [_756445, _756447] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _756445), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _756447)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _756445, _756447)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _756445, c_Int_OPls))], (6220 ^ _543626) ^ [_757023, _757025] : [class_Int_Onumber__ring(_757023), class_Rings_Olinordered__idom(_757023), 6227 ^ _543626 : [(6228 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_757023, c_Int_Onumber__class_Onumber__of(_757023, _757025), c_Groups_Ozero__class_Ozero(_757023)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _757025, c_Int_OPls))], (6234 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _757025, c_Int_OPls), -(c_Orderings_Oord__class_Oless__eq(_757023, c_Int_Onumber__class_Onumber__of(_757023, _757025), c_Groups_Ozero__class_Ozero(_757023)))]]], (6240 ^ _543626) ^ [_757591, _757593] : [class_Int_Onumber__ring(_757591), class_Rings_Olinordered__idom(_757591), 6247 ^ _543626 : [(6248 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_757591, c_Groups_Ozero__class_Ozero(_757591), c_Int_Onumber__class_Onumber__of(_757591, _757593)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Int_OPls, _757593))], (6254 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Int_OPls, _757593), -(c_Orderings_Oord__class_Oless__eq(_757591, c_Groups_Ozero__class_Ozero(_757591), c_Int_Onumber__class_Onumber__of(_757591, _757593)))]]], (6260 ^ _543626) ^ [_758159, _758161] : [class_Int_Onumber__ring(_758159), class_Rings_Olinordered__idom(_758159), 6267 ^ _543626 : [(6268 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(_758159, c_Int_Onumber__class_Onumber__of(_758159, _758161), c_Groups_Ozero__class_Ozero(_758159)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _758161, c_Int_OPls))], (6274 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _758161, c_Int_OPls), -(c_Orderings_Oord__class_Oless(_758159, c_Int_Onumber__class_Onumber__of(_758159, _758161), c_Groups_Ozero__class_Ozero(_758159)))]]], (6280 ^ _543626) ^ [_758727, _758729] : [class_Int_Onumber__ring(_758727), class_Rings_Olinordered__idom(_758727), 6287 ^ _543626 : [(6288 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(_758727, c_Groups_Ozero__class_Ozero(_758727), c_Int_Onumber__class_Onumber__of(_758727, _758729)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Int_OPls, _758729))], (6294 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Int_OPls, _758729), -(c_Orderings_Oord__class_Oless(_758727, c_Groups_Ozero__class_Ozero(_758727), c_Int_Onumber__class_Onumber__of(_758727, _758729)))]]], (6300 ^ _543626) ^ [_759310] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _759310)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Int_OPls, _759310))], (6306 ^ _543626) ^ [_759476] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Int_OPls, _759476), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _759476)))], (6312 ^ _543626) ^ [_759712, _759714] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _759712, c_Int_OPls), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _759712), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _759714)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _759714))], (6318 ^ _543626) ^ [_759902, _759904] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _759902, c_Int_OPls)), 6321 ^ _543626 : [(6322 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _759904, c_Int_OPls), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _759902), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _759904)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _759902))], (6328 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _759904, c_Int_OPls)), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _759902), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _759904)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _759902, _759904)))]]], (6334 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Int_Onumber__class_Onumber__of(tc_Int_Oint, c_Int_OPls)))], (6336 ^ _543626) ^ [_760498] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _760498, c_Int_OPls), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _760498), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6342 ^ _543626) ^ [_760670] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _760670, c_Int_OPls)), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _760670), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Int_Opred(_760670)))], (6348 ^ _543626) ^ [_760905, _760907] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Int_OPls, _760905), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_760907), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _760905)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _760907, c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Int_Opred(_760905))))], (6354 ^ _543626) ^ [] : [-(c_Complex_Oexpi(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))], (6356 ^ _543626) ^ [_761177] : [-(c_Int_Osucc(c_Int_Opred(_761177)) = _761177)], (6358 ^ _543626) ^ [_761317, _761319] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _761317, _761319), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Int_Opred(_761317), _761319))], (6364 ^ _543626) ^ [_761487, _761489] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Int_Opred(_761487), _761489), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _761487, _761489))], (6370 ^ _543626) ^ [_761678] : [-(c_Int_Opred(_761678) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, _761678, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (6372 ^ _543626) ^ [_761806] : [c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint, c_Int_Opred(_761806))), -(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _761806) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6378 ^ _543626) ^ [_761976] : [c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _761976) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint, c_Int_Opred(_761976))))], (6384 ^ _543626) ^ [_762210, _762212, _762214] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _762210), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _762212, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oabs__class_Oabs(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _762212, _762214)), c_Groups_Oone__class_Oone(tc_Int_Oint))), _762210)), _762214))], (6390 ^ _543626) ^ [_762486, _762488, _762490] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _762486), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _762488, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _762490, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oabs__class_Oabs(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _762490, _762488)), c_Groups_Oone__class_Oone(tc_Int_Oint))), _762486))))], (6396 ^ _543626) ^ [_762748, _762750] : [class_Int_Onumber__ring(_762748), 6399 ^ _543626 : [(6400 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Int_Onumber__class_Onumber__of(tc_Int_Oint, _762750)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_762748), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _762750)) = c_Int_Onumber__class_Onumber__of(_762748, _762750))], (6406 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Int_Onumber__class_Onumber__of(tc_Int_Oint, _762750))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_762748), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _762750)) = c_Groups_Ozero__class_Ozero(_762748))]]], (6412 ^ _543626) ^ [_763284, _763286, _763288] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _763284, _763286), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _763288), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _763288)), _763284), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _763288)), _763286)))], (6422 ^ _543626) ^ [_763635, _763637] : [class_RealVector_Oreal__normed__algebra(_763635), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_763635), _763637), c_Groups_Ozero__class_Ozero(_763635)) = c_Groups_Ozero__class_Ozero(_763635))], (6428 ^ _543626) ^ [_763867, _763869] : [class_RealVector_Oreal__normed__algebra(_763867), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_763867), _763869), c_Groups_Ozero__class_Ozero(_763867)) = c_Groups_Ozero__class_Ozero(_763867))], (6434 ^ _543626) ^ [_764099, _764101] : [class_RealVector_Oreal__normed__algebra(_764099), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_764099), c_Groups_Ozero__class_Ozero(_764099)), _764101) = c_Groups_Ozero__class_Ozero(_764099))], (6440 ^ _543626) ^ [_764331, _764333] : [class_RealVector_Oreal__normed__algebra(_764331), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_764331), c_Groups_Ozero__class_Ozero(_764331)), _764333) = c_Groups_Ozero__class_Ozero(_764331))], (6446 ^ _543626) ^ [_764563, _764565] : [class_Rings_Ocomm__semiring__1(_764563), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_764563), c_Groups_Ozero__class_Ozero(_764563)), _764565) = c_Groups_Ozero__class_Ozero(_764563))], (6452 ^ _543626) ^ [_764795, _764797] : [class_Rings_Ocomm__semiring__1(_764795), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_764795), _764797), c_Groups_Ozero__class_Ozero(_764795)) = c_Groups_Ozero__class_Ozero(_764795))], (6458 ^ _543626) ^ [_765027, _765029] : [class_Rings_Omult__zero(_765027), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_765027), c_Groups_Ozero__class_Ozero(_765027)), _765029) = c_Groups_Ozero__class_Ozero(_765027))], (6464 ^ _543626) ^ [_765259, _765261] : [class_Rings_Omult__zero(_765259), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_765259), _765261), c_Groups_Ozero__class_Ozero(_765259)) = c_Groups_Ozero__class_Ozero(_765259))], (6470 ^ _543626) ^ [_765505, _765507, _765509] : [class_Rings_Oring__no__zero__divisors(_765505), 6473 ^ _543626 : [(6484 ^ _543626) ^ [] : [6485 ^ _543626 : [(6486 ^ _543626) ^ [] : [_765507 = c_Groups_Ozero__class_Ozero(_765505)], (6488 ^ _543626) ^ [] : [_765509 = c_Groups_Ozero__class_Ozero(_765505)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_765505), _765507), _765509) = c_Groups_Ozero__class_Ozero(_765505))], (6474 ^ _543626) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_765505), _765507), _765509) = c_Groups_Ozero__class_Ozero(_765505), -(_765507 = c_Groups_Ozero__class_Ozero(_765505)), -(_765509 = c_Groups_Ozero__class_Ozero(_765505))]]], (6492 ^ _543626) ^ [_766199, _766201, _766203] : [class_Rings_Ono__zero__divisors(_766199), -(_766201 = c_Groups_Ozero__class_Ozero(_766199)), -(_766203 = c_Groups_Ozero__class_Ozero(_766199)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_766199), _766201), _766203) = c_Groups_Ozero__class_Ozero(_766199)], (6506 ^ _543626) ^ [_766648, _766650, _766652] : [class_Rings_Ono__zero__divisors(_766648), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_766648), _766650), _766652) = c_Groups_Ozero__class_Ozero(_766648), -(_766650 = c_Groups_Ozero__class_Ozero(_766648)), -(_766652 = c_Groups_Ozero__class_Ozero(_766648))], (6520 ^ _543626) ^ [_767105, _767107, _767109, _767111] : [class_Int_Onumber__ring(_767105), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_767105), c_Int_Onumber__class_Onumber__of(_767105, _767107)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_767105), c_Int_Onumber__class_Onumber__of(_767105, _767109)), _767111)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_767105), c_Int_Onumber__class_Onumber__of(_767105, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _767107), _767109))), _767111))], (6526 ^ _543626) ^ [_767388, _767390] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_Onumber__class_Onumber__of(tc_Int_Oint, _767388)), c_Int_Onumber__class_Onumber__of(tc_Int_Oint, _767390)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _767388), _767390)))], (6528 ^ _543626) ^ [_767532, _767534, _767536] : [class_Int_Onumber__ring(_767532), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_767532), c_Int_Onumber__class_Onumber__of(_767532, _767534)), c_Int_Onumber__class_Onumber__of(_767532, _767536)) = c_Int_Onumber__class_Onumber__of(_767532, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _767534), _767536)))], (6534 ^ _543626) ^ [_767806, _767808, _767810] : [class_Int_Onumber__ring(_767806), -(c_Int_Onumber__class_Onumber__of(_767806, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _767808), _767810)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_767806), c_Int_Onumber__class_Onumber__of(_767806, _767808)), c_Int_Onumber__class_Onumber__of(_767806, _767810)))], (6540 ^ _543626) ^ [_768036] : [c_Nat__Numeral_Oneg(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _768036))], (6542 ^ _543626) ^ [_768116] : [-(c_Groups_Oabs__class_Oabs(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _768116)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _768116))], (6544 ^ _543626) ^ [_768232, _768234] : [class_Rings_Olinordered__idom(_768232), -(c_Groups_Oabs__class_Oabs(_768232, hAPP(c_Nat_Osemiring__1__class_Oof__nat(_768232), _768234)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_768232), _768234))], (6550 ^ _543626) ^ [_768494, _768496, _768498, _768500] : [class_RealVector_Oreal__normed__algebra(_768494), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_768494), _768496), c_Groups_Oplus__class_Oplus(_768494, _768498, _768500)) = c_Groups_Oplus__class_Oplus(_768494, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_768494), _768496), _768498), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_768494), _768496), _768500)))], (6556 ^ _543626) ^ [_768806, _768808, _768810, _768812] : [class_RealVector_Oreal__normed__algebra(_768806), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_768806), _768808), c_Groups_Oplus__class_Oplus(_768806, _768810, _768812)) = c_Groups_Oplus__class_Oplus(_768806, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_768806), _768808), _768810), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_768806), _768808), _768812)))], (6562 ^ _543626) ^ [_769118, _769120, _769122, _769124] : [class_RealVector_Oreal__normed__algebra(_769118), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_769118), c_Groups_Oplus__class_Oplus(_769118, _769120, _769122)), _769124) = c_Groups_Oplus__class_Oplus(_769118, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_769118), _769120), _769124), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_769118), _769122), _769124)))], (6568 ^ _543626) ^ [_769430, _769432, _769434, _769436] : [class_RealVector_Oreal__normed__algebra(_769430), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_769430), c_Groups_Oplus__class_Oplus(_769430, _769432, _769434)), _769436) = c_Groups_Oplus__class_Oplus(_769430, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_769430), _769432), _769436), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_769430), _769434), _769436)))], (6574 ^ _543626) ^ [_769713, _769715, _769717] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _769713, _769715)), _769717) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _769713), _769717), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _769715), _769717)))], (6576 ^ _543626) ^ [_769849, _769851, _769853] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _769849), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _769851, _769853)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _769849), _769851), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _769849), _769853)))], (6578 ^ _543626) ^ [_770028, _770030, _770032, _770034, _770036] : [class_Rings_Osemiring(_770028), -(c_Groups_Oplus__class_Oplus(_770028, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_770028), _770030), _770032), c_Groups_Oplus__class_Oplus(_770028, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_770028), _770034), _770032), _770036)) = c_Groups_Oplus__class_Oplus(_770028, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_770028), c_Groups_Oplus__class_Oplus(_770028, _770030, _770034)), _770032), _770036))], (6584 ^ _543626) ^ [_770362, _770364, _770366, _770368] : [class_Rings_Ocomm__semiring(_770362), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_770362), c_Groups_Oplus__class_Oplus(_770362, _770364, _770366)), _770368) = c_Groups_Oplus__class_Oplus(_770362, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_770362), _770364), _770368), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_770362), _770366), _770368)))], (6590 ^ _543626) ^ [_770688, _770690, _770692, _770694, _770696] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_770688), 6593 ^ _543626 : [(6604 ^ _543626) ^ [] : [6605 ^ _543626 : [(6606 ^ _543626) ^ [] : [_770690 = _770694], (6608 ^ _543626) ^ [] : [_770692 = _770696]], -(c_Groups_Oplus__class_Oplus(_770688, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_770688), _770690), _770692), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_770688), _770694), _770696)) = c_Groups_Oplus__class_Oplus(_770688, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_770688), _770690), _770696), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_770688), _770694), _770692)))], (6594 ^ _543626) ^ [] : [c_Groups_Oplus__class_Oplus(_770688, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_770688), _770690), _770692), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_770688), _770694), _770696)) = c_Groups_Oplus__class_Oplus(_770688, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_770688), _770690), _770696), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_770688), _770694), _770692)), -(_770690 = _770694), -(_770692 = _770696)]]], (6612 ^ _543626) ^ [_771518, _771520, _771522, _771524] : [class_Rings_Ocomm__semiring__1(_771518), -(c_Groups_Oplus__class_Oplus(_771518, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_771518), _771520), _771522), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_771518), _771524), _771522)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_771518), c_Groups_Oplus__class_Oplus(_771518, _771520, _771524)), _771522))], (6618 ^ _543626) ^ [_771830, _771832, _771834, _771836] : [class_Rings_Ocomm__semiring__1(_771830), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_771830), c_Groups_Oplus__class_Oplus(_771830, _771832, _771834)), _771836) = c_Groups_Oplus__class_Oplus(_771830, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_771830), _771832), _771836), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_771830), _771834), _771836)))], (6624 ^ _543626) ^ [_772156, _772158, _772160, _772162, _772164] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_772156), 6627 ^ _543626 : [(6638 ^ _543626) ^ [] : [-(c_Groups_Oplus__class_Oplus(_772156, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_772156), _772158), _772162), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_772156), _772160), _772164)) = c_Groups_Oplus__class_Oplus(_772156, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_772156), _772158), _772164), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_772156), _772160), _772162))), 6641 ^ _543626 : [(6642 ^ _543626) ^ [] : [_772158 = _772160], (6644 ^ _543626) ^ [] : [_772162 = _772164]]], (6628 ^ _543626) ^ [] : [c_Groups_Oplus__class_Oplus(_772156, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_772156), _772158), _772162), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_772156), _772160), _772164)) = c_Groups_Oplus__class_Oplus(_772156, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_772156), _772158), _772164), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_772156), _772160), _772162)), -(_772158 = _772160), -(_772162 = _772164)]]], (6646 ^ _543626) ^ [_772992, _772994, _772996, _772998] : [class_Rings_Ocomm__semiring__1(_772992), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_772992), _772994), c_Groups_Oplus__class_Oplus(_772992, _772996, _772998)) = c_Groups_Oplus__class_Oplus(_772992, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_772992), _772994), _772996), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_772992), _772994), _772998)))], (6652 ^ _543626) ^ [_773276, _773278] : [class_Rings_Olinordered__idom(_773276), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_773276), c_Groups_Oabs__class_Oabs(_773276, _773278)), c_Groups_Oabs__class_Oabs(_773276, _773278)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_773276), _773278), _773278))], (6658 ^ _543626) ^ [_773542, _773544, _773546] : [class_Rings_Olinordered__idom(_773542), -(c_Groups_Oabs__class_Oabs(_773542, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_773542), _773544), _773546)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_773542), c_Groups_Oabs__class_Oabs(_773542, _773544)), c_Groups_Oabs__class_Oabs(_773542, _773546)))], (6664 ^ _543626) ^ [] : [-(c_RealDef_Oreal(tc_Nat_Onat) = c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal))], (6666 ^ _543626) ^ [] : [-(c_RealDef_Oreal(tc_Nat_Onat) = c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal))], (6668 ^ _543626) ^ [_773940, _773942, _773944, _773946] : [class_Groups_Oab__semigroup__mult(_773940), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_773940), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_773940), _773942), _773944)), _773946) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_773940), _773942), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_773940), _773944), _773946)))], (6674 ^ _543626) ^ [_774238, _774240, _774242] : [class_Nat_Osemiring__char__0(_774238), 6677 ^ _543626 : [(6678 ^ _543626) ^ [] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(_774238), _774240) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_774238), _774242), -(_774240 = _774242)], (6684 ^ _543626) ^ [] : [_774240 = _774242, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_774238), _774240) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_774238), _774242))]]], (6690 ^ _543626) ^ [_774756, _774758, _774760] : [class_Rings_Osemiring__1(_774756), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_774756), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _774758), _774760)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_774756), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_774756), _774758)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_774756), _774760)))], (6696 ^ _543626) ^ [_775070, _775072, _775074, _775076, _775078] : [class_Rings_Ocomm__semiring__1(_775070), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_775070), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_775070), _775072), _775074)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_775070), _775076), _775078)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_775070), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_775070), _775072), _775076)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_775070), _775074), _775078)))], (6702 ^ _543626) ^ [_775434, _775436, _775438, _775440, _775442] : [class_Rings_Ocomm__semiring__1(_775434), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_775434), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_775434), _775436), _775438)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_775434), _775440), _775442)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_775434), _775440), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_775434), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_775434), _775436), _775438)), _775442)))], (6708 ^ _543626) ^ [_775798, _775800, _775802, _775804, _775806] : [class_Rings_Ocomm__semiring__1(_775798), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_775798), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_775798), _775800), _775802)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_775798), _775804), _775806)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_775798), _775800), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_775798), _775802), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_775798), _775804), _775806))))], (6714 ^ _543626) ^ [_776148, _776150, _776152, _776154] : [class_Rings_Ocomm__semiring__1(_776148), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_776148), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_776148), _776150), _776152)), _776154) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_776148), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_776148), _776150), _776154)), _776152))], (6720 ^ _543626) ^ [_776460, _776462, _776464, _776466] : [class_Rings_Ocomm__semiring__1(_776460), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_776460), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_776460), _776462), _776464)), _776466) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_776460), _776462), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_776460), _776464), _776466)))], (6726 ^ _543626) ^ [_776772, _776774, _776776, _776778] : [class_Rings_Ocomm__semiring__1(_776772), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_776772), _776774), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_776772), _776776), _776778)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_776772), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_776772), _776774), _776776)), _776778))], (6732 ^ _543626) ^ [_777084, _777086, _777088, _777090] : [class_Rings_Ocomm__semiring__1(_777084), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_777084), _777086), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_777084), _777088), _777090)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_777084), _777088), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_777084), _777086), _777090)))], (6738 ^ _543626) ^ [_777382, _777384, _777386] : [class_Rings_Ocomm__semiring__1(_777382), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_777382), _777384), _777386) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_777382), _777386), _777384))], (6744 ^ _543626) ^ [_777627, _777629, _777631] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _777627), _777629)), _777631) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _777627), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _777629), _777631)))], (6746 ^ _543626) ^ [_777747, _777749] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _777747), _777749) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _777749), _777747))], (6748 ^ _543626) ^ [_777867, _777869, _777871] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Ominus__class_Ominus(tc_Int_Oint, _777867, _777869)), _777871) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _777867), _777871), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _777869), _777871)))], (6750 ^ _543626) ^ [_778003, _778005, _778007] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _778003), c_Groups_Ominus__class_Ominus(tc_Int_Oint, _778005, _778007)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _778003), _778005), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _778003), _778007)))], (6752 ^ _543626) ^ [_778154, _778156, _778158] : [class_RealVector_Oreal__normed__div__algebra(_778154), -(c_RealVector_Onorm__class_Onorm(_778154, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_778154), _778156), _778158)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_778154, _778156)), c_RealVector_Onorm__class_Onorm(_778154, _778158)))], (6758 ^ _543626) ^ [_778414, _778416] : [class_RealVector_Oreal__normed__algebra__1(_778414), -(c_RealVector_Onorm__class_Onorm(_778414, hAPP(c_Nat_Osemiring__1__class_Oof__nat(_778414), _778416)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal), _778416))], (6764 ^ _543626) ^ [_778658, _778660, _778662] : [class_RealVector_Oreal__normed__algebra(_778658), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_778658, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_778658), _778660), _778662)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_778658, _778660)), c_RealVector_Onorm__class_Onorm(_778658, _778662))))], (6770 ^ _543626) ^ [_778948, _778950, _778952, _778954] : [class_RealVector_Oreal__normed__algebra(_778948), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_778948), c_Groups_Ominus__class_Ominus(_778948, _778950, _778952)), _778954) = c_Groups_Ominus__class_Ominus(_778948, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_778948), _778950), _778954), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_778948), _778952), _778954)))], (6776 ^ _543626) ^ [_779260, _779262, _779264, _779266] : [class_RealVector_Oreal__normed__algebra(_779260), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_779260), c_Groups_Ominus__class_Ominus(_779260, _779262, _779264)), _779266) = c_Groups_Ominus__class_Ominus(_779260, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_779260), _779262), _779266), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_779260), _779264), _779266)))], (6782 ^ _543626) ^ [_779572, _779574, _779576, _779578] : [class_RealVector_Oreal__normed__algebra(_779572), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_779572), _779574), c_Groups_Ominus__class_Ominus(_779572, _779576, _779578)) = c_Groups_Ominus__class_Ominus(_779572, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_779572), _779574), _779576), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_779572), _779574), _779578)))], (6788 ^ _543626) ^ [_779884, _779886, _779888, _779890] : [class_RealVector_Oreal__normed__algebra(_779884), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_779884), _779886), c_Groups_Ominus__class_Ominus(_779884, _779888, _779890)) = c_Groups_Ominus__class_Ominus(_779884, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_779884), _779886), _779888), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_779884), _779886), _779890)))], (6794 ^ _543626) ^ [_780210, _780212, _780214, _780216, _780218] : [class_RealVector_Oreal__normed__algebra(_780210), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_780210, _780212), _780214), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_780210, _780216), _780218), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_780210, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_780210), _780212), _780216)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _780214), _780218)))], (6808 ^ _543626) ^ [_780661] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _780661), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _780661)], (6810 ^ _543626) ^ [_780745] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _780745) = _780745)], (6812 ^ _543626) ^ [_780855, _780857] : [class_Groups_Omonoid__mult(_780855), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_780855), c_Groups_Oone__class_Oone(_780855)), _780857) = _780857)], (6818 ^ _543626) ^ [_781083, _781085] : [class_Groups_Ocomm__monoid__mult(_781083), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_781083), c_Groups_Oone__class_Oone(_781083)), _781085) = _781085)], (6824 ^ _543626) ^ [_781311, _781313] : [class_Groups_Omonoid__mult(_781311), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_781311), _781313), c_Groups_Oone__class_Oone(_781311)) = _781313)], (6830 ^ _543626) ^ [_781539, _781541] : [class_Groups_Ocomm__monoid__mult(_781539), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_781539), _781541), c_Groups_Oone__class_Oone(_781539)) = _781541)], (6836 ^ _543626) ^ [_781767, _781769] : [class_Rings_Ocomm__semiring__1(_781767), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_781767), _781769), c_Groups_Oone__class_Oone(_781767)) = _781769)], (6842 ^ _543626) ^ [_781995, _781997] : [class_Rings_Ocomm__semiring__1(_781995), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_781995), c_Groups_Oone__class_Oone(_781995)), _781997) = _781997)], (6848 ^ _543626) ^ [_782194] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OPls), _782194) = c_Int_OPls)], (6850 ^ _543626) ^ [_782304, _782306] : [class_Rings_Olinordered__semidom(_782304), -(c_Orderings_Oord__class_Oless__eq(_782304, c_Groups_Ozero__class_Ozero(_782304), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_782304), _782306)))], (6856 ^ _543626) ^ [_782528, _782530] : [class_Rings_Olinordered__semidom(_782528), -(c_Orderings_Oord__class_Oless__eq(_782528, c_Groups_Ozero__class_Ozero(_782528), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_782528), _782530)))], (6862 ^ _543626) ^ [_782752, _782754] : [class_Rings_Olinordered__semidom(_782752), c_Orderings_Oord__class_Oless(_782752, hAPP(c_Nat_Osemiring__1__class_Oof__nat(_782752), _782754), c_Groups_Ozero__class_Ozero(_782752))], (6868 ^ _543626) ^ [_782963] : [class_Rings_Osemiring__1(_782963), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_782963), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_782963))], (6874 ^ _543626) ^ [_783193, _783195, _783197] : [class_Rings_Olinordered__semidom(_783193), c_Orderings_Oord__class_Oless(_783193, hAPP(c_Nat_Osemiring__1__class_Oof__nat(_783193), _783195), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_783193), _783197)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _783195, _783197))], (6884 ^ _543626) ^ [_783538, _783540, _783542] : [class_Rings_Olinordered__semidom(_783538), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _783540, _783542), -(c_Orderings_Oord__class_Oless(_783538, hAPP(c_Nat_Osemiring__1__class_Oof__nat(_783538), _783540), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_783538), _783542)))], (6894 ^ _543626) ^ [_783883, _783885, _783887] : [class_Rings_Olinordered__semidom(_783883), 6897 ^ _543626 : [(6898 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(_783883, hAPP(c_Nat_Osemiring__1__class_Oof__nat(_783883), _783885), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_783883), _783887)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _783885, _783887))], (6904 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _783885, _783887), -(c_Orderings_Oord__class_Oless(_783883, hAPP(c_Nat_Osemiring__1__class_Oof__nat(_783883), _783885), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_783883), _783887)))]]], (6910 ^ _543626) ^ [_784407, _784409, _784411] : [class_Rings_Olinordered__semidom(_784407), 6913 ^ _543626 : [(6914 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_784407, hAPP(c_Nat_Osemiring__1__class_Oof__nat(_784407), _784409), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_784407), _784411)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _784409, _784411))], (6920 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _784409, _784411), -(c_Orderings_Oord__class_Oless__eq(_784407, hAPP(c_Nat_Osemiring__1__class_Oof__nat(_784407), _784409), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_784407), _784411)))]]], (6926 ^ _543626) ^ [_784931, _784933, _784935] : [class_Rings_Osemiring__1(_784931), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_784931), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _784933, _784935)) = c_Groups_Oplus__class_Oplus(_784931, hAPP(c_Nat_Osemiring__1__class_Oof__nat(_784931), _784933), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_784931), _784935)))], (6932 ^ _543626) ^ [_785177] : [class_Rings_Osemiring__1(_785177), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_785177), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_785177))], (6938 ^ _543626) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (6940 ^ _543626) ^ [] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (6942 ^ _543626) ^ [_785514] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _785514) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_785514 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6948 ^ _543626) ^ [_785676] : [_785676 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _785676) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (6954 ^ _543626) ^ [_785888, _785890] : [class_Rings_Olinordered__ring(_785888), -(c_Orderings_Oord__class_Oless__eq(_785888, c_Groups_Ozero__class_Ozero(_785888), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_785888), _785890), _785890)))], (6960 ^ _543626) ^ [_786132, _786134, _786136] : [class_Rings_Olinordered__ring__strict(_786132), 6963 ^ _543626 : [(6964 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_786132, c_Groups_Ozero__class_Ozero(_786132), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_786132), _786134), _786136)), 6969 ^ _543626 : [(6970 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_786132, c_Groups_Ozero__class_Ozero(_786132), _786134))], (6972 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_786132, c_Groups_Ozero__class_Ozero(_786132), _786136))]], 6973 ^ _543626 : [(6974 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_786132, _786134, c_Groups_Ozero__class_Ozero(_786132)))], (6976 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_786132, _786136, c_Groups_Ozero__class_Ozero(_786132)))]]], (6978 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_786132, c_Groups_Ozero__class_Ozero(_786132), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_786132), _786134), _786136))), 6979 ^ _543626 : [(6980 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_786132, c_Groups_Ozero__class_Ozero(_786132), _786134), c_Orderings_Oord__class_Oless__eq(_786132, c_Groups_Ozero__class_Ozero(_786132), _786136)], (6986 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_786132, _786134, c_Groups_Ozero__class_Ozero(_786132)), c_Orderings_Oord__class_Oless__eq(_786132, _786136, c_Groups_Ozero__class_Ozero(_786132))]]]]], (6994 ^ _543626) ^ [_787181, _787183, _787185] : [class_Rings_Olinordered__ring__strict(_787181), 6997 ^ _543626 : [(6998 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_787181, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_787181), _787183), _787185), c_Groups_Ozero__class_Ozero(_787181)), 7003 ^ _543626 : [(7004 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_787181, c_Groups_Ozero__class_Ozero(_787181), _787183))], (7006 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_787181, _787185, c_Groups_Ozero__class_Ozero(_787181)))]], 7007 ^ _543626 : [(7008 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_787181, _787183, c_Groups_Ozero__class_Ozero(_787181)))], (7010 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_787181, c_Groups_Ozero__class_Ozero(_787181), _787185))]]], (7012 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_787181, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_787181), _787183), _787185), c_Groups_Ozero__class_Ozero(_787181))), 7013 ^ _543626 : [(7014 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_787181, c_Groups_Ozero__class_Ozero(_787181), _787183), c_Orderings_Oord__class_Oless__eq(_787181, _787185, c_Groups_Ozero__class_Ozero(_787181))], (7020 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_787181, _787183, c_Groups_Ozero__class_Ozero(_787181)), c_Orderings_Oord__class_Oless__eq(_787181, c_Groups_Ozero__class_Ozero(_787181), _787185)]]]]], (7028 ^ _543626) ^ [_788230, _788232, _788234] : [class_Rings_Oordered__cancel__semiring(_788230), c_Orderings_Oord__class_Oless__eq(_788230, c_Groups_Ozero__class_Ozero(_788230), _788232), c_Orderings_Oord__class_Oless__eq(_788230, c_Groups_Ozero__class_Ozero(_788230), _788234), -(c_Orderings_Oord__class_Oless__eq(_788230, c_Groups_Ozero__class_Ozero(_788230), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_788230), _788232), _788234)))], (7042 ^ _543626) ^ [_788678, _788680, _788682] : [class_Rings_Oordered__cancel__semiring(_788678), c_Orderings_Oord__class_Oless__eq(_788678, c_Groups_Ozero__class_Ozero(_788678), _788680), c_Orderings_Oord__class_Oless__eq(_788678, _788682, c_Groups_Ozero__class_Ozero(_788678)), -(c_Orderings_Oord__class_Oless__eq(_788678, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_788678), _788680), _788682), c_Groups_Ozero__class_Ozero(_788678)))], (7056 ^ _543626) ^ [_789126, _789128, _789130] : [class_Rings_Oordered__cancel__semiring(_789126), c_Orderings_Oord__class_Oless__eq(_789126, c_Groups_Ozero__class_Ozero(_789126), _789128), c_Orderings_Oord__class_Oless__eq(_789126, _789130, c_Groups_Ozero__class_Ozero(_789126)), -(c_Orderings_Oord__class_Oless__eq(_789126, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_789126), _789130), _789128), c_Groups_Ozero__class_Ozero(_789126)))], (7070 ^ _543626) ^ [_789574, _789576, _789578] : [class_Rings_Oordered__cancel__semiring(_789574), c_Orderings_Oord__class_Oless__eq(_789574, _789576, c_Groups_Ozero__class_Ozero(_789574)), c_Orderings_Oord__class_Oless__eq(_789574, c_Groups_Ozero__class_Ozero(_789574), _789578), -(c_Orderings_Oord__class_Oless__eq(_789574, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_789574), _789576), _789578), c_Groups_Ozero__class_Ozero(_789574)))], (7084 ^ _543626) ^ [_790022, _790024, _790026] : [class_Rings_Oordered__ring(_790022), c_Orderings_Oord__class_Oless__eq(_790022, _790024, c_Groups_Ozero__class_Ozero(_790022)), c_Orderings_Oord__class_Oless__eq(_790022, _790026, c_Groups_Ozero__class_Ozero(_790022)), -(c_Orderings_Oord__class_Oless__eq(_790022, c_Groups_Ozero__class_Ozero(_790022), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_790022), _790024), _790026)))], (7098 ^ _543626) ^ [_790484, _790486, _790488, _790490] : [class_Rings_Oordered__semiring(_790484), c_Orderings_Oord__class_Oless__eq(_790484, _790486, _790488), c_Orderings_Oord__class_Oless__eq(_790484, c_Groups_Ozero__class_Ozero(_790484), _790490), -(c_Orderings_Oord__class_Oless__eq(_790484, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_790484), _790486), _790490), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_790484), _790488), _790490)))], (7112 ^ _543626) ^ [_790968, _790970, _790972, _790974] : [class_Rings_Oordered__semiring(_790968), c_Orderings_Oord__class_Oless__eq(_790968, _790970, _790972), c_Orderings_Oord__class_Oless__eq(_790968, c_Groups_Ozero__class_Ozero(_790968), _790974), -(c_Orderings_Oord__class_Oless__eq(_790968, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_790968), _790974), _790970), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_790968), _790974), _790972)))], (7126 ^ _543626) ^ [_791452, _791454, _791456, _791458] : [class_Rings_Oordered__comm__semiring(_791452), c_Orderings_Oord__class_Oless__eq(_791452, _791454, _791456), c_Orderings_Oord__class_Oless__eq(_791452, c_Groups_Ozero__class_Ozero(_791452), _791458), -(c_Orderings_Oord__class_Oless__eq(_791452, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_791452), _791458), _791454), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_791452), _791458), _791456)))], (7140 ^ _543626) ^ [_791936, _791938, _791940, _791942] : [class_Rings_Oordered__ring(_791936), c_Orderings_Oord__class_Oless__eq(_791936, _791938, _791940), c_Orderings_Oord__class_Oless__eq(_791936, _791942, c_Groups_Ozero__class_Ozero(_791936)), -(c_Orderings_Oord__class_Oless__eq(_791936, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_791936), _791940), _791942), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_791936), _791938), _791942)))], (7154 ^ _543626) ^ [_792420, _792422, _792424, _792426] : [class_Rings_Oordered__ring(_792420), c_Orderings_Oord__class_Oless__eq(_792420, _792422, _792424), c_Orderings_Oord__class_Oless__eq(_792420, _792426, c_Groups_Ozero__class_Ozero(_792420)), -(c_Orderings_Oord__class_Oless__eq(_792420, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_792420), _792426), _792424), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_792420), _792426), _792422)))], (7168 ^ _543626) ^ [_792918, _792920, _792922, _792924, _792926] : [class_Rings_Oordered__semiring(_792918), c_Orderings_Oord__class_Oless__eq(_792918, _792920, _792922), c_Orderings_Oord__class_Oless__eq(_792918, _792924, _792926), c_Orderings_Oord__class_Oless__eq(_792918, c_Groups_Ozero__class_Ozero(_792918), _792920), c_Orderings_Oord__class_Oless__eq(_792918, c_Groups_Ozero__class_Ozero(_792918), _792924), -(c_Orderings_Oord__class_Oless__eq(_792918, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_792918), _792920), _792924), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_792918), _792922), _792926)))], (7190 ^ _543626) ^ [_793640, _793642, _793644, _793646, _793648] : [class_Rings_Oordered__semiring(_793640), c_Orderings_Oord__class_Oless__eq(_793640, _793642, _793644), c_Orderings_Oord__class_Oless__eq(_793640, _793646, _793648), c_Orderings_Oord__class_Oless__eq(_793640, c_Groups_Ozero__class_Ozero(_793640), _793644), c_Orderings_Oord__class_Oless__eq(_793640, c_Groups_Ozero__class_Ozero(_793640), _793646), -(c_Orderings_Oord__class_Oless__eq(_793640, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_793640), _793642), _793646), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_793640), _793644), _793648)))], (7212 ^ _543626) ^ [_794334, _794336, _794338] : [class_Rings_Oordered__ring(_794334), -(c_Orderings_Oord__class_Oless__eq(_794334, c_Groups_Ozero__class_Ozero(_794334), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_794334), _794336), _794338))), 7217 ^ _543626 : [(7218 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_794334, c_Groups_Ozero__class_Ozero(_794334), _794336), c_Orderings_Oord__class_Oless__eq(_794334, c_Groups_Ozero__class_Ozero(_794334), _794338)], (7224 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_794334, _794336, c_Groups_Ozero__class_Ozero(_794334)), c_Orderings_Oord__class_Oless__eq(_794334, _794338, c_Groups_Ozero__class_Ozero(_794334))]]], (7232 ^ _543626) ^ [_794963, _794965, _794967] : [class_Rings_Oordered__cancel__semiring(_794963), -(c_Orderings_Oord__class_Oless__eq(_794963, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_794963), _794965), _794967), c_Groups_Ozero__class_Ozero(_794963))), 7237 ^ _543626 : [(7238 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_794963, c_Groups_Ozero__class_Ozero(_794963), _794965), c_Orderings_Oord__class_Oless__eq(_794963, _794967, c_Groups_Ozero__class_Ozero(_794963))], (7244 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_794963, _794965, c_Groups_Ozero__class_Ozero(_794963)), c_Orderings_Oord__class_Oless__eq(_794963, c_Groups_Ozero__class_Ozero(_794963), _794967)]]], (7252 ^ _543626) ^ [_795578, _795580] : [class_Rings_Olinordered__ring(_795578), c_Orderings_Oord__class_Oless(_795578, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_795578), _795580), _795580), c_Groups_Ozero__class_Ozero(_795578))], (7258 ^ _543626) ^ [_795837, _795839, _795841, _795843] : [class_Rings_Olinordered__ring__strict(_795837), 7261 ^ _543626 : [(7262 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(_795837, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_795837), _795839), _795841), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_795837), _795843), _795841)), 7267 ^ _543626 : [(7268 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(_795837, c_Groups_Ozero__class_Ozero(_795837), _795841))], (7270 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(_795837, _795839, _795843))]], 7271 ^ _543626 : [(7272 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(_795837, _795841, c_Groups_Ozero__class_Ozero(_795837)))], (7274 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(_795837, _795843, _795839))]]], (7276 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(_795837, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_795837), _795839), _795841), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_795837), _795843), _795841))), 7277 ^ _543626 : [(7278 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(_795837, c_Groups_Ozero__class_Ozero(_795837), _795841), c_Orderings_Oord__class_Oless(_795837, _795839, _795843)], (7284 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(_795837, _795841, c_Groups_Ozero__class_Ozero(_795837)), c_Orderings_Oord__class_Oless(_795837, _795843, _795839)]]]]], (7292 ^ _543626) ^ [_796940, _796942, _796944, _796946] : [class_Rings_Olinordered__ring__strict(_796940), 7295 ^ _543626 : [(7296 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(_796940, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_796940), _796942), _796944), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_796940), _796942), _796946)), 7301 ^ _543626 : [(7302 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(_796940, c_Groups_Ozero__class_Ozero(_796940), _796942))], (7304 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(_796940, _796944, _796946))]], 7305 ^ _543626 : [(7306 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(_796940, _796942, c_Groups_Ozero__class_Ozero(_796940)))], (7308 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(_796940, _796946, _796944))]]], (7310 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(_796940, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_796940), _796942), _796944), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_796940), _796942), _796946))), 7311 ^ _543626 : [(7312 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(_796940, c_Groups_Ozero__class_Ozero(_796940), _796942), c_Orderings_Oord__class_Oless(_796940, _796944, _796946)], (7318 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(_796940, _796942, c_Groups_Ozero__class_Ozero(_796940)), c_Orderings_Oord__class_Oless(_796940, _796946, _796944)]]]]], (7326 ^ _543626) ^ [_798043, _798045, _798047, _798049] : [class_Rings_Olinordered__ring__strict(_798043), c_Orderings_Oord__class_Oless(_798043, c_Groups_Ozero__class_Ozero(_798043), _798045), 7333 ^ _543626 : [(7334 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(_798043, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_798043), _798045), _798047), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_798043), _798045), _798049)), -(c_Orderings_Oord__class_Oless(_798043, _798047, _798049))], (7340 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(_798043, _798047, _798049), -(c_Orderings_Oord__class_Oless(_798043, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_798043), _798045), _798047), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_798043), _798045), _798049)))]]], (7346 ^ _543626) ^ [_798704, _798706, _798708] : [class_Rings_Olinordered__semiring__strict(_798704), c_Orderings_Oord__class_Oless(_798704, c_Groups_Ozero__class_Ozero(_798704), _798706), c_Orderings_Oord__class_Oless(_798704, c_Groups_Ozero__class_Ozero(_798704), _798708), -(c_Orderings_Oord__class_Oless(_798704, c_Groups_Ozero__class_Ozero(_798704), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_798704), _798706), _798708)))], (7360 ^ _543626) ^ [_799152, _799154, _799156] : [class_Rings_Olinordered__semiring__strict(_799152), c_Orderings_Oord__class_Oless(_799152, c_Groups_Ozero__class_Ozero(_799152), _799154), c_Orderings_Oord__class_Oless(_799152, _799156, c_Groups_Ozero__class_Ozero(_799152)), -(c_Orderings_Oord__class_Oless(_799152, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_799152), _799154), _799156), c_Groups_Ozero__class_Ozero(_799152)))], (7374 ^ _543626) ^ [_799600, _799602, _799604] : [class_Rings_Olinordered__semiring__strict(_799600), c_Orderings_Oord__class_Oless(_799600, c_Groups_Ozero__class_Ozero(_799600), _799602), c_Orderings_Oord__class_Oless(_799600, _799604, c_Groups_Ozero__class_Ozero(_799600)), -(c_Orderings_Oord__class_Oless(_799600, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_799600), _799604), _799602), c_Groups_Ozero__class_Ozero(_799600)))], (7388 ^ _543626) ^ [_800048, _800050, _800052] : [class_Rings_Olinordered__semiring__strict(_800048), c_Orderings_Oord__class_Oless(_800048, c_Groups_Ozero__class_Ozero(_800048), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_800048), _800050), _800052)), c_Orderings_Oord__class_Oless(_800048, c_Groups_Ozero__class_Ozero(_800048), _800050), -(c_Orderings_Oord__class_Oless(_800048, c_Groups_Ozero__class_Ozero(_800048), _800052))], (7402 ^ _543626) ^ [_800496, _800498, _800500] : [class_Rings_Olinordered__semiring__strict(_800496), c_Orderings_Oord__class_Oless(_800496, c_Groups_Ozero__class_Ozero(_800496), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_800496), _800498), _800500)), c_Orderings_Oord__class_Oless(_800496, c_Groups_Ozero__class_Ozero(_800496), _800500), -(c_Orderings_Oord__class_Oless(_800496, c_Groups_Ozero__class_Ozero(_800496), _800498))], (7416 ^ _543626) ^ [_800958, _800960, _800962, _800964] : [class_Rings_Olinordered__ring__strict(_800958), c_Orderings_Oord__class_Oless(_800958, _800960, c_Groups_Ozero__class_Ozero(_800958)), 7423 ^ _543626 : [(7424 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(_800958, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_800958), _800960), _800962), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_800958), _800960), _800964)), -(c_Orderings_Oord__class_Oless(_800958, _800964, _800962))], (7430 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(_800958, _800964, _800962), -(c_Orderings_Oord__class_Oless(_800958, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_800958), _800960), _800962), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_800958), _800960), _800964)))]]], (7436 ^ _543626) ^ [_801619, _801621, _801623] : [class_Rings_Olinordered__semiring__strict(_801619), c_Orderings_Oord__class_Oless(_801619, _801621, c_Groups_Ozero__class_Ozero(_801619)), c_Orderings_Oord__class_Oless(_801619, c_Groups_Ozero__class_Ozero(_801619), _801623), -(c_Orderings_Oord__class_Oless(_801619, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_801619), _801621), _801623), c_Groups_Ozero__class_Ozero(_801619)))], (7450 ^ _543626) ^ [_802067, _802069, _802071] : [class_Rings_Olinordered__ring__strict(_802067), c_Orderings_Oord__class_Oless(_802067, _802069, c_Groups_Ozero__class_Ozero(_802067)), c_Orderings_Oord__class_Oless(_802067, _802071, c_Groups_Ozero__class_Ozero(_802067)), -(c_Orderings_Oord__class_Oless(_802067, c_Groups_Ozero__class_Ozero(_802067), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_802067), _802069), _802071)))], (7464 ^ _543626) ^ [_802529, _802531, _802533, _802535] : [class_Rings_Olinordered__semiring__strict(_802529), c_Orderings_Oord__class_Oless(_802529, _802531, _802533), c_Orderings_Oord__class_Oless(_802529, c_Groups_Ozero__class_Ozero(_802529), _802535), -(c_Orderings_Oord__class_Oless(_802529, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_802529), _802531), _802535), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_802529), _802533), _802535)))], (7478 ^ _543626) ^ [_803013, _803015, _803017, _803019] : [class_Rings_Olinordered__semiring__strict(_803013), c_Orderings_Oord__class_Oless(_803013, _803015, _803017), c_Orderings_Oord__class_Oless(_803013, c_Groups_Ozero__class_Ozero(_803013), _803019), -(c_Orderings_Oord__class_Oless(_803013, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_803013), _803019), _803015), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_803013), _803019), _803017)))], (7492 ^ _543626) ^ [_803497, _803499, _803501, _803503] : [class_Rings_Olinordered__comm__semiring__strict(_803497), c_Orderings_Oord__class_Oless(_803497, _803499, _803501), c_Orderings_Oord__class_Oless(_803497, c_Groups_Ozero__class_Ozero(_803497), _803503), -(c_Orderings_Oord__class_Oless(_803497, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_803497), _803503), _803499), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_803497), _803503), _803501)))], (7506 ^ _543626) ^ [_803981, _803983, _803985, _803987] : [class_Rings_Olinordered__ring__strict(_803981), c_Orderings_Oord__class_Oless(_803981, _803983, _803985), c_Orderings_Oord__class_Oless(_803981, _803987, c_Groups_Ozero__class_Ozero(_803981)), -(c_Orderings_Oord__class_Oless(_803981, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_803981), _803985), _803987), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_803981), _803983), _803987)))], (7520 ^ _543626) ^ [_804465, _804467, _804469, _804471] : [class_Rings_Olinordered__ring__strict(_804465), c_Orderings_Oord__class_Oless(_804465, _804467, _804469), c_Orderings_Oord__class_Oless(_804465, _804471, c_Groups_Ozero__class_Ozero(_804465)), -(c_Orderings_Oord__class_Oless(_804465, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_804465), _804471), _804469), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_804465), _804471), _804467)))], (7534 ^ _543626) ^ [_804936] : [7536 ^ _543626 : [(7537 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), 7535 ^ [_804936]))], (7539 ^ _543626) ^ [] : [hBOOL(hAPP(_804936, 7535 ^ [_804936]))]], 7540 ^ _543626 : [(7541 ^ _543626) ^ [_805196] : [-(hBOOL(hAPP(_804936, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _805196))))]]], (7543 ^ _543626) ^ [_805268] : [hBOOL(hAPP(_805268, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 7544 ^ [_805268]))), 7547 ^ _543626 : [(7548 ^ _543626) ^ [_805470] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _805470), -(hBOOL(hAPP(_805268, _805470)))]]], (7565 ^ _543626) ^ [_806087] : [7566 ^ _543626 : [(7567 ^ _543626) ^ [_806174] : [hBOOL(hAPP(_806087, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _806174)))]], 7569 ^ _543626 : [(7570 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), 7568 ^ [_806087]))], (7572 ^ _543626) ^ [] : [-(hBOOL(hAPP(_806087, 7568 ^ [_806087])))]]], (7554 ^ _543626) ^ [_805710] : [-(hBOOL(hAPP(_805710, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 7561 ^ [_805710])))), 7555 ^ _543626 : [(7556 ^ _543626) ^ [_805813] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _805813), hBOOL(hAPP(_805710, _805813))]]], (7574 ^ _543626) ^ [_806440] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _806440)))], (7576 ^ _543626) ^ [_806522] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _806522)))], (7578 ^ _543626) ^ [_806603] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _806603), c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (7580 ^ _543626) ^ [_806728, _806730, _806732] : [class_Rings_Olinordered__ring__strict(_806728), 7583 ^ _543626 : [(7584 ^ _543626) ^ [] : [c_Groups_Oplus__class_Oplus(_806728, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_806728), _806730), _806730), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_806728), _806732), _806732)) = c_Groups_Ozero__class_Ozero(_806728), 7587 ^ _543626 : [(7588 ^ _543626) ^ [] : [-(_806730 = c_Groups_Ozero__class_Ozero(_806728))], (7590 ^ _543626) ^ [] : [-(_806732 = c_Groups_Ozero__class_Ozero(_806728))]]], (7592 ^ _543626) ^ [] : [-(c_Groups_Oplus__class_Oplus(_806728, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_806728), _806730), _806730), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_806728), _806732), _806732)) = c_Groups_Ozero__class_Ozero(_806728)), _806730 = c_Groups_Ozero__class_Ozero(_806728), _806732 = c_Groups_Ozero__class_Ozero(_806728)]]], (7602 ^ _543626) ^ [_807500, _807502, _807504, _807506, _807508, _807510] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_807500), -(_807502 = c_Groups_Ozero__class_Ozero(_807500)), c_Groups_Oplus__class_Oplus(_807500, _807504, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_807500), _807502), _807508)) = c_Groups_Oplus__class_Oplus(_807500, _807506, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_807500), _807502), _807510)), _807504 = _807506, -(_807508 = _807510)], (7620 ^ _543626) ^ [_808135, _808137] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _808135), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _808137)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _808135, _808137))], (7626 ^ _543626) ^ [_808313, _808315] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _808313, _808315), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _808313), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _808315)))], (7632 ^ _543626) ^ [_808570, _808572] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _808570), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _808572)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _808570, _808572))], (7638 ^ _543626) ^ [_808748, _808750] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _808748, _808750), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _808748), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _808750)))], (7644 ^ _543626) ^ [_809005, _809007] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _809005), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _809007)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _809005, _809007))], (7650 ^ _543626) ^ [_809183, _809185] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _809183, _809185), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _809183), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _809185)))], (7656 ^ _543626) ^ [_809440, _809442] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _809440), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _809442)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _809440, _809442))], (7662 ^ _543626) ^ [_809618, _809620] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _809618, _809620), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _809618), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _809620)))], (7668 ^ _543626) ^ [_809860, _809862, _809864] : [class_Rings_Olinordered__semidom(_809860), c_Orderings_Oord__class_Oless(_809860, c_Groups_Oone__class_Oone(_809860), _809862), c_Orderings_Oord__class_Oless(_809860, c_Groups_Oone__class_Oone(_809860), _809864), -(c_Orderings_Oord__class_Oless(_809860, c_Groups_Oone__class_Oone(_809860), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_809860), _809862), _809864)))], (7682 ^ _543626) ^ [_810322, _810324, _810326, _810328] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_810322), c_Groups_Oplus__class_Oplus(_810322, _810324, _810326)), c_Int_Onumber__class_Onumber__of(_810322, _810328)) = c_Groups_Oplus__class_Oplus(_810322, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_810322), _810324), c_Int_Onumber__class_Onumber__of(_810322, _810328)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_810322), _810326), c_Int_Onumber__class_Onumber__of(_810322, _810328)))), class_Int_Onumber(_810322), class_Rings_Osemiring(_810322)], (7692 ^ _543626) ^ [_810747, _810749, _810751, _810753] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_810747), c_Int_Onumber__class_Onumber__of(_810747, _810749)), c_Groups_Oplus__class_Oplus(_810747, _810751, _810753)) = c_Groups_Oplus__class_Oplus(_810747, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_810747), c_Int_Onumber__class_Onumber__of(_810747, _810749)), _810751), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_810747), c_Int_Onumber__class_Onumber__of(_810747, _810749)), _810753))), class_Int_Onumber(_810747), class_Rings_Osemiring(_810747)], (7702 ^ _543626) ^ [_811173, _811175] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _811173, _811175), -(_811175 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _811173, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 7705 ^ [_811173, _811175])))], (7709 ^ _543626) ^ [_811415, _811417] : [7710 ^ _543626 : [(7711 ^ _543626) ^ [_811493] : [_811417 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _811415, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _811493))]], -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _811415, _811417))], (7715 ^ _543626) ^ [_811650, _811652] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _811650), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _811652)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _811650, _811652)))], (7717 ^ _543626) ^ [_811761, _811763] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _811761), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _811763)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _811761, _811763)))], (7719 ^ _543626) ^ [_811886, _811888, _811890] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _811886), c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _811888), _811890)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _811886, _811888)), _811890))], (7721 ^ _543626) ^ [_812078, _812080, _812082, _812084, _812086, _812088] : [class_Rings_Oring(_812078), 7724 ^ _543626 : [(7725 ^ _543626) ^ [] : [c_Groups_Oplus__class_Oplus(_812078, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_812078), _812080), _812082), _812084) = c_Groups_Oplus__class_Oplus(_812078, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_812078), _812086), _812082), _812088), -(_812084 = c_Groups_Oplus__class_Oplus(_812078, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_812078), c_Groups_Ominus__class_Ominus(_812078, _812086, _812080)), _812082), _812088))], (7731 ^ _543626) ^ [] : [_812084 = c_Groups_Oplus__class_Oplus(_812078, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_812078), c_Groups_Ominus__class_Ominus(_812078, _812086, _812080)), _812082), _812088), -(c_Groups_Oplus__class_Oplus(_812078, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_812078), _812080), _812082), _812084) = c_Groups_Oplus__class_Oplus(_812078, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_812078), _812086), _812082), _812088))]]], (7737 ^ _543626) ^ [_812776, _812778, _812780, _812782, _812784, _812786] : [class_Rings_Oring(_812776), 7740 ^ _543626 : [(7741 ^ _543626) ^ [] : [c_Groups_Oplus__class_Oplus(_812776, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_812776), _812778), _812780), _812782) = c_Groups_Oplus__class_Oplus(_812776, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_812776), _812784), _812780), _812786), -(c_Groups_Oplus__class_Oplus(_812776, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_812776), c_Groups_Ominus__class_Ominus(_812776, _812778, _812784)), _812780), _812782) = _812786)], (7747 ^ _543626) ^ [] : [c_Groups_Oplus__class_Oplus(_812776, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_812776), c_Groups_Ominus__class_Ominus(_812776, _812778, _812784)), _812780), _812782) = _812786, -(c_Groups_Oplus__class_Oplus(_812776, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_812776), _812778), _812780), _812782) = c_Groups_Oplus__class_Oplus(_812776, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_812776), _812784), _812780), _812786))]]], (7753 ^ _543626) ^ [_813460, _813462, _813464, _813466, _813468] : [class_Rings_Oring(_813460), -(c_Groups_Ominus__class_Ominus(_813460, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_813460), _813462), _813464), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_813460), _813466), _813468)) = c_Groups_Oplus__class_Oplus(_813460, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_813460), _813462), c_Groups_Ominus__class_Ominus(_813460, _813464, _813468)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_813460), c_Groups_Ominus__class_Ominus(_813460, _813462, _813466)), _813468)))], (7759 ^ _543626) ^ [_813824, _813826, _813828, _813830, _813832] : [class_RealVector_Oreal__normed__algebra(_813824), -(c_Groups_Ominus__class_Ominus(_813824, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_813824), _813826), _813828), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_813824), _813830), _813832)) = c_Groups_Oplus__class_Oplus(_813824, c_Groups_Oplus__class_Oplus(_813824, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_813824), c_Groups_Ominus__class_Ominus(_813824, _813826, _813830)), c_Groups_Ominus__class_Ominus(_813824, _813828, _813832)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_813824), c_Groups_Ominus__class_Ominus(_813824, _813826, _813830)), _813832)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_813824), _813830), c_Groups_Ominus__class_Ominus(_813824, _813828, _813832))))], (7765 ^ _543626) ^ [_814186, _814188] : [class_Rings_Ocomm__semiring__1(_814186), -(c_Groups_Oplus__class_Oplus(_814186, _814188, _814188) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_814186), c_Groups_Oplus__class_Oplus(_814186, c_Groups_Oone__class_Oone(_814186), c_Groups_Oone__class_Oone(_814186))), _814188))], (7771 ^ _543626) ^ [_814448, _814450, _814452] : [class_Rings_Ocomm__semiring__1(_814448), -(c_Groups_Oplus__class_Oplus(_814448, _814450, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_814448), _814452), _814450)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_814448), c_Groups_Oplus__class_Oplus(_814448, _814452, c_Groups_Oone__class_Oone(_814448))), _814450))], (7777 ^ _543626) ^ [_814728, _814730, _814732] : [class_Rings_Ocomm__semiring__1(_814728), -(c_Groups_Oplus__class_Oplus(_814728, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_814728), _814730), _814732), _814732) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_814728), c_Groups_Oplus__class_Oplus(_814728, _814730, c_Groups_Oone__class_Oone(_814728))), _814732))], (7783 ^ _543626) ^ [_815022, _815024, _815026, _815028] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_815022), c_Int_Onumber__class_Onumber__of(_815022, _815024)), c_Groups_Ominus__class_Ominus(_815022, _815026, _815028)) = c_Groups_Ominus__class_Ominus(_815022, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_815022), c_Int_Onumber__class_Onumber__of(_815022, _815024)), _815026), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_815022), c_Int_Onumber__class_Onumber__of(_815022, _815024)), _815028))), class_Int_Onumber(_815022), class_Rings_Oring(_815022)], (7793 ^ _543626) ^ [_815447, _815449, _815451, _815453] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_815447), c_Groups_Ominus__class_Ominus(_815447, _815449, _815451)), c_Int_Onumber__class_Onumber__of(_815447, _815453)) = c_Groups_Ominus__class_Ominus(_815447, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_815447), _815449), c_Int_Onumber__class_Onumber__of(_815447, _815453)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_815447), _815451), c_Int_Onumber__class_Onumber__of(_815447, _815453)))), class_Int_Onumber(_815447), class_Rings_Oring(_815447)], (7803 ^ _543626) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (7805 ^ _543626) ^ [] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (7807 ^ _543626) ^ [_815992, _815994, _815996, _815998, _816000] : [class_Rings_Olinordered__idom(_815992), c_Orderings_Oord__class_Oless(_815992, c_Groups_Oabs__class_Oabs(_815992, _815994), _815996), c_Orderings_Oord__class_Oless(_815992, c_Groups_Oabs__class_Oabs(_815992, _815998), _816000), -(c_Orderings_Oord__class_Oless(_815992, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_815992), c_Groups_Oabs__class_Oabs(_815992, _815994)), c_Groups_Oabs__class_Oabs(_815992, _815998)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_815992), _815996), _816000)))], (7821 ^ _543626) ^ [_816482, _816484] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _816482), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _816484), -(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), _816482), _816484)))], (7831 ^ _543626) ^ [_816813, _816815, _816817] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _816813, _816815), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _816817), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _816817), _816813), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _816817), _816815)))], (7841 ^ _543626) ^ [_817152, _817154] : [c_Groups_Oabs__class_Oabs(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _817152), _817154)) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(c_Groups_Oabs__class_Oabs(tc_Int_Oint, _817152) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (7847 ^ _543626) ^ [_817371, _817373] : [-(c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _817371), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _817373)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _817371, _817373)))], (7849 ^ _543626) ^ [_817496, _817498] : [class_Rings_Osemiring__1(_817496), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_817496), c_Nat_OSuc(_817498)) = c_Groups_Oplus__class_Oplus(_817496, c_Groups_Oone__class_Oone(_817496), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_817496), _817498)))], (7855 ^ _543626) ^ [_817754, _817756, _817758] : [class_Rings_Oring__1(_817754), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _817756, _817758), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_817754), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _817758, _817756)) = c_Groups_Ominus__class_Ominus(_817754, hAPP(c_Nat_Osemiring__1__class_Oof__nat(_817754), _817758), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_817754), _817756)))], (7865 ^ _543626) ^ [_818137, _818139, _818141, _818143] : [class_Rings_Olinordered__ring__strict(_818137), c_Orderings_Oord__class_Oless(_818137, c_Groups_Ozero__class_Ozero(_818137), _818139), 7872 ^ _543626 : [(7873 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_818137, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_818137), _818139), _818141), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_818137), _818139), _818143)), -(c_Orderings_Oord__class_Oless__eq(_818137, _818141, _818143))], (7879 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_818137, _818141, _818143), -(c_Orderings_Oord__class_Oless__eq(_818137, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_818137), _818139), _818141), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_818137), _818139), _818143)))]]], (7885 ^ _543626) ^ [_818812, _818814, _818816, _818818] : [class_Rings_Olinordered__ring__strict(_818812), c_Orderings_Oord__class_Oless(_818812, _818814, c_Groups_Ozero__class_Ozero(_818812)), 7892 ^ _543626 : [(7893 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_818812, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_818812), _818814), _818816), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_818812), _818814), _818818)), -(c_Orderings_Oord__class_Oless__eq(_818812, _818818, _818816))], (7899 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_818812, _818818, _818816), -(c_Orderings_Oord__class_Oless__eq(_818812, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_818812), _818814), _818816), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_818812), _818814), _818818)))]]], (7905 ^ _543626) ^ [_819501, _819503, _819505, _819507, _819509] : [class_Rings_Olinordered__semiring__strict(_819501), c_Orderings_Oord__class_Oless(_819501, _819503, _819505), c_Orderings_Oord__class_Oless(_819501, _819507, _819509), c_Orderings_Oord__class_Oless(_819501, c_Groups_Ozero__class_Ozero(_819501), _819505), c_Orderings_Oord__class_Oless__eq(_819501, c_Groups_Ozero__class_Ozero(_819501), _819507), -(c_Orderings_Oord__class_Oless(_819501, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_819501), _819503), _819507), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_819501), _819505), _819509)))], (7927 ^ _543626) ^ [_820223, _820225, _820227, _820229, _820231] : [class_Rings_Olinordered__semiring__strict(_820223), c_Orderings_Oord__class_Oless(_820223, _820225, _820227), c_Orderings_Oord__class_Oless(_820223, _820229, _820231), c_Orderings_Oord__class_Oless__eq(_820223, c_Groups_Ozero__class_Ozero(_820223), _820225), c_Orderings_Oord__class_Oless__eq(_820223, c_Groups_Ozero__class_Ozero(_820223), _820229), -(c_Orderings_Oord__class_Oless(_820223, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_820223), _820225), _820229), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_820223), _820227), _820231)))], (7949 ^ _543626) ^ [_820945, _820947, _820949, _820951, _820953] : [class_Rings_Olinordered__semiring__strict(_820945), c_Orderings_Oord__class_Oless(_820945, _820947, _820949), c_Orderings_Oord__class_Oless__eq(_820945, _820951, _820953), c_Orderings_Oord__class_Oless__eq(_820945, c_Groups_Ozero__class_Ozero(_820945), _820947), c_Orderings_Oord__class_Oless(_820945, c_Groups_Ozero__class_Ozero(_820945), _820951), -(c_Orderings_Oord__class_Oless(_820945, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_820945), _820947), _820951), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_820945), _820949), _820953)))], (7971 ^ _543626) ^ [_821667, _821669, _821671, _821673, _821675] : [class_Rings_Olinordered__semiring__strict(_821667), c_Orderings_Oord__class_Oless__eq(_821667, _821669, _821671), c_Orderings_Oord__class_Oless(_821667, _821673, _821675), c_Orderings_Oord__class_Oless(_821667, c_Groups_Ozero__class_Ozero(_821667), _821669), c_Orderings_Oord__class_Oless__eq(_821667, c_Groups_Ozero__class_Ozero(_821667), _821673), -(c_Orderings_Oord__class_Oless(_821667, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_821667), _821669), _821673), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_821667), _821671), _821675)))], (7993 ^ _543626) ^ [_822375, _822377, _822379, _822381] : [class_Rings_Olinordered__semiring(_822375), c_Orderings_Oord__class_Oless(_822375, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_822375), _822377), _822379), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_822375), _822381), _822379)), c_Orderings_Oord__class_Oless__eq(_822375, c_Groups_Ozero__class_Ozero(_822375), _822379), -(c_Orderings_Oord__class_Oless(_822375, _822377, _822381))], (8007 ^ _543626) ^ [_822859, _822861, _822863, _822865] : [class_Rings_Olinordered__semiring__strict(_822859), c_Orderings_Oord__class_Oless(_822859, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_822859), _822861), _822863), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_822859), _822865), _822863)), c_Orderings_Oord__class_Oless__eq(_822859, c_Groups_Ozero__class_Ozero(_822859), _822863), -(c_Orderings_Oord__class_Oless(_822859, _822861, _822865))], (8021 ^ _543626) ^ [_823343, _823345, _823347, _823349] : [class_Rings_Olinordered__semiring(_823343), c_Orderings_Oord__class_Oless(_823343, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_823343), _823345), _823347), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_823343), _823345), _823349)), c_Orderings_Oord__class_Oless__eq(_823343, c_Groups_Ozero__class_Ozero(_823343), _823345), -(c_Orderings_Oord__class_Oless(_823343, _823347, _823349))], (8035 ^ _543626) ^ [_823827, _823829, _823831, _823833] : [class_Rings_Olinordered__semiring__strict(_823827), c_Orderings_Oord__class_Oless(_823827, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_823827), _823829), _823831), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_823827), _823829), _823833)), c_Orderings_Oord__class_Oless__eq(_823827, c_Groups_Ozero__class_Ozero(_823827), _823829), -(c_Orderings_Oord__class_Oless(_823827, _823831, _823833))], (8049 ^ _543626) ^ [_824311, _824313, _824315, _824317] : [class_Rings_Olinordered__semiring__strict(_824311), c_Orderings_Oord__class_Oless__eq(_824311, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_824311), _824313), _824315), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_824311), _824317), _824315)), c_Orderings_Oord__class_Oless(_824311, c_Groups_Ozero__class_Ozero(_824311), _824315), -(c_Orderings_Oord__class_Oless__eq(_824311, _824313, _824317))], (8063 ^ _543626) ^ [_824795, _824797, _824799, _824801] : [class_Rings_Olinordered__semiring__strict(_824795), c_Orderings_Oord__class_Oless__eq(_824795, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_824795), _824797), _824799), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_824795), _824797), _824801)), c_Orderings_Oord__class_Oless(_824795, c_Groups_Ozero__class_Ozero(_824795), _824797), -(c_Orderings_Oord__class_Oless__eq(_824795, _824799, _824801))], (8077 ^ _543626) ^ [_825266] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _825266), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_825266 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8083 ^ _543626) ^ [_825430] : [_825430 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _825430), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (8089 ^ _543626) ^ [_825658, _825660, _825662] : [class_Rings_Olinordered__ring__strict(_825658), 8092 ^ _543626 : [(8093 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_825658, c_Groups_Oplus__class_Oplus(_825658, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_825658), _825660), _825660), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_825658), _825662), _825662)), c_Groups_Ozero__class_Ozero(_825658)), 8096 ^ _543626 : [(8097 ^ _543626) ^ [] : [-(_825660 = c_Groups_Ozero__class_Ozero(_825658))], (8099 ^ _543626) ^ [] : [-(_825662 = c_Groups_Ozero__class_Ozero(_825658))]]], (8101 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_825658, c_Groups_Oplus__class_Oplus(_825658, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_825658), _825660), _825660), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_825658), _825662), _825662)), c_Groups_Ozero__class_Ozero(_825658))), _825660 = c_Groups_Ozero__class_Ozero(_825658), _825662 = c_Groups_Ozero__class_Ozero(_825658)]]], (8111 ^ _543626) ^ [_826391, _826393, _826395] : [class_Rings_Olinordered__ring(_826391), -(c_Orderings_Oord__class_Oless__eq(_826391, c_Groups_Ozero__class_Ozero(_826391), c_Groups_Oplus__class_Oplus(_826391, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_826391), _826393), _826393), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_826391), _826395), _826395))))], (8117 ^ _543626) ^ [] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (8119 ^ _543626) ^ [_826718, _826720, _826722] : [class_Rings_Olinordered__ring(_826718), c_Orderings_Oord__class_Oless(_826718, c_Groups_Oplus__class_Oplus(_826718, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_826718), _826720), _826720), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_826718), _826722), _826722)), c_Groups_Ozero__class_Ozero(_826718))], (8125 ^ _543626) ^ [_826993, _826995, _826997] : [class_Rings_Olinordered__ring__strict(_826993), 8128 ^ _543626 : [(8139 ^ _543626) ^ [] : [8140 ^ _543626 : [(8141 ^ _543626) ^ [] : [-(_826995 = c_Groups_Ozero__class_Ozero(_826993))], (8143 ^ _543626) ^ [] : [-(_826997 = c_Groups_Ozero__class_Ozero(_826993))]], -(c_Orderings_Oord__class_Oless(_826993, c_Groups_Ozero__class_Ozero(_826993), c_Groups_Oplus__class_Oplus(_826993, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_826993), _826995), _826995), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_826993), _826997), _826997))))], (8129 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(_826993, c_Groups_Ozero__class_Ozero(_826993), c_Groups_Oplus__class_Oplus(_826993, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_826993), _826995), _826995), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_826993), _826997), _826997))), _826995 = c_Groups_Ozero__class_Ozero(_826993), _826997 = c_Groups_Ozero__class_Ozero(_826993)]]], (8147 ^ _543626) ^ [_827730, _827732, _827734] : [class_Rings_Olinordered__idom(_827730), c_Orderings_Oord__class_Oless__eq(_827730, c_Groups_Ozero__class_Ozero(_827730), _827732), c_Orderings_Oord__class_Oless__eq(_827730, c_Groups_Ozero__class_Ozero(_827730), _827734), c_Orderings_Oord__class_Oless__eq(_827730, _827734, c_Groups_Oone__class_Oone(_827730)), -(c_Orderings_Oord__class_Oless__eq(_827730, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_827730), _827732), _827734), _827732))], (8165 ^ _543626) ^ [_828273, _828275, _828277] : [class_Rings_Olinordered__idom(_828273), c_Orderings_Oord__class_Oless__eq(_828273, c_Groups_Ozero__class_Ozero(_828273), _828275), c_Orderings_Oord__class_Oless__eq(_828273, c_Groups_Ozero__class_Ozero(_828273), _828277), c_Orderings_Oord__class_Oless__eq(_828273, _828277, c_Groups_Oone__class_Oone(_828273)), -(c_Orderings_Oord__class_Oless__eq(_828273, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_828273), _828277), _828275), _828275))], (8183 ^ _543626) ^ [_828858, _828860, _828862, _828864, _828866, _828868] : [class_Rings_Oordered__ring(_828858), 8186 ^ _543626 : [(8187 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_828858, c_Groups_Oplus__class_Oplus(_828858, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_828858), _828860), _828862), _828864), c_Groups_Oplus__class_Oplus(_828858, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_828858), _828866), _828862), _828868)), -(c_Orderings_Oord__class_Oless__eq(_828858, c_Groups_Oplus__class_Oplus(_828858, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_828858), c_Groups_Ominus__class_Ominus(_828858, _828860, _828866)), _828862), _828864), _828868))], (8193 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_828858, c_Groups_Oplus__class_Oplus(_828858, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_828858), c_Groups_Ominus__class_Ominus(_828858, _828860, _828866)), _828862), _828864), _828868), -(c_Orderings_Oord__class_Oless__eq(_828858, c_Groups_Oplus__class_Oplus(_828858, 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hAPP(hAPP(c_Groups_Otimes__class_Otimes(_829562), c_Groups_Ominus__class_Ominus(_829562, _829570, _829564)), _829566), _829572)), -(c_Orderings_Oord__class_Oless__eq(_829562, c_Groups_Oplus__class_Oplus(_829562, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_829562), _829564), _829566), _829568), c_Groups_Oplus__class_Oplus(_829562, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_829562), _829570), _829566), _829572)))]]], (8215 ^ _543626) ^ [_830266, _830268, _830270, _830272, _830274, _830276] : [class_Rings_Oordered__ring(_830266), 8218 ^ _543626 : [(8219 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(_830266, c_Groups_Oplus__class_Oplus(_830266, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_830266), _830268), _830270), _830272), c_Groups_Oplus__class_Oplus(_830266, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_830266), _830274), _830270), _830276)), -(c_Orderings_Oord__class_Oless(_830266, _830272, c_Groups_Oplus__class_Oplus(_830266, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_830266), 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hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Nat_OSuc(8250 ^ [_831647, _831649]))))], (8254 ^ _543626) ^ [_831895, _831897] : [8255 ^ _543626 : [(8256 ^ _543626) ^ [_831975] : [_831897 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _831895, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Nat_OSuc(_831975)))]], -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _831895, _831897))], (8260 ^ _543626) ^ [_832120] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Nat_OSuc(_832120)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _832120)))], (8262 ^ _543626) ^ [_832239, _832241] : [class_Rings_Oring__1(_832239), -(c_Groups_Ominus__class_Ominus(_832239, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_832239), _832241), _832241), c_Groups_Oone__class_Oone(_832239)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_832239), c_Groups_Oplus__class_Oplus(_832239, _832241, c_Groups_Oone__class_Oone(_832239))), c_Groups_Ominus__class_Ominus(_832239, _832241, c_Groups_Oone__class_Oone(_832239))))], (8268 ^ _543626) ^ [_832529, _832531, _832533] : [class_Rings_Oordered__ring__abs(_832529), -(c_Groups_Oabs__class_Oabs(_832529, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_832529), _832531), _832533)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_832529), c_Groups_Oabs__class_Oabs(_832529, _832531)), c_Groups_Oabs__class_Oabs(_832529, _832533))), 8275 ^ _543626 : [(8276 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_832529, c_Groups_Ozero__class_Ozero(_832529), _832531)], (8278 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_832529, _832531, c_Groups_Ozero__class_Ozero(_832529))]], 8279 ^ _543626 : [(8280 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_832529, c_Groups_Ozero__class_Ozero(_832529), _832533)], (8282 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_832529, _832533, c_Groups_Ozero__class_Ozero(_832529))]]], (8286 ^ _543626) ^ [_833169, _833171, _833173] : [class_Rings_Olinordered__idom(_833169), c_Orderings_Oord__class_Oless__eq(_833169, c_Groups_Ozero__class_Ozero(_833169), _833171), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_833169), c_Groups_Oabs__class_Oabs(_833169, _833173)), _833171) = c_Groups_Oabs__class_Oabs(_833169, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_833169), _833173), _833171)))], (8296 ^ _543626) ^ [_833526, _833528] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _833526, _833528), -(c_Groups_Ominus__class_Ominus(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _833528), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _833526)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _833528, _833526)))], (8302 ^ _543626) ^ [_833772, _833774] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _833772), 8305 ^ _543626 : [(8306 ^ _543626) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _833772), _833774) = c_Groups_Oone__class_Oone(tc_Int_Oint), 8309 ^ _543626 : [(8310 ^ _543626) ^ [] : [-(_833772 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (8312 ^ _543626) ^ [] : [-(_833774 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (8314 ^ _543626) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _833772), _833774) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _833772 = c_Groups_Oone__class_Oone(tc_Int_Oint), _833774 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (8324 ^ _543626) ^ [_834410, _834412] : [class_Rings_Olinordered__semidom(_834410), 8327 ^ _543626 : [(8328 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(_834410, c_Groups_Ozero__class_Ozero(_834410), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_834410), _834412)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _834412))], (8334 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _834412), -(c_Orderings_Oord__class_Oless(_834410, c_Groups_Ozero__class_Ozero(_834410), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_834410), _834412)))]]], (8340 ^ _543626) ^ [_834910] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _834910)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _834910))], (8346 ^ _543626) ^ [_835076] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _835076), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _835076)))], (8352 ^ _543626) ^ [_835348, _835350, _835352, _835354, _835356, _835358] : [class_Rings_Olinordered__semiring__1(_835348), c_Orderings_Oord__class_Oless__eq(_835348, _835350, _835352), c_Orderings_Oord__class_Oless__eq(_835348, _835354, _835352), c_Orderings_Oord__class_Oless__eq(_835348, c_Groups_Ozero__class_Ozero(_835348), _835356), c_Orderings_Oord__class_Oless__eq(_835348, c_Groups_Ozero__class_Ozero(_835348), _835358), c_Groups_Oplus__class_Oplus(_835348, _835356, _835358) = c_Groups_Oone__class_Oone(_835348), -(c_Orderings_Oord__class_Oless__eq(_835348, c_Groups_Oplus__class_Oplus(_835348, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_835348), _835356), _835350), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_835348), _835358), _835354)), _835352))], (8378 ^ _543626) ^ [_836181] : [c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint, _836181)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _836181)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (8384 ^ _543626) ^ [_836353] : [-(c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint, _836353))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _836353)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint, _836353))], (8390 ^ _543626) ^ [_836584, _836586] : [class_Int_Onumber__ring(_836584), 8393 ^ _543626 : [(8394 ^ _543626) ^ [] : [c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint, _836586)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_836584), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _836586)) = c_Groups_Ozero__class_Ozero(_836584))], (8400 ^ _543626) ^ [] : [-(c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint, _836586))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_836584), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _836586)) = c_Int_Onumber__class_Onumber__of(_836584, _836586))]]], (8406 ^ _543626) ^ [_837154, _837156, _837158, _837160, _837162, _837164] : [class_Rings_Olinordered__semiring__1__strict(_837154), c_Orderings_Oord__class_Oless(_837154, _837156, _837158), c_Orderings_Oord__class_Oless(_837154, _837160, _837158), c_Orderings_Oord__class_Oless__eq(_837154, c_Groups_Ozero__class_Ozero(_837154), _837162), c_Orderings_Oord__class_Oless__eq(_837154, c_Groups_Ozero__class_Ozero(_837154), _837164), c_Groups_Oplus__class_Oplus(_837154, _837162, _837164) = c_Groups_Oone__class_Oone(_837154), -(c_Orderings_Oord__class_Oless(_837154, c_Groups_Oplus__class_Oplus(_837154, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_837154), _837162), _837156), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_837154), _837164), _837160)), _837158))], (8448 ^ _543626) ^ [_838505, _838507, _838509] : [-(hBOOL(hAPP(_838505, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _838507, _838509))))), 8451 ^ _543626 : [(8452 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _838509, _838507))], (8454 ^ _543626) ^ [] : [hBOOL(hAPP(_838505, c_Groups_Ominus__class_Ominus(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _838507), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _838509))))]], 8455 ^ _543626 : [(8456 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _838507, _838509))], (8458 ^ _543626) ^ [] : [hBOOL(hAPP(_838505, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (8432 ^ _543626) ^ [_838024, _838026, _838028] : [hBOOL(hAPP(_838024, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _838026, _838028)))), 8435 ^ _543626 : [(8436 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _838028, _838026), -(hBOOL(hAPP(_838024, c_Groups_Ominus__class_Ominus(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _838026), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _838028)))))], (8442 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _838026, _838028), -(hBOOL(hAPP(_838024, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (8462 ^ _543626) ^ [_839034, _839036, _839038] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _839034), _839034 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _839036, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _839034), _839038)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _839036), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _839038, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (8476 ^ _543626) ^ [_839476, _839478, _839480] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _839476), _839476 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _839478, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _839476), _839480)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _839478, _839476), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _839480))], (8490 ^ _543626) ^ [_839960, _839962, _839964, _839966, _839968, _839970] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _839960), _839962), _839964) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _839966), _839968), _839970), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _839966), _839968), _839970), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _839964, _839960), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _839970), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _839966), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _839966, _839960), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _839968, _839962))], (8516 ^ _543626) ^ [_840805, _840807, _840809] : [-(_840805 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 8519 ^ _543626 : [(8520 ^ _543626) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _840807), _840805) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _840809), _840805), -(_840807 = _840809)], (8526 ^ _543626) ^ [] : [_840807 = _840809, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _840807), _840805) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _840809), _840805))]]], (8532 ^ _543626) ^ [_841334, _841336, _841338] : [-(_841334 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 8535 ^ _543626 : [(8536 ^ _543626) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _841334), _841336) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _841334), _841338), -(_841336 = _841338)], (8542 ^ _543626) ^ [] : [_841336 = _841338, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _841334), _841336) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _841334), _841338))]]], (8548 ^ _543626) ^ [_841820] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _841820) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8550 ^ _543626) ^ [_841901] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _841901), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8562 ^ _543626) ^ [_842307, _842309] : [8563 ^ _543626 : [(8564 ^ _543626) ^ [] : [_842307 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (8566 ^ _543626) ^ [] : [_842309 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _842307), _842309) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8552 ^ _543626) ^ [_842043, _842045] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _842043), _842045) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_842043 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_842045 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8580 ^ _543626) ^ [_842934, _842936, _842938] : [8581 ^ _543626 : [(8582 ^ _543626) ^ [] : [_842936 = _842938], (8584 ^ _543626) ^ [] : [_842934 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _842934), _842936) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _842934), _842938))], (8570 ^ _543626) ^ [_842648, _842650, _842652] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _842648), _842650) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _842648), _842652), -(_842650 = _842652), -(_842648 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8598 ^ _543626) ^ [_843581, _843583, _843585] : [8599 ^ _543626 : [(8600 ^ _543626) ^ [] : [_843581 = _843585], (8602 ^ _543626) ^ [] : [_843583 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _843581), _843583) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _843585), _843583))], (8588 ^ _543626) ^ [_843295, _843297, _843299] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _843295), _843297) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _843299), _843297), -(_843295 = _843299), -(_843297 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8606 ^ _543626) ^ [_843898, _843900, _843902] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _843898, _843900)), _843902) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _843898), _843902), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _843900), _843902)))], (8608 ^ _543626) ^ [_844034, _844036, _844038] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _844034), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _844036, _844038)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _844034), _844036), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _844034), _844038)))], (8610 ^ _543626) ^ [_844170, _844172, _844174] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _844170, _844172)), _844174) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _844170), _844174), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _844172), _844174)))], (8612 ^ _543626) ^ [_844292, _844294] : [-(hAPP(c_RealDef_Oreal(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _844292), _844294)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(c_RealDef_Oreal(tc_Nat_Onat), _844292)), hAPP(c_RealDef_Oreal(tc_Nat_Onat), _844294)))], (8614 ^ _543626) ^ [_844421, _844423, _844425] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _844421), _844423)), _844425) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _844421), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _844423), _844425)))], (8616 ^ _543626) ^ [_844541, _844543] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _844541), _844543) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _844543), _844541))], (8618 ^ _543626) ^ [_844661, _844663, _844665] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _844661), _844663)), _844665) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _844661), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _844663), _844665)))], (8620 ^ _543626) ^ [_844781, _844783] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _844781), _844783) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _844783), _844781))], (8622 ^ _543626) ^ [_844931, _844933] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _844931) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _844933), -(_844931 = _844933)], (8628 ^ _543626) ^ [_845105, _845107] : [_845105 = _845107, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _845105) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _845107))], (8634 ^ _543626) ^ [_845314, _845316] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _845314)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _845316)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _845314), _845316)))], (8636 ^ _543626) ^ [_845429, _845431] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _845429), _845431)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _845429)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _845431)))], (8638 ^ _543626) ^ [_845587, _845589, _845591, _845593] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _845587, _845589), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _845591, _845593), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _845587), _845591), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _845589), _845593)))], (8648 ^ _543626) ^ [_845950, _845952, _845954] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _845950, _845952), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _845954), _845950), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _845954), _845952)))], (8654 ^ _543626) ^ [_846208, _846210, _846212] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _846208, _846210), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _846208), _846212), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _846210), _846212)))], (8660 ^ _543626) ^ [_846423] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _846423, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _846423), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _846423), _846423))))], (8662 ^ _543626) ^ [_846514] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _846514, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _846514), _846514)))], (8664 ^ _543626) ^ [_846671, _846673, _846675] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_846671)), _846673) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_846671)), _846675), -(_846673 = _846675)], (8670 ^ _543626) ^ [_846871, _846873, _846875] : [_846873 = _846875, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_846871)), _846873) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_846871)), _846875))], (8676 ^ _543626) ^ [_847120, _847122, _847124] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _847120, _847122)), _847124) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _847120), _847124), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _847122), _847124)))], (8678 ^ _543626) ^ [_847256, _847258, _847260] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _847256), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _847258, _847260)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _847256), _847258), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _847256), _847260)))], (8680 ^ _543626) ^ [_847422, _847424] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _847422) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _847424), -(_847422 = _847424)], (8686 ^ _543626) ^ [_847596, _847598] : [_847596 = _847598, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _847596) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _847598))], (8692 ^ _543626) ^ [_847805, _847807] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _847805)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _847807)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _847805), _847807)))], (8694 ^ _543626) ^ [_847906] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _847906) = _847906)], (8696 ^ _543626) ^ [_847987] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _847987) = _847987)], (8698 ^ _543626) ^ [_848126, _848128] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _848126), _848128), 8701 ^ _543626 : [(8702 ^ _543626) ^ [] : [-(_848126 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (8704 ^ _543626) ^ [] : [-(_848128 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (8706 ^ _543626) ^ [_848375, _848377] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _848375), _848377)), _848375 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _848377 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (8716 ^ _543626) ^ [_848659] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _848659), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _848659)], (8718 ^ _543626) ^ [_848801, _848803] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _848801), _848803) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 8721 ^ _543626 : [(8722 ^ _543626) ^ [] : [-(_848801 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (8724 ^ _543626) ^ [] : [-(_848803 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (8726 ^ _543626) ^ [_849050, _849052] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _849050), _849052) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _849050 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _849052 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (8736 ^ _543626) ^ [_849363, _849365] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _849363), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _849365), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_RComplete_Onatfloor(_849363)), c_RComplete_Onatfloor(_849365)), c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _849363), _849365))))], (8746 ^ _543626) ^ [_849733, _849735] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _849733), _849735) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 8749 ^ _543626 : [(8750 ^ _543626) ^ [] : [-(_849733 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (8752 ^ _543626) ^ [] : [-(_849735 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (8754 ^ _543626) ^ [_849982, _849984] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _849982), _849984) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _849982 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _849984 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8764 ^ _543626) ^ [_850324, _850326] : [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), _850324), _850326)), 8767 ^ _543626 : [(8768 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _850324))], (8770 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _850326))]]], (8772 ^ _543626) ^ [_850579, _850581] : [-(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), _850579), _850581))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _850579), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _850581)], (8782 ^ _543626) ^ [_850941, _850943, _850945] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _850941), _850943), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _850941), _850945)), 8785 ^ _543626 : [(8786 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _850941))], (8788 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _850943, _850945))]]], (8790 ^ _543626) ^ [_851216, _851218, _851220] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _851216), _851218), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _851216), _851220))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _851216), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _851218, _851220)], (8800 ^ _543626) ^ [_851600, _851602, _851604] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _851600), _851602), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _851604), _851602)), 8803 ^ _543626 : [(8804 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _851602))], (8806 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _851600, _851604))]]], (8808 ^ _543626) ^ [_851875, _851877, _851879] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _851875), _851877), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _851879), _851877))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _851877), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _851875, _851879)], (8818 ^ _543626) ^ [_852230, _852232, _852234] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _852230, _852232), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _852234), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _852230), _852234), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _852232), _852234)))], (8828 ^ _543626) ^ [_852583, _852585, _852587] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _852583, _852585), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _852587), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _852587), _852583), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _852587), _852585)))], (8838 ^ _543626) ^ [_852936, _852938, _852940] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _852936), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _852938, _852940), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _852936), _852938), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _852936), _852940)))], (8848 ^ _543626) ^ [_853275, _853277] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _853275), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _853277), -(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), _853275), _853277)))], (8858 ^ _543626) ^ [_853606, _853608, _853610] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _853606), 8861 ^ _543626 : [(8862 