TSTP Solution File: SWW220+1 by nanoCoP---2.0

%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWW220+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n008.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 12:25:47 EDT 2023

% Result   : Theorem 44.91s 43.77s
% Output   : Proof 44.91s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWW220+1 : TPTP v8.1.2. Released v5.2.0.
% 0.03/0.12  % Command  : nanocop.sh %s %d
% 0.13/0.33  % Computer : n008.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Thu May 18 22:04:09 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 44.91/43.77  
% 44.91/43.77  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 44.91/43.77  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 44.91/43.77  %-----------------------------------------------------
% 44.91/43.77  ncf(matrix, plain, [(12344 ^ _947313) ^ [] : [v_thesis____], !, (1901 ^ _490194) ^ [_552629, _552631, _552633, _552635, _552637] : [class_Groups_Oab__group__add(_552629), c_Groups_Ominus__class_Ominus(_552629, _552631, _552633) = c_Groups_Ominus__class_Ominus(_552629, _552635, _552637), 1908 ^ _490194 : [(1915 ^ _490194) ^ [] : [_552635 = _552637, -(_552631 = _552633)], (1909 ^ _490194) ^ [] : [_552631 = _552633, -(_552635 = _552637)]]], (12310 ^ _490194) ^ [_926736] : [class_Rings_Ocomm__ring(_926736), -(class_Rings_Oring(tc_Polynomial_Opoly(_926736)))], (11758 ^ _490194) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (5637 ^ _490194) ^ [_683738, _683740, _683742, _683744] : [class_RealVector_Oreal__normed__algebra(_683738), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_683738), _683740), c_Groups_Ominus__class_Ominus(_683738, _683742, _683744)) = c_Groups_Ominus__class_Ominus(_683738, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_683738), _683740), _683742), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_683738), _683740), _683744)))], (11568 ^ _490194) ^ [_905285, _905287] : [class_Orderings_Opreorder(_905285), -(class_Orderings_Opreorder(tc_fun(_905287, _905285)))], (2623 ^ _490194) ^ [_576923, _576925] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _576923, _576925), _576923 = _576925], (782 ^ _490194) ^ [_513984, _513986] : [-(class_Groups_Ozero(_513984)), _513986 = _513984, class_Groups_Ozero(_513986)], (9963 ^ _490194) ^ [_843668, _843670, _843672] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _843668, _843670), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _843668, _843672)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _843670, _843672))], (12286 ^ _490194) ^ [_925976] : [class_Rings_Olinordered__idom(_925976), -(class_Orderings_Oord(tc_Polynomial_Opoly(_925976)))], (10505 ^ _490194) ^ [_865211] : [-(hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Nat_OSuc(_865211)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _865211), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (8830 ^ _490194) ^ [_800999, _801001] : [class_Groups_Olinordered__ab__group__add(_800999), 8833 ^ _490194 : [(8840 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(_800999, c_Groups_Ozero__class_Ozero(_800999), _801001), -(c_Orderings_Oord__class_Oless(_800999, c_Groups_Ozero__class_Ozero(_800999), c_Groups_Oplus__class_Oplus(_800999, _801001, _801001)))], (8834 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(_800999, c_Groups_Ozero__class_Ozero(_800999), c_Groups_Oplus__class_Oplus(_800999, _801001, _801001)), -(c_Orderings_Oord__class_Oless(_800999, c_Groups_Ozero__class_Ozero(_800999), _801001))]]], (8698 ^ _490194) ^ [_796723, _796725] : [class_Groups_Olinordered__ab__group__add(_796723), 8701 ^ _490194 : [(8708 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_796723, c_Groups_Ozero__class_Ozero(_796723)), _796725)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_796723, c_Groups_Ozero__class_Ozero(_796723)), c_Groups_Oplus__class_Oplus(_796723, _796725, _796725))))], (8702 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_796723, c_Groups_Ozero__class_Ozero(_796723)), c_Groups_Oplus__class_Oplus(_796723, _796725, _796725))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_796723, c_Groups_Ozero__class_Ozero(_796723)), _796725)))]]], (5181 ^ _490194) ^ [_667408] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _667408)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _667408)) = _667408)], (12184 ^ _490194) ^ [_922746] : [class_Fields_Ofield(_922746), -(class_Divides_Osemiring__div(tc_Polynomial_Opoly(_922746)))], (11876 ^ _490194) ^ [] : [-(class_Orderings_Olinorder(tc_RealDef_Oreal))], (12190 ^ _490194) ^ [_922936] : [class_Rings_Ocomm__semiring__0(_922936), -(class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(_922936)))], (6527 ^ _490194) ^ [_716282] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _716282) = _716282)], (8612 ^ _490194) ^ [_793318, _793320, _793322] : [class_Rings_Osemiring__1(_793318), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_793318), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _793320, _793322)) = c_Groups_Oplus__class_Oplus(_793318, hAPP(c_Nat_Osemiring__1__class_Oof__nat(_793318), _793320), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_793318), _793322)))], (11414 ^ _490194) ^ [_900047, _900049, _900051] : [class_Fields_Ofield__inverse__zero(_900047), -(c_Rings_Oinverse__class_Odivide(_900047, c_Groups_Oone__class_Oone(_900047), hAPP(hAPP(c_Power_Opower__class_Opower(_900047), _900049), _900051)) = hAPP(hAPP(c_Power_Opower__class_Opower(_900047), c_Rings_Oinverse__class_Odivide(_900047, c_Groups_Oone__class_Oone(_900047), _900049)), _900051))], (4360 ^ _490194) ^ [_639147, _639149] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _639147)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _639149))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _639147), _639149)))], (642 ^ _490194) ^ [_509854, _509856] : [-(class_Groups_Omonoid__add(_509854)), _509856 = _509854, class_Groups_Omonoid__add(_509856)], (1372 ^ _490194) ^ [_535495, _535497] : [class_RealVector_Oreal__normed__vector(_535495), 1375 ^ _490194 : [(1382 ^ _490194) ^ [] : [_535497 = c_Groups_Ozero__class_Ozero(_535495), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_535495, _535497)), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))], (1376 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_535495, _535497)), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), -(_535497 = c_Groups_Ozero__class_Ozero(_535495))]]], (4003 ^ _490194) ^ [_626392, _626394] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _626392, _626394)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _626394, c_Nat_OSuc(_626392)))], (10605 ^ _490194) ^ [_869646, _869648] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _869646, _869648), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _869646), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), hAPP(c_RealDef_Oreal(tc_Nat_Onat), _869648))))], (5697 ^ _490194) ^ [_686277, _686279] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _686277), _686279) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_686277 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_686279 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11574 ^ _490194) ^ [_905497, _905499] : [class_Orderings_Oorder(_905497), -(class_Orderings_Oorder(tc_fun(_905499, _905497)))], (9357 ^ _490194) ^ [_820769, _820771, _820773] : [class_Groups_Oordered__ab__group__add__abs(_820769), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_820769, c_Groups_Oabs__class_Oabs(_820769, c_Groups_Ominus__class_Ominus(_820769, _820771, _820773))), c_Groups_Oplus__class_Oplus(_820769, c_Groups_Oabs__class_Oabs(_820769, _820771), c_Groups_Oabs__class_Oabs(_820769, _820773)))))], (9514 ^ _490194) ^ [_826776, _826778, _826780, _826782, _826784, _826786] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _826776), _826778), _826780) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _826782), _826784), _826786), hBOOL(hAPP(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), _826782), _826784), _826786))), c_Orderings_Oord__class_Oless(tc_Int_Oint, _826786, _826782), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _826780)), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _826782), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _826782), _826776)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _826778), _826784)))], (12238 ^ _490194) ^ [_924456] : [class_Rings_Ocomm__ring__1(_924456), -(class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(_924456)))], (11612 ^ _490194) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (5769 ^ _490194) ^ [_689170, _689172] : [class_Divides_Osemiring__div(_689170), -(c_Divides_Odiv__class_Odiv(_689170, _689172, c_Groups_Oone__class_Oone(_689170)) = _689172)], (1598 ^ _490194) ^ [_542904, _542906, _542908] : [class_Orderings_Olinorder(_542904), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_542904, _542906), _542908))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_542904, _542908), _542906)))], (11746 ^ _490194) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (8552 ^ _490194) ^ [_790806, _790808, _790810, _790812, _790814] : [class_Groups_Oab__group__add(_790806), -(c_Groups_Ominus__class_Ominus(_790806, c_Groups_Oplus__class_Oplus(_790806, _790808, _790810), c_Groups_Oplus__class_Oplus(_790806, _790812, _790814)) = c_Groups_Oplus__class_Oplus(_790806, c_Groups_Ominus__class_Ominus(_790806, _790808, _790812), c_Groups_Ominus__class_Ominus(_790806, _790810, _790814)))], (5607 ^ _490194) ^ [_682390, _682392] : [class_RealVector_Oreal__normed__algebra(_682390), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_682390), _682392), c_Groups_Ozero__class_Ozero(_682390)) = c_Groups_Ozero__class_Ozero(_682390))], (4722 ^ _490194) ^ [_652035, _652037, _652039] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _652035)), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _652037), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _652037), _652039)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _652035, _652039)), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _652035, _652037))))], (11420 ^ _490194) ^ [_900331, _900333, _900335] : [class_Rings_Odivision__ring(_900331), -(_900333 = c_Groups_Ozero__class_Ozero(_900331)), 11427 ^ _490194 : [(11434 ^ _490194) ^ [] : [_900335 = _900333, -(c_Rings_Oinverse__class_Odivide(_900331, _900335, _900333) = c_Groups_Oone__class_Oone(_900331))], (11428 ^ _490194) ^ [] : [c_Rings_Oinverse__class_Odivide(_900331, _900335, _900333) = c_Groups_Oone__class_Oone(_900331), -(_900335 = _900333)]]], (11800 ^ _490194) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal))], (11918 ^ _490194) ^ [] : [-(class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex))], (116 ^ _490194) ^ [_494117, _494119] : [-(c_RealDef_Opositive(_494117)), _494119 = _494117, c_RealDef_Opositive(_494119)], (5511 ^ _490194) ^ [_678726, _678728, _678730, _678732] : [class_Groups_Oab__semigroup__mult(_678726), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_678726), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_678726), _678728), _678730)), _678732) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_678726), _678728), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_678726), _678730), _678732)))], (4161 ^ _490194) ^ [_632039, _632041] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _632039, _632041), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_632039)), _632041)))], (3634 ^ _490194) ^ [_612941] : [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), _612941)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _612941))], (11484 ^ _490194) ^ [_902455, _902457, _902459, _902461] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Complex_Orcis(_902455, _902457)), c_Complex_Orcis(_902459, _902461)) = c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _902455), _902459), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _902457, _902461)))], (9171 ^ _490194) ^ [_813404, _813406, _813408] : [class_Groups_Oordered__comm__monoid__add(_813404), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_813404, _813406), c_Groups_Ozero__class_Ozero(_813404))), c_Orderings_Oord__class_Oless(_813404, _813408, c_Groups_Ozero__class_Ozero(_813404)), -(c_Orderings_Oord__class_Oless(_813404, c_Groups_Oplus__class_Oplus(_813404, _813406, _813408), c_Groups_Ozero__class_Ozero(_813404)))], (4899 ^ _490194) ^ [_657635, _657637, _657639, _657641] : [class_Groups_Ozero(_657635), hAPP(hAPP(hAPP(_657637, c_Groups_Ozero__class_Ozero(_657635)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_657635))), _657639) = _657639, -(c_Polynomial_Opoly__rec(_657641, _657635, _657639, _657637, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_657635))) = _657639)], (2715 ^ _490194) ^ [_580101] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _580101)))], (4095 ^ _490194) ^ [_629719, _629721] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_629719), c_Groups_Ozero__class_Ozero(_629719)), c_Nat_OSuc(_629721)) = c_Groups_Ozero__class_Ozero(_629719)), class_Power_Opower(_629719), class_Rings_Osemiring__0(_629719)], (4929 ^ _490194) ^ [_658810, _658812] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _658810)), -(hAPP(c_Int_Onat, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _658810, _658812)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(c_Int_Onat, _658810), hAPP(c_Int_Onat, _658812)))], (11608 ^ _490194) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (9241 ^ _490194) ^ [_815863] : [class_Rings_Olinordered__semidom(_815863), -(c_Orderings_Oord__class_Oless(_815863, c_Groups_Ozero__class_Ozero(_815863), c_Groups_Oplus__class_Oplus(_815863, c_Groups_Oone__class_Oone(_815863), c_Groups_Oone__class_Oone(_815863))))], (7973 ^ _490194) ^ [_766647, _766649, _766651, _766653] : [class_Rings_Ocomm__semiring__1(_766647), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_766647), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_766647), _766649), _766651)), _766653) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_766647), _766649), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_766647), _766651), _766653)))], (7991 ^ _490194) ^ [_767649, _767651, _767653, _767655, _767657] : [class_Rings_Ocomm__semiring__1(_767649), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_767649), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_767649), _767651), _767653)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_767649), _767655), _767657)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_767649), _767655), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_767649), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_767649), _767651), _767653)), _767657)))], (6449 ^ _490194) ^ [_713460, _713462, _713464] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _713460), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _713460), _713462), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _713460), _713464)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _713462, _713464))], (302 ^ _490194) ^ [_499824, _499826] : [-(class_Rings_Olinordered__semiring__strict(_499824)), _499826 = _499824, class_Rings_Olinordered__semiring__strict(_499826)], (11940 ^ _490194) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex))], (10047 ^ _490194) ^ [_847361, _847363, _847365] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _847361, _847363)), _847365)), 10050 ^ _490194 : [(10053 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _847363), _847365)))], (10051 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _847361), _847365)))]]], (11110 ^ _490194) ^ [_888408, _888410] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _888408)), _888410)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _888408), c_RComplete_Onatfloor(_888410))))], (2999 ^ _490194) ^ [_590446, _590448, _590450] : [class_RealVector_Oreal__normed__vector(_590446), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_590446, _590448), c_RealVector_Onorm__class_Onorm(_590446, _590450)))), c_RealVector_Onorm__class_Onorm(_590446, c_Groups_Ominus__class_Ominus(_590446, _590448, _590450)))))], (6663 ^ _490194) ^ [_721177, _721179] : [_721177 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _721177), _721179), -(_721179 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_721177 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3416 ^ _490194) ^ [_605257, _605259] : [class_Rings_Olinordered__semidom(_605257), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_605257, c_Groups_Ozero__class_Ozero(_605257)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_605257), _605259))))], (1783 ^ _490194) ^ [_548985, _548987, _548989] : [class_Orderings_Opreorder(_548985), c_Orderings_Oord__class_Oless(_548985, _548987, _548989), c_Orderings_Oord__class_Oless(_548985, _548989, _548987)], (5785 ^ _490194) ^ [_689990, _689992, _689994] : [class_Rings_Olinordered__semidom(_689990), c_Orderings_Oord__class_Oless(_689990, c_Groups_Ozero__class_Ozero(_689990), _689992), c_Orderings_Oord__class_Oless(_689990, _689992, c_Groups_Oone__class_Oone(_689990)), -(c_Orderings_Oord__class_Oless(_689990, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_689990), _689992), hAPP(hAPP(c_Power_Opower__class_Opower(_689990), _689992), _689994)), hAPP(hAPP(c_Power_Opower__class_Opower(_689990), _689992), _689994)))], (10827 ^ _490194) ^ [_878032] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _878032), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_878032)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (12202 ^ _490194) ^ [_923316] : [class_Groups_Oab__group__add(_923316), -(class_Groups_Oab__group__add(tc_Polynomial_Opoly(_923316)))], (3546 ^ _490194) ^ [] : [c_RealDef_Opositive(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (7841 ^ _490194) ^ [_761707, _761709, _761711, _761713] : [class_Rings_Olinordered__semiring__strict(_761707), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_761707, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_761707), _761709), _761711)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_761707), _761709), _761713))), c_Orderings_Oord__class_Oless(_761707, c_Groups_Ozero__class_Ozero(_761707), _761709), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_761707, _761711), _761713)))], (6401 ^ _490194) ^ [_711739, _711741, _711743] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _711739), 6404 ^ _490194 : [(6405 ^ _490194) ^ [] : [-(_711741 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _711743, _711739)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _711739), _711741)), _711743)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _711743, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _711739), c_Nat_OSuc(_711741)))], (6415 ^ _490194) ^ [] : [_711741 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _711743, _711739), 6418 ^ _490194 : [(6421 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _711743, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _711739), c_Nat_OSuc(_711741))))], (6419 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _711739), _711741)), _711743)))]]]]], (1494 ^ _490194) ^ [_539506, _539508, _539510, _539512] : [class_Orderings_Oord(_539506), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_539506, _539508), _539510)), _539510 = _539512, -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_539506, _539508), _539512)))], (4520 ^ _490194) ^ [_645109] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _645109), 4524 ^ _490194 : [(4527 ^ _490194) ^ [] : [-(_645109 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 4523 ^ [_645109]))], (4525 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 4523 ^ [_645109]))]]], (6545 ^ _490194) ^ [_716987] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _716987) = _716987)], (11930 ^ _490194) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex))], (2803 ^ _490194) ^ [_583260, _583262] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _583260), _583262)), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _583262, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _583262, _583260)) = _583260)], (11798 ^ _490194) ^ [] : [-(class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal))], (10507 ^ _490194) ^ [_865372, _865374, _865376, _865378, _865380] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _865372), _865374)), 10510 ^ _490194 : [(10517 ^ _490194) ^ [] : [hBOOL(hAPP(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, _865374, _865372)), _865376), _865378)), _865380)), -(hBOOL(hAPP(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), _865374), _865376), _865378)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _865372), _865376), _865380))))], (10511 ^ _490194) ^ [] : [hBOOL(hAPP(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), _865374), _865376), _865378)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _865372), _865376), _865380))), -(hBOOL(hAPP(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, _865374, _865372)), _865376), _865378)), _865380)))]]], (5529 ^ _490194) ^ [_679466, _679468] : [class_Groups_Oone(_679466), 5532 ^ _490194 : [(5539 ^ _490194) ^ [] : [_679468 = c_Groups_Oone__class_Oone(_679466), -(c_Groups_Oone__class_Oone(_679466) = _679468)], (5533 ^ _490194) ^ [] : [c_Groups_Oone__class_Oone(_679466) = _679468, -(_679468 = c_Groups_Oone__class_Oone(_679466))]]], (8622 ^ _490194) ^ [_793805, _793807, _793809] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _793805, _793807), _793809) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _793805, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _793807, _793809)))], (542 ^ _490194) ^ [_506904, _506906] : [-(class_Fields_Ofield(_506904)), _506906 = _506904, class_Fields_Ofield(_506906)], (1388 ^ _490194) ^ [_535983, _535985] : [class_Groups_Ozero(_535983), 1391 ^ _490194 : [(1398 ^ _490194) ^ [] : [_535985 = c_Groups_Ozero__class_Ozero(_535983), -(c_Groups_Ozero__class_Ozero(_535983) = _535985)], (1392 ^ _490194) ^ [] : [c_Groups_Ozero__class_Ozero(_535983) = _535985, -(_535985 = c_Groups_Ozero__class_Ozero(_535983))]]], (4037 ^ _490194) ^ [_627613, _627615] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_627613)), c_Nat_OSuc(_627615))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _627613), _627615)))], (3869 ^ _490194) ^ [_621857] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_621857)], (10297 ^ _490194) ^ [_856962, _856964, _856966, _856968] : [class_Groups_Ocomm__monoid__add(_856962), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_856962, _856964), _856966), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_856962, _856968), _856966), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_856962, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_856962), _856964, _856968)), _856966))], (5412 ^ _490194) ^ [_675017, _675019, _675021] : [class_Rings_Oidom(_675017), -(_675019 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_675017))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Oorder(_675017, _675021, _675019)), c_Polynomial_Odegree(_675017, _675019))))], (4470 ^ _490194) ^ [_643249, _643251] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _643249)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _643249), _643251))))], (11598 ^ _490194) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (3104 ^ _490194) ^ [_594136, _594138] : [-(hAPP(c_RealDef_Oreal(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _594136), _594138)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), hAPP(c_RealDef_Oreal(tc_Nat_Onat), _594136)), _594138))], (9997 ^ _490194) ^ [_845148, _845150, _845152] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _845148, _845150) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _845152, _845150), -(_845148 = _845152)], (4961 ^ _490194) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2771 ^ _490194) ^ [_582015, _582017] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _582015), _582017)), -(_582015 = _582017), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _582015, _582017))], (4508 ^ _490194) ^ [_644706, _644708] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _644706), _644708)), -(c_Nat__Transfer_Otsub(_644708, _644706) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, _644708, _644706))], (1360 ^ _490194) ^ [_535019, _535021, _535023] : [class_RealVector_Oreal__normed__vector(_535019), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_535019, _535021), c_RealVector_Onorm__class_Onorm(_535019, _535023))), c_RealVector_Onorm__class_Onorm(_535019, c_Groups_Ominus__class_Ominus(_535019, _535021, _535023)))))], (10095 ^ _490194) ^ [_849430, _849432, _849434] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _849430, _849432)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _849430, _849434))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _849432), _849434)))], (2891 ^ _490194) ^ [_586407, _586409, _586411, _586413] : [class_RealVector_Oreal__normed__vector(_586407), 2897 ^ _490194 : [(2900 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_586407, hAPP(_586411, 2896 ^ [_586407, _586409, _586411, _586413]))), _586413))], (2898 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _586409), 2896 ^ [_586407, _586409, _586411, _586413])))]], -(c_SEQ_OBseq(_586407, _586411))], (3656 ^ _490194) ^ [_613620, _613622] : [3657 ^ _490194 : [(3660 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _613620)], (3658 ^ _490194) ^ [] : [_613622 = 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), _613620), _613622)))], (752 ^ _490194) ^ [_513099, _513101] : [-(class_Rings_Ocomm__ring__1(_513099)), _513101 = _513099, class_Rings_Ocomm__ring__1(_513101)], (11586 ^ _490194) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (6919 ^ _490194) ^ [_730174] : [class_Rings_Ozero__neq__one(_730174), c_Groups_Oone__class_Oone(_730174) = c_Groups_Ozero__class_Ozero(_730174)], (6505 ^ _490194) ^ [_715572, _715574, _715576] : [-(_715572 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 6508 ^ _490194 : [(6515 ^ _490194) ^ [] : [_715574 = _715576, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _715574), _715572) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _715576), _715572))], (6509 ^ _490194) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _715574), _715572) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _715576), _715572), -(_715574 = _715576)]]], (4852 ^ _490194) ^ [_656027, _656029] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _656027), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _656027), _656029)), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _656029, _656027) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _656029, _656027), _656027)))], (6595 ^ _490194) ^ [_718939, _718941] : [c_RealDef_Opositive(_718939), c_RealDef_Opositive(_718941), -(c_RealDef_Opositive(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _718939), _718941)))], (8095 ^ _490194) ^ [_772440] : [class_RealVector_Oreal__normed__algebra(_772440), 8099 ^ _490194 : [(8102 ^ _490194) ^ [_772777, _772779] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_772440, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_772440), _772779), _772777))), 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(_772440, _772779)), c_RealVector_Onorm__class_Onorm(_772440, _772777))), 8098 ^ [_772440]))))], (8100 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 8098 ^ [_772440]))]]], (8558 ^ _490194) ^ [_791094, _791096, _791098] : [class_Groups_Ogroup__add(_791094), -(c_Groups_Ominus__class_Ominus(_791094, c_Groups_Oplus__class_Oplus(_791094, _791096, _791098), _791098) = _791096)], (12280 ^ _490194) ^ [_925786] : [class_Rings_Ocomm__semiring__0(_925786), -(class_Rings_Osemiring(tc_Polynomial_Opoly(_925786)))], (10323 ^ _490194) ^ [_857931, _857933, _857935] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _857931), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _857935, _857933))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _857931, _857933)), _857935)))], (8312 ^ _490194) ^ [_782248, _782250] : [class_Rings_Ocomm__semiring__1(_782248), -(c_Groups_Oplus__class_Oplus(_782248, _782250, c_Groups_Ozero__class_Ozero(_782248)) = _782250)], (1763 ^ _490194) ^ [_548335, _548337, _548339] : [class_Orderings_Oorder(_548335), c_Orderings_Oord__class_Oless(_548335, _548337, _548339), _548337 = _548339], (5725 ^ _490194) ^ [_687264, _687266, _687268, _687270] : [class_Groups_Omonoid__mult(_687264), -(hAPP(hAPP(c_Power_Opower__class_Opower(_687264), _687266), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _687268), _687270)) = hAPP(hAPP(c_Power_Opower__class_Opower(_687264), hAPP(hAPP(c_Power_Opower__class_Opower(_687264), _687266), _687268)), _687270))], (10876 ^ _490194) ^ [_879761, _879763] : [-(_879761 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), -(_879763 = 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), _879761), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), 10883 ^ [_879761, _879763]), _879763)))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (11222 ^ _490194) ^ [_892567, _892569, _892571, _892573] : [class_RealVector_Oreal__normed__field(_892567), -(c_Rings_Oinverse__class_Odivide(_892567, c_Groups_Oplus__class_Oplus(_892567, _892569, _892571), _892573) = c_Groups_Oplus__class_Oplus(_892567, c_Rings_Oinverse__class_Odivide(_892567, _892569, _892573), c_Rings_Oinverse__class_Odivide(_892567, _892571, _892573)))], (4322 ^ _490194) ^ [] : [-(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))], (10529 ^ _490194) ^ [_866428, _866430, _866432, _866434, _866436] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _866428), _866430)), 10532 ^ _490194 : [(10539 ^ _490194) ^ [] : [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, _866430, _866428)), _866432), _866434) = _866436, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _866430), _866432), _866434) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _866428), _866432), _866436))], (10533 ^ _490194) ^ [] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _866430), _866432), _866434) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _866428), _866432), _866436), -(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, _866430, _866428)), _866432), _866434) = _866436)]]], (1817 ^ _490194) ^ [_550059, _550061, _550063] : [class_Orderings_Olinorder(_550059), -(c_Orderings_Oord__class_Oless(_550059, _550061, _550063)), 1824 ^ _490194 : [(1831 ^ _490194) ^ [] : [_550063 = _550061, c_Orderings_Oord__class_Oless(_550059, _550063, _550061)], (1825 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(_550059, _550063, _550061)), -(_550063 = _550061)]]], (6925 ^ _490194) ^ [_730371] : [class_Rings_Ozero__neq__one(_730371), c_Groups_Ozero__class_Ozero(_730371) = c_Groups_Oone__class_Oone(_730371)], (9279 ^ _490194) ^ [_817599, _817601, _817603, _817605, _817607, _817609] : [class_Rings_Oordered__ring(_817599), 9282 ^ _490194 : [(9289 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(_817599, _817605, c_Groups_Oplus__class_Oplus(_817599, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_817599), c_Groups_Ominus__class_Ominus(_817599, _817607, _817601)), _817603), _817609)), -(c_Orderings_Oord__class_Oless(_817599, c_Groups_Oplus__class_Oplus(_817599, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_817599), _817601), _817603), _817605), c_Groups_Oplus__class_Oplus(_817599, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_817599), _817607), _817603), _817609)))], (9283 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(_817599, c_Groups_Oplus__class_Oplus(_817599, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_817599), _817601), _817603), _817605), c_Groups_Oplus__class_Oplus(_817599, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_817599), _817607), _817603), _817609)), -(c_Orderings_Oord__class_Oless(_817599, _817605, c_Groups_Oplus__class_Oplus(_817599, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_817599), c_Groups_Ominus__class_Ominus(_817599, _817607, _817601)), _817603), _817609)))]]], (8021 ^ _490194) ^ [_769027, _769029] : [class_Rings_Ocomm__semiring__1(_769027), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_769027), _769029), c_Groups_Oone__class_Oone(_769027)) = _769029)], (5205 ^ _490194) ^ [_668240, _668242] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _668240), 5208 ^ _490194 : [(5215 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _668242, _668240)), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _668242, _668240) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _668242, _668240), _668240)))], (5209 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _668242, _668240), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _668242, _668240) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (12160 ^ _490194) ^ [_921986] : [class_Rings_Olinordered__idom(_921986), -(class_Rings_Olinordered__ring(tc_Polynomial_Opoly(_921986)))], (6023 ^ _490194) ^ [_698700, _698702, _698704] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _698702), _698704)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_698700)), _698702)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_698700)), _698704))))], (11638 ^ _490194) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (5231 ^ _490194) ^ [_669097] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Int_Onat, _669097)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _669097))], (5509 ^ _490194) ^ [_678577, _678579] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _678577), _678579) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _678579), _678577))], (11762 ^ _490194) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (10029 ^ _490194) ^ [_846500, _846502, _846504] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _846500, _846502), _846504) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _846500, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _846502, _846504)))], (10124 ^ _490194) ^ [_850644, _850646, _850648, _850650] : [class_Rings_Ocomm__semiring__1(_850644), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_850644), hAPP(hAPP(c_Power_Opower__class_Opower(_850644), _850646), _850648)), hAPP(hAPP(c_Power_Opower__class_Opower(_850644), _850646), _850650)) = hAPP(hAPP(c_Power_Opower__class_Opower(_850644), _850646), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _850648, _850650)))], (8862 ^ _490194) ^ [_801989, _801991, _801993] : [class_Groups_Oordered__comm__monoid__add(_801989), c_Orderings_Oord__class_Oless(_801989, c_Groups_Ozero__class_Ozero(_801989), _801991), c_Orderings_Oord__class_Oless(_801989, c_Groups_Ozero__class_Ozero(_801989), _801993), -(c_Orderings_Oord__class_Oless(_801989, c_Groups_Ozero__class_Ozero(_801989), c_Groups_Oplus__class_Oplus(_801989, _801991, _801993)))], (632 ^ _490194) ^ [_509559, _509561] : [-(class_Groups_Ocomm__monoid__add(_509559)), _509561 = _509559, class_Groups_Ocomm__monoid__add(_509561)], (5279 ^ _490194) ^ [_670548, _670550] : [5280 ^ _490194 : [(5283 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _670550))], (5281 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _670548)]], 5284 ^ _490194 : [(5291 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _670548), _670550)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(c_Int_Onat, _670548)), hAPP(c_Int_Onat, _670550))))], (5285 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(c_Int_Onat, _670548)), hAPP(c_Int_Onat, _670550))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _670548), _670550)))]]], (11730 ^ _490194) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (2491 ^ _490194) ^ [_572426] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _572426, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9393 ^ _490194) ^ [_822333, _822335] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _822333, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _822335, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _822333), _822335)))], (4919 ^ _490194) ^ [_658342, _658344] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _658342, _658344)), _658342)))], (9540 ^ _490194) ^ [_827669, _827671, _827673, _827675, _827677] : [hBOOL(hAPP(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), _827669), _827671), _827673)), c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _827669), _827675), _827677))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _827673)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _827673, _827669), c_Orderings_Oord__class_Oless(tc_Int_Oint, _827677, _827669), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _827671), _827675)))], (9024 ^ _490194) ^ [_808121, _808123] : [class_Rings_Ocomm__semiring__1(_808121), -(c_Groups_Oplus__class_Oplus(_808121, _808123, _808123) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_808121), c_Groups_Oplus__class_Oplus(_808121, c_Groups_Oone__class_Oone(_808121), c_Groups_Oone__class_Oone(_808121))), _808123))], (12292 ^ _490194) ^ [_926166] : [class_Rings_Ocomm__ring__1(_926166), -(class_Rings_Oring__1(tc_Polynomial_Opoly(_926166)))], (8368 ^ _490194) ^ [_784092, _784094] : [class_Groups_Ocomm__monoid__add(_784092), -(c_Groups_Oplus__class_Oplus(_784092, c_Groups_Ozero__class_Ozero(_784092), _784094) = _784094)], (9935 ^ _490194) ^ [_842550, _842552, _842554, _842556] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _842550, _842552), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _842554, _842556), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _842550, _842554), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _842552, _842556)))], (8119 ^ _490194) ^ [_773667, _773669] : [class_Rings_Ocomm__semiring__0(_773667), -(c_Polynomial_Opcompose(_773667, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_773667)), _773669) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_773667)))], (2797 ^ _490194) ^ [_583008, _583010, _583012] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _583008), _583010)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _583008, _583012)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _583010, _583012))))], (11732 ^ _490194) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (4105 ^ _490194) ^ [_630071, _630073] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _630071, c_Nat_OSuc(_630073)), -(_630071 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 4113 ^ _490194 : [(4116 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, 4112 ^ [_630071, _630073], _630073))], (4114 ^ _490194) ^ [] : [-(_630071 = c_Nat_OSuc(4112 ^ [_630071, _630073]))]]], (5809 ^ _490194) ^ [_690845, _690847, _690849, _690851] : [class_Rings_Olinordered__semidom(_690845), c_Orderings_Oord__class_Oless(_690845, c_Groups_Oone__class_Oone(_690845), _690847), 5816 ^ _490194 : [(5823 ^ _490194) ^ [] : [_690849 = _690851, -(hAPP(hAPP(c_Power_Opower__class_Opower(_690845), _690847), _690849) = hAPP(hAPP(c_Power_Opower__class_Opower(_690845), _690847), _690851))], (5817 ^ _490194) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_690845), _690847), _690849) = hAPP(hAPP(c_Power_Opower__class_Opower(_690845), _690847), _690851), -(_690849 = _690851)]]], (7933 ^ _490194) ^ [_764873] : [-(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), _764873), _764873))), -(_764873 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (6829 ^ _490194) ^ [_727088] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _727088), -(c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _727088, c_Groups_Oone__class_Oone(tc_Nat_Onat))) = _727088)], (11968 ^ _490194) ^ [] : [-(class_Rings_Osemiring__1(tc_Complex_Ocomplex))], (2527 ^ _490194) ^ [_573687, _573689] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _573687, _573689)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _573689, _573687))], (950 ^ _490194) ^ [_520102, _520104, _520106, _520108, _520110, _520112] : [-(c_Power_Opower_Opower(_520112, _520108, _520104) = c_Power_Opower_Opower(_520110, _520106, _520102)), _520112 = _520110, _520108 = _520106, _520104 = _520102], (4963 ^ _490194) ^ [_660009, _660011] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _660009)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _660011)), 4970 ^ _490194 : [(4977 ^ _490194) ^ [] : [_660009 = _660011, -(hAPP(c_Int_Onat, _660009) = hAPP(c_Int_Onat, _660011))], (4971 ^ _490194) ^ [] : [hAPP(c_Int_Onat, _660009) = hAPP(c_Int_Onat, _660011), -(_660009 = _660011)]]], (1536 ^ _490194) ^ [_540878, _540880, _540882] : [class_Orderings_Oorder(_540878), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_540878, _540880), _540882)), 1543 ^ _490194 : [(1550 ^ _490194) ^ [] : [_540882 = _540880, -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_540878, _540882), _540880)))], (1544 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_540878, _540882), _540880)), -(_540882 = _540880)]]], (9985 ^ _490194) ^ [_844687, _844689, _844691] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _844687, _844689) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _844687, _844691), -(_844689 = _844691)], (10635 ^ _490194) ^ [_870740, _870742] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _870740), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _870742), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _870740), _870742)))], (10267 ^ _490194) ^ [_855810, _855812, _855814] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _855810, _855814), _855812), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _855810, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _855812, _855814)))], (3839 ^ _490194) ^ [_620908, _620910] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _620908, _620910)), -(_620908 = _620910), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _620910, _620908))], (12256 ^ _490194) ^ [_925026] : [class_Rings_Ocomm__semiring__0(_925026), -(class_Rings_Osemiring__0(tc_Polynomial_Opoly(_925026)))], (4652 ^ _490194) ^ [_649786, _649788] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _649786), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), c_Orderings_Oord__class_Oless(tc_Int_Oint, _649788, _649786), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _649786, _649788) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (5855 ^ _490194) ^ [_692476, _692478, _692480] : [class_Divides_Osemiring__div(_692476), -(_692478 = c_Groups_Ozero__class_Ozero(_692476)), -(c_Divides_Odiv__class_Odiv(_692476, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_692476), _692478), _692480), _692478) = _692480)], (11748 ^ _490194) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (4702 ^ _490194) ^ [_651385, _651387] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _651385)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _651385, _651387), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _651385, _651387) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (2965 ^ _490194) ^ [_589100, _589102] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _589100), _589102))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _589102), _589100)))], (5643 ^ _490194) ^ [_684050, _684052, _684054, _684056] : [class_RealVector_Oreal__normed__algebra(_684050), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_684050), _684052), c_Groups_Ominus__class_Ominus(_684050, _684054, _684056)) = c_Groups_Ominus__class_Ominus(_684050, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_684050), _684052), _684054), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_684050), _684052), _684056)))], (11682 ^ _490194) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (12136 ^ _490194) ^ [_921226] : [class_Rings_Olinordered__idom(_921226), -(class_Rings_Oordered__semiring(tc_Polynomial_Opoly(_921226)))], (10421 ^ _490194) ^ [_861812, _861814, _861816] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _861812), c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _861814), _861816)) = 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, _861812, _861814)), _861816))], (11684 ^ _490194) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (11974 ^ _490194) ^ [] : [-(class_Rings_Omult__zero(tc_Complex_Ocomplex))], (11158 ^ _490194) ^ [_890125] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _890125, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_RComplete_Onatfloor(_890125))))], (4021 ^ _490194) ^ [_627020, _627022] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _627020), c_Nat_OSuc(_627022))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _627020), _627022))), -(_627020 = c_Nat_OSuc(_627022))], (11986 ^ _490194) ^ [] : [-(class_Rings_Oring(tc_Complex_Ocomplex))], (11872 ^ _490194) ^ [] : [-(class_Rings_Oordered__ring(tc_RealDef_Oreal))], (3957 ^ _490194) ^ [_624879, _624881] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _624879, _624881)), 3960 ^ _490194 : [(3967 ^ _490194) ^ [] : [_624879 = _624881, -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _624879, c_Nat_OSuc(_624881)))], (3961 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _624879, c_Nat_OSuc(_624881)), -(_624879 = _624881)]]], (9438 ^ _490194) ^ [_824097, _824099, _824101, _824103, _824105, _824107] : [class_Rings_Olinordered__semiring__1(_824097), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_824097, _824099), _824101)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_824097, _824103), _824101)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_824097, c_Groups_Ozero__class_Ozero(_824097)), _824105)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_824097, c_Groups_Ozero__class_Ozero(_824097)), _824107)), c_Groups_Oplus__class_Oplus(_824097, _824105, _824107) = c_Groups_Oone__class_Oone(_824097), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_824097, c_Groups_Oplus__class_Oplus(_824097, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_824097), _824105), _824099), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_824097), _824107), _824103))), _824101)))], (8204 ^ _490194) ^ [_777392, _777394, _777396, _777398, _777400] : [class_Rings_Osemiring(_777392), -(c_Groups_Oplus__class_Oplus(_777392, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_777392), _777394), _777396), c_Groups_Oplus__class_Oplus(_777392, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_777392), _777398), _777396), _777400)) = c_Groups_Oplus__class_Oplus(_777392, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_777392), c_Groups_Oplus__class_Oplus(_777392, _777394, _777398)), _777396), _777400))], (5951 ^ _490194) ^ [_696058, _696060, _696062] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _696058), _696060), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _696062), _696060)), 5954 ^ _490194 : [(5957 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _696058, _696062))], (5955 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _696060))]]], (5913 ^ _490194) ^ [_694747, _694749] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _694747), _694749) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 5916 ^ _490194 : [(5919 ^ _490194) ^ [] : [-(_694749 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (5917 ^ _490194) ^ [] : [-(_694747 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (11152 ^ _490194) ^ [_889898, _889900] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _889898)), _889900)), -(c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _889900, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _889898))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_RComplete_Onatfloor(_889900), _889898))], (7785 ^ _490194) ^ [_759731, _759733, _759735, _759737] : [class_Rings_Olinordered__semiring__strict(_759731), c_Orderings_Oord__class_Oless(_759731, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_759731), _759733), _759735), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_759731), _759737), _759735)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_759731, c_Groups_Ozero__class_Ozero(_759731)), _759735)), -(c_Orderings_Oord__class_Oless(_759731, _759733, _759737))], (6641 ^ _490194) ^ [_720448, _720450] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _720448)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _720450)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _720448), _720450))))], (1102 ^ _490194) ^ [_525588, _525590] : [_525590 = _525588, -(c_Groups_Otimes__class_Otimes(_525590) = c_Groups_Otimes__class_Otimes(_525588))], (9951 ^ _490194) ^ [_843155, _843157, _843159] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _843155, _843157), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _843155, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _843159, _843157)))], (11736 ^ _490194) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (11854 ^ _490194) ^ [] : [-(class_Rings_Olinordered__idom(tc_RealDef_Oreal))], (5775 ^ _490194) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (10136 ^ _490194) ^ [_851285, _851287] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _851285, _851287) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 10141 ^ _490194 : [(10144 ^ _490194) ^ [] : [-(_851287 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10142 ^ _490194) ^ [] : [-(_851285 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 10145 ^ _490194 : [(10148 ^ _490194) ^ [] : [-(_851287 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10146 ^ _490194) ^ [] : [-(_851285 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (2273 ^ _490194) ^ [_564366, _564368] : [class_Groups_Ogroup__add(_564366), -(c_Groups_Ominus__class_Ominus(_564366, _564368, c_Groups_Ozero__class_Ozero(_564366)) = _564368)], (3540 ^ _490194) ^ [_609583, _609585] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _609583), _609585)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _609583)), hAPP(c_RealDef_Oreal(tc_Nat_Onat), _609585))))], (10009 ^ _490194) ^ [_845551, _845553] : [-(hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _845551, _845553)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _845551), hAPP(c_RealDef_Oreal(tc_Nat_Onat), _845553)))], (6565 ^ _490194) ^ [_717659] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _717659), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _717659)], (1753 ^ _490194) ^ [_548011, _548013, _548015] : [class_Orderings_Oorder(_548011), c_Orderings_Oord__class_Oless(_548011, _548013, _548015), _548015 = _548013], (1663 ^ _490194) ^ [_545141, _545143, _545145, _545147] : [class_Orderings_Opreorder(_545141), c_Orderings_Oord__class_Oless(_545141, _545143, _545145), c_Orderings_Oord__class_Oless(_545141, _545145, _545147), -(c_Orderings_Oord__class_Oless(_545141, _545143, _545147))], (10403 ^ _490194) ^ [_861117, _861119, _861121, _861123] : [class_Groups_Ocomm__monoid__add(_861117), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_861117, _861119)), _861121)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_861117, _861123)), _861121)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_861117, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_861117), _861119, _861123))), _861121)))], (10799 ^ _490194) ^ [_877088, _877090] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _877088), hAPP(c_RealDef_Oreal(tc_Nat_Onat), _877090))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_877088)), _877090)))], (11380 ^ _490194) ^ [_898707, _898709, _898711, _898713] : [class_Rings_Odivision__ring(_898707), -(_898709 = c_Groups_Ozero__class_Ozero(_898707)), _898711 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_898707), _898713), _898709), -(c_Rings_Oinverse__class_Odivide(_898707, _898711, _898709) = _898713)], (262 ^ _490194) ^ [_498644, _498646] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_498644)), _498646 = _498644, class_Groups_Oordered__cancel__ab__semigroup__add(_498646)], (10150 ^ _490194) ^ [_851695, _851697] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _851695, _851697) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 10151 ^ _490194 : [(10158 ^ _490194) ^ [] : [_851695 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _851697 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10152 ^ _490194) ^ [] : [_851695 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _851697 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (382 ^ _490194) ^ [_502184, _502186] : [-(class_Rings_Olinordered__ring__strict(_502184)), _502186 = _502184, class_Rings_Olinordered__ring__strict(_502186)], (4873 ^ _490194) ^ [_656766, _656768] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _656766)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _656768)), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(c_Int_Onat, _656766), hAPP(c_Int_Onat, _656768)) = hAPP(c_Int_Onat, c_Nat__Transfer_Otsub(_656766, _656768)))], (2073 ^ _490194) ^ [_558067, _558069, _558071] : [class_Orderings_Oorder(_558067), -(_558069 = _558071), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_558067, _558069), _558071)), -(c_Orderings_Oord__class_Oless(_558067, _558069, _558071))], (11934 ^ _490194) ^ [] : [-(class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex))], (4372 ^ _490194) ^ [_639585, _639587] : [class_RealVector_Oreal__normed__vector(_639585), 4375 ^ _490194 : [(4383 ^ _490194) ^ [] : [4385 ^ _490194 : [(4386 ^ _490194) ^ [_640086] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_639585, hAPP(_639587, 4384 ^ [_639585, _639587, _640086]))), hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Nat_OSuc(_640086))))]], -(c_SEQ_OBseq(_639585, _639587))], (4376 ^ _490194) ^ [] : [c_SEQ_OBseq(_639585, _639587), 4380 ^ _490194 : [(4381 ^ _490194) ^ [_639900] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_639585, hAPP(_639587, _639900))), hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Nat_OSuc(4379 ^ [_639585, _639587])))))]]]]], (1006 ^ _490194) ^ [_522119, _522121, _522123, _522125] : [-(c_Polynomial_Odegree(_522125, _522121) = c_Polynomial_Odegree(_522123, _522119)), _522125 = _522123, _522121 = _522119], (602 ^ _490194) ^ [_508674, _508676] : [-(class_Orderings_Opreorder(_508674)), _508676 = _508674, class_Orderings_Opreorder(_508676)], (842 ^ _490194) ^ [_515754, _515756] : [-(c_SEQ_Osubseq(_515754)), _515756 = _515754, c_SEQ_Osubseq(_515756)], (5595 ^ _490194) ^ [_681888, _681890, _681892] : [class_RealVector_Oreal__normed__algebra(_681888), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_681888, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_681888), _681890), _681892))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_681888, _681890)), c_RealVector_Onorm__class_Onorm(_681888, _681892)))))], (5897 ^ _490194) ^ [_694174, _694176] : [class_Divides_Osemiring__div(_694174), -(_694176 = c_Groups_Ozero__class_Ozero(_694174)), -(c_Divides_Odiv__class_Odiv(_694174, _694176, _694176) = c_Groups_Oone__class_Oone(_694174))], (9207 ^ _490194) ^ [_814597, _814599, _814601] : [class_Rings_Olinordered__ring(_814597), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_814597, c_Groups_Ozero__class_Ozero(_814597)), c_Groups_Oplus__class_Oplus(_814597, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_814597), _814599), _814599), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_814597), _814601), _814601)))))], (6367 ^ _490194) ^ [_710610, _710612, _710614, _710616] : [class_Rings_Olinordered__semidom(_710610), c_Orderings_Oord__class_Oless(_710610, c_Groups_Oone__class_Oone(_710610), _710612), 6374 ^ _490194 : [(6381 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _710614), _710616)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_710610, hAPP(hAPP(c_Power_Opower__class_Opower(_710610), _710612), _710614)), hAPP(hAPP(c_Power_Opower__class_Opower(_710610), _710612), _710616))))], (6375 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_710610, hAPP(hAPP(c_Power_Opower__class_Opower(_710610), _710612), _710614)), hAPP(hAPP(c_Power_Opower__class_Opower(_710610), _710612), _710616))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _710614), _710616)))]]], (8186 ^ _490194) ^ [_776442, _776444, _776446, _776448] : [class_Rings_Ocomm__semiring(_776442), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_776442), c_Groups_Oplus__class_Oplus(_776442, _776444, _776446)), _776448) = c_Groups_Oplus__class_Oplus(_776442, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_776442), _776444), _776448), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_776442), _776446), _776448)))], (6423 ^ _490194) ^ [_712481, _712483, _712485, _712487] : [class_Groups_Omonoid__mult(_712481), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _712483), _712485)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_712481), _712487), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_712485), _712483)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_712481), hAPP(hAPP(c_Power_Opower__class_Opower(_712481), _712487), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _712485, _712483))), _712487))], (8250 ^ _490194) ^ [_779506, _779508, _779510, _779512] : [class_RealVector_Oreal__normed__algebra(_779506), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_779506), _779508), c_Groups_Oplus__class_Oplus(_779506, _779510, _779512)) = c_Groups_Oplus__class_Oplus(_779506, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_779506), _779508), _779510), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_779506), _779508), _779512)))], (6719 ^ _490194) ^ [_723308, _723310, _723312] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _723308), 6722 ^ _490194 : [(6729 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _723310), _723312)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _723308), _723310)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _723308), _723312))))], (6723 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _723308), _723310)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _723308), _723312))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _723310), _723312)))]]], (10641 ^ _490194) ^ [_871026, _871028, _871030, _871032, _871034] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _871026), _871028)), 10644 ^ _490194 : [(10651 ^ _490194) ^ [] : [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, _871028, _871026)), _871030), _871032), _871034), -(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), _871028), _871030), _871032), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _871026), _871030), _871034)))], (10645 ^ _490194) ^ [] : [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), _871028), _871030), _871032), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _871026), _871030), _871034)), -(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, _871028, _871026)), _871030), _871032), _871034))]]], (2737 ^ _490194) ^ [_580886, _580888] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _580886, _580888)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _580886), _580888)), -(_580886 = _580888)], (5891 ^ _490194) ^ [_693908, _693910, _693912] : [class_Power_Opower(_693908), -(hAPP(hAPP(c_Power_Opower__class_Opower(_693908), _693910), c_Nat_OSuc(_693912)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_693908), _693910), hAPP(hAPP(c_Power_Opower__class_Opower(_693908), _693910), _693912)))], (9840 ^ _490194) ^ [_838784, _838786, _838788] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _838784), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _838786, _838788)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _838784), _838786), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _838784), _838788)))], (4043 ^ _490194) ^ [_627803, _627805] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _627803), _627805)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_627803)), c_Nat_OSuc(_627805))))], (6433 ^ _490194) ^ [_712890, _712892, _712894] : [class_Power_Opower(_712890), 6436 ^ _490194 : [(6443 ^ _490194) ^ [] : [-(_712892 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_712890), _712894), _712892) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_712890), _712894), hAPP(hAPP(c_Power_Opower__class_Opower(_712890), _712894), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _712892, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (6437 ^ _490194) ^ [] : [_712892 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_712890), _712894), _712892) = c_Groups_Oone__class_Oone(_712890))]]], (11590 ^ _490194) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (10789 ^ _490194) ^ [] : [-(c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (8434 ^ _490194) ^ [_786600, _786602, _786604, _786606] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_786600), 8437 ^ _490194 : [(8444 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_786600, _786604), _786606)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_786600, c_Groups_Oplus__class_Oplus(_786600, _786602, _786604)), c_Groups_Oplus__class_Oplus(_786600, _786602, _786606))))], (8438 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_786600, c_Groups_Oplus__class_Oplus(_786600, _786602, _786604)), c_Groups_Oplus__class_Oplus(_786600, _786602, _786606))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_786600, _786604), _786606)))]]], (6253 ^ _490194) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (3160 ^ _490194) ^ [_596475, _596477] : [class_Rings_Olinordered__idom(_596475), -(c_Groups_Oabs__class_Oabs(_596475, hAPP(c_Nat_Osemiring__1__class_Oof__nat(_596475), _596477)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_596475), _596477))], (11658 ^ _490194) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (3194 ^ _490194) ^ [_597707, _597709] : [class_Groups_Oordered__ab__group__add__abs(_597707), 3197 ^ _490194 : [(3204 ^ _490194) ^ [] : [_597709 = c_Groups_Ozero__class_Ozero(_597707), -(c_Groups_Oabs__class_Oabs(_597707, _597709) = c_Groups_Ozero__class_Ozero(_597707))], (3198 ^ _490194) ^ [] : [c_Groups_Oabs__class_Oabs(_597707, _597709) = c_Groups_Ozero__class_Ozero(_597707), -(_597709 = c_Groups_Ozero__class_Ozero(_597707))]]], (8039 ^ _490194) ^ [_769891, _769893] : [class_Rings_Ocomm__semiring__1(_769891), -(hAPP(hAPP(c_Power_Opower__class_Opower(_769891), _769893), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _769893)], (11840 ^ _490194) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal))], (11936 ^ _490194) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex))], (3182 ^ _490194) ^ [_597241, _597243, _597245] : [class_RealVector_Oreal__normed__algebra__1(_597241), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_597241, hAPP(hAPP(c_Power_Opower__class_Opower(_597241), _597243), _597245))), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_597241, _597243)), _597245))))], (3106 ^ _490194) ^ [_594248, _594250] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), hAPP(c_RealDef_Oreal(tc_Nat_Onat), _594248)), _594250) = hAPP(c_RealDef_Oreal(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _594248), _594250)))], (1130 ^ _490194) ^ [_526629, _526631, _526633, _526635] : [-(c_Orderings_Oord__class_Oless__eq(_526635, _526631) = c_Orderings_Oord__class_Oless__eq(_526633, _526629)), _526635 = _526633, _526631 = _526629], (3931 ^ _490194) ^ [_624037, _624039] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _624037, _624039), -(c_Nat_OSuc(_624037) = _624039), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_624037), _624039))], (11312 ^ _490194) ^ [_896187, _896189] : [class_Rings_Odivision__ring(_896187), -(c_Rings_Oinverse__class_Odivide(_896187, c_Groups_Ozero__class_Ozero(_896187), _896189) = c_Groups_Ozero__class_Ozero(_896187))], (11628 ^ _490194) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (11642 ^ _490194) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (8500 ^ _490194) ^ [_788966, _788968, _788970, _788972] : [class_Groups_Oordered__cancel__ab__semigroup__add(_788966), c_Orderings_Oord__class_Oless(_788966, _788968, _788970), -(c_Orderings_Oord__class_Oless(_788966, c_Groups_Oplus__class_Oplus(_788966, _788972, _788968), c_Groups_Oplus__class_Oplus(_788966, _788972, _788970)))], (5631 ^ _490194) ^ [_683426, _683428, _683430, _683432] : [class_RealVector_Oreal__normed__algebra(_683426), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_683426), c_Groups_Ominus__class_Ominus(_683426, _683428, _683430)), _683432) = c_Groups_Ominus__class_Ominus(_683426, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_683426), _683428), _683432), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_683426), _683430), _683432)))], (6585 ^ _490194) ^ [_718362, _718364, _718366] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _718362), c_Groups_Ominus__class_Ominus(tc_Int_Oint, _718364, _718366)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _718362), _718364), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _718362), _718366)))], (822 ^ _490194) ^ [_515164, _515166] : [-(class_Rings_Ocomm__semiring__1(_515164)), _515166 = _515164, class_Rings_Ocomm__semiring__1(_515166)], (8692 ^ _490194) ^ [_796421, _796423, _796425, _796427, _796429] : [class_RealVector_Oreal__normed__vector(_796421), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_796421, c_Groups_Ominus__class_Ominus(_796421, c_Groups_Oplus__class_Oplus(_796421, _796423, _796425), c_Groups_Oplus__class_Oplus(_796421, _796427, _796429)))), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_796421, c_Groups_Ominus__class_Ominus(_796421, _796423, _796427)), c_RealVector_Onorm__class_Onorm(_796421, c_Groups_Ominus__class_Ominus(_796421, _796425, _796429))))))], (11912 ^ _490194) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex))], (5023 ^ _490194) ^ [_662150, _662152] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _662150)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _662152)), 5030 ^ _490194 : [(5037 ^ _490194) ^ [] : [_662150 = _662152, -(hAPP(c_Int_Onat, _662150) = hAPP(c_Int_Onat, _662152))], (5031 ^ _490194) ^ [] : [hAPP(c_Int_Onat, _662150) = hAPP(c_Int_Onat, _662152), -(_662150 = _662152)]]], (10019 ^ _490194) ^ [_846021, _846023] : [class_Groups_Ocomm__monoid__add(_846021), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_846021), _846023, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_846021))) = _846023)], (12022 ^ _490194) ^ [_917616] : [class_Rings_Olinordered__idom(_917616), -(class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(_917616)))], (5091 ^ _490194) ^ [_664509] : [hAPP(c_Int_Onat, _664509) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _664509), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (3023 ^ _490194) ^ [_591310] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _591310), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), hAPP(c_RealDef_Oreal(tc_Nat_Onat), _591310)))], (3122 ^ _490194) ^ [_594869, _594871, _594873] : [class_Rings_Olinordered__idom(_594869), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_594869, c_Groups_Ozero__class_Ozero(_594869)), hAPP(hAPP(c_Power_Opower__class_Opower(_594869), c_Groups_Oabs__class_Oabs(_594869, _594871)), _594873))))], (11714 ^ _490194) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (1949 ^ _490194) ^ [_554192, _554194, _554196, _554198] : [class_Orderings_Oorder(_554192), c_Orderings_Oord__class_Oless(_554192, _554194, _554196), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_554192, _554198), _554194)), -(c_Orderings_Oord__class_Oless(_554192, _554198, _554196))], (3102 ^ _490194) ^ [_594035] : [-(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _594035)) = hAPP(c_RealDef_Oreal(tc_Nat_Onat), _594035))], (1140 ^ _490194) ^ [_526988, _526990, _526992, _526994] : [-(c_RealVector_Onorm__class_Onorm(_526994, _526990) = c_RealVector_Onorm__class_Onorm(_526992, _526988)), _526994 = _526992, _526990 = _526988], (5575 ^ _490194) ^ [_681136] : [class_Rings_Osemiring__1(_681136), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_681136), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_681136))], (2971 ^ _490194) ^ [_589302] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _589302), _589302)))], (622 ^ _490194) ^ [_509264, _509266] : [-(class_Groups_Omonoid__mult(_509264)), _509266 = _509264, class_Groups_Omonoid__mult(_509266)], (3064 ^ _490194) ^ [_592760, _592762] : [class_Groups_Oab__group__add(_592760), -(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_592760), _592762, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_592760))) = _592762)], (9048 ^ _490194) ^ [_809201, _809203] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _809201)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _809203)), -(hBOOL(hAPP(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, _809201, _809203))))], (11844 ^ _490194) ^ [] : [-(class_Rings_Oordered__semiring(tc_RealDef_Oreal))], (7985 ^ _490194) ^ [_767285, _767287, _767289, _767291, _767293] : [class_Rings_Ocomm__semiring__1(_767285), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_767285), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_767285), _767287), _767289)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_767285), _767291), _767293)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_767285), _767287), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_767285), _767289), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_767285), _767291), _767293))))], (2 ^ _490194) ^ [_490318] : [-(_490318 = _490318)], (6271 ^ _490194) ^ [_707327, _707329] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _707327, _707329), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _707327), c_Groups_Ominus__class_Ominus(tc_Int_Oint, _707329, c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (8272 ^ _490194) ^ [_780614, _780616, _780618, _780620] : [class_Rings_Ocomm__semiring__1(_780614), -(c_Groups_Oplus__class_Oplus(_780614, _780616, c_Groups_Oplus__class_Oplus(_780614, _780618, _780620)) = c_Groups_Oplus__class_Oplus(_780614, c_Groups_Oplus__class_Oplus(_780614, _780616, _780618), _780620))], (6797 ^ _490194) ^ [_725942, _725944, _725946] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _725942, _725944), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _725946), -(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), _725946)), _725942), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _725946)), _725944)))], (4909 ^ _490194) ^ [_658016, _658018, _658020] : [class_Fields_Ofield(_658016), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_658016, _658018), c_Polynomial_Odegree(_658016, _658020)), -(c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_658016), _658018, _658020) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_658016)))], (2729 ^ _490194) ^ [_580636, _580638] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _580636, _580638), 2732 ^ _490194 : [(2735 ^ _490194) ^ [] : [_580636 = _580638], (2733 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _580636), _580638)))]]], (11674 ^ _490194) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (8486 ^ _490194) ^ [_788488, _788490, _788492, _788494, _788496] : [class_Groups_Oordered__cancel__ab__semigroup__add(_788488), c_Orderings_Oord__class_Oless(_788488, _788490, _788492), c_Orderings_Oord__class_Oless(_788488, _788494, _788496), -(c_Orderings_Oord__class_Oless(_788488, c_Groups_Oplus__class_Oplus(_788488, _788490, _788494), c_Groups_Oplus__class_Oplus(_788488, _788492, _788496)))], (2835 ^ _490194) ^ [_584456, _584458] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _584456, _584458)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _584456), _584458)), -(_584456 = _584458)], (11468 ^ _490194) ^ [_901809] : [-(c_Complex_Orcis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _901809) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))], (8232 ^ _490194) ^ [_778570, _778572, _778574, _778576] : [class_RealVector_Oreal__normed__algebra(_778570), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_778570), c_Groups_Oplus__class_Oplus(_778570, _778572, _778574)), _778576) = c_Groups_Oplus__class_Oplus(_778570, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_778570), _778572), _778576), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_778570), _778574), _778576)))], (11318 ^ _490194) ^ [_896411, _896413] : [class_Rings_Odivision__ring__inverse__zero(_896411), -(c_Rings_Oinverse__class_Odivide(_896411, _896413, c_Groups_Ozero__class_Ozero(_896411)) = c_Groups_Ozero__class_Ozero(_896411))], (11754 ^ _490194) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (11728 ^ _490194) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (4276 ^ _490194) ^ [_636223, _636225, _636227, _636229] : [class_Rings_Olinordered__semidom(_636223), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_636223, hAPP(hAPP(c_Power_Opower__class_Opower(_636223), _636225), c_Nat_OSuc(_636227))), hAPP(hAPP(c_Power_Opower__class_Opower(_636223), _636229), c_Nat_OSuc(_636227)))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_636223, c_Groups_Ozero__class_Ozero(_636223)), _636229)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_636223, _636225), _636229)))], (2235 ^ _490194) ^ [_563148, _563150, _563152] : [class_Groups_Ogroup__add(_563148), 2238 ^ _490194 : [(2245 ^ _490194) ^ [] : [_563150 = _563152, -(c_Groups_Ominus__class_Ominus(_563148, _563150, _563152) = c_Groups_Ozero__class_Ozero(_563148))], (2239 ^ _490194) ^ [] : [c_Groups_Ominus__class_Ominus(_563148, _563150, _563152) = c_Groups_Ozero__class_Ozero(_563148), -(_563150 = _563152)]]], (11870 ^ _490194) ^ [] : [-(class_Rings_Ozero__neq__one(tc_RealDef_Oreal))], (11606 ^ _490194) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (5343 ^ _490194) ^ [_672542, _672544] : [-(_672542 = hAPP(c_Int_Onat, _672544)), 5346 ^ _490194 : [(5349 ^ _490194) ^ [] : [_672544 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _672542)], (5347 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _672544)))]], 5350 ^ _490194 : [(5353 ^ _490194) ^ [] : [_672542 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5351 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _672544))]]], (11670 ^ _490194) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (1733 ^ _490194) ^ [_547359, _547361, _547363] : [class_Orderings_Oorder(_547359), c_Orderings_Oord__class_Oless(_547359, _547361, _547363), c_Orderings_Oord__class_Oless(_547359, _547363, _547361)], (7663 ^ _490194) ^ [_755596, _755598, _755600, _755602] : [class_Rings_Olinordered__ring__strict(_755596), c_Orderings_Oord__class_Oless(_755596, _755598, c_Groups_Ozero__class_Ozero(_755596)), 7670 ^ _490194 : [(7677 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_755596, _755602), _755600)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_755596, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_755596), _755598), _755600)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_755596), _755598), _755602))))], (7671 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_755596, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_755596), _755598), _755600)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_755596), _755598), _755602))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_755596, _755602), _755600)))]]], (5497 ^ _490194) ^ [_678095, _678097, _678099] : [class_Rings_Olinordered__semidom(_678095), c_Orderings_Oord__class_Oless(_678095, c_Groups_Oone__class_Oone(_678095), _678097), -(c_Orderings_Oord__class_Oless(_678095, hAPP(hAPP(c_Power_Opower__class_Opower(_678095), _678097), _678099), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_678095), _678097), hAPP(hAPP(c_Power_Opower__class_Opower(_678095), _678097), _678099))))], (6129 ^ _490194) ^ [_702416, _702418, _702420, _702422] : [class_Rings_Olinordered__semidom(_702416), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _702418), _702420)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_702416, c_Groups_Oone__class_Oone(_702416)), _702422)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_702416, hAPP(hAPP(c_Power_Opower__class_Opower(_702416), _702422), _702418)), hAPP(hAPP(c_Power_Opower__class_Opower(_702416), _702422), _702420))))], (2171 ^ _490194) ^ [_561126, _561128, _561130] : [class_Orderings_Oorder(_561126), 2174 ^ _490194 : [(2183 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(_561126, _561128, _561130)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_561126, _561128), _561130)), -(_561128 = _561130)], (2175 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(_561126, _561128, _561130), 2178 ^ _490194 : [(2181 ^ _490194) ^ [] : [_561128 = _561130], (2179 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_561126, _561128), _561130)))]]]]], (6051 ^ _490194) ^ [_699791, _699793] : [class_Power_Opower(_699791), class_Rings_Osemiring__0(_699791), 6058 ^ _490194 : [(6065 ^ _490194) ^ [] : [-(_699793 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_699791), c_Groups_Ozero__class_Ozero(_699791)), _699793) = c_Groups_Ozero__class_Ozero(_699791))], (6059 ^ _490194) ^ [] : [_699793 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_699791), c_Groups_Ozero__class_Ozero(_699791)), _699793) = c_Groups_Oone__class_Oone(_699791))]]], (11566 ^ _490194) ^ [] : [-(class_Rings_Ocomm__ring(tc_Int_Oint))], (9913 ^ _490194) ^ [_841685, _841687, _841689] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _841685, _841687), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _841685, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _841687, _841689)))], (6757 ^ _490194) ^ [_724504, _724506, _724508] : [class_Rings_Olinordered__idom(_724504), -(_724506 = _724508), -(c_Orderings_Oord__class_Oless(_724504, _724506, _724508)), -(c_Orderings_Oord__class_Oless(_724504, _724508, _724506))], (8258 ^ _490194) ^ [_779925, _779927, _779929] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _779925), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _779927, _779929)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _779925), _779927), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _779925), _779929)))], (11660 ^ _490194) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (9464 ^ _490194) ^ [_824950] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _824950)), -(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), _824950)))], (5601 ^ _490194) ^ [_682158, _682160] : [class_RealVector_Oreal__normed__algebra(_682158), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_682158), _682160), c_Groups_Ozero__class_Ozero(_682158)) = c_Groups_Ozero__class_Ozero(_682158))], (3813 ^ _490194) ^ [_619899, _619901] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _619899), _619901)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _619899)), _619901))], (9295 ^ _490194) ^ [_818303, _818305, _818307, _818309, _818311, _818313] : [class_Rings_Oordered__ring(_818303), 9298 ^ _490194 : [(9305 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(_818303, c_Groups_Oplus__class_Oplus(_818303, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_818303), c_Groups_Ominus__class_Ominus(_818303, _818305, _818311)), _818307), _818309), _818313), -(c_Orderings_Oord__class_Oless(_818303, c_Groups_Oplus__class_Oplus(_818303, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_818303), _818305), _818307), _818309), c_Groups_Oplus__class_Oplus(_818303, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_818303), _818311), _818307), _818313)))], (9299 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(_818303, c_Groups_Oplus__class_Oplus(_818303, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_818303), _818305), _818307), _818309), c_Groups_Oplus__class_Oplus(_818303, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_818303), _818311), _818307), _818313)), -(c_Orderings_Oord__class_Oless(_818303, c_Groups_Oplus__class_Oplus(_818303, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_818303), c_Groups_Ominus__class_Ominus(_818303, _818305, _818311)), _818307), _818309), _818313))]]], (11272 ^ _490194) ^ [_894530, _894532] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, _894530, _894532)))), 11275 ^ _490194 : [(11278 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _894532))], (11276 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _894530), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))]], 11279 ^ _490194 : [(11282 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _894532), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (11280 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _894530))]]], (6335 ^ _490194) ^ [_709491, _709493, _709495, _709497] : [class_Rings_Olinordered__semidom(_709491), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _709493), _709495)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_709491, c_Groups_Ozero__class_Ozero(_709491)), _709497)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_709491, _709497), c_Groups_Oone__class_Oone(_709491))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_709491, hAPP(hAPP(c_Power_Opower__class_Opower(_709491), _709497), _709495)), hAPP(hAPP(c_Power_Opower__class_Opower(_709491), _709497), _709493))))], (6689 ^ _490194) ^ [_722230] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_722230), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _722230)], (1991 ^ _490194) ^ [_555519, _555521, _555523] : [class_Orderings_Oorder(_555519), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_555519, _555521), _555523)), -(_555521 = _555523), -(c_Orderings_Oord__class_Oless(_555519, _555521, _555523))], (4308 ^ _490194) ^ [_637318, _637320] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _637318), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _637318, c_Nat_OSuc(_637320)), _637318))], (3947 ^ _490194) ^ [_624569, _624571] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _624569, _624571)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _624569, c_Nat_OSuc(_624571)), -(_624571 = _624569)], (11066 ^ _490194) ^ [_886846, _886848, _886850, _886852, _886854, _886856, _886858] : [class_Fields_Ofield(_886846), c_Polynomial_Opdivmod__rel(_886846, _886848, _886850, _886852, _886854), c_Polynomial_Opdivmod__rel(_886846, _886848, _886850, _886856, _886858), -(_886854 = _886858)], (502 ^ _490194) ^ [_505724, _505726] : [-(class_Rings_Oordered__semiring(_505724)), _505726 = _505724, class_Rings_Oordered__semiring(_505726)], (8662 ^ _490194) ^ [_795324, _795326, _795328, _795330] : [class_Groups_Ocancel__semigroup__add(_795324), c_Groups_Oplus__class_Oplus(_795324, _795326, _795328) = c_Groups_Oplus__class_Oplus(_795324, _795326, _795330), -(_795328 = _795330)], (1851 ^ _490194) ^ [_551070, _551072, _551074] : [class_Orderings_Olinorder(_551070), 1854 ^ _490194 : [(1855 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(_551070, _551072, _551074)), -(c_Orderings_Oord__class_Oless(_551070, _551074, _551072)), -(_551072 = _551074)], (1865 ^ _490194) ^ [] : [1866 ^ _490194 : [(1869 ^ _490194) ^ [] : [_551072 = _551074], (1867 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(_551070, _551074, _551072)]], c_Orderings_Oord__class_Oless(_551070, _551072, _551074)]]], (9925 ^ _490194) ^ [_842183, _842185, _842187, _842189] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _842183, _842185), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _842187, _842185) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _842183, _842189), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _842187, _842189))], (9423 ^ _490194) ^ [_823449, _823451] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _823449, _823451), -(_823451 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _823449, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Nat_OSuc(9426 ^ [_823449, _823451]))))], (11928 ^ _490194) ^ [] : [-(class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex))], (5661 ^ _490194) ^ [_684997, _684999, _685001] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _684997), _684999) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _685001), _684999), -(_684997 = _685001), -(_684999 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4290 ^ _490194) ^ [_636739, _636741, _636743, _636745] : [class_Rings_Olinordered__semidom(_636739), hAPP(hAPP(c_Power_Opower__class_Opower(_636739), _636741), c_Nat_OSuc(_636743)) = hAPP(hAPP(c_Power_Opower__class_Opower(_636739), _636745), c_Nat_OSuc(_636743)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_636739, c_Groups_Ozero__class_Ozero(_636739)), _636741)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_636739, c_Groups_Ozero__class_Ozero(_636739)), _636745)), -(_636741 = _636745)], (126 ^ _490194) ^ [_494524, _494526, _494528, _494530, _494532, _494534, _494536, _494538, _494540, _494542] : [-(c_Polynomial_Opdivmod__rel(_494540, _494536, _494532, _494528, _494524)), c_Polynomial_Opdivmod__rel(_494542, _494538, _494534, _494530, _494526), _494542 = _494540, _494538 = _494536, _494534 = _494532, _494530 = _494528, _494526 = _494524], (3911 ^ _490194) ^ [_623394, _623396] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _623394, c_Nat_OSuc(_623396)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _623394, _623396)), -(_623394 = _623396)], (9157 ^ _490194) ^ [_812956, _812958, _812960] : [class_Groups_Oordered__comm__monoid__add(_812956), c_Orderings_Oord__class_Oless(_812956, _812958, c_Groups_Ozero__class_Ozero(_812956)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_812956, _812960), c_Groups_Ozero__class_Ozero(_812956))), -(c_Orderings_Oord__class_Oless(_812956, c_Groups_Oplus__class_Oplus(_812956, _812958, _812960), c_Groups_Ozero__class_Ozero(_812956)))], (3829 ^ _490194) ^ [_620530, _620532] : [_620530 = _620532, -(c_Nat_OSuc(_620530) = c_Nat_OSuc(_620532))], (9030 ^ _490194) ^ [_808383, _808385, _808387] : [class_Rings_Ocomm__semiring__1(_808383), -(c_Groups_Oplus__class_Oplus(_808383, _808385, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_808383), _808387), _808385)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_808383), c_Groups_Oplus__class_Oplus(_808383, _808387, c_Groups_Oone__class_Oone(_808383))), _808385))], (7055 ^ _490194) ^ [_734903, _734905, _734907] : [class_Rings_Oordered__cancel__semiring(_734903), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_734903, c_Groups_Ozero__class_Ozero(_734903)), _734905)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_734903, _734907), c_Groups_Ozero__class_Ozero(_734903))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_734903, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_734903), _734905), _734907)), c_Groups_Ozero__class_Ozero(_734903))))], (11634 ^ _490194) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (212 ^ _490194) ^ [_497169, _497171] : [-(class_RealVector_Oreal__normed__field(_497169)), _497171 = _497169, class_RealVector_Oreal__normed__field(_497171)], (2469 ^ _490194) ^ [_571765, _571767, _571769] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _571765), _571767)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _571765), _571769)), 2476 ^ _490194 : [(2483 ^ _490194) ^ [] : [_571767 = _571769, -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _571767, _571765) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _571769, _571765))], (2477 ^ _490194) ^ [] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _571767, _571765) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _571769, _571765), -(_571767 = _571769)]]], (6863 ^ _490194) ^ [_728370, _728372] : [class_Rings_Omult__zero(_728370), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_728370), _728372), c_Groups_Ozero__class_Ozero(_728370)) = c_Groups_Ozero__class_Ozero(_728370))], (10872 ^ _490194) ^ [] : [c_Complex_Oii = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)], (6807 ^ _490194) ^ [_726293, _726295] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _726293)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _726293), _726295)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _726293)), hAPP(c_Int_Onat, _726295)))], (11726 ^ _490194) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (6233 ^ _490194) ^ [_706076, _706078] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _706076), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _706076), _706078), _706076) = _706078)], (6791 ^ _490194) ^ [_725686, _725688, _725690] : [class_Rings_Ocomm__semiring__0(_725686), -(c_Polynomial_Odegree(_725686, c_Polynomial_Osynthetic__div(_725686, _725688, _725690)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Polynomial_Odegree(_725686, _725688), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (8890 ^ _490194) ^ [_802855, _802857] : [class_Rings_Olinordered__idom(_802855), 8893 ^ _490194 : [(8900 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(_802855, _802857, c_Groups_Ozero__class_Ozero(_802855)), -(c_Orderings_Oord__class_Oless(_802855, c_Groups_Oplus__class_Oplus(_802855, _802857, _802857), c_Groups_Ozero__class_Ozero(_802855)))], (8894 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(_802855, c_Groups_Oplus__class_Oplus(_802855, _802857, _802857), c_Groups_Ozero__class_Ozero(_802855)), -(c_Orderings_Oord__class_Oless(_802855, _802857, c_Groups_Ozero__class_Ozero(_802855)))]]], (12244 ^ _490194) ^ [_924646] : [class_Groups_Ocomm__monoid__add(_924646), -(class_Groups_Omonoid__add(tc_Polynomial_Opoly(_924646)))], (5263 ^ _490194) ^ [_670060, _670062] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _670060)), 5266 ^ _490194 : [(5273 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _670060, _670062), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(c_Int_Onat, _670060), hAPP(c_Int_Onat, _670062)))], (5267 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(c_Int_Onat, _670060), hAPP(c_Int_Onat, _670062)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _670060, _670062))]]], (9969 ^ _490194) ^ [_843856, _843858, _843860] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _843858, _843860), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _843856, _843858), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _843856, _843860)))], (7961 ^ _490194) ^ [_766023, _766025, _766027, _766029] : [class_Rings_Ocomm__semiring__1(_766023), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_766023), _766025), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_766023), _766027), _766029)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_766023), _766027), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_766023), _766025), _766029)))], (11650 ^ _490194) ^ [] : [-(class_Divides_Osemiring__div(tc_Int_Oint))], (9411 ^ _490194) ^ [_822958, _822960] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _822958, _822960), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _822958, c_Groups_Oone__class_Oone(tc_Int_Oint))), _822960)))], (10317 ^ _490194) ^ [_857727, _857729, _857731] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _857727, _857729)), _857731)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _857727), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _857731, _857729))))], (9311 ^ _490194) ^ [_818951, _818953] : [class_Rings_Oring__1(_818951), -(c_Groups_Ominus__class_Ominus(_818951, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_818951), _818953), _818953), c_Groups_Oone__class_Oone(_818951)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_818951), c_Groups_Oplus__class_Oplus(_818951, _818953, c_Groups_Oone__class_Oone(_818951))), c_Groups_Ominus__class_Ominus(_818951, _818953, c_Groups_Oone__class_Oone(_818951))))], (4488 ^ _490194) ^ [_643921] : [4490 ^ _490194 : [(4493 ^ _490194) ^ [] : [hBOOL(hAPP(_643921, 4489 ^ [_643921]))], (4491 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 4489 ^ [_643921])))]], 4494 ^ _490194 : [(4495 ^ _490194) ^ [_644184] : [-(hBOOL(hAPP(_643921, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _644184))))]]], (10261 ^ _490194) ^ [_855622, _855624, _855626] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _855622, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _855624, _855626)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _855622, _855626), _855624))], (4269 ^ _490194) ^ [_635908] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(_635908, 4270 ^ [_635908]), hAPP(_635908, c_Nat_OSuc(4270 ^ [_635908]))), -(c_SEQ_Osubseq(_635908))], (352 ^ _490194) ^ [_501299, _501301] : [-(class_Groups_Ocancel__ab__semigroup__add(_501299)), _501301 = _501299, class_Groups_Ocancel__ab__semigroup__add(_501301)], (20 ^ _490194) ^ [_490970, _490972, _490974, _490976] : [-(c_SEQ_Odecseq(_490974, _490970)), c_SEQ_Odecseq(_490976, _490972), _490976 = _490974, _490972 = _490970], (9012 ^ _490194) ^ [_807395, _807397, _807399, _807401, _807403] : [class_Rings_Oring(_807395), -(c_Groups_Ominus__class_Ominus(_807395, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_807395), _807397), _807399), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_807395), _807401), _807403)) = c_Groups_Oplus__class_Oplus(_807395, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_807395), _807397), c_Groups_Ominus__class_Ominus(_807395, _807399, _807403)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_807395), c_Groups_Ominus__class_Ominus(_807395, _807397, _807401)), _807403)))], (8256 ^ _490194) ^ [_779789, _779791, _779793] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _779789, _779791)), _779793) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _779789), _779793), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _779791), _779793)))], (3128 ^ _490194) ^ [_595090] : [-(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, _595090) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _595090))], (532 ^ _490194) ^ [_506609, _506611] : [-(class_Rings_Olinordered__ring(_506609)), _506611 = _506609, class_Rings_Olinordered__ring(_506611)], (11104 ^ _490194) ^ [_888180] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _888180)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_RComplete_Onatfloor(_888180))), _888180)))], (5163 ^ _490194) ^ [_666832, _666834] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _666832) = _666834, 5166 ^ _490194 : [(5169 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _666834)))], (5167 ^ _490194) ^ [] : [-(_666832 = hAPP(c_Int_Onat, _666834))]]], (5783 ^ _490194) ^ [_689841, _689843, _689845] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _689841), _689843)), _689845) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _689841), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _689843), _689845)))], (11724 ^ _490194) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (2409 ^ _490194) ^ [_569747, _569749, _569751] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _569747, _569749), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _569751), _569747)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _569747, _569751), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _569749, _569751)))], (3142 ^ _490194) ^ [_595719, _595721, _595723] : [class_Rings_Olinordered__idom(_595719), -(c_Groups_Oabs__class_Oabs(_595719, hAPP(hAPP(c_Power_Opower__class_Opower(_595719), _595721), _595723)) = hAPP(hAPP(c_Power_Opower__class_Opower(_595719), c_Groups_Oabs__class_Oabs(_595719, _595721)), _595723))], (9907 ^ _490194) ^ [_841443, _841445, _841447] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _841443, _841445), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _841443, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _841447, _841445)))], (8466 ^ _490194) ^ [_787744, _787746, _787748, _787750] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_787744), c_Orderings_Oord__class_Oless(_787744, c_Groups_Oplus__class_Oplus(_787744, _787746, _787748), c_Groups_Oplus__class_Oplus(_787744, _787746, _787750)), -(c_Orderings_Oord__class_Oless(_787744, _787748, _787750))], (612 ^ _490194) ^ [_508969, _508971] : [-(class_Orderings_Olinorder(_508969)), _508971 = _508969, class_Orderings_Olinorder(_508971)], (11192 ^ _490194) ^ [_891396, _891398] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _891396)), _891398)), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _891398, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _891396), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_RComplete_Onatfloor(_891398) = _891396)], (11228 ^ _490194) ^ [_892855, _892857, _892859, _892861] : [class_Rings_Odivision__ring(_892855), -(c_Rings_Oinverse__class_Odivide(_892855, c_Groups_Oplus__class_Oplus(_892855, _892857, _892859), _892861) = c_Groups_Oplus__class_Oplus(_892855, c_Rings_Oinverse__class_Odivide(_892855, _892857, _892861), c_Rings_Oinverse__class_Odivide(_892855, _892859, _892861)))], (7097 ^ _490194) ^ [_736319, _736321, _736323] : [class_Rings_Oordered__ring(_736319), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_736319, _736321), c_Groups_Ozero__class_Ozero(_736319))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_736319, _736323), c_Groups_Ozero__class_Ozero(_736319))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_736319, c_Groups_Ozero__class_Ozero(_736319)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_736319), _736321), _736323))))], (11744 ^ _490194) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Nat_Onat))], (9957 ^ _490194) ^ [_843397, _843399, _843401] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _843397, _843399), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _843397, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _843399, _843401)))], (12004 ^ _490194) ^ [_917046] : [class_Rings_Olinordered__idom(_917046), -(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(_917046)))], (3410 ^ _490194) ^ [_604999, _605001, _605003] : [class_Groups_Oordered__ab__group__add__abs(_604999), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_604999, c_Groups_Ominus__class_Ominus(_604999, c_Groups_Oabs__class_Oabs(_604999, _605001), c_Groups_Oabs__class_Oabs(_604999, _605003))), c_Groups_Oabs__class_Oabs(_604999, c_Groups_Ominus__class_Ominus(_604999, _605003, _605001)))))], (7167 ^ _490194) ^ [_738837, _738839, _738841, _738843] : [class_Rings_Oordered__ring(_738837), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_738837, _738839), _738841)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_738837, _738843), c_Groups_Ozero__class_Ozero(_738837))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_738837, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_738837), _738843), _738841)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_738837), _738843), _738839))))], (6547 ^ _490194) ^ [_717126, _717128] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _717126), _717128), 6550 ^ _490194 : [(6553 ^ _490194) ^ [] : [-(_717128 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (6551 ^ _490194) ^ [] : [-(_717126 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (11978 ^ _490194) ^ [] : [-(class_Rings_Oring__1(tc_Complex_Ocomplex))], (10329 ^ _490194) ^ [_858199, _858201, _858203] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _858199), _858201)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _858203), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _858201, _858203), _858199))))], (3130 ^ _490194) ^ [_595203, _595205] : [class_Groups_Oordered__ab__group__add__abs(_595203), -(c_Groups_Oabs__class_Oabs(_595203, c_Groups_Oabs__class_Oabs(_595203, _595205)) = c_Groups_Oabs__class_Oabs(_595203, _595205))], (2005 ^ _490194) ^ [_555948, _555950, _555952] : [class_Orderings_Oorder(_555948), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_555948, _555950), _555952)), -(c_Orderings_Oord__class_Oless(_555948, _555950, _555952)), -(_555950 = _555952)], (8318 ^ _490194) ^ [_782468, _782470] : [class_Rings_Ocomm__semiring__1(_782468), -(c_Groups_Oplus__class_Oplus(_782468, c_Groups_Ozero__class_Ozero(_782468), _782470) = _782470)], (6555 ^ _490194) ^ [_717375, _717377] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _717375), _717377)), _717375 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _717377 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (1207 ^ _490194) ^ [_529559] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _529559), 1211 ^ _490194 : [(1212 ^ _490194) ^ [_529787] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, 1210 ^ [_529559]), _529787)), -(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(1202 ^ [], _529787)), 1205 ^ [])), _529559))]]], (2589 ^ _490194) ^ [_575797, _575799] : [-(_575797 = _575799), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _575797, _575799)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _575799, _575797))], (9213 ^ _490194) ^ [_814879, _814881, _814883] : [class_Rings_Olinordered__ring__strict(_814879), 9216 ^ _490194 : [(9217 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(_814879, c_Groups_Ozero__class_Ozero(_814879), c_Groups_Oplus__class_Oplus(_814879, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_814879), _814881), _814881), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_814879), _814883), _814883))), _814881 = c_Groups_Ozero__class_Ozero(_814879), _814883 = c_Groups_Ozero__class_Ozero(_814879)], (9227 ^ _490194) ^ [] : [9228 ^ _490194 : [(9231 ^ _490194) ^ [] : [-(_814883 = c_Groups_Ozero__class_Ozero(_814879))], (9229 ^ _490194) ^ [] : [-(_814881 = c_Groups_Ozero__class_Ozero(_814879))]], -(c_Orderings_Oord__class_Oless(_814879, c_Groups_Ozero__class_Ozero(_814879), c_Groups_Oplus__class_Oplus(_814879, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_814879), _814881), _814881), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_814879), _814883), _814883))))]]], (11704 ^ _490194) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (3614 ^ _490194) ^ [_612149, _612151, _612153] : [-(hBOOL(hAPP(_612149, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _612151, _612153))))), 3617 ^ _490194 : [(3620 ^ _490194) ^ [] : [hBOOL(hAPP(_612149, c_Groups_Ominus__class_Ominus(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _612151), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _612153))))], (3618 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _612153), _612151)))]], 3621 ^ _490194 : [(3624 ^ _490194) ^ [] : [hBOOL(hAPP(_612149, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (3622 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _612151, _612153))]]], (7491 ^ _490194) ^ [_749614, _749616, _749618, _749620] : [class_Rings_Olinordered__semiring__strict(_749614), c_Orderings_Oord__class_Oless(_749614, _749616, _749618), c_Orderings_Oord__class_Oless(_749614, c_Groups_Ozero__class_Ozero(_749614), _749620), -(c_Orderings_Oord__class_Oless(_749614, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_749614), _749620), _749616), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_749614), _749620), _749618)))], (6835 ^ _490194) ^ [_727326, _727328] : [_727326 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _727328), _727326) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (1977 ^ _490194) ^ [_555090, _555092, _555094] : [class_Orderings_Oorder(_555090), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_555090, _555092), _555094)), -(_555094 = _555092), -(c_Orderings_Oord__class_Oless(_555090, _555092, _555094))], (9851 ^ _490194) ^ [_839327, _839329] : [9852 ^ _490194 : [(9853 ^ _490194) ^ [_839406] : [_839329 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _839327, _839406)]], -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _839327), _839329)))], (3372 ^ _490194) ^ [_603642, _603644] : [class_Groups_Oordered__ab__group__add__abs(_603642), 3375 ^ _490194 : [(3382 ^ _490194) ^ [] : [-(_603644 = c_Groups_Ozero__class_Ozero(_603642)), -(c_Orderings_Oord__class_Oless(_603642, c_Groups_Ozero__class_Ozero(_603642), c_Groups_Oabs__class_Oabs(_603642, _603644)))], (3376 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(_603642, c_Groups_Ozero__class_Ozero(_603642), c_Groups_Oabs__class_Oabs(_603642, _603644)), _603644 = c_Groups_Ozero__class_Ozero(_603642)]]], (3476 ^ _490194) ^ [_607390, _607392, _607394, _607396] : [class_Rings_Olinordered__semidom(_607390), c_Orderings_Oord__class_Oless(_607390, hAPP(hAPP(c_Power_Opower__class_Opower(_607390), _607392), _607394), hAPP(hAPP(c_Power_Opower__class_Opower(_607390), _607396), _607394)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_607390, c_Groups_Ozero__class_Ozero(_607390)), _607396)), -(c_Orderings_Oord__class_Oless(_607390, _607392, _607396))], (5671 ^ _490194) ^ [_685283, _685285, _685287] : [5672 ^ _490194 : [(5675 ^ _490194) ^ [] : [_685285 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5673 ^ _490194) ^ [] : [_685283 = _685287]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _685283), _685285) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _685287), _685285))], (11018 ^ _490194) ^ [_884795] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_RComplete_Onatfloor(_884795))))], (3238 ^ _490194) ^ [_599253, _599255, _599257] : [class_Rings_Olinordered__semidom(_599253), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_599253, c_Groups_Ozero__class_Ozero(_599253)), _599255)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_599253, c_Groups_Ozero__class_Ozero(_599253)), hAPP(hAPP(c_Power_Opower__class_Opower(_599253), _599255), _599257))))], (10966 ^ _490194) ^ [_883079, _883081] : [class_Fields_Ofield(_883079), -(c_Polynomial_Opdivmod__rel(_883079, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_883079)), _883081, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_883079)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_883079))))], (10130 ^ _490194) ^ [_850964, _850966, _850968, _850970] : [class_Groups_Omonoid__mult(_850964), -(hAPP(hAPP(c_Power_Opower__class_Opower(_850964), _850966), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _850968, _850970)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_850964), hAPP(hAPP(c_Power_Opower__class_Opower(_850964), _850966), _850968)), hAPP(hAPP(c_Power_Opower__class_Opower(_850964), _850966), _850970)))], (292 ^ _490194) ^ [_499529, _499531] : [-(class_Rings_Olinordered__semiring__1__strict(_499529)), _499531 = _499529, class_Rings_Olinordered__semiring__1__strict(_499531)], (10391 ^ _490194) ^ [_860559, _860561, _860563] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _860559), _860561)), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _860561, _860559), _860563) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _860561, _860563), _860559))], (3995 ^ _490194) ^ [_626069, _626071] : [3996 ^ _490194 : [(3999 ^ _490194) ^ [] : [_626069 = _626071], (3997 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _626069, _626071)]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _626069, c_Nat_OSuc(_626071)))], (9842 ^ _490194) ^ [_838920, _838922, _838924] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _838920, _838922)), _838924) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _838920), _838924), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _838922), _838924)))], (11618 ^ _490194) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (6239 ^ _490194) ^ [_706323] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint)), _706323)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _706323))], (11556 ^ _490194) ^ [] : [-(class_Rings_Ocomm__ring(tc_Complex_Ocomplex))], (11394 ^ _490194) ^ [_899180, _899182, _899184, _899186] : [class_Rings_Odivision__ring(_899180), -(_899182 = c_Groups_Ozero__class_Ozero(_899180)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_899180), _899184), _899182) = _899186, -(_899184 = c_Rings_Oinverse__class_Odivide(_899180, _899186, _899182))], (6937 ^ _490194) ^ [_730860, _730862] : [class_Rings_Olinordered__idom(_730860), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_730860), c_Groups_Oabs__class_Oabs(_730860, _730862)), c_Groups_Oabs__class_Oabs(_730860, _730862)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_730860), _730862), _730862))], (900 ^ _490194) ^ [_518248, _518250, _518252, _518254, _518256, _518258, _518260, _518262, _518264, _518266] : [-(c_Polynomial_Opoly__rec(_518266, _518262, _518258, _518254, _518250) = c_Polynomial_Opoly__rec(_518264, _518260, _518256, _518252, _518248)), _518266 = _518264, _518262 = _518260, _518258 = _518256, _518254 = _518252, _518250 = _518248], (4774 ^ _490194) ^ [_653626, _653628] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _653626), 4777 ^ _490194 : [(4784 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _653628)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _653628, _653626))))], (4778 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _653628, _653626))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _653628)))]]], (3324 ^ _490194) ^ [_602043, _602045, _602047] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _602043), c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _602043), _602045), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _602043), _602047)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _602045, _602047))], (3799 ^ _490194) ^ [_619404, _619406] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _619404) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _619406), -(_619404 = _619406)], (6869 ^ _490194) ^ [_728616, _728618, _728620] : [class_Rings_Oring__no__zero__divisors(_728616), 6872 ^ _490194 : [(6873 ^ _490194) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_728616), _728618), _728620) = c_Groups_Ozero__class_Ozero(_728616), -(_728618 = c_Groups_Ozero__class_Ozero(_728616)), -(_728620 = c_Groups_Ozero__class_Ozero(_728616))], (6883 ^ _490194) ^ [] : [6884 ^ _490194 : [(6887 ^ _490194) ^ [] : [_728620 = c_Groups_Ozero__class_Ozero(_728616)], (6885 ^ _490194) ^ [] : [_728618 = c_Groups_Ozero__class_Ozero(_728616)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_728616), _728618), _728620) = c_Groups_Ozero__class_Ozero(_728616))]]], (6575 ^ _490194) ^ [_718050, _718052] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _718050), _718052) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _718050 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _718052 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (10222 ^ _490194) ^ [_853971, _853973] : [-(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _853971), _853971), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _853973), _853973)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _853971 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _853973 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)], (1290 ^ _490194) ^ [_532444, _532446, _532448] : [class_RealVector_Oreal__normed__vector(_532444), -(c_RealVector_Onorm__class_Onorm(_532444, c_Groups_Ominus__class_Ominus(_532444, _532446, _532448)) = c_RealVector_Onorm__class_Onorm(_532444, c_Groups_Ominus__class_Ominus(_532444, _532448, _532446)))], (5845 ^ _490194) ^ [_692124, _692126, _692128] : [class_Divides_Osemiring__div(_692124), -(_692126 = c_Groups_Ozero__class_Ozero(_692124)), -(c_Divides_Odiv__class_Odiv(_692124, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_692124), _692128), _692126), _692126) = _692128)], (2203 ^ _490194) ^ [_562132, _562134, _562136] : [class_Orderings_Olinorder(_562132), 2206 ^ _490194 : [(2213 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(_562132, _562136, _562134), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_562132, _562134), _562136))], (2207 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_562132, _562134), _562136))), -(c_Orderings_Oord__class_Oless(_562132, _562136, _562134))]]], (7559 ^ _490194) ^ [_751921] : [class_Rings_Olinordered__semidom(_751921), c_Orderings_Oord__class_Oless(_751921, c_Groups_Oone__class_Oone(_751921), c_Groups_Ozero__class_Ozero(_751921))], (12172 ^ _490194) ^ [_922366] : [class_Rings_Ocomm__semiring__1(_922366), -(class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(_922366)))], (552 ^ _490194) ^ [_507199, _507201] : [-(class_Divides_Osemiring__div(_507199)), _507201 = _507199, class_Divides_Osemiring__div(_507201)], (8045 ^ _490194) ^ [_770129, _770131, _770133] : [class_Rings_Ocomm__semiring__1(_770129), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_770129), hAPP(hAPP(c_Power_Opower__class_Opower(_770129), _770131), _770133)), _770131) = hAPP(hAPP(c_Power_Opower__class_Opower(_770129), _770131), c_Nat_OSuc(_770133)))], (3875 ^ _490194) ^ [_622094] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_622094)], (6173 ^ _490194) ^ [_703876, _703878] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _703876), _703878))), 6176 ^ _490194 : [(6179 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _703878)))], (6177 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _703876)))]]], (9867 ^ _490194) ^ [_839894, _839896, _839898] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _839894), _839896)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _839898, _839894)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _839898, _839896))))], (7599 ^ _490194) ^ [_753326, _753328, _753330] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _753326), 7602 ^ _490194 : [(7609 ^ _490194) ^ [] : [_753328 = _753330, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _753326), _753328) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _753326), _753330))], (7603 ^ _490194) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _753326), _753328) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _753326), _753330), -(_753328 = _753330)]]], (11620 ^ _490194) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (7083 ^ _490194) ^ [_735847, _735849, _735851] : [class_Rings_Oordered__cancel__semiring(_735847), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_735847, _735849), c_Groups_Ozero__class_Ozero(_735847))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_735847, c_Groups_Ozero__class_Ozero(_735847)), _735851)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_735847, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_735847), _735849), _735851)), c_Groups_Ozero__class_Ozero(_735847))))], (10629 ^ _490194) ^ [_870546, _870548] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _870546), _870548)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _870546), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _870548), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))], (3793 ^ _490194) ^ [_619151, _619153] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _619151, _619153), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _619151, _619153))], (5689 ^ _490194) ^ [_685930, _685932, _685934] : [5690 ^ _490194 : [(5693 ^ _490194) ^ [] : [_685930 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5691 ^ _490194) ^ [] : [_685932 = _685934]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _685930), _685932) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _685930), _685934))], (5199 ^ _490194) ^ [_668012, _668014] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _668012), _668014), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _668012, hAPP(c_Int_Onat, _668014)))], (7553 ^ _490194) ^ [_751715] : [class_Rings_Olinordered__semidom(_751715), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_751715, c_Groups_Ozero__class_Ozero(_751715)), c_Groups_Oone__class_Oone(_751715))))], (11810 ^ _490194) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal))], (1508 ^ _490194) ^ [_539968, _539970, _539972, _539974] : [class_Orderings_Oorder(_539968), _539970 = _539972, hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_539968, _539974), _539972)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_539968, _539974), _539970)))], (11668 ^ _490194) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (11648 ^ _490194) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Int_Oint))], (7571 ^ _490194) ^ [_752346, _752348, _752350] : [class_Rings_Olinordered__semidom(_752346), c_Orderings_Oord__class_Oless(_752346, c_Groups_Oone__class_Oone(_752346), _752348), c_Orderings_Oord__class_Oless(_752346, c_Groups_Oone__class_Oone(_752346), _752350), -(c_Orderings_Oord__class_Oless(_752346, c_Groups_Oone__class_Oone(_752346), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_752346), _752348), _752350)))], (9764 ^ _490194) ^ [_835784, _835786, _835788, _835790] : [class_Rings_Olinordered__idom(_835784), 9767 ^ _490194 : [(9776 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(_835784, c_Groups_Oabs__class_Oabs(_835784, c_Groups_Ominus__class_Ominus(_835784, _835786, _835788)), _835790)), c_Orderings_Oord__class_Oless(_835784, c_Groups_Ominus__class_Ominus(_835784, _835788, _835790), _835786), c_Orderings_Oord__class_Oless(_835784, _835786, c_Groups_Oplus__class_Oplus(_835784, _835788, _835790))], (9768 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(_835784, c_Groups_Oabs__class_Oabs(_835784, c_Groups_Ominus__class_Ominus(_835784, _835786, _835788)), _835790), 9771 ^ _490194 : [(9774 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(_835784, _835786, c_Groups_Oplus__class_Oplus(_835784, _835788, _835790)))], (9772 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(_835784, c_Groups_Ominus__class_Ominus(_835784, _835788, _835790), _835786))]]]]], (11794 ^ _490194) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal))], (1773 ^ _490194) ^ [_548659, _548661, _548663] : [class_Orderings_Opreorder(_548659), c_Orderings_Oord__class_Oless(_548659, _548661, _548663), c_Orderings_Oord__class_Oless(_548659, _548663, _548661)], (6029 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (7007 ^ _490194) ^ [_733322, _733324, _733326] : [class_Rings_Olinordered__ring__strict(_733322), 7010 ^ _490194 : [(7025 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_733322, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_733322), _733324), _733326)), c_Groups_Ozero__class_Ozero(_733322)))), 7026 ^ _490194 : [(7033 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_733322, _733324), c_Groups_Ozero__class_Ozero(_733322))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_733322, c_Groups_Ozero__class_Ozero(_733322)), _733326))], (7027 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_733322, c_Groups_Ozero__class_Ozero(_733322)), _733324)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_733322, _733326), c_Groups_Ozero__class_Ozero(_733322)))]]], (7011 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_733322, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_733322), _733324), _733326)), c_Groups_Ozero__class_Ozero(_733322))), 7016 ^ _490194 : [(7019 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_733322, _733326), c_Groups_Ozero__class_Ozero(_733322))))], (7017 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_733322, c_Groups_Ozero__class_Ozero(_733322)), _733324)))]], 7020 ^ _490194 : [(7023 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_733322, c_Groups_Ozero__class_Ozero(_733322)), _733326)))], (7021 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_733322, _733324), c_Groups_Ozero__class_Ozero(_733322))))]]]]], (6017 ^ _490194) ^ [_698480, _698482, _698484] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_698480)), _698482)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_698480)), _698484))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _698482), _698484)))], (9095 ^ _490194) ^ [_810852, _810854] : [9096 ^ _490194 : [(9097 ^ _490194) ^ [_810934] : [_810854 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _810852, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _810934))]], -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _810852), _810854)))], (3100 ^ _490194) ^ [] : [-(c_RealDef_Oreal(tc_Nat_Onat) = c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal))], (8296 ^ _490194) ^ [_781756, _781758, _781760] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_781756), 8299 ^ _490194 : [(8306 ^ _490194) ^ [] : [_781760 = c_Groups_Ozero__class_Ozero(_781756), -(_781758 = c_Groups_Oplus__class_Oplus(_781756, _781758, _781760))], (8300 ^ _490194) ^ [] : [_781758 = c_Groups_Oplus__class_Oplus(_781756, _781758, _781760), -(_781760 = c_Groups_Ozero__class_Ozero(_781756))]]], (11138 ^ _490194) ^ [_889424] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat)), c_RComplete_Onatfloor(_889424))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _889424)))], (10089 ^ _490194) ^ [_849143, _849145, _849147] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _849143), _849145)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _849143), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _849145, _849147))))], (11150 ^ _490194) ^ [_889781] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _889781, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_RComplete_Onatfloor(_889781)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))], (152 ^ _490194) ^ [_495399, _495401] : [-(class_Fields_Olinordered__field__inverse__zero(_495399)), _495401 = _495399, class_Fields_Olinordered__field__inverse__zero(_495401)], (8774 ^ _490194) ^ [_799135, _799137, _799139, _799141] : [class_Groups_Oordered__comm__monoid__add(_799135), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_799135, c_Groups_Ozero__class_Ozero(_799135)), _799137)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_799135, _799139), _799141)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_799135, _799139), c_Groups_Oplus__class_Oplus(_799135, _799137, _799141))))], (812 ^ _490194) ^ [_514869, _514871] : [-(class_Rings_Oidom(_514869)), _514871 = _514869, class_Rings_Oidom(_514871)], (12064 ^ _490194) ^ [_918946] : [class_Rings_Olinordered__idom(_918946), -(class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(_918946)))], (6699 ^ _490194) ^ [] : [-(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)))], (11902 ^ _490194) ^ [] : [-(class_Power_Opower(tc_RealDef_Oreal))], (4574 ^ _490194) ^ [_647248, _647250] : [class_Divides_Osemiring__div(_647248), -(c_Divides_Odiv__class_Odiv(_647248, c_Groups_Ozero__class_Ozero(_647248), _647250) = c_Groups_Ozero__class_Ozero(_647248))], (9903 ^ _490194) ^ [_841202, _841204] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Nat_OSuc(_841202), _841204) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _841202, _841204)))], (11622 ^ _490194) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (11828 ^ _490194) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal))], (4564 ^ _490194) ^ [_646817, _646819] : [-(c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _646817), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _646819)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _646817, _646819)))], (11802 ^ _490194) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal))], (6771 ^ _490194) ^ [_724928, _724930, _724932] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _724928), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _724930, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _724932), _724928)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _724930, _724932), _724928))], (10417 ^ _490194) ^ [_861576, _861578] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _861576), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _861578)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _861576, _861578)))], (11860 ^ _490194) ^ [] : [-(class_RealVector_Oreal__field(tc_RealDef_Oreal))], (12082 ^ _490194) ^ [_919516] : [class_Rings_Olinordered__idom(_919516), -(class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(_919516)))], (1921 ^ _490194) ^ [_553280, _553282, _553284, _553286] : [class_Orderings_Oorder(_553280), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_553280, _553282), _553284)), c_Orderings_Oord__class_Oless(_553280, _553286, _553282), -(c_Orderings_Oord__class_Oless(_553280, _553286, _553284))], (9897 ^ _490194) ^ [_840918] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _840918, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _840918)], (7951 ^ _490194) ^ [_765494, _765496, _765498] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _765494), _765496)), _765498) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _765494), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _765496), _765498)))], (5649 ^ _490194) ^ [_684348, _684350, _684352] : [class_Groups_Omonoid__mult(_684348), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_684348), hAPP(hAPP(c_Power_Opower__class_Opower(_684348), _684350), _684352)), _684350) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_684348), _684350), hAPP(hAPP(c_Power_Opower__class_Opower(_684348), _684350), _684352)))], (10874 ^ _490194) ^ [] : [c_Complex_Oii = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)], (11812 ^ _490194) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal))], (1164 ^ _490194) ^ [_527835, _527837] : [_527837 = _527835, -(v_g____(_527837) = v_g____(_527835))], (12100 ^ _490194) ^ [_920086] : [class_Groups_Ocancel__comm__monoid__add(_920086), -(class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(_920086)))], (7265 ^ _490194) ^ [_742179, _742181] : [class_Rings_Olinordered__ring(_742179), c_Orderings_Oord__class_Oless(_742179, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_742179), _742181), _742181), c_Groups_Ozero__class_Ozero(_742179))], (2193 ^ _490194) ^ [_561798, _561800, _561802] : [class_Orderings_Olinorder(_561798), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_561798, _561800), _561802))), -(c_Orderings_Oord__class_Oless(_561798, _561802, _561800))], (5731 ^ _490194) ^ [_687587, _687589, _687591] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_687587)), _687589) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_687587)), _687591), -(_687589 = _687591)], (9080 ^ _490194) ^ [_810275, _810277] : [9081 ^ _490194 : [(9084 ^ _490194) ^ [] : [_810275 = _810277], (9082 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _810275, _810277)]], -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _810275, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _810277, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (9572 ^ _490194) ^ [_828736, _828738, _828740] : [hBOOL(hAPP(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), _828736), _828738), _828740))), c_Orderings_Oord__class_Oless(tc_Int_Oint, _828740, _828736), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _828736), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _828738)))], (3941 ^ _490194) ^ [_624351, _624353] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _624351, _624353), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _624351, c_Nat_OSuc(_624353)))], (890 ^ _490194) ^ [_517805, _517807, _517809, _517811] : [-(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_517811, _517807) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_517809, _517805)), _517811 = _517809, _517807 = _517805], (5313 ^ _490194) ^ [_671603, _671605] : [-(hAPP(c_Int_Onat, _671603) = _671605), 5316 ^ _490194 : [(5319 ^ _490194) ^ [] : [_671603 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _671605)], (5317 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _671603)))]], 5320 ^ _490194 : [(5323 ^ _490194) ^ [] : [_671605 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5321 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _671603))]]], (12322 ^ _490194) ^ [_927116] : [class_Rings_Ocomm__semiring__1(_927116), -(class_Groups_Oone(tc_Polynomial_Opoly(_927116)))], (1452 ^ _490194) ^ [_538138, _538140, _538142, _538144] : [class_Orderings_Opreorder(_538138), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_538138, _538140), _538142)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_538138, _538142), _538144)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_538138, _538140), _538144)))], (10031 ^ _490194) ^ [_846612, _846614] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _846612, _846614), _846612) = _846614)], (11878 ^ _490194) ^ [] : [-(class_Groups_Omonoid__mult(tc_RealDef_Oreal))], (1566 ^ _490194) ^ [_541891, _541893, _541895] : [class_Orderings_Opreorder(_541891), _541893 = _541895, -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_541891, _541893), _541895)))], (11720 ^ _490194) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (6673 ^ _490194) ^ [_721474, _721476] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _721474)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _721476)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _721474), _721476)))], (3356 ^ _490194) ^ [_603104, _603106] : [class_Groups_Oordered__ab__group__add__abs(_603104), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_603104, c_Groups_Ozero__class_Ozero(_603104)), _603106)), -(c_Groups_Oabs__class_Oabs(_603104, _603106) = _603106)], (6697 ^ _490194) ^ [] : [-(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))], (3576 ^ _490194) ^ [_610764] : [_610764 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _610764)), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))], (6317 ^ _490194) ^ [_708904, _708906, _708908, _708910] : [class_Rings_Olinordered__semidom(_708904), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _708906, _708908), c_Orderings_Oord__class_Oless(_708904, c_Groups_Ozero__class_Ozero(_708904), _708910), c_Orderings_Oord__class_Oless(_708904, _708910, c_Groups_Oone__class_Oone(_708904)), -(c_Orderings_Oord__class_Oless(_708904, hAPP(hAPP(c_Power_Opower__class_Opower(_708904), _708910), _708908), hAPP(hAPP(c_Power_Opower__class_Opower(_708904), _708910), _708906)))], (11688 ^ _490194) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (11884 ^ _490194) ^ [] : [-(class_Rings_Osemiring__1(tc_RealDef_Oreal))], (5517 ^ _490194) ^ [_679010, _679012] : [class_Groups_Ocomm__monoid__mult(_679010), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_679010), _679012), c_Groups_Oone__class_Oone(_679010)) = _679012)], (4185 ^ _490194) ^ [_632909, _632911] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_632909)), _632911)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _632909, _632911))], (6687 ^ _490194) ^ [_722136, _722138] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _722136, c_Nat_OSuc(_722138)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _722136, c_Groups_Oone__class_Oone(tc_Nat_Onat)), _722138))], (6539 ^ _490194) ^ [_716772, _716774] : [class_Rings_Ocomm__semiring__0(_716772), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_716772)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_716772))), _716774) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_716772)))], (11604 ^ _490194) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (11960 ^ _490194) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Complex_Ocomplex))], (10041 ^ _490194) ^ [_847103, _847105, _847107] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _847103), _847105)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _847103), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _847105, _847107))))], (6701 ^ _490194) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (2439 ^ _490194) ^ [_570733, _570735, _570737] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _570733), _570735)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _570733), _570737)), 2446 ^ _490194 : [(2453 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _570735), _570737)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _570735, _570733)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _570737, _570733))))], (2447 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _570735, _570733)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _570737, _570733))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _570735), _570737)))]]], (11676 ^ _490194) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (12094 ^ _490194) ^ [_919896] : [class_Rings_Olinordered__idom(_919896), -(class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(_919896)))], (11296 ^ _490194) ^ [_895615, _895617, _895619] : [class_RealVector_Oreal__normed__field(_895615), -(_895617 = c_Groups_Ozero__class_Ozero(_895615)), -(c_RealVector_Onorm__class_Onorm(_895615, c_Rings_Oinverse__class_Odivide(_895615, _895619, _895617)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_895615, _895619), c_RealVector_Onorm__class_Onorm(_895615, _895617)))], (8630 ^ _490194) ^ [_794240, _794242, _794244, _794246] : [class_Groups_Ocancel__semigroup__add(_794240), 8633 ^ _490194 : [(8640 ^ _490194) ^ [] : [_794244 = _794246, -(c_Groups_Oplus__class_Oplus(_794240, _794242, _794244) = c_Groups_Oplus__class_Oplus(_794240, _794242, _794246))], (8634 ^ _490194) ^ [] : [c_Groups_Oplus__class_Oplus(_794240, _794242, _794244) = c_Groups_Oplus__class_Oplus(_794240, _794242, _794246), -(_794244 = _794246)]]], (6779 ^ _490194) ^ [_725235, _725237] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _725235), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _725237), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _725237, _725235), _725237))], (5237 ^ _490194) ^ [_669263] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _669263), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Int_Onat, _669263)))], (6489 ^ _490194) ^ [_715043, _715045, _715047] : [-(_715043 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 6492 ^ _490194 : [(6499 ^ _490194) ^ [] : [_715045 = _715047, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _715043), _715045) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _715043), _715047))], (6493 ^ _490194) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _715043), _715045) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _715043), _715047), -(_715045 = _715047)]]], (4921 ^ _490194) ^ [_658474, _658476, _658478] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _658474), _658476)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _658474, _658478)), c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _658476, _658478))))], (11186 ^ _490194) ^ [_891156, _891158] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatfloor(_891156), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _891158)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _891156, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _891158)))], (7967 ^ _490194) ^ [_766335, _766337, _766339, _766341] : [class_Rings_Ocomm__semiring__1(_766335), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_766335), _766337), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_766335), _766339), _766341)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_766335), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_766335), _766337), _766339)), _766341))], (3422 ^ _490194) ^ [_605489, _605491] : [class_Rings_Olinordered__semidom(_605489), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_605489, c_Groups_Ozero__class_Ozero(_605489)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_605489), _605491))))], (11972 ^ _490194) ^ [] : [-(class_Groups_Ogroup__add(tc_Complex_Ocomplex))], (3849 ^ _490194) ^ [_621242, _621244] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _621242, _621244), 3852 ^ _490194 : [(3855 ^ _490194) ^ [] : [_621242 = _621244], (3853 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _621242), _621244)))]]], (11716 ^ _490194) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (10462 ^ _490194) ^ [_863554, _863556, _863558] : [hBOOL(hAPP(_863554, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _863556, _863558))), 10465 ^ _490194 : [(10472 ^ _490194) ^ [_863892] : [_863556 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _863558, _863892), -(hBOOL(hAPP(_863554, _863892)))], (10466 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _863556, _863558), -(hBOOL(hAPP(_863554, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (6589 ^ _490194) ^ [_718663, _718665, _718667, _718669] : [class_Fields_Ofield(_718663), -(c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_718663), _718665, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_718663)), _718667), _718669)) = c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_718663), c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_718663), _718665, _718667), _718669))], (8996 ^ _490194) ^ [_806711, _806713, _806715, _806717, _806719, _806721] : [class_Rings_Oring(_806711), 8999 ^ _490194 : [(9006 ^ _490194) ^ [] : [_806717 = c_Groups_Oplus__class_Oplus(_806711, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_806711), c_Groups_Ominus__class_Ominus(_806711, _806719, _806713)), _806715), _806721), -(c_Groups_Oplus__class_Oplus(_806711, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_806711), _806713), _806715), _806717) = c_Groups_Oplus__class_Oplus(_806711, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_806711), _806719), _806715), _806721))], (9000 ^ _490194) ^ [] : [c_Groups_Oplus__class_Oplus(_806711, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_806711), _806713), _806715), _806717) = c_Groups_Oplus__class_Oplus(_806711, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_806711), _806719), _806715), _806721), -(_806717 = c_Groups_Oplus__class_Oplus(_806711, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_806711), c_Groups_Ominus__class_Ominus(_806711, _806719, _806713)), _806715), _806721))]]], (772 ^ _490194) ^ [_513689, _513691] : [-(class_Power_Opower(_513689)), _513691 = _513689, class_Power_Opower(_513691)], (1218 ^ _490194) ^ [_530052, _530054] : [class_RealVector_Oreal__normed__vector(_530052), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_530052, _530054), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (3440 ^ _490194) ^ [_606162, _606164, _606166] : [class_Rings_Olinordered__semidom(_606162), 3443 ^ _490194 : [(3450 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _606164, _606166), -(c_Orderings_Oord__class_Oless(_606162, hAPP(c_Nat_Osemiring__1__class_Oof__nat(_606162), _606164), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_606162), _606166)))], (3444 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(_606162, hAPP(c_Nat_Osemiring__1__class_Oof__nat(_606162), _606164), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_606162), _606166)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _606164, _606166))]]], (8400 ^ _490194) ^ [_785336, _785338, _785340, _785342, _785344] : [class_Groups_Oordered__ab__semigroup__add(_785336), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_785336, _785338), _785340)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_785336, _785342), _785344)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_785336, c_Groups_Oplus__class_Oplus(_785336, _785338, _785342)), c_Groups_Oplus__class_Oplus(_785336, _785340, _785344))))], (4420 ^ _490194) ^ [_641445] : [-(hBOOL(hAPP(_641445, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 4427 ^ [_641445])))), 4421 ^ _490194 : [(4422 ^ _490194) ^ [_641549] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _641549)), hBOOL(hAPP(_641445, _641549))]]], (7631 ^ _490194) ^ [_754408, _754410, _754412] : [_754408 = 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), _754408), _754410), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _754408), _754412)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3905 ^ _490194) ^ [_623176, _623178] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_623176), _623178), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _623176, _623178))], (12052 ^ _490194) ^ [_918566] : [class_Groups_Ocancel__comm__monoid__add(_918566), -(class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(_918566)))], (12328 ^ _490194) ^ [_927286] : [c_SEQ_Osubseq(_927286), 12334 ^ _490194 : [(12340 ^ _490194) ^ [_927806, _927808] : [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(_927286, 12336 ^ [_927286, _927806, _927808])), _927808)), 12333 ^ [_927286, _927808])], (12338 ^ _490194) ^ [_927745, _927747] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _927745), 12336 ^ [_927286, _927745, _927747])))], (12335 ^ _490194) ^ [_927581] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 12333 ^ [_927286, _927581]))]], -(v_thesis____)], (11848 ^ _490194) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_RealDef_Oreal))], (4712 ^ _490194) ^ [_651698, _651700] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _651698)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _651700, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _651698, _651700)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (11786 ^ _490194) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal))], (3248 ^ _490194) ^ [_599632, _599634, _599636, _599638] : [class_Rings_Olinordered__semidom(_599632), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_599632, _599634), _599636)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_599632, c_Groups_Ozero__class_Ozero(_599632)), _599634)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_599632, hAPP(hAPP(c_Power_Opower__class_Opower(_599632), _599634), _599638)), hAPP(hAPP(c_Power_Opower__class_Opower(_599632), _599636), _599638))))], (6905 ^ _490194) ^ [_729759, _729761, _729763] : [class_Rings_Ono__zero__divisors(_729759), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_729759), _729761), _729763) = c_Groups_Ozero__class_Ozero(_729759), -(_729761 = c_Groups_Ozero__class_Ozero(_729759)), -(_729763 = c_Groups_Ozero__class_Ozero(_729759))], (6487 ^ _490194) ^ [_714919] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _714919) = _714919)], (12010 ^ _490194) ^ [_917236] : [class_Rings_Olinordered__idom(_917236), -(class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(_917236)))], (1556 ^ _490194) ^ [_541512, _541514, _541516, _541518, _541520] : [class_Orderings_Oord(_541512), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_541514, _541512), _541516), _541518)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_541512, hAPP(_541516, _541520)), hAPP(_541518, _541520))))], (3787 ^ _490194) ^ [_618977, _618979] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _618977, _618979), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _618977, _618979), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (9618 ^ _490194) ^ [_830355] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _830355)), -(c_Nat_OSuc(hAPP(c_Int_Onat, _830355)) = hAPP(c_Int_Onat, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _830355)))], (9430 ^ _490194) ^ [_823697, _823699] : [9431 ^ _490194 : [(9432 ^ _490194) ^ [_823777] : [_823699 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _823697, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Nat_OSuc(_823777)))]], -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _823697, _823699))], (1180 ^ _490194) ^ [_528574, _528576] : [hAPP(_528574, 1181 ^ [_528574, _528576]) = hAPP(_528576, 1181 ^ [_528574, _528576]), -(_528574 = _528576)], (1224 ^ _490194) ^ [_530255] : [class_RealVector_Oreal__normed__vector(_530255), -(c_RealVector_Onorm__class_Onorm(_530255, c_Groups_Ozero__class_Ozero(_530255)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (9235 ^ _490194) ^ [_815616, _815618, _815620] : [class_Rings_Olinordered__ring(_815616), c_Orderings_Oord__class_Oless(_815616, c_Groups_Oplus__class_Oplus(_815616, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_815616), _815618), _815618), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_815616), _815620), _815620)), c_Groups_Ozero__class_Ozero(_815616))], (12304 ^ _490194) ^ [_926546] : [class_Groups_Ozero(_926546), -(class_Groups_Ozero(tc_Polynomial_Opoly(_926546)))], (1038 ^ _490194) ^ [_523273, _523275, _523277, _523279] : [-(c_Complex_Orcis(_523279, _523275) = c_Complex_Orcis(_523277, _523273)), _523279 = _523277, _523275 = _523273], (402 ^ _490194) ^ [_502774, _502776] : [-(class_Rings_Oordered__comm__semiring(_502774)), _502776 = _502774, class_Rings_Oordered__comm__semiring(_502776)], (3759 ^ _490194) ^ [_617877] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _617877, c_Nat_OSuc(_617877)))], (472 ^ _490194) ^ [_504839, _504841] : [-(class_Groups_Oab__semigroup__mult(_504839)), _504841 = _504839, class_Groups_Oab__semigroup__mult(_504841)], (11288 ^ _490194) ^ [_895219, _895221, _895223, _895225] : [class_Rings_Odivision__ring(_895219), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_895219), _895221), c_Rings_Oinverse__class_Odivide(_895219, _895223, _895225)) = c_Rings_Oinverse__class_Odivide(_895219, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_895219), _895221), _895223), _895225))], (11712 ^ _490194) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (11554 ^ _490194) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex))], (3120 ^ _490194) ^ [] : [-(c_RealDef_Oreal(tc_Nat_Onat) = c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal))], (4826 ^ _490194) ^ [_655222, _655224] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _655222)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _655224)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Nat__Transfer_Otsub(_655222, _655224))))], (10423 ^ _490194) ^ [_861947, _861949, _861951] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _861947), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _861949, _861951)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _861947), _861949)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _861947), _861951)))], (5799 ^ _490194) ^ [_690466, _690468, _690470] : [class_Rings_Olinordered__semidom(_690466), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_690466, c_Groups_Oone__class_Oone(_690466)), _690468)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_690466, c_Groups_Oone__class_Oone(_690466)), hAPP(hAPP(c_Power_Opower__class_Opower(_690466), _690468), _690470))))], (1837 ^ _490194) ^ [_550650, _550652, _550654] : [class_Orderings_Olinorder(_550650), -(c_Orderings_Oord__class_Oless(_550650, _550652, _550654)), -(_550652 = _550654), -(c_Orderings_Oord__class_Oless(_550650, _550654, _550652))], (3232 ^ _490194) ^ [_599013, _599015] : [class_RealVector_Oreal__normed__vector(_599013), -(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_599013, _599015)) = c_RealVector_Onorm__class_Onorm(_599013, _599015))], (8284 ^ _490194) ^ [_781174, _781176, _781178, _781180] : [class_Rings_Ocomm__semiring__1(_781174), -(c_Groups_Oplus__class_Oplus(_781174, c_Groups_Oplus__class_Oplus(_781174, _781176, _781178), _781180) = c_Groups_Oplus__class_Oplus(_781174, c_Groups_Oplus__class_Oplus(_781174, _781176, _781180), _781178))], (1963 ^ _490194) ^ [_554648, _554650, _554652, _554654] : [class_Orderings_Opreorder(_554648), c_Orderings_Oord__class_Oless(_554648, _554650, _554652), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_554648, _554652), _554654)), -(c_Orderings_Oord__class_Oless(_554648, _554650, _554654))], (1068 ^ _490194) ^ [_524394, _524396, _524398, _524400, _524402, _524404] : [-(c_Divides_Odiv__class_Odiv(_524404, _524400, _524396) = c_Divides_Odiv__class_Odiv(_524402, _524398, _524394)), _524404 = _524402, _524400 = _524398, _524396 = _524394], (5422 ^ _490194) ^ [_675373, _675375, _675377] : [class_Rings_Ocomm__semiring__0(_675373), 5425 ^ _490194 : [(5432 ^ _490194) ^ [] : [c_Polynomial_Odegree(_675373, _675375) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Polynomial_Osynthetic__div(_675373, _675375, _675377) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_675373)))], (5426 ^ _490194) ^ [] : [c_Polynomial_Osynthetic__div(_675373, _675375, _675377) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_675373)), -(c_Polynomial_Odegree(_675373, _675375) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (7705 ^ _490194) ^ [_757039, _757041, _757043, _757045, _757047] : [class_Rings_Olinordered__semiring__strict(_757039), c_Orderings_Oord__class_Oless(_757039, _757041, _757043), c_Orderings_Oord__class_Oless(_757039, _757045, _757047), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_757039, c_Groups_Ozero__class_Ozero(_757039)), _757041)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_757039, c_Groups_Ozero__class_Ozero(_757039)), _757045)), -(c_Orderings_Oord__class_Oless(_757039, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_757039), _757041), _757045), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_757039), _757043), _757047)))], (8069 ^ _490194) ^ [_771163, _771165] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _771163), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _771165)), 8077 ^ _490194 : [(8080 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _771165, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Nat_OSuc(8076 ^ [_771163, _771165]))), _771163)))], (8078 ^ _490194) ^ [] : [-(hBOOL(hAPP(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), 8076 ^ [_771163, _771165])), _771163)), _771165)))]]], (4402 ^ _490194) ^ [] : [-(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)))], (8238 ^ _490194) ^ [_778882, _778884, _778886, _778888] : [class_RealVector_Oreal__normed__algebra(_778882), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_778882), c_Groups_Oplus__class_Oplus(_778882, _778884, _778886)), _778888) = c_Groups_Oplus__class_Oplus(_778882, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_778882), _778884), _778888), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_778882), _778886), _778888)))], (11488 ^ _490194) ^ [_902695, _902697] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _902695), hAPP(c_RealDef_Oreal(tc_Nat_Onat), _902697)), hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _902695, _902697)))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))], (6857 ^ _490194) ^ [_728138, _728140] : [class_Rings_Omult__zero(_728138), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_728138), c_Groups_Ozero__class_Ozero(_728138)), _728140) = c_Groups_Ozero__class_Ozero(_728138))], (9830 ^ _490194) ^ [_838185, _838187, _838189, _838191] : [class_Rings_Ocomm__semiring__0(_838185), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_838185)), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_838185), _838187, _838189)), _838191) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_838185), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_838185)), _838187), _838191), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_838185)), _838189), _838191)))], (4330 ^ _490194) ^ [_638062] : [_638062 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _638062) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (12106 ^ _490194) ^ [_920276] : [class_Rings_Olinordered__idom(_920276), -(class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(_920276)))], (2815 ^ _490194) ^ [_583715, _583717] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _583715, _583717)), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _583715), _583717)))], (8788 ^ _490194) ^ [_799619, _799621, _799623, _799625] : [class_Groups_Oordered__comm__monoid__add(_799619), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_799619, c_Groups_Ozero__class_Ozero(_799619)), _799621)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_799619, _799623), _799625)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_799619, _799623), c_Groups_Oplus__class_Oplus(_799619, _799625, _799621))))], (9698 ^ _490194) ^ [_833166, _833168, _833170] : [-(hBOOL(hAPP(_833166, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _833168, _833170)))), 9701 ^ _490194 : [(9704 ^ _490194) ^ [] : [hBOOL(hAPP(_833166, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (9702 ^ _490194) ^ [] : [-(_833170 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], 9707 ^ _490194 : [(9708 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _833170))], (9714 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, 9710 ^ [_833166, _833168, _833170], _833170))], (9718 ^ _490194) ^ [] : [hBOOL(hAPP(_833166, 9709 ^ [_833166, _833168, _833170]))], (9716 ^ _490194) ^ [] : [-(_833168 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _833170), 9709 ^ [_833166, _833168, _833170]), 9710 ^ [_833166, _833168, _833170]))], (9712 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 9710 ^ [_833166, _833168, _833170])))]], 9719 ^ _490194 : [(9720 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _833170, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (9726 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, 9722 ^ [_833166, _833168, _833170]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (9730 ^ _490194) ^ [] : [hBOOL(hAPP(_833166, 9721 ^ [_833166, _833168, _833170]))], (9728 ^ _490194) ^ [] : [-(_833168 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _833170), 9721 ^ [_833166, _833168, _833170]), 9722 ^ [_833166, _833168, _833170]))], (9724 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _833170, 9722 ^ [_833166, _833168, _833170]))]]], (242 ^ _490194) ^ [_498054, _498056] : [-(class_Rings_Odivision__ring(_498054)), _498056 = _498054, class_Rings_Odivision__ring(_498056)], (3272 ^ _490194) ^ [_600475, _600477, _600479] : [class_Power_Opower(_600475), class_Rings_Omult__zero(_600475), class_Rings_Ono__zero__divisors(_600475), class_Rings_Ozero__neq__one(_600475), 3287 ^ _490194 : [(3296 ^ _490194) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_600475), _600477), _600479) = c_Groups_Ozero__class_Ozero(_600475)), _600477 = c_Groups_Ozero__class_Ozero(_600475), -(_600479 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3288 ^ _490194) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_600475), _600477), _600479) = c_Groups_Ozero__class_Ozero(_600475), 3291 ^ _490194 : [(3294 ^ _490194) ^ [] : [_600479 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (3292 ^ _490194) ^ [] : [-(_600477 = c_Groups_Ozero__class_Ozero(_600475))]]]]], (11908 ^ _490194) ^ [] : [-(class_Rings_Oidom(tc_RealDef_Oreal))], (11882 ^ _490194) ^ [] : [-(class_Groups_Omonoid__add(tc_RealDef_Oreal))], (312 ^ _490194) ^ [_500119, _500121] : [-(class_Groups_Oordered__ab__semigroup__add(_500119)), _500121 = _500119, class_Groups_Oordered__ab__semigroup__add(_500121)], (11594 ^ _490194) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (10277 ^ _490194) ^ [_856230, _856232, _856234] : [class_Groups_Ocomm__monoid__add(_856230), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_856230, _856232), c_Polynomial_Odegree(_856230, _856234)), -(c_Polynomial_Odegree(_856230, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_856230), _856234, _856232)) = c_Polynomial_Odegree(_856230, _856234))], (442 ^ _490194) ^ [_503954, _503956] : [-(class_Groups_Ocancel__semigroup__add(_503954)), _503956 = _503954, class_Groups_Ocancel__semigroup__add(_503956)], (11656 ^ _490194) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (11626 ^ _490194) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (4263 ^ _490194) ^ [_635714] : [c_SEQ_Osubseq(_635714), 4266 ^ _490194 : [(4267 ^ _490194) ^ [_635833] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(_635714, _635833), hAPP(_635714, c_Nat_OSuc(_635833))))]]], (3456 ^ _490194) ^ [_606686, _606688, _606690] : [class_Rings_Olinordered__semidom(_606686), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _606688, _606690), -(c_Orderings_Oord__class_Oless(_606686, hAPP(c_Nat_Osemiring__1__class_Oof__nat(_606686), _606688), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_606686), _606690)))], (9018 ^ _490194) ^ [_807759, _807761, _807763, _807765, _807767] : [class_RealVector_Oreal__normed__algebra(_807759), -(c_Groups_Ominus__class_Ominus(_807759, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_807759), _807761), _807763), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_807759), _807765), _807767)) = c_Groups_Oplus__class_Oplus(_807759, c_Groups_Oplus__class_Oplus(_807759, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_807759), c_Groups_Ominus__class_Ominus(_807759, _807761, _807765)), c_Groups_Ominus__class_Ominus(_807759, _807763, _807767)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_807759), c_Groups_Ominus__class_Ominus(_807759, _807761, _807765)), _807767)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_807759), _807765), c_Groups_Ominus__class_Ominus(_807759, _807763, _807767))))], (8876 ^ _490194) ^ [_802429, _802431, _802433] : [class_Groups_Oordered__comm__monoid__add(_802429), c_Orderings_Oord__class_Oless(_802429, _802431, c_Groups_Ozero__class_Ozero(_802429)), c_Orderings_Oord__class_Oless(_802429, _802433, c_Groups_Ozero__class_Ozero(_802429)), -(c_Orderings_Oord__class_Oless(_802429, c_Groups_Oplus__class_Oplus(_802429, _802431, _802433), c_Groups_Ozero__class_Ozero(_802429)))], (5327 ^ _490194) ^ [_672104, _672106] : [_672104 = hAPP(c_Int_Onat, _672106), 5330 ^ _490194 : [(5337 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _672106))), -(_672104 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5331 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _672106)), -(_672106 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _672104))]]], (4083 ^ _490194) ^ [_629320, _629322] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_629320), c_Nat_OSuc(_629322)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _629320, _629322))], (4155 ^ _490194) ^ [_631780, _631782] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _631780)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _631780), _631782))))], (11906 ^ _490194) ^ [] : [-(class_Rings_Oring(tc_RealDef_Oreal))], (9873 ^ _490194) ^ [_840146, _840148] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _840146, _840148) = _840146, -(_840148 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8146 ^ _490194) ^ [_774714, _774716, _774718] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _774714), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _774716, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _774718, 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, _774718, _774716)), c_Groups_Oone__class_Oone(tc_Int_Oint))), _774714))))], (10025 ^ _490194) ^ [_846248, _846250, _846252] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _846248, _846250), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _846252, _846250)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _846248, _846252))], (8956 ^ _490194) ^ [_805129, _805131, _805133, _805135, _805137, _805139] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_805129), -(_805131 = c_Groups_Ozero__class_Ozero(_805129)), c_Groups_Oplus__class_Oplus(_805129, _805133, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_805129), _805131), _805137)) = c_Groups_Oplus__class_Oplus(_805129, _805135, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_805129), _805131), _805139)), _805133 = _805135, -(_805137 = _805139)], (10287 ^ _490194) ^ [_856589, _856591, _856593] : [class_Groups_Ocomm__monoid__add(_856589), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_856589, _856591), c_Polynomial_Odegree(_856589, _856593)), -(c_Polynomial_Odegree(_856589, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_856589), _856591, _856593)) = c_Polynomial_Odegree(_856589, _856593))], (4197 ^ _490194) ^ [_633315, _633317] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _633315), _633317)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _633315, c_Nat_OSuc(_633317)))], (11664 ^ _490194) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (1082 ^ _490194) ^ [_524854, _524856] : [_524856 = _524854, -(c_Groups_Oone__class_Oone(_524856) = c_Groups_Oone__class_Oone(_524854))], (12298 ^ _490194) ^ [_926356] : [class_Rings_Ocomm__semiring__1(_926356), -(class_Power_Opower(tc_Polynomial_Opoly(_926356)))], (2635 ^ _490194) ^ [_577392, _577394, _577396] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _577392, _577394), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _577392, _577396), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _577396, _577394), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _577396, _577392)))], (4225 ^ _490194) ^ [_634246, _634248] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_634246)), _634248)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _634246, _634248))], (10787 ^ _490194) ^ [_876631] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _876631), hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_RComplete_Onatceiling(_876631)))))], (11548 ^ _490194) ^ [_904710] : [class_Rings_Ocomm__ring(_904710), -(class_Rings_Ocomm__ring(tc_Polynomial_Opoly(_904710)))], (8646 ^ _490194) ^ [_794782, _794784, _794786, _794788] : [class_Groups_Ocancel__semigroup__add(_794782), 8649 ^ _490194 : [(8656 ^ _490194) ^ [] : [_794784 = _794788, -(c_Groups_Oplus__class_Oplus(_794782, _794784, _794786) = c_Groups_Oplus__class_Oplus(_794782, _794788, _794786))], (8650 ^ _490194) ^ [] : [c_Groups_Oplus__class_Oplus(_794782, _794784, _794786) = c_Groups_Oplus__class_Oplus(_794782, _794788, _794786), -(_794784 = _794788)]]], (11698 ^ _490194) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (4191 ^ _490194) ^ [_633087, _633089] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _633087, _633089), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_633087)), _633089)))], (1414 ^ _490194) ^ [_536839, _536841, _536843, _536845, _536847] : [class_Orderings_Oord(_536839), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_536841, _536839), _536843), _536845)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_536839, hAPP(_536843, _536847)), hAPP(_536845, _536847))))], (11616 ^ _490194) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (8390 ^ _490194) ^ [_784941, _784943, _784945, _784947] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_784941), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_784941, c_Groups_Oplus__class_Oplus(_784941, _784943, _784945)), c_Groups_Oplus__class_Oplus(_784941, _784947, _784945))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_784941, _784943), _784947)))], (8352 ^ _490194) ^ [_783610, _783612] : [class_Groups_Olinordered__ab__group__add(_783610), 8355 ^ _490194 : [(8362 ^ _490194) ^ [] : [_783612 = c_Groups_Ozero__class_Ozero(_783610), -(c_Groups_Ozero__class_Ozero(_783610) = c_Groups_Oplus__class_Oplus(_783610, _783612, _783612))], (8356 ^ _490194) ^ [] : [c_Groups_Ozero__class_Ozero(_783610) = c_Groups_Oplus__class_Oplus(_783610, _783612, _783612), -(_783612 = c_Groups_Ozero__class_Ozero(_783610))]]], (2876 ^ _490194) ^ [_585881, _585883, _585885] : [class_RealVector_Oreal__normed__vector(_585881), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _585883), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_585881, hAPP(_585885, 2885 ^ [_585881, _585883, _585885]))), _585883)), -(c_SEQ_OBseq(_585881, _585885))], (12166 ^ _490194) ^ [_922176] : [class_Rings_Olinordered__idom(_922176), -(class_Rings_Olinordered__idom(tc_Polynomial_Opoly(_922176)))], (11690 ^ _490194) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (7429 ^ _490194) ^ [_747559, _747561, _747563, _747565] : [class_Rings_Olinordered__ring__strict(_747559), c_Orderings_Oord__class_Oless(_747559, _747561, c_Groups_Ozero__class_Ozero(_747559)), 7436 ^ _490194 : [(7443 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(_747559, _747565, _747563), -(c_Orderings_Oord__class_Oless(_747559, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_747559), _747561), _747563), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_747559), _747561), _747565)))], (7437 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(_747559, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_747559), _747561), _747563), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_747559), _747561), _747565)), -(c_Orderings_Oord__class_Oless(_747559, _747565, _747563))]]], (3769 ^ _490194) ^ [_618366, _618368] : [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, _618366)), _618368)), _618366 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_618368 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3070 ^ _490194) ^ [_593016, _593018, _593020, _593022] : [class_Rings_Olinordered__semidom(_593016), c_Orderings_Oord__class_Oless(_593016, _593018, _593020), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_593016, c_Groups_Ozero__class_Ozero(_593016)), _593018)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _593022), -(c_Orderings_Oord__class_Oless(_593016, hAPP(hAPP(c_Power_Opower__class_Opower(_593016), _593018), _593022), hAPP(hAPP(c_Power_Opower__class_Opower(_593016), _593020), _593022)))], (5717 ^ _490194) ^ [_686894] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _686894) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9247 ^ _490194) ^ [_816143, _816145, _816147, _816149, _816151, _816153] : [class_Rings_Oordered__ring(_816143), 9250 ^ _490194 : [(9257 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_816143, c_Groups_Oplus__class_Oplus(_816143, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_816143), c_Groups_Ominus__class_Ominus(_816143, _816145, _816151)), _816147), _816149)), _816153)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_816143, c_Groups_Oplus__class_Oplus(_816143, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_816143), _816145), _816147), _816149)), c_Groups_Oplus__class_Oplus(_816143, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_816143), _816151), _816147), _816153))))], (9251 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_816143, c_Groups_Oplus__class_Oplus(_816143, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_816143), _816145), _816147), _816149)), c_Groups_Oplus__class_Oplus(_816143, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_816143), _816151), _816147), _816153))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_816143, c_Groups_Oplus__class_Oplus(_816143, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_816143), c_Groups_Ominus__class_Ominus(_816143, _816145, _816151)), _816147), _816149)), _816153)))]]], (8164 ^ _490194) ^ [_775606, _775608, _775610, _775612, _775614] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_775606), 8167 ^ _490194 : [(8168 ^ _490194) ^ [] : [c_Groups_Oplus__class_Oplus(_775606, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_775606), _775608), _775612), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_775606), _775610), _775614)) = c_Groups_Oplus__class_Oplus(_775606, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_775606), _775608), _775614), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_775606), _775610), _775612)), -(_775608 = _775610), -(_775612 = _775614)], (8178 ^ _490194) ^ [] : [-(c_Groups_Oplus__class_Oplus(_775606, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_775606), _775608), _775612), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_775606), _775610), _775614)) = c_Groups_Oplus__class_Oplus(_775606, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_775606), _775608), _775614), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_775606), _775610), _775612))), 8181 ^ _490194 : [(8184 ^ _490194) ^ [] : [_775612 = _775614], (8182 ^ _490194) ^ [] : [_775608 = _775610]]]]], (1016 ^ _490194) ^ [_522450, _522452] : [_522452 = _522450, -(c_RComplete_Onatfloor(_522452) = c_RComplete_Onatfloor(_522450))], (11644 ^ _490194) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (2781 ^ _490194) ^ [_582329, _582331] : [2782 ^ _490194 : [(2785 ^ _490194) ^ [] : [_582329 = _582331], (2783 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _582329, _582331)]], -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _582329), _582331)))], (3837 ^ _490194) ^ [_620799] : [_620799 = c_Nat_OSuc(_620799)], (11858 ^ _490194) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal))], (12274 ^ _490194) ^ [_925596] : [class_Rings_Olinordered__idom(_925596), -(class_Orderings_Oorder(tc_Polynomial_Opoly(_925596)))], (10707 ^ _490194) ^ [_873580, _873582, _873584] : [hBOOL(hAPP(_873580, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _873582, _873584))), 10710 ^ _490194 : [(10717 ^ _490194) ^ [] : [-(_873584 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 10720 ^ _490194 : [(10721 ^ _490194) ^ [_874034, _874036] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _874034, _873584), _873582 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _873584), _874036), _874034), -(hBOOL(hAPP(_873580, _874036)))]]], (10711 ^ _490194) ^ [] : [_873584 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_873580, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (7585 ^ _490194) ^ [_752822, _752824, _752826, _752828, _752830] : [class_Rings_Olinordered__idom(_752822), c_Orderings_Oord__class_Oless(_752822, c_Groups_Oabs__class_Oabs(_752822, _752824), _752826), c_Orderings_Oord__class_Oless(_752822, c_Groups_Oabs__class_Oabs(_752822, _752828), _752830), -(c_Orderings_Oord__class_Oless(_752822, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_752822), c_Groups_Oabs__class_Oabs(_752822, _752824)), c_Groups_Oabs__class_Oabs(_752822, _752828)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_752822), _752826), _752830)))], (9638 ^ _490194) ^ [_831045, _831047, _831049] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _831045), _831045 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _831047, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _831045), _831049)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _831047)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _831049), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (2661 ^ _490194) ^ [_578247, _578249, _578251] : [2662 ^ _490194 : [(2665 ^ _490194) ^ [] : [hBOOL(hAPP(hAPP(_578251, _578249), _578247))], (2663 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _578247, _578249))]], 2668 ^ _490194 : [(2671 ^ _490194) ^ [] : [hBOOL(hAPP(hAPP(_578251, _578249), _578247))], (2669 ^ _490194) ^ [] : [-(_578247 = _578249)]], 2674 ^ _490194 : [(2677 ^ _490194) ^ [] : [hBOOL(hAPP(hAPP(_578251, _578249), _578247))], (2675 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _578249, _578247))]], -(hBOOL(hAPP(hAPP(_578251, _578249), _578247)))], (11988 ^ _490194) ^ [] : [-(class_Rings_Oidom(tc_Complex_Ocomplex))], (880 ^ _490194) ^ [_517446, _517448, _517450, _517452] : [-(c_Nat__Transfer_Otsub(_517452, _517448) = c_Nat__Transfer_Otsub(_517450, _517446)), _517452 = _517450, _517448 = _517446], (8906 ^ _490194) ^ [_803385, _803387, _803389, _803391, _803393] : [class_Groups_Oordered__cancel__ab__semigroup__add(_803385), c_Orderings_Oord__class_Oless(_803385, _803387, _803389), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_803385, _803391), _803393)), -(c_Orderings_Oord__class_Oless(_803385, c_Groups_Oplus__class_Oplus(_803385, _803387, _803391), c_Groups_Oplus__class_Oplus(_803385, _803389, _803393)))], (9919 ^ _490194) ^ [_841927, _841929, _841931] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _841927, _841929), _841931), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _841927, _841931))], (10253 ^ _490194) ^ [_855221, _855223] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_855221)), _855223) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _855223, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _855221), _855223)))], (4529 ^ _490194) ^ [_645476, _645478, _645480] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _645476, _645478), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _645478, _645480), 4537 ^ _490194 : [(4540 ^ _490194) ^ [_645899] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _645478, _645899)), 4536 ^ [_645476, _645478, _645480]), 4543 ^ _490194 : [(4546 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _645899, _645480))], (4544 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _645476, _645899))]]], (4538 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 4536 ^ [_645476, _645478, _645480]))]]], (5781 ^ _490194) ^ [_689713, _689715, _689717] : [-(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _689713, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _689715), _689717)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _689713, _689715), _689717))], (1118 ^ _490194) ^ [_526165, _526167] : [_526167 = _526165, -(tc_Polynomial_Opoly(_526167) = tc_Polynomial_Opoly(_526165))], (11340 ^ _490194) ^ [_897391, _897393, _897395, _897397] : [class_Rings_Odivision__ring(_897391), -(_897393 = c_Groups_Ozero__class_Ozero(_897391)), 11347 ^ _490194 : [(11354 ^ _490194) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_897391), _897395), _897393) = _897397, -(_897395 = c_Rings_Oinverse__class_Odivide(_897391, _897397, _897393))], (11348 ^ _490194) ^ [] : [_897395 = c_Rings_Oinverse__class_Odivide(_897391, _897397, _897393), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_897391), _897395), _897393) = _897397)]]], (11098 ^ _490194) ^ [_887976] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _887976), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), -(c_RComplete_Onatfloor(_887976) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (182 ^ _490194) ^ [_496284, _496286] : [-(class_RealVector_Oreal__normed__algebra__1(_496284)), _496286 = _496284, class_RealVector_Oreal__normed__algebra__1(_496286)], (5557 ^ _490194) ^ [_680378] : [class_RealVector_Oreal__normed__algebra__1(_680378), -(c_RealVector_Onorm__class_Onorm(_680378, c_Groups_Oone__class_Oone(_680378)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (11830 ^ _490194) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal))], (5467 ^ _490194) ^ [_676987, _676989, _676991] : [-(hBOOL(hAPP(_676987, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _676989, _676991)))), 5468 ^ _490194 : [(5475 ^ _490194) ^ [_677285] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _676991), _677285)), _676989)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _676989, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _676991), c_Nat_OSuc(_677285))), hBOOL(hAPP(_676987, _677285))], (5469 ^ _490194) ^ [] : [_676991 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hBOOL(hAPP(_676987, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (8520 ^ _490194) ^ [_789696, _789698, _789700, _789702] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_789696), 8523 ^ _490194 : [(8530 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(_789696, _789700, _789702), -(c_Orderings_Oord__class_Oless(_789696, c_Groups_Oplus__class_Oplus(_789696, _789698, _789700), c_Groups_Oplus__class_Oplus(_789696, _789698, _789702)))], (8524 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(_789696, c_Groups_Oplus__class_Oplus(_789696, _789698, _789700), c_Groups_Oplus__class_Oplus(_789696, _789698, _789702)), -(c_Orderings_Oord__class_Oless(_789696, _789700, _789702))]]], (392 ^ _490194) ^ [_502479, _502481] : [-(class_Rings_Oring__no__zero__divisors(_502479)), _502481 = _502479, class_Rings_Oring__no__zero__divisors(_502481)], (2987 ^ _490194) ^ [_590038, _590040] : [c_HOL_Oequal__class_Oequal(tc_RealDef_Oreal, _590038, _590040), -(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _590038, _590040) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (7827 ^ _490194) ^ [_761207, _761209, _761211, _761213] : [class_Rings_Olinordered__semiring__strict(_761207), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_761207, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_761207), _761209), _761211)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_761207), _761213), _761211))), c_Orderings_Oord__class_Oless(_761207, c_Groups_Ozero__class_Ozero(_761207), _761211), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_761207, _761209), _761213)))], (11864 ^ _490194) ^ [] : [-(class_Rings_Ocomm__semiring(tc_RealDef_Oreal))], (1336 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), v_r)))], (4476 ^ _490194) ^ [_643508, _643510] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _643508) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _643510), -(_643508 = _643510)], (1625 ^ _490194) ^ [_543929, _543931, _543933] : [class_Orderings_Olinorder(_543929), -(c_Orderings_Oord__class_Oless(_543929, _543931, _543933)), -(_543931 = _543933), -(c_Orderings_Oord__class_Oless(_543929, _543933, _543931))], (10697 ^ _490194) ^ [_873196, _873198] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _873196)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _873198)), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(c_Int_Onat, _873196), hAPP(c_Int_Onat, _873198)) = hAPP(c_Int_Onat, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _873196, _873198)))], (3598 ^ _490194) ^ [_611660, _611662, _611664] : [hBOOL(hAPP(_611660, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _611662, _611664)))), 3601 ^ _490194 : [(3608 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _611662, _611664), -(hBOOL(hAPP(_611660, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (3602 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _611664), _611662)), -(hBOOL(hAPP(_611660, c_Groups_Ominus__class_Ominus(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _611662), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _611664)))))]]], (2567 ^ _490194) ^ [_575076, _575078, _575080] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _575076, _575078), _575080) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _575076, _575080), _575078))], (4994 ^ _490194) ^ [_660979] : [4996 ^ _490194 : [(4999 ^ _490194) ^ [] : [hBOOL(hAPP(_660979, hAPP(c_Int_Onat, 4995 ^ [_660979])))], (4997 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 4995 ^ [_660979])))]], 5000 ^ _490194 : [(5001 ^ _490194) ^ [_661248] : [-(hBOOL(hAPP(_660979, _661248)))]]], (10077 ^ _490194) ^ [_848619, _848621, _848623] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _848619), _848621)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _848619, _848623)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _848621, _848623))))], (10055 ^ _490194) ^ [_847710, _847712, _847714] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _847710, _847712)), _847714)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _847710), _847714)))], (11910 ^ _490194) ^ [] : [-(class_Groups_Oone(tc_RealDef_Oreal))], (11750 ^ _490194) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (11542 ^ _490194) ^ [_904520] : [class_Groups_Ocancel__comm__monoid__add(_904520), -(class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(_904520)))], (2645 ^ _490194) ^ [_577723, _577725] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _577723, _577725) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _577725, _577723) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_577723 = _577725)], (4736 ^ _490194) ^ [_652479, _652481] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _652479)), 4739 ^ _490194 : [(4748 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _652479, _652481))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _652481), _652479)), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _652481)], (4740 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _652479, _652481)), 4743 ^ _490194 : [(4746 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _652481))], (4744 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _652481), _652479)))]]]]], (10761 ^ _490194) ^ [_875726, _875728] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _875726), _875728), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _875728), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _875726), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))), -(c_RComplete_Onatceiling(_875728) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _875726, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (11440 ^ _490194) ^ [_900923, _900925] : [class_Rings_Odivision__ring(_900923), -(_900925 = c_Groups_Ozero__class_Ozero(_900923)), -(c_Rings_Oinverse__class_Odivide(_900923, _900925, _900925) = c_Groups_Oone__class_Oone(_900923))], (7373 ^ _490194) ^ [_745753, _745755, _745757] : [class_Rings_Olinordered__semiring__strict(_745753), c_Orderings_Oord__class_Oless(_745753, c_Groups_Ozero__class_Ozero(_745753), _745755), c_Orderings_Oord__class_Oless(_745753, _745757, c_Groups_Ozero__class_Ozero(_745753)), -(c_Orderings_Oord__class_Oless(_745753, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_745753), _745755), _745757), c_Groups_Ozero__class_Ozero(_745753)))], (9836 ^ _490194) ^ [_838502, _838504, _838506, _838508] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _838502), _838504), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _838506), _838504), _838508)) = 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, _838502, _838506)), _838504), _838508))], (762 ^ _490194) ^ [_513394, _513396] : [-(class_Rings_Oring__1(_513394)), _513396 = _513394, class_Rings_Oring__1(_513396)], (3873 ^ _490194) ^ [_622015] : [c_Nat_OSuc(_622015) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (11466 ^ _490194) ^ [_901720, _901722] : [-(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Complex_Orcis(_901720, _901722)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _901720))], (5444 ^ _490194) ^ [_676061] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _676061), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _676061)))], (9983 ^ _490194) ^ [_844517, _844519, _844521] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _844517, _844519), _844521) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _844517, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _844519, _844521)))], (9058 ^ _490194) ^ [_809490] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _809490), _809490) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (11706 ^ _490194) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (8624 ^ _490194) ^ [_793960, _793962, _793964, _793966] : [class_Groups_Oab__semigroup__add(_793960), -(c_Groups_Oplus__class_Oplus(_793960, c_Groups_Oplus__class_Oplus(_793960, _793962, _793964), _793966) = c_Groups_Oplus__class_Oplus(_793960, _793962, c_Groups_Oplus__class_Oplus(_793960, _793964, _793966)))], (3823 ^ _490194) ^ [_620360, _620362] : [c_Nat_OSuc(_620360) = c_Nat_OSuc(_620362), -(_620360 = _620362)], (11602 ^ _490194) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (984 ^ _490194) ^ [_521296, _521298] : [_521298 = _521296, -(c_Nat_OSuc(_521298) = c_Nat_OSuc(_521296))], (8244 ^ _490194) ^ [_779194, _779196, _779198, _779200] : [class_RealVector_Oreal__normed__algebra(_779194), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_779194), _779196), c_Groups_Oplus__class_Oplus(_779194, _779198, _779200)) = c_Groups_Oplus__class_Oplus(_779194, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_779194), _779196), _779198), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_779194), _779196), _779200)))], (8374 ^ _490194) ^ [_784312, _784314] : [class_Groups_Omonoid__add(_784312), -(c_Groups_Oplus__class_Oplus(_784312, c_Groups_Ozero__class_Ozero(_784312), _784314) = _784314)], (11922 ^ _490194) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex))], (3334 ^ _490194) ^ [_602382, _602384] : [class_Groups_Oordered__ab__group__add__abs(_602382), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_602382, c_Groups_Ozero__class_Ozero(_602382)), c_Groups_Oabs__class_Oabs(_602382, _602384))))], (3889 ^ _490194) ^ [_622575, _622577] : [3890 ^ _490194 : [(3893 ^ _490194) ^ [] : [_622575 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3891 ^ _490194) ^ [] : [_622577 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _622575), _622577) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (66 ^ _490194) ^ [_492467, _492469, _492471, _492473] : [-(c_SEQ_OBseq(_492471, _492467)), c_SEQ_OBseq(_492473, _492469), _492473 = _492471, _492469 = _492467], (11874 ^ _490194) ^ [] : [-(class_Orderings_Opreorder(tc_RealDef_Oreal))], (3979 ^ _490194) ^ [_625556, _625558] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _625556, _625558), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_625556), c_Nat_OSuc(_625558)))], (1278 ^ _490194) ^ [_531988, _531990] : [c_SEQ_Osubseq(_531988), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _531990), hAPP(_531988, _531990))))], (4836 ^ _490194) ^ [_655539, _655541] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _655539)), 4839 ^ _490194 : [(4846 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _655539, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _655541)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(c_Int_Onat, _655539), _655541))], (4840 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(c_Int_Onat, _655539), _655541), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _655539, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _655541)))]]], (11630 ^ _490194) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (11824 ^ _490194) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal))], (11820 ^ _490194) ^ [] : [-(class_RealVector_Oreal__normed__field(tc_RealDef_Oreal))], (4049 ^ _490194) ^ [_628072, _628074] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _628072), c_Nat_OSuc(_628074))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _628072), _628074))), -(_628072 = c_Nat_OSuc(_628074))], (3735 ^ _490194) ^ [_617009, _617011] : [class_RealVector_Oreal__normed__vector(_617009), 3738 ^ _490194 : [(3746 ^ _490194) ^ [] : [3748 ^ _490194 : [(3749 ^ _490194) ^ [_617494] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_617009, hAPP(_617011, 3747 ^ [_617009, _617011, _617494])), hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Nat_OSuc(_617494)))]], -(c_SEQ_OBseq(_617009, _617011))], (3739 ^ _490194) ^ [] : [c_SEQ_OBseq(_617009, _617011), 3743 ^ _490194 : [(3744 ^ _490194) ^ [_617316] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_617009, hAPP(_617011, _617316)), hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Nat_OSuc(3742 ^ [_617009, _617011]))))]]]]], (10180 ^ _490194) ^ [_852606, _852608] : [-(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _852606, _852608)), 10181 ^ _490194 : [(10188 ^ _490194) ^ [] : [_852606 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _852608 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10182 ^ _490194) ^ [] : [_852606 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _852608 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (10523 ^ _490194) ^ [_866064, _866066, _866068, _866070, _866072] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _866064), _866066)), -(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), _866066), _866068), _866070), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _866064), _866068), _866072)) = 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, _866066, _866064)), _866068), _866070), _866072))], (94 ^ _490194) ^ [_493411, _493413, _493415, _493417, _493419, _493421, _493423, _493425] : [-(c_Nat__Transfer_Otransfer__morphism(_493423, _493419, _493415, _493411)), c_Nat__Transfer_Otransfer__morphism(_493425, _493421, _493417, _493413), _493425 = _493423, _493421 = _493419, _493417 = _493415, _493413 = _493411], (562 ^ _490194) ^ [_507494, _507496] : [-(class_Rings_Ocomm__semiring(_507494)), _507496 = _507494, class_Rings_Ocomm__semiring(_507496)], (10617 ^ _490194) ^ [_870104, _870106] : [_870104 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _870104, _870106) = _870106)], (3434 ^ _490194) ^ [_605932] : [class_Rings_Osemiring__1(_605932), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_605932), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_605932))], (4431 ^ _490194) ^ [_641825] : [4432 ^ _490194 : [(4433 ^ _490194) ^ [_641913] : [hBOOL(hAPP(_641825, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _641913)))]], 4435 ^ _490194 : [(4438 ^ _490194) ^ [] : [-(hBOOL(hAPP(_641825, 4434 ^ [_641825])))], (4436 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 4434 ^ [_641825])))]]], (3985 ^ _490194) ^ [_625809, _625811] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _625809, c_Nat_OSuc(_625811)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _625809, _625811)), -(_625809 = _625811)], (2087 ^ _490194) ^ [_558496, _558498, _558500] : [class_Orderings_Olinorder(_558496), -(c_Orderings_Oord__class_Oless(_558496, _558498, _558500)), 2094 ^ _490194 : [(2101 ^ _490194) ^ [] : [_558498 = _558500, -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_558496, _558498), _558500)))], (2095 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_558496, _558498), _558500)), -(_558498 = _558500)]]], (4418 ^ _490194) ^ [_641318] : [-(hBOOL(hAPP(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), _641318))))], (3404 ^ _490194) ^ [_604727, _604729, _604731] : [class_Groups_Oordered__ab__group__add__abs(_604727), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_604727, c_Groups_Ominus__class_Ominus(_604727, c_Groups_Oabs__class_Oabs(_604727, _604729), c_Groups_Oabs__class_Oabs(_604727, _604731))), c_Groups_Oabs__class_Oabs(_604727, c_Groups_Ominus__class_Ominus(_604727, _604729, _604731)))))], (582 ^ _490194) ^ [_508084, _508086] : [-(class_Rings_Ozero__neq__one(_508084)), _508086 = _508084, class_Rings_Ozero__neq__one(_508086)], (702 ^ _490194) ^ [_511624, _511626] : [-(class_Orderings_Oorder(_511624)), _511626 = _511624, class_Orderings_Oorder(_511626)], (9945 ^ _490194) ^ [_842905, _842907, _842909] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _842905, _842907), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _842905, _842909), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _842907, _842909)))], (11842 ^ _490194) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_RealDef_Oreal))], (11788 ^ _490194) ^ [] : [-(class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal))], (6227 ^ _490194) ^ [_705844, _705846] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _705844), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _705846), _705844), _705844) = _705846)], (11738 ^ _490194) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Nat_Onat))], (9143 ^ _490194) ^ [_812502, _812504, _812506, _812508] : [class_Groups_Oordered__comm__monoid__add(_812502), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_812502, c_Groups_Ozero__class_Ozero(_812502)), _812504)), c_Orderings_Oord__class_Oless(_812502, _812506, _812508), -(c_Orderings_Oord__class_Oless(_812502, _812506, c_Groups_Oplus__class_Oplus(_812502, _812504, _812508)))], (8346 ^ _490194) ^ [_783390, _783392] : [class_Groups_Omonoid__add(_783390), -(c_Groups_Oplus__class_Oplus(_783390, _783392, c_Groups_Ozero__class_Ozero(_783390)) = _783392)], (3340 ^ _490194) ^ [_602610, _602612] : [class_Groups_Oordered__ab__group__add__abs(_602610), 3343 ^ _490194 : [(3350 ^ _490194) ^ [] : [_602612 = c_Groups_Ozero__class_Ozero(_602610), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_602610, c_Groups_Oabs__class_Oabs(_602610, _602612)), c_Groups_Ozero__class_Ozero(_602610))))], (3344 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_602610, c_Groups_Oabs__class_Oabs(_602610, _602612)), c_Groups_Ozero__class_Ozero(_602610))), -(_602612 = c_Groups_Ozero__class_Ozero(_602610))]]], (5931 ^ _490194) ^ [_695323, _695325, _695327] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _695323, _695325), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _695327), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _695327), _695323), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _695327), _695325)))], (3664 ^ _490194) ^ [_613922, _613924] : [class_RealVector_Oreal__normed__vector(_613922), 3667 ^ _490194 : [(3668 ^ _490194) ^ [] : [3677 ^ _490194 : [(3678 ^ _490194) ^ [_614495] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_613922, hAPP(_613924, _614495)), hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Nat_OSuc(3676 ^ [_613922, _613924]))))]], 3669 ^ _490194 : [(3670 ^ _490194) ^ [_614165] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _614165), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_613922, hAPP(_613924, 3673 ^ [_613922, _613924, _614165]))), _614165))]]], (3680 ^ _490194) ^ [] : [3682 ^ _490194 : [(3683 ^ _490194) ^ [_614674] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_613922, hAPP(_613924, 3681 ^ [_613922, _613924, _614674])), hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Nat_OSuc(_614674)))]], 3685 ^ _490194 : [(3688 ^ _490194) ^ [_614899] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_613922, hAPP(_613924, _614899))), 3684 ^ [_613922, _613924])))], (3686 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 3684 ^ [_613922, _613924]))]]]]], (1366 ^ _490194) ^ [_535277, _535279] : [class_RealVector_Oreal__normed__vector(_535277), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_RealVector_Onorm__class_Onorm(_535277, _535279))))], (6039 ^ _490194) ^ [_699358, _699360] : [class_Rings_Ocomm__semiring__0(_699358), -(c_Polynomial_Osynthetic__div(_699358, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_699358)), _699360) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_699358)))], (9042 ^ _490194) ^ [_808943, _808945, _808947] : [class_Groups_Oordered__ab__group__add__abs(_808943), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_808943, c_Groups_Oabs__class_Oabs(_808943, c_Groups_Oplus__class_Oplus(_808943, _808945, _808947))), c_Groups_Oplus__class_Oplus(_808943, c_Groups_Oabs__class_Oabs(_808943, _808945), c_Groups_Oabs__class_Oabs(_808943, _808947)))))], (12232 ^ _490194) ^ [_924266] : [class_Rings_Ocomm__semiring__1(_924266), -(class_Groups_Omonoid__mult(tc_Polynomial_Opoly(_924266)))], (6031 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (1350 ^ _490194) ^ [_534557] : [1353 ^ _490194 : [(1356 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(_534557, 1351 ^ [_534557]), hAPP(_534557, 1352 ^ [_534557]))], (1354 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, 1351 ^ [_534557], 1352 ^ [_534557]))]], -(c_SEQ_Osubseq(_534557))], (11838 ^ _490194) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal))], (9337 ^ _490194) ^ [_820041, _820043, _820045] : [class_Divides_Osemiring__div(_820041), -(_820043 = c_Groups_Ozero__class_Ozero(_820041)), -(c_Divides_Odiv__class_Odiv(_820041, c_Groups_Oplus__class_Oplus(_820041, _820043, _820045), _820043) = c_Groups_Oplus__class_Oplus(_820041, c_Divides_Odiv__class_Odiv(_820041, _820045, _820043), c_Groups_Oone__class_Oone(_820041)))], (10067 ^ _490194) ^ [_848240, _848242, _848244, _848246] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _848240), _848242)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _848244), _848246)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _848240, _848244)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _848242, _848246))))], (11686 ^ _490194) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (4142 ^ _490194) ^ [_631331] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _631331), -(_631331 = c_Nat_OSuc(4145 ^ [_631331]))], (10003 ^ _490194) ^ [_845332, _845334, _845336] : [_845332 = _845336, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _845332, _845334) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _845336, _845334))], (2821 ^ _490194) ^ [_583955, _583957] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _583955, _583957), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _583955), _583957)))], (11966 ^ _490194) ^ [] : [-(class_Groups_Omonoid__add(tc_Complex_Ocomplex))], (6191 ^ _490194) ^ [_704505, _704507, _704509] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _704505), _704507)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _704505), _704509))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _704505), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _704507), _704509)))], (5193 ^ _490194) ^ [_667834, _667836] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _667834, hAPP(c_Int_Onat, _667836)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _667834), _667836))], (6847 ^ _490194) ^ [_727773, _727775, _727777] : [class_Groups_Omonoid__mult(_727773), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _727775), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_727773), hAPP(hAPP(c_Power_Opower__class_Opower(_727773), _727777), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _727775, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _727777) = hAPP(hAPP(c_Power_Opower__class_Opower(_727773), _727777), _727775))], (10120 ^ _490194) ^ [_850395, _850397] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _850395), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _850395, _850397))))], (4548 ^ _490194) ^ [_646255, _646257] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _646255), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _646257), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _646257), _646255), _646257) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _646257), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _646255, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (7939 ^ _490194) ^ [_765046] : [_765046 = 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), _765046), _765046))], (5715 ^ _490194) ^ [_686810] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _686810), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4497 ^ _490194) ^ [_644256] : [hBOOL(hAPP(_644256, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 4498 ^ [_644256]))), 4501 ^ _490194 : [(4502 ^ _490194) ^ [_644459] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _644459)), -(hBOOL(hAPP(_644256, _644459)))]]], (6201 ^ _490194) ^ [_704812, _704814, _704816] : [6202 ^ _490194 : [(6205 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _704814), _704816))], (6203 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _704812))]], -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _704812), _704814)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _704812), _704816))))], (11982 ^ _490194) ^ [] : [-(class_Power_Opower(tc_Complex_Ocomplex))], (7771 ^ _490194) ^ [_759239, _759241, _759243, _759245] : [class_Rings_Olinordered__semiring(_759239), c_Orderings_Oord__class_Oless(_759239, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_759239), _759241), _759243), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_759239), _759245), _759243)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_759239, c_Groups_Ozero__class_Ozero(_759239)), _759243)), -(c_Orderings_Oord__class_Oless(_759239, _759241, _759245))], (9036 ^ _490194) ^ [_808663, _808665, _808667] : [class_Rings_Ocomm__semiring__1(_808663), -(c_Groups_Oplus__class_Oplus(_808663, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_808663), _808665), _808667), _808667) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_808663), c_Groups_Oplus__class_Oplus(_808663, _808665, c_Groups_Oone__class_Oone(_808663))), _808667))], (3877 ^ _490194) ^ [_622173] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_622173)], (8424 ^ _490194) ^ [_786219, _786221, _786223, _786225] : [class_Groups_Oordered__ab__semigroup__add(_786219), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_786219, _786221), _786223)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_786219, c_Groups_Oplus__class_Oplus(_786219, _786221, _786225)), c_Groups_Oplus__class_Oplus(_786219, _786223, _786225))))], (7799 ^ _490194) ^ [_760223, _760225, _760227, _760229] : [class_Rings_Olinordered__semiring(_760223), c_Orderings_Oord__class_Oless(_760223, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_760223), _760225), _760227), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_760223), _760225), _760229)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_760223, c_Groups_Ozero__class_Ozero(_760223)), _760225)), -(c_Orderings_Oord__class_Oless(_760223, _760227, _760229))], (1338 ^ _490194) ^ [_534076] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_g____(_534076))), v_r)))], (10887 ^ _490194) ^ [_880211, _880213, _880215, _880217] : [class_RealVector_Oreal__normed__vector(_880211), class_Orderings_Oord(_880213), 10897 ^ _490194 : [(10900 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_880211, c_Groups_Ominus__class_Ominus(_880211, hAPP(_880217, _880215), hAPP(_880217, 10896 ^ [_880211, _880213, _880215, _880217]))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (10898 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_880213, _880215), 10896 ^ [_880211, _880213, _880215, _880217])))]], 10901 ^ _490194 : [(10902 ^ _490194) ^ [_880785] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_880213, _880215), _880785)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_880211, hAPP(_880217, _880785)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_880211, hAPP(_880217, _880215)))))]]], (4600 ^ _490194) ^ [_648104, _648106] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _648104, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 4603 ^ _490194 : [(4610 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _648106), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _648106, _648104), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (4604 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _648106, _648104), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _648106))]]], (11856 ^ _490194) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal))], (10478 ^ _490194) ^ [_864093, _864095, _864097] : [-(hBOOL(hAPP(_864093, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _864095, _864097)))), 10481 ^ _490194 : [(10484 ^ _490194) ^ [] : [hBOOL(hAPP(_864093, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10482 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _864095, _864097))]], 10486 ^ _490194 : [(10489 ^ _490194) ^ [] : [hBOOL(hAPP(_864093, 10485 ^ [_864093, _864095, _864097]))], (10487 ^ _490194) ^ [] : [-(_864095 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _864097, 10485 ^ [_864093, _864095, _864097]))]]], (3779 ^ _490194) ^ [_618639, _618641] : [3780 ^ _490194 : [(3783 ^ _490194) ^ [] : [_618641 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (3781 ^ _490194) ^ [] : [-(_618639 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], -(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, _618639)), _618641)))], (10347 ^ _490194) ^ [_858973, _858975, _858977] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _858973), _858975)), 10350 ^ _490194 : [(10357 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _858977, _858973)), _858975)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _858977), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _858975, _858973))))], (10351 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _858977), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _858975, _858973))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _858977, _858973)), _858975)))]]], (11852 ^ _490194) ^ [] : [-(class_Rings_Olinordered__ring(tc_RealDef_Oreal))], (592 ^ _490194) ^ [_508379, _508381] : [-(class_Rings_Oordered__ring(_508379)), _508381 = _508379, class_Rings_Oordered__ring(_508381)], (4239 ^ _490194) ^ [_634817, _634819] : [class_Orderings_Oorder(_634817), 4242 ^ _490194 : [(4243 ^ _490194) ^ [] : [c_SEQ_Omonoseq(_634817, _634819), 4248 ^ _490194 : [(4249 ^ _490194) ^ [_635116] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_634817, hAPP(_634819, _635116)), hAPP(_634819, c_Nat_OSuc(_635116)))))]], 4250 ^ _490194 : [(4251 ^ _490194) ^ [_635191] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_634817, hAPP(_634819, c_Nat_OSuc(_635191))), hAPP(_634819, _635191))))]]], (4253 ^ _490194) ^ [] : [4255 ^ _490194 : [(4259 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_634817, hAPP(_634819, c_Nat_OSuc(4257 ^ [_634817, _634819]))), hAPP(_634819, 4257 ^ [_634817, _634819])))], (4256 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_634817, hAPP(_634819, 4254 ^ [_634817, _634819])), hAPP(_634819, c_Nat_OSuc(4254 ^ [_634817, _634819]))))]], -(c_SEQ_Omonoseq(_634817, _634819))]]], (6163 ^ _490194) ^ [_703530, _703532] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _703530), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _703532), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _703530, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _703532), _703530)))], (2757 ^ _490194) ^ [_581495, _581497] : [2758 ^ _490194 : [(2761 ^ _490194) ^ [] : [_581495 = _581497], (2759 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _581495, _581497)]], -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _581495), _581497)))], (332 ^ _490194) ^ [_500709, _500711] : [-(class_Groups_Oordered__comm__monoid__add(_500709)), _500711 = _500709, class_Groups_Oordered__comm__monoid__add(_500711)], (7547 ^ _490194) ^ [_751508] : [class_Rings_Olinordered__semidom(_751508), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_751508, c_Groups_Oone__class_Oone(_751508)), c_Groups_Ozero__class_Ozero(_751508)))], (1150 ^ _490194) ^ [_527375, _527377, _527379, _527381, _527383, _527385] : [-(c_Groups_Ominus__class_Ominus(_527385, _527381, _527377) = c_Groups_Ominus__class_Ominus(_527383, _527379, _527375)), _527385 = _527383, _527381 = _527379, _527377 = _527375], (5765 ^ _490194) ^ [_688957] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _688957), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _688957), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _688957), _688957)))))], (11034 ^ _490194) ^ [_885501] : [-(c_RComplete_Onatfloor(hAPP(c_RealDef_Oreal(tc_Nat_Onat), _885501)) = _885501)], (6677 ^ _490194) ^ [_721704, _721706] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _721704)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _721706)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _721704), _721706)))], (10122 ^ _490194) ^ [_850498, _850500] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _850498), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _850500, _850498))))], (10214 ^ _490194) ^ [_853702, _853704] : [c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _853702), _853702), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _853704), _853704)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 10217 ^ _490194 : [(10220 ^ _490194) ^ [] : [-(_853704 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (10218 ^ _490194) ^ [] : [-(_853702 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))]]], (8570 ^ _490194) ^ [_791539] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _791539, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _791539)], (7505 ^ _490194) ^ [_750098, _750100, _750102, _750104] : [class_Rings_Olinordered__comm__semiring__strict(_750098), c_Orderings_Oord__class_Oless(_750098, _750100, _750102), c_Orderings_Oord__class_Oless(_750098, c_Groups_Ozero__class_Ozero(_750098), _750104), -(c_Orderings_Oord__class_Oless(_750098, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_750098), _750104), _750100), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_750098), _750104), _750102)))], (7359 ^ _490194) ^ [_745305, _745307, _745309] : [class_Rings_Olinordered__semiring__strict(_745305), c_Orderings_Oord__class_Oless(_745305, c_Groups_Ozero__class_Ozero(_745305), _745307), c_Orderings_Oord__class_Oless(_745305, c_Groups_Ozero__class_Ozero(_745305), _745309), -(c_Orderings_Oord__class_Oless(_745305, c_Groups_Ozero__class_Ozero(_745305), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_745305), _745307), _745309)))], (2579 ^ _490194) ^ [_575500, _575502] : [class_Orderings_Oorder(_575500), c_SEQ_Oincseq(_575500, _575502), -(c_SEQ_Omonoseq(_575500, _575502))], (3805 ^ _490194) ^ [_619578, _619580] : [_619578 = _619580, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _619578) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _619580))], (10275 ^ _490194) ^ [_856103] : [-(c_Nat_OSuc(_856103) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _856103))], (2279 ^ _490194) ^ [_564557] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _564557)))], (4862 ^ _490194) ^ [_656366, _656368] : [class_Orderings_Oorder(_656366), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_656366, hAPP(_656368, 4867 ^ [_656366, _656368])), hAPP(_656368, c_Nat_OSuc(4867 ^ [_656366, _656368])))), -(c_SEQ_Oincseq(_656366, _656368))], (2765 ^ _490194) ^ [_581793, _581795] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _581793, _581795), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _581793), _581795)))], (10335 ^ _490194) ^ [_858451, _858453] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _858451), _858453)), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _858451, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _858453, _858451)) = _858453)], (11596 ^ _490194) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (11770 ^ _490194) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (192 ^ _490194) ^ [_496579, _496581] : [-(class_RealVector_Oreal__normed__algebra(_496579)), _496581 = _496579, class_RealVector_Oreal__normed__algebra(_496581)], (10232 ^ _490194) ^ [_854333, _854335] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _854333, _854335), -(_854335 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _854333, 10235 ^ [_854333, _854335])))], (3029 ^ _490194) ^ [_591526, _591528] : [-(hBOOL(hAPP(_591526, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_591526, _591528)), 3037 ^ _490194 : [(3040 ^ _490194) ^ [_591966] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _591966, 3036 ^ [_591526, _591528]), hBOOL(hAPP(_591526, _591966))], (3046 ^ _490194) ^ [] : [-(hBOOL(hAPP(_591526, 3036 ^ [_591526, _591528])))], (3038 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, 3036 ^ [_591526, _591528]), _591528)))]]], (11286 ^ _490194) ^ [_895018, _895020, _895022] : [-(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, hAPP(_895018, _895020), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, hAPP(_895018, _895022), hAPP(_895018, _895020)), c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _895022, _895020))), _895020)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, hAPP(_895018, _895022), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, hAPP(_895018, _895022), hAPP(_895018, _895020)), c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _895022, _895020))), _895022)))], (792 ^ _490194) ^ [_514279, _514281] : [-(class_Rings_Ocomm__ring(_514279)), _514281 = _514279, class_Rings_Ocomm__ring(_514281)], (6289 ^ _490194) ^ [_707966, _707968, _707970] : [class_Rings_Olinordered__semidom(_707966), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_707966, c_Groups_Ozero__class_Ozero(_707966)), _707968)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_707966, _707968), c_Groups_Oone__class_Oone(_707966))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_707966, hAPP(hAPP(c_Power_Opower__class_Opower(_707966), _707968), c_Nat_OSuc(_707970))), _707968)))], (232 ^ _490194) ^ [_497759, _497761] : [-(class_RealVector_Oreal__field(_497759)), _497761 = _497759, class_RealVector_Oreal__field(_497761)], (5137 ^ _490194) ^ [_665992, _665994] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _665992)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _665994)), 5144 ^ _490194 : [(5151 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _665992), _665994)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(c_Int_Onat, _665992)), hAPP(c_Int_Onat, _665994))))], (5145 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(c_Int_Onat, _665992)), hAPP(c_Int_Onat, _665994))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _665992), _665994)))]]], (10114 ^ _490194) ^ [_850158, _850160] : [10115 ^ _490194 : [(10116 ^ _490194) ^ [_850237] : [_850160 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _850158, _850237)]], -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _850158), _850160)))], (10994 ^ _490194) ^ [_884066, _884068, _884070, _884072] : [class_Fields_Ofield(_884066), 10997 ^ _490194 : [(11006 ^ _490194) ^ [] : [-(c_Polynomial_Opdivmod__rel(_884066, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_884066)), _884068, _884070, _884072)), _884070 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_884066)), _884072 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_884066))], (10998 ^ _490194) ^ [] : [c_Polynomial_Opdivmod__rel(_884066, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_884066)), _884068, _884070, _884072), 11001 ^ _490194 : [(11004 ^ _490194) ^ [] : [-(_884072 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_884066)))], (11002 ^ _490194) ^ [] : [-(_884070 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_884066)))]]]]], (8104 ^ _490194) ^ [_772934, _772936] : [class_RealVector_Oreal__normed__algebra(_772934), 8108 ^ _490194 : [(8111 ^ _490194) ^ [_773241] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_772934, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_772934), _772936), _773241))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_772934, _773241)), 