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _853608), _853606), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _853610), _853606)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _853608, _853610))], (8868 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _853608, _853610), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _853608), _853606), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _853610), _853606)))]]], (8874 ^ _543626) ^ [_854169, _854171, _854173] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_854169)), _854171), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_854169)), _854173)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _854171, _854173))], (8880 ^ _543626) ^ [_854373, _854375, _854377] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _854375, _854377), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_854373)), _854375), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_854373)), _854377)))], (8886 ^ _543626) ^ [_854612, _854614] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _854612), c_Nat_OSuc(_854614)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _854612, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _854612), _854614)))], (8888 ^ _543626) ^ [_854724, _854726] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_854724)), _854726) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _854726, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _854724), _854726)))], (8890 ^ _543626) ^ [_854894, _854896, _854898] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_854894)), _854896), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_854894)), _854898)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _854896, _854898))], (8896 ^ _543626) ^ [_855098, _855100, _855102] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _855100, _855102), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_855098)), _855100), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_855098)), _855102)))], (8902 ^ _543626) ^ [_855352, _855354] : [_855352 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _855352), _855354), -(_855354 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_855352 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8912 ^ _543626) ^ [_855693, _855695] : [c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _855693), _855693), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _855695), _855695)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 8915 ^ _543626 : [(8916 ^ _543626) ^ [] : [-(_855693 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (8918 ^ _543626) ^ [] : [-(_855695 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))]]], (8920 ^ _543626) ^ [_855962, _855964] : [-(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _855962), _855962), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _855964), _855964)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _855962 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _855964 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)], (8930 ^ _543626) ^ [_856280, _856282] : [-(c_Complex_Oexpi(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, _856280, _856282)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Complex_Oexpi(_856280)), c_Complex_Oexpi(_856282)))], (8932 ^ _543626) ^ [_856405, _856407] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _856405), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _856407), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _856405, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _856407), _856405)))], (8942 ^ _543626) ^ [_856722, _856724] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _856722), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _856724), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _856722, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _856722), _856724)))], (8952 ^ _543626) ^ [_857039, _857041] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _857039), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _857041), -(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), _857041), _857039)))], (8962 ^ _543626) ^ [_857370, _857372, _857374] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _857370), 8965 ^ _543626 : [(8966 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _857370), _857372), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _857370), _857374)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _857372, _857374))], (8972 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _857372, _857374), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _857370), _857372), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _857370), _857374)))]]], (8978 ^ _543626) ^ [_857904, _857906, _857908] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _857904), 8981 ^ _543626 : [(8982 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _857906), _857904), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _857908), _857904)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _857906, _857908))], (8988 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _857906, _857908), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _857906), _857904), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _857908), _857904)))]]], (8994 ^ _543626) ^ [_858453, _858455] : [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), _858453), _858455)), 8997 ^ _543626 : [(8998 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _858453))], (9000 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _858455))]]], (9002 ^ _543626) ^ [_858708, _858710] : [-(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), _858708), _858710))), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _858708), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _858710)], (9022 ^ _543626) ^ [_859361, _859363, _859365] : [9023 ^ _543626 : [(9024 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _859363))], (9026 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _859361, _859365)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _859361), _859363), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _859365), _859363)))], (9012 ^ _543626) ^ [_859070, _859072, _859074] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _859070), _859072), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _859074), _859072)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _859072), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _859070, _859074))], (9040 ^ _543626) ^ [_860020, _860022, _860024] : [9041 ^ _543626 : [(9042 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _860020))], (9044 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _860022, _860024)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _860020), _860022), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _860020), _860024)))], (9030 ^ _543626) ^ [_859729, _859731, _859733] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _859729), _859731), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _859729), _859733)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _859729), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _859731, _859733))], (9048 ^ _543626) ^ [_860359, _860361, _860363] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _860359, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _860361), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _860359), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _860363))), -(_860361 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (9058 ^ _543626) ^ [_860724, _860726, _860728, _860730] : [class_RealVector_Oreal__normed__vector(_860724), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _860726, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_860724, _860728), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _860726), c_RealVector_Onorm__class_Onorm(_860724, _860730))), -(_860728 = c_Groups_Ozero__class_Ozero(_860724))], (9072 ^ _543626) ^ [_861190, _861192] : [_861190 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _861190), _861192) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9078 ^ _543626) ^ [_861364, _861366] : [-(_861364 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _861364), _861366) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _861366, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _861364, c_Groups_Oone__class_Oone(tc_Nat_Onat))), _861366)))], (9084 ^ _543626) ^ [_861639, _861641] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _861639, c_Int_OPls), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _861639)), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _861641)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9090 ^ _543626) ^ [_861827, _861829] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _861827, c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _861827)), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _861829)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _861827), _861829)))], (9096 ^ _543626) ^ [_862120, _862122, _862124] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _862120, c_Int_OPls), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _862120)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _862122)), _862124)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9102 ^ _543626) ^ [_862326, _862328, _862330] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _862326, c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _862326)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _862328)), _862330)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _862326), _862328))), _862330))], (9108 ^ _543626) ^ [_862629, _862631, _862633] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _862629), _862631), _862633)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _862633, _862629), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _862629), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _862631))], (9122 ^ _543626) ^ [_863073, _863075, _863077] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _863073), _863075), _863077), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _863077), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _863073), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _863075, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (9136 ^ _543626) ^ [_863545, _863547, _863549, _863551, _863553] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _863545), _863547), _863549), c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _863545), _863551), _863553)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _863549), c_Orderings_Oord__class_Oless(tc_Int_Oint, _863549, _863545), c_Orderings_Oord__class_Oless(tc_Int_Oint, _863553, _863545), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _863547, _863551))], (9154 ^ _543626) ^ [_864182, _864184, _864186, _864188, _864190, _864192] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _864182), _864184), _864186) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _864188), _864190), _864192), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _864188), _864190), _864192)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _864192, _864188), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _864186), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _864188), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _864188, _864182), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _864184, _864190))], (9180 ^ _543626) ^ [_865055, _865057, _865059, _865061, _865063] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _865055), _865057), _865059), c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _865055), _865061), _865063)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _865063, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _865055, _865063), c_Orderings_Oord__class_Oless(tc_Int_Oint, _865055, _865059), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _865061, _865057))], (9198 ^ _543626) ^ [_865678, _865680, _865682, _865684, _865686] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _865678, _865680), 9201 ^ _543626 : [(9202 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _865678), _865682), _865684), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _865680), _865682), _865686)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _865684, 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, _865680, _865678)), _865682), _865686)))], (9208 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _865684, 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, _865680, _865678)), _865682), _865686)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _865678), _865682), _865684), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _865680), _865682), _865686)))]]], (9214 ^ _543626) ^ [_866338, _866340, _866342, _866344, _866346] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _866338, _866340), 9217 ^ _543626 : [(9218 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _866340), _866342), _866344), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _866338), _866342), _866346)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _866340, _866338)), _866342), _866344), _866346))], (9224 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _866340, _866338)), _866342), _866344), _866346), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _866340), _866342), _866344), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _866338), _866342), _866346)))]]], (9240 ^ _543626) ^ [_867285, _867287, _867289] : [9241 ^ _543626 : [(9242 ^ _543626) ^ [] : [_867285 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (9244 ^ _543626) ^ [] : [_867287 = _867289]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _867285), _867287) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _867285), _867289))], (9230 ^ _543626) ^ [_866999, _867001, _867003] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _866999), _867001) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _866999), _867003), -(_866999 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_867001 = _867003)], (9248 ^ _543626) ^ [_867616, _867618, _867620, _867622] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _867616), _867618), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _867620), _867618), _867622)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _867616, _867620)), _867618), _867622))], (9250 ^ _543626) ^ [_867777, _867779, _867781] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _867777), 9253 ^ _543626 : [(9254 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _867777), _867779), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _867777), _867781)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _867779, _867781))], (9260 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _867779, _867781), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _867777), _867779), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _867777), _867781)))]]], (9266 ^ _543626) ^ [_868311, _868313, _868315] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _868311), 9269 ^ _543626 : [(9270 ^ _543626) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _868311), _868313) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _868311), _868315), -(_868313 = _868315)], (9276 ^ _543626) ^ [] : [_868313 = _868315, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _868311), _868313) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _868311), _868315))]]], (9282 ^ _543626) ^ [_868839, _868841, _868843] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _868839), 9285 ^ _543626 : [(9286 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _868839), _868841), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _868839), _868843)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _868841, _868843))], (9292 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _868841, _868843), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _868839), _868841), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _868839), _868843)))]]], (9298 ^ _543626) ^ [_869401, _869403, _869405, _869407, _869409] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _869401, _869403), 9301 ^ _543626 : [(9302 ^ _543626) ^ [] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _869401), _869405), _869407) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _869403), _869405), _869409), -(_869407 = 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, _869403, _869401)), _869405), _869409))], (9308 ^ _543626) ^ [] : [_869407 = 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, _869403, _869401)), _869405), _869409), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _869401), _869405), _869407) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _869403), _869405), _869409))]]], (9314 ^ _543626) ^ [_870055, _870057, _870059, _870061, _870063] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _870055, _870057), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _870055), _870059), _870061), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _870057), _870059), _870063)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _870061, 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, _870057, _870055)), _870059), _870063)))], (9320 ^ _543626) ^ [_870411, _870413, _870415, _870417, _870419] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _870411, _870413), 9323 ^ _543626 : [(9324 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _870411), _870415), _870417), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _870413), _870415), _870419)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _870417, 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, _870413, _870411)), _870415), _870419)))], (9330 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _870417, 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, _870413, _870411)), _870415), _870419)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _870411), _870415), _870417), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _870413), _870415), _870419)))]]], (9336 ^ _543626) ^ [_871071, _871073, _871075, _871077, _871079] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _871071, _871073), 9339 ^ _543626 : [(9340 ^ _543626) ^ [] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _871073), _871075), _871077) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _871071), _871075), _871079), -(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, _871073, _871071)), _871075), _871077) = _871079)], (9346 ^ _543626) ^ [] : [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, _871073, _871071)), _871075), _871077) = _871079, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _871073), _871075), _871077) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _871071), _871075), _871079))]]], (9352 ^ _543626) ^ [_871725, _871727, _871729, _871731, _871733] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _871725, _871727), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _871727), _871729), _871731), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _871725), _871729), _871733)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _871727, _871725)), _871729), _871731), _871733))], (9358 ^ _543626) ^ [_872081, _872083, _872085, _872087, _872089] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _872081, _872083), 9361 ^ _543626 : [(9362 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _872083), _872085), _872087), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _872081), _872085), _872089)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _872083, _872081)), _872085), _872087), _872089))], (9368 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _872083, _872081)), _872085), _872087), _872089), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _872083), _872085), _872087), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _872081), _872085), _872089)))]]], (9374 ^ _543626) ^ [_872714] : [-(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), _872714), _872714))), -(_872714 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (9380 ^ _543626) ^ [_872887] : [_872887 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _872887), _872887))], (9386 ^ _543626) ^ [_873108, _873110] : [class_RealVector_Oreal__normed__algebra(_873108), 9390 ^ _543626 : [(9391 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 9389 ^ [_873108, _873110]))], (9393 ^ _543626) ^ [_873407] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_873108, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_873108), _873407), _873110)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_873108, _873407)), 9389 ^ [_873108, _873110])))]]], (9395 ^ _543626) ^ [_873539] : [class_RealVector_Oreal__normed__algebra(_873539), 9399 ^ _543626 : [(9400 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 9398 ^ [_873539]))], (9402 ^ _543626) ^ [_873868, _873870] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_873539, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_873539), _873870), _873868)), 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(_873539, _873870)), c_RealVector_Onorm__class_Onorm(_873539, _873868))), 9398 ^ [_873539])))]]], (9404 ^ _543626) ^ [_874021, _874023] : [class_RealVector_Oreal__normed__algebra(_874021), 9408 ^ _543626 : [(9409 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 9407 ^ [_874021, _874023]))], (9411 ^ _543626) ^ [_874320] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_874021, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_874021), _874023), _874320)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_874021, _874320)), 9407 ^ [_874021, _874023])))]]], (9413 ^ _543626) ^ [_874480, _874482, _874484] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _874480), 9419 ^ _543626 : [(9420 ^ _543626) ^ [] : [-(hBOOL(hAPP(_874482, 9418 ^ [_874480, _874482, _874484])))], (9422 ^ _543626) ^ [] : [hBOOL(hAPP(_874482, c_Groups_Ominus__class_Ominus(tc_Int_Oint, 9418 ^ [_874480, _874482, _874484], _874480)))]], c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _874484), 9427 ^ _543626 : [(9428 ^ _543626) ^ [_874995] : [hBOOL(hAPP(_874482, _874995)), -(hBOOL(hAPP(_874482, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _874995, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _874484), _874480)))))]]], (9434 ^ _543626) ^ [_875279, _875281, _875283] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _875279), 9440 ^ _543626 : [(9441 ^ _543626) ^ [] : [-(hBOOL(hAPP(_875281, 9439 ^ [_875279, _875281, _875283])))], (9443 ^ _543626) ^ [] : [hBOOL(hAPP(_875281, c_Groups_Oplus__class_Oplus(tc_Int_Oint, 9439 ^ [_875279, _875281, _875283], _875279)))]], c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _875283), 9448 ^ _543626 : [(9449 ^ _543626) ^ [_875794] : [hBOOL(hAPP(_875281, _875794)), -(hBOOL(hAPP(_875281, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _875794, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _875283), _875279)))))]]], (9455 ^ _543626) ^ [_876050] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _876050), 9459 ^ _543626 : [(9460 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 9458 ^ [_876050]))], (9462 ^ _543626) ^ [] : [-(_876050 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 9458 ^ [_876050]))]]], (9464 ^ _543626) ^ [_876389] : [class_RealVector_Oreal__normed__algebra(_876389), 9468 ^ _543626 : [(9469 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 9467 ^ [_876389]))], (9471 ^ _543626) ^ [_876718, _876720] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_876389, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_876389), _876720), _876718)), 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(_876389, _876720)), c_RealVector_Onorm__class_Onorm(_876389, _876718))), 9467 ^ [_876389])))]]], (9473 ^ _543626) ^ [_876871, _876873] : [class_RealVector_Oreal__normed__algebra(_876871), 9477 ^ _543626 : [(9478 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 9476 ^ [_876871, _876873]))], (9480 ^ _543626) ^ [_877170] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_876871, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_876871), _877170), _876873)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_876871, _877170)), 9476 ^ [_876871, _876873])))]]], (9482 ^ _543626) ^ [_877316, _877318] : [class_RealVector_Oreal__normed__algebra(_877316), 9486 ^ _543626 : [(9487 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 9485 ^ [_877316, _877318]))], (9489 ^ _543626) ^ [_877615] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_877316, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_877316), _877318), _877615)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_877316, _877615)), 9485 ^ [_877316, _877318])))]]], (9491 ^ _543626) ^ [_877761, _877763] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _877761), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(c_RealDef_Oreal(tc_Nat_Onat), _877763)), _877761), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _877761, c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), _877763)))], (9497 ^ _543626) ^ [_878006, _878008] : [-(c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Nat_OSuc(_878006))), _878008)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Complex_Ocis(_878008)), c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(c_RealDef_Oreal(tc_Nat_Onat), _878006)), _878008))))], (9499 ^ _543626) ^ [_878147, _878149] : [class_Rings_Ocomm__semiring__1(_878147), -(hAPP(hAPP(c_Power_Opower__class_Opower(_878147), _878149), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_878147))], (9505 ^ _543626) ^ [_878389, _878391, _878393] : [class_RealVector_Oreal__normed__div__algebra(_878389), -(c_RealVector_Onorm__class_Onorm(_878389, hAPP(hAPP(c_Power_Opower__class_Opower(_878389), _878391), _878393)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_878389, _878391)), _878393))], (9511 ^ _543626) ^ [_878657, _878659, _878661] : [class_RealVector_Oreal__normed__algebra__1(_878657), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_878657, hAPP(hAPP(c_Power_Opower__class_Opower(_878657), _878659), _878661)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_878657, _878659)), _878661)))], (9517 ^ _543626) ^ [_878913, _878915] : [class_Rings_Ocomm__semiring__1(_878913), -(hAPP(hAPP(c_Power_Opower__class_Opower(_878913), _878915), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _878915)], (9523 ^ _543626) ^ [_879165, _879167, _879169, _879171] : [class_Rings_Ocomm__semiring__1(_879165), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_879165), hAPP(hAPP(c_Power_Opower__class_Opower(_879165), _879167), _879169)), hAPP(hAPP(c_Power_Opower__class_Opower(_879165), _879167), _879171)) = hAPP(hAPP(c_Power_Opower__class_Opower(_879165), _879167), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _879169, _879171)))], (9529 ^ _543626) ^ [_879471, _879473, _879475] : [class_Rings_Ocomm__semiring__1(_879471), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_879471), hAPP(hAPP(c_Power_Opower__class_Opower(_879471), _879473), _879475)), _879473) = hAPP(hAPP(c_Power_Opower__class_Opower(_879471), _879473), c_Nat_OSuc(_879475)))], (9535 ^ _543626) ^ [_879751, _879753, _879755] : [class_Rings_Ocomm__semiring__1(_879751), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_879751), _879753), hAPP(hAPP(c_Power_Opower__class_Opower(_879751), _879753), _879755)) = hAPP(hAPP(c_Power_Opower__class_Opower(_879751), _879753), c_Nat_OSuc(_879755)))], (9541 ^ _543626) ^ [_880031, _880033, _880035] : [class_Rings_Ocomm__semiring__1(_880031), -(hAPP(hAPP(c_Power_Opower__class_Opower(_880031), _880033), c_Nat_OSuc(_880035)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_880031), _880033), hAPP(hAPP(c_Power_Opower__class_Opower(_880031), _880033), _880035)))], (9547 ^ _543626) ^ [_880325, _880327, _880329, _880331] : [class_Rings_Ocomm__semiring__1(_880325), -(hAPP(hAPP(c_Power_Opower__class_Opower(_880325), hAPP(hAPP(c_Power_Opower__class_Opower(_880325), _880327), _880329)), _880331) = hAPP(hAPP(c_Power_Opower__class_Opower(_880325), _880327), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _880329), _880331)))], (9553 ^ _543626) ^ [_880633, _880635, _880637, _880639] : [class_Rings_Ocomm__semiring__1(_880633), -(hAPP(hAPP(c_Power_Opower__class_Opower(_880633), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_880633), _880635), _880637)), _880639) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_880633), hAPP(hAPP(c_Power_Opower__class_Opower(_880633), _880635), _880639)), hAPP(hAPP(c_Power_Opower__class_Opower(_880633), _880637), _880639)))], (9559 ^ _543626) ^ [_880947, _880949, _880951] : [class_Power_Opower(_880947), class_Rings_Omult__zero(_880947), class_Rings_Ono__zero__divisors(_880947), class_Rings_Ozero__neq__one(_880947), 9574 ^ _543626 : [(9575 ^ _543626) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_880947), _880949), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _880951)) = c_Groups_Ozero__class_Ozero(_880947), 9578 ^ _543626 : [(9579 ^ _543626) ^ [] : [-(_880949 = c_Groups_Ozero__class_Ozero(_880947))], (9581 ^ _543626) ^ [] : [c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _880951) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (9583 ^ _543626) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_880947), _880949), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _880951)) = c_Groups_Ozero__class_Ozero(_880947)), _880949 = c_Groups_Ozero__class_Ozero(_880947), -(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _880951) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (9593 ^ _543626) ^ [_881905, _881907] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Complex_Ocis(_881905)), c_Complex_Ocis(_881907)) = c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _881905, _881907)))], (9595 ^ _543626) ^ [] : [-(c_Complex_Ocis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))], (9597 ^ _543626) ^ [_882097, _882099, _882101] : [class_Rings_Olinordered__semidom(_882097), c_Orderings_Oord__class_Oless__eq(_882097, c_Groups_Ozero__class_Ozero(_882097), _882099), c_Orderings_Oord__class_Oless__eq(_882097, _882099, c_Groups_Oone__class_Oone(_882097)), -(c_Orderings_Oord__class_Oless__eq(_882097, hAPP(hAPP(c_Power_Opower__class_Opower(_882097), _882099), c_Nat_OSuc(_882101)), _882099))], (9611 ^ _543626) ^ [_882531, _882533] : [class_Power_Opower(_882531), class_Rings_Osemiring__0(_882531), 9618 ^ _543626 : [(9619 ^ _543626) ^ [] : [c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _882533) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_882531), c_Groups_Ozero__class_Ozero(_882531)), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _882533)) = c_Groups_Oone__class_Oone(_882531))], (9625 ^ _543626) ^ [] : [-(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _882533) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_882531), c_Groups_Ozero__class_Ozero(_882531)), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _882533)) = c_Groups_Ozero__class_Ozero(_882531))]]], (9631 ^ _543626) ^ [_883170, _883172, _883174] : [class_Rings_Ocomm__ring__1(_883170), -(c_Groups_Ominus__class_Ominus(_883170, hAPP(hAPP(c_Power_Opower__class_Opower(_883170), _883172), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(hAPP(c_Power_Opower__class_Opower(_883170), _883174), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_883170), c_Groups_Ominus__class_Ominus(_883170, _883172, _883174)), c_Groups_Oplus__class_Oplus(_883170, _883172, _883174)))], (9637 ^ _543626) ^ [_883470, _883472, _883474] : [class_Groups_Omonoid__mult(_883470), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _883472), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_883470), hAPP(hAPP(c_Power_Opower__class_Opower(_883470), _883474), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _883472, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _883474) = hAPP(hAPP(c_Power_Opower__class_Opower(_883470), _883474), _883472))], (9647 ^ _543626) ^ [_883849, _883851, _883853] : [class_Power_Opower(_883849), 9650 ^ _543626 : [(9651 ^ _543626) ^ [] : [_883851 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_883849), _883853), _883851) = c_Groups_Oone__class_Oone(_883849))], (9657 ^ _543626) ^ [] : [-(_883851 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_883849), _883853), _883851) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_883849), _883853), hAPP(hAPP(c_Power_Opower__class_Opower(_883849), _883853), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _883851, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (9663 ^ _543626) ^ [_884433, _884435, _884437, _884439] : [class_Rings_Olinordered__semidom(_884433), c_Orderings_Oord__class_Oless(_884433, _884435, _884437), c_Orderings_Oord__class_Oless__eq(_884433, c_Groups_Ozero__class_Ozero(_884433), _884435), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _884439), -(c_Orderings_Oord__class_Oless(_884433, hAPP(hAPP(c_Power_Opower__class_Opower(_884433), _884435), _884439), hAPP(hAPP(c_Power_Opower__class_Opower(_884433), _884437), _884439)))], (9681 ^ _543626) ^ [_884973, _884975] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _884973)), _884975) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _884973), _884975)))], (9683 ^ _543626) ^ [_885085, _885087] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _885085), _885087)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _885085)), _885087))], (9685 ^ _543626) ^ [_885197, _885199] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _885197)), _885199) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _885197), _885199)))], (9687 ^ _543626) ^ [_885324, _885326] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _885324), -(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), _885324), _885326)))], (9703 ^ _543626) ^ [_885847, _885849] : [9704 ^ _543626 : [(9705 ^ _543626) ^ [] : [_885849 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (9707 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _885847)]], -(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), _885847), _885849)))], (9693 ^ _543626) ^ [_885579, _885581] : [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), _885579), _885581)), -(_885581 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _885579))], (9711 ^ _543626) ^ [_886149, _886151] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _886149), -(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), _886149), _886151)))], (9727 ^ _543626) ^ [_886672, _886674] : [9728 ^ _543626 : [(9729 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _886672)], (9731 ^ _543626) ^ [] : [_886674 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _886672), _886674)))], (9717 ^ _543626) ^ [_886404, _886406] : [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), _886404), _886406)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _886404)), -(_886406 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9735 ^ _543626) ^ [_886988, _886990, _886992] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _886988), c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _886988), _886990), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _886988), _886992)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _886990, _886992))], (9745 ^ _543626) ^ [_887298] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _887298) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (9757 ^ _543626) ^ [_887701, _887703] : [9758 ^ _543626 : [(9759 ^ _543626) ^ [] : [_887703 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (9761 ^ _543626) ^ [] : [_887701 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _887701), _887703) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (9747 ^ _543626) ^ [_887437, _887439] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _887437), _887439) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_887439 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_887437 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (9765 ^ _543626) ^ [_887984, _887986] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), hAPP(c_RealDef_Oreal(tc_Nat_Onat), _887984)), _887986) = hAPP(c_RealDef_Oreal(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _887984), _887986)))], (9767 ^ _543626) ^ [_888096, _888098] : [-(hAPP(c_RealDef_Oreal(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _888096), _888098)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), hAPP(c_RealDef_Oreal(tc_Nat_Onat), _888096)), _888098))], (9769 ^ _543626) ^ [_888222, _888224, _888226] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _888222), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _888224, _888226)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _888222), _888224)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _888222), _888226)))], (9771 ^ _543626) ^ [_888360, _888362, _888364] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _888360), _888362)), _888364) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _888360), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _888362), _888364)))], (9783 ^ _543626) ^ [_888804, _888806] : [9784 ^ _543626 : [(9785 ^ _543626) ^ [] : [c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _888806) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (9787 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _888804)]], -(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), _888804), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _888806))))], (9773 ^ _543626) ^ [_888524, _888526] : [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), _888524), c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _888526))), -(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, _888526) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _888524))], (9791 ^ _543626) ^ [_889103, _889105] : [-(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, _889103)), _889105)))], (9793 ^ _543626) ^ [_889222, _889224] : [_889222 = hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_RComplete_Onatfloor(_889222)), -(c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _889222), _889224)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_RComplete_Onatfloor(_889222)), _889224))], (9799 ^ _543626) ^ [_889459, _889461] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Complex_Ocis(_889459)), _889461) = c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(c_RealDef_Oreal(tc_Nat_Onat), _889461)), _889459)))], (9801 ^ _543626) ^ [_889607, _889609] : [_889607 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _889609), _889607) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (9807 ^ _543626) ^ [_889781, _889783] : [-(_889781 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _889783), _889781) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _889783), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _889783), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _889781, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (9823 ^ _543626) ^ [_890342, _890344] : [9824 ^ _543626 : [(9825 ^ _543626) ^ [] : [-(_890342 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (9827 ^ _543626) ^ [] : [_890344 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), c_Groups_Oabs__class_Oabs(tc_Int_Oint, _890342)), _890344)))], (9813 ^ _543626) ^ [_890069, _890071] : [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, _890069)), _890071)), _890069 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_890071 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9831 ^ _543626) ^ [_890665, _890667, _890669] : [class_Rings_Oring__1__no__zero__divisors(_890665), -(_890667 = c_Groups_Ozero__class_Ozero(_890665)), hAPP(hAPP(c_Power_Opower__class_Opower(_890665), _890667), _890669) = c_Groups_Ozero__class_Ozero(_890665)], (9841 ^ _543626) ^ [_891014, _891016, _891018] : [class_Groups_Omonoid__mult(_891014), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_891014), hAPP(hAPP(c_Power_Opower__class_Opower(_891014), _891016), _891018)), _891016) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_891014), _891016), hAPP(hAPP(c_Power_Opower__class_Opower(_891014), _891016), _891018)))], (9847 ^ _543626) ^ [_891320, _891322, _891324, _891326] : [class_Groups_Ocomm__monoid__mult(_891320), -(hAPP(hAPP(c_Power_Opower__class_Opower(_891320), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_891320), _891322), _891324)), _891326) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_891320), hAPP(hAPP(c_Power_Opower__class_Opower(_891320), _891322), _891326)), hAPP(hAPP(c_Power_Opower__class_Opower(_891320), _891324), _891326)))], (9853 ^ _543626) ^ [_891620, _891622] : [class_Groups_Omonoid__mult(_891620), -(hAPP(hAPP(c_Power_Opower__class_Opower(_891620), c_Groups_Oone__class_Oone(_891620)), _891622) = c_Groups_Oone__class_Oone(_891620))], (9859 ^ _543626) ^ [_891866, _891868, _891870] : [class_Rings_Olinordered__idom(_891866), -(c_Groups_Oabs__class_Oabs(_891866, hAPP(hAPP(c_Power_Opower__class_Opower(_891866), _891868), _891870)) = hAPP(hAPP(c_Power_Opower__class_Opower(_891866), c_Groups_Oabs__class_Oabs(_891866, _891868)), _891870))], (9865 ^ _543626) ^ [_892138, _892140, _892142] : [class_Rings_Osemiring__1(_892138), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_892138), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _892140), _892142)) = hAPP(hAPP(c_Power_Opower__class_Opower(_892138), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_892138), _892140)), _892142))], (9871 ^ _543626) ^ [_892428, _892430, _892432, _892434] : [class_Groups_Omonoid__mult(_892428), -(hAPP(hAPP(c_Power_Opower__class_Opower(_892428), _892430), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _892432), _892434)) = hAPP(hAPP(c_Power_Opower__class_Opower(_892428), hAPP(hAPP(c_Power_Opower__class_Opower(_892428), _892430), _892432)), _892434))], (9877 ^ _543626) ^ [_892708, _892710] : [class_Groups_Omonoid__mult(_892708), -(hAPP(hAPP(c_Power_Opower__class_Opower(_892708), _892710), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _892710)], (9883 ^ _543626) ^ [_892946, _892948, _892950] : [class_Rings_Olinordered__semidom(_892946), c_Orderings_Oord__class_Oless__eq(_892946, c_Groups_Ozero__class_Ozero(_892946), _892948), -(c_Orderings_Oord__class_Oless__eq(_892946, c_Groups_Ozero__class_Ozero(_892946), hAPP(hAPP(c_Power_Opower__class_Opower(_892946), _892948), _892950)))], (9893 ^ _543626) ^ [_893309, _893311, _893313, _893315] : [class_Rings_Olinordered__semidom(_893309), c_Orderings_Oord__class_Oless__eq(_893309, _893311, _893313), c_Orderings_Oord__class_Oless__eq(_893309, c_Groups_Ozero__class_Ozero(_893309), _893311), -(c_Orderings_Oord__class_Oless__eq(_893309, hAPP(hAPP(c_Power_Opower__class_Opower(_893309), _893311), _893315), hAPP(hAPP(c_Power_Opower__class_Opower(_893309), _893313), _893315)))], (9907 ^ _543626) ^ [_893779, _893781, _893783] : [class_Rings_Olinordered__semidom(_893779), c_Orderings_Oord__class_Oless(_893779, c_Groups_Ozero__class_Ozero(_893779), _893781), -(c_Orderings_Oord__class_Oless(_893779, c_Groups_Ozero__class_Ozero(_893779), hAPP(hAPP(c_Power_Opower__class_Opower(_893779), _893781), _893783)))], (9917 ^ _543626) ^ [_894128, _894130, _894132] : [class_Rings_Olinordered__semidom(_894128), c_Orderings_Oord__class_Oless__eq(_894128, c_Groups_Oone__class_Oone(_894128), _894130), -(c_Orderings_Oord__class_Oless__eq(_894128, c_Groups_Oone__class_Oone(_894128), hAPP(hAPP(c_Power_Opower__class_Opower(_894128), _894130), _894132)))], (9927 ^ _543626) ^ [_894491, _894493, _894495, _894497] : [class_Rings_Olinordered__semidom(_894491), c_Orderings_Oord__class_Oless(_894491, c_Groups_Oone__class_Oone(_894491), _894493), 9934 ^ _543626 : [(9935 ^ _543626) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_894491), _894493), _894495) = hAPP(hAPP(c_Power_Opower__class_Opower(_894491), _894493), _894497), -(_894495 = _894497)], (9941 ^ _543626) ^ [] : [_894495 = _894497, -(hAPP(hAPP(c_Power_Opower__class_Opower(_894491), _894493), _894495) = hAPP(hAPP(c_Power_Opower__class_Opower(_894491), _894493), _894497))]]], (9947 ^ _543626) ^ [_895146, _895148, _895150] : [class_Power_Opower(_895146), class_Rings_Omult__zero(_895146), class_Rings_Ono__zero__divisors(_895146), class_Rings_Ozero__neq__one(_895146), 9962 ^ _543626 : [(9963 ^ _543626) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_895146), _895148), _895150) = c_Groups_Ozero__class_Ozero(_895146), 9966 ^ _543626 : [(9967 ^ _543626) ^ [] : [-(_895148 = c_Groups_Ozero__class_Ozero(_895146))], (9969 ^ _543626) ^ [] : [_895150 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (9971 ^ _543626) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_895146), _895148), _895150) = c_Groups_Ozero__class_Ozero(_895146)), _895148 = c_Groups_Ozero__class_Ozero(_895146), -(_895150 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (9981 ^ _543626) ^ [_896101, _896103] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_896101), c_Groups_Ozero__class_Ozero(_896101)), c_Nat_OSuc(_896103)) = c_Groups_Ozero__class_Ozero(_896101)), class_Power_Opower(_896101), class_Rings_Osemiring__0(_896101)], (9991 ^ _543626) ^ [_896438, _896440, _896442] : [class_Power_Opower(_896438), -(hAPP(hAPP(c_Power_Opower__class_Opower(_896438), _896440), c_Nat_OSuc(_896442)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_896438), _896440), hAPP(hAPP(c_Power_Opower__class_Opower(_896438), _896440), _896442)))], (9997 ^ _543626) ^ [_896718, _896720, _896722] : [class_Groups_Omonoid__mult(_896718), -(hAPP(hAPP(c_Power_Opower__class_Opower(_896718), _896720), c_Nat_OSuc(_896722)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_896718), hAPP(hAPP(c_Power_Opower__class_Opower(_896718), _896720), _896722)), _896720))], (10003 ^ _543626) ^ [_896984, _896986] : [class_Power_Opower(_896984), -(hAPP(hAPP(c_Power_Opower__class_Opower(_896984), _896986), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_896984))], (10009 ^ _543626) ^ [_897240, _897242, _897244, _897246] : [class_Groups_Omonoid__mult(_897240), -(hAPP(hAPP(c_Power_Opower__class_Opower(_897240), _897242), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _897244, _897246)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_897240), hAPP(hAPP(c_Power_Opower__class_Opower(_897240), _897242), _897244)), hAPP(hAPP(c_Power_Opower__class_Opower(_897240), _897242), _897246)))], (10015 ^ _543626) ^ [_897560, _897562, _897564, _897566] : [class_Rings_Olinordered__semidom(_897560), c_Orderings_Oord__class_Oless(_897560, hAPP(hAPP(c_Power_Opower__class_Opower(_897560), _897562), _897564), hAPP(hAPP(c_Power_Opower__class_Opower(_897560), _897566), _897564)), c_Orderings_Oord__class_Oless__eq(_897560, c_Groups_Ozero__class_Ozero(_897560), _897566), -(c_Orderings_Oord__class_Oless(_897560, _897562, _897566))], (10029 ^ _543626) ^ [_898044, _898046, _898048, _898050] : [class_Rings_Olinordered__semidom(_898044), hAPP(hAPP(c_Power_Opower__class_Opower(_898044), _898046), c_Nat_OSuc(_898048)) = hAPP(hAPP(c_Power_Opower__class_Opower(_898044), _898050), c_Nat_OSuc(_898048)), c_Orderings_Oord__class_Oless__eq(_898044, c_Groups_Ozero__class_Ozero(_898044), _898046), c_Orderings_Oord__class_Oless__eq(_898044, c_Groups_Ozero__class_Ozero(_898044), _898050), -(_898046 = _898050)], (10047 ^ _543626) ^ [_898635, _898637, _898639, _898641] : [class_Rings_Olinordered__semidom(_898635), c_Orderings_Oord__class_Oless__eq(_898635, hAPP(hAPP(c_Power_Opower__class_Opower(_898635), _898637), c_Nat_OSuc(_898639)), hAPP(hAPP(c_Power_Opower__class_Opower(_898635), _898641), c_Nat_OSuc(_898639))), c_Orderings_Oord__class_Oless__eq(_898635, c_Groups_Ozero__class_Ozero(_898635), _898641), -(c_Orderings_Oord__class_Oless__eq(_898635, _898637, _898641))], (10061 ^ _543626) ^ [_899113, _899115, _899117] : [class_Rings_Olinordered__semidom(_899113), c_Orderings_Oord__class_Oless(_899113, c_Groups_Oone__class_Oone(_899113), _899115), -(c_Orderings_Oord__class_Oless(_899113, hAPP(hAPP(c_Power_Opower__class_Opower(_899113), _899115), _899117), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_899113), _899115), hAPP(hAPP(c_Power_Opower__class_Opower(_899113), _899115), _899117))))], (10071 ^ _543626) ^ [_899490, _899492, _899494] : [class_Rings_Olinordered__semidom(_899490), c_Orderings_Oord__class_Oless(_899490, c_Groups_Oone__class_Oone(_899490), _899492), -(c_Orderings_Oord__class_Oless(_899490, c_Groups_Oone__class_Oone(_899490), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_899490), _899492), hAPP(hAPP(c_Power_Opower__class_Opower(_899490), _899492), _899494))))], (10081 ^ _543626) ^ [_899841, _899843] : [class_Power_Opower(_899841), class_Rings_Osemiring__0(_899841), 10088 ^ _543626 : [(10089 ^ _543626) ^ [] : [_899843 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_899841), c_Groups_Ozero__class_Ozero(_899841)), _899843) = c_Groups_Oone__class_Oone(_899841))], (10095 ^ _543626) ^ [] : [-(_899843 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_899841), c_Groups_Ozero__class_Ozero(_899841)), _899843) = c_Groups_Ozero__class_Ozero(_899841))]]], (10101 ^ _543626) ^ [_900456, _900458, _900460] : [class_Rings_Olinordered__idom(_900456), -(c_Orderings_Oord__class_Oless__eq(_900456, c_Groups_Ozero__class_Ozero(_900456), hAPP(hAPP(c_Power_Opower__class_Opower(_900456), c_Groups_Oabs__class_Oabs(_900456, _900458)), _900460)))], (10107 ^ _543626) ^ [_900712, _900714, _900716] : [class_Rings_Olinordered__semidom(_900712), c_Orderings_Oord__class_Oless(_900712, c_Groups_Oone__class_Oone(_900712), _900714), -(c_Orderings_Oord__class_Oless(_900712, c_Groups_Oone__class_Oone(_900712), hAPP(hAPP(c_Power_Opower__class_Opower(_900712), _900714), c_Nat_OSuc(_900716))))], (10117 ^ _543626) ^ [_901079, _901081, _901083, _901085] : [class_Rings_Olinordered__semidom(_901079), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _901081, _901083), c_Orderings_Oord__class_Oless(_901079, c_Groups_Oone__class_Oone(_901079), _901085), -(c_Orderings_Oord__class_Oless(_901079, hAPP(hAPP(c_Power_Opower__class_Opower(_901079), _901085), _901081), hAPP(hAPP(c_Power_Opower__class_Opower(_901079), _901085), _901083)))], (10131 ^ _543626) ^ [_901563, _901565, _901567, _901569] : [class_Rings_Olinordered__semidom(_901563), c_Orderings_Oord__class_Oless(_901563, c_Groups_Oone__class_Oone(_901563), _901565), c_Orderings_Oord__class_Oless(_901563, hAPP(hAPP(c_Power_Opower__class_Opower(_901563), _901565), _901567), hAPP(hAPP(c_Power_Opower__class_Opower(_901563), _901565), _901569)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _901567, _901569))], (10145 ^ _543626) ^ [_902047, _902049, _902051, _902053] : [class_Rings_Olinordered__semidom(_902047), c_Orderings_Oord__class_Oless(_902047, c_Groups_Oone__class_Oone(_902047), _902049), 10152 ^ _543626 : [(10153 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(_902047, hAPP(hAPP(c_Power_Opower__class_Opower(_902047), _902049), _902051), hAPP(hAPP(c_Power_Opower__class_Opower(_902047), _902049), _902053)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _902051, _902053))], (10159 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _902051, _902053), -(c_Orderings_Oord__class_Oless(_902047, hAPP(hAPP(c_Power_Opower__class_Opower(_902047), _902049), _902051), hAPP(hAPP(c_Power_Opower__class_Opower(_902047), _902049), _902053)))]]], (10165 ^ _543626) ^ [_902722, _902724, _902726, _902728] : [class_Rings_Olinordered__semidom(_902722), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _902724, _902726), c_Orderings_Oord__class_Oless__eq(_902722, c_Groups_Oone__class_Oone(_902722), _902728), -(c_Orderings_Oord__class_Oless__eq(_902722, hAPP(hAPP(c_Power_Opower__class_Opower(_902722), _902728), _902724), hAPP(hAPP(c_Power_Opower__class_Opower(_902722), _902728), _902726)))], (10179 ^ _543626) ^ [_903192, _903194, _903196] : [class_Rings_Olinordered__semidom(_903192), c_Orderings_Oord__class_Oless(_903192, c_Groups_Ozero__class_Ozero(_903192), _903194), c_Orderings_Oord__class_Oless(_903192, _903194, c_Groups_Oone__class_Oone(_903192)), -(c_Orderings_Oord__class_Oless(_903192, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_903192), _903194), hAPP(hAPP(c_Power_Opower__class_Opower(_903192), _903194), _903196)), hAPP(hAPP(c_Power_Opower__class_Opower(_903192), _903194), _903196)))], (10193 ^ _543626) ^ [_903668, _903670, _903672] : [class_Rings_Olinordered__semidom(_903668), c_Orderings_Oord__class_Oless(_903668, c_Groups_Ozero__class_Ozero(_903668), _903670), c_Orderings_Oord__class_Oless(_903668, _903670, c_Groups_Oone__class_Oone(_903668)), -(c_Orderings_Oord__class_Oless(_903668, hAPP(hAPP(c_Power_Opower__class_Opower(_903668), _903670), c_Nat_OSuc(_903672)), c_Groups_Oone__class_Oone(_903668)))], (10207 ^ _543626) ^ [_904134, _904136, _904138, _904140] : [class_Rings_Olinordered__semidom(_904134), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _904136, _904138), c_Orderings_Oord__class_Oless(_904134, c_Groups_Ozero__class_Ozero(_904134), _904140), c_Orderings_Oord__class_Oless(_904134, _904140, c_Groups_Oone__class_Oone(_904134)), -(c_Orderings_Oord__class_Oless(_904134, hAPP(hAPP(c_Power_Opower__class_Opower(_904134), _904140), _904138), hAPP(hAPP(c_Power_Opower__class_Opower(_904134), _904140), _904136)))], (10225 ^ _543626) ^ [_904721, _904723, _904725, _904727] : [class_Rings_Olinordered__semidom(_904721), hAPP(hAPP(c_Power_Opower__class_Opower(_904721), _904723), _904725) = hAPP(hAPP(c_Power_Opower__class_Opower(_904721), _904727), _904725), c_Orderings_Oord__class_Oless__eq(_904721, c_Groups_Ozero__class_Ozero(_904721), _904723), c_Orderings_Oord__class_Oless__eq(_904721, c_Groups_Ozero__class_Ozero(_904721), _904727), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _904725), -(_904723 = _904727)], (10247 ^ _543626) ^ [_905403, _905405, _905407, _905409] : [class_Rings_Olinordered__semidom(_905403), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _905405, _905407), c_Orderings_Oord__class_Oless__eq(_905403, c_Groups_Ozero__class_Ozero(_905403), _905409), c_Orderings_Oord__class_Oless__eq(_905403, _905409, c_Groups_Oone__class_Oone(_905403)), -(c_Orderings_Oord__class_Oless__eq(_905403, hAPP(hAPP(c_Power_Opower__class_Opower(_905403), _905409), _905407), hAPP(hAPP(c_Power_Opower__class_Opower(_905403), _905409), _905405)))], (10265 ^ _543626) ^ [_905990, _905992, _905994, _905996] : [class_Rings_Olinordered__semidom(_905990), c_Orderings_Oord__class_Oless(_905990, c_Groups_Oone__class_Oone(_905990), _905992), c_Orderings_Oord__class_Oless__eq(_905990, hAPP(hAPP(c_Power_Opower__class_Opower(_905990), _905992), _905994), hAPP(hAPP(c_Power_Opower__class_Opower(_905990), _905992), _905996)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _905994, _905996))], (10279 ^ _543626) ^ [_906474, _906476, _906478, _906480] : [class_Rings_Olinordered__semidom(_906474), c_Orderings_Oord__class_Oless(_906474, c_Groups_Oone__class_Oone(_906474), _906476), 10286 ^ _543626 : [(10287 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(_906474, hAPP(hAPP(c_Power_Opower__class_Opower(_906474), _906476), _906478), hAPP(hAPP(c_Power_Opower__class_Opower(_906474), _906476), _906480)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _906478, _906480))], (10293 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _906478, _906480), -(c_Orderings_Oord__class_Oless__eq(_906474, hAPP(hAPP(c_Power_Opower__class_Opower(_906474), _906476), _906478), hAPP(hAPP(c_Power_Opower__class_Opower(_906474), _906476), _906480)))]]], (10299 ^ _543626) ^ [_907135, _907137, _907139] : [class_Rings_Olinordered__semidom(_907135), c_Orderings_Oord__class_Oless(_907135, c_Groups_Oone__class_Oone(_907135), _907137), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _907139), -(c_Orderings_Oord__class_Oless(_907135, c_Groups_Oone__class_Oone(_907135), hAPP(hAPP(c_Power_Opower__class_Opower(_907135), _907137), _907139)))], (10313 ^ _543626) ^ [_907593, _907595, _907597, _907599] : [class_Groups_Omonoid__mult(_907593), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _907595, _907597), -(hAPP(hAPP(c_Power_Opower__class_Opower(_907593), _907599), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_907597), _907595)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_907593), hAPP(hAPP(c_Power_Opower__class_Opower(_907593), _907599), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _907597, _907595))), _907599))], (10323 ^ _543626) ^ [_907980, _907982] : [-(_907980 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), -(_907982 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), _907980), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), 10330 ^ [_907980, _907982]), _907982)))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (10334 ^ _543626) ^ [_908388] : [class_Power_Opower(_908388), -(c_Power_Opower__class_Opower(_908388) = c_Power_Opower_Opower(_908388, c_Groups_Oone__class_Oone(_908388), c_Groups_Otimes__class_Otimes(_908388)))], (10340 ^ _543626) ^ [_908623, _908625, _908627, _908629] : [-(hAPP(hAPP(c_Power_Opower_Opower(_908623, _908625, _908627), _908629), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _908625)], (10342 ^ _543626) ^ [_908773, _908775, _908777, _908779, _908781] : [-(hAPP(hAPP(c_Power_Opower_Opower(_908773, _908775, _908777), _908779), c_Nat_OSuc(_908781)) = hAPP(hAPP(_908777, _908779), hAPP(hAPP(c_Power_Opower_Opower(_908773, _908775, _908777), _908779), _908781)))], (10344 ^ _543626) ^ [_908916, _908918] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _908916), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _908918), 10352 ^ _543626 : [(10353 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(c_RealDef_Oreal(tc_Nat_Onat), 10351 ^ [_908916, _908918])), _908916), _908918))], (10355 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _908918, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Nat_OSuc(10351 ^ [_908916, _908918]))), _908916)))]]], (10357 ^ _543626) ^ [_909430, _909432] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _909430), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _909432), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _909432), _909430), _909432) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _909432), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _909430, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (10367 ^ _543626) ^ [_909787, _909789, _909791] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _909787, _909789), c_Orderings_Oord__class_Oless(tc_Int_Oint, _909791, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _909789, _909791), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _909787, _909791)))], (10377 ^ _543626) ^ [_910132, _910134, _910136] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _910132, _910134), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _910136), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _910132, _910136), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _910134, _910136)))], (10387 ^ _543626) ^ [_910463, _910465] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _910463, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _910465, _910463), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _910463, _910465) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (10397 ^ _543626) ^ [_910788, _910790, _910792] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _910788, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _910790), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _910790, _910792), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _910788, _910790), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _910788, _910792)))], (10411 ^ _543626) ^ [_911214, _911216] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _911214, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _911216), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _911214, _911216), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (10421 ^ _543626) ^ [_911527, _911529] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _911527, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 10424 ^ _543626 : [(10425 ^ _543626) ^ [] : [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, _911529, _911527)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _911529, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (10431 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _911529, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _911529, _911527)))]]], (10437 ^ _543626) ^ [_912007, _912009] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _912007), c_Orderings_Oord__class_Oless(tc_Int_Oint, _912007, _912009), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _912007, _912009) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (10447 ^ _543626) ^ [_912318, _912320] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _912318), c_Orderings_Oord__class_Oless(tc_Int_Oint, _912320, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _912318, _912320), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (10457 ^ _543626) ^ [_912645, _912647, _912649] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _912645), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _912647), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _912647, _912649), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _912645, _912649), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _912645, _912647)))], (10471 ^ _543626) ^ [_913071, _913073] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _913071), 10474 ^ _543626 : [(10475 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _913071, _913073)), 10478 ^ _543626 : [(10479 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _913073, _913071))], (10481 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _913073))]]], (10483 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _913071, _913073))), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _913073, _913071), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _913073)]]], (10493 ^ _543626) ^ [_913712, _913714] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _913712), 10496 ^ _543626 : [(10497 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _913714, _913712)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _913712, _913714))], (10503 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _913712, _913714), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _913714, _913712)))]]], (10509 ^ _543626) ^ [_914192, _914194] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _914192), 10512 ^ _543626 : [(10513 ^ _543626) ^ [] : [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, _914194, _914192)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _914194))], (10519 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _914194), -(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, _914194, _914192)))]]], (10525 ^ _543626) ^ [_914701, _914703] : [c_Divides_Odiv__class_Odiv(tc_Int_Oint, _914701, _914703) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_914703 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 10534 ^ _543626 : [(10535 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _914701))], (10537 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _914701, _914703))]], 10538 ^ _543626 : [(10539 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _914701, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (10541 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _914703, _914701))]]], (10543 ^ _543626) ^ [_915209, _915211] : [-(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _915209, _915211) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 10544 ^ _543626 : [(10545 ^ _543626) ^ [] : [_915211 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (10547 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _915209), c_Orderings_Oord__class_Oless(tc_Int_Oint, _915209, _915211)], (10553 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _915209, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _915211, _915209)]]], (10561 ^ _543626) ^ [_915762, _915764] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _915762), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _915764), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _915762, _915764), _915762))], (10571 ^ _543626) ^ [_916089, _916091, _916093] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _916089), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _916091, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _916093), _916089)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _916091, _916093), _916089))], (10577 ^ _543626) ^ [_916371, _916373, _916375, _916377] : [class_Divides_Osemiring__div(_916371), -(_916373 = c_Groups_Ozero__class_Ozero(_916371)), -(c_Divides_Odiv__class_Odiv(_916371, c_Groups_Oplus__class_Oplus(_916371, _916375, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_916371), _916377), _916373)), _916373) = c_Groups_Oplus__class_Oplus(_916371, _916377, c_Divides_Odiv__class_Odiv(_916371, _916375, _916373)))], (10587 ^ _543626) ^ [_916771, _916773, _916775, _916777] : [class_Divides_Osemiring__div(_916771), -(_916773 = c_Groups_Ozero__class_Ozero(_916771)), -(c_Divides_Odiv__class_Odiv(_916771, c_Groups_Oplus__class_Oplus(_916771, _916775, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_916771), _916773), _916777)), _916773) = c_Groups_Oplus__class_Oplus(_916771, _916777, c_Divides_Odiv__class_Odiv(_916771, _916775, _916773)))], (10597 ^ _543626) ^ [_917157, _917159, _917161] : [class_Divides_Osemiring__div(_917157), -(_917159 = c_Groups_Ozero__class_Ozero(_917157)), -(c_Divides_Odiv__class_Odiv(_917157, c_Groups_Oplus__class_Oplus(_917157, _917161, _917159), _917159) = c_Groups_Oplus__class_Oplus(_917157, c_Divides_Odiv__class_Odiv(_917157, _917161, _917159), c_Groups_Oone__class_Oone(_917157)))], (10607 ^ _543626) ^ [_917521, _917523, _917525] : [class_Divides_Osemiring__div(_917521), -(_917523 = c_Groups_Ozero__class_Ozero(_917521)), -(c_Divides_Odiv__class_Odiv(_917521, c_Groups_Oplus__class_Oplus(_917521, _917523, _917525), _917523) = c_Groups_Oplus__class_Oplus(_917521, c_Divides_Odiv__class_Odiv(_917521, _917525, _917523), c_Groups_Oone__class_Oone(_917521)))], (10617 ^ _543626) ^ [_917899, _917901, _917903, _917905] : [class_Divides_Osemiring__div(_917899), -(_917901 = c_Groups_Ozero__class_Ozero(_917899)), -(c_Divides_Odiv__class_Odiv(_917899, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_917899), _917901), _917903), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_917899), _917901), _917905)) = c_Divides_Odiv__class_Odiv(_917899, _917903, _917905))], (10627 ^ _543626) ^ [_918299, _918301, _918303, _918305] : [class_Divides_Osemiring__div(_918299), -(_918301 = c_Groups_Ozero__class_Ozero(_918299)), -(c_Divides_Odiv__class_Odiv(_918299, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_918299), _918303), _918301), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_918299), _918305), _918301)) = c_Divides_Odiv__class_Odiv(_918299, _918303, _918305))], (10637 ^ _543626) ^ [_918685, _918687, _918689] : [class_Divides_Osemiring__div(_918685), -(_918687 = c_Groups_Ozero__class_Ozero(_918685)), -(c_Divides_Odiv__class_Odiv(_918685, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_918685), _918687), _918689), _918687) = _918689)], (10647 ^ _543626) ^ [_919037, _919039, _919041] : [class_Divides_Osemiring__div(_919037), -(_919039 = c_Groups_Ozero__class_Ozero(_919037)), -(c_Divides_Odiv__class_Odiv(_919037, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_919037), _919041), _919039), _919039) = _919041)], (10657 ^ _543626) ^ [_919403, _919405, _919407, _919409] : [class_Divides_Osemiring__div(_919403), 10660 ^ _543626 : [(10661 ^ _543626) ^ [] : [_919405 = c_Groups_Ozero__class_Ozero(_919403), -(c_Divides_Odiv__class_Odiv(_919403, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_919403), _919405), _919407), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_919403), _919405), _919409)) = c_Groups_Ozero__class_Ozero(_919403))], (10667 ^ _543626) ^ [] : [-(_919405 = c_Groups_Ozero__class_Ozero(_919403)), -(c_Divides_Odiv__class_Odiv(_919403, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_919403), _919405), _919407), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_919403), _919405), _919409)) = c_Divides_Odiv__class_Odiv(_919403, _919407, _919409))]]], (10673 ^ _543626) ^ [_919985] : [-(_919985 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _919985, _919985) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (10679 ^ _543626) ^ [_920200, _920202] : [class_Divides_Osemiring__div(_920200), -(_920202 = c_Groups_Ozero__class_Ozero(_920200)), -(c_Divides_Odiv__class_Odiv(_920200, _920202, _920202) = c_Groups_Oone__class_Oone(_920200))], (10689 ^ _543626) ^ [_920487] : [-(c_Divides_Odiv__class_Odiv(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _920487) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (10691 ^ _543626) ^ [_920598, _920600] : [class_Divides_Osemiring__div(_920598), -(c_Divides_Odiv__class_Odiv(_920598, c_Groups_Ozero__class_Ozero(_920598), _920600) = c_Groups_Ozero__class_Ozero(_920598))], (10697 ^ _543626) ^ [_920822, _920824] : [class_Divides_Osemiring__div(_920822), -(c_Divides_Odiv__class_Odiv(_920822, _920824, c_Groups_Ozero__class_Ozero(_920822)) = c_Groups_Ozero__class_Ozero(_920822))], (10703 ^ _543626) ^ [_921046, _921048] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _921046), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _921048), -(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, _921046, _921048)))], (10713 ^ _543626) ^ [_921359, _921361] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _921359), 10716 ^ _543626 : [(10717 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _921361, _921359), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _921361, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (10723 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _921361, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _921361, _921359), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (10729 ^ _543626) ^ [_921839, _921841] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _921839, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 10732 ^ _543626 : [(10733 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _921841, _921839), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _921841))], (10739 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _921841), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _921841, _921839), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (10745 ^ _543626) ^ [_922319, _922321] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _922319, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _922321), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _922319, _922321), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (10755 ^ _543626) ^ [_922632, _922634] : [class_Divides_Osemiring__div(_922632), -(c_Divides_Odiv__class_Odiv(_922632, _922634, c_Groups_Oone__class_Oone(_922632)) = _922634)], (10761 ^ _543626) ^ [_922880, _922882, _922884, _922886] : [_922880 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _922882), _922884), _922886), -(_922882 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _922880, _922882) = _922884), 10768 ^ _543626 : [(10769 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _922882))], (10771 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _922886), c_Orderings_Oord__class_Oless(tc_Int_Oint, _922886, _922882)]], 10776 ^ _543626 : [(10777 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _922882)], (10779 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _922882, _922886), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _922886, c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (10837 ^ _543626) ^ [_925454, _925456, _925458] : [-(hBOOL(hAPP(_925454, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _925456, _925458)))), 10840 ^ _543626 : [(10841 ^ _543626) ^ [] : [-(_925458 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (10843 ^ _543626) ^ [] : [hBOOL(hAPP(_925454, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], 10846 ^ _543626 : [(10847 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _925458))], (10851 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), 10849 ^ [_925454, _925456, _925458]))], (10853 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, 10849 ^ [_925454, _925456, _925458], _925458))], (10855 ^ _543626) ^ [] : [-(_925456 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _925458), 10848 ^ [_925454, _925456, _925458]), 10849 ^ [_925454, _925456, _925458]))], (10857 ^ _543626) ^ [] : [hBOOL(hAPP(_925454, 10848 ^ [_925454, _925456, _925458]))]], 10858 ^ _543626 : [(10859 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _925458, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (10863 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _925458, 10861 ^ [_925454, _925456, _925458]))], (10865 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, 10861 ^ [_925454, _925456, _925458], c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (10867 ^ _543626) ^ [] : [-(_925456 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _925458), 10860 ^ [_925454, _925456, _925458]), 10861 ^ [_925454, _925456, _925458]))], (10869 ^ _543626) ^ [] : [hBOOL(hAPP(_925454, 10860 ^ [_925454, _925456, _925458]))]]], (10791 ^ _543626) ^ [_923834, _923836, _923838] : [hBOOL(hAPP(_923834, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _923836, _923838))), 10794 ^ _543626 : [(10795 ^ _543626) ^ [] : [_923838 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_923834, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (10801 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _923838), 10804 ^ _543626 : [(10805 ^ _543626) ^ [_924355] : [-(hBOOL(hAPP(_923834, _924355))), 10806 ^ _543626 : [(10807 ^ _543626) ^ [_924477] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _924477), c_Orderings_Oord__class_Oless(tc_Int_Oint, _924477, _923838), _923836 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _923838), _924355), _924477)]]]]], (10819 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _923838, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 10822 ^ _543626 : [(10823 ^ _543626) ^ [_924949] : [-(hBOOL(hAPP(_923834, _924949))), 10824 ^ _543626 : [(10825 ^ _543626) ^ [_925071] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _923838, _925071), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _925071, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _923836 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _923838), _924949), _925071)]]]]]]], (10873 ^ _543626) ^ [_927074, _927076, _927078] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Complex_Orcis(_927074, _927076)), _927078) = c_Complex_Orcis(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _927074), _927078), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(c_RealDef_Oreal(tc_Nat_Onat), _927078)), _927076)))], (10875 ^ _543626) ^ [_927212, _927214] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _927212), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _927214), 10883 ^ _543626 : [(10884 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 10882 ^ [_927212, _927214]))], (10886 ^ _543626) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), 10882 ^ [_927212, _927214]), _927212) = _927214)], (10888 ^ _543626) ^ [_927716] : [-(_927716 = 10882 ^ [_927212, _927214]), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _927716), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _927716), _927212) = _927214]]], (10898 ^ _543626) ^ [_928104, _928106, _928108] : [_928104 = 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), _928104), _928106), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _928104), _928108)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10904 ^ _543626) ^ [_928304, _928306, _928308] : [-(_928304 = 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), _928304), _928306), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _928304), _928308)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _928306, _928308))], (10910 ^ _543626) ^ [_928564, _928566, _928568] : [-(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _928564, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _928566), _928568)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _928564, _928566), _928568))], (10912 ^ _543626) ^ [_928693, _928695] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _928693, _928695), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _928693, _928695) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10918 ^ _543626) ^ [_928884] : [-(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _928884, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = _928884)], (10920 ^ _543626) ^ [_928980, _928982] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _928980, _928982), _928980))], (10922 ^ _543626) ^ [_929108, _929110, _929112] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _929108, _929110), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _929108, _929112), c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _929110, _929112)))], (10928 ^ _543626) ^ [_929329, _929331] : [-(c_Divides_Odiv__class_Odiv(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _929329), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _929331)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _929329, _929331)))], (10930 ^ _543626) ^ [_929440, _929442] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _929440, _929442)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _929440), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _929442)))], (10932 ^ _543626) ^ [_929566, _929568] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _929566), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _929568), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _929568, _929566), _929568))], (10942 ^ _543626) ^ [_929893, _929895, _929897] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _929893), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _929893), _929895), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _929893), _929897)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _929895, _929897))], (10948 ^ _543626) ^ [_930151, _930153] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _930151), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _930153), _930151), _930151) = _930153)], (10954 ^ _543626) ^ [_930383, _930385] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _930383), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _930383), _930385), _930383) = _930385)], (10960 ^ _543626) ^ [_930629, _930631, _930633] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _930629), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _930629, _930631), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _930633, _930631), c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _930633, _930629)))], (10970 ^ _543626) ^ [_930945, _930947] : [-(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Complex_Orcis(_930945, _930947)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _930945))], (10972 ^ _543626) ^ [_931034] : [-(c_Complex_Orcis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _931034) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))], (10974 ^ _543626) ^ [_931115] : [-(c_Complex_Ocis(_931115) = c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _931115))], (10976 ^ _543626) ^ [_931227, _931229] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _931227), 10979 ^ _543626 : [(10980 ^ _543626) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _931229, _931227), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _931229, _931227) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10986 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _931229, _931227)), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _931229, _931227) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _931229, _931227), _931227)))]]], (10992 ^ _543626) ^ [_931735, _931737] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _931735), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _931737, _931735)), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _931737, _931735) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _931737, _931735), _931735)))], (11026 ^ _543626) ^ [_932891, _932893, _932895] : [-(hBOOL(hAPP(_932891, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _932893, _932895)))), 11029 ^ _543626 : [(11030 ^ _543626) ^ [] : [-(_932895 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11032 ^ _543626) ^ [] : [hBOOL(hAPP(_932891, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 11033 ^ _543626 : [(11034 ^ _543626) ^ [] : [_932895 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (11038 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, 11036 ^ [_932891, _932893, _932895], _932895))], (11040 ^ _543626) ^ [] : [-(_932893 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _932895), 11035 ^ [_932891, _932893, _932895]), 11036 ^ [_932891, _932893, _932895]))], (11042 ^ _543626) ^ [] : [hBOOL(hAPP(_932891, 11035 ^ [_932891, _932893, _932895]))]]], (11002 ^ _543626) ^ [_932112, _932114, _932116] : [hBOOL(hAPP(_932112, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _932114, _932116))), 11005 ^ _543626 : [(11006 ^ _543626) ^ [] : [_932116 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_932112, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (11012 ^ _543626) ^ [] : [-(_932116 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 11015 ^ _543626 : [(11016 ^ _543626) ^ [_932566, _932568] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _932566, _932116), _932114 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _932116), _932568), _932566), -(hBOOL(hAPP(_932112, _932568)))]]]]], (11046 ^ _543626) ^ [_933782, _933784, _933786] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _933782), 11049 ^ _543626 : [(11060 ^ _543626) ^ [] : [_933784 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _933786, _933782), 11063 ^ _543626 : [(11064 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _933782), _933784), _933786))], (11066 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _933786, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _933782), c_Nat_OSuc(_933784))))]]], (11050 ^ _543626) ^ [] : [-(_933784 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _933786, _933782)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _933782), _933784), _933786), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _933786, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _933782), c_Nat_OSuc(_933784)))]]], (11068 ^ _543626) ^ [_934527, _934529, _934531] : [hBOOL(hAPP(_934527, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _934529, _934531))), 11073 ^ _543626 : [(11074 ^ _543626) ^ [] : [-(_934531 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11076 ^ _543626) ^ [] : [-(hBOOL(hAPP(_934527, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]], 11078 ^ _543626 : [(11079 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _934531), 11077 ^ [_934527, _934529, _934531]), _934529))], (11081 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _934529, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _934531), c_Nat_OSuc(11077 ^ [_934527, _934529, _934531]))))], (11083 ^ _543626) ^ [] : [-(hBOOL(hAPP(_934527, 11077 ^ [_934527, _934529, _934531])))]]], (11085 ^ _543626) ^ [_935182, _935184, _935186] : [-(hBOOL(hAPP(_935182, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _935184, _935186)))), 11086 ^ _543626 : [(11087 ^ _543626) ^ [] : [_935186 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hBOOL(hAPP(_935182, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (11093 ^ _543626) ^ [_935476] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _935186), _935476), _935184), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _935184, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _935186), c_Nat_OSuc(_935476))), hBOOL(hAPP(_935182, _935476))]]], (11105 ^ _543626) ^ [_935899, _935901] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _935899), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _935899, _935901), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _935901, _935899) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _935901, _935899), _935899)))], (11115 ^ _543626) ^ [_936243, _936245, _936247, _936249] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Complex_Orcis(_936243, _936245)), c_Complex_Orcis(_936247, _936249)) = c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _936243), _936247), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _936245, _936249)))], (11117 ^ _543626) ^ [_936381, _936383] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _936381), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _936383), 11125 ^ _543626 : [(11126 ^ _543626) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 11124 ^ [_936381, _936383]))], (11128 ^ _543626) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), 11124 ^ [_936381, _936383]), _936381) = _936383)]]], (11130 ^ _543626) ^ [_936850, _936852] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _936850), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _936852), -(c_RComplete_Onatfloor(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, _936850, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _936852))) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, c_RComplete_Onatfloor(_936850), _936852))], (11140 ^ _543626) ^ [_937168, _937170] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _937168, _937170)), c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _937168), hAPP(c_RealDef_Oreal(tc_Nat_Onat), _937170))))], (11142 ^ _543626) ^ [_937323, _937325, _937327, _937329] : [class_Fields_Ofield(_937323), -(_937325 = c_Groups_Ozero__class_Ozero(_937323)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_937323), c_Rings_Oinverse__class_Odivide(_937323, _937327, _937325)), _937329) = c_Rings_Oinverse__class_Odivide(_937323, hAPP(hAPP(c_Power_Opower__class_Opower(_937323), _937327), _937329), hAPP(hAPP(c_Power_Opower__class_Opower(_937323), _937325), _937329)))], (11152 ^ _543626) ^ [_937697] : [class_Rings_Oidom(_937697), -(class_Rings_Oidom(tc_Polynomial_Opoly(_937697)))], (11158 ^ _543626) ^ [_937887] : [class_Groups_Ocancel__comm__monoid__add(_937887), -(class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(_937887)))], (11164 ^ _543626) ^ [_938077] : [class_Rings_Ocomm__semiring__0(_938077), -(class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(_938077)))], (11170 ^ _543626) ^ [_938267] : [class_Rings_Ocomm__ring(_938267), -(class_Rings_Ocomm__ring(tc_Polynomial_Opoly(_938267)))], (11176 ^ _543626) ^ [] : [-(class_Rings_Oidom(tc_Complex_Ocomplex))], (11178 ^ _543626) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex))], (11180 ^ _543626) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex))], (11182 ^ _543626) ^ [] : [-(class_Rings_Ocomm__ring(tc_Complex_Ocomplex))], (11184 ^ _543626) ^ [] : [-(class_Rings_Oidom(tc_RealDef_Oreal))], (11186 ^ _543626) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal))], (11188 ^ _543626) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal))], (11190 ^ _543626) ^ [] : [-(class_Rings_Ocomm__ring(tc_RealDef_Oreal))], (11192 ^ _543626) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat))], (11194 ^ _543626) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Nat_Onat))], (11196 ^ _543626) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (11198 ^ _543626) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint))], (11200 ^ _543626) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Int_Oint))], (11202 ^ _543626) ^ [] : [-(class_Rings_Ocomm__ring(tc_Int_Oint))], (11204 ^ _543626) ^ [_939213, _939215] : [class_Orderings_Opreorder(_939213), -(class_Orderings_Opreorder(tc_fun(_939215, _939213)))], (11210 ^ _543626) ^ [_939425, _939427] : [class_Orderings_Oorder(_939425), -(class_Orderings_Oorder(tc_fun(_939427, _939425)))], (11216 ^ _543626) ^ [_939637, _939639] : [class_Orderings_Oord(_939637), -(class_Orderings_Oord(tc_fun(_939639, _939637)))], (11222 ^ _543626) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (11224 ^ _543626) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (11226 ^ _543626) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (11228 ^ _543626) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (11230 ^ _543626) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (11232 ^ _543626) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (11234 ^ _543626) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (11236 ^ _543626) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))], (11238 ^ _543626) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (11240 ^ _543626) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (11242 ^ _543626) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (11244 ^ _543626) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (11246 ^ _543626) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (11248 ^ _543626) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (11250 ^ _543626) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (11252 ^ _543626) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (11254 ^ _543626) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (11256 ^ _543626) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (11258 ^ _543626) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (11260 ^ _543626) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (11262 ^ _543626) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (11264 ^ _543626) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (11266 ^ _543626) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (11268 ^ _543626) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (11270 ^ _543626) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (11272 ^ _543626) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_Int_Oint))], (11274 ^ _543626) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (11276 ^ _543626) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (11278 ^ _543626) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (11280 ^ _543626) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (11282 ^ _543626) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (11284 ^ _543626) ^ [] : [-(class_Divides_Osemiring__div(tc_Int_Oint))], (11286 ^ _543626) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (11288 ^ _543626) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Int_Oint))], (11290 ^ _543626) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (11292 ^ _543626) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (11294 ^ _543626) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (11296 ^ _543626) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (11298 ^ _543626) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (11300 ^ _543626) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (11302 ^ _543626) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (11304 ^ _543626) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (11306 ^ _543626) ^ [] : [-(class_Rings_Osemiring__1(tc_Int_Oint))], (11308 ^ _543626) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (11310 ^ _543626) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (11312 ^ _543626) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (11314 ^ _543626) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (11316 ^ _543626) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (11318 ^ _543626) ^ [] : [-(class_Int_Onumber__ring(tc_Int_Oint))], (11320 ^ _543626) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (11322 ^ _543626) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (11324 ^ _543626) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (11326 ^ _543626) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (11328 ^ _543626) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (11330 ^ _543626) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (11332 ^ _543626) ^ [] : [-(class_Int_Onumber(tc_Int_Oint))], (11334 ^ _543626) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (11336 ^ _543626) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (11338 ^ _543626) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (11340 ^ _543626) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (11342 ^ _543626) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (11344 ^ _543626) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (11346 ^ _543626) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (11348 ^ _543626) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (11350 ^ _543626) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (11352 ^ _543626) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (11354 ^ _543626) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (11356 ^ _543626) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (11358 ^ _543626) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (11360 ^ _543626) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (11362 ^ _543626) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (11364 ^ _543626) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (11366 ^ _543626) ^ [] : 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^ _543626) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (11396 ^ _543626) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (11398 ^ _543626) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (11400 ^ _543626) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (11402 ^ _543626) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (11404 ^ _543626) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (11406 ^ _543626) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (11408 ^ _543626) ^ [] : [-(class_Int_Onumber(tc_Nat_Onat))], (11410 ^ _543626) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (11412 ^ _543626) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (11414 ^ _543626) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (11416 ^ _543626) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (11418 ^ _543626) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal))], (11420 ^ _543626) ^ [] : 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[-(class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal))], (11464 ^ _543626) ^ [] : [-(class_Rings_Olinordered__semiring(tc_RealDef_Oreal))], (11466 ^ _543626) ^ [] : [-(class_Rings_Olinordered__semidom(tc_RealDef_Oreal))], (11468 ^ _543626) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal))], (11470 ^ _543626) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal))], (11472 ^ _543626) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_RealDef_Oreal))], (11474 ^ _543626) ^ [] : [-(class_Rings_Oordered__semiring(tc_RealDef_Oreal))], (11476 ^ _543626) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_RealDef_Oreal))], (11478 ^ _543626) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_RealDef_Oreal))], (11480 ^ _543626) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal))], (11482 ^ _543626) ^ [] : [-(class_Rings_Olinordered__ring(tc_RealDef_Oreal))], (11484 ^ _543626) ^ [] : [-(class_Rings_Olinordered__idom(tc_RealDef_Oreal))], (11486 ^ _543626) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal))], (11488 ^ _543626) ^ [] : [-(class_Rings_Ocomm__semiring(tc_RealDef_Oreal))], (11490 ^ _543626) ^ [] : [-(class_Nat_Osemiring__char__0(tc_RealDef_Oreal))], (11492 ^ _543626) ^ [] : [-(class_Groups_Oab__group__add(tc_RealDef_Oreal))], (11494 ^ _543626) ^ [] : [-(class_Rings_Ozero__neq__one(tc_RealDef_Oreal))], (11496 ^ _543626) ^ [] : [-(class_Rings_Oordered__ring(tc_RealDef_Oreal))], (11498 ^ _543626) ^ [] : [-(class_Orderings_Opreorder(tc_RealDef_Oreal))], (11500 ^ _543626) ^ [] : [-(class_Orderings_Olinorder(tc_RealDef_Oreal))], (11502 ^ _543626) ^ [] : [-(class_Groups_Omonoid__mult(tc_RealDef_Oreal))], (11504 ^ _543626) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_RealDef_Oreal))], (11506 ^ _543626) ^ [] : [-(class_Groups_Omonoid__add(tc_RealDef_Oreal))], (11508 ^ _543626) ^ [] : [-(class_Rings_Osemiring__1(tc_RealDef_Oreal))], (11510 ^ _543626) ^ [] : [-(class_Rings_Osemiring__0(tc_RealDef_Oreal))], (11512 ^ _543626) ^ [] : [-(class_Groups_Ogroup__add(tc_RealDef_Oreal))], (11514 ^ _543626) ^ [] : [-(class_Rings_Omult__zero(tc_RealDef_Oreal))], (11516 ^ _543626) ^ [] : [-(class_Orderings_Oorder(tc_RealDef_Oreal))], (11518 ^ _543626) ^ [] : [-(class_Int_Oring__char__0(tc_RealDef_Oreal))], (11520 ^ _543626) ^ [] : [-(class_Int_Onumber__ring(tc_RealDef_Oreal))], (11522 ^ _543626) ^ [] : [-(class_Rings_Osemiring(tc_RealDef_Oreal))], (11524 ^ _543626) ^ [] : [-(class_Orderings_Oord(tc_RealDef_Oreal))], (11526 ^ _543626) ^ [] : [-(class_Rings_Oring__1(tc_RealDef_Oreal))], (11528 ^ _543626) ^ [] : [-(class_Fields_Ofield(tc_RealDef_Oreal))], (11530 ^ _543626) ^ [] : [-(class_Power_Opower(tc_RealDef_Oreal))], (11532 ^ _543626) ^ [] : [-(class_Groups_Ozero(tc_RealDef_Oreal))], (11534 ^ _543626) ^ [] : [-(class_Rings_Oring(tc_RealDef_Oreal))], (11536 ^ _543626) ^ [] : [-(class_Int_Onumber(tc_RealDef_Oreal))], (11538 ^ _543626) ^ [] : [-(class_Groups_Oone(tc_RealDef_Oreal))], (11540 ^ _543626) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex))], (11542 ^ _543626) ^ [] : [-(class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex))], (11544 ^ _543626) ^ [] : [-(class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex))], (11546 ^ _543626) ^ [] : [-(class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex))], (11548 ^ _543626) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex))], (11550 ^ _543626) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex))], (11552 ^ _543626) ^ [] : [-(class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex))], (11554 ^ _543626) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex))], (11556 ^ _543626) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex))], (11558 ^ _543626) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex))], (11560 ^ _543626) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex))], (11562 ^ _543626) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex))], (11564 ^ _543626) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex))], (11566 ^ _543626) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex))], (11568 ^ _543626) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex))], (11570 ^ _543626) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Complex_Ocomplex))], (11572 ^ _543626) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Complex_Ocomplex))], (11574 ^ _543626) ^ [] : [-(class_Groups_Oab__group__add(tc_Complex_Ocomplex))], (11576 ^ _543626) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Complex_Ocomplex))], (11578 ^ _543626) ^ [] : [-(class_Groups_Omonoid__mult(tc_Complex_Ocomplex))], (11580 ^ _543626) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex))], (11582 ^ _543626) ^ [] : [-(class_Groups_Omonoid__add(tc_Complex_Ocomplex))], (11584 ^ _543626) ^ [] : [-(class_Rings_Osemiring__1(tc_Complex_Ocomplex))], (11586 ^ _543626) ^ [] : [-(class_Rings_Osemiring__0(tc_Complex_Ocomplex))], (11588 ^ _543626) ^ [] : [-(class_Groups_Ogroup__add(tc_Complex_Ocomplex))], (11590 ^ _543626) ^ [] : [-(class_Rings_Omult__zero(tc_Complex_Ocomplex))], (11592 ^ _543626) ^ [] : [-(class_Int_Oring__char__0(tc_Complex_Ocomplex))], (11594 ^ _543626) ^ [] : [-(class_Int_Onumber__ring(tc_Complex_Ocomplex))], (11596 ^ _543626) ^ [] : [-(class_Rings_Osemiring(tc_Complex_Ocomplex))], (11598 ^ _543626) ^ [] : [-(class_Rings_Oring__1(tc_Complex_Ocomplex))], (11600 ^ _543626) ^ [] : [-(class_Fields_Ofield(tc_Complex_Ocomplex))], (11602 ^ _543626) ^ [] : [-(class_Power_Opower(tc_Complex_Ocomplex))], (11604 ^ _543626) ^ [] : [-(class_Groups_Ozero(tc_Complex_Ocomplex))], (11606 ^ _543626) ^ [] : [-(class_Rings_Oring(tc_Complex_Ocomplex))], (11608 ^ _543626) ^ [] : [-(class_Int_Onumber(tc_Complex_Ocomplex))], (11610 ^ _543626) ^ [] : [-(class_Groups_Oone(tc_Complex_Ocomplex))], (11612 ^ _543626) ^ [_950170] : [class_Rings_Oidom(_950170), -(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(_950170)))], (11618 ^ _543626) ^ [_950360] : [class_Rings_Olinordered__idom(_950360), -(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(_950360)))], (11624 ^ _543626) ^ [_950550] : [class_Rings_Olinordered__idom(_950550), -(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(_950550)))], (11630 ^ _543626) ^ [_950740] : [class_Rings_Olinordered__idom(_950740), -(class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(_950740)))], (11636 ^ _543626) ^ [_950930] : [class_Rings_Olinordered__idom(_950930), -(class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(_950930)))], (11642 ^ _543626) ^ [_951120] : [class_Rings_Olinordered__idom(_951120), -(class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(_951120)))], (11648 ^ _543626) ^ [_951310] : [class_Rings_Olinordered__idom(_951310), -(class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(_951310)))], (11654 ^ _543626) ^ [_951500] : [class_Rings_Olinordered__idom(_951500), -(class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(_951500)))], (11660 ^ _543626) ^ [_951690] : [class_Rings_Olinordered__idom(_951690), -(class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(_951690)))], (11666 ^ _543626) ^ [_951880] : [class_Rings_Olinordered__idom(_951880), -(class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(_951880)))], (11672 ^ _543626) ^ [_952070] : [class_Groups_Ocancel__comm__monoid__add(_952070), -(class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(_952070)))], (11678 ^ _543626) ^ [_952260] : [class_Rings_Oidom(_952260), -(class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(_952260)))], (11684 ^ _543626) ^ [_952450] : [class_Rings_Olinordered__idom(_952450), -(class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(_952450)))], (11690 ^ _543626) ^ [_952640] : [class_Rings_Olinordered__idom(_952640), -(class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(_952640)))], (11696 ^ _543626) ^ [_952830] : [class_Rings_Oidom(_952830), -(class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(_952830)))], (11702 ^ _543626) ^ [_953020] : [class_Rings_Olinordered__idom(_953020), -(class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(_953020)))], (11708 ^ _543626) ^ [_953210] : [class_Rings_Olinordered__idom(_953210), -(class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(_953210)))], (11714 ^ _543626) ^ [_953400] : [class_Rings_Olinordered__idom(_953400), -(class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(_953400)))], (11720 ^ _543626) ^ [_953590] : [class_Groups_Ocancel__comm__monoid__add(_953590), -(class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(_953590)))], (11726 ^ _543626) ^ [_953780] : [class_Rings_Olinordered__idom(_953780), -(class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(_953780)))], (11732 ^ _543626) ^ [_953970] : [class_Rings_Olinordered__idom(_953970), -(class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(_953970)))], (11738 ^ _543626) ^ [_954160] : [class_Rings_Ocomm__semiring__0(_954160), -(class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(_954160)))], (11744 ^ _543626) ^ [_954350] : [class_Rings_Ocomm__semiring__1(_954350), -(class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(_954350)))], (11750 ^ _543626) ^ [_954540] : [class_Groups_Ocomm__monoid__add(_954540), -(class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(_954540)))], (11756 ^ _543626) ^ [_954730] : [class_Rings_Olinordered__idom(_954730), -(class_Rings_Oordered__semiring(tc_Polynomial_Opoly(_954730)))], (11762 ^ _543626) ^ [_954920] : [class_Rings_Olinordered__idom(_954920), -(class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(_954920)))], (11768 ^ _543626) ^ [_955110] : [class_Rings_Oidom(_955110), -(class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(_955110)))], (11774 ^ _543626) ^ [_955300] : [class_Groups_Ocomm__monoid__add(_955300), -(class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(_955300)))], (11780 ^ _543626) ^ [_955490] : [class_Rings_Olinordered__idom(_955490), -(class_Rings_Olinordered__ring(tc_Polynomial_Opoly(_955490)))], (11786 ^ _543626) ^ [_955680] : [class_Rings_Olinordered__idom(_955680), -(class_Rings_Olinordered__idom(tc_Polynomial_Opoly(_955680)))], (11792 ^ _543626) ^ [_955870] : [class_Rings_Ocomm__semiring__1(_955870), -(class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(_955870)))], (11798 ^ _543626) ^ [_956060] : [class_Fields_Ofield(_956060), -(class_Divides_Osemiring__div(tc_Polynomial_Opoly(_956060)))], (11804 ^ _543626) ^ [_956250] : [class_Rings_Ocomm__semiring__0(_956250), -(class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(_956250)))], (11810 ^ _543626) ^ [_956440] : [class_Rings_Olinordered__idom(_956440), -(class_Nat_Osemiring__char__0(tc_Polynomial_Opoly(_956440)))], (11816 ^ _543626) ^ [_956630] : [class_Groups_Oab__group__add(_956630), -(class_Groups_Oab__group__add(tc_Polynomial_Opoly(_956630)))], (11822 ^ _543626) ^ [_956820] : [class_Rings_Ocomm__semiring__1(_956820), -(class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(_956820)))], (11828 ^ _543626) ^ [_957010] : [class_Rings_Olinordered__idom(_957010), -(class_Rings_Oordered__ring(tc_Polynomial_Opoly(_957010)))], (11834 ^ _543626) ^ [_957200] : [class_Rings_Olinordered__idom(_957200), -(class_Orderings_Opreorder(tc_Polynomial_Opoly(_957200)))], (11840 ^ _543626) ^ [_957390] : [class_Rings_Olinordered__idom(_957390), -(class_Orderings_Olinorder(tc_Polynomial_Opoly(_957390)))], (11846 ^ _543626) ^ [_957580] : [class_Rings_Ocomm__semiring__1(_957580), -(class_Groups_Omonoid__mult(tc_Polynomial_Opoly(_957580)))], (11852 ^ _543626) ^ [_957770] : [class_Rings_Ocomm__ring__1(_957770), -(class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(_957770)))], (11858 ^ _543626) ^ [_957960] : [class_Groups_Ocomm__monoid__add(_957960), -(class_Groups_Omonoid__add(tc_Polynomial_Opoly(_957960)))], (11864 ^ _543626) ^ [_958150] : [class_Rings_Ocomm__semiring__1(_958150), -(class_Rings_Osemiring__1(tc_Polynomial_Opoly(_958150)))], (11870 ^ _543626) ^ [_958340] : [class_Rings_Ocomm__semiring__0(_958340), -(class_Rings_Osemiring__0(tc_Polynomial_Opoly(_958340)))], (11876 ^ _543626) ^ [_958530] : [class_Groups_Oab__group__add(_958530), -(class_Groups_Ogroup__add(tc_Polynomial_Opoly(_958530)))], (11882 ^ _543626) ^ [_958720] : [class_Rings_Ocomm__semiring__0(_958720), -(class_Rings_Omult__zero(tc_Polynomial_Opoly(_958720)))], (11888 ^ _543626) ^ [_958910] : [class_Rings_Olinordered__idom(_958910), -(class_Orderings_Oorder(tc_Polynomial_Opoly(_958910)))], (11894 ^ _543626) ^ [_959100] : [class_Rings_Olinordered__idom(_959100), -(class_Int_Oring__char__0(tc_Polynomial_Opoly(_959100)))], (11900 ^ _543626) ^ [_959290] : [class_Rings_Ocomm__ring__1(_959290), -(class_Int_Onumber__ring(tc_Polynomial_Opoly(_959290)))], (11906 ^ _543626) ^ [_959480] : [class_Rings_Ocomm__semiring__0(_959480), -(class_Rings_Osemiring(tc_Polynomial_Opoly(_959480)))], (11912 ^ _543626) ^ [_959670] : [class_Rings_Olinordered__idom(_959670), -(class_Orderings_Oord(tc_Polynomial_Opoly(_959670)))], (11918 ^ _543626) ^ [_959860] : [class_Rings_Ocomm__ring__1(_959860), -(class_Rings_Oring__1(tc_Polynomial_Opoly(_959860)))], (11924 ^ _543626) ^ [_960050] : [class_Rings_Ocomm__semiring__1(_960050), -(class_Power_Opower(tc_Polynomial_Opoly(_960050)))], (11930 ^ _543626) ^ [_960240] : [class_Groups_Ozero(_960240), -(class_Groups_Ozero(tc_Polynomial_Opoly(_960240)))], (11936 ^ _543626) ^ [_960430] : [class_Rings_Ocomm__ring(_960430), -(class_Rings_Oring(tc_Polynomial_Opoly(_960430)))], (11942 ^ _543626) ^ [_960620] : [class_Rings_Ocomm__ring__1(_960620), -(class_Int_Onumber(tc_Polynomial_Opoly(_960620)))], (11948 ^ _543626) ^ [_960790] : [class_Rings_Ocomm__semiring__1(_960790), -(class_Groups_Oone(tc_Polynomial_Opoly(_960790)))]], input).
% 5.91/6.57  ncf('1',plain,[c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____))), hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Nat_OSuc(hAPP(v_f____, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____)))))],start(11954 ^ 0)).
% 5.91/6.57  ncf('1.1',plain,[-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____))), hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Nat_OSuc(hAPP(v_f____, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____)))))), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____)), c_Nat_OSuc(hAPP(v_f____, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____))))],extension(1693 ^ 1,bind([[_600102, _600104], [c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____)), c_Nat_OSuc(hAPP(v_f____, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____)))]]))).
% 5.91/6.57  ncf('1.1.1',plain,[-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____)), c_Nat_OSuc(hAPP(v_f____, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____))))), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____), hAPP(v_f____, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____)))],extension(1231 ^ 2,bind([[_583800, _583802], [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____), hAPP(v_f____, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____))]]))).
% 5.91/6.57  ncf('1.1.1.1',plain,[-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____), hAPP(v_f____, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_N1____, v_N2____))))],extension(1069 ^ 3)).
% 5.91/6.57  %-----------------------------------------------------
% 5.91/6.57  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------