8107 ^ [_772934, _772936]))))], (8109 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 8107 ^ [_772934, _772936]))]]], (10033 ^ _490194) ^ [_846714, _846716] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _846714, _846716), _846716) = _846714)], (9060 ^ _490194) ^ [_809633, _809635, _809637, _809639] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _809633, _809635), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _809637), _809639)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _809633, _809637), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _809635, _809639)))], (6605 ^ _490194) ^ [_719258, _719260, _719262] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _719258), 6608 ^ _490194 : [(6615 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _719260, _719262), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _719260), _719258), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _719262), _719258)))], (6609 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _719260), _719258), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _719262), _719258)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _719260, _719262))]]], (10585 ^ _490194) ^ [_868865, _868867, _868869] : [class_Rings_Ocomm__semiring__0(_868865), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_868865, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_868865)), _868867), _868869))), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Polynomial_Odegree(_868865, _868867), c_Polynomial_Odegree(_868865, _868869)))))], (5127 ^ _490194) ^ [_665673, _665675] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(c_Int_Onat, _665673), hAPP(c_Int_Onat, _665675))), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _665675), c_Orderings_Oord__class_Oless(tc_Int_Oint, _665673, _665675)], (8063 ^ _490194) ^ [_770941] : [class_Power_Opower(_770941), -(c_Power_Opower__class_Opower(_770941) = c_Power_Opower_Opower(_770941, c_Groups_Oone__class_Oone(_770941), c_Groups_Otimes__class_Otimes(_770941)))], (1522 ^ _490194) ^ [_540430, _540432, _540434, _540436] : [class_Orderings_Oord(_540430), _540432 = _540434, hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_540430, _540434), _540436)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_540430, _540432), _540436)))], (11764 ^ _490194) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (5977 ^ _490194) ^ [_696992, _696994, _696996] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _696992), _696994), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _696992), _696996))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _696992), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _696994, _696996)], (8260 ^ _490194) ^ [_780076, _780078, _780080] : [class_Rings_Ocomm__semiring__1(_780076), -(c_Groups_Oplus__class_Oplus(_780076, _780078, _780080) = c_Groups_Oplus__class_Oplus(_780076, _780080, _780078))], (9887 ^ _490194) ^ [_840638, _840640] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _840638, _840640) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _840638 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _840640 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (11990 ^ _490194) ^ [] : [-(class_Groups_Oone(tc_Complex_Ocomplex))], (3817 ^ _490194) ^ [_620113, _620115] : [c_Nat_OSuc(_620113) = c_Nat_OSuc(_620115), -(_620113 = _620115)], (3210 ^ _490194) ^ [_598186, _598188] : [class_Groups_Oordered__ab__group__add__abs(_598186), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_598186, _598188), c_Groups_Oabs__class_Oabs(_598186, _598188))))], (9088 ^ _490194) ^ [_810602, _810604] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _810602), _810604)), -(_810604 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _810602, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 9091 ^ [_810602, _810604])))], (9387 ^ _490194) ^ [_822078] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _822078, 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), _822078), _822078), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (8580 ^ _490194) ^ [_792020, _792022, _792024] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _792020), _792022)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _792024, _792020)), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _792024, _792022))))], (5487 ^ _490194) ^ [_677730, _677732, _677734] : [class_Rings_Olinordered__semidom(_677730), c_Orderings_Oord__class_Oless(_677730, c_Groups_Oone__class_Oone(_677730), _677732), -(c_Orderings_Oord__class_Oless(_677730, c_Groups_Oone__class_Oone(_677730), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_677730), _677732), hAPP(hAPP(c_Power_Opower__class_Opower(_677730), _677732), _677734))))], (3114 ^ _490194) ^ [_594578, _594580] : [_594578 = _594580, -(hAPP(c_RealDef_Oreal(tc_Nat_Onat), _594578) = hAPP(c_RealDef_Oreal(tc_Nat_Onat), _594580))], (5613 ^ _490194) ^ [_682622, _682624] : [class_RealVector_Oreal__normed__algebra(_682622), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_682622), c_Groups_Ozero__class_Ozero(_682622)), _682624) = c_Groups_Ozero__class_Ozero(_682622))], (11450 ^ _490194) ^ [_901239, _901241] : [class_Rings_Odivision__ring__inverse__zero(_901239), 11453 ^ _490194 : [(11460 ^ _490194) ^ [] : [-(_901241 = c_Groups_Ozero__class_Ozero(_901239)), -(c_Rings_Oinverse__class_Odivide(_901239, _901241, _901241) = c_Groups_Oone__class_Oone(_901239))], (11454 ^ _490194) ^ [] : [_901241 = c_Groups_Ozero__class_Ozero(_901239), -(c_Rings_Oinverse__class_Odivide(_901239, _901241, _901241) = c_Groups_Ozero__class_Ozero(_901239))]]], (3316 ^ _490194) ^ [_601727, _601729] : [3317 ^ _490194 : [(3320 ^ _490194) ^ [] : [_601729 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (3318 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _601727)]], -(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), _601727), _601729)))], (8009 ^ _490194) ^ [_768567, _768569] : [class_Rings_Ocomm__semiring__1(_768567), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_768567), c_Groups_Ozero__class_Ozero(_768567)), _768569) = c_Groups_Ozero__class_Ozero(_768567))], (11948 ^ _490194) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex))], (6471 ^ _490194) ^ [_714290, _714292, _714294] : [class_Rings_Olinordered__idom(_714290), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_714290, c_Groups_Ozero__class_Ozero(_714290)), _714292)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_714290), c_Groups_Oabs__class_Oabs(_714290, _714294)), _714292) = c_Groups_Oabs__class_Oabs(_714290, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_714290), _714294), _714292)))], (6483 ^ _490194) ^ [_714707, _714709, _714711] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _714707), _714709)), _714711) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _714707), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _714709), _714711)))], (10759 ^ _490194) ^ [_875595, _875597] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, _875595, _875597)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _875595))), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _875597))))], (1048 ^ _490194) ^ [_523660, _523662, _523664, _523666, _523668, _523670] : [-(c_Groups_Oplus__class_Oplus(_523670, _523666, _523662) = c_Groups_Oplus__class_Oplus(_523668, _523664, _523660)), _523670 = _523668, _523666 = _523664, _523662 = _523660], (11700 ^ _490194) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (2403 ^ _490194) ^ [_569505, _569507] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _569505), _569507)), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _569505, _569507) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3520 ^ _490194) ^ [_608814] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _608814), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (8082 ^ _490194) ^ [_771691, _771693] : [class_RealVector_Oreal__normed__algebra(_771691), 8086 ^ _490194 : [(8089 ^ _490194) ^ [_771998] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_771691, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_771691), _771998), _771693))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_771691, _771998)), 8085 ^ [_771691, _771693]))))], (8087 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 8085 ^ [_771691, _771693]))]]], (11080 ^ _490194) ^ [_887384, _887386, _887388, _887390, _887392, _887394, _887396] : [class_Fields_Ofield(_887384), c_Polynomial_Opdivmod__rel(_887384, _887386, _887388, _887390, _887392), c_Polynomial_Opdivmod__rel(_887384, _887386, _887388, _887394, _887396), 11091 ^ _490194 : [(11094 ^ _490194) ^ [] : [-(_887392 = _887396)], (11092 ^ _490194) ^ [] : [-(_887390 = _887394)]]], (412 ^ _490194) ^ [_503069, _503071] : [-(class_Rings_Olinordered__semiring__1(_503069)), _503071 = _503069, class_Rings_Olinordered__semiring__1(_503071)], (5875 ^ _490194) ^ [_693242, _693244, _693246, _693248] : [class_Divides_Osemiring__div(_693242), -(_693244 = c_Groups_Ozero__class_Ozero(_693242)), -(c_Divides_Odiv__class_Odiv(_693242, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_693242), _693244), _693246), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_693242), _693244), _693248)) = c_Divides_Odiv__class_Odiv(_693242, _693246, _693248))], (422 ^ _490194) ^ [_503364, _503366] : [-(class_Groups_Oordered__ab__group__add(_503364)), _503366 = _503364, class_Groups_Oordered__ab__group__add(_503366)], (3921 ^ _490194) ^ [_623718, _623720, _623722] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _623718, _623720), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _623720, _623722), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_623718), _623722))], (10385 ^ _490194) ^ [_860287, _860289, _860291] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _860287), _860289)), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _860291, _860289), _860287) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _860291, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _860289, _860287)))], (11846 ^ _490194) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_RealDef_Oreal))], (7953 ^ _490194) ^ [_765614, _765616] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _765614), _765616) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _765616), _765614))], (6485 ^ _490194) ^ [_714827, _714829] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _714827), _714829) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _714829), _714827))], (8198 ^ _490194) ^ [_777066, _777068, _777070, _777072] : [class_Rings_Ocomm__semiring__1(_777066), -(c_Groups_Oplus__class_Oplus(_777066, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_777066), _777068), _777070), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_777066), _777072), _777070)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_777066), c_Groups_Oplus__class_Oplus(_777066, _777068, _777072)), _777070))], (12226 ^ _490194) ^ [_924076] : [class_Rings_Olinordered__idom(_924076), -(class_Orderings_Olinorder(tc_Polynomial_Opoly(_924076)))], (10239 ^ _490194) ^ [_854572, _854574] : [10240 ^ _490194 : [(10241 ^ _490194) ^ [_854649] : [_854574 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _854572, _854649))]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _854572, _854574))], (11672 ^ _490194) ^ [] : [-(class_Rings_Osemiring__1(tc_Int_Oint))], (5157 ^ _490194) ^ [_666583] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _666583)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _666583)) = _666583)], (452 ^ _490194) ^ [_504249, _504251] : [-(class_Rings_Olinordered__semiring(_504249)), _504251 = _504249, class_Rings_Olinordered__semiring(_504251)], (2855 ^ _490194) ^ [_585065, _585067] : [2856 ^ _490194 : [(2859 ^ _490194) ^ [] : [_585065 = _585067], (2857 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _585065, _585067)]], -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _585065), _585067)))], (6813 ^ _490194) ^ [_726549, _726551] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _726549)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _726551)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _726549)), hAPP(c_Int_Onat, _726551)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _726549), _726551)))], (11970 ^ _490194) ^ [] : [-(class_Rings_Osemiring__0(tc_Complex_Ocomplex))], (11486 ^ _490194) ^ [_902578, _902580] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _902578), hAPP(c_RealDef_Oreal(tc_Nat_Onat), _902580)), hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _902578, _902580))))))], (11886 ^ _490194) ^ [] : [-(class_Rings_Osemiring__0(tc_RealDef_Oreal))], (6521 ^ _490194) ^ [_716087, _716089] : [class_Groups_Omonoid__mult(_716087), -(hAPP(hAPP(c_Power_Opower__class_Opower(_716087), _716089), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _716089)], (11900 ^ _490194) ^ [] : [-(class_Fields_Ofield(tc_RealDef_Oreal))], (2039 ^ _490194) ^ [_556971, _556973, _556975] : [class_Orderings_Opreorder(_556971), c_Orderings_Oord__class_Oless(_556971, _556973, _556975), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_556971, _556973), _556975)))], (9101 ^ _490194) ^ [_811124, _811126, _811128] : [class_Groups_Oordered__comm__monoid__add(_811124), c_Orderings_Oord__class_Oless(_811124, c_Groups_Ozero__class_Ozero(_811124), _811126), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_811124, c_Groups_Ozero__class_Ozero(_811124)), _811128)), -(c_Orderings_Oord__class_Oless(_811124, c_Groups_Ozero__class_Ozero(_811124), c_Groups_Oplus__class_Oplus(_811124, _811126, _811128)))], (12016 ^ _490194) ^ [_917426] : [class_Rings_Olinordered__idom(_917426), -(class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(_917426)))], (6841 ^ _490194) ^ [_727500, _727502] : [-(_727500 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _727502), _727500) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _727502), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _727502), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _727500, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (11652 ^ _490194) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (4209 ^ _490194) ^ [_633767, _633769] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _633767), _633769)), 4212 ^ _490194 : [(4219 ^ _490194) ^ [] : [_633769 = _633767, -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _633769, c_Nat_OSuc(_633767)))], (4213 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _633769, c_Nat_OSuc(_633767)), -(_633769 = _633767)]]], (2609 ^ _490194) ^ [_576389] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _576389, _576389)], (1108 ^ _490194) ^ [_525834, _525836, _525838, _525840] : [-(tc_fun(_525840, _525836) = tc_fun(_525838, _525834)), _525840 = _525838, _525836 = _525834], (4 ^ _490194) ^ [_490425, _490427] : [_490427 = _490425, -(_490425 = _490427)], (12118 ^ _490194) ^ [_920656] : [class_Rings_Ocomm__semiring__0(_920656), -(class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(_920656)))], (11956 ^ _490194) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Complex_Ocomplex))], (2683 ^ _490194) ^ [_579007, _579009] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _579007), _579009))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _579009), _579007)))], (3690 ^ _490194) ^ [_615043, _615045] : [class_RealVector_Oreal__normed__vector(_615043), 3693 ^ _490194 : [(3694 ^ _490194) ^ [] : [3703 ^ _490194 : [(3704 ^ _490194) ^ [_615624] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_615043, hAPP(_615045, _615624))), hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Nat_OSuc(3702 ^ [_615043, _615045])))))]], 3695 ^ _490194 : [(3696 ^ _490194) ^ [_615290] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _615290), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_615043, hAPP(_615045, 3699 ^ [_615043, _615045, _615290]))), _615290))]]], (3706 ^ _490194) ^ [] : [3708 ^ _490194 : [(3709 ^ _490194) ^ [_615811] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_615043, hAPP(_615045, 3707 ^ [_615043, _615045, _615811]))), hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Nat_OSuc(_615811))))]], 3711 ^ _490194 : [(3714 ^ _490194) ^ [_616040] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_615043, hAPP(_615045, _616040))), 3710 ^ [_615043, _615045])))], (3712 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 3710 ^ [_615043, _615045]))]]]]], (10779 ^ _490194) ^ [_876311] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_RComplete_Onatceiling(_876311))))], (10425 ^ _490194) ^ [_862100, _862102, _862104] : [class_RealVector_Oreal__normed__vector(_862100), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_862100, c_Groups_Ominus__class_Ominus(_862100, _862102, _862104))), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_862100, _862102), c_RealVector_Onorm__class_Onorm(_862100, _862104)))))], (6967 ^ _490194) ^ [_731961, _731963] : [class_Rings_Olinordered__ring(_731961), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_731961, c_Groups_Ozero__class_Ozero(_731961)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_731961), _731963), _731963))))], (12112 ^ _490194) ^ [_920466] : [class_Rings_Olinordered__idom(_920466), -(class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(_920466)))], (11710 ^ _490194) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (4686 ^ _490194) ^ [_650890, _650892] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _650890, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 4689 ^ _490194 : [(4696 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _650892), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _650892, _650890))))], (4690 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _650892, _650890))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _650892), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (11580 ^ _490194) ^ [_905709, _905711] : [class_Orderings_Oord(_905709), -(class_Orderings_Oord(tc_fun(_905711, _905709)))], (3388 ^ _490194) ^ [_604126, _604128] : [class_Groups_Oordered__ab__group__add__abs(_604126), c_Orderings_Oord__class_Oless(_604126, c_Groups_Ozero__class_Ozero(_604126), _604128), -(c_Groups_Oabs__class_Oabs(_604126, _604128) = _604128)], (10419 ^ _490194) ^ [_861687, _861689] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _861687), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _861689)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _861687, _861689)))], (936 ^ _490194) ^ [_519586, _519588, _519590, _519592, _519594, _519596] : [-(c_Polynomial_Osynthetic__div(_519596, _519592, _519588) = c_Polynomial_Osynthetic__div(_519594, _519590, _519586)), _519596 = _519594, _519592 = _519590, _519588 = _519586], (10914 ^ _490194) ^ [_881337, _881339, _881341, _881343, _881345] : [class_Fields_Ofield(_881337), 10917 ^ _490194 : [(10918 ^ _490194) ^ [] : [c_Polynomial_Opdivmod__rel(_881337, _881339, _881341, _881343, _881345), 10921 ^ _490194 : [(10930 ^ _490194) ^ [] : [-(_881341 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_881337))), -(_881345 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_881337))), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_881337, _881345), c_Polynomial_Odegree(_881337, _881341)))], (10924 ^ _490194) ^ [] : [_881341 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_881337)), -(_881343 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_881337)))], (10922 ^ _490194) ^ [] : [-(_881339 = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_881337), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_881337)), _881343), _881341), _881345))]]], (10940 ^ _490194) ^ [] : [-(c_Polynomial_Opdivmod__rel(_881337, _881339, _881341, _881343, _881345)), _881339 = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_881337), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_881337)), _881343), _881341), _881345), 10947 ^ _490194 : [(10950 ^ _490194) ^ [] : [_881343 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_881337))], (10948 ^ _490194) ^ [] : [-(_881341 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_881337)))]], 10951 ^ _490194 : [(10956 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_881337, _881345), c_Polynomial_Odegree(_881337, _881341))], (10954 ^ _490194) ^ [] : [_881345 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_881337))], (10952 ^ _490194) ^ [] : [_881341 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_881337))]]]]], (9879 ^ _490194) ^ [_840393, _840395] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _840393, _840395) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 9882 ^ _490194 : [(9885 ^ _490194) ^ [] : [-(_840395 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9883 ^ _490194) ^ [] : [-(_840393 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (7153 ^ _490194) ^ [_738329, _738331, _738333, _738335] : [class_Rings_Oordered__ring(_738329), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_738329, _738331), _738333)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_738329, _738335), c_Groups_Ozero__class_Ozero(_738329))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_738329, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_738329), _738333), _738335)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_738329), _738331), _738335))))], (1793 ^ _490194) ^ [_549311, _549313, _549315] : [class_Orderings_Oorder(_549311), c_Orderings_Oord__class_Oless(_549311, _549313, _549315), _549313 = _549315], (11984 ^ _490194) ^ [] : [-(class_Groups_Ozero(tc_Complex_Ocomplex))], (11898 ^ _490194) ^ [] : [-(class_Rings_Oring__1(tc_RealDef_Oreal))], (6005 ^ _490194) ^ [_697979, _697981, _697983] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_697979)), _697981), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_697979)), _697983)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _697981, _697983))], (10 ^ _490194) ^ [_490629, _490631, _490633] : [-(_490633 = _490629), _490633 = _490631, _490631 = _490629], (10083 ^ _490194) ^ [_848885, _848887, _848889] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _848885), _848887)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _848885), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _848889, _848887))))], (2353 ^ _490194) ^ [_567468, _567470] : [class_Orderings_Oorder(_567468), 2356 ^ _490194 : [(2357 ^ _490194) ^ [] : [c_SEQ_Omonoseq(_567468, _567470), 2362 ^ _490194 : [(2363 ^ _490194) ^ [_567824, _567826] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _567826), _567824)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_567468, hAPP(_567470, _567826)), hAPP(_567470, _567824))))]], 2368 ^ _490194 : [(2369 ^ _490194) ^ [_568062, _568064] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _568064), _568062)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_567468, hAPP(_567470, _568062)), hAPP(_567470, _568064))))]]], (2375 ^ _490194) ^ [] : [2378 ^ _490194 : [(2381 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_567468, hAPP(_567470, 2376 ^ [_567468, _567470])), hAPP(_567470, 2377 ^ [_567468, _567470])))], (2385 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, 2382 ^ [_567468, _567470]), 2383 ^ [_567468, _567470])))], (2387 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_567468, hAPP(_567470, 2383 ^ [_567468, _567470])), hAPP(_567470, 2382 ^ [_567468, _567470])))], (2379 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, 2376 ^ [_567468, _567470]), 2377 ^ [_567468, _567470])))]], -(c_SEQ_Omonoseq(_567468, _567470))]]], (12040 ^ _490194) ^ [_918186] : [class_Rings_Olinordered__idom(_918186), -(class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(_918186)))], (10839 ^ _490194) ^ [_878518, _878520] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _878518)), -(c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _878518, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _878520))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatceiling(_878518), _878520))], (5061 ^ _490194) ^ [_663453, _663455, _663457, _663459] : [class_Groups_Oab__group__add(_663453), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_663453, _663455)), _663457)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_663453, _663459)), _663457)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_663453, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_663453), _663455, _663459))), _663457)))], (2495 ^ _490194) ^ [_572627] : [-(_572627 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _572627))], (7749 ^ _490194) ^ [_758515, _758517, _758519, _758521, _758523] : [class_Rings_Olinordered__semiring__strict(_758515), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_758515, _758517), _758519)), c_Orderings_Oord__class_Oless(_758515, _758521, _758523), c_Orderings_Oord__class_Oless(_758515, c_Groups_Ozero__class_Ozero(_758515), _758517), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_758515, c_Groups_Ozero__class_Ozero(_758515)), _758521)), -(c_Orderings_Oord__class_Oless(_758515, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_758515), _758517), _758521), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_758515), _758519), _758523)))], (10771 ^ _490194) ^ [_876055] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _876055)), -(c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _876055, c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatceiling(_876055), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (8113 ^ _490194) ^ [_773405, _773407, _773409] : [class_Rings_Ocomm__semiring__0(_773405), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_773405, c_Polynomial_Opcompose(_773405, _773407, _773409))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Polynomial_Odegree(_773405, _773407)), c_Polynomial_Odegree(_773405, _773409)))))], (11814 ^ _490194) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal))], (11144 ^ _490194) ^ [_889592] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _889592)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat)), c_RComplete_Onatfloor(_889592))))], (8510 ^ _490194) ^ [_789331, _789333, _789335, _789337] : [class_Groups_Oordered__cancel__ab__semigroup__add(_789331), c_Orderings_Oord__class_Oless(_789331, _789333, _789335), -(c_Orderings_Oord__class_Oless(_789331, c_Groups_Oplus__class_Oplus(_789331, _789333, _789337), c_Groups_Oplus__class_Oplus(_789331, _789335, _789337)))], (3592 ^ _490194) ^ [_611363, _611365] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _611363), _611365)), -(hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _611365, _611363)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _611365), hAPP(c_RealDef_Oreal(tc_Nat_Onat), _611363)))], (6353 ^ _490194) ^ [_710110, _710112, _710114, _710116] : [class_Rings_Olinordered__semidom(_710110), c_Orderings_Oord__class_Oless(_710110, c_Groups_Oone__class_Oone(_710110), _710112), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_710110, hAPP(hAPP(c_Power_Opower__class_Opower(_710110), _710112), _710114)), hAPP(hAPP(c_Power_Opower__class_Opower(_710110), _710112), _710116))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _710114), _710116)))], (9375 ^ _490194) ^ [_821629, _821631, _821633] : [class_RealVector_Oreal__normed__vector(_821629), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_821629, _821631), c_RealVector_Onorm__class_Onorm(_821629, _821633))), c_RealVector_Onorm__class_Onorm(_821629, c_Groups_Oplus__class_Oplus(_821629, _821631, _821633)))))], (10854 ^ _490194) ^ [_879125] : [c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _879125) = 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, _879125, 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, _879125, 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, _879125, 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, _879125, c_Complex_Oii)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (6587 ^ _490194) ^ [_718498, _718500, _718502] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Ominus__class_Ominus(tc_Int_Oint, _718498, _718500)), _718502) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _718498), _718502), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _718500), _718502)))], (7997 ^ _490194) ^ [_768013, _768015, _768017, _768019, _768021] : [class_Rings_Ocomm__semiring__1(_768013), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_768013), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_768013), _768015), _768017)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_768013), _768019), _768021)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_768013), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_768013), _768015), _768019)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_768013), _768017), _768021)))], (5767 ^ _490194) ^ [_689052] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _689052), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _689052), _689052))))], (12124 ^ _490194) ^ [_920846] : [class_Rings_Ocomm__semiring__1(_920846), -(class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(_920846)))], (482 ^ _490194) ^ [_505134, _505136] : [-(class_Groups_Ocomm__monoid__mult(_505134)), _505136 = _505134, class_Groups_Ocomm__monoid__mult(_505136)], (11170 ^ _490194) ^ [_890559, _890561] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _890559)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _890561)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_RComplete_Onatfloor(_890559)), c_RComplete_Onatfloor(_890561))), c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _890559), _890561)))))], (9905 ^ _490194) ^ [_841308, _841310] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _841308, c_Nat_OSuc(_841310)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _841308, _841310)))], (4320 ^ _490194) ^ [_637719] : [-(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(_637719))))], (11944 ^ _490194) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex))], (1691 ^ _490194) ^ [_546035, _546037, _546039, _546041] : [class_Orderings_Oord(_546035), c_Orderings_Oord__class_Oless(_546035, _546037, _546039), _546039 = _546041, -(c_Orderings_Oord__class_Oless(_546035, _546037, _546041))], (272 ^ _490194) ^ [_498939, _498941] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_498939)), _498941 = _498939, class_Groups_Oordered__ab__semigroup__add__imp__le(_498941)], (7041 ^ _490194) ^ [_734431, _734433, _734435] : [class_Rings_Oordered__cancel__semiring(_734431), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_734431, c_Groups_Ozero__class_Ozero(_734431)), _734433)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_734431, c_Groups_Ozero__class_Ozero(_734431)), _734435)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_734431, c_Groups_Ozero__class_Ozero(_734431)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_734431), _734433), _734435))))], (2517 ^ _490194) ^ [_573285, _573287] : [2518 ^ _490194 : [(2521 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _573287, _573285)], (2519 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _573285, _573287)]], _573285 = _573287], (5969 ^ _490194) ^ [_696717, _696719, _696721] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _696717), _696719), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _696717), _696721)), 5972 ^ _490194 : [(5975 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _696719, _696721))], (5973 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _696717))]]], (3216 ^ _490194) ^ [_598424, _598426, _598428] : [class_Groups_Oordered__ab__group__add__abs(_598424), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_598424, c_Groups_Oabs__class_Oabs(_598424, _598426)), _598428)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_598424, _598426), _598428)))], (11610 ^ _490194) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (1719 ^ _490194) ^ [_546927, _546929, _546931, _546933] : [class_Orderings_Oord(_546927), _546929 = _546931, c_Orderings_Oord__class_Oless(_546927, _546931, _546933), -(c_Orderings_Oord__class_Oless(_546927, _546929, _546933))], (8290 ^ _490194) ^ [_781468, _781470, _781472, _781474, _781476] : [class_Rings_Ocomm__semiring__1(_781468), -(c_Groups_Oplus__class_Oplus(_781468, c_Groups_Oplus__class_Oplus(_781468, _781470, _781472), c_Groups_Oplus__class_Oplus(_781468, _781474, _781476)) = c_Groups_Oplus__class_Oplus(_781468, c_Groups_Oplus__class_Oplus(_781468, _781470, _781474), c_Groups_Oplus__class_Oplus(_781468, _781472, _781476)))], (742 ^ _490194) ^ [_512804, _512806] : [-(class_Orderings_Oord(_512804)), _512806 = _512804, class_Orderings_Oord(_512806)], (5438 ^ _490194) ^ [_675895] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _675895)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _675895))], (4149 ^ _490194) ^ [_631546] : [4150 ^ _490194 : [(4151 ^ _490194) ^ [_631617] : [_631546 = c_Nat_OSuc(_631617)]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _631546))], (3867 ^ _490194) ^ [_621778] : [c_Nat_OSuc(_621778) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (6265 ^ _490194) ^ [_707145, _707147] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _707145), c_Groups_Ominus__class_Ominus(tc_Int_Oint, _707147, c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _707145, _707147))], (5187 ^ _490194) ^ [_667580] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _667580))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _667580)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (4231 ^ _490194) ^ [_634457, _634459] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _634457, _634459), c_Nat_OSuc(_634457)))], (2629 ^ _490194) ^ [_577150, _577152, _577154] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _577150, _577152), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _577150, _577154), _577152))], (9734 ^ _490194) ^ [_834835, _834837, _834839, _834841] : [_834835 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _834837), _834839), _834841), -(_834837 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _834835, _834837) = _834839), 9741 ^ _490194 : [(9744 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _834841)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _834841, _834837)], (9742 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _834837))]], 9749 ^ _490194 : [(9752 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _834837, _834841), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _834841), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (9750 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _834837)]]], (2049 ^ _490194) ^ [_557304, _557306, _557308] : [class_Orderings_Olinorder(_557304), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_557304, _557306), _557308)), c_Orderings_Oord__class_Oless(_557304, _557308, _557306)], (3765 ^ _490194) ^ [_618120] : [-(hBOOL(hAPP(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), _618120))))], (2543 ^ _490194) ^ [_574216] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _574216, _574216) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2945 ^ _490194) ^ [_588428, _588430] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _588428), _588430)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _588430), _588428)), -(_588428 = _588430)], (11408 ^ _490194) ^ [_899681, _899683, _899685, _899687, _899689, _899691] : [class_RealVector_Oreal__field(_899681), -(c_Rings_Oinverse__class_Odivide(_899681, c_Groups_Ominus__class_Ominus(_899681, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_899681), _899683), _899685), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_899681), _899687), _899689)), _899691) = c_Groups_Oplus__class_Oplus(_899681, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_899681), _899683), c_Rings_Oinverse__class_Odivide(_899681, c_Groups_Ominus__class_Ominus(_899681, _899685, _899689), _899691)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_899681), c_Rings_Oinverse__class_Odivide(_899681, c_Groups_Ominus__class_Ominus(_899681, _899683, _899687), _899691)), _899689)))], (462 ^ _490194) ^ [_504544, _504546] : [-(class_Rings_Olinordered__semidom(_504544)), _504546 = _504544, class_Rings_Olinordered__semidom(_504546)], (10369 ^ _490194) ^ [_859763, _859765, _859767] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _859763), _859765)), 10372 ^ _490194 : [(10379 ^ _490194) ^ [] : [_859765 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _859767, _859763), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _859765, _859763) = _859767)], (10373 ^ _490194) ^ [] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _859765, _859763) = _859767, -(_859765 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _859767, _859763))]]], (5103 ^ _490194) ^ [_664903, _664905] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _664903), 5106 ^ _490194 : [(5113 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _664905, _664903), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(c_Int_Onat, _664905), hAPP(c_Int_Onat, _664903)))], (5107 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(c_Int_Onat, _664905), hAPP(c_Int_Onat, _664903)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _664905, _664903))]]], (9977 ^ _490194) ^ [_844176, _844178] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _844176, _844178), _844176)], (3166 ^ _490194) ^ [_596723, _596725, _596727] : [class_Nat_Osemiring__char__0(_596723), 3169 ^ _490194 : [(3176 ^ _490194) ^ [] : [_596725 = _596727, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_596723), _596725) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_596723), _596727))], (3170 ^ _490194) ^ [] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(_596723), _596725) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_596723), _596727), -(_596725 = _596727)]]], (8802 ^ _490194) ^ [_800089, _800091, _800093] : [class_Groups_Oordered__comm__monoid__add(_800089), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_800089, _800091), c_Groups_Ozero__class_Ozero(_800089))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_800089, _800093), c_Groups_Ozero__class_Ozero(_800089))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_800089, c_Groups_Oplus__class_Oplus(_800089, _800091, _800093)), c_Groups_Ozero__class_Ozero(_800089))))], (8846 ^ _490194) ^ [_801487, _801489] : [class_Groups_Olinordered__ab__group__add(_801487), 8849 ^ _490194 : [(8856 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(_801487, _801489, c_Groups_Ozero__class_Ozero(_801487)), -(c_Orderings_Oord__class_Oless(_801487, c_Groups_Oplus__class_Oplus(_801487, _801489, _801489), c_Groups_Ozero__class_Ozero(_801487)))], (8850 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(_801487, c_Groups_Oplus__class_Oplus(_801487, _801489, _801489), c_Groups_Ozero__class_Ozero(_801487)), -(c_Orderings_Oord__class_Oless(_801487, _801489, c_Groups_Ozero__class_Ozero(_801487)))]]], (11914 ^ _490194) ^ [] : [-(class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex))], (6531 ^ _490194) ^ [] : [c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)], (11734 ^ _490194) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (6277 ^ _490194) ^ [_707574] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oabs__class_Oabs(tc_Int_Oint, _707574), c_Groups_Oone__class_Oone(tc_Int_Oint)), -(_707574 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (8125 ^ _490194) ^ [_773913, _773915, _773917] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _773913), 8131 ^ _490194 : [(8134 ^ _490194) ^ [] : [hBOOL(hAPP(_773915, c_Groups_Ominus__class_Ominus(tc_Int_Oint, 8130 ^ [_773913, _773915, _773917], _773913)))], (8132 ^ _490194) ^ [] : [-(hBOOL(hAPP(_773915, 8130 ^ [_773913, _773915, _773917])))]], hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _773917)), 8139 ^ _490194 : [(8140 ^ _490194) ^ [_774430] : [hBOOL(hAPP(_773915, _774430)), -(hBOOL(hAPP(_773915, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _774430, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _773917), _773913)))))]]], (862 ^ _490194) ^ [_516380, _516382, _516384, _516386, _516388, _516390] : [-(c_Orderings_Oord__class_Oless(_516388, _516384, _516380)), c_Orderings_Oord__class_Oless(_516390, _516386, _516382), _516390 = _516388, _516386 = _516384, _516382 = _516380], (12154 ^ _490194) ^ [_921796] : [class_Groups_Ocomm__monoid__add(_921796), -(class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(_921796)))], (5075 ^ _490194) ^ [_663941, _663943, _663945] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _663941), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _663941), _663943)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _663945, _663943)), c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _663945, _663941))))], (4396 ^ _490194) ^ [_640487, _640489] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _640487, _640489), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _640487), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _640489)))], (9838 ^ _490194) ^ [_838648, _838650, _838652] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _838648, _838650)), _838652) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _838648), _838652), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _838650), _838652)))], (4203 ^ _490194) ^ [_633541, _633543] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _633541, _633543), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_633541)), _633543)))], (4118 ^ _490194) ^ [_630483, _630485] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _630483, c_Nat_OSuc(_630485))), 4119 ^ _490194 : [(4122 ^ _490194) ^ [_630652] : [_630483 = c_Nat_OSuc(_630652), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _630652, _630485)], (4120 ^ _490194) ^ [] : [_630483 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (11202 ^ _490194) ^ [_891731, _891733] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _891731)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _891733), -(c_RComplete_Onatfloor(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, _891731, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _891733))) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, c_RComplete_Onatfloor(_891731), _891733))], (4935 ^ _490194) ^ [_659058, _659060] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _659058)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _659060)), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(c_Int_Onat, _659058), hAPP(c_Int_Onat, _659060)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _659058, _659060)))], (5865 ^ _490194) ^ [_692842, _692844, _692846, _692848] : [class_Divides_Osemiring__div(_692842), -(_692844 = c_Groups_Ozero__class_Ozero(_692842)), -(c_Divides_Odiv__class_Odiv(_692842, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_692842), _692846), _692844), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_692842), _692848), _692844)) = c_Divides_Odiv__class_Odiv(_692842, _692846, _692848))], (6685 ^ _490194) ^ [_722021, _722023] : [-(hAPP(c_RealDef_Oreal(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _722021), _722023)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(c_RealDef_Oreal(tc_Nat_Onat), _722021)), hAPP(c_RealDef_Oreal(tc_Nat_Onat), _722023)))], (12316 ^ _490194) ^ [_926926] : [class_Rings_Oidom(_926926), -(class_Rings_Oidom(tc_Polynomial_Opoly(_926926)))], (10687 ^ _490194) ^ [_872855, _872857] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _872855)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _872857)), -(hAPP(c_Int_Onat, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _872855, _872857)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(c_Int_Onat, _872855), hAPP(c_Int_Onat, _872857)))], (1000 ^ _490194) ^ [_521873, _521875] : [_521875 = _521873, -(c_RComplete_Onatceiling(_521875) = c_RComplete_Onatceiling(_521873))], (2251 ^ _490194) ^ [_563654, _563656, _563658] : [class_Groups_Oab__group__add(_563654), 2254 ^ _490194 : [(2261 ^ _490194) ^ [] : [c_Groups_Ominus__class_Ominus(_563654, _563656, _563658) = c_Groups_Ozero__class_Ozero(_563654), -(_563656 = _563658)], (2255 ^ _490194) ^ [] : [_563656 = _563658, -(c_Groups_Ominus__class_Ominus(_563654, _563656, _563658) = c_Groups_Ozero__class_Ozero(_563654))]]], (3973 ^ _490194) ^ [_625382, _625384] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_625382), c_Nat_OSuc(_625384)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _625382, _625384))], (11256 ^ _490194) ^ [_894073, _894075] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, _894073, _894075))), 11259 ^ _490194 : [(11266 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _894073))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _894075), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))], (11260 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _894073), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _894075)))]]], (11294 ^ _490194) ^ [_895472, _895474] : [-(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _895472), _895474), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _895472), _895472)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, _895474, _895472))], (4440 ^ _490194) ^ [_642181] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _642181), _642181)))], (4945 ^ _490194) ^ [_659370] : [-(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _659370, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = _659370)], (172 ^ _490194) ^ [_495989, _495991] : [-(class_Rings_Odivision__ring__inverse__zero(_495989)), _495991 = _495989, class_Rings_Odivision__ring__inverse__zero(_495991)], (5398 ^ _490194) ^ [_674450, _674452] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _674450)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _674450)), _674452) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _674450), _674452)))], (2920 ^ _490194) ^ [_587430, _587432, _587434] : [class_RealVector_Oreal__normed__vector(_587430), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_587430, hAPP(_587432, 2925 ^ [_587430, _587432, _587434]))), _587434)), -(c_SEQ_OBseq(_587430, _587432))], (11324 ^ _490194) ^ [_896663, _896665, _896667, _896669] : [class_Fields_Ofield__inverse__zero(_896663), -(hAPP(hAPP(c_Power_Opower__class_Opower(_896663), c_Rings_Oinverse__class_Odivide(_896663, _896665, _896667)), _896669) = c_Rings_Oinverse__class_Odivide(_896663, hAPP(hAPP(c_Power_Opower__class_Opower(_896663), _896665), _896669), hAPP(hAPP(c_Power_Opower__class_Opower(_896663), _896667), _896669)))], (12046 ^ _490194) ^ [_918376] : [class_Rings_Olinordered__idom(_918376), -(class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(_918376)))], (11600 ^ _490194) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))], (10845 ^ _490194) ^ [_878748] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _878748)), 10849 ^ _490194 : [(10852 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _878748, hAPP(c_RealDef_Oreal(tc_Nat_Onat), 10848 ^ [_878748])))], (10850 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, 10848 ^ [_878748], c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _878748)))]]], (5569 ^ _490194) ^ [_680878, _680880, _680882] : [class_Rings_Osemiring__1(_680878), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_680878), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _680880), _680882)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_680878), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_680878), _680880)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_680878), _680882)))], (5987 ^ _490194) ^ [_697362, _697364] : [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), _697362), _697364)), 5990 ^ _490194 : [(5993 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _697364))], (5991 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _697362))]]], (10101 ^ _490194) ^ [_849634, _849636, _849638] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _849636), _849638)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _849634, _849636)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _849634, _849638))))], (11894 ^ _490194) ^ [] : [-(class_Rings_Osemiring(tc_RealDef_Oreal))], (4412 ^ _490194) ^ [_641103, _641105] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _641103), _641105)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _641103)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _641105))))], (3188 ^ _490194) ^ [_597491] : [class_Groups_Oordered__ab__group__add__abs(_597491), -(c_Groups_Oabs__class_Oabs(_597491, c_Groups_Ozero__class_Ozero(_597491)) = c_Groups_Ozero__class_Ozero(_597491))], (3528 ^ _490194) ^ [_609132, _609134] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _609132, _609134), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _609132), hAPP(c_RealDef_Oreal(tc_Nat_Onat), _609134)))], (11862 ^ _490194) ^ [] : [-(class_Rings_Odivision__ring(tc_RealDef_Oreal))], (2219 ^ _490194) ^ [_562640, _562642, _562644] : [class_Orderings_Olinorder(_562640), 2222 ^ _490194 : [(2229 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_562640, _562644), _562642)), c_Orderings_Oord__class_Oless(_562640, _562642, _562644)], (2223 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(_562640, _562642, _562644)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_562640, _562644), _562642)))]]], (9786 ^ _490194) ^ [_836512, _836514, _836516] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _836512), 9792 ^ _490194 : [(9795 ^ _490194) ^ [] : [hBOOL(hAPP(_836514, c_Groups_Oplus__class_Oplus(tc_Int_Oint, 9791 ^ [_836512, _836514, _836516], _836512)))], (9793 ^ _490194) ^ [] : [-(hBOOL(hAPP(_836514, 9791 ^ [_836512, _836514, _836516])))]], hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _836516)), 9800 ^ _490194 : [(9801 ^ _490194) ^ [_837029] : [hBOOL(hAPP(_836514, _837029)), -(hBOOL(hAPP(_836514, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _837029, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _836516), _836512)))))]]], (9991 ^ _490194) ^ [_844871, _844873, _844875] : [_844873 = _844875, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _844871, _844873) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _844871, _844875))], (432 ^ _490194) ^ [_503659, _503661] : [-(class_Groups_Ocancel__comm__monoid__add(_503659)), _503661 = _503659, class_Groups_Ocancel__comm__monoid__add(_503661)], (11360 ^ _490194) ^ [_898049, _898051, _898053, _898055] : [class_Rings_Odivision__ring(_898049), -(_898051 = c_Groups_Ozero__class_Ozero(_898049)), 11367 ^ _490194 : [(11374 ^ _490194) ^ [] : [_898053 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_898049), _898055), _898051), -(c_Rings_Oinverse__class_Odivide(_898049, _898053, _898051) = _898055)], (11368 ^ _490194) ^ [] : [c_Rings_Oinverse__class_Odivide(_898049, _898053, _898051) = _898055, -(_898053 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_898049), _898055), _898051))]]], (1480 ^ _490194) ^ [_539044, _539046, _539048, _539050] : [class_Orderings_Oorder(_539044), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_539044, _539046), _539048)), _539046 = _539050, -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_539044, _539050), _539048)))], (11832 ^ _490194) ^ [] : [-(class_Rings_Olinordered__semiring(tc_RealDef_Oreal))], (80 ^ _490194) ^ [_492911, _492913, _492915, _492917] : [-(c_SEQ_Oincseq(_492915, _492911)), c_SEQ_Oincseq(_492917, _492913), _492917 = _492915, _492913 = _492911], (11702 ^ _490194) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (7339 ^ _490194) ^ [_744644, _744646, _744648, _744650] : [class_Rings_Olinordered__ring__strict(_744644), c_Orderings_Oord__class_Oless(_744644, c_Groups_Ozero__class_Ozero(_744644), _744646), 7346 ^ _490194 : [(7353 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(_744644, _744648, _744650), -(c_Orderings_Oord__class_Oless(_744644, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_744644), _744646), _744648), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_744644), _744646), _744650)))], (7347 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(_744644, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_744644), _744646), _744648), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_744644), _744646), _744650)), -(c_Orderings_Oord__class_Oless(_744644, _744648, _744650))]]], (5047 ^ _490194) ^ [_662975, _662977, _662979, _662981] : [class_Groups_Oab__group__add(_662975), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_662975, _662977), _662979), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_662975, _662981), _662979), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_662975, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_662975), _662977, _662981)), _662979))], (7533 ^ _490194) ^ [_751066, _751068, _751070, _751072] : [class_Rings_Olinordered__ring__strict(_751066), c_Orderings_Oord__class_Oless(_751066, _751068, _751070), c_Orderings_Oord__class_Oless(_751066, _751072, c_Groups_Ozero__class_Ozero(_751066)), -(c_Orderings_Oord__class_Oless(_751066, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_751066), _751072), _751070), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_751066), _751072), _751068)))], (5753 ^ _490194) ^ [_688452, _688454, _688456] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _688452), _688454)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _688456), _688452)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _688456), _688454))))], (6621 ^ _490194) ^ [_719778, _719780] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _719778), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _719780), -(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), _719778), _719780)))], (7727 ^ _490194) ^ [_757777, _757779, _757781, _757783, _757785] : [class_Rings_Olinordered__semiring__strict(_757777), c_Orderings_Oord__class_Oless(_757777, _757779, _757781), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_757777, _757783), _757785)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_757777, c_Groups_Ozero__class_Ozero(_757777)), _757779)), c_Orderings_Oord__class_Oless(_757777, c_Groups_Ozero__class_Ozero(_757777), _757783), -(c_Orderings_Oord__class_Oless(_757777, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_757777), _757779), _757783), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_757777), _757781), _757785)))], (3136 ^ _490194) ^ [_595443, _595445, _595447] : [class_Rings_Osemiring__1(_595443), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_595443), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _595445), _595447)) = hAPP(hAPP(c_Power_Opower__class_Opower(_595443), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_595443), _595445)), _595447))], (2541 ^ _490194) ^ [_574134] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _574134, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _574134)], (9363 ^ _490194) ^ [_821069, _821071, _821073, _821075, _821077] : [class_Groups_Oordered__ab__group__add__abs(_821069), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_821069, c_Groups_Oabs__class_Oabs(_821069, c_Groups_Ominus__class_Ominus(_821069, c_Groups_Oplus__class_Oplus(_821069, _821071, _821073), c_Groups_Oplus__class_Oplus(_821069, _821075, _821077)))), c_Groups_Oplus__class_Oplus(_821069, c_Groups_Oabs__class_Oabs(_821069, c_Groups_Ominus__class_Ominus(_821069, _821071, _821075)), c_Groups_Oabs__class_Oabs(_821069, c_Groups_Ominus__class_Ominus(_821069, _821073, _821077))))))], (8598 ^ _490194) ^ [_792836, _792838, _792840, _792842, _792844] : [class_RealVector_Oreal__normed__vector(_792836), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_792836, _792838), _792840), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_792836, _792842), _792844), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_792836, c_Groups_Oplus__class_Oplus(_792836, _792838, _792842)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _792840, _792844)))], (2689 ^ _490194) ^ [_579238, _579240] : [_579238 = _579240, -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _579238), _579240)))], (12070 ^ _490194) ^ [_919136] : [class_Rings_Olinordered__idom(_919136), -(class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(_919136)))], (8682 ^ _490194) ^ [_796046, _796048, _796050, _796052] : [class_Groups_Ocancel__semigroup__add(_796046), c_Groups_Oplus__class_Oplus(_796046, _796048, _796050) = c_Groups_Oplus__class_Oplus(_796046, _796052, _796050), -(_796048 = _796052)], (7069 ^ _490194) ^ [_735375, _735377, _735379] : [class_Rings_Oordered__cancel__semiring(_735375), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_735375, c_Groups_Ozero__class_Ozero(_735375)), _735377)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_735375, _735379), c_Groups_Ozero__class_Ozero(_735375))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_735375, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_735375), _735379), _735377)), c_Groups_Ozero__class_Ozero(_735375))))], (10363 ^ _490194) ^ [_859513, _859515] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _859513), _859515)), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _859515, _859513), _859513) = _859515)], (990 ^ _490194) ^ [_521542, _521544, _521546, _521548] : [-(c_Int_Onat__aux(_521548, _521544) = c_Int_Onat__aux(_521546, _521542)), _521548 = _521546, _521544 = _521542], (1062 ^ _490194) ^ [_524120, _524122] : [_524122 = _524120, -(c_RealDef_Oreal(_524122) = c_RealDef_Oreal(_524120))], (11952 ^ _490194) ^ [] : [-(class_Rings_Odivision__ring(tc_Complex_Ocomplex))], (3512 ^ _490194) ^ [_608579] : [_608579 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_RealDef_Oreal(tc_Nat_Onat), _608579) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (3366 ^ _490194) ^ [_603421, _603423] : [class_Groups_Oordered__ab__group__add__abs(_603421), c_Orderings_Oord__class_Oless(_603421, c_Groups_Oabs__class_Oabs(_603421, _603423), c_Groups_Ozero__class_Ozero(_603421))], (7923 ^ _490194) ^ [_764505, _764507, _764509] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _764505), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _764507)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _764505), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _764509)))), -(_764507 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (4558 ^ _490194) ^ [_646598, _646600] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _646598), _646600)), -(c_Nat__Transfer_Otsub(_646600, _646598) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, _646600, _646598))], (11892 ^ _490194) ^ [] : [-(class_Orderings_Oorder(tc_RealDef_Oreal))], (6631 ^ _490194) ^ [_720109, _720111, _720113] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _720109), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _720111, _720113), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _720109), _720111), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _720109), _720113)))], (10245 ^ _490194) ^ [_854805, _854807] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _854805, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _854807, _854805))))], (362 ^ _490194) ^ [_501594, _501596] : [-(class_Rings_Oring__1__no__zero__divisors(_501594)), _501596 = _501594, class_Rings_Oring__1__no__zero__divisors(_501596)], (4959 ^ _490194) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (11330 ^ _490194) ^ [_896975, _896977, _896979, _896981] : [class_Fields_Ofield(_896975), -(_896977 = c_Groups_Ozero__class_Ozero(_896975)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_896975), c_Rings_Oinverse__class_Odivide(_896975, _896979, _896977)), _896981) = c_Rings_Oinverse__class_Odivide(_896975, hAPP(hAPP(c_Power_Opower__class_Opower(_896975), _896979), _896981), hAPP(hAPP(c_Power_Opower__class_Opower(_896975), _896977), _896981)))], (5097 ^ _490194) ^ [_664681] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _664681), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _664681) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3763 ^ _490194) ^ [_618038] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _618038), c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (4366 ^ _490194) ^ [_639341, _639343] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _639341), _639343)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _639341)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _639343))))], (11816 ^ _490194) ^ [] : [-(class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal))], (11096 ^ _490194) ^ [] : [-(c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (3879 ^ _490194) ^ [_622311, _622313] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _622311), _622313) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_622313 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_622311 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (11766 ^ _490194) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (10751 ^ _490194) ^ [_875236, _875238] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _875236)), -(hBOOL(hAPP(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), _875238)), _875236), 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, _875236, c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), _875238))))], (4130 ^ _490194) ^ [_630950] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _630950, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_630950 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1230 ^ _490194) ^ [_530467, _530469] : [class_RealVector_Oreal__normed__vector(_530467), 1233 ^ _490194 : [(1240 ^ _490194) ^ [] : [_530469 = c_Groups_Ozero__class_Ozero(_530467), -(c_RealVector_Onorm__class_Onorm(_530467, _530469) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (1234 ^ _490194) ^ [] : [c_RealVector_Onorm__class_Onorm(_530467, _530469) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_530469 = c_Groups_Ozero__class_Ozero(_530467))]]], (2955 ^ _490194) ^ [_588761, _588763, _588765] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _588761), _588763)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _588763), _588765)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _588761), _588765)))], (8572 ^ _490194) ^ [_791621] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _791621) = _791621)], (12268 ^ _490194) ^ [_925406] : [class_Rings_Ocomm__semiring__0(_925406), -(class_Rings_Omult__zero(tc_Polynomial_Opoly(_925406)))], (9470 ^ _490194) ^ [_825224, _825226, _825228, _825230, _825232, _825234] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _825224), _825226), _825228) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _825230), _825232), _825234), 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), _825230), _825232), _825234), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _825228, _825224), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _825234)), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _825230), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _825230), _825224)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _825232), _825226)))], (202 ^ _490194) ^ [_496874, _496876] : [-(class_RealVector_Oreal__normed__vector(_496874)), _496876 = _496874, class_RealVector_Oreal__normed__vector(_496876)], (5995 ^ _490194) ^ [_697617, _697619] : [-(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), _697617), _697619))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _697617), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _697619)], (11976 ^ _490194) ^ [] : [-(class_Rings_Osemiring(tc_Complex_Ocomplex))], (4167 ^ _490194) ^ [_632217, _632219] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_632217)), _632219)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _632217, _632219))], (7387 ^ _490194) ^ [_746201, _746203, _746205] : [class_Rings_Olinordered__semiring__strict(_746201), c_Orderings_Oord__class_Oless(_746201, c_Groups_Ozero__class_Ozero(_746201), _746203), c_Orderings_Oord__class_Oless(_746201, _746205, c_Groups_Ozero__class_Ozero(_746201)), -(c_Orderings_Oord__class_Oless(_746201, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_746201), _746205), _746203), c_Groups_Ozero__class_Ozero(_746201)))], (1022 ^ _490194) ^ [_522696, _522698, _522700, _522702] : [-(c_Groups_Oabs__class_Oabs(_522702, _522698) = c_Groups_Oabs__class_Oabs(_522700, _522696)), _522702 = _522700, _522698 = _522696], (4458 ^ _490194) ^ [_642877, _642879] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _642877), _642879)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _642879), _642877)), -(_642877 = _642879)], (4233 ^ _490194) ^ [_634573, _634575] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _634573), _634575)), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_634575), _634573) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _634575, _634573)))], (10561 ^ _490194) ^ [_867782, _867784, _867786, _867788, _867790] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _867782), _867784)), -(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), _867782), _867786), _867788), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _867784), _867786), _867790)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _867788, 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, _867784, _867782)), _867786), _867790)))], (11560 ^ _490194) ^ [] : [-(class_Rings_Ocomm__ring(tc_RealDef_Oreal))], (9652 ^ _490194) ^ [_831526, _831528, _831530] : [hBOOL(hAPP(_831526, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _831528, _831530))), 9655 ^ _490194 : [(9680 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _831530, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 9683 ^ _490194 : [(9684 ^ _490194) ^ [_832649] : [-(hBOOL(hAPP(_831526, _832649))), 9685 ^ _490194 : [(9686 ^ _490194) ^ [_832775] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _831530, _832775), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _832775), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _831528 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _831530), _832649), _832775)]]]]], (9662 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _831530), 9665 ^ _490194 : [(9666 ^ _490194) ^ [_832052] : [-(hBOOL(hAPP(_831526, _832052))), 9667 ^ _490194 : [(9668 ^ _490194) ^ [_832175] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _832175)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _832175, _831530), _831528 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _831530), _832052), _832175)]]]]], (9656 ^ _490194) ^ [] : [_831530 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_831526, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (10196 ^ _490194) ^ [_853107, _853109] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _853107, _853109)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _853107)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _853109))], (9899 ^ _490194) ^ [_841000] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _841000) = _841000)], (6219 ^ _490194) ^ [_705503, _705505, _705507] : [6220 ^ _490194 : [(6223 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _705503), _705507))], (6221 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _705505))]], -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _705503), _705505)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _705507), _705505))))], (12178 ^ _490194) ^ [_922556] : [class_Rings_Ocomm__semiring__0(_922556), -(class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(_922556)))], (8152 ^ _490194) ^ [_774990, _774992, _774994] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _774990), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _774992, 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, _774992, _774994)), c_Groups_Oone__class_Oone(tc_Int_Oint))), _774990)), _774994))], (964 ^ _490194) ^ [_520618, _520620, _520622, _520624, _520626, _520628] : [-(c_Polynomial_Opcompose(_520628, _520624, _520620) = c_Polynomial_Opcompose(_520626, _520622, _520618)), _520628 = _520626, _520624 = _520622, _520620 = _520618], (2973 ^ _490194) ^ [_589414, _589416] : [class_Orderings_Oorder(_589414), 2980 ^ _490194 : [(2983 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_589414, hAPP(_589416, 2978 ^ [_589414, _589416])), hAPP(_589416, 2979 ^ [_589414, _589416])))], (2981 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, 2978 ^ [_589414, _589416]), 2979 ^ [_589414, _589416])))]], -(c_SEQ_Omonoseq(_589414, _589416))], (1639 ^ _490194) ^ [_544353, _544355, _544357] : [class_Orderings_Opreorder(_544353), c_Orderings_Oord__class_Oless(_544353, _544355, _544357), c_Orderings_Oord__class_Oless(_544353, _544357, _544355)], (9612 ^ _490194) ^ [_830083, _830085, _830087] : [class_Rings_Ocomm__ring__1(_830083), -(c_Groups_Ominus__class_Ominus(_830083, hAPP(hAPP(c_Power_Opower__class_Opower(_830083), _830085), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(hAPP(c_Power_Opower__class_Opower(_830083), _830087), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_830083), c_Groups_Ominus__class_Ominus(_830083, _830085, _830087)), c_Groups_Oplus__class_Oplus(_830083, _830085, _830087)))], (10731 ^ _490194) ^ [_874359, _874361, _874363] : [-(hBOOL(hAPP(_874359, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _874361, _874363)))), 10734 ^ _490194 : [(10737 ^ _490194) ^ [] : [hBOOL(hAPP(_874359, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10735 ^ _490194) ^ [] : [-(_874363 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 10738 ^ _490194 : [(10743 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, 10741 ^ [_874359, _874361, _874363], _874363))], (10745 ^ _490194) ^ [] : [-(_874361 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _874363), 10740 ^ [_874359, _874361, _874363]), 10741 ^ [_874359, _874361, _874363]))], (10747 ^ _490194) ^ [] : [hBOOL(hAPP(_874359, 10740 ^ [_874359, _874361, _874363]))], (10739 ^ _490194) ^ [] : [_874363 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (5885 ^ _490194) ^ [_693628, _693630, _693632] : [class_Groups_Omonoid__mult(_693628), -(hAPP(hAPP(c_Power_Opower__class_Opower(_693628), _693630), c_Nat_OSuc(_693632)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_693628), hAPP(hAPP(c_Power_Opower__class_Opower(_693628), _693630), _693632)), _693630))], (12088 ^ _490194) ^ [_919706] : [class_Rings_Olinordered__idom(_919706), -(class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(_919706)))], (4947 ^ _490194) ^ [_659481, _659483] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _659481, _659483), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _659481, _659483) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4568 ^ _490194) ^ [_647024, _647026] : [class_Divides_Osemiring__div(_647024), -(c_Divides_Odiv__class_Odiv(_647024, _647026, c_Groups_Ozero__class_Ozero(_647024)) = c_Groups_Ozero__class_Ozero(_647024))], (4953 ^ _490194) ^ [_659687] : [class_Groups_Ozero(_659687), -(c_Polynomial_Odegree(_659687, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_659687))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3871 ^ _490194) ^ [_621936] : [c_Nat_OSuc(_621936) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5221 ^ _490194) ^ [_668748, _668750] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _668748), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _668750, _668748)), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _668750, _668748) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _668750, _668748), _668748)))], (7111 ^ _490194) ^ [_736805, _736807, _736809, _736811] : [class_Rings_Oordered__semiring(_736805), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_736805, _736807), _736809)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_736805, c_Groups_Ozero__class_Ozero(_736805)), _736811)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_736805, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_736805), _736807), _736811)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_736805), _736809), _736811))))], (6071 ^ _490194) ^ [_700406, _700408, _700410] : [class_Rings_Olinordered__semidom(_700406), c_Orderings_Oord__class_Oless(_700406, c_Groups_Oone__class_Oone(_700406), _700408), -(c_Orderings_Oord__class_Oless(_700406, c_Groups_Oone__class_Oone(_700406), hAPP(hAPP(c_Power_Opower__class_Opower(_700406), _700408), c_Nat_OSuc(_700410))))], (9558 ^ _490194) ^ [_828282, _828284, _828286] : [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), _828282), _828284), _828286), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _828286)), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _828282), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _828284), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (5551 ^ _490194) ^ [_680164, _680166] : [class_Groups_Omonoid__mult(_680164), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_680164), c_Groups_Oone__class_Oone(_680164)), _680166) = _680166)], (9347 ^ _490194) ^ [_820405, _820407, _820409] : [class_Divides_Osemiring__div(_820405), -(_820407 = c_Groups_Ozero__class_Ozero(_820405)), -(c_Divides_Odiv__class_Odiv(_820405, c_Groups_Oplus__class_Oplus(_820405, _820409, _820407), _820407) = c_Groups_Oplus__class_Oplus(_820405, c_Divides_Odiv__class_Odiv(_820405, _820409, _820407), c_Groups_Oone__class_Oone(_820405)))], (6455 ^ _490194) ^ [_713732, _713734, _713736] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _713732), 6458 ^ _490194 : [(6465 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _713734), _713736)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _713732), _713734)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _713732), _713736))))], (6459 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _713732), _713734)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _713732), _713736))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _713734), _713736)))]]], (11784 ^ _490194) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal))], (7565 ^ _490194) ^ [_752120] : [class_Rings_Olinordered__semidom(_752120), -(c_Orderings_Oord__class_Oless(_752120, c_Groups_Ozero__class_Ozero(_752120), c_Groups_Oone__class_Oone(_752120)))], (4336 ^ _490194) ^ [_638289] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _638289)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_638289 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11680 ^ _490194) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (6691 ^ _490194) ^ [_722343, _722345] : [c_Groups_Oabs__class_Oabs(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _722343), _722345)) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(c_Groups_Oabs__class_Oabs(tc_Int_Oint, _722343) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (692 ^ _490194) ^ [_511329, _511331] : [-(class_Rings_Omult__zero(_511329)), _511331 = _511329, class_Rings_Omult__zero(_511331)], (6181 ^ _490194) ^ [_704137, _704139] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _704137), _704139)))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _704137)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _704139))], (11640 ^ _490194) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (5297 ^ _490194) ^ [_671165, _671167] : [hAPP(c_Int_Onat, _671165) = _671167, 5300 ^ _490194 : [(5307 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _671165))), -(_671167 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5301 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _671165)), -(_671165 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _671167))]]], (10447 ^ _490194) ^ [_862932, _862934, _862936] : [-(hBOOL(hAPP(_862932, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _862934, _862936)))), 10450 ^ _490194 : [(10453 ^ _490194) ^ [] : [hBOOL(hAPP(_862932, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10451 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _862934, _862936))]], 10455 ^ _490194 : [(10458 ^ _490194) ^ [] : [hBOOL(hAPP(_862932, 10454 ^ [_862932, _862934, _862936]))], (10456 ^ _490194) ^ [] : [-(_862934 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _862936, 10454 ^ [_862932, _862934, _862936]))]]], (11992 ^ _490194) ^ [_916666] : [class_Rings_Oidom(_916666), -(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(_916666)))], (11240 ^ _490194) ^ [_893417, _893419, _893421] : [-(c_RealVector_Onorm__class_Onorm(_893417, c_Rings_Oinverse__class_Odivide(_893417, _893419, _893421)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_893417, _893419), c_RealVector_Onorm__class_Onorm(_893417, _893421))), class_Fields_Ofield__inverse__zero(_893417), class_RealVector_Oreal__normed__field(_893417)], (11718 ^ _490194) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (9807 ^ _490194) ^ [_837299, _837301] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _837299), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _837301), 9815 ^ _490194 : [(9820 ^ _490194) ^ [_837803] : [-(_837803 = 9814 ^ [_837299, _837301]), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _837803), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _837803), _837299) = _837301], (9818 ^ _490194) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), 9814 ^ [_837299, _837301]), _837299) = _837301)], (9816 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 9814 ^ [_837299, _837301]))]]], (8934 ^ _490194) ^ [_804357, _804359, _804361] : [class_Rings_Olinordered__ring__strict(_804357), 8937 ^ _490194 : [(8946 ^ _490194) ^ [] : [-(c_Groups_Oplus__class_Oplus(_804357, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_804357), _804359), _804359), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_804357), _804361), _804361)) = c_Groups_Ozero__class_Ozero(_804357)), _804359 = c_Groups_Ozero__class_Ozero(_804357), _804361 = c_Groups_Ozero__class_Ozero(_804357)], (8938 ^ _490194) ^ [] : [c_Groups_Oplus__class_Oplus(_804357, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_804357), _804359), _804359), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_804357), _804361), _804361)) = c_Groups_Ozero__class_Ozero(_804357), 8941 ^ _490194 : [(8944 ^ _490194) ^ [] : [-(_804361 = c_Groups_Ozero__class_Ozero(_804357))], (8942 ^ _490194) ^ [] : [-(_804359 = c_Groups_Ozero__class_Ozero(_804357))]]]]], (8278 ^ _490194) ^ [_780894, _780896, _780898, _780900] : [class_Rings_Ocomm__semiring__1(_780894), -(c_Groups_Oplus__class_Oplus(_780894, c_Groups_Oplus__class_Oplus(_780894, _780896, _780898), _780900) = c_Groups_Oplus__class_Oplus(_780894, _780896, c_Groups_Oplus__class_Oplus(_780894, _780898, _780900)))], (11694 ^ _490194) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (12208 ^ _490194) ^ [_923506] : [class_Rings_Ocomm__semiring__1(_923506), -(class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(_923506)))], (12220 ^ _490194) ^ [_923886] : [class_Rings_Olinordered__idom(_923886), -(class_Orderings_Opreorder(tc_Polynomial_Opoly(_923886)))], (8324 ^ _490194) ^ [_782688, _782690] : [class_Groups_Olinordered__ab__group__add(_782688), 8327 ^ _490194 : [(8334 ^ _490194) ^ [] : [_782690 = c_Groups_Ozero__class_Ozero(_782688), -(c_Groups_Oplus__class_Oplus(_782688, _782690, _782690) = c_Groups_Ozero__class_Ozero(_782688))], (8328 ^ _490194) ^ [] : [c_Groups_Oplus__class_Oplus(_782688, _782690, _782690) = c_Groups_Ozero__class_Ozero(_782688), -(_782690 = c_Groups_Ozero__class_Ozero(_782688))]]], (11998 ^ _490194) ^ [_916856] : [class_Rings_Olinordered__idom(_916856), -(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(_916856)))], (10166 ^ _490194) ^ [_852196, _852198] : [c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _852196, _852198), 10171 ^ _490194 : [(10174 ^ _490194) ^ [] : [-(_852198 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10172 ^ _490194) ^ [] : [-(_852196 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 10175 ^ _490194 : [(10178 ^ _490194) ^ [] : [-(_852198 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10176 ^ _490194) ^ [] : [-(_852196 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (11806 ^ _490194) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal))], (10681 ^ _490194) ^ [_872600, _872602] : [-(_872600 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _872600), _872602) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _872602, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _872600, c_Groups_Oone__class_Oone(tc_Nat_Onat))), _872602)))], (162 ^ _490194) ^ [_495694, _495696] : [-(class_RealVector_Oreal__normed__div__algebra(_495694)), _495696 = _495694, class_RealVector_Oreal__normed__div__algebra(_495696)], (3428 ^ _490194) ^ [_605721, _605723] : [class_Rings_Olinordered__semidom(_605721), c_Orderings_Oord__class_Oless(_605721, hAPP(c_Nat_Osemiring__1__class_Oof__nat(_605721), _605723), c_Groups_Ozero__class_Ozero(_605721))], (8714 ^ _490194) ^ [_797235, _797237] : [class_Groups_Olinordered__ab__group__add(_797235), 8717 ^ _490194 : [(8724 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_797235, _797237), c_Groups_Ozero__class_Ozero(_797235))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_797235, c_Groups_Oplus__class_Oplus(_797235, _797237, _797237)), c_Groups_Ozero__class_Ozero(_797235))))], (8718 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_797235, c_Groups_Oplus__class_Oplus(_797235, _797237, _797237)), c_Groups_Ozero__class_Ozero(_797235))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_797235, _797237), c_Groups_Ozero__class_Ozero(_797235))))]]], (11646 ^ _490194) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (2681 ^ _490194) ^ [_578895] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _578895), _578895)))], (4179 ^ _490194) ^ [_632652, _632654] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _632652), _632654)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _632652, c_Nat_OSuc(_632654)))], (9399 ^ _490194) ^ [_822515, _822517] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _822515), _822517)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _822515, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _822517, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (52 ^ _490194) ^ [_492023, _492025, _492027, _492029] : [-(c_SEQ_Omonoseq(_492027, _492023)), c_SEQ_Omonoseq(_492029, _492025), _492029 = _492027, _492025 = _492023], (2717 ^ _490194) ^ [_580225] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _580225), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_580225 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4468 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (8620 ^ _490194) ^ [_793679, _793681, _793683] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _793679, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _793681, _793683)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _793681, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _793679, _793683)))], (6661 ^ _490194) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (1677 ^ _490194) ^ [_545589, _545591, _545593, _545595] : [class_Orderings_Oorder(_545589), c_Orderings_Oord__class_Oless(_545589, _545591, _545593), _545591 = _545595, -(c_Orderings_Oord__class_Oless(_545589, _545595, _545593))], (832 ^ _490194) ^ [_515459, _515461] : [-(class_Groups_Oone(_515459)), _515461 = _515459, class_Groups_Oone(_515461)], (1608 ^ _490194) ^ [_543260, _543262, _543264, _543266] : [class_Orderings_Oord(_543260), 1611 ^ _490194 : [(1618 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_543260, hAPP(_543264, 1619 ^ [_543260, _543262, _543264, _543266])), hAPP(_543266, 1619 ^ [_543260, _543262, _543264, _543266]))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_543262, _543260), _543264), _543266)))], (1612 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_543262, _543260), _543264), _543266)), 1615 ^ _490194 : [(1616 ^ _490194) ^ [_543531] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_543260, hAPP(_543264, _543531)), hAPP(_543266, _543531))))]]]]], (7401 ^ _490194) ^ [_746649, _746651, _746653] : [class_Rings_Olinordered__semiring__strict(_746649), c_Orderings_Oord__class_Oless(_746649, c_Groups_Ozero__class_Ozero(_746649), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_746649), _746651), _746653)), c_Orderings_Oord__class_Oless(_746649, c_Groups_Ozero__class_Ozero(_746649), _746651), -(c_Orderings_Oord__class_Oless(_746649, c_Groups_Ozero__class_Ozero(_746649), _746653))], (11880 ^ _490194) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_RealDef_Oreal))], (2459 ^ _490194) ^ [_571390, _571392, _571394] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _571390), _571392)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _571390), _571394)), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _571392, _571390), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _571394, _571390)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _571392, _571394))], (4079 ^ _490194) ^ [_629091] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_629091)), _629091))], (8266 ^ _490194) ^ [_780334, _780336, _780338, _780340] : [class_Rings_Ocomm__semiring__1(_780334), -(c_Groups_Oplus__class_Oplus(_780334, _780336, c_Groups_Oplus__class_Oplus(_780334, _780338, _780340)) = c_Groups_Oplus__class_Oplus(_780334, _780338, c_Groups_Oplus__class_Oplus(_780334, _780336, _780340)))], (3835 ^ _490194) ^ [_620720] : [c_Nat_OSuc(_620720) = _620720], (2267 ^ _490194) ^ [_564146, _564148] : [class_Groups_Ogroup__add(_564146), -(c_Groups_Ominus__class_Ominus(_564146, _564148, _564148) = c_Groups_Ozero__class_Ozero(_564146))], (2705 ^ _490194) ^ [_579811, _579813] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _579811), _579813)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _579813), _579811)), -(_579811 = _579813)], (10673 ^ _490194) ^ [_872291] : [-(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, _872291))))], (10793 ^ _490194) ^ [_876870] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _876870), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), -(c_RComplete_Onatceiling(_876870) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6529 ^ _490194) ^ [_716363] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _716363), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _716363)], (12142 ^ _490194) ^ [_921416] : [class_Rings_Olinordered__idom(_921416), -(class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(_921416)))], (11866 ^ _490194) ^ [] : [-(class_Nat_Osemiring__char__0(tc_RealDef_Oreal))], (8093 ^ _490194) ^ [_772311, _772313, _772315, _772317, _772319] : [-(hAPP(hAPP(c_Power_Opower_Opower(_772311, _772313, _772315), _772317), c_Nat_OSuc(_772319)) = hAPP(hAPP(_772315, _772317), hAPP(hAPP(c_Power_Opower_Opower(_772311, _772313, _772315), _772317), _772319)))], (11916 ^ _490194) ^ [] : [-(class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex))], (1187 ^ _490194) ^ [_528866, _528868] : [class_RealVector_Oreal__normed__vector(_528866), 1190 ^ _490194 : [(1197 ^ _490194) ^ [] : [-(_528868 = c_Groups_Ozero__class_Ozero(_528866)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_528866, _528868)))], (1191 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_528866, _528868)), _528868 = c_Groups_Ozero__class_Ozero(_528866)]]], (9185 ^ _490194) ^ [_813852, _813854, _813856] : [class_Rings_Olinordered__ring__strict(_813852), 9188 ^ _490194 : [(9197 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_813852, c_Groups_Oplus__class_Oplus(_813852, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_813852), _813854), _813854), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_813852), _813856), _813856))), c_Groups_Ozero__class_Ozero(_813852)))), _813854 = c_Groups_Ozero__class_Ozero(_813852), _813856 = c_Groups_Ozero__class_Ozero(_813852)], (9189 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_813852, c_Groups_Oplus__class_Oplus(_813852, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_813852), _813854), _813854), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_813852), _813856), _813856))), c_Groups_Ozero__class_Ozero(_813852))), 9192 ^ _490194 : [(9195 ^ _490194) ^ [] : [-(_813856 = c_Groups_Ozero__class_Ozero(_813852))], (9193 ^ _490194) ^ [] : [-(_813854 = c_Groups_Ozero__class_Ozero(_813852))]]]]], (10908 ^ _490194) ^ [_881063] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _881063)), -(c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _881063, c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatfloor(_881063), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (4073 ^ _490194) ^ [_628884, _628886] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_628886)), _628884)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _628884), _628886))], (7979 ^ _490194) ^ [_766959, _766961, _766963, _766965] : [class_Rings_Ocomm__semiring__1(_766959), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_766959), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_766959), _766961), _766963)), _766965) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_766959), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_766959), _766961), _766965)), _766963))], (1895 ^ _490194) ^ [_552376, _552378] : [class_Orderings_Opreorder(_552376), c_Orderings_Oord__class_Oless(_552376, _552378, _552378)], (3011 ^ _490194) ^ [_590909, _590911] : [c_RealDef_Opositive(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _590911, _590909)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _590909, _590911))], (2599 ^ _490194) ^ [_576106, _576108] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _576106), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _576108), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _576108, _576106), _576108))], (12034 ^ _490194) ^ [_917996] : [class_Rings_Olinordered__idom(_917996), -(class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(_917996)))], (4342 ^ _490194) ^ [_638461] : [_638461 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _638461)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (6109 ^ _490194) ^ [_701741, _701743, _701745, _701747] : [class_Rings_Olinordered__semidom(_701741), c_Orderings_Oord__class_Oless(_701741, c_Groups_Oone__class_Oone(_701741), _701743), 6116 ^ _490194 : [(6123 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _701745, _701747), -(c_Orderings_Oord__class_Oless(_701741, hAPP(hAPP(c_Power_Opower__class_Opower(_701741), _701743), _701745), hAPP(hAPP(c_Power_Opower__class_Opower(_701741), _701743), _701747)))], (6117 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(_701741, hAPP(hAPP(c_Power_Opower__class_Opower(_701741), _701743), _701745), hAPP(hAPP(c_Power_Opower__class_Opower(_701741), _701743), _701747)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _701745, _701747))]]], (2489 ^ _490194) ^ [_572348] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _572348, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3226 ^ _490194) ^ [_598771, _598773, _598775] : [class_Groups_Oordered__ab__group__add__abs(_598771), -(c_Groups_Oabs__class_Oabs(_598771, c_Groups_Ominus__class_Ominus(_598771, _598773, _598775)) = c_Groups_Oabs__class_Oabs(_598771, c_Groups_Ominus__class_Ominus(_598771, _598775, _598773)))], (4632 ^ _490194) ^ [_649078, _649080, _649082] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _649078), _649080)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _649082, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _649080, _649082)), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _649078, _649082))))], (8564 ^ _490194) ^ [_791338, _791340, _791342] : [class_Groups_Ogroup__add(_791338), -(c_Groups_Oplus__class_Oplus(_791338, c_Groups_Ominus__class_Ominus(_791338, _791340, _791342), _791342) = _791340)], (2545 ^ _490194) ^ [_574355, _574357, _574359, _574361] : [class_Orderings_Oord(_574355), 2548 ^ _490194 : [(2557 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_fun(_574357, _574355), _574359, _574361)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_574357, _574355), _574359), _574361)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_574357, _574355), _574361), _574359)))], (2549 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_fun(_574357, _574355), _574359, _574361), 2552 ^ _490194 : [(2555 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_574357, _574355), _574361), _574359))], (2553 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_574357, _574355), _574359), _574361)))]]]]], (4580 ^ _490194) ^ [_647472, _647474] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _647472)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _647474)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _647472, _647474))))], (5085 ^ _490194) ^ [_664274] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _664274), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _664274) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6533 ^ _490194) ^ [_716528, _716530] : [class_Rings_Ocomm__semiring__0(_716528), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_716528)), _716530), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_716528))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_716528)))], (12262 ^ _490194) ^ [_925216] : [class_Groups_Oab__group__add(_925216), -(class_Groups_Ogroup__add(tc_Polynomial_Opoly(_925216)))], (11306 ^ _490194) ^ [_895963, _895965] : [class_RealVector_Oreal__normed__field(_895963), -(c_Rings_Oinverse__class_Odivide(_895963, c_Groups_Ozero__class_Ozero(_895963), _895965) = c_Groups_Ozero__class_Ozero(_895963))], (12250 ^ _490194) ^ [_924836] : [class_Rings_Ocomm__semiring__1(_924836), -(class_Rings_Osemiring__1(tc_Polynomial_Opoly(_924836)))], (5619 ^ _490194) ^ [_682854, _682856] : [class_RealVector_Oreal__normed__algebra(_682854), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_682854), c_Groups_Ozero__class_Ozero(_682854)), _682856) = c_Groups_Ozero__class_Ozero(_682854))], (11980 ^ _490194) ^ [] : [-(class_Fields_Ofield(tc_Complex_Ocomplex))], (6255 ^ _490194) ^ [_706803, _706805] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _706803), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _706805), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _706803, _706805), _706803))], (10251 ^ _490194) ^ [_855109, _855111] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _855109), c_Nat_OSuc(_855111)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _855109, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _855109), _855111)))], (3088 ^ _490194) ^ [_593550] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), hAPP(c_RealDef_Oreal(tc_Nat_Onat), _593550))))], (11116 ^ _490194) ^ [_888648, _888650] : [_888648 = hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_RComplete_Onatfloor(_888648)), -(c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _888648), _888650)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_RComplete_Onatfloor(_888648)), _888650))], (10206 ^ _490194) ^ [_853373, _853375] : [10207 ^ _490194 : [(10210 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _853375)], (10208 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _853373)]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _853373, _853375)))], (10781 ^ _490194) ^ [_876422, _876424] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _876422), _876424)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_876422)), c_RComplete_Onatceiling(_876424))))], (5707 ^ _490194) ^ [_686541, _686543] : [5708 ^ _490194 : [(5711 ^ _490194) ^ [] : [_686543 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5709 ^ _490194) ^ [] : [_686541 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _686541), _686543) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11214 ^ _490194) ^ [_892203, _892205] : [class_Rings_Odivision__ring(_892203), -(c_Rings_Oinverse__class_Odivide(_892203, _892205, c_Groups_Oone__class_Oone(_892203)) = _892205)], (11708 ^ _490194) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (1743 ^ _490194) ^ [_547685, _547687, _547689] : [class_Orderings_Opreorder(_547685), c_Orderings_Oord__class_Oless(_547685, _547687, _547689), c_Orderings_Oord__class_Oless(_547685, _547689, _547687)], (9115 ^ _490194) ^ [_811572, _811574, _811576] : [class_Groups_Oordered__comm__monoid__add(_811572), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_811572, c_Groups_Ozero__class_Ozero(_811572)), _811574)), c_Orderings_Oord__class_Oless(_811572, c_Groups_Ozero__class_Ozero(_811572), _811576), -(c_Orderings_Oord__class_Oless(_811572, c_Groups_Ozero__class_Ozero(_811572), c_Groups_Oplus__class_Oplus(_811572, _811574, _811576)))], (2789 ^ _490194) ^ [_582610, _582612] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _582610, _582612)), _582610)))], (10273 ^ _490194) ^ [_856019] : [-(c_Nat_OSuc(_856019) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _856019, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (11588 ^ _490194) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (9070 ^ _490194) ^ [_810011, _810013] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _810011, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _810013, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _810011, _810013)), -(_810011 = _810013)], (2617 ^ _490194) ^ [_576710, _576712] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _576710, _576712), _576712 = _576710], (7945 ^ _490194) ^ [_765267, _765269] : [class_Rings_Ocomm__semiring__1(_765267), -(hAPP(hAPP(c_Power_Opower__class_Opower(_765267), _765269), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_765267))], (5012 ^ _490194) ^ [_661720] : [-(hBOOL(hAPP(_661720, 5019 ^ [_661720]))), 5013 ^ _490194 : [(5014 ^ _490194) ^ [_661824] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _661824)), hBOOL(hAPP(_661720, hAPP(c_Int_Onat, _661824)))]]], (8672 ^ _490194) ^ [_795685, _795687, _795689, _795691] : [class_Groups_Ocancel__ab__semigroup__add(_795685), c_Groups_Oplus__class_Oplus(_795685, _795687, _795689) = c_Groups_Oplus__class_Oplus(_795685, _795687, _795691), -(_795689 = _795691)], (11920 ^ _490194) ^ [] : [-(class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex))], (4448 ^ _490194) ^ [_642538, _642540, _642542] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _642538), _642540)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _642540), _642542)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _642538), _642542)))], (4059 ^ _490194) ^ [_628352, _628354] : [4060 ^ _490194 : [(4063 ^ _490194) ^ [] : [_628352 = c_Nat_OSuc(_628354)], (4061 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _628352), _628354))]], -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _628352), c_Nat_OSuc(_628354))))], (10249 ^ _490194) ^ [_855007, _855009] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _855007, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _855007, _855009)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5410 ^ _490194) ^ [] : [-(c_Nat__Transfer_Otransfer__morphism(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat, c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (11868 ^ _490194) ^ [] : [-(class_Groups_Oab__group__add(tc_RealDef_Oreal))], (3628 ^ _490194) ^ [_612672, _612674] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _612672), _612674)), -(c_Groups_Ominus__class_Ominus(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _612674), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _612672)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _612674, _612672)))], (6251 ^ _490194) ^ [] : [-(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))], (10611 ^ _490194) ^ [_869840, _869842] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _869840), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), hAPP(c_RealDef_Oreal(tc_Nat_Onat), _869842))), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _869840, _869842))], (4676 ^ _490194) ^ [_650561, _650563] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _650561), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _650563), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _650561, _650563)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (11790 ^ _490194) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal))], (8744 ^ _490194) ^ [_798225, _798227, _798229] : [class_Groups_Oordered__comm__monoid__add(_798225), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_798225, c_Groups_Ozero__class_Ozero(_798225)), _798227)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_798225, c_Groups_Ozero__class_Ozero(_798225)), _798229)), 8755 ^ _490194 : [(8764 ^ _490194) ^ [] : [-(c_Groups_Oplus__class_Oplus(_798225, _798227, _798229) = c_Groups_Ozero__class_Ozero(_798225)), _798227 = c_Groups_Ozero__class_Ozero(_798225), _798229 = c_Groups_Ozero__class_Ozero(_798225)], (8756 ^ _490194) ^ [] : [c_Groups_Oplus__class_Oplus(_798225, _798227, _798229) = c_Groups_Ozero__class_Ozero(_798225), 8759 ^ _490194 : [(8762 ^ _490194) ^ [] : [-(_798229 = c_Groups_Ozero__class_Ozero(_798225))], (8760 ^ _490194) ^ [] : [-(_798227 = c_Groups_Ozero__class_Ozero(_798225))]]]]], (342 ^ _490194) ^ [_501004, _501006] : [-(class_Groups_Olinordered__ab__group__add(_501004)), _501006 = _501004, class_Groups_Olinordered__ab__group__add(_501006)], (2507 ^ _490194) ^ [_573026, _573028] : [-(_573026 = _573028), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _573026, _573028)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _573028, _573026))], (7181 ^ _490194) ^ [_739359, _739361, _739363, _739365, _739367] : [class_Rings_Oordered__semiring(_739359), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_739359, _739361), _739363)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_739359, _739365), _739367)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_739359, c_Groups_Ozero__class_Ozero(_739359)), _739361)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_739359, c_Groups_Ozero__class_Ozero(_739359)), _739365)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_739359, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_739359), _739361), _739365)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_739359), _739363), _739367))))], (11946 ^ _490194) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex))], (10583 ^ _490194) ^ [_868736] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _868736), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _868736)], (6679 ^ _490194) ^ [_721820] : [class_Rings_Ocomm__semiring__1(_721820), -(c_Polynomial_Odegree(_721820, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_721820))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10431 ^ _490194) ^ [_862401, _862403, _862405] : [hBOOL(hAPP(_862401, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _862403, _862405))), 10434 ^ _490194 : [(10441 ^ _490194) ^ [_862733] : [_862403 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _862405, _862733), -(hBOOL(hAPP(_862401, _862733)))], (10435 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _862403, _862405), -(hBOOL(hAPP(_862401, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (12058 ^ _490194) ^ [_918756] : [class_Rings_Oidom(_918756), -(class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(_918756)))], (9586 ^ _490194) ^ [_829226, _829228, _829230, _829232, _829234, _829236] : [class_Rings_Olinordered__semiring__1__strict(_829226), c_Orderings_Oord__class_Oless(_829226, _829228, _829230), c_Orderings_Oord__class_Oless(_829226, _829232, _829230), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_829226, c_Groups_Ozero__class_Ozero(_829226)), _829234)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_829226, c_Groups_Ozero__class_Ozero(_829226)), _829236)), c_Groups_Oplus__class_Oplus(_829226, _829234, _829236) = c_Groups_Oone__class_Oone(_829226), -(c_Orderings_Oord__class_Oless(_829226, c_Groups_Oplus__class_Oplus(_829226, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_829226), _829234), _829228), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_829226), _829236), _829232)), _829230))], (8340 ^ _490194) ^ [_783170, _783172] : [class_Groups_Ocomm__monoid__add(_783170), -(c_Groups_Oplus__class_Oplus(_783170, _783172, c_Groups_Ozero__class_Ozero(_783170)) = _783172)], (11666 ^ _490194) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (5404 ^ _490194) ^ [_674700, _674702] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _674700)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _674700), _674702)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _674700)), _674702))], (4324 ^ _490194) ^ [_637900] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _637900) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_637900 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1284 ^ _490194) ^ [_532212, _532214] : [class_Orderings_Opreorder(_532212), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_532212, _532214), _532214)))], (3534 ^ _490194) ^ [_609389, _609391] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _609389)), hAPP(c_RealDef_Oreal(tc_Nat_Onat), _609391))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _609389), _609391)))], (712 ^ _490194) ^ [_511919, _511921] : [-(class_Rings_Ocomm__semiring__0(_511919)), _511921 = _511919, class_Rings_Ocomm__semiring__0(_511921)], (8586 ^ _490194) ^ [_792286, _792288, _792290] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _792286, _792288), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _792286, _792290), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _792288, _792290)))], (3857 ^ _490194) ^ [_621492, _621494] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _621492, _621494)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _621492), _621494)), -(_621492 = _621494)], (7449 ^ _490194) ^ [_748220, _748222, _748224] : [class_Rings_Olinordered__semiring__strict(_748220), c_Orderings_Oord__class_Oless(_748220, _748222, c_Groups_Ozero__class_Ozero(_748220)), c_Orderings_Oord__class_Oless(_748220, c_Groups_Ozero__class_Ozero(_748220), _748224), -(c_Orderings_Oord__class_Oless(_748220, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_748220), _748222), _748224), c_Groups_Ozero__class_Ozero(_748220)))], (9981 ^ _490194) ^ [_844391, _844393, _844395] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _844391, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _844393, _844395)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _844393, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _844391, _844395)))], (11558 ^ _490194) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal))], (11696 ^ _490194) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (922 ^ _490194) ^ [_519070, _519072, _519074, _519076, _519078, _519080] : [-(c_Polynomial_Oorder(_519080, _519076, _519072) = c_Polynomial_Oorder(_519078, _519074, _519070)), _519080 = _519078, _519076 = _519074, _519072 = _519070], (11020 ^ _490194) ^ [_884990, _884992, _884994, _884996, _884998, _885000, _885002, _885004] : [class_Fields_Ofield(_884990), c_Polynomial_Opdivmod__rel(_884990, _884992, _884994, _884996, _884998), c_Polynomial_Opdivmod__rel(_884990, _884996, _885000, _885002, _885004), -(c_Polynomial_Opdivmod__rel(_884990, _884992, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_884990)), _884994), _885000), _885002, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_884990), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_884990)), _884994), _885004), _884998)))], (4067 ^ _490194) ^ [_628695, _628697] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _628695), _628697))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_628697)), _628695)))], (11822 ^ _490194) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal))], (2539 ^ _490194) ^ [_574055] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _574055, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5959 ^ _490194) ^ [_696333, _696335, _696337] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _696333), _696335), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _696337), _696335))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _696335), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _696333, _696337)], (11624 ^ _490194) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (11958 ^ _490194) ^ [] : [-(class_Groups_Oab__group__add(tc_Complex_Ocomplex))], (662 ^ _490194) ^ [_510444, _510446] : [-(class_Rings_Osemiring__0(_510444)), _510446 = _510444, class_Rings_Osemiring__0(_510446)], (1438 ^ _490194) ^ [_537690, _537692, _537694] : [class_Orderings_Oorder(_537690), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_537690, _537692), _537694)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_537690, _537694), _537692)), -(_537694 = _537692)], (11632 ^ _490194) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (9369 ^ _490194) ^ [_821371, _821373] : [class_Rings_Osemiring__1(_821371), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_821371), c_Nat_OSuc(_821373)) = c_Groups_Oplus__class_Oplus(_821371, c_Groups_Oone__class_Oone(_821371), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_821371), _821373)))], (7415 ^ _490194) ^ [_747097, _747099, _747101] : [class_Rings_Olinordered__semiring__strict(_747097), c_Orderings_Oord__class_Oless(_747097, c_Groups_Ozero__class_Ozero(_747097), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_747097), _747099), _747101)), c_Orderings_Oord__class_Oless(_747097, c_Groups_Ozero__class_Ozero(_747097), _747101), -(c_Orderings_Oord__class_Oless(_747097, c_Groups_Ozero__class_Ozero(_747097), _747099))], (1649 ^ _490194) ^ [_544693, _544695, _544697, _544699] : [class_Orderings_Oorder(_544693), c_Orderings_Oord__class_Oless(_544693, _544695, _544697), c_Orderings_Oord__class_Oless(_544693, _544699, _544695), -(c_Orderings_Oord__class_Oless(_544693, _544699, _544697))], (11016 ^ _490194) ^ [] : [-(c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2723 ^ _490194) ^ [_580391] : [_580391 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _580391), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (8450 ^ _490194) ^ [_787172, _787174, _787176, _787178] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_787172), 8453 ^ _490194 : [(8460 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_787172, _787174), _787178)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_787172, c_Groups_Oplus__class_Oplus(_787172, _787174, _787176)), c_Groups_Oplus__class_Oplus(_787172, _787178, _787176))))], (8454 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_787172, c_Groups_Oplus__class_Oplus(_787172, _787174, _787176)), c_Groups_Oplus__class_Oplus(_787172, _787178, _787176))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_787172, _787174), _787178)))]]], (11962 ^ _490194) ^ [] : [-(class_Groups_Omonoid__mult(tc_Complex_Ocomplex))], (8003 ^ _490194) ^ [_768335, _768337] : [class_Rings_Ocomm__semiring__1(_768335), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_768335), _768337), c_Groups_Ozero__class_Ozero(_768335)) = c_Groups_Ozero__class_Ozero(_768335))], (2525 ^ _490194) ^ [_573547] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _573547) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11792 ^ _490194) ^ [] : [-(class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal))], (2904 ^ _490194) ^ [_586937, _586939] : [class_Groups_Ozero(_586937), 2907 ^ _490194 : [(2914 ^ _490194) ^ [] : [_586939 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_586937)), -(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_586937, _586939) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2908 ^ _490194) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_586937, _586939) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_586939 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_586937)))]]], (5655 ^ _490194) ^ [_684654, _684656, _684658, _684660] : [class_Groups_Ocomm__monoid__mult(_684654), -(hAPP(hAPP(c_Power_Opower__class_Opower(_684654), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_684654), _684656), _684658)), _684660) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_684654), hAPP(hAPP(c_Power_Opower__class_Opower(_684654), _684656), _684660)), hAPP(hAPP(c_Power_Opower__class_Opower(_684654), _684658), _684660)))], (6931 ^ _490194) ^ [_730596, _730598, _730600] : [class_Rings_Olinordered__idom(_730596), -(c_Groups_Oabs__class_Oabs(_730596, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_730596), _730598), _730600)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_730596), c_Groups_Oabs__class_Oabs(_730596, _730598)), c_Groups_Oabs__class_Oabs(_730596, _730600)))], (3090 ^ _490194) ^ [_593676, _593678, _593680] : [class_Rings_Oring__1__no__zero__divisors(_593676), -(_593678 = c_Groups_Ozero__class_Ozero(_593676)), hAPP(hAPP(c_Power_Opower__class_Opower(_593676), _593678), _593680) = c_Groups_Ozero__class_Ozero(_593676)], (11778 ^ _490194) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (3761 ^ _490194) ^ [_617958] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(_617958)))], (8974 ^ _490194) ^ [_805735, _805737] : [class_Rings_Olinordered__semidom(_805735), -(c_Orderings_Oord__class_Oless(_805735, _805737, c_Groups_Oplus__class_Oplus(_805735, _805737, c_Groups_Oone__class_Oone(_805735))))], (322 ^ _490194) ^ [_500414, _500416] : [-(class_Groups_Oordered__ab__group__add__abs(_500414)), _500416 = _500414, class_Groups_Oordered__ab__group__add__abs(_500416)], (12214 ^ _490194) ^ [_923696] : [class_Rings_Olinordered__idom(_923696), -(class_Rings_Oordered__ring(tc_Polynomial_Opoly(_923696)))], (11808 ^ _490194) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal))], (10567 ^ _490194) ^ [_868146, _868148, _868150, _868152, _868154] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _868146), _868148)), 10570 ^ _490194 : [(10577 ^ _490194) ^ [] : [_868152 = 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, _868148, _868146)), _868150), _868154), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _868146), _868150), _868152) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _868148), _868150), _868154))], (10571 ^ _490194) ^ [] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _868146), _868150), _868152) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _868148), _868150), _868154), -(_868152 = 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, _868148, _868146)), _868150), _868154))]]], (2305 ^ _490194) ^ [_565615, _565617] : [class_Orderings_Oorder(_565615), 2308 ^ _490194 : [(2309 ^ _490194) ^ [] : [c_SEQ_Oincseq(_565615, _565617), 2312 ^ _490194 : [(2313 ^ _490194) ^ [_565899, _565901] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _565901), _565899)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_565615, hAPP(_565617, _565901)), hAPP(_565617, _565899))))]]], (2319 ^ _490194) ^ [] : [2322 ^ _490194 : [(2325 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_565615, hAPP(_565617, 2320 ^ [_565615, _565617])), hAPP(_565617, 2321 ^ [_565615, _565617])))], (2323 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, 2320 ^ [_565615, _565617]), 2321 ^ [_565615, _565617])))]], -(c_SEQ_Oincseq(_565615, _565617))]]], (6891 ^ _490194) ^ [_729310, _729312, _729314] : [class_Rings_Ono__zero__divisors(_729310), -(_729312 = c_Groups_Ozero__class_Ozero(_729310)), -(_729314 = c_Groups_Ozero__class_Ozero(_729310)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_729310), _729312), _729314) = c_Groups_Ozero__class_Ozero(_729310)], (1404 ^ _490194) ^ [_536467, _536469, _536471] : [class_Orderings_Olinorder(_536467), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_536467, _536469), _536471))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_536467, _536471), _536469)))], (11564 ^ _490194) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint))], (8027 ^ _490194) ^ [_769283, _769285, _769287, _769289] : [class_Rings_Ocomm__semiring__1(_769283), -(hAPP(hAPP(c_Power_Opower__class_Opower(_769283), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_769283), _769285), _769287)), _769289) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_769283), hAPP(hAPP(c_Power_Opower__class_Opower(_769283), _769285), _769289)), hAPP(hAPP(c_Power_Opower__class_Opower(_769283), _769287), _769289)))], (8210 ^ _490194) ^ [_777740, _777742, _777744, _777746, _777748] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_777740), 8213 ^ _490194 : [(8214 ^ _490194) ^ [] : [c_Groups_Oplus__class_Oplus(_777740, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_777740), _777742), _777744), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_777740), _777746), _777748)) = c_Groups_Oplus__class_Oplus(_777740, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_777740), _777742), _777748), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_777740), _777746), _777744)), -(_777742 = _777746), -(_777744 = _777748)], (8224 ^ _490194) ^ [] : [8225 ^ _490194 : [(8228 ^ _490194) ^ [] : [_777744 = _777748], (8226 ^ _490194) ^ [] : [_777742 = _777746]], -(c_Groups_Oplus__class_Oplus(_777740, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_777740), _777742), _777744), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_777740), _777746), _777748)) = c_Groups_Oplus__class_Oplus(_777740, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_777740), _777742), _777748), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_777740), _777746), _777744)))]]], (9975 ^ _490194) ^ [_844078, _844080] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _844078, _844080), _844080)], (11924 ^ _490194) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex))], (6703 ^ _490194) ^ [_722750, _722752, _722754] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _722750), 6706 ^ _490194 : [(6713 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _722752), _722754)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _722752), _722750)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _722754), _722750))))], (6707 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _722752), _722750)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _722754), _722750))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _722752), _722754)))]]], (10341 ^ _490194) ^ [_858701, _858703, _858705] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _858701), _858703)), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _858705, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _858703, _858701)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _858705, _858703), _858701))], (7139 ^ _490194) ^ [_737821, _737823, _737825, _737827] : [class_Rings_Oordered__comm__semiring(_737821), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_737821, _737823), _737825)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_737821, c_Groups_Ozero__class_Ozero(_737821)), _737827)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_737821, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_737821), _737827), _737823)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_737821), _737827), _737825))))], (10791 ^ _490194) ^ [_876772] : [-(c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat), _876772)) = _876772)], (5679 ^ _490194) ^ [_685644, _685646, _685648] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _685644), _685646) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _685644), _685648), -(_685646 = _685648), -(_685644 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6567 ^ _490194) ^ [_717801, _717803] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _717801), _717803) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 6570 ^ _490194 : [(6573 ^ _490194) ^ [] : [-(_717803 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (6571 ^ _490194) ^ [] : [-(_717801 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (11774 ^ _490194) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (4566 ^ _490194) ^ [_646913] : [-(c_Divides_Odiv__class_Odiv(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _646913) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (5759 ^ _490194) ^ [_688726, _688728, _688730] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _688726), _688728)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _688726), _688730)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _688728), _688730))))], (3398 ^ _490194) ^ [_604449, _604451, _604453] : [class_Groups_Oordered__ab__group__add__abs(_604449), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_604449, c_Groups_Oabs__class_Oabs(_604449, c_Groups_Ominus__class_Ominus(_604449, c_Groups_Oabs__class_Oabs(_604449, _604451), c_Groups_Oabs__class_Oabs(_604449, _604453)))), c_Groups_Oabs__class_Oabs(_604449, c_Groups_Ominus__class_Ominus(_604449, _604451, _604453)))))], (1088 ^ _490194) ^ [_525128, _525130, _525132, _525134, _525136, _525138] : [-(c_Rings_Oinverse__class_Odivide(_525138, _525134, _525130) = c_Rings_Oinverse__class_Odivide(_525136, _525132, _525128)), _525138 = _525136, _525134 = _525132, _525130 = _525128], (3753 ^ _490194) ^ [_617684, _617686] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _617684, _617686), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_617684), c_Nat_OSuc(_617686)))], (4642 ^ _490194) ^ [_649439, _649441, _649443] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _649439), _649441)), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _649443), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _649439, _649443)), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _649441, _649443))))], (12130 ^ _490194) ^ [_921036] : [class_Groups_Ocomm__monoid__add(_921036), -(class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(_921036)))], (722 ^ _490194) ^ [_512214, _512216] : [-(class_Rings_Osemiring(_512214)), _512216 = _512214, class_Rings_Osemiring(_512216)], (3466 ^ _490194) ^ [_607031, _607033, _607035] : [class_Rings_Olinordered__semidom(_607031), c_Orderings_Oord__class_Oless(_607031, hAPP(c_Nat_Osemiring__1__class_Oof__nat(_607031), _607033), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_607031), _607035)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _607033, _607035))], (10247 ^ _490194) ^ [_854906, _854908] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _854906, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _854906, _854908))))], (492 ^ _490194) ^ [_505429, _505431] : [-(class_Groups_Oab__semigroup__add(_505429)), _505431 = _505429, class_Groups_Oab__semigroup__add(_505431)], (9844 ^ _490194) ^ [_839086, _839088] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _839086), _839088)), -(_839088 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _839086, 9847 ^ [_839086, _839088]))], (3548 ^ _490194) ^ [_609907, _609909, _609911, _609913] : [class_Rings_Olinordered__semidom(_609907), hAPP(hAPP(c_Power_Opower__class_Opower(_609907), _609909), _609911) = hAPP(hAPP(c_Power_Opower__class_Opower(_609907), _609913), _609911), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_609907, c_Groups_Ozero__class_Ozero(_609907)), _609909)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_609907, c_Groups_Ozero__class_Ozero(_609907)), _609913)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _609911), -(_609909 = _609913)], (4758 ^ _490194) ^ [_653134, _653136] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _653134), 4761 ^ _490194 : [(4768 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _653134), _653136)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _653136, _653134)))], (4762 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _653136, _653134)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _653134), _653136)))]]], (2281 ^ _490194) ^ [_564666, _564668] : [class_Orderings_Oorder(_564666), 2284 ^ _490194 : [(2285 ^ _490194) ^ [] : [c_SEQ_Odecseq(_564666, _564668), 2288 ^ _490194 : [(2289 ^ _490194) ^ [_564950, _564952] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _564952), _564950)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_564666, hAPP(_564668, _564950)), hAPP(_564668, _564952))))]]], (2295 ^ _490194) ^ [] : [2298 ^ _490194 : [(2301 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_564666, hAPP(_564668, 2297 ^ [_564666, _564668])), hAPP(_564668, 2296 ^ [_564666, _564668])))], (2299 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, 2296 ^ [_564666, _564668]), 2297 ^ [_564666, _564668])))]], -(c_SEQ_Odecseq(_564666, _564668))]]], (4081 ^ _490194) ^ [_629204, _629206, _629208] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_629204), _629206), c_Nat_OSuc(_629208)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _629204, _629206), _629208))], (7955 ^ _490194) ^ [_765749, _765751, _765753] : [class_Rings_Ocomm__semiring__1(_765749), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_765749), _765751), _765753) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_765749), _765753), _765751))], (1466 ^ _490194) ^ [_538596, _538598, _538600] : [class_Orderings_Oorder(_538596), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_538596, _538598), _538600)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_538596, _538600), _538598)), -(_538598 = _538600)], (11742 ^ _490194) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (11834 ^ _490194) ^ [] : [-(class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal))], (11180 ^ _490194) ^ [_890912, _890914] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _890912)), -(c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _890912, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _890914))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatfloor(_890912), _890914))], (9979 ^ _490194) ^ [_844275, _844277] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _844275, _844277) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _844277, _844275))], (11756 ^ _490194) ^ [] : [-(class_Rings_Osemiring__1(tc_Nat_Onat))], (652 ^ _490194) ^ [_510149, _510151] : [-(class_Rings_Osemiring__1(_510149)), _510151 = _510149, class_Rings_Osemiring__1(_510151)], (8574 ^ _490194) ^ [_791746, _791748, _791750] : [class_Groups_Oordered__ab__group__add__abs(_791746), -(c_Groups_Oabs__class_Oabs(_791746, c_Groups_Oplus__class_Oplus(_791746, c_Groups_Oabs__class_Oabs(_791746, _791748), c_Groups_Oabs__class_Oabs(_791746, _791750))) = c_Groups_Oplus__class_Oplus(_791746, c_Groups_Oabs__class_Oabs(_791746, _791748), c_Groups_Oabs__class_Oabs(_791746, _791750)))], (4015 ^ _490194) ^ [_626786, _626788] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_626786)), _626788)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _626786), _626788)))], (672 ^ _490194) ^ [_510739, _510741] : [-(class_Groups_Oab__group__add(_510739)), _510741 = _510739, class_Groups_Oab__group__add(_510741)], (10972 ^ _490194) ^ [_883345, _883347, _883349, _883351] : [class_Fields_Ofield(_883345), 10975 ^ _490194 : [(10984 ^ _490194) ^ [] : [-(c_Polynomial_Opdivmod__rel(_883345, _883347, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_883345)), _883349, _883351)), _883349 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_883345)), _883351 = _883347], (10976 ^ _490194) ^ [] : [c_Polynomial_Opdivmod__rel(_883345, _883347, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_883345)), _883349, _883351), 10979 ^ _490194 : [(10982 ^ _490194) ^ [] : [-(_883351 = _883347)], (10980 ^ _490194) ^ [] : [-(_883349 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_883345)))]]]]], (10675 ^ _490194) ^ [_872426, _872428] : [_872426 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _872426), _872428) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1803 ^ _490194) ^ [_549635, _549637, _549639] : [class_Orderings_Olinorder(_549635), -(_549637 = _549639), -(c_Orderings_Oord__class_Oless(_549635, _549637, _549639)), -(c_Orderings_Oord__class_Oless(_549635, _549639, _549637))], (7643 ^ _490194) ^ [_754897, _754899, _754901, _754903] : [class_Rings_Olinordered__ring__strict(_754897), c_Orderings_Oord__class_Oless(_754897, c_Groups_Ozero__class_Ozero(_754897), _754899), 7650 ^ _490194 : [(7657 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_754897, _754901), _754903)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_754897, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_754897), _754899), _754901)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_754897), _754899), _754903))))], (7651 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_754897, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_754897), _754899), _754901)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_754897), _754899), _754903))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_754897, _754901), _754903)))]]], (6651 ^ _490194) ^ [_720785, _720787, _720789] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _720785, _720787), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _720789), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _720789), _720785), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _720789), _720787)))], (3767 ^ _490194) ^ [_618217, _618219] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), c_Groups_Oabs__class_Oabs(tc_Int_Oint, _618217)), _618219))))], (10960 ^ _490194) ^ [_882849, _882851] : [class_Fields_Ofield(_882849), -(c_Polynomial_Opdivmod__rel(_882849, _882851, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_882849)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_882849)), _882851))], (5779 ^ _490194) ^ [_689577, _689579, _689581] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _689577), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _689579, _689581)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _689577), _689579), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _689577), _689581)))], (10255 ^ _490194) ^ [_855348, _855350] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _855348, _855350)), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _855350, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _855348, _855350)) = _855348)], (6959 ^ _490194) ^ [_731643, _731645, _731647] : [6960 ^ _490194 : [(6963 ^ _490194) ^ [] : [_731645 = _731647], (6961 ^ _490194) ^ [] : [_731643 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _731643), _731645) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _731643), _731647))], (1316 ^ _490194) ^ [_533399, _533401, _533403, _533405, _533407] : [class_Groups_Oordered__ab__group__add(_533399), c_Groups_Ominus__class_Ominus(_533399, _533401, _533403) = c_Groups_Ominus__class_Ominus(_533399, _533405, _533407), 1323 ^ _490194 : [(1330 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_533399, _533405), _533407)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_533399, _533401), _533403)))], (1324 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_533399, _533401), _533403)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_533399, _533405), _533407)))]]], (2107 ^ _490194) ^ [_559097, _559099, _559101] : [class_Orderings_Olinorder(_559097), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_559097, _559099), _559101))), -(c_Orderings_Oord__class_Oless(_559097, _559101, _559099))], (4662 ^ _490194) ^ [_650119, _650121, _650123] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _650119, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _650121), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _650121), _650123)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _650119, _650121)), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _650119, _650123))))], (2791 ^ _490194) ^ [_582742, _582744, _582746] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _582742), _582744)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _582746, _582744)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _582746, _582742))))], (2397 ^ _490194) ^ [_569275, _569277] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _569275), _569277)), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _569275, _569277) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11896 ^ _490194) ^ [] : [-(class_Orderings_Oord(tc_RealDef_Oreal))], (11212 ^ _490194) ^ [_892065, _892067, _892069] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Complex_Orcis(_892065, _892067)), _892069) = c_Complex_Orcis(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _892065), _892069), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(c_RealDef_Oreal(tc_Nat_Onat), _892069)), _892067)))], (6949 ^ _490194) ^ [_731357, _731359, _731361] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _731357), _731359) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _731357), _731361), -(_731357 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_731359 = _731361)], (11036 ^ _490194) ^ [_885613, _885615] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _885613), _885615)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatfloor(_885613)), c_RComplete_Onatfloor(_885615))))], (11776 ^ _490194) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (11760 ^ _490194) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (5545 ^ _490194) ^ [_679936, _679938] : [class_Groups_Ocomm__monoid__mult(_679936), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_679936), c_Groups_Oone__class_Oone(_679936)), _679938) = _679938)], (11926 ^ _490194) ^ [] : [-(class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex))], (9263 ^ _490194) ^ [_816871, _816873, _816875, _816877, _816879, _816881] : [class_Rings_Oordered__ring(_816871), 9266 ^ _490194 : [(9273 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_816871, _816877), c_Groups_Oplus__class_Oplus(_816871, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_816871), c_Groups_Ominus__class_Ominus(_816871, _816879, _816873)), _816875), _816881))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_816871, c_Groups_Oplus__class_Oplus(_816871, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_816871), _816873), _816875), _816877)), c_Groups_Oplus__class_Oplus(_816871, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_816871), _816879), _816875), _816881))))], (9267 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_816871, c_Groups_Oplus__class_Oplus(_816871, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_816871), _816873), _816875), _816877)), c_Groups_Oplus__class_Oplus(_816871, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_816871), _816879), _816875), _816881))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_816871, _816877), c_Groups_Oplus__class_Oplus(_816871, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_816871), c_Groups_Ominus__class_Ominus(_816871, _816879, _816873)), _816875), _816881))))]]], (10545 ^ _490194) ^ [_867090, _867092, _867094, _867096, _867098] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _867090), _867092)), 10548 ^ _490194 : [(10555 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _867096), 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, _867092, _867090)), _867094), _867098))), -(hBOOL(hAPP(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), _867090), _867094), _867096)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _867092), _867094), _867098))))], (10549 ^ _490194) ^ [] : [hBOOL(hAPP(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), _867090), _867094), _867096)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _867092), _867094), _867098))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _867096), 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, _867092, _867090)), _867094), _867098))))]]], (2127 ^ _490194) ^ [_559769, _559771, _559773] : [class_Orderings_Oorder(_559769), 2130 ^ _490194 : [(2131 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_559769, _559771), _559773)), -(c_Orderings_Oord__class_Oless(_559769, _559771, _559773)), -(_559771 = _559773)], (2141 ^ _490194) ^ [] : [2142 ^ _490194 : [(2145 ^ _490194) ^ [] : [_559771 = _559773], (2143 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(_559769, _559771, _559773)]], -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_559769, _559771), _559773)))]]], (11890 ^ _490194) ^ [] : [-(class_Rings_Omult__zero(tc_RealDef_Oreal))], (3306 ^ _490194) ^ [_601459, _601461] : [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), _601459), _601461)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _601459)), -(_601461 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11850 ^ _490194) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal))], (8592 ^ _490194) ^ [_792536, _792538, _792540] : [class_RealVector_Oreal__normed__vector(_792536), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_792536, c_Groups_Oplus__class_Oplus(_792536, _792538, _792540))), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_792536, _792538), c_RealVector_Onorm__class_Onorm(_792536, _792540)))))], (11636 ^ _490194) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_Int_Oint))], (8920 ^ _490194) ^ [_803885, _803887, _803889, _803891, _803893] : [class_Groups_Oordered__cancel__ab__semigroup__add(_803885), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_803885, _803887), _803889)), c_Orderings_Oord__class_Oless(_803885, _803891, _803893), -(c_Orderings_Oord__class_Oless(_803885, c_Groups_Oplus__class_Oplus(_803885, _803887, _803891), c_Groups_Oplus__class_Oplus(_803885, _803889, _803893)))], (3017 ^ _490194) ^ [_591144] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), hAPP(c_RealDef_Oreal(tc_Nat_Onat), _591144)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _591144))], (2863 ^ _490194) ^ [_585363, _585365] : [class_RealVector_Oreal__normed__vector(_585363), c_SEQ_OBseq(_585363, _585365), 2871 ^ _490194 : [(2874 ^ _490194) ^ [_585727] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_585363, hAPP(_585365, _585727))), 2870 ^ [_585363, _585365])))], (2872 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 2870 ^ [_585363, _585365]))]]], (1262 ^ _490194) ^ [_531466, _531468, _531470] : [class_Groups_Oordered__ab__group__add(_531466), 1265 ^ _490194 : [(1272 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_531466, c_Groups_Ominus__class_Ominus(_531466, _531468, _531470)), c_Groups_Ozero__class_Ozero(_531466))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_531466, _531468), _531470)))], (1266 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_531466, _531468), _531470)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_531466, c_Groups_Ominus__class_Ominus(_531466, _531468, _531470)), c_Groups_Ozero__class_Ozero(_531466))))]]], (2419 ^ _490194) ^ [_570100, _570102, _570104] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _570100), _570102)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _570100), _570104)), 2426 ^ _490194 : [(2433 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _570102, _570104), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _570102, _570100), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _570104, _570100)))], (2427 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _570102, _570100), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _570104, _570100)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _570102, _570104))]]], (4883 ^ _490194) ^ [_657105, _657107] : [class_Groups_Ozero(_657105), 4886 ^ _490194 : [(4893 ^ _490194) ^ [] : [-(_657107 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_657105))), -(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_657105, _657107) = c_Nat_OSuc(c_Polynomial_Odegree(_657105, _657107)))], (4887 ^ _490194) ^ [] : [_657107 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_657105)), -(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_657105, _657107) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (11932 ^ _490194) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex))], (11796 ^ _490194) ^ [] : [-(class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal))], (522 ^ _490194) ^ [_506314, _506316] : [-(class_Rings_Ono__zero__divisors(_506314)), _506316 = _506314, class_Rings_Ono__zero__divisors(_506316)], (10499 ^ _490194) ^ [_864974, _864976, _864978] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _864974), _864976)), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _864978, c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _864976, _864974))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _864978, _864974), c_Nat_OSuc(_864976)))], (4136 ^ _490194) ^ [_631108] : [_631108 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _631108, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (10777 ^ _490194) ^ [] : [-(c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2655 ^ _490194) ^ [_578024] : [-(_578024 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _578024))], (34 ^ _490194) ^ [_491442, _491444, _491446, _491448, _491450, _491452] : [-(c_HOL_Oequal__class_Oequal(_491450, _491446, _491442)), c_HOL_Oequal__class_Oequal(_491452, _491448, _491444), _491452 = _491450, _491448 = _491446, _491444 = _491442], (6011 ^ _490194) ^ [_698183, _698185, _698187] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _698185, _698187), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_698183)), _698185), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_698183)), _698187)))], (10821 ^ _490194) ^ [_877852] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_877852)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _877852), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))], (10657 ^ _490194) ^ [_871694, _871696, _871698, _871700, _871702] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _871694), _871696)), 10660 ^ _490194 : [(10667 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _871700, 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, _871696, _871694)), _871698), _871702)), -(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), _871694), _871698), _871700), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _871696), _871698), _871702)))], (10661 ^ _490194) ^ [] : [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), _871694), _871698), _871700), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _871696), _871698), _871702)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _871700, 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, _871696, _871694)), _871698), _871702)))]]], (6303 ^ _490194) ^ [_708438, _708440, _708442] : [class_Rings_Olinordered__semidom(_708438), c_Orderings_Oord__class_Oless(_708438, c_Groups_Ozero__class_Ozero(_708438), _708440), c_Orderings_Oord__class_Oless(_708438, _708440, c_Groups_Oone__class_Oone(_708438)), -(c_Orderings_Oord__class_Oless(_708438, hAPP(hAPP(c_Power_Opower__class_Opower(_708438), _708440), c_Nat_OSuc(_708442)), c_Groups_Oone__class_Oone(_708438)))], (9857 ^ _490194) ^ [_839579, _839581] : [c_RealDef_Opositive(_839579), c_RealDef_Opositive(_839581), -(c_RealDef_Opositive(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _839579, _839581)))], (7305 ^ _490194) ^ [_743541, _743543, _743545, _743547] : [class_Rings_Olinordered__ring__strict(_743541), 7308 ^ _490194 : [(7323 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(_743541, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_743541), _743543), _743545), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_743541), _743543), _743547))), 7324 ^ _490194 : [(7331 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(_743541, _743543, c_Groups_Ozero__class_Ozero(_743541)), c_Orderings_Oord__class_Oless(_743541, _743547, _743545)], (7325 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(_743541, c_Groups_Ozero__class_Ozero(_743541), _743543), c_Orderings_Oord__class_Oless(_743541, _743545, _743547)]]], (7309 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(_743541, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_743541), _743543), _743545), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_743541), _743543), _743547)), 7314 ^ _490194 : [(7317 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(_743541, _743545, _743547))], (7315 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(_743541, c_Groups_Ozero__class_Ozero(_743541), _743543))]], 7318 ^ _490194 : [(7321 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(_743541, _743547, _743545))], (7319 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(_743541, _743543, c_Groups_Ozero__class_Ozero(_743541)))]]]]], (2845 ^ _490194) ^ [_584801, _584803] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _584801), _584803)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _584801, _584803)), -(_584801 = _584803)], (5045 ^ _490194) ^ [_662821, _662823] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _662821, _662823)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _662821), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _662823)))], (4514 ^ _490194) ^ [_644892, _644894] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _644892), _644894))), -(c_Nat__Transfer_Otsub(_644894, _644892) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (2149 ^ _490194) ^ [_560439, _560441, _560443] : [class_Orderings_Opreorder(_560439), 2152 ^ _490194 : [(2161 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(_560439, _560441, _560443)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_560439, _560441), _560443)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_560439, _560443), _560441)))], (2153 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(_560439, _560441, _560443), 2156 ^ _490194 : [(2159 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_560439, _560443), _560441))], (2157 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_560439, _560441), _560443)))]]]]], (11950 ^ _490194) ^ [] : [-(class_RealVector_Oreal__field(tc_Complex_Ocomplex))], (2569 ^ _490194) ^ [_575203, _575205] : [class_Orderings_Oorder(_575203), c_SEQ_Odecseq(_575203, _575205), -(c_SEQ_Omonoseq(_575203, _575205))], (7519 ^ _490194) ^ [_750582, _750584, _750586, _750588] : [class_Rings_Olinordered__ring__strict(_750582), c_Orderings_Oord__class_Oless(_750582, _750584, _750586), c_Orderings_Oord__class_Oless(_750582, _750588, c_Groups_Ozero__class_Ozero(_750582)), -(c_Orderings_Oord__class_Oless(_750582, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_750582), _750586), _750588), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_750582), _750584), _750588)))], (4808 ^ _490194) ^ [_654659, _654661] : [-(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _654659, _654661) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 4809 ^ _490194 : [(4818 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _654659), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), c_Orderings_Oord__class_Oless(tc_Int_Oint, _654661, _654659)], (4812 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _654659)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _654659, _654661)], (4810 ^ _490194) ^ [] : [_654661 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]]], (2695 ^ _490194) ^ [_579472, _579474, _579476] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _579472), _579474)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _579474), _579476)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _579472), _579476)))], (10011 ^ _490194) ^ [_845662, _845664] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _845662)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, _845662, _845664)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _845664)))))], (7813 ^ _490194) ^ [_760715, _760717, _760719, _760721] : [class_Rings_Olinordered__semiring__strict(_760715), c_Orderings_Oord__class_Oless(_760715, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_760715), _760717), _760719), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_760715), _760717), _760721)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_760715, c_Groups_Ozero__class_Ozero(_760715)), _760717)), -(c_Orderings_Oord__class_Oless(_760715, _760719, _760721))], (732 ^ _490194) ^ [_512509, _512511] : [-(class_Rings_Olinordered__idom(_512509)), _512511 = _512509, class_Rings_Olinordered__idom(_512511)], (4482 ^ _490194) ^ [_643682, _643684] : [_643682 = _643684, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _643682) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _643684))], (9327 ^ _490194) ^ [_819655, _819657, _819659, _819661] : [class_Divides_Osemiring__div(_819655), -(_819657 = c_Groups_Ozero__class_Ozero(_819655)), -(c_Divides_Odiv__class_Odiv(_819655, c_Groups_Oplus__class_Oplus(_819655, _819659, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_819655), _819657), _819661)), _819657) = c_Groups_Oplus__class_Oplus(_819655, _819661, c_Divides_Odiv__class_Odiv(_819655, _819659, _819657)))], (252 ^ _490194) ^ [_498349, _498351] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_498349)), _498351 = _498349, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_498351)], (10107 ^ _490194) ^ [_849917, _849919] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _849917), _849919)), -(_849919 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _849917, 10110 ^ [_849917, _849919]))], (4031 ^ _490194) ^ [_627350, _627352] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _627350), _627352)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _627350), c_Nat_OSuc(_627352))))], (4616 ^ _490194) ^ [_648584, _648586] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _648584), 4619 ^ _490194 : [(4626 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _648586, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _648586, _648584), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (4620 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _648586, _648584), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _648586, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (5373 ^ _490194) ^ [_673551, _673553] : [-(hBOOL(hAPP(_673551, hAPP(c_Int_Onat, _673553)))), 5377 ^ _490194 : [(5380 ^ _490194) ^ [] : [hBOOL(hAPP(_673551, 5376 ^ [_673551, _673553]))], (5378 ^ _490194) ^ [] : [-(_673553 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 5376 ^ [_673551, _673553]))]], 5381 ^ _490194 : [(5384 ^ _490194) ^ [] : [hBOOL(hAPP(_673551, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (5382 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _673553, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (8091 ^ _490194) ^ [_772161, _772163, _772165, _772167] : [-(hAPP(hAPP(c_Power_Opower_Opower(_772161, _772163, _772165), _772167), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _772163)], (7125 ^ _490194) ^ [_737313, _737315, _737317, _737319] : [class_Rings_Oordered__semiring(_737313), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_737313, _737315), _737317)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_737313, c_Groups_Ozero__class_Ozero(_737313)), _737319)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_737313, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_737313), _737319), _737315)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_737313), _737319), _737317))))], (4314 ^ _490194) ^ [_637530] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _637530), -(c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _637530, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = _637530)], (10027 ^ _490194) ^ [_846374, _846376, _846378] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _846374, _846376), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _846374, _846378)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _846376, _846378))], (11490 ^ _490194) ^ [_902858, _902860, _902862, _902864] : [class_Fields_Olinordered__field__inverse__zero(_902858), 11493 ^ _490194 : [(11494 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_902858, _902860), c_Rings_Oinverse__class_Odivide(_902858, _902862, _902864))), 11497 ^ _490194 : [(11504 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(_902858, c_Groups_Ozero__class_Ozero(_902858), _902864)), 11507 ^ _490194 : [(11514 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(_902858, _902864, c_Groups_Ozero__class_Ozero(_902858))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_902858, _902860), c_Groups_Ozero__class_Ozero(_902858))))], (11508 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(_902858, _902864, c_Groups_Ozero__class_Ozero(_902858)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_902858, _902862), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_902858), _902860), _902864))))]]], (11498 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(_902858, c_Groups_Ozero__class_Ozero(_902858), _902864), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_902858, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_902858), _902860), _902864)), _902862)))]]], (11520 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_902858, _902860), c_Rings_Oinverse__class_Odivide(_902858, _902862, _902864)))), 11523 ^ _490194 : [(11526 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_902858, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_902858), _902860), _902864)), _902862))], (11524 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(_902858, c_Groups_Ozero__class_Ozero(_902858), _902864))]], 11527 ^ _490194 : [(11530 ^ _490194) ^ [] : [11531 ^ _490194 : [(11534 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_902858, _902862), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_902858), _902860), _902864)))], (11532 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(_902858, _902864, c_Groups_Ozero__class_Ozero(_902858)))]], 11535 ^ _490194 : [(11538 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_902858, _902860), c_Groups_Ozero__class_Ozero(_902858)))], (11536 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(_902858, _902864, c_Groups_Ozero__class_Ozero(_902858))]]], (11528 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(_902858, c_Groups_Ozero__class_Ozero(_902858), _902864)]]]]], (4590 ^ _490194) ^ [_647791, _647793] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _647791, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _647793), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _647791, _647793), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (11470 ^ _490194) ^ [_901947, _901949, _901951, _901953] : [class_Fields_Ofield(_901947), -(_901949 = c_Groups_Ozero__class_Ozero(_901947)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _901951), _901953)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_901947), _901949), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _901953, _901951)) = c_Rings_Oinverse__class_Odivide(_901947, hAPP(hAPP(c_Power_Opower__class_Opower(_901947), _901949), _901953), hAPP(hAPP(c_Power_Opower__class_Opower(_901947), _901949), _901951)))], (11782 ^ _490194) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal))], (5388 ^ _490194) ^ [_674103, _674105] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _674103)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _674103), _674105)), -(hAPP(c_Int_Onat, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _674105, _674103)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(c_Int_Onat, _674105), hAPP(c_Int_Onat, _674103)))], (7463 ^ _490194) ^ [_748668, _748670, _748672] : [class_Rings_Olinordered__ring__strict(_748668), c_Orderings_Oord__class_Oless(_748668, _748670, c_Groups_Ozero__class_Ozero(_748668)), c_Orderings_Oord__class_Oless(_748668, _748672, c_Groups_Ozero__class_Ozero(_748668)), -(c_Orderings_Oord__class_Oless(_748668, c_Groups_Ozero__class_Ozero(_748668), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_748668), _748670), _748672)))], (2329 ^ _490194) ^ [_566564, _566566] : [class_RealVector_Oreal__normed__vector(_566564), 2332 ^ _490194 : [(2342 ^ _490194) ^ [] : [-(c_SEQ_OBseq(_566564, _566566)), 2343 ^ _490194 : [(2344 ^ _490194) ^ [_567093] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _567093), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_566564, hAPP(_566566, 2347 ^ [_566564, _566566, _567093]))), _567093))]]], (2333 ^ _490194) ^ [] : [c_SEQ_OBseq(_566564, _566566), 2337 ^ _490194 : [(2340 ^ _490194) ^ [_566957] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_566564, hAPP(_566566, _566957))), 2336 ^ [_566564, _566566])))], (2338 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 2336 ^ [_566564, _566566]))]]]]], (7203 ^ _490194) ^ [_740121, _740123, _740125, _740127, _740129] : [class_Rings_Oordered__semiring(_740121), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_740121, _740123), _740125)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_740121, _740127), _740129)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_740121, c_Groups_Ozero__class_Ozero(_740121)), _740125)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_740121, c_Groups_Ozero__class_Ozero(_740121)), _740127)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_740121, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_740121), _740123), _740127)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_740121), _740125), _740129))))], (1246 ^ _490194) ^ [_530954, _530956, _530958] : [class_Groups_Oordered__ab__group__add(_530954), 1249 ^ _490194 : [(1256 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(_530954, c_Groups_Ominus__class_Ominus(_530954, _530956, _530958), c_Groups_Ozero__class_Ozero(_530954)), -(c_Orderings_Oord__class_Oless(_530954, _530956, _530958))], (1250 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(_530954, _530956, _530958), -(c_Orderings_Oord__class_Oless(_530954, c_Groups_Ominus__class_Ominus(_530954, _530956, _530958), c_Groups_Ozero__class_Ozero(_530954)))]]], (6209 ^ _490194) ^ [_705196, _705198, _705200] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _705196), _705198)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _705200), _705198))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _705198), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _705196), _705200)))], (2827 ^ _490194) ^ [_584206, _584208] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _584206, _584208), 2830 ^ _490194 : [(2833 ^ _490194) ^ [] : [_584206 = _584208], (2831 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _584206), _584208)))]]], (7891 ^ _490194) ^ [_763343, _763345, _763347] : [class_Rings_Oordered__ring__abs(_763343), -(c_Groups_Oabs__class_Oabs(_763343, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_763343), _763345), _763347)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_763343), c_Groups_Oabs__class_Oabs(_763343, _763345)), c_Groups_Oabs__class_Oabs(_763343, _763347))), 7898 ^ _490194 : [(7901 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_763343, _763345), c_Groups_Ozero__class_Ozero(_763343)))], (7899 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_763343, c_Groups_Ozero__class_Ozero(_763343)), _763345))]], 7902 ^ _490194 : [(7905 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_763343, _763347), c_Groups_Ozero__class_Ozero(_763343)))], (7903 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_763343, c_Groups_Ozero__class_Ozero(_763343)), _763347))]]], (10833 ^ _490194) ^ [_878262, _878264] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _878262)), _878264)), -(c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _878264, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _878262))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_RComplete_Onatceiling(_878264), _878262))], (3048 ^ _490194) ^ [_592275, _592277] : [class_Rings_Olinordered__semidom(_592275), 3051 ^ _490194 : [(3058 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _592277), -(c_Orderings_Oord__class_Oless(_592275, c_Groups_Ozero__class_Ozero(_592275), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_592275), _592277)))], (3052 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(_592275, c_Groups_Ozero__class_Ozero(_592275), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_592275), _592277)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _592277))]]], (7271 ^ _490194) ^ [_742438, _742440, _742442, _742444] : [class_Rings_Olinordered__ring__strict(_742438), 7274 ^ _490194 : [(7289 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(_742438, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_742438), _742440), _742442), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_742438), _742444), _742442))), 7290 ^ _490194 : [(7297 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(_742438, _742442, c_Groups_Ozero__class_Ozero(_742438)), c_Orderings_Oord__class_Oless(_742438, _742444, _742440)], (7291 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(_742438, c_Groups_Ozero__class_Ozero(_742438), _742442), c_Orderings_Oord__class_Oless(_742438, _742440, _742444)]]], (7275 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(_742438, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_742438), _742440), _742442), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_742438), _742444), _742442)), 7280 ^ _490194 : [(7283 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(_742438, _742440, _742444))], (7281 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(_742438, c_Groups_Ozero__class_Ozero(_742438), _742442))]], 7284 ^ _490194 : [(7287 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(_742438, _742444, _742440))], (7285 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(_742438, _742442, c_Groups_Ozero__class_Ozero(_742438)))]]]]], (3005 ^ _490194) ^ [_590739, _590741] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _590739, _590741), -(c_RealDef_Opositive(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _590741, _590739)))], (8015 ^ _490194) ^ [_768799, _768801] : [class_Rings_Ocomm__semiring__1(_768799), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_768799), c_Groups_Oone__class_Oone(_768799)), _768801) = _768801)], (3522 ^ _490194) ^ [_608954, _608956] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _608954), hAPP(c_RealDef_Oreal(tc_Nat_Onat), _608956)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _608954, _608956))], (11904 ^ _490194) ^ [] : [-(class_Groups_Ozero(tc_RealDef_Oreal))], (11250 ^ _490194) ^ [_893784, _893786, _893788, _893790] : [class_RealVector_Oreal__normed__field(_893784), -(c_Rings_Oinverse__class_Odivide(_893784, c_Groups_Ominus__class_Ominus(_893784, _893786, _893788), _893790) = c_Groups_Ominus__class_Ominus(_893784, c_Rings_Oinverse__class_Odivide(_893784, _893786, _893790), c_Rings_Oinverse__class_Odivide(_893784, _893788, _893790)))], (3897 ^ _490194) ^ [_622844] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _622844) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (8414 ^ _490194) ^ [_785838, _785840, _785842, _785844] : [class_Groups_Oordered__ab__semigroup__add(_785838), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_785838, _785840), _785842)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_785838, c_Groups_Oplus__class_Oplus(_785838, _785844, _785840)), c_Groups_Oplus__class_Oplus(_785838, _785844, _785842))))], (5581 ^ _490194) ^ [_681394, _681396, _681398, _681400, _681402] : [class_RealVector_Oreal__normed__algebra(_681394), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_681394, _681396), _681398), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_681394, _681400), _681402), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_681394, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_681394), _681396), _681400)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _681398), _681402)))], (6095 ^ _490194) ^ [_701257, _701259, _701261, _701263] : [class_Rings_Olinordered__semidom(_701257), c_Orderings_Oord__class_Oless(_701257, c_Groups_Oone__class_Oone(_701257), _701259), c_Orderings_Oord__class_Oless(_701257, hAPP(hAPP(c_Power_Opower__class_Opower(_701257), _701259), _701261), hAPP(hAPP(c_Power_Opower__class_Opower(_701257), _701259), _701263)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _701261, _701263))], (6789 ^ _490194) ^ [_725533, _725535] : [-(hAPP(c_Int_Onat, c_Groups_Oabs__class_Oabs(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _725533), _725535))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, c_Groups_Oabs__class_Oabs(tc_Int_Oint, _725533))), hAPP(c_Int_Onat, c_Groups_Oabs__class_Oabs(tc_Int_Oint, _725535))))], (8380 ^ _490194) ^ [_784560, _784562, _784564, _784566] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_784560), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_784560, c_Groups_Oplus__class_Oplus(_784560, _784562, _784564)), c_Groups_Oplus__class_Oplus(_784560, _784562, _784566))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_784560, _784564), _784566)))], (4442 ^ _490194) ^ [_642293, _642295] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _642293), _642295))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _642295), _642293)))], (4348 ^ _490194) ^ [_638712, _638714] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _638712), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _638714)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _638712, _638714))], (8033 ^ _490194) ^ [_769611, _769613, _769615, _769617] : [class_Rings_Ocomm__semiring__1(_769611), -(hAPP(hAPP(c_Power_Opower__class_Opower(_769611), hAPP(hAPP(c_Power_Opower__class_Opower(_769611), _769613), _769615)), _769617) = hAPP(hAPP(c_Power_Opower__class_Opower(_769611), _769613), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _769615), _769617)))], (3899 ^ _490194) ^ [_622954, _622956] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_622954), c_Nat_OSuc(_622956)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _622954, _622956))], (6153 ^ _490194) ^ [_703213, _703215] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _703213), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _703215), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _703213, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _703213), _703215)))], (978 ^ _490194) ^ [_521078, _521080] : [_521080 = _521078, -(c_Nat_Osemiring__1__class_Oof__nat(_521080) = c_Nat_Osemiring__1__class_Oof__nat(_521078))], (5357 ^ _490194) ^ [_673043, _673045] : [hBOOL(hAPP(_673043, hAPP(c_Int_Onat, _673045))), 5360 ^ _490194 : [(5367 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _673045, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(_673043, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (5361 ^ _490194) ^ [_673230] : [_673045 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _673230), -(hBOOL(hAPP(_673043, _673230)))]]], (3518 ^ _490194) ^ [] : [-(hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (5119 ^ _490194) ^ [_665418, _665420] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(c_Int_Onat, _665418), hAPP(c_Int_Onat, _665420)), 5122 ^ _490194 : [(5125 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _665418, _665420))], (5123 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _665420))]]], (2533 ^ _490194) ^ [_573861, _573863] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _573863, _573861), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _573861, _573863)))], (8057 ^ _490194) ^ [_770689, _770691, _770693] : [class_Rings_Ocomm__semiring__1(_770689), -(hAPP(hAPP(c_Power_Opower__class_Opower(_770689), _770691), c_Nat_OSuc(_770693)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_770689), _770691), hAPP(hAPP(c_Power_Opower__class_Opower(_770689), _770691), _770693)))], (2931 ^ _490194) ^ [_587833, _587835] : [class_Orderings_Oorder(_587833), 2938 ^ _490194 : [(2941 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_587833, hAPP(_587835, 2937 ^ [_587833, _587835])), hAPP(_587835, 2936 ^ [_587833, _587835])))], (2939 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, 2936 ^ [_587833, _587835]), 2937 ^ [_587833, _587835])))]], -(c_SEQ_Omonoseq(_587833, _587835))], (7909 ^ _490194) ^ [_764029, _764031, _764033, _764035] : [class_RealVector_Oreal__normed__vector(_764029), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _764031), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_764029, _764033)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _764031), c_RealVector_Onorm__class_Onorm(_764029, _764035)))), -(_764033 = c_Groups_Ozero__class_Ozero(_764029))], (7225 ^ _490194) ^ [_740855, _740857, _740859] : [class_Rings_Oordered__ring(_740855), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_740855, c_Groups_Ozero__class_Ozero(_740855)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_740855), _740857), _740859)))), 7230 ^ _490194 : [(7237 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_740855, _740857), c_Groups_Ozero__class_Ozero(_740855))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_740855, _740859), c_Groups_Ozero__class_Ozero(_740855)))], (7231 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_740855, c_Groups_Ozero__class_Ozero(_740855)), _740857)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_740855, c_Groups_Ozero__class_Ozero(_740855)), _740859))]]], (7683 ^ _490194) ^ [_756309, _756311, _756313, _756315, _756317] : [class_Rings_Olinordered__semiring__strict(_756309), c_Orderings_Oord__class_Oless(_756309, _756311, _756313), c_Orderings_Oord__class_Oless(_756309, _756315, _756317), c_Orderings_Oord__class_Oless(_756309, c_Groups_Ozero__class_Ozero(_756309), _756313), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_756309, c_Groups_Ozero__class_Ozero(_756309)), _756315)), -(c_Orderings_Oord__class_Oless(_756309, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_756309), _756311), _756315), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_756309), _756313), _756317)))], (2391 ^ _490194) ^ [_569095, _569097] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _569095, _569097) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _569095), _569097)))], (10623 ^ _490194) ^ [_870274, _870276] : [-(_870274 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _870274, _870276) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _870274, c_Groups_Oone__class_Oone(tc_Nat_Onat)), _870276)))], (11234 ^ _490194) ^ [_893143, _893145, _893147, _893149] : [class_Rings_Odivision__ring(_893143), -(c_Rings_Oinverse__class_Odivide(_893143, c_Groups_Ominus__class_Ominus(_893143, _893145, _893147), _893149) = c_Groups_Ominus__class_Ominus(_893143, c_Rings_Oinverse__class_Odivide(_893143, _893145, _893149), c_Rings_Oinverse__class_Odivide(_893143, _893147, _893149)))], (5907 ^ _490194) ^ [_694490, _694492] : [class_Power_Opower(_694490), -(hAPP(hAPP(c_Power_Opower__class_Opower(_694490), _694492), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_694490))], (9901 ^ _490194) ^ [_841096, _841098] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Nat_OSuc(_841096), _841098) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _841096, c_Nat_OSuc(_841098)))], (11752 ^ _490194) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (4983 ^ _490194) ^ [_660599] : [hBOOL(hAPP(_660599, 4984 ^ [_660599])), 4987 ^ _490194 : [(4988 ^ _490194) ^ [_660796] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _660796)), -(hBOOL(hAPP(_660599, hAPP(c_Int_Onat, _660796))))]]], (3815 ^ _490194) ^ [_619997] : [-(c_Groups_Oabs__class_Oabs(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _619997)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _619997))], (5003 ^ _490194) ^ [_661382] : [5004 ^ _490194 : [(5005 ^ _490194) ^ [_661470] : [hBOOL(hAPP(_661382, _661470))]], 5007 ^ _490194 : [(5010 ^ _490194) ^ [] : [-(hBOOL(hAPP(_661382, hAPP(c_Int_Onat, 5006 ^ [_661382]))))], (5008 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 5006 ^ [_661382])))]]], (10013 ^ _490194) ^ [_845793, _845795] : [class_Groups_Ocomm__monoid__add(_845793), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_845793), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_845793)), _845795) = _845795)], (8816 ^ _490194) ^ [_800567, _800569, _800571, _800573] : [class_Rings_Olinordered__semidom(_800567), c_Orderings_Oord__class_Oless(_800567, c_Groups_Ozero__class_Ozero(_800567), _800569), c_Orderings_Oord__class_Oless(_800567, _800571, _800573), -(c_Orderings_Oord__class_Oless(_800567, _800571, c_Groups_Oplus__class_Oplus(_800567, _800569, _800573)))], (2611 ^ _490194) ^ [_576497, _576499] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _576497, _576499), _576499 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (11768 ^ _490194) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (852 ^ _490194) ^ [_516049, _516051] : [-(hBOOL(_516049)), _516051 = _516049, hBOOL(_516051)], (9436 ^ _490194) ^ [_823922] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Nat_OSuc(_823922)) = 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), _823922)))], (282 ^ _490194) ^ [_499234, _499236] : [-(class_Rings_Olinordered__comm__semiring__strict(_499234)), _499236 = _499234, class_Rings_Olinordered__comm__semiring__strict(_499236)], (10757 ^ _490194) ^ [_875491, _875493] : [-(c_Int_Onat__aux(_875491, _875493) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(c_Int_Onat, _875491), _875493))], (7245 ^ _490194) ^ [_741524, _741526, _741528] : [class_Rings_Oordered__cancel__semiring(_741524), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_741524, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_741524), _741526), _741528)), c_Groups_Ozero__class_Ozero(_741524)))), 7250 ^ _490194 : [(7257 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_741524, _741526), c_Groups_Ozero__class_Ozero(_741524))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_741524, c_Groups_Ozero__class_Ozero(_741524)), _741528))], (7251 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_741524, c_Groups_Ozero__class_Ozero(_741524)), _741526)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_741524, _741528), c_Groups_Ozero__class_Ozero(_741524)))]]], (4354 ^ _490194) ^ [_638890, _638892] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _638890, _638892), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _638890), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _638892)))], (10805 ^ _490194) ^ [_877328, _877330] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _877328)), 10808 ^ _490194 : [(10815 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _877328), hAPP(c_RealDef_Oreal(tc_Nat_Onat), _877330))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_877328)), _877330)))], (10809 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_877328)), _877330)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _877328), hAPP(c_RealDef_Oreal(tc_Nat_Onat), _877330))))]]], (6735 ^ _490194) ^ [_723852, _723854] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _723852), 6738 ^ _490194 : [(6747 ^ _490194) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _723852), _723854) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _723852 = c_Groups_Oone__class_Oone(tc_Int_Oint), _723854 = c_Groups_Oone__class_Oone(tc_Int_Oint)], (6739 ^ _490194) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _723852), _723854) = c_Groups_Oone__class_Oone(tc_Int_Oint), 6742 ^ _490194 : [(6745 ^ _490194) ^ [] : [-(_723854 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (6743 ^ _490194) ^ [] : [-(_723852 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]]]], (5737 ^ _490194) ^ [_687787, _687789, _687791] : [_687789 = _687791, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_687787)), _687789) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_687787)), _687791))], (1576 ^ _490194) ^ [_542222, _542224, _542226] : [class_Orderings_Oorder(_542222), 1579 ^ _490194 : [(1588 ^ _490194) ^ [] : [-(_542224 = _542226), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_542222, _542224), _542226)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_542222, _542226), _542224))], (1580 ^ _490194) ^ [] : [_542224 = _542226, 1583 ^ _490194 : [(1586 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_542222, _542226), _542224)))], (1584 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_542222, _542224), _542226)))]]]]], (11220 ^ _490194) ^ [_892408, _892410] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _892408, _892410))), c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _892408), hAPP(c_RealDef_Oreal(tc_Nat_Onat), _892410)))))], (11614 ^ _490194) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (5829 ^ _490194) ^ [_691514, _691516, _691518, _691520] : [class_Divides_Osemiring__div(_691514), 5832 ^ _490194 : [(5839 ^ _490194) ^ [] : [-(_691516 = c_Groups_Ozero__class_Ozero(_691514)), -(c_Divides_Odiv__class_Odiv(_691514, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_691514), _691516), _691518), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_691514), _691516), _691520)) = c_Divides_Odiv__class_Odiv(_691514, _691518, _691520))], (5833 ^ _490194) ^ [] : [_691516 = c_Groups_Ozero__class_Ozero(_691514), -(c_Divides_Odiv__class_Odiv(_691514, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_691514), _691516), _691518), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_691514), _691516), _691520)) = c_Groups_Ozero__class_Ozero(_691514))]]], (1170 ^ _490194) ^ [_528061, _528063, _528065, _528067] : [-(hAPP(_528067, _528063) = hAPP(_528065, _528061)), _528067 = _528065, _528063 = _528061], (6283 ^ _490194) ^ [_707738] : [_707738 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oabs__class_Oabs(tc_Int_Oint, _707738), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (7873 ^ _490194) ^ [_762768, _762770, _762772] : [class_Rings_Olinordered__idom(_762768), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_762768, c_Groups_Ozero__class_Ozero(_762768)), _762770)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_762768, c_Groups_Ozero__class_Ozero(_762768)), _762772)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_762768, _762772), c_Groups_Oone__class_Oone(_762768))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_762768, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_762768), _762770), _762772)), _762770)))], (7477 ^ _490194) ^ [_749130, _749132, _749134, _749136] : [class_Rings_Olinordered__semiring__strict(_749130), c_Orderings_Oord__class_Oless(_749130, _749132, _749134), c_Orderings_Oord__class_Oless(_749130, c_Groups_Ozero__class_Ozero(_749130), _749136), -(c_Orderings_Oord__class_Oless(_749130, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_749130), _749132), _749136), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_749130), _749134), _749136)))], (3154 ^ _490194) ^ [_596245, _596247] : [class_RealVector_Oreal__normed__algebra__1(_596245), -(c_RealVector_Onorm__class_Onorm(_596245, hAPP(c_Nat_Osemiring__1__class_Oof__nat(_596245), _596247)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal), _596247))], (6033 ^ _490194) ^ [_699090, _699092, _699094] : [class_Rings_Ocomm__semiring__1(_699090), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_699090, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_699090)), _699092), _699094))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Polynomial_Odegree(_699090, _699092)), _699094))))], (4927 ^ _490194) ^ [_658697] : [-(hAPP(c_Int_Onat, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _658697)) = _658697)], (5523 ^ _490194) ^ [_679238, _679240] : [class_Groups_Omonoid__mult(_679238), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_679238), _679240), c_Groups_Oone__class_Oone(_679238)) = _679240)], (5719 ^ _490194) ^ [_687004, _687006] : [class_Groups_Omonoid__mult(_687004), -(hAPP(hAPP(c_Power_Opower__class_Opower(_687004), c_Groups_Oone__class_Oone(_687004)), _687006) = c_Groups_Oone__class_Oone(_687004))], (6943 ^ _490194) ^ [_731098] : [class_Rings_Olinordered__idom(_731098), -(c_Groups_Oabs__class_Oabs(_731098, c_Groups_Oone__class_Oone(_731098)) = c_Groups_Oone__class_Oone(_731098))], (11562 ^ _490194) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat))], (2993 ^ _490194) ^ [_590210, _590212] : [c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _590210, _590212) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(c_HOL_Oequal__class_Oequal(tc_RealDef_Oreal, _590210, _590212))], (2493 ^ _490194) ^ [_572504] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _572504, _572504)], (1705 ^ _490194) ^ [_546481, _546483, _546485, _546487] : [class_Orderings_Oorder(_546481), _546483 = _546485, c_Orderings_Oord__class_Oless(_546481, _546487, _546485), -(c_Orderings_Oord__class_Oless(_546481, _546487, _546483))], (1424 ^ _490194) ^ [_537232, _537234, _537236, _537238] : [class_Orderings_Oorder(_537232), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_537232, _537234), _537236)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_537232, _537238), _537234)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_537232, _537238), _537236)))], (6081 ^ _490194) ^ [_700773, _700775, _700777, _700779] : [class_Rings_Olinordered__semidom(_700773), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _700775, _700777), c_Orderings_Oord__class_Oless(_700773, c_Groups_Oone__class_Oone(_700773), _700779), -(c_Orderings_Oord__class_Oless(_700773, hAPP(hAPP(c_Power_Opower__class_Opower(_700773), _700779), _700775), hAPP(hAPP(c_Power_Opower__class_Opower(_700773), _700779), _700777)))], (6045 ^ _490194) ^ [_699576] : [-(_699576 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _699576, _699576) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (2059 ^ _490194) ^ [_557638, _557640, _557642] : [class_Orderings_Oorder(_557638), -(_557640 = _557642), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_557638, _557642), _557640)), -(c_Orderings_Oord__class_Oless(_557638, _557642, _557640))], (372 ^ _490194) ^ [_501889, _501891] : [-(class_Rings_Oordered__cancel__semiring(_501889)), _501891 = _501889, class_Rings_Oordered__cancel__semiring(_501891)], (12028 ^ _490194) ^ [_917806] : [class_Rings_Olinordered__idom(_917806), -(class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(_917806)))], (8536 ^ _490194) ^ [_790244, _790246, _790248, _790250] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_790244), 8539 ^ _490194 : [(8546 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(_790244, _790246, _790250), -(c_Orderings_Oord__class_Oless(_790244, c_Groups_Oplus__class_Oplus(_790244, _790246, _790248), c_Groups_Oplus__class_Oplus(_790244, _790250, _790248)))], (8540 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(_790244, c_Groups_Oplus__class_Oplus(_790244, _790246, _790248), c_Groups_Oplus__class_Oplus(_790244, _790250, _790248)), -(c_Orderings_Oord__class_Oless(_790244, _790246, _790250))]]], (8476 ^ _490194) ^ [_788109, _788111, _788113, _788115] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_788109), c_Orderings_Oord__class_Oless(_788109, c_Groups_Oplus__class_Oplus(_788109, _788111, _788113), c_Groups_Oplus__class_Oplus(_788109, _788115, _788113)), -(c_Orderings_Oord__class_Oless(_788109, _788111, _788115))], (7855 ^ _490194) ^ [_762193, _762195, _762197] : [class_Rings_Olinordered__idom(_762193), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_762193, c_Groups_Ozero__class_Ozero(_762193)), _762195)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_762193, c_Groups_Ozero__class_Ozero(_762193)), _762197)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_762193, _762197), c_Groups_Oone__class_Oone(_762193))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_762193, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_762193), _762197), _762195)), _762195)))], (3811 ^ _490194) ^ [_619787, _619789] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _619787)), _619789) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _619787), _619789)))], (9417 ^ _490194) ^ [_823190, _823192] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _823190, _823192), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _823190, c_Groups_Oone__class_Oone(tc_Int_Oint))), _823192)))], (8192 ^ _490194) ^ [_776754, _776756, _776758, _776760] : [class_Rings_Ocomm__semiring__1(_776754), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_776754), c_Groups_Oplus__class_Oplus(_776754, _776756, _776758)), _776760) = c_Groups_Oplus__class_Oplus(_776754, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_776754), _776756), _776760), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_776754), _776758), _776760)))], (4173 ^ _490194) ^ [_632474, _632476] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _632474, c_Nat_OSuc(_632476)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _632474), _632476)))], (5450 ^ _490194) ^ [_676320, _676322, _676324] : [hBOOL(hAPP(_676320, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _676322, _676324))), 5455 ^ _490194 : [(5458 ^ _490194) ^ [] : [-(hBOOL(hAPP(_676320, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (5456 ^ _490194) ^ [] : [-(_676324 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 5460 ^ _490194 : [(5465 ^ _490194) ^ [] : [-(hBOOL(hAPP(_676320, 5459 ^ [_676320, _676322, _676324])))], (5463 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _676322, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _676324), c_Nat_OSuc(5459 ^ [_676320, _676322, _676324]))))], (5461 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _676324), 5459 ^ [_676320, _676322, _676324])), _676322)))]]], (5507 ^ _490194) ^ [_678457, _678459, _678461] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _678457), _678459)), _678461) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _678457), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _678459), _678461)))], (11122 ^ _490194) ^ [_888900, _888902] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _888900)), 11125 ^ _490194 : [(11132 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _888902)), _888900)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _888902), c_RComplete_Onatfloor(_888900))))], (11126 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _888902), c_RComplete_Onatfloor(_888900))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _888902)), _888900)))]]], (9317 ^ _490194) ^ [_819255, _819257, _819259, _819261] : [class_Divides_Osemiring__div(_819255), -(_819257 = c_Groups_Ozero__class_Ozero(_819255)), -(c_Divides_Odiv__class_Odiv(_819255, c_Groups_Oplus__class_Oplus(_819255, _819259, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_819255), _819261), _819257)), _819257) = c_Groups_Oplus__class_Oplus(_819255, _819261, c_Divides_Odiv__class_Odiv(_819255, _819259, _819257)))], (11804 ^ _490194) ^ [] : [-(class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal))], (6143 ^ _490194) ^ [_702896, _702898] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _702896), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _702898), -(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), _702898), _702896)))], (5243 ^ _490194) ^ [_669479, _669481] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _669479)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _669481)), 5250 ^ _490194 : [(5257 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _669479, _669481), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(c_Int_Onat, _669479), hAPP(c_Int_Onat, _669481)))], (5251 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(c_Int_Onat, _669479), hAPP(c_Int_Onat, _669481)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _669479, _669481))]]], (1204 ^ _490194) ^ [] : [-(c_SEQ_Osubseq(1202 ^ []))], (6481 ^ _490194) ^ [] : [-(hAPP(c_RealDef_Oreal(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (9496 ^ _490194) ^ [_826115, _826117, _826119, _826121, _826123] : [hBOOL(hAPP(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), _826115), _826117), _826119)), c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _826115), _826121), _826123))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _826123), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), c_Orderings_Oord__class_Oless(tc_Int_Oint, _826115, _826123), c_Orderings_Oord__class_Oless(tc_Int_Oint, _826115, _826119), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _826121), _826117)))], (4009 ^ _490194) ^ [_626565, _626567] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _626567, c_Nat_OSuc(_626565)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _626565, _626567)], (12196 ^ _490194) ^ [_923126] : [class_Rings_Olinordered__idom(_923126), -(class_Nat_Osemiring__char__0(tc_Polynomial_Opoly(_923126)))], (3262 ^ _490194) ^ [_600126, _600128, _600130] : [class_Rings_Olinordered__semidom(_600126), c_Orderings_Oord__class_Oless(_600126, c_Groups_Ozero__class_Ozero(_600126), _600128), -(c_Orderings_Oord__class_Oless(_600126, c_Groups_Ozero__class_Ozero(_600126), hAPP(hAPP(c_Power_Opower__class_Opower(_600126), _600128), _600130)))], (11942 ^ _490194) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex))], (7637 ^ _490194) ^ [_754608, _754610, _754612] : [-(_754608 = 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), _754608), _754610), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _754608), _754612)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _754610, _754612))], (3640 ^ _490194) ^ [_613107] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _613107), -(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), _613107)))], (10061 ^ _490194) ^ [_847968, _847970, _847972] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _847968, _847970)), _847972)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _847970), _847972)))], (9405 ^ _490194) ^ [_822776, _822778] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _822776, c_Groups_Oone__class_Oone(tc_Int_Oint))), _822778)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _822776, _822778))], (3148 ^ _490194) ^ [_595991, _595993, _595995] : [class_RealVector_Oreal__normed__div__algebra(_595991), -(c_RealVector_Onorm__class_Onorm(_595991, hAPP(hAPP(c_Power_Opower__class_Opower(_595991), _595993), _595995)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_595991, _595993)), _595995))], (10493 ^ _490194) ^ [_864694, _864696, _864698] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _864694), _864696)), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _864696, _864694)), _864698) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_864696), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _864694, _864698)))], (1032 ^ _490194) ^ [_523027, _523029] : [_523029 = _523027, -(c_Power_Opower__class_Opower(_523029) = c_Power_Opower__class_Opower(_523027))], (5625 ^ _490194) ^ [_683114, _683116, _683118, _683120] : [class_RealVector_Oreal__normed__algebra(_683114), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_683114), c_Groups_Ominus__class_Ominus(_683114, _683116, _683118)), _683120) = c_Groups_Ominus__class_Ominus(_683114, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_683114), _683116), _683120), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_683114), _683118), _683120)))], (3570 ^ _490194) ^ [_610592] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _610592)), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), -(_610592 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5043 ^ _490194) ^ [_662710, _662712] : [-(c_Divides_Odiv__class_Odiv(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _662710), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _662712)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _662710, _662712)))], (11964 ^ _490194) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex))], (4404 ^ _490194) ^ [_640753, _640755] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _640753)), _640755) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _640753), _640755)))], (3108 ^ _490194) ^ [_594404, _594406] : [hAPP(c_RealDef_Oreal(tc_Nat_Onat), _594404) = hAPP(c_RealDef_Oreal(tc_Nat_Onat), _594406), -(_594404 = _594406)], (5563 ^ _490194) ^ [_680604, _680606, _680608] : [class_RealVector_Oreal__normed__div__algebra(_680604), -(c_RealVector_Onorm__class_Onorm(_680604, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_680604), _680606), _680608)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_680604, _680606)), c_RealVector_Onorm__class_Onorm(_680604, _680608)))], (1935 ^ _490194) ^ [_553736, _553738, _553740, _553742] : [class_Orderings_Opreorder(_553736), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_553736, _553738), _553740)), c_Orderings_Oord__class_Oless(_553736, _553740, _553742), -(c_Orderings_Oord__class_Oless(_553736, _553738, _553742))], (3506 ^ _490194) ^ [_608417] : [hAPP(c_RealDef_Oreal(tc_Nat_Onat), _608417) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_608417 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2809 ^ _490194) ^ [_583525, _583527] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _583525), _583527)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _583525, _583527)), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))], (2019 ^ _490194) ^ [_556375, _556377, _556379] : [class_Orderings_Olinorder(_556375), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_556375, _556377), _556379)), 2026 ^ _490194 : [(2033 ^ _490194) ^ [] : [_556377 = _556379, c_Orderings_Oord__class_Oless(_556375, _556377, _556379)], (2027 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(_556375, _556377, _556379)), -(_556377 = _556379)]]], (11836 ^ _490194) ^ [] : [-(class_Rings_Olinordered__semidom(tc_RealDef_Oreal))], (8051 ^ _490194) ^ [_770409, _770411, _770413] : [class_Rings_Ocomm__semiring__1(_770409), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_770409), _770411), hAPP(hAPP(c_Power_Opower__class_Opower(_770409), _770411), _770413)) = hAPP(hAPP(c_Power_Opower__class_Opower(_770409), _770411), c_Nat_OSuc(_770413)))], (11692 ^ _490194) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (12076 ^ _490194) ^ [_919326] : [class_Rings_Oidom(_919326), -(class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(_919326)))], (6823 ^ _490194) ^ [_726884] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _726884), -(_726884 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _726884, c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (4406 ^ _490194) ^ [_640909, _640911] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _640909)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _640911))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _640909), _640911)))], (6387 ^ _490194) ^ [_711295, _711297, _711299] : [class_Rings_Olinordered__semidom(_711295), c_Orderings_Oord__class_Oless(_711295, c_Groups_Oone__class_Oone(_711295), _711297), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _711299), -(c_Orderings_Oord__class_Oless(_711295, c_Groups_Oone__class_Oone(_711295), hAPP(hAPP(c_Power_Opower__class_Opower(_711295), _711297), _711299)))], (1124 ^ _490194) ^ [_526383, _526385] : [_526385 = _526383, -(c_Groups_Ozero__class_Ozero(_526385) = c_Groups_Ozero__class_Ozero(_526383))], (11042 ^ _490194) ^ [_885893, _885895, _885897, _885899, _885901] : [class_Fields_Ofield(_885893), c_Polynomial_Opdivmod__rel(_885893, _885895, _885897, _885899, _885901), -(c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_885893), _885895, _885897) = _885899)], (10035 ^ _490194) ^ [_846845, _846847, _846849] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _846845), _846847)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _846845), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _846849, _846847))))], (11740 ^ _490194) ^ [] : [-(class_Divides_Osemiring__div(tc_Nat_Onat))], (5743 ^ _490194) ^ [_688065, _688067, _688069, _688071] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _688065), _688067)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _688069), _688071)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _688065), _688069)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _688067), _688071))))], (802 ^ _490194) ^ [_514574, _514576] : [-(class_Rings_Oring(_514574)), _514576 = _514574, class_Rings_Oring(_514576)], (222 ^ _490194) ^ [_497464, _497466] : [-(class_Fields_Ofield__inverse__zero(_497464)), _497466 = _497464, class_Fields_Ofield__inverse__zero(_497466)], (8618 ^ _490194) ^ [_793563, _793565] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _793563, _793565) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _793565, _793563))], (6675 ^ _490194) ^ [_721589, _721591] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _721589), _721591)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _721589)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _721591)))], (2117 ^ _490194) ^ [_559433, _559435, _559437] : [class_Orderings_Olinorder(_559433), -(c_Orderings_Oord__class_Oless(_559433, _559435, _559437)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_559433, _559437), _559435)))], (11954 ^ _490194) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Complex_Ocomplex))], (7615 ^ _490194) ^ [_753854, _753856, _753858] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _753854), 7618 ^ _490194 : [(7625 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _753856, _753858), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _753854), _753856), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _753854), _753858)))], (7619 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _753854), _753856), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _753854), _753858)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _753856, _753858))]]], (4085 ^ _490194) ^ [_629427] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _629427, c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_629427 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_629427 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (6973 ^ _490194) ^ [_732213, _732215, _732217] : [class_Rings_Olinordered__ring__strict(_732213), 6976 ^ _490194 : [(6991 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_732213, c_Groups_Ozero__class_Ozero(_732213)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_732213), _732215), _732217)))), 6992 ^ _490194 : [(6999 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_732213, _732215), c_Groups_Ozero__class_Ozero(_732213))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_732213, _732217), c_Groups_Ozero__class_Ozero(_732213)))], (6993 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_732213, c_Groups_Ozero__class_Ozero(_732213)), _732215)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_732213, c_Groups_Ozero__class_Ozero(_732213)), _732217))]]], (6977 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_732213, c_Groups_Ozero__class_Ozero(_732213)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_732213), _732215), _732217))), 6982 ^ _490194 : [(6985 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_732213, c_Groups_Ozero__class_Ozero(_732213)), _732217)))], (6983 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_732213, c_Groups_Ozero__class_Ozero(_732213)), _732215)))]], 6986 ^ _490194 : [(6989 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_732213, _732217), c_Groups_Ozero__class_Ozero(_732213))))], (6987 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_732213, _732215), c_Groups_Ozero__class_Ozero(_732213))))]]]]], (11780 ^ _490194) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal))], (3490 ^ _490194) ^ [_607868, _607870, _607872] : [class_Rings_Olinordered__semidom(_607868), 3493 ^ _490194 : [(3500 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _607870), _607872)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_607868, hAPP(c_Nat_Osemiring__1__class_Oof__nat(_607868), _607870)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_607868), _607872))))], (3494 ^ _490194) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_607868, hAPP(c_Nat_Osemiring__1__class_Oof__nat(_607868), _607870)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_607868), _607872))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _607870), _607872)))]]], (11722 ^ _490194) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (8730 ^ _490194) ^ [_797761, _797763, _797765] : [class_Groups_Oordered__comm__monoid__add(_797761), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_797761, c_Groups_Ozero__class_Ozero(_797761)), _797763)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_797761, c_Groups_Ozero__class_Ozero(_797761)), _797765)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_797761, c_Groups_Ozero__class_Ozero(_797761)), c_Groups_Oplus__class_Oplus(_797761, _797763, _797765))))], (6777 ^ _490194) ^ [] : [-(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))], (11818 ^ _490194) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal))], (1873 ^ _490194) ^ [_551730, _551732, _551734] : [class_Orderings_Olinorder(_551730), 1876 ^ _490194 : [(1877 ^ _490194) ^ [] : [-(_551732 = _551734), -(c_Orderings_Oord__class_Oless(_551730, _551732, _551734)), -(c_Orderings_Oord__class_Oless(_551730, _551734, _551732))], (1887 ^ _490194) ^ [] : [1888 ^ _490194 : [(1891 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(_551730, _551734, _551732)], (1889 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(_551730, _551732, _551734)]], _551732 = _551734]]], (1296 ^ _490194) ^ [_532728, _532730, _532732, _532734, _532736] : [class_Groups_Oordered__ab__group__add(_532728), c_Groups_Ominus__class_Ominus(_532728, _532730, _532732) = c_Groups_Ominus__class_Ominus(_532728, _532734, _532736), 1303 ^ _490194 : [(1310 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(_532728, _532734, _532736), -(c_Orderings_Oord__class_Oless(_532728, _532730, _532732))], (1304 ^ _490194) ^ [] : [c_Orderings_Oord__class_Oless(_532728, _532730, _532732), -(c_Orderings_Oord__class_Oless(_532728, _532734, _532736))]]], (3582 ^ _490194) ^ [_611000, _611002, _611004] : [class_Rings_Oring__1(_611000), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _611002), _611004)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_611000), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _611004, _611002)) = c_Groups_Ominus__class_Ominus(_611000, hAPP(c_Nat_Osemiring__1__class_Oof__nat(_611000), _611004), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_611000), _611002)))], (3646 ^ _490194) ^ [_613352, _613354] : [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), _613352), _613354)), -(_613354 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _613352))], (572 ^ _490194) ^ [_507789, _507791] : [-(class_Nat_Osemiring__char__0(_507789)), _507791 = _507789, class_Nat_Osemiring__char__0(_507791)], (682 ^ _490194) ^ [_511034, _511036] : [-(class_Groups_Ogroup__add(_511034)), _511036 = _511034, class_Groups_Ogroup__add(_511036)], (5921 ^ _490194) ^ [_694996, _694998] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _694996), _694998) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _694996 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _694998 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8980 ^ _490194) ^ [_806013, _806015, _806017, _806019, _806021, _806023] : [class_Rings_Oring(_806013), 8983 ^ _490194 : [(8990 ^ _490194) ^ [] : [c_Groups_Oplus__class_Oplus(_806013, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_806013), c_Groups_Ominus__class_Ominus(_806013, _806015, _806021)), _806017), _806019) = _806023, -(c_Groups_Oplus__class_Oplus(_806013, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_806013), _806015), _806017), _806019) = c_Groups_Oplus__class_Oplus(_806013, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_806013), _806021), _806017), _806023))], (8984 ^ _490194) ^ [] : [c_Groups_Oplus__class_Oplus(_806013, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_806013), _806015), _806017), _806019) = c_Groups_Oplus__class_Oplus(_806013, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_806013), _806021), _806017), _806023), -(c_Groups_Oplus__class_Oplus(_806013, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_806013), c_Groups_Ominus__class_Ominus(_806013, _806015, _806021)), _806017), _806019) = _806023)]]], (12148 ^ _490194) ^ [_921606] : [class_Rings_Oidom(_921606), -(class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(_921606)))], (4790 ^ _490194) ^ [_654141, _654143] : [c_Divides_Odiv__class_Odiv(tc_Int_Oint, _654141, _654143) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_654143 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 4799 ^ _490194 : [(4802 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _654141, _654143))], (4800 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _654141)))]], 4803 ^ _490194 : [(4806 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _654143, _654141))], (4804 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _654141), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (11654 ^ _490194) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Int_Oint))], (11772 ^ _490194) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (512 ^ _490194) ^ [_506019, _506021] : [-(class_Rings_Oordered__ring__abs(_506019)), _506021 = _506019, class_Rings_Oordered__ring__abs(_506021)], (2501 ^ _490194) ^ [_572788] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _572788), _572788 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10591 ^ _490194) ^ [_869149, _869151, _869153] : [class_Rings_Oidom(_869149), -(_869151 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_869149))), -(_869153 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_869149))), -(c_Polynomial_Odegree(_869149, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_869149)), _869151), _869153)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Polynomial_Odegree(_869149, _869151), c_Polynomial_Odegree(_869149, _869153)))], (11052 ^ _490194) ^ [_886308, _886310, _886312, _886314, _886316, _886318, _886320] : [class_Fields_Ofield(_886308), c_Polynomial_Opdivmod__rel(_886308, _886310, _886312, _886314, _886316), c_Polynomial_Opdivmod__rel(_886308, _886310, _886312, _886318, _886320), -(_886314 = _886318)], (10311 ^ _490194) ^ [_857426, _857428, _857430] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _857426), _857428)), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _857430, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _857428, _857426)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _857430, _857426), _857428))], (2747 ^ _490194) ^ [_581231, _581233] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _581231), _581233)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _581231, _581233)), -(_581231 = _581233)], (4390 ^ _490194) ^ [_640309, _640311] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _640309), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _640311)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _640309, _640311))], (11592 ^ _490194) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (10397 ^ _490194) ^ [_860831, _860833, _860835] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _860831), _860833)), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _860833, _860835), _860831) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _860833, _860831), _860835))], (11826 ^ _490194) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal))], (1340 ^ _490194) ^ [_534208] : [c_SEQ_Osubseq(_534208), 1343 ^ _490194 : [(1344 ^ _490194) ^ [_534366, _534368] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _534368, _534366), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(_534208, _534368), hAPP(_534208, _534366)))]]], (9129 ^ _490194) ^ [_812034, _812036, _812038, _812040] : [class_Groups_Oordered__comm__monoid__add(_812034), c_Orderings_Oord__class_Oless(_812034, c_Groups_Ozero__class_Ozero(_812034), _812036), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_812034, _812038), _812040)), -(c_Orderings_Oord__class_Oless(_812034, _812038, c_Groups_Oplus__class_Oplus(_812034, _812036, _812040)))], (9381 ^ _490194) ^ [_821902] : [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), _821902), _821902), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _821902, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (11678 ^ _490194) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (5777 ^ _490194) ^ [_689441, _689443, _689445] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _689441, _689443)), _689445) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _689441), _689445), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _689443), _689445)))], (3716 ^ _490194) ^ [_616198, _616200, _616202] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _616198, _616200), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _616200, _616202), 3724 ^ _490194 : [(3727 ^ _490194) ^ [_616637] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _616200, _616637)), 3723 ^ [_616198, _616200, _616202]), 3730 ^ _490194 : [(3733 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _616637), _616202)))], (3731 ^ _490194) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _616198), _616637)))]]], (3725 ^ _490194) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 3723 ^ [_616198, _616200, _616202]))]]], (11662 ^ _490194) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (5171 ^ _490194) ^ [_667085, _667087] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _667085) = _667087), _667085 = hAPP(c_Int_Onat, _667087), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _667087))], (11888 ^ _490194) ^ [] : [-(class_Groups_Ogroup__add(tc_RealDef_Oreal))], (11938 ^ _490194) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex))], (6245 ^ _490194) ^ [_706485] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _706485), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint)), _706485)))], (8158 ^ _490194) ^ [_775280, _775282, _775284, _775286] : [class_Rings_Ocomm__semiring__1(_775280), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_775280), _775282), c_Groups_Oplus__class_Oplus(_775280, _775284, _775286)) = c_Groups_Oplus__class_Oplus(_775280, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_775280), _775282), _775284), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_775280), _775282), _775286)))], (11160 ^ _490194) ^ [_890242, _890244] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _890242)), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _890242, hAPP(c_RealDef_Oreal(tc_Nat_Onat), _890244)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_RComplete_Onatfloor(_890242), _890244))], (5941 ^ _490194) ^ [_695676, _695678, _695680] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _695676, _695678), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _695680), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _695676), _695680), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _695678), _695680)))], (9624 ^ _490194) ^ [_830601, _830603, _830605] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _830601), _830601 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _830603, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _830601), _830605)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _830603, _830601), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint)), _830605)))]], input).
% 44.91/43.77  ncf('1',plain,[v_thesis____],start(12344 ^ 0)).
% 44.91/43.77  ncf('1.1',plain,[-(v_thesis____), c_SEQ_Osubseq(1202 ^ []), 12340 : 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(1202 ^ [], 12336 ^ [1202 ^ [], 1210 ^ [12333 ^ [1202 ^ [], 1205 ^ []]], 1205 ^ []])), 1205 ^ [])), 12333 ^ [1202 ^ [], 1205 ^ []])],extension(12328 ^ 1,bind([[_927286, _927806, _927808], [1202 ^ [], 1210 ^ [12333 ^ [1202 ^ [], 1205 ^ []]], 1205 ^ []]]))).
% 44.91/43.77  ncf('1.1.1',plain,[-(c_SEQ_Osubseq(1202 ^ []))],extension(1204 ^ 2)).
% 44.91/43.77  ncf('1.1.2',plain,[-(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(1202 ^ [], 12336 ^ [1202 ^ [], 1210 ^ [12333 ^ [1202 ^ [], 1205 ^ []]], 1205 ^ []])), 1205 ^ [])), 12333 ^ [1202 ^ [], 1205 ^ []])), 1212 : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, 1210 ^ [12333 ^ [1202 ^ [], 1205 ^ []]]), 12336 ^ [1202 ^ [], 1210 ^ [12333 ^ [1202 ^ [], 1205 ^ []]], 1205 ^ []])), 1212 : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 12333 ^ [1202 ^ [], 1205 ^ []])],extension(1207 ^ 4,bind([[_529559, _529787], [12333 ^ [1202 ^ [], 1205 ^ []], 12336 ^ [1202 ^ [], 1210 ^ [12333 ^ [1202 ^ [], 1205 ^ []]], 1205 ^ []]]]))).
% 44.91/43.77  ncf('1.1.2.1',plain,[-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, 1210 ^ [12333 ^ [1202 ^ [], 1205 ^ []]]), 12336 ^ [1202 ^ [], 1210 ^ [12333 ^ [1202 ^ [], 1205 ^ []]], 1205 ^ []])))],extension(12338 ^ 7,bind([[_927745, _927747], [1210 ^ [12333 ^ [1202 ^ [], 1205 ^ []]], 1205 ^ []]]))).
% 44.91/43.77  ncf('1.1.2.2',plain,[-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 12333 ^ [1202 ^ [], 1205 ^ []]))],extension(12335 ^ 5,bind([[_927581], [1205 ^ []]]))).
% 44.91/43.77  %-----------------------------------------------------
% 44.91/43.77  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------