TSTP Solution File: SWW265+1 by nanoCoP---2.0

%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWW265+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n011.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 12:25:51 EDT 2023

% Result   : Theorem 170.86s 164.92s
% Output   : Proof 170.86s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SWW265+1 : TPTP v8.1.2. Released v5.2.0.
% 0.10/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n011.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Thu May 18 22:16:33 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 170.86/164.92  
% 170.86/164.92  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 170.86/164.92  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 170.86/164.92  %-----------------------------------------------------
% 170.86/164.92  ncf(matrix, plain, [(11932 ^ _690083) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, 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(tc_Complex_Ocomplex, v_w____)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), v_k____))), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)))), 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(tc_Complex_Ocomplex, v_w____)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), v_k____))), v_m____))], !, (8365 ^ _257747) ^ [_552530, _552532] : [class_Rings_Olinordered__idom(_552530), 8368 ^ _257747 : [(8369 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_552530, c_Groups_Oplus__class_Oplus(_552530, _552532, _552532), c_Groups_Ozero__class_Ozero(_552530)), -(c_Orderings_Oord__class_Oless(_552530, _552532, c_Groups_Ozero__class_Ozero(_552530)))], (8375 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_552530, _552532, c_Groups_Ozero__class_Ozero(_552530)), -(c_Orderings_Oord__class_Oless(_552530, c_Groups_Oplus__class_Oplus(_552530, _552532, _552532), c_Groups_Ozero__class_Ozero(_552530)))]]], (5504 ^ _257747) ^ [_450027] : [-(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), _450027) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), _450027)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))], (182 ^ _257747) ^ [_263570, _263572] : [-(class_RealVector_Oreal__normed__algebra(_263570)), _263572 = _263570, class_RealVector_Oreal__normed__algebra(_263572)], (8598 ^ _257747) ^ [_560806, _560808] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _560806, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _560808, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _560806, _560808))], (7554 ^ _257747) ^ [_522145, _522147, _522149] : [class_Groups_Oordered__ab__group__add(_522145), 7557 ^ _257747 : [(7558 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_522145, _522147, _522149), -(c_Orderings_Oord__class_Oless(_522145, c_Groups_Ominus__class_Ominus(_522145, _522147, _522149), c_Groups_Ozero__class_Ozero(_522145)))], (7564 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_522145, c_Groups_Ominus__class_Ominus(_522145, _522147, _522149), c_Groups_Ozero__class_Ozero(_522145)), -(c_Orderings_Oord__class_Oless(_522145, _522147, _522149))]]], (5748 ^ _257747) ^ [_458007, _458009] : [-(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, _458007, _458009) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, _458007, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, _458009)))], (622 ^ _257747) ^ [_276550, _276552] : [-(class_Rings_Osemiring__0(_276550)), _276552 = _276550, class_Rings_Osemiring__0(_276552)], (8406 ^ _257747) ^ [_554054, _554056] : [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, _554054)), _554056)), _554054 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_554056 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4742 ^ _257747) ^ [] : [hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)], (8790 ^ _257747) ^ [_567754, _567756] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _567754, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _567756)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, _567754, _567756))], (11136 ^ _257747) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (10692 ^ _257747) ^ [_632322] : [class_RealVector_Oreal__normed__algebra__1(_632322), -(c_Groups_Osgn__class_Osgn(_632322, c_Groups_Oone__class_Oone(_632322)) = c_Groups_Oone__class_Oone(_632322))], (1287 ^ _257747) ^ [_299541, _299543, _299545] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _299541), 1290 ^ _257747 : [(1291 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _299541), _299543), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _299541), _299545)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _299543, _299545))], (1297 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _299543, _299545), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _299541), _299543), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _299541), _299545)))]]], (11916 ^ _257747) ^ [_670046] : [class_Rings_Ocomm__semiring__1(_670046), -(class_Groups_Oone(tc_Polynomial_Opoly(_670046)))], (7348 ^ _257747) ^ [_515611, _515613] : [class_Groups_Olinordered__ab__group__add(_515611), 7351 ^ _257747 : [(7352 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_515611, c_Groups_Oplus__class_Oplus(_515611, _515613, _515613), c_Groups_Ozero__class_Ozero(_515611)), -(c_Orderings_Oord__class_Oless__eq(_515611, _515613, c_Groups_Ozero__class_Ozero(_515611)))], (7358 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_515611, _515613, c_Groups_Ozero__class_Ozero(_515611)), -(c_Orderings_Oord__class_Oless__eq(_515611, c_Groups_Oplus__class_Oplus(_515611, _515613, _515613), c_Groups_Ozero__class_Ozero(_515611)))]]], (8604 ^ _257747) ^ [_560980, _560982] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _560980, _560982), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _560980, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _560982, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (9859 ^ _257747) ^ [_602208] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _602208, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_602208), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (312 ^ _257747) ^ [_267405, _267407] : [-(class_Groups_Oordered__ab__semigroup__add(_267405)), _267407 = _267405, class_Groups_Oordered__ab__semigroup__add(_267407)], (2864 ^ _257747) ^ [_354217, _354219, _354221] : [class_Rings_Oordered__cancel__semiring(_354217), -(c_Orderings_Oord__class_Oless__eq(_354217, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_354217), _354219), _354221), c_Groups_Ozero__class_Ozero(_354217))), 2869 ^ _257747 : [(2870 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_354217, c_Groups_Ozero__class_Ozero(_354217), _354219), c_Orderings_Oord__class_Oless__eq(_354217, _354221, c_Groups_Ozero__class_Ozero(_354217))], (2876 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_354217, _354219, c_Groups_Ozero__class_Ozero(_354217)), c_Orderings_Oord__class_Oless__eq(_354217, c_Groups_Ozero__class_Ozero(_354217), _354221)]]], (11166 ^ _257747) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (11616 ^ _257747) ^ [_660546] : [class_Rings_Olinordered__idom(_660546), -(class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(_660546)))], (11286 ^ _257747) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (11434 ^ _257747) ^ [] : [-(class_Orderings_Olinorder(tc_RealDef_Oreal))], (11922 ^ _257747) ^ [_670236] : [class_Rings_Ocomm__semiring__1(_670236), -(class_Rings_Odvd(tc_Polynomial_Opoly(_670236)))], (4916 ^ _257747) ^ [_428122, _428124, _428126, _428128, _428130] : [class_Rings_Olinordered__idom(_428122), c_Orderings_Oord__class_Oless(_428122, c_Groups_Oabs__class_Oabs(_428122, _428124), _428126), c_Orderings_Oord__class_Oless(_428122, c_Groups_Oabs__class_Oabs(_428122, _428128), _428130), -(c_Orderings_Oord__class_Oless(_428122, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_428122), c_Groups_Oabs__class_Oabs(_428122, _428124)), c_Groups_Oabs__class_Oabs(_428122, _428128)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_428122), _428126), _428130)))], (1797 ^ _257747) ^ [_317175, _317177, _317179, _317181] : [class_Rings_Olinordered__semidom(_317175), c_Orderings_Oord__class_Oless(_317175, c_Groups_Oone__class_Oone(_317175), _317177), 1804 ^ _257747 : [(1805 ^ _257747) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_317175), _317177), _317179) = hAPP(hAPP(c_Power_Opower__class_Opower(_317175), _317177), _317181), -(_317179 = _317181)], (1811 ^ _257747) ^ [] : [_317179 = _317181, -(hAPP(hAPP(c_Power_Opower__class_Opower(_317175), _317177), _317179) = hAPP(hAPP(c_Power_Opower__class_Opower(_317175), _317177), _317181))]]], (6772 ^ _257747) ^ [_495840, _495842] : [class_Groups_Ocomm__monoid__add(_495840), -(c_Groups_Oplus__class_Oplus(_495840, _495842, c_Groups_Ozero__class_Ozero(_495840)) = _495842)], (6493 ^ _257747) ^ [_485773, _485775, _485777, _485779] : [class_Rings_Ocomm__semiring__0(_485773), -(hAPP(c_Polynomial_Opoly(_485773, c_Polynomial_Osmult(_485773, _485775, _485777)), _485779) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_485773), _485775), hAPP(c_Polynomial_Opoly(_485773, _485777), _485779)))], (7422 ^ _257747) ^ [_517907, _517909, _517911, _517913] : [class_Groups_Oordered__comm__monoid__add(_517907), c_Orderings_Oord__class_Oless__eq(_517907, c_Groups_Ozero__class_Ozero(_517907), _517909), c_Orderings_Oord__class_Oless__eq(_517907, _517911, _517913), -(c_Orderings_Oord__class_Oless__eq(_517907, _517911, c_Groups_Oplus__class_Oplus(_517907, _517913, _517909)))], (782 ^ _257747) ^ [_281270, _281272] : [-(class_Power_Opower(_281270)), _281272 = _281270, class_Power_Opower(_281272)], (4309 ^ _257747) ^ [_405980, _405982] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _405980, _405982), _405982)], (8722 ^ _257747) ^ [_565113] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _565113, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _565113)], (5354 ^ _257747) ^ [_444541, _444543, _444545, _444547, _444549] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _444541, _444543), -(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), _444543), _444545), _444547), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _444541), _444545), _444549)) = 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, _444543, _444541)), _444545), _444547), _444549))], (5166 ^ _257747) ^ [_437206, _437208, _437210] : [class_Rings_Olinordered__idom(_437206), c_Orderings_Oord__class_Oless__eq(_437206, c_Groups_Ozero__class_Ozero(_437206), _437208), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_437206), c_Groups_Oabs__class_Oabs(_437206, _437210)), _437208) = c_Groups_Oabs__class_Oabs(_437206, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_437206), _437210), _437208)))], (1871 ^ _257747) ^ [_319501] : [class_RealVector_Oreal__algebra__1(_319501), -(c_RealVector_Oof__real(_319501, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(_319501))], (11712 ^ _257747) ^ [_663586] : [class_Rings_Olinordered__idom(_663586), -(class_Rings_Oordered__semiring(tc_Polynomial_Opoly(_663586)))], (10251 ^ _257747) ^ [_616601] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _616601)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _616601))], (4693 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 4691 ^ []))], (5704 ^ _257747) ^ [_456636, _456638] : [class_Fields_Olinordered__field__inverse__zero(_456636), 5707 ^ _257747 : [(5708 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_456636, c_Rings_Oinverse__class_Oinverse(_456636, _456638), c_Groups_Ozero__class_Ozero(_456636)), -(c_Orderings_Oord__class_Oless(_456636, _456638, c_Groups_Ozero__class_Ozero(_456636)))], (5714 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_456636, _456638, c_Groups_Ozero__class_Ozero(_456636)), -(c_Orderings_Oord__class_Oless(_456636, c_Rings_Oinverse__class_Oinverse(_456636, _456638), c_Groups_Ozero__class_Ozero(_456636)))]]], (11574 ^ _257747) ^ [_659216] : [class_Rings_Olinordered__idom(_659216), -(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(_659216)))], (492 ^ _257747) ^ [_272715, _272717] : [-(class_Groups_Oab__semigroup__add(_272715)), _272717 = _272715, class_Groups_Oab__semigroup__add(_272717)], (11826 ^ _257747) ^ [_667196] : [class_Rings_Ocomm__semiring__0(_667196), -(class_Rings_Omult__zero(tc_Polynomial_Opoly(_667196)))], (5006 ^ _257747) ^ [_431269, _431271] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _431269, _431271) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _431269, _431271))], (4952 ^ _257747) ^ [_429305, _429307, _429309] : [class_Rings_Olinordered__idom(_429305), -(c_Groups_Oabs__class_Oabs(_429305, hAPP(hAPP(c_Power_Opower__class_Opower(_429305), c_Groups_Ouminus__class_Ouminus(_429305, _429307)), _429309)) = c_Groups_Oabs__class_Oabs(_429305, hAPP(hAPP(c_Power_Opower__class_Opower(_429305), _429307), _429309)))], (11628 ^ _257747) ^ [_660926] : [class_Groups_Ocancel__comm__monoid__add(_660926), -(class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(_660926)))], (11206 ^ _257747) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (8971 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 8969 ^ []))], (9754 ^ _257747) ^ [_598597, _598599, _598601, _598603] : [class_Orderings_Oorder(_598597), c_Orderings_Oord__class_Oless(_598597, _598599, _598601), c_Orderings_Oord__class_Oless__eq(_598597, _598603, _598599), -(c_Orderings_Oord__class_Oless(_598597, _598603, _598601))], (11340 ^ _257747) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal))], (10031 ^ _257747) ^ [_608925, _608927] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _608925, _608927), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _608925, _608927))], (8253 ^ _257747) ^ [_547806, _547808, _547810, _547812] : [class_Rings_Ocomm__semiring__1(_547806), -(c_Groups_Oplus__class_Oplus(_547806, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_547806), _547808), _547810), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_547806), _547812), _547810)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_547806), c_Groups_Oplus__class_Oplus(_547806, _547808, _547812)), _547810))], (8868 ^ _257747) ^ [_570540, _570542, _570544, _570546, _570548, _570550] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _570540), _570542), _570544) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _570546), _570548), _570550), 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), _570546), _570548), _570550)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _570550, _570546), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _570544), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _570546), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _570546, _570540), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _570542, _570548))], (5941 ^ _257747) ^ [] : [hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), 5938 ^ []) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), 5939 ^ [])], (412 ^ _257747) ^ [_270355, _270357] : [-(class_Rings_Olinordered__semiring__1(_270355)), _270357 = _270355, class_Rings_Olinordered__semiring__1(_270357)], (9524 ^ _257747) ^ [_591567, _591569, _591571] : [class_Orderings_Oorder(_591567), 9527 ^ _257747 : [(9528 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_591567, _591569, _591571), 9531 ^ _257747 : [(9532 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_591567, _591569, _591571))], (9534 ^ _257747) ^ [] : [_591569 = _591571]]], (9536 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(_591567, _591569, _591571)), c_Orderings_Oord__class_Oless__eq(_591567, _591569, _591571), -(_591569 = _591571)]]], (11120 ^ _257747) ^ [_647062, _647064] : [class_Groups_Ouminus(_647062), -(class_Groups_Ouminus(tc_fun(_647064, _647062)))], (11554 ^ _257747) ^ [] : [-(class_Fields_Ofield(tc_Complex_Ocomplex))], (10832 ^ _257747) ^ [_636982, _636984, _636986] : [class_Rings_Ocomm__ring__1(_636982), 10835 ^ _257747 : [(10836 ^ _257747) ^ [] : [c_Rings_Odvd__class_Odvd(_636982, _636984, c_Groups_Ouminus__class_Ouminus(_636982, _636986)), -(c_Rings_Odvd__class_Odvd(_636982, _636984, _636986))], (10842 ^ _257747) ^ [] : [c_Rings_Odvd__class_Odvd(_636982, _636984, _636986), -(c_Rings_Odvd__class_Odvd(_636982, _636984, c_Groups_Ouminus__class_Ouminus(_636982, _636986)))]]], (6279 ^ _257747) ^ [_476892, _476894, _476896, _476898] : [class_Rings_Ocomm__semiring__0(_476892), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_476892)), _476894), c_Polynomial_Osmult(_476892, _476896, _476898)) = c_Polynomial_Osmult(_476892, _476896, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_476892)), _476894), _476898)))], (8728 ^ _257747) ^ [] : [c_Complex_Oii = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)], (10269 ^ _257747) ^ [_617198, _617200] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _617198), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), c_RealDef_Oreal(tc_Nat_Onat, _617200)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _617198, _617200))], (7510 ^ _257747) ^ [_520677, _520679, _520681, _520683, _520685] : [class_Groups_Oordered__cancel__ab__semigroup__add(_520677), c_Orderings_Oord__class_Oless(_520677, _520679, _520681), c_Orderings_Oord__class_Oless__eq(_520677, _520683, _520685), -(c_Orderings_Oord__class_Oless(_520677, c_Groups_Oplus__class_Oplus(_520677, _520679, _520683), c_Groups_Oplus__class_Oplus(_520677, _520681, _520685)))], (11344 ^ _257747) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal))], (3244 ^ _257747) ^ [_366809, _366811, _366813, _366815, _366817] : [class_Rings_Olinordered__semiring__strict(_366809), c_Orderings_Oord__class_Oless(_366809, _366811, _366813), c_Orderings_Oord__class_Oless(_366809, _366815, _366817), c_Orderings_Oord__class_Oless(_366809, c_Groups_Ozero__class_Ozero(_366809), _366813), c_Orderings_Oord__class_Oless__eq(_366809, c_Groups_Ozero__class_Ozero(_366809), _366815), -(c_Orderings_Oord__class_Oless(_366809, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_366809), _366811), _366815), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_366809), _366813), _366817)))], (4482 ^ _257747) ^ [_412769, _412771] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _412769), _412771) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 4485 ^ _257747 : [(4486 ^ _257747) ^ [] : [-(_412769 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (4488 ^ _257747) ^ [] : [-(_412771 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (6207 ^ _257747) ^ [_474313, _474315] : [class_Groups_Ocomm__monoid__add(_474313), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_474313), _474315, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_474313))) = _474315)], (7650 ^ _257747) ^ [_525056, _525058] : [class_Groups_Oordered__ab__group__add(_525056), 7653 ^ _257747 : [(7654 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_525056, c_Groups_Ouminus__class_Ouminus(_525056, _525058), c_Groups_Ozero__class_Ozero(_525056)), -(c_Orderings_Oord__class_Oless(_525056, c_Groups_Ozero__class_Ozero(_525056), _525058))], (7660 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_525056, c_Groups_Ozero__class_Ozero(_525056), _525058), -(c_Orderings_Oord__class_Oless(_525056, c_Groups_Ouminus__class_Ouminus(_525056, _525058), c_Groups_Ozero__class_Ozero(_525056)))]]], (10145 ^ _257747) ^ [_612937, _612939] : [c_RealDef_Oreal(tc_Nat_Onat, _612937) = c_RealDef_Oreal(tc_Nat_Onat, _612939), -(_612937 = _612939)], (8979 ^ _257747) ^ [_574179, _574181] : [class_Orderings_Opreorder(_574179), -(c_Orderings_Oord__class_Oless__eq(_574179, _574181, _574181))], (8335 ^ _257747) ^ [_551174, _551176, _551178] : [class_Rings_Ocomm__semiring__1(_551174), -(c_Groups_Oplus__class_Oplus(_551174, _551176, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_551174), _551178), _551176)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_551174), c_Groups_Oplus__class_Oplus(_551174, _551178, c_Groups_Oone__class_Oone(_551174))), _551176))], (1369 ^ _257747) ^ [_302312, _302314] : [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), _302312), _302314)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _302312)), -(_302314 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11398 ^ _257747) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal))], (2073 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), v_t____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), v_m____)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (382 ^ _257747) ^ [_269470, _269472] : [-(class_Rings_Olinordered__ring__strict(_269470)), _269472 = _269470, class_Rings_Olinordered__ring__strict(_269472)], (3817 ^ _257747) ^ [_387673, _387675] : [c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _387673), _387673), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _387675), _387675)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 3820 ^ _257747 : [(3821 ^ _257747) ^ [] : [-(_387673 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (3823 ^ _257747) ^ [] : [-(_387675 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))]]], (8562 ^ _257747) ^ [_559559, _559561] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _559559, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _559561, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _559559, _559561))], (2466 ^ _257747) ^ [_341097, _341099, _341101] : [class_Rings_Oring__1(_341097), -(hAPP(hAPP(c_Power_Opower__class_Opower(_341097), c_Groups_Ouminus__class_Ouminus(_341097, _341099)), _341101) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_341097), hAPP(hAPP(c_Power_Opower__class_Opower(_341097), c_Groups_Ouminus__class_Ouminus(_341097, c_Groups_Oone__class_Oone(_341097))), _341101)), hAPP(hAPP(c_Power_Opower__class_Opower(_341097), _341099), _341101)))], (9837 ^ _257747) ^ [_601448] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_RComplete_Onatceiling(_601448)))], (10543 ^ _257747) ^ [_627279] : [10551 ^ _257747 : [(10552 ^ _257747) ^ [_627555] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_627279, c_RealVector_Oof__real(_627279, _627555)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, _627555)), 10550 ^ [_627279])))]], class_RealVector_Oreal__algebra__1(_627279), class_RealVector_Oreal__normed__vector(_627279)], (6459 ^ _257747) ^ [_484607, _484609] : [class_Rings_Ocomm__semiring__0(_484607), -(c_Polynomial_Osmult(_484607, c_Groups_Ozero__class_Ozero(_484607), _484609) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_484607)))], (11182 ^ _257747) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_Int_Oint))], (8185 ^ _257747) ^ [_545126, _545128] : [class_Rings_Ocomm__semiring__1(_545126), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_545126), _545128), c_Groups_Ozero__class_Ozero(_545126)) = c_Groups_Ozero__class_Ozero(_545126))], (11814 ^ _257747) ^ [_666816] : [class_Rings_Ocomm__semiring__0(_666816), -(class_Rings_Osemiring__0(tc_Polynomial_Opoly(_666816)))], (11646 ^ _257747) ^ [_661496] : [class_Rings_Olinordered__idom(_661496), -(class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(_661496)))], (7732 ^ _257747) ^ [_527778, _527780] : [class_Groups_Oordered__ab__group__add__abs(_527778), -(c_Orderings_Oord__class_Oless__eq(_527778, c_Groups_Ozero__class_Ozero(_527778), c_Groups_Oabs__class_Oabs(_527778, _527780)))], (4836 ^ _257747) ^ [_425063, _425065, _425067] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _425063, _425065), _425067) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _425063, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _425065, _425067)))], (1213 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)))], (552 ^ _257747) ^ [_274485, _274487] : [-(class_Rings_Ozero__neq__one(_274485)), _274487 = _274485, class_Rings_Ozero__neq__one(_274487)], (1090 ^ _257747) ^ [_292445, _292447, _292449, _292451, _292453, _292455] : [-(c_Polynomial_Osmult(_292455, _292451, _292447) = c_Polynomial_Osmult(_292453, _292449, _292445)), _292455 = _292453, _292451 = _292449, _292447 = _292445], (8792 ^ _257747) ^ [_567859, _567861] : [-(c_Groups_Ominus__class_Ominus(tc_Int_Oint, _567859, _567861) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _567859, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _567861)))], (8488 ^ _257747) ^ [_556795] : [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), _556795), _556795), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _556795, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (9044 ^ _257747) ^ [_576393, _576395, _576397, _576399, _576401] : [class_Orderings_Oord(_576393), c_Orderings_Oord__class_Oless__eq(tc_fun(_576395, _576393), _576397, _576399), -(c_Orderings_Oord__class_Oless__eq(_576393, hAPP(_576397, _576401), hAPP(_576399, _576401)))], (3375 ^ _257747) ^ [_371020] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _371020))], (11510 ^ _257747) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex))], (6251 ^ _257747) ^ [_475862, _475864, _475866, _475868, _475870] : [class_Groups_Ozero(_475862), 6254 ^ _257747 : [(6255 ^ _257747) ^ [] : [c_Polynomial_OpCons(_475862, _475864, _475866) = c_Polynomial_OpCons(_475862, _475868, _475870), 6258 ^ _257747 : [(6259 ^ _257747) ^ [] : [-(_475864 = _475868)], (6261 ^ _257747) ^ [] : [-(_475866 = _475870)]]], (6263 ^ _257747) ^ [] : [-(c_Polynomial_OpCons(_475862, _475864, _475866) = c_Polynomial_OpCons(_475862, _475868, _475870)), _475864 = _475868, _475866 = _475870]]], (6363 ^ _257747) ^ [_481068, _481070, _481072, _481074] : [class_Rings_Ocomm__semiring__0(_481068), -(c_Polynomial_Osmult(_481068, c_Groups_Oplus__class_Oplus(_481068, _481070, _481072), _481074) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_481068), c_Polynomial_Osmult(_481068, _481070, _481074), c_Polynomial_Osmult(_481068, _481072, _481074)))], (5194 ^ _257747) ^ [_438217, _438219, _438221] : [class_Rings_Olinordered__idom(_438217), -(c_Orderings_Oord__class_Oless__eq(_438217, c_Groups_Ozero__class_Ozero(_438217), hAPP(hAPP(c_Power_Opower__class_Opower(_438217), c_Groups_Oabs__class_Oabs(_438217, _438219)), _438221)))], (5694 ^ _257747) ^ [_456321, _456323] : [class_Fields_Olinordered__field(_456321), c_Orderings_Oord__class_Oless(_456321, c_Groups_Ozero__class_Ozero(_456321), _456323), -(c_Orderings_Oord__class_Oless(_456321, c_Groups_Ozero__class_Ozero(_456321), c_Rings_Oinverse__class_Oinverse(_456321, _456323)))], (3172 ^ _257747) ^ [_364360] : [class_Rings_Olinordered__semidom(_364360), -(c_Orderings_Oord__class_Oless__eq(_364360, c_Groups_Ozero__class_Ozero(_364360), c_Groups_Oone__class_Oone(_364360)))], (1451 ^ _257747) ^ [_305343, _305345, _305347] : [class_Rings_Olinordered__semidom(_305343), c_Orderings_Oord__class_Oless(_305343, c_Groups_Oone__class_Oone(_305343), _305345), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _305347), -(c_Orderings_Oord__class_Oless(_305343, c_Groups_Oone__class_Oone(_305343), hAPP(hAPP(c_Power_Opower__class_Opower(_305343), _305345), _305347)))], (9800 ^ _257747) ^ [] : [9795 ^ [] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (4715 ^ _257747) ^ [] : [-(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, 4713 ^ []) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, v_pa____))], (9458 ^ _257747) ^ [_589499, _589501, _589503] : [class_Orderings_Opreorder(_589499), c_Orderings_Oord__class_Oless(_589499, _589501, _589503), c_Orderings_Oord__class_Oless(_589499, _589503, _589501)], (11498 ^ _257747) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex))], (332 ^ _257747) ^ [_267995, _267997] : [-(class_Groups_Oordered__comm__monoid__add(_267995)), _267997 = _267995, class_Groups_Oordered__comm__monoid__add(_267997)], (11256 ^ _257747) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (11108 ^ _257747) ^ [_646638, _646640] : [class_Orderings_Oorder(_646638), -(class_Orderings_Oorder(tc_fun(_646640, _646638)))], (9468 ^ _257747) ^ [_589825, _589827, _589829] : [class_Orderings_Olinorder(_589825), -(c_Orderings_Oord__class_Oless(_589825, _589827, _589829)), -(_589827 = _589829), -(c_Orderings_Oord__class_Oless(_589825, _589829, _589827))], (4966 ^ _257747) ^ [_429853, _429855] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _429853), _429855)), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _429855), _429853), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _429853, _429855)], (4584 ^ _257747) ^ [_416262, _416264, _416266] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _416262), _416264), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _416266), _416264))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _416264), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _416262, _416266)], (5086 ^ _257747) ^ [_434201, _434203, _434205] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _434201, _434203), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _434205, _434203), _434201) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _434205, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _434203, _434201)))], (6732 ^ _257747) ^ [_494472, _494474] : [class_Groups_Oordered__ab__group__add__abs(_494472), -(c_Groups_Oabs__class_Oabs(_494472, c_Groups_Oabs__class_Oabs(_494472, _494474)) = c_Groups_Oabs__class_Oabs(_494472, _494474))], (8305 ^ _257747) ^ [_550026, _550028] : [class_Rings_Ocomm__semiring__1(_550026), -(hAPP(hAPP(c_Power_Opower__class_Opower(_550026), _550028), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _550028)], (8574 ^ _257747) ^ [_559963] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _559963, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Groups_Oabs__class_Oabs(tc_Int_Oint, _559963) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _559963))], (11850 ^ _257747) ^ [_667956] : [class_Rings_Ocomm__semiring__0(_667956), -(class_Rings_Osemiring(tc_Polynomial_Opoly(_667956)))], (6345 ^ _257747) ^ [_480148, _480150, _480152, _480154] : [class_Rings_Ocomm__semiring__1(_480148), -(hAPP(c_Polynomial_Opoly(_480148, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_480148)), _480150), _480152)), _480154) = hAPP(hAPP(c_Power_Opower__class_Opower(_480148), hAPP(c_Polynomial_Opoly(_480148, _480150), _480154)), _480152))], (6726 ^ _257747) ^ [_494252, _494254] : [class_Groups_Ogroup__add(_494252), -(c_Groups_Ouminus__class_Ouminus(_494252, c_Groups_Ouminus__class_Ouminus(_494252, _494254)) = _494254)], (4842 ^ _257747) ^ [_425408, _425410, _425412] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _425408, _425410), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _425408, _425412), 4849 ^ _257747 : [(4850 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _425410, _425408), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _425412, _425408)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _425410, _425412))], (4856 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _425410, _425412), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _425410, _425408), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _425412, _425408)))]]], (9907 ^ _257747) ^ [_604105] : [class_RealVector_Oreal__normed__algebra(_604105), 9911 ^ _257747 : [(9912 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 9910 ^ [_604105]))], (9914 ^ _257747) ^ [_604434, _604436] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_604105, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_604105), _604436), _604434)), 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(_604105, _604436)), c_RealVector_Onorm__class_Onorm(_604105, _604434))), 9910 ^ [_604105])))]]], (11404 ^ _257747) ^ [] : [-(class_Fields_Olinordered__field(tc_RealDef_Oreal))], (4914 ^ _257747) ^ [_427943, _427945, _427947] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _427943, _427945)), _427947) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _427943), _427947), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _427945), _427947)))], (732 ^ _257747) ^ [_279795, _279797] : [-(class_Groups_Oabs__if(_279795)), _279797 = _279795, class_Groups_Oabs__if(_279797)], (9807 ^ _257747) ^ [_600468] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _600468), -(c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _600468, c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatceiling(_600468), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (5614 ^ _257747) ^ [_453890, _453892, _453894] : [class_Fields_Olinordered__field(_453890), c_Orderings_Oord__class_Oless(_453890, c_Rings_Oinverse__class_Oinverse(_453890, _453892), c_Rings_Oinverse__class_Oinverse(_453890, _453894)), c_Orderings_Oord__class_Oless(_453890, c_Groups_Ozero__class_Ozero(_453890), _453892), -(c_Orderings_Oord__class_Oless(_453890, _453894, _453892))], (3835 ^ _257747) ^ [_388275, _388277] : [class_Groups_Ozero(_388275), 3838 ^ _257747 : [(3839 ^ _257747) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_388275, _388277) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_388277 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_388275)))], (3845 ^ _257747) ^ [] : [_388277 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_388275)), -(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_388275, _388277) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (11184 ^ _257747) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (94 ^ _257747) ^ [_260896, _260898] : [-(hBOOL(_260896)), _260898 = _260896, hBOOL(_260898)], (9813 ^ _257747) ^ [_600726, _600728, _600730, _600732] : [class_Orderings_Oord(_600726), 9816 ^ _257747 : [(9817 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(tc_fun(_600728, _600726), _600730, _600732), 9820 ^ _257747 : [(9821 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_fun(_600728, _600726), _600730, _600732))], (9823 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_600728, _600726), _600732, _600730)]]], (9825 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_fun(_600728, _600726), _600730, _600732)), c_Orderings_Oord__class_Oless__eq(tc_fun(_600728, _600726), _600730, _600732), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_600728, _600726), _600732, _600730))]]], (11838 ^ _257747) ^ [_667576] : [class_Rings_Olinordered__idom(_667576), -(class_Orderings_Oorder(tc_Polynomial_Opoly(_667576)))], (3399 ^ _257747) ^ [_371883, _371885] : [-(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _371883, _371885) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _371883, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _371885)))], (8077 ^ _257747) ^ [_539845] : [_539845 = 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), _539845), _539845))], (9388 ^ _257747) ^ [_587279, _587281, _587283, _587285] : [class_Orderings_Oorder(_587279), _587281 = _587283, c_Orderings_Oord__class_Oless(_587279, _587285, _587283), -(c_Orderings_Oord__class_Oless(_587279, _587285, _587281))], (11306 ^ _257747) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (9884 ^ _257747) ^ [_603126, _603128, _603130, _603132] : [-(hAPP(hAPP(c_Power_Opower_Opower(_603126, _603128, _603130), _603132), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _603128)], (11560 ^ _257747) ^ [] : [-(class_Rings_Oring(tc_Complex_Ocomplex))], (1240 ^ _257747) ^ [_297842, _297844, _297846] : [class_Rings_Olinordered__semidom(_297842), c_Orderings_Oord__class_Oless(_297842, c_Groups_Ozero__class_Ozero(_297842), _297844), c_Orderings_Oord__class_Oless(_297842, _297844, c_Groups_Oone__class_Oone(_297842)), -(c_Orderings_Oord__class_Oless(_297842, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_297842), _297844), hAPP(hAPP(c_Power_Opower__class_Opower(_297842), _297844), _297846)), hAPP(hAPP(c_Power_Opower__class_Opower(_297842), _297844), _297846)))], (1617 ^ _257747) ^ [_311147, _311149] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _311147, _311149), 1620 ^ _257747 : [(1621 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _311147, _311149))], (1623 ^ _257747) ^ [] : [_311147 = _311149]]], (11432 ^ _257747) ^ [] : [-(class_Orderings_Opreorder(tc_RealDef_Oreal))], (6195 ^ _257747) ^ [_473841, _473843] : [class_Rings_Ocomm__semiring__0(_473841), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_473841)), _473843), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_473841))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_473841)))], (11436 ^ _257747) ^ [] : [-(class_Groups_Omonoid__mult(tc_RealDef_Oreal))], (11772 ^ _257747) ^ [_665486] : [class_Rings_Ocomm__semiring__1(_665486), -(class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(_665486)))], (2486 ^ _257747) ^ [_341871, _341873, _341875, _341877, _341879, _341881] : [class_Rings_Olinordered__semiring__1__strict(_341871), c_Orderings_Oord__class_Oless(_341871, _341873, _341875), c_Orderings_Oord__class_Oless(_341871, _341877, _341875), c_Orderings_Oord__class_Oless__eq(_341871, c_Groups_Ozero__class_Ozero(_341871), _341879), c_Orderings_Oord__class_Oless__eq(_341871, c_Groups_Ozero__class_Ozero(_341871), _341881), c_Groups_Oplus__class_Oplus(_341871, _341879, _341881) = c_Groups_Oone__class_Oone(_341871), -(c_Orderings_Oord__class_Oless(_341871, c_Groups_Oplus__class_Oplus(_341871, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_341871), _341879), _341873), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_341871), _341881), _341877)), _341875))], (9847 ^ _257747) ^ [_601819] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _601819, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_RComplete_Onatceiling(_601819) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11358 ^ _257747) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal))], (762 ^ _257747) ^ [_280680, _280682] : [-(class_Groups_Oab__group__add(_280680)), _280682 = _280680, class_Groups_Oab__group__add(_280682)], (4009 ^ _257747) ^ [_395124, _395126] : [-(_395124 = _395126), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _395124, _395126)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _395126, _395124))], (9945 ^ _257747) ^ [] : [-(c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (6950 ^ _257747) ^ [_502170, _502172, _502174] : [class_Groups_Ogroup__add(_502170), 6953 ^ _257747 : [(6954 ^ _257747) ^ [] : [c_Groups_Ominus__class_Ominus(_502170, _502172, _502174) = c_Groups_Ozero__class_Ozero(_502170), -(_502172 = _502174)], (6960 ^ _257747) ^ [] : [_502172 = _502174, -(c_Groups_Ominus__class_Ominus(_502170, _502172, _502174) = c_Groups_Ozero__class_Ozero(_502170))]]], (10095 ^ _257747) ^ [_611100, _611102] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _611100, _611102), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _611100), c_RealDef_Oreal(tc_Nat_Onat, _611102)))], (7786 ^ _257747) ^ [_529494, _529496] : [class_Groups_Oordered__ab__group__add__abs(_529494), c_Orderings_Oord__class_Oless(_529494, c_Groups_Ozero__class_Ozero(_529494), _529496), -(c_Groups_Oabs__class_Oabs(_529494, _529496) = _529496)], (11330 ^ _257747) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (2586 ^ _257747) ^ [_345142, _345144] : [class_Rings_Olinordered__ring(_345142), -(c_Orderings_Oord__class_Oless__eq(_345142, c_Groups_Ozero__class_Ozero(_345142), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_345142), _345144), _345144)))], (4992 ^ _257747) ^ [_430740, _430742] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _430740, _430742)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _430742, _430740))], (8125 ^ _257747) ^ [_542164, _542166, _542168, _542170, _542172] : [class_Rings_Ocomm__semiring__1(_542164), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_542164), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_542164), _542166), _542168)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_542164), _542170), _542172)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_542164), _542166), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_542164), _542168), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_542164), _542170), _542172))))], (11392 ^ _257747) ^ [] : [-(class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal))], (11536 ^ _257747) ^ [] : [-(class_Rings_Osemiring__0(tc_Complex_Ocomplex))], (9402 ^ _257747) ^ [_587725, _587727, _587729, _587731] : [class_Orderings_Oord(_587725), c_Orderings_Oord__class_Oless(_587725, _587727, _587729), _587729 = _587731, -(c_Orderings_Oord__class_Oless(_587725, _587727, _587731))], (2334 ^ _257747) ^ [_336110, _336112, _336114] : [class_RealVector_Oreal__normed__algebra(_336110), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_336110), c_Groups_Ouminus__class_Ouminus(_336110, _336112)), _336114) = c_Groups_Ouminus__class_Ouminus(_336110, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_336110), _336112), _336114)))], (3360 ^ _257747) ^ [] : [-(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), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_a____, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))))))) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_RealVector_Oof__real(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))))))], (2069 ^ _257747) ^ [] : [-(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_a____, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)))))) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), v_w____), v_k____)), v_a____))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)))))], (7258 ^ _257747) ^ [_512379, _512381, _512383] : [class_Groups_Ogroup__add(_512379), -(c_Groups_Ouminus__class_Ouminus(_512379, c_Groups_Oplus__class_Oplus(_512379, _512381, _512383)) = c_Groups_Oplus__class_Oplus(_512379, c_Groups_Ouminus__class_Ouminus(_512379, _512383), c_Groups_Ouminus__class_Ouminus(_512379, _512381)))], (2290 ^ _257747) ^ [_334200, _334202, _334204, _334206, _334208] : [class_Rings_Osemiring(_334200), -(c_Groups_Oplus__class_Oplus(_334200, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_334200), _334202), _334204), c_Groups_Oplus__class_Oplus(_334200, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_334200), _334206), _334204), _334208)) = c_Groups_Oplus__class_Oplus(_334200, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_334200), c_Groups_Oplus__class_Oplus(_334200, _334202, _334206)), _334204), _334208))], (9514 ^ _257747) ^ [_591241, _591243, _591245] : [class_Orderings_Olinorder(_591241), -(c_Orderings_Oord__class_Oless__eq(_591241, _591243, _591245)), -(c_Orderings_Oord__class_Oless(_591241, _591245, _591243))], (11802 ^ _257747) ^ [_666436] : [class_Rings_Ocomm__ring__1(_666436), -(class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(_666436)))], (8293 ^ _257747) ^ [_549418, _549420, _549422, _549424] : [class_Rings_Ocomm__semiring__1(_549418), -(hAPP(hAPP(c_Power_Opower__class_Opower(_549418), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_549418), _549420), _549422)), _549424) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_549418), hAPP(hAPP(c_Power_Opower__class_Opower(_549418), _549420), _549424)), hAPP(hAPP(c_Power_Opower__class_Opower(_549418), _549422), _549424)))], (2067 ^ _257747) ^ [] : [-(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), v_t____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)))))))], (8023 ^ _257747) ^ [_537781, _537783] : [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), _537781), _537783)), -(_537783 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _537781))], (1130 ^ _257747) ^ [_293869, _293871, _293873, _293875] : [-(c_Polynomial_Opoly(_293875, _293871) = c_Polynomial_Opoly(_293873, _293869)), _293875 = _293873, _293871 = _293869], (8634 ^ _257747) ^ [_562192, _562194] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _562192)), _562194) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _562192), _562194)))], (3507 ^ _257747) ^ [_375677, _375679] : [class_RealVector_Oreal__normed__div__algebra(_375677), -(_375679 = c_Groups_Ozero__class_Ozero(_375677)), -(c_RealVector_Onorm__class_Onorm(_375677, c_Rings_Oinverse__class_Oinverse(_375677, _375679)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_375677, _375679)))], (9805 ^ _257747) ^ [_600347] : [-(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), _600347) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), _600347), 9795 ^ [])), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, 9796 ^ [], 9801 ^ [])), _600347))))], (956 ^ _257747) ^ [_287529, _287531, _287533, _287535] : [-(c_Nat__Transfer_Otsub(_287535, _287531) = c_Nat__Transfer_Otsub(_287533, _287529)), _287535 = _287533, _287531 = _287529], (3178 ^ _257747) ^ [_364558] : [class_Rings_Olinordered__semidom(_364558), c_Orderings_Oord__class_Oless(_364558, c_Groups_Oone__class_Oone(_364558), c_Groups_Ozero__class_Ozero(_364558))], (2284 ^ _257747) ^ [_333874, _333876, _333878, _333880] : [class_Rings_Ocomm__semiring(_333874), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_333874), c_Groups_Oplus__class_Oplus(_333874, _333876, _333878)), _333880) = c_Groups_Oplus__class_Oplus(_333874, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_333874), _333876), _333880), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_333874), _333878), _333880)))], (2758 ^ _257747) ^ [_350706, _350708, _350710, _350712] : [class_Rings_Oordered__comm__semiring(_350706), c_Orderings_Oord__class_Oless__eq(_350706, _350708, _350710), c_Orderings_Oord__class_Oless__eq(_350706, c_Groups_Ozero__class_Ozero(_350706), _350712), -(c_Orderings_Oord__class_Oless__eq(_350706, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_350706), _350712), _350708), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_350706), _350712), _350710)))], (2262 ^ _257747) ^ [_333151, _333153, _333155] : [class_Rings_Oidom(_333151), 2265 ^ _257747 : [(2276 ^ _257747) ^ [] : [2277 ^ _257747 : [(2278 ^ _257747) ^ [] : [_333153 = _333155], (2280 ^ _257747) ^ [] : [_333153 = c_Groups_Ouminus__class_Ouminus(_333151, _333155)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_333151), _333153), _333153) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_333151), _333155), _333155))], (2266 ^ _257747) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_333151), _333153), _333153) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_333151), _333155), _333155), -(_333153 = _333155), -(_333153 = c_Groups_Ouminus__class_Ouminus(_333151, _333155))]]], (11440 ^ _257747) ^ [] : [-(class_Groups_Omonoid__add(tc_RealDef_Oreal))], (4697 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, 4691 ^ [], c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), v_m____))))], (8612 ^ _257747) ^ [_561339, _561341, _561343] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Ominus__class_Ominus(tc_Int_Oint, _561339, _561341)), _561343) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _561339), _561343), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _561341), _561343)))], (3184 ^ _257747) ^ [_364757] : [class_Rings_Olinordered__semidom(_364757), -(c_Orderings_Oord__class_Oless(_364757, c_Groups_Ozero__class_Ozero(_364757), c_Groups_Oone__class_Oone(_364757)))], (9955 ^ _257747) ^ [_606201] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_RComplete_Onatfloor(_606201)))], (10151 ^ _257747) ^ [_613111, _613113] : [_613111 = _613113, -(c_RealDef_Oreal(tc_Nat_Onat, _613111) = c_RealDef_Oreal(tc_Nat_Onat, _613113))], (11266 ^ _257747) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (152 ^ _257747) ^ [_262685, _262687] : [-(class_RealVector_Oreal__normed__div__algebra(_262685)), _262687 = _262685, class_RealVector_Oreal__normed__div__algebra(_262687)], (9256 ^ _257747) ^ [_583108, _583110, _583112] : [class_Orderings_Olinorder(_583108), -(c_Orderings_Oord__class_Oless(_583108, _583110, _583112)), -(_583110 = _583112), -(c_Orderings_Oord__class_Oless(_583108, _583112, _583110))], (6584 ^ _257747) ^ [_489541, _489543, _489545, _489547] : [class_Groups_Ocancel__ab__semigroup__add(_489541), c_Groups_Oplus__class_Oplus(_489541, _489543, _489545) = c_Groups_Oplus__class_Oplus(_489541, _489543, _489547), -(_489545 = _489547)], (742 ^ _257747) ^ [_280090, _280092] : [-(class_Rings_Ocomm__ring__1(_280090)), _280092 = _280090, class_Rings_Ocomm__ring__1(_280092)], (11428 ^ _257747) ^ [] : [-(class_Rings_Ozero__neq__one(tc_RealDef_Oreal))], (11222 ^ _257747) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (5584 ^ _257747) ^ [_452955, _452957] : [class_Fields_Olinordered__field__inverse__zero(_452955), 5587 ^ _257747 : [(5588 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_452955, c_Groups_Ozero__class_Ozero(_452955), c_Rings_Oinverse__class_Oinverse(_452955, _452957)), -(c_Orderings_Oord__class_Oless__eq(_452955, c_Groups_Ozero__class_Ozero(_452955), _452957))], (5594 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_452955, c_Groups_Ozero__class_Ozero(_452955), _452957), -(c_Orderings_Oord__class_Oless__eq(_452955, c_Groups_Ozero__class_Ozero(_452955), c_Rings_Oinverse__class_Oinverse(_452955, _452957)))]]], (5322 ^ _257747) ^ [_443227, _443229, _443231, _443233, _443235] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _443227, _443229), 5325 ^ _257747 : [(5326 ^ _257747) ^ [] : [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), _443227), _443231), _443233), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _443229), _443231), _443235)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _443233, 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, _443229, _443227)), _443231), _443235)))], (5332 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _443233, 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, _443229, _443227)), _443231), _443235)), -(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), _443227), _443231), _443233), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _443229), _443231), _443235)))]]], (282 ^ _257747) ^ [_266520, _266522] : [-(class_Rings_Olinordered__comm__semiring__strict(_266520)), _266522 = _266520, class_Rings_Olinordered__comm__semiring__strict(_266522)], (8225 ^ _257747) ^ [_546658, _546660, _546662, _546664, _546666] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_546658), 8228 ^ _257747 : [(8239 ^ _257747) ^ [] : [-(c_Groups_Oplus__class_Oplus(_546658, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_546658), _546660), _546664), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_546658), _546662), _546666)) = c_Groups_Oplus__class_Oplus(_546658, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_546658), _546660), _546666), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_546658), _546662), _546664))), 8242 ^ _257747 : [(8243 ^ _257747) ^ [] : [_546660 = _546662], (8245 ^ _257747) ^ [] : [_546664 = _546666]]], (8229 ^ _257747) ^ [] : [c_Groups_Oplus__class_Oplus(_546658, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_546658), _546660), _546664), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_546658), _546662), _546666)) = c_Groups_Oplus__class_Oplus(_546658, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_546658), _546660), _546666), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_546658), _546662), _546664)), -(_546660 = _546662), -(_546664 = _546666)]]], (4726 ^ _257747) ^ [] : [-(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, v_q____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, v_pa____))], (10646 ^ _257747) ^ [_630641, _630643] : [class_Rings_Olinordered__idom(_630641), 10649 ^ _257747 : [(10650 ^ _257747) ^ [] : [c_Groups_Osgn__class_Osgn(_630641, _630643) = c_Groups_Ozero__class_Ozero(_630641), -(_630643 = c_Groups_Ozero__class_Ozero(_630641))], (10656 ^ _257747) ^ [] : [_630643 = c_Groups_Ozero__class_Ozero(_630641), -(c_Groups_Osgn__class_Osgn(_630641, _630643) = c_Groups_Ozero__class_Ozero(_630641))]]], (6678 ^ _257747) ^ [_492748, _492750, _492752] : [class_Groups_Ogroup__add(_492748), 6681 ^ _257747 : [(6682 ^ _257747) ^ [] : [c_Groups_Ouminus__class_Ouminus(_492748, _492750) = c_Groups_Ouminus__class_Ouminus(_492748, _492752), -(_492750 = _492752)], (6688 ^ _257747) ^ [] : [_492750 = _492752, -(c_Groups_Ouminus__class_Ouminus(_492748, _492750) = c_Groups_Ouminus__class_Ouminus(_492748, _492752))]]], (8131 ^ _257747) ^ [_542528, _542530, _542532, _542534, _542536] : [class_Rings_Ocomm__semiring__1(_542528), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_542528), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_542528), _542530), _542532)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_542528), _542534), _542536)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_542528), _542534), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_542528), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_542528), _542530), _542532)), _542536)))], (11580 ^ _257747) ^ [_659406] : [class_Rings_Olinordered__idom(_659406), -(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(_659406)))], (6327 ^ _257747) ^ [_479252, _479254, _479256, _479258] : [class_Rings_Ocomm__ring(_479252), -(hAPP(c_Polynomial_Opoly(_479252, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_479252), _479254, _479256)), _479258) = c_Groups_Ominus__class_Ominus(_479252, hAPP(c_Polynomial_Opoly(_479252, _479254), _479258), hAPP(c_Polynomial_Opoly(_479252, _479256), _479258)))], (2302 ^ _257747) ^ [_334812, _334814, _334816, _334818, _334820] : [class_RealVector_Oreal__normed__vector(_334812), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_334812, _334814), _334816), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_334812, _334818), _334820), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_334812, c_Groups_Oplus__class_Oplus(_334812, _334814, _334818)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _334816, _334820)))], (10531 ^ _257747) ^ [_626823, _626825, _626827, _626829] : [class_Groups_Ouminus(_626823), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_626825, _626823), _626827), _626829) = c_Groups_Ouminus__class_Ouminus(_626823, hAPP(_626827, _626829)))], (3687 ^ _257747) ^ [_382127, _382129, _382131, _382133] : [class_RealVector_Oreal__normed__algebra(_382127), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_382127), _382129), c_Groups_Ominus__class_Ominus(_382127, _382131, _382133)) = c_Groups_Ominus__class_Ominus(_382127, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_382127), _382129), _382131), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_382127), _382129), _382133)))], (6351 ^ _257747) ^ [_480470, _480472, _480474, _480476, _480478] : [class_Groups_Oab__group__add(_480470), -(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_480470), c_Polynomial_OpCons(_480470, _480472, _480474), c_Polynomial_OpCons(_480470, _480476, _480478)) = c_Polynomial_OpCons(_480470, c_Groups_Ominus__class_Ominus(_480470, _480472, _480476), c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_480470), _480474, _480478)))], (10105 ^ _257747) ^ [_611506, _611508] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _611506)), _611508) = c_RealDef_Oreal(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _611506), _611508)))], (10418 ^ _257747) ^ [_622439, _622441, _622443] : [class_Groups_Oab__group__add(_622439), -(c_Groups_Ominus__class_Ominus(_622439, c_Groups_Ouminus__class_Ouminus(_622439, _622441), c_Groups_Ouminus__class_Ouminus(_622439, _622443)) = c_Groups_Ouminus__class_Ouminus(_622439, c_Groups_Ominus__class_Ominus(_622439, _622441, _622443)))], (2626 ^ _257747) ^ [_346435, _346437, _346439] : [class_Rings_Olinordered__ring__strict(_346435), 2629 ^ _257747 : [(2630 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_346435, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_346435), _346437), _346439), c_Groups_Ozero__class_Ozero(_346435)), 2635 ^ _257747 : [(2636 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_346435, c_Groups_Ozero__class_Ozero(_346435), _346437))], (2638 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_346435, _346439, c_Groups_Ozero__class_Ozero(_346435)))]], 2639 ^ _257747 : [(2640 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_346435, _346437, c_Groups_Ozero__class_Ozero(_346435)))], (2642 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_346435, c_Groups_Ozero__class_Ozero(_346435), _346439))]]], (2644 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_346435, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_346435), _346437), _346439), c_Groups_Ozero__class_Ozero(_346435))), 2645 ^ _257747 : [(2646 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_346435, c_Groups_Ozero__class_Ozero(_346435), _346437), c_Orderings_Oord__class_Oless__eq(_346435, _346439, c_Groups_Ozero__class_Ozero(_346435))], (2652 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_346435, _346437, c_Groups_Ozero__class_Ozero(_346435)), c_Orderings_Oord__class_Oless__eq(_346435, c_Groups_Ozero__class_Ozero(_346435), _346439)]]]]], (6766 ^ _257747) ^ [_495620, _495622] : [class_Groups_Omonoid__add(_495620), -(c_Groups_Oplus__class_Oplus(_495620, _495622, c_Groups_Ozero__class_Ozero(_495620)) = _495622)], (7602 ^ _257747) ^ [_523607, _523609] : [class_Groups_Oordered__ab__group__add(_523607), 7605 ^ _257747 : [(7606 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_523607, c_Groups_Ouminus__class_Ouminus(_523607, _523609), c_Groups_Ozero__class_Ozero(_523607)), -(c_Orderings_Oord__class_Oless__eq(_523607, c_Groups_Ozero__class_Ozero(_523607), _523609))], (7612 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_523607, c_Groups_Ozero__class_Ozero(_523607), _523609), -(c_Orderings_Oord__class_Oless__eq(_523607, c_Groups_Ouminus__class_Ouminus(_523607, _523609), c_Groups_Ozero__class_Ozero(_523607)))]]], (11378 ^ _257747) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal))], (8137 ^ _257747) ^ [_542892, _542894, _542896, _542898, _542900] : [class_Rings_Ocomm__semiring__1(_542892), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_542892), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_542892), _542894), _542896)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_542892), _542898), _542900)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_542892), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_542892), _542894), _542898)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_542892), _542896), _542900)))], (4782 ^ _257747) ^ [_422950] : [class_Rings_Olinordered__idom(_422950), -(c_Groups_Oabs__class_Oabs(_422950, c_Groups_Oone__class_Oone(_422950)) = c_Groups_Oone__class_Oone(_422950))], (4177 ^ _257747) ^ [_401089] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _401089) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9803 ^ _257747) ^ [] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, 9801 ^ []), 9795 ^ []), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)))], (132 ^ _257747) ^ [_262095, _262097] : [-(class_Fields_Olinordered__field__inverse__zero(_262095)), _262097 = _262095, class_Fields_Olinordered__field__inverse__zero(_262097)], (11706 ^ _257747) ^ [_663396] : [class_Groups_Ocomm__monoid__add(_663396), -(class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(_663396)))], (10537 ^ _257747) ^ [_627073, _627075] : [class_Lattices_Oboolean__algebra(_627073), -(c_Groups_Ouminus__class_Ouminus(_627073, c_Groups_Ouminus__class_Ouminus(_627073, _627075)) = _627075)], (9740 ^ _257747) ^ [_598149, _598151, _598153, _598155] : [class_Orderings_Opreorder(_598149), c_Orderings_Oord__class_Oless(_598149, _598151, _598153), c_Orderings_Oord__class_Oless__eq(_598149, _598153, _598155), -(c_Orderings_Oord__class_Oless(_598149, _598151, _598155))], (8750 ^ _257747) ^ [_566256, _566258, _566260] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _566256, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _566258, _566260)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _566258, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _566256, _566260)))], (4748 ^ _257747) ^ [_421741, _421743] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _421741), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _421741, _421743), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _421743, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _421743)), _421741), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (11360 ^ _257747) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal))], (4103 ^ _257747) ^ [_398503, _398505, _398507] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _398503), _398505)), _398507) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _398503), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _398505), _398507)))], (11350 ^ _257747) ^ [] : [-(class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal))], (5508 ^ _257747) ^ [] : [-(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, v_q____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)))], (11610 ^ _257747) ^ [_660356] : [class_Rings_Olinordered__idom(_660356), -(class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(_660356)))], (4744 ^ _257747) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____))], (4121 ^ _257747) ^ [_399177] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _399177, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1036 ^ _257747) ^ [_290461, _290463, _290465, _290467, _290469, _290471] : [-(c_Groups_Ominus__class_Ominus(_290471, _290467, _290463) = c_Groups_Ominus__class_Ominus(_290469, _290465, _290461)), _290471 = _290469, _290467 = _290465, _290463 = _290461], (4452 ^ _257747) ^ [_411398, _411400, _411402] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _411398, _411400)), _411402) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _411398), _411402), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _411400), _411402)))], (3332 ^ _257747) ^ [_369683, _369685, _369687, _369689] : [class_Rings_Olinordered__semiring(_369683), c_Orderings_Oord__class_Oless(_369683, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_369683), _369685), _369687), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_369683), _369689), _369687)), c_Orderings_Oord__class_Oless__eq(_369683, c_Groups_Ozero__class_Ozero(_369683), _369687), -(c_Orderings_Oord__class_Oless(_369683, _369685, _369689))], (8762 ^ _257747) ^ [_566838, _566840] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _566838, _566840)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _566840, _566838))], (4019 ^ _257747) ^ [_395462, _395464] : [-(_395462 = _395464), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _395462, _395464)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _395464, _395462))], (4045 ^ _257747) ^ [_396487, _396489, _396491] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _396487, _396489) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _396487, _396491), -(_396489 = _396491)], (5042 ^ _257747) ^ [_432568, _432570] : [-(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _432568, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _432570))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _432570, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _432568))))], (11676 ^ _257747) ^ [_662446] : [class_Groups_Ocancel__comm__monoid__add(_662446), -(class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(_662446)))], (2844 ^ _257747) ^ [_353588, _353590, _353592] : [class_Rings_Oordered__ring(_353588), -(c_Orderings_Oord__class_Oless__eq(_353588, c_Groups_Ozero__class_Ozero(_353588), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_353588), _353590), _353592))), 2849 ^ _257747 : [(2850 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_353588, c_Groups_Ozero__class_Ozero(_353588), _353590), c_Orderings_Oord__class_Oless__eq(_353588, c_Groups_Ozero__class_Ozero(_353588), _353592)], (2856 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_353588, _353590, c_Groups_Ozero__class_Ozero(_353588)), c_Orderings_Oord__class_Oless__eq(_353588, _353592, c_Groups_Ozero__class_Ozero(_353588))]]], (682 ^ _257747) ^ [_278320, _278322] : [-(class_Rings_Osemiring(_278320)), _278322 = _278320, class_Rings_Osemiring(_278322)], (11062 ^ _257747) ^ [_645094, _645096, _645098, _645100] : [class_Rings_Ocomm__semiring__1(_645094), c_Rings_Odvd__class_Odvd(_645094, _645096, _645098), -(c_Rings_Odvd__class_Odvd(_645094, hAPP(hAPP(c_Power_Opower__class_Opower(_645094), _645096), _645100), hAPP(hAPP(c_Power_Opower__class_Opower(_645094), _645098), _645100)))], (11424 ^ _257747) ^ [] : [-(class_Rings_Ocomm__semiring(tc_RealDef_Oreal))], (11326 ^ _257747) ^ [] : [-(class_Lattices_Oboolean__algebra(tc_HOL_Obool))], (1937 ^ _257747) ^ [_321836, _321838, _321840] : [class_RealVector_Oreal__normed__div__algebra(_321836), -(c_RealVector_Onorm__class_Onorm(_321836, hAPP(hAPP(c_Power_Opower__class_Opower(_321836), _321838), _321840)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_321836, _321838)), _321840))], (11154 ^ _257747) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (5856 ^ _257747) ^ [_461433, _461435] : [class_Fields_Olinordered__field__inverse__zero(_461433), 5859 ^ _257747 : [(5860 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_461433, c_Groups_Oone__class_Oone(_461433), c_Rings_Oinverse__class_Oinverse(_461433, _461435)), 5863 ^ _257747 : [(5864 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(_461433, c_Groups_Ozero__class_Ozero(_461433), _461435))], (5866 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(_461433, _461435, c_Groups_Oone__class_Oone(_461433)))]]], (5868 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(_461433, c_Groups_Oone__class_Oone(_461433), c_Rings_Oinverse__class_Oinverse(_461433, _461435))), c_Orderings_Oord__class_Oless(_461433, c_Groups_Ozero__class_Ozero(_461433), _461435), c_Orderings_Oord__class_Oless(_461433, _461435, c_Groups_Oone__class_Oone(_461433))]]], (11492 ^ _257747) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex))], (1635 ^ _257747) ^ [_311711, _311713, _311715] : [-(_311711 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 1638 ^ _257747 : [(1639 ^ _257747) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _311711), _311713) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _311711), _311715), -(_311713 = _311715)], (1645 ^ _257747) ^ [] : [_311713 = _311715, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _311711), _311713) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _311711), _311715))]]], (6528 ^ _257747) ^ [] : [-(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Polynomial_Omonom(tc_Complex_Ocomplex, v_a____, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))), 6526 ^ []) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))], (11138 ^ _257747) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (11880 ^ _257747) ^ [_668906] : [class_Rings_Ocomm__ring__1(_668906), -(class_Rings_Oring__1(tc_Polynomial_Opoly(_668906)))], (1271 ^ _257747) ^ [_299007, _299009, _299011] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _299007), 1274 ^ _257747 : [(1275 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _299009), _299007), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _299011), _299007)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _299009, _299011))], (1281 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _299009, _299011), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _299009), _299007), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _299011), _299007)))]]], (7276 ^ _257747) ^ [_513139, _513141] : [class_Groups_Oordered__ab__group__add__abs(_513139), 7279 ^ _257747 : [(7280 ^ _257747) ^ [] : [c_Groups_Oabs__class_Oabs(_513139, _513141) = c_Groups_Ozero__class_Ozero(_513139), -(_513141 = c_Groups_Ozero__class_Ozero(_513139))], (7286 ^ _257747) ^ [] : [_513141 = c_Groups_Ozero__class_Ozero(_513139), -(c_Groups_Oabs__class_Oabs(_513139, _513141) = c_Groups_Ozero__class_Ozero(_513139))]]], (5502 ^ _257747) ^ [] : [-(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))], (2786 ^ _257747) ^ [_351674, _351676, _351678, _351680] : [class_Rings_Oordered__ring(_351674), c_Orderings_Oord__class_Oless__eq(_351674, _351676, _351678), c_Orderings_Oord__class_Oless__eq(_351674, _351680, c_Groups_Ozero__class_Ozero(_351674)), -(c_Orderings_Oord__class_Oless__eq(_351674, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_351674), _351680), _351678), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_351674), _351680), _351676)))], (11544 ^ _257747) ^ [] : [-(class_Int_Oring__char__0(tc_Complex_Ocomplex))], (5506 ^ _257747) ^ [] : [-(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))], (966 ^ _257747) ^ [_287860, _287862] : [_287862 = _287860, -(c_RComplete_Onatfloor(_287862) = c_RComplete_Onatfloor(_287860))], (11472 ^ _257747) ^ [] : [-(class_Groups_Ozero(tc_RealDef_Oreal))], (2075 ^ _257747) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), v_w____), v_k____)), v_a____) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))], (3527 ^ _257747) ^ [_376343, _376345, _376347] : [class_RealVector_Oreal__normed__vector(_376343), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_376343, _376345), c_RealVector_Onorm__class_Onorm(_376343, _376347)), c_RealVector_Onorm__class_Onorm(_376343, c_Groups_Ominus__class_Ominus(_376343, _376345, _376347))))], (11134 ^ _257747) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (10662 ^ _257747) ^ [_631134, _631136, _631138] : [class_Rings_Olinordered__idom(_631134), -(c_Groups_Osgn__class_Osgn(_631134, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_631134), _631136), _631138)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_631134), c_Groups_Osgn__class_Osgn(_631134, _631136)), c_Groups_Osgn__class_Osgn(_631134, _631138)))], (8530 ^ _257747) ^ [_558405, _558407] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _558405, c_Groups_Oone__class_Oone(tc_Int_Oint)), _558407), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _558405, _558407))], (4375 ^ _257747) ^ [_408238, _408240] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _408238, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _408238, _408240)))], (6167 ^ _257747) ^ [_472843, _472845] : [class_Groups_Ozero(_472843), -(c_Polynomial_Omonom(_472843, _472845, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(_472843, _472845, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_472843))))], (5524 ^ _257747) ^ [_450708] : [-(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), _450708) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), _450708), v_k____)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, v_a____, v_s____)), _450708))))], (8428 ^ _257747) ^ [_554908, _554910] : [class_Groups_Olinordered__ab__group__add(_554908), 8431 ^ _257747 : [(8432 ^ _257747) ^ [] : [c_Groups_Oplus__class_Oplus(_554908, _554910, _554910) = c_Groups_Ozero__class_Ozero(_554908), -(_554910 = c_Groups_Ozero__class_Ozero(_554908))], (8438 ^ _257747) ^ [] : [_554910 = c_Groups_Ozero__class_Ozero(_554908), -(c_Groups_Oplus__class_Oplus(_554908, _554910, _554910) = c_Groups_Ozero__class_Ozero(_554908))]]], (9835 ^ _257747) ^ [] : [-(c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (202 ^ _257747) ^ [_264160, _264162] : [-(class_RealVector_Oreal__div__algebra(_264160)), _264162 = _264160, class_RealVector_Oreal__div__algebra(_264162)], (5238 ^ _257747) ^ [_439896, _439898, _439900] : [hBOOL(hAPP(_439896, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _439898, _439900))), 5241 ^ _257747 : [(5242 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _439898, _439900), -(hBOOL(hAPP(_439896, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (5248 ^ _257747) ^ [_440234] : [_439898 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _439900, _440234), -(hBOOL(hAPP(_439896, _440234)))]]], (11142 ^ _257747) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (11520 ^ _257747) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex))], (612 ^ _257747) ^ [_276255, _276257] : [-(class_Groups_Omonoid__add(_276255)), _276257 = _276255, class_Groups_Omonoid__add(_276257)], (4041 ^ _257747) ^ [_396191, _396193, _396195] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _396191, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _396193, _396195)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _396193, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _396191, _396195)))], (6517 ^ _257747) ^ [_487021, _487023, _487025, _487027] : [class_Rings_Ocomm__semiring__0(_487021), c_Polynomial_Osmult(_487021, _487023, _487025) = c_Polynomial_OpCons(_487021, _487027, _487025), -(_487025 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_487021)))], (10189 ^ _257747) ^ [_614431, _614433] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _614431), c_RealDef_Oreal(tc_Nat_Onat, _614433)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _614431, _614433))], (4057 ^ _257747) ^ [_396948, _396950, _396952] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _396948, _396950) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _396952, _396950), -(_396948 = _396952)], (8796 ^ _257747) ^ [_568104, _568106, _568108] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _568104), _568104 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _568106, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _568104), _568108)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _568106), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _568108, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (9034 ^ _257747) ^ [_576042, _576044, _576046] : [class_Orderings_Opreorder(_576042), _576044 = _576046, -(c_Orderings_Oord__class_Oless__eq(_576042, _576044, _576046))], (3575 ^ _257747) ^ [_378203, _378205] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _378203, _378205)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _378203), _378205))], (11324 ^ _257747) ^ [] : [-(class_Rings_Odvd(tc_Nat_Onat))], (10263 ^ _257747) ^ [_617012, _617014] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _617012, _617014), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _617012), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), c_RealDef_Oreal(tc_Nat_Onat, _617014)))], (8824 ^ _257747) ^ [_569030, _569032, _569034, _569036, _569038, _569040] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _569030), _569032), _569034) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _569036), _569038), _569040), 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), _569036), _569038), _569040), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _569034, _569030), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _569040), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _569036), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _569036, _569030), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _569038, _569032))], (10013 ^ _257747) ^ [_608215, _608217] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _608215, _608217), -(c_Nat__Transfer_Otsub(_608217, _608215) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, _608217, _608215))], (8985 ^ _257747) ^ [_574417, _574419, _574421, _574423] : [class_Orderings_Oord(_574417), 8988 ^ _257747 : [(8989 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_574419, _574417), _574421, _574423), 8992 ^ _257747 : [(8993 ^ _257747) ^ [_574676] : [-(c_Orderings_Oord__class_Oless__eq(_574417, hAPP(_574421, _574676), hAPP(_574423, _574676)))]]], (8995 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_574417, hAPP(_574421, 8996 ^ [_574417, _574419, _574421, _574423]), hAPP(_574423, 8996 ^ [_574417, _574419, _574421, _574423])), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_574419, _574417), _574421, _574423))]]], (5114 ^ _257747) ^ [_435209, _435211, _435213] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _435209, _435211), 5117 ^ _257747 : [(5118 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _435213, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _435211, _435209)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _435213, _435209), _435211))], (5124 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _435213, _435209), _435211), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _435213, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _435211, _435209)))]]], (3933 ^ _257747) ^ [_392082, _392084, _392086, _392088, _392090, _392092] : [class_Rings_Oordered__ring(_392082), 3936 ^ _257747 : [(3937 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_392082, c_Groups_Oplus__class_Oplus(_392082, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_392082), _392084), _392086), _392088), c_Groups_Oplus__class_Oplus(_392082, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_392082), _392090), _392086), _392092)), -(c_Orderings_Oord__class_Oless(_392082, _392088, c_Groups_Oplus__class_Oplus(_392082, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_392082), c_Groups_Ominus__class_Ominus(_392082, _392090, _392084)), _392086), _392092)))], (3943 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_392082, _392088, c_Groups_Oplus__class_Oplus(_392082, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_392082), c_Groups_Ominus__class_Ominus(_392082, _392090, _392084)), _392086), _392092)), -(c_Orderings_Oord__class_Oless(_392082, c_Groups_Oplus__class_Oplus(_392082, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_392082), _392084), _392086), _392088), c_Groups_Oplus__class_Oplus(_392082, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_392082), _392090), _392086), _392092)))]]], (11542 ^ _257747) ^ [] : [-(class_Rings_Ocomm__ring(tc_Complex_Ocomplex))], (4701 ^ _257747) ^ [_420242] : [-(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), _420242) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_c____, _420242)))], (7252 ^ _257747) ^ [_512129, _512131, _512133] : [class_Groups_Ogroup__add(_512129), -(c_Groups_Oplus__class_Oplus(_512129, _512131, c_Groups_Oplus__class_Oplus(_512129, c_Groups_Ouminus__class_Ouminus(_512129, _512131), _512133)) = _512133)], (6381 ^ _257747) ^ [_481836, _481838, _481840] : [class_Groups_Oab__group__add(_481836), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_481836), c_Polynomial_OpCons(_481836, _481838, _481840)) = c_Polynomial_OpCons(_481836, c_Groups_Ouminus__class_Ouminus(_481836, _481838), c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_481836), _481840)))], (1625 ^ _257747) ^ [_311389, _311391] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _311389, _311391)), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _311389, _311391), -(_311389 = _311391)], (1817 ^ _257747) ^ [_317802] : [class_RealVector_Oreal__normed__vector(_317802), -(c_RealVector_Onorm__class_Onorm(_317802, c_Groups_Ozero__class_Ozero(_317802)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (8500 ^ _257747) ^ [_557183] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _557183), -(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), _557183)))], (4171 ^ _257747) ^ [_400910] : [_400910 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _400910, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (4007 ^ _257747) ^ [_395016] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _395016, _395016)], (8632 ^ _257747) ^ [_562088, _562090] : [-(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, _562088)), _562090)))], (2175 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v_t____, c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), v_m____))))], (6940 ^ _257747) ^ [_501819, _501821, _501823, _501825] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_501819), c_Orderings_Oord__class_Oless(_501819, c_Groups_Oplus__class_Oplus(_501819, _501821, _501823), c_Groups_Oplus__class_Oplus(_501819, _501821, _501825)), -(c_Orderings_Oord__class_Oless(_501819, _501823, _501825))], (8580 ^ _257747) ^ [_560133] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _560133, c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Groups_Oabs__class_Oabs(tc_Int_Oint, _560133) = _560133)], (2592 ^ _257747) ^ [_345386, _345388, _345390] : [class_Rings_Olinordered__ring__strict(_345386), 2595 ^ _257747 : [(2596 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_345386, c_Groups_Ozero__class_Ozero(_345386), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_345386), _345388), _345390)), 2601 ^ _257747 : [(2602 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_345386, c_Groups_Ozero__class_Ozero(_345386), _345388))], (2604 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_345386, c_Groups_Ozero__class_Ozero(_345386), _345390))]], 2605 ^ _257747 : [(2606 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_345386, _345388, c_Groups_Ozero__class_Ozero(_345386)))], (2608 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_345386, _345390, c_Groups_Ozero__class_Ozero(_345386)))]]], (2610 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_345386, c_Groups_Ozero__class_Ozero(_345386), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_345386), _345388), _345390))), 2611 ^ _257747 : [(2612 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_345386, c_Groups_Ozero__class_Ozero(_345386), _345388), c_Orderings_Oord__class_Oless__eq(_345386, c_Groups_Ozero__class_Ozero(_345386), _345390)], (2618 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_345386, _345388, c_Groups_Ozero__class_Ozero(_345386)), c_Orderings_Oord__class_Oless__eq(_345386, _345390, c_Groups_Ozero__class_Ozero(_345386))]]]]], (10239 ^ _257747) ^ [_616110, _616112] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _616110, c_RealDef_Oreal(tc_Nat_Onat, _616112)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_616110), _616112))], (11886 ^ _257747) ^ [_669096] : [class_Groups_Oab__group__add(_669096), -(class_Groups_Ominus(tc_Polynomial_Opoly(_669096)))], (6225 ^ _257747) ^ [_474993] : [class_Groups_Oab__group__add(_474993), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_474993), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_474993))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_474993)))], (162 ^ _257747) ^ [_262980, _262982] : [-(class_Rings_Odivision__ring__inverse__zero(_262980)), _262982 = _262980, class_Rings_Odivision__ring__inverse__zero(_262982)], (11192 ^ _257747) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (8940 ^ _257747) ^ [_572882, _572884] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _572882), -(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), _572882), _572884)))], (11474 ^ _257747) ^ [] : [-(class_Rings_Oring(tc_RealDef_Oreal))], (2071 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), v_t____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), v_m____))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))], (3379 ^ _257747) ^ [_371220, _371222, _371224] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _371220), 3382 ^ _257747 : [(3383 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _371220), _371222), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _371220), _371224)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _371222, _371224))], (3389 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _371222, _371224), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _371220), _371222), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _371220), _371224)))]]], (11530 ^ _257747) ^ [] : [-(class_Groups_Omonoid__mult(tc_Complex_Ocomplex))], (6087 ^ _257747) ^ [_469483, _469485, _469487, _469489] : [class_Groups_Ozero(_469483), 6090 ^ _257747 : [(6091 ^ _257747) ^ [] : [c_Polynomial_Omonom(_469483, _469485, _469487) = c_Polynomial_Omonom(_469483, _469489, _469487), -(_469485 = _469489)], (6097 ^ _257747) ^ [] : [_469485 = _469489, -(c_Polynomial_Omonom(_469483, _469485, _469487) = c_Polynomial_Omonom(_469483, _469489, _469487))]]], (4576 ^ _257747) ^ [_415987, _415989, _415991] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _415987), _415989), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _415991), _415989)), 4579 ^ _257747 : [(4580 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _415989))], (4582 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _415987, _415991))]]], (6536 ^ _257747) ^ [_487761, _487763, _487765, _487767, _487769] : [class_Groups_Oordered__ab__group__add__abs(_487761), -(c_Orderings_Oord__class_Oless__eq(_487761, c_Groups_Oabs__class_Oabs(_487761, c_Groups_Ominus__class_Ominus(_487761, c_Groups_Oplus__class_Oplus(_487761, _487763, _487765), c_Groups_Oplus__class_Oplus(_487761, _487767, _487769))), c_Groups_Oplus__class_Oplus(_487761, c_Groups_Oabs__class_Oabs(_487761, c_Groups_Ominus__class_Ominus(_487761, _487763, _487767)), c_Groups_Oabs__class_Oabs(_487761, c_Groups_Ominus__class_Ominus(_487761, _487765, _487769)))))], (3865 ^ _257747) ^ [_389254, _389256] : [class_Rings_Odivision__ring(_389254), -(_389256 = c_Groups_Ozero__class_Ozero(_389254)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_389254), c_Rings_Oinverse__class_Oinverse(_389254, _389256)), _389256) = c_Groups_Oone__class_Oone(_389254))], (6273 ^ _257747) ^ [_476596, _476598, _476600, _476602] : [class_Rings_Ocomm__ring(_476596), -(c_Polynomial_Osmult(_476596, _476598, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_476596), _476600, _476602)) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_476596), c_Polynomial_Osmult(_476596, _476598, _476600), c_Polynomial_Osmult(_476596, _476598, _476602)))], (11284 ^ _257747) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (8203 ^ _257747) ^ [_545812, _545814, _545816] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_545812), 8206 ^ _257747 : [(8207 ^ _257747) ^ [] : [_545814 = c_Groups_Oplus__class_Oplus(_545812, _545814, _545816), -(_545816 = c_Groups_Ozero__class_Ozero(_545812))], (8213 ^ _257747) ^ [] : [_545816 = c_Groups_Ozero__class_Ozero(_545812), -(_545814 = c_Groups_Oplus__class_Oplus(_545812, _545814, _545816))]]], (7932 ^ _257747) ^ [_534653, _534655, _534657, _534659] : [class_Groups_Oordered__comm__monoid__add(_534653), c_Orderings_Oord__class_Oless__eq(_534653, c_Groups_Ozero__class_Ozero(_534653), _534655), c_Orderings_Oord__class_Oless(_534653, _534657, _534659), -(c_Orderings_Oord__class_Oless(_534653, _534657, c_Groups_Oplus__class_Oplus(_534653, _534655, _534659)))], (602 ^ _257747) ^ [_275960, _275962] : [-(class_Groups_Ocomm__monoid__add(_275960)), _275962 = _275960, class_Groups_Ocomm__monoid__add(_275962)], (4179 ^ _257747) ^ [_401170] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _401170), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11376 ^ _257747) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal))], (10580 ^ _257747) ^ [_628518, _628520] : [class_Rings_Olinordered__idom(_628518), 10583 ^ _257747 : [(10584 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_628518, c_Groups_Osgn__class_Osgn(_628518, _628520), c_Groups_Ozero__class_Ozero(_628518)), -(c_Orderings_Oord__class_Oless(_628518, _628520, c_Groups_Ozero__class_Ozero(_628518)))], (10590 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_628518, _628520, c_Groups_Ozero__class_Ozero(_628518)), -(c_Orderings_Oord__class_Oless(_628518, c_Groups_Osgn__class_Osgn(_628518, _628520), c_Groups_Ozero__class_Ozero(_628518)))]]], (6930 ^ _257747) ^ [_501454, _501456, _501458, _501460] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_501454), c_Orderings_Oord__class_Oless(_501454, c_Groups_Oplus__class_Oplus(_501454, _501456, _501458), c_Groups_Oplus__class_Oplus(_501454, _501460, _501458)), -(c_Orderings_Oord__class_Oless(_501454, _501456, _501460))], (10037 ^ _257747) ^ [_609153, _609155, _609157] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _609153, _609155), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _609153, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _609157, _609155)))], (7710 ^ _257747) ^ [_526987, _526989] : [class_Groups_Oab__group__add(_526987), -(c_Groups_Oplus__class_Oplus(_526987, c_Groups_Ouminus__class_Ouminus(_526987, _526989), _526989) = c_Groups_Ozero__class_Ozero(_526987))], (10409 ^ _257747) ^ [_622048] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _622048), 10413 ^ _257747 : [(10414 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, 10412 ^ [_622048], c_Groups_Oone__class_Oone(tc_Nat_Onat))), _622048))], (10416 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _622048, c_RealDef_Oreal(tc_Nat_Onat, 10412 ^ [_622048])))]]], (11150 ^ _257747) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (8197 ^ _257747) ^ [_545578, _545580] : [class_Rings_Ocomm__semiring__1(_545578), -(c_Groups_Oplus__class_Oplus(_545578, _545580, c_Groups_Ozero__class_Ozero(_545578)) = _545580)], (7214 ^ _257747) ^ [_510855, _510857, _510859] : [class_Groups_Oordered__ab__group__add(_510855), 7217 ^ _257747 : [(7218 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_510855, c_Groups_Ouminus__class_Ouminus(_510855, _510857), _510859), -(c_Orderings_Oord__class_Oless(_510855, c_Groups_Ouminus__class_Ouminus(_510855, _510859), _510857))], (7224 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_510855, c_Groups_Ouminus__class_Ouminus(_510855, _510859), _510857), -(c_Orderings_Oord__class_Oless(_510855, c_Groups_Ouminus__class_Ouminus(_510855, _510857), _510859))]]], (2005 ^ _257747) ^ [_324238, _324240, _324242, _324244] : [class_Rings_Olinordered__semidom(_324238), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _324240, _324242), c_Orderings_Oord__class_Oless(_324238, c_Groups_Ozero__class_Ozero(_324238), _324244), c_Orderings_Oord__class_Oless(_324238, _324244, c_Groups_Oone__class_Oone(_324238)), -(c_Orderings_Oord__class_Oless(_324238, hAPP(hAPP(c_Power_Opower__class_Opower(_324238), _324244), _324242), hAPP(hAPP(c_Power_Opower__class_Opower(_324238), _324244), _324240)))], (2370 ^ _257747) ^ [_337842, _337844] : [class_Rings_Olinordered__idom(_337842), 2373 ^ _257747 : [(2374 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_337842, _337844, c_Groups_Ouminus__class_Ouminus(_337842, _337844)), -(c_Orderings_Oord__class_Oless(_337842, _337844, c_Groups_Ozero__class_Ozero(_337842)))], (2380 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_337842, _337844, c_Groups_Ozero__class_Ozero(_337842)), -(c_Orderings_Oord__class_Oless(_337842, _337844, c_Groups_Ouminus__class_Ouminus(_337842, _337844)))]]], (4982 ^ _257747) ^ [_430398, _430400] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _430398), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _430400), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _430400, _430398), _430400))], (6431 ^ _257747) ^ [_483711, _483713, _483715] : [class_Groups_Ozero(_483711), 6434 ^ _257747 : [(6435 ^ _257747) ^ [] : [c_Polynomial_OpCons(_483711, _483713, _483715) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_483711)), 6438 ^ _257747 : [(6439 ^ _257747) ^ [] : [-(_483713 = c_Groups_Ozero__class_Ozero(_483711))], (6441 ^ _257747) ^ [] : [-(_483715 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_483711)))]]], (6443 ^ _257747) ^ [] : [-(c_Polynomial_OpCons(_483711, _483713, _483715) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_483711))), _483713 = c_Groups_Ozero__class_Ozero(_483711), _483715 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_483711))]]], (3715 ^ _257747) ^ [_383432, _383434, _383436] : [class_Rings_Odivision__ring(_383432), -(_383434 = c_Groups_Ozero__class_Ozero(_383432)), -(_383436 = c_Groups_Ozero__class_Ozero(_383432)), -(c_Rings_Oinverse__class_Oinverse(_383432, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_383432), _383434), _383436)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_383432), c_Rings_Oinverse__class_Oinverse(_383432, _383436)), c_Rings_Oinverse__class_Oinverse(_383432, _383434)))], (4129 ^ _257747) ^ [_399484] : [-(_399484 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _399484))], (11784 ^ _257747) ^ [_665866] : [class_Rings_Olinordered__idom(_665866), -(class_Orderings_Opreorder(tc_Polynomial_Opoly(_665866)))], (11898 ^ _257747) ^ [_669476] : [class_Groups_Ozero(_669476), -(class_Groups_Ozero(tc_Polynomial_Opoly(_669476)))], (792 ^ _257747) ^ [_281565, _281567] : [-(class_Groups_Ozero(_281565)), _281567 = _281565, class_Groups_Ozero(_281567)], (6419 ^ _257747) ^ [_483233, _483235] : [class_Rings_Ocomm__semiring__0(_483233), -(c_Polynomial_Osmult(_483233, _483235, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_483233))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_483233)))], (11170 ^ _257747) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (8542 ^ _257747) ^ [_558802, _558804, _558806] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _558802), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _558804, _558806)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _558802), _558804), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _558802), _558806)))], (1887 ^ _257747) ^ [_320066, _320068] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _320066), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _320068), -(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), _320066), _320068)))], (10225 ^ _257747) ^ [_615570] : [-(c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat, _615570)) = _615570)], (7884 ^ _257747) ^ [_533063, _533065] : [class_Groups_Oordered__ab__group__add__abs(_533063), -(c_Orderings_Oord__class_Oless__eq(_533063, c_Groups_Ouminus__class_Ouminus(_533063, _533065), c_Groups_Oabs__class_Oabs(_533063, _533065)))], (10886 ^ _257747) ^ [_638923, _638925, _638927, _638929] : [class_Rings_Ocomm__ring(_638923), class_Rings_Odvd(_638923), c_Rings_Odvd__class_Odvd(_638923, _638925, _638927), 10897 ^ _257747 : [(10898 ^ _257747) ^ [_639326, _639328] : [c_Rings_Odvd__class_Odvd(_638923, _638925, c_Groups_Oplus__class_Oplus(_638923, _639328, _638929)), -(c_Rings_Odvd__class_Odvd(_638923, _638925, c_Groups_Oplus__class_Oplus(_638923, c_Groups_Ominus__class_Ominus(_638923, _639328, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_638923), _639326), _638927)), _638929)))], (10904 ^ _257747) ^ [_639564, _639566] : [c_Rings_Odvd__class_Odvd(_638923, _638925, c_Groups_Oplus__class_Oplus(_638923, c_Groups_Ominus__class_Ominus(_638923, _639566, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_638923), _639564), _638927)), _638929)), -(c_Rings_Odvd__class_Odvd(_638923, _638925, c_Groups_Oplus__class_Oplus(_638923, _639566, _638929)))]]], (3371 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), v_m____))))], (2518 ^ _257747) ^ [_342930, _342932] : [class_Rings_Omult__zero(_342930), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_342930), _342932), c_Groups_Ozero__class_Ozero(_342930)) = c_Groups_Ozero__class_Ozero(_342930))], (9947 ^ _257747) ^ [] : [-(c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11462 ^ _257747) ^ [] : [-(class_Groups_Oabs__if(tc_RealDef_Oreal))], (10862 ^ _257747) ^ [_637955, _637957, _637959, _637961] : [class_Rings_Ocomm__ring(_637955), class_Rings_Odvd(_637955), c_Rings_Odvd__class_Odvd(_637955, _637957, _637959), 10873 ^ _257747 : [(10874 ^ _257747) ^ [_638358, _638360] : [c_Rings_Odvd__class_Odvd(_637955, _637957, c_Groups_Oplus__class_Oplus(_637955, _638360, _637961)), -(c_Rings_Odvd__class_Odvd(_637955, _637957, c_Groups_Oplus__class_Oplus(_637955, c_Groups_Ominus__class_Ominus(_637955, _638360, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_637955), _638358), _637959)), _637961)))], (10880 ^ _257747) ^ [_638596, _638598] : [c_Rings_Odvd__class_Odvd(_637955, _637957, c_Groups_Oplus__class_Oplus(_637955, c_Groups_Ominus__class_Ominus(_637955, _638598, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_637955), _638596), _637959)), _637961)), -(c_Rings_Odvd__class_Odvd(_637955, _637957, c_Groups_Oplus__class_Oplus(_637955, _638598, _637961)))]]], (6155 ^ _257747) ^ [_472283, _472285, _472287, _472289] : [class_Rings_Ocomm__semiring__0(_472283), -(c_Polynomial_Osmult(_472283, _472285, c_Polynomial_Omonom(_472283, _472287, _472289)) = c_Polynomial_Omonom(_472283, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_472283), _472285), _472287), _472289))], (4269 ^ _257747) ^ [_404452, _404454, _404456, _404458] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _404452, _404454), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _404456, _404458), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _404452, _404456), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _404454, _404458)))], (4071 ^ _257747) ^ [_397445, _397447] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _397445, _397447)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _397447, _397445))], (802 ^ _257747) ^ [_281860, _281862] : [-(class_Rings_Ocomm__ring(_281860)), _281862 = _281860, class_Rings_Ocomm__ring(_281862)], (5210 ^ _257747) ^ [_438816] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _438816, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _438816) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _438816))], (1671 ^ _257747) ^ [_312916, _312918, _312920, _312922] : [class_Rings_Olinordered__semidom(_312916), c_Orderings_Oord__class_Oless__eq(_312916, _312918, _312920), c_Orderings_Oord__class_Oless__eq(_312916, c_Groups_Ozero__class_Ozero(_312916), _312918), -(c_Orderings_Oord__class_Oless__eq(_312916, hAPP(hAPP(c_Power_Opower__class_Opower(_312916), _312918), _312922), hAPP(hAPP(c_Power_Opower__class_Opower(_312916), _312920), _312922)))], (9158 ^ _257747) ^ [_579992, _579994, _579996] : [class_Orderings_Oorder(_579992), c_Orderings_Oord__class_Oless__eq(_579992, _579994, _579996), c_Orderings_Oord__class_Oless__eq(_579992, _579996, _579994), -(_579996 = _579994)], (10674 ^ _257747) ^ [_631662] : [class_Groups_Osgn__if(_631662), -(c_Groups_Osgn__class_Osgn(_631662, c_Groups_Ozero__class_Ozero(_631662)) = c_Groups_Ozero__class_Ozero(_631662))], (3068 ^ _257747) ^ [_360873, _360875, _360877] : [class_Rings_Olinordered__semiring__strict(_360873), c_Orderings_Oord__class_Oless(_360873, _360875, c_Groups_Ozero__class_Ozero(_360873)), c_Orderings_Oord__class_Oless(_360873, c_Groups_Ozero__class_Ozero(_360873), _360877), -(c_Orderings_Oord__class_Oless(_360873, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_360873), _360875), _360877), c_Groups_Ozero__class_Ozero(_360873)))], (11144 ^ _257747) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (10233 ^ _257747) ^ [_615886, _615888] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _615886), _615888), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _615886, c_RComplete_Onatfloor(_615888)))], (4656 ^ _257747) ^ [_418726, _418728, _418730] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _418726), _418728), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _418726), _418730)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _418726), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _418728, _418730))], (5360 ^ _257747) ^ [_444897, _444899, _444901, _444903, _444905] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _444897, _444899), 5363 ^ _257747 : [(5364 ^ _257747) ^ [] : [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), _444899), _444901), _444903), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _444897), _444901), _444905)), -(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, _444899, _444897)), _444901), _444903), _444905))], (5370 ^ _257747) ^ [] : [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, _444899, _444897)), _444901), _444903), _444905), -(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), _444899), _444901), _444903), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _444897), _444901), _444905)))]]], (1587 ^ _257747) ^ [_310033, _310035, _310037] : [class_Groups_Omonoid__mult(_310033), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_310033), hAPP(hAPP(c_Power_Opower__class_Opower(_310033), _310035), _310037)), _310035) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_310033), _310035), hAPP(hAPP(c_Power_Opower__class_Opower(_310033), _310035), _310037)))], (11140 ^ _257747) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (3465 ^ _257747) ^ [_374160, _374162] : [c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _374160, _374162) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_374162 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _374160))], (11604 ^ _257747) ^ [_660166] : [class_Rings_Olinordered__idom(_660166), -(class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(_660166)))], (76 ^ _257747) ^ [_260343, _260345, _260347, _260349, _260351, _260353] : [-(c_Orderings_Oord__class_Oless(_260351, _260347, _260343)), c_Orderings_Oord__class_Oless(_260353, _260349, _260345), _260353 = _260351, _260349 = _260347, _260345 = _260343], (10 ^ _257747) ^ [_258182, _258184, _258186] : [-(_258186 = _258182), _258186 = _258184, _258184 = _258182], (6750 ^ _257747) ^ [_495138, _495140] : [class_Groups_Olinordered__ab__group__add(_495138), 6753 ^ _257747 : [(6754 ^ _257747) ^ [] : [c_Groups_Ozero__class_Ozero(_495138) = c_Groups_Oplus__class_Oplus(_495138, _495140, _495140), -(_495140 = c_Groups_Ozero__class_Ozero(_495138))], (6760 ^ _257747) ^ [] : [_495140 = c_Groups_Ozero__class_Ozero(_495138), -(c_Groups_Ozero__class_Ozero(_495138) = c_Groups_Oplus__class_Oplus(_495138, _495140, _495140))]]], (7770 ^ _257747) ^ [_529010, _529012] : [class_Groups_Oordered__ab__group__add__abs(_529010), 7773 ^ _257747 : [(7774 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_529010, c_Groups_Ozero__class_Ozero(_529010), c_Groups_Oabs__class_Oabs(_529010, _529012)), _529012 = c_Groups_Ozero__class_Ozero(_529010)], (7780 ^ _257747) ^ [] : [-(_529012 = c_Groups_Ozero__class_Ozero(_529010)), -(c_Orderings_Oord__class_Oless(_529010, c_Groups_Ozero__class_Ozero(_529010), c_Groups_Oabs__class_Oabs(_529010, _529012)))]]], (8626 ^ _257747) ^ [_561889] : [_561889 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oabs__class_Oabs(tc_Int_Oint, _561889), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (9871 ^ _257747) ^ [_602616] : [9879 ^ _257747 : [(9880 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 9878 ^ [_602616]))], (9882 ^ _257747) ^ [_602976] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_602616, c_RealVector_Oof__real(_602616, _602976)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, _602976)), 9878 ^ [_602616])))]], class_RealVector_Oreal__algebra__1(_602616), class_RealVector_Oreal__normed__vector(_602616)], (2524 ^ _257747) ^ [_343176, _343178, _343180] : [class_Rings_Oring__no__zero__divisors(_343176), 2527 ^ _257747 : [(2538 ^ _257747) ^ [] : [2539 ^ _257747 : [(2540 ^ _257747) ^ [] : [_343178 = c_Groups_Ozero__class_Ozero(_343176)], (2542 ^ _257747) ^ [] : [_343180 = c_Groups_Ozero__class_Ozero(_343176)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_343176), _343178), _343180) = c_Groups_Ozero__class_Ozero(_343176))], (2528 ^ _257747) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_343176), _343178), _343180) = c_Groups_Ozero__class_Ozero(_343176), -(_343178 = c_Groups_Ozero__class_Ozero(_343176)), -(_343180 = c_Groups_Ozero__class_Ozero(_343176))]]], (1303 ^ _257747) ^ [_300103, _300105, _300107, _300109, _300111] : [class_RealVector_Oreal__normed__algebra(_300103), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_300103, _300105), _300107), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_300103, _300109), _300111), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_300103, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_300103), _300105), _300109)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _300107), _300111)))], (292 ^ _257747) ^ [_266815, _266817] : [-(class_Rings_Olinordered__semiring__1__strict(_266815)), _266817 = _266815, class_Rings_Olinordered__semiring__1__strict(_266817)], (2346 ^ _257747) ^ [_336708, _336710, _336712, _336714] : [class_RealVector_Oreal__normed__algebra(_336708), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_336708), _336710), c_Groups_Oplus__class_Oplus(_336708, _336712, _336714)) = c_Groups_Oplus__class_Oplus(_336708, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_336708), _336710), _336712), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_336708), _336710), _336714)))], (6530 ^ _257747) ^ [_487469, _487471, _487473] : [class_Groups_Oordered__ab__group__add__abs(_487469), -(c_Orderings_Oord__class_Oless__eq(_487469, c_Groups_Oabs__class_Oabs(_487469, c_Groups_Ominus__class_Ominus(_487469, _487471, _487473)), c_Groups_Oplus__class_Oplus(_487469, c_Groups_Oabs__class_Oabs(_487469, _487471), c_Groups_Oabs__class_Oabs(_487469, _487473))))], (5080 ^ _257747) ^ [_433937, _433939, _433941] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _433937, _433939), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _433939, _433937), _433941) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _433939, _433941), _433937))], (6357 ^ _257747) ^ [_480780, _480782, _480784, _480786] : [class_Rings_Ocomm__semiring__0(_480780), -(c_Polynomial_Osmult(_480780, _480782, c_Polynomial_Osmult(_480780, _480784, _480786)) = c_Polynomial_Osmult(_480780, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_480780), _480782), _480784), _480786))], (7974 ^ _257747) ^ [_535965, _535967] : [class_Groups_Oordered__ab__group__add__abs(_535965), -(c_Orderings_Oord__class_Oless__eq(_535965, c_Groups_Ouminus__class_Ouminus(_535965, c_Groups_Oabs__class_Oabs(_535965, _535967)), c_Groups_Ozero__class_Ozero(_535965)))], (11226 ^ _257747) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (2155 ^ _257747) ^ [_329164, _329166, _329168, _329170] : [class_Rings_Olinordered__semiring(_329164), c_Orderings_Oord__class_Oless(_329164, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_329164), _329166), _329168), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_329164), _329166), _329170)), c_Orderings_Oord__class_Oless__eq(_329164, c_Groups_Ozero__class_Ozero(_329164), _329166), -(c_Orderings_Oord__class_Oless(_329164, _329168, _329170))], (9935 ^ _257747) ^ [] : [-(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, 9933 ^ []) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, v_pa____))], (3477 ^ _257747) ^ [_374576, _374578, _374580] : [-(c_RealVector_Oof__real(_374576, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _374578, _374580)) = c_Groups_Ominus__class_Ominus(_374576, c_RealVector_Oof__real(_374576, _374578), c_RealVector_Oof__real(_374576, _374580))), class_RealVector_Oreal__algebra__1(_374576), class_RealVector_Oreal__normed__vector(_374576)], (10387 ^ _257747) ^ [_621301, _621303, _621305] : [class_Rings_Olinordered__idom(_621301), 10390 ^ _257747 : [(10391 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_621301), _621303, _621305), -(c_Polynomial_Opos__poly(_621301, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_621301), _621305, _621303)))], (10397 ^ _257747) ^ [] : [c_Polynomial_Opos__poly(_621301, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_621301), _621305, _621303)), -(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_621301), _621303, _621305))]]], (3443 ^ _257747) ^ [_373381, _373383] : [-(c_RealVector_Oof__real(_373381, c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, _373383)) = c_Rings_Oinverse__class_Oinverse(_373381, c_RealVector_Oof__real(_373381, _373383))), class_RealVector_Oreal__div__algebra(_373381), class_Rings_Odivision__ring__inverse__zero(_373381)], (11348 ^ _257747) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal))], (4083 ^ _257747) ^ [_397886, _397888, _397890] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _397886, _397888), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _397888, _397890), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _397886, _397890))], (4898 ^ _257747) ^ [_427223, _427225, _427227] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _427223, _427225), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _427223, _427227), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _427225, _427227)))], (2472 ^ _257747) ^ [_341405, _341407, _341409] : [class_Rings_Olinordered__idom(_341405), -(_341407 = _341409), -(c_Orderings_Oord__class_Oless(_341405, _341407, _341409)), -(c_Orderings_Oord__class_Oless(_341405, _341409, _341407))], (11362 ^ _257747) ^ [] : [-(class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal))], (11496 ^ _257747) ^ [] : [-(class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex))], (7848 ^ _257747) ^ [_531966, _531968, _531970] : [class_Groups_Oordered__ab__group__add__abs(_531966), c_Orderings_Oord__class_Oless__eq(_531966, _531968, _531970), c_Orderings_Oord__class_Oless__eq(_531966, c_Groups_Ouminus__class_Ouminus(_531966, _531968), _531970), -(c_Orderings_Oord__class_Oless__eq(_531966, c_Groups_Oabs__class_Oabs(_531966, _531968), _531970))], (4812 ^ _257747) ^ [_424032] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _424032, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _424032)], (6854 ^ _257747) ^ [_498771, _498773, _498775, _498777] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_498771), c_Orderings_Oord__class_Oless__eq(_498771, c_Groups_Oplus__class_Oplus(_498771, _498773, _498775), c_Groups_Oplus__class_Oplus(_498771, _498773, _498777)), -(c_Orderings_Oord__class_Oless__eq(_498771, _498775, _498777))], (4958 ^ _257747) ^ [_429598, _429600] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _429598), _429600), 4961 ^ _257747 : [(4962 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _429600), _429598))], (4964 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _429598, _429600))]]], (10121 ^ _257747) ^ [_612060, _612062] : [-(c_RealDef_Oreal(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _612060), _612062)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _612060)), c_RealDef_Oreal(tc_Nat_Onat, _612062)))], (1669 ^ _257747) ^ [_312778] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _312778) = _312778)], (362 ^ _257747) ^ [_268880, _268882] : [-(class_Rings_Oring__1__no__zero__divisors(_268880)), _268882 = _268880, class_Rings_Oring__1__no__zero__divisors(_268882)], (11422 ^ _257747) ^ [] : [-(class_Rings_Odivision__ring(tc_RealDef_Oreal))], (692 ^ _257747) ^ [_278615, _278617] : [-(class_Orderings_Oord(_278615)), _278617 = _278615, class_Orderings_Oord(_278617)], (11490 ^ _257747) ^ [] : [-(class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex))], (4684 ^ _257747) ^ [_419676, _419678, _419680] : [4685 ^ _257747 : [(4686 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _419678))], (4688 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _419676, _419680)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _419676), _419678), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _419680), _419678)))], (1215 ^ _257747) ^ [_296894, _296896] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, _296894)), _296896) = c_RealVector_Oof__real(tc_Complex_Ocomplex, hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _296894), _296896)))], (5074 ^ _257747) ^ [_433673, _433675, _433677] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _433673, _433675), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _433675, _433677), _433673) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _433675, _433673), _433677))], (6425 ^ _257747) ^ [_483465, _483467] : [class_Rings_Ocomm__semiring__0(_483465), -(hAPP(c_Polynomial_Opoly(_483465, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_483465))), _483467) = c_Groups_Ozero__class_Ozero(_483465))], (11494 ^ _257747) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex))], (3787 ^ _257747) ^ [_386465, _386467, _386469, _386471, _386473, _386475] : [class_Rings_Oring(_386465), 3790 ^ _257747 : [(3791 ^ _257747) ^ [] : [c_Groups_Oplus__class_Oplus(_386465, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_386465), _386467), _386469), _386471) = c_Groups_Oplus__class_Oplus(_386465, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_386465), _386473), _386469), _386475), -(_386471 = c_Groups_Oplus__class_Oplus(_386465, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_386465), c_Groups_Ominus__class_Ominus(_386465, _386473, _386467)), _386469), _386475))], (3797 ^ _257747) ^ [] : [_386471 = c_Groups_Oplus__class_Oplus(_386465, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_386465), c_Groups_Ominus__class_Ominus(_386465, _386473, _386467)), _386469), _386475), -(c_Groups_Oplus__class_Oplus(_386465, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_386465), _386467), _386469), _386471) = c_Groups_Oplus__class_Oplus(_386465, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_386465), _386473), _386469), _386475))]]], (11000 ^ _257747) ^ [_643067, _643069] : [class_Rings_Ocomm__semiring__1(_643067), -(c_Rings_Odvd__class_Odvd(_643067, _643069, _643069))], (11478 ^ _257747) ^ [] : [-(class_Groups_Oone(tc_RealDef_Oreal))], (7496 ^ _257747) ^ [_520209, _520211, _520213] : [class_Groups_Oordered__comm__monoid__add(_520209), c_Orderings_Oord__class_Oless(_520209, _520211, c_Groups_Ozero__class_Ozero(_520209)), c_Orderings_Oord__class_Oless(_520209, _520213, c_Groups_Ozero__class_Ozero(_520209)), -(c_Orderings_Oord__class_Oless(_520209, c_Groups_Oplus__class_Oplus(_520209, _520211, _520213), c_Groups_Ozero__class_Ozero(_520209)))], (1475 ^ _257747) ^ [_306090, _306092, _306094] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _306090, _306092), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _306092, _306094), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _306090, _306094))], (2190 ^ _257747) ^ [_330382, _330384, _330386] : [class_Groups_Ogroup__add(_330382), 2193 ^ _257747 : [(2194 ^ _257747) ^ [] : [c_Groups_Oplus__class_Oplus(_330382, _330384, _330386) = c_Groups_Ozero__class_Ozero(_330382), -(_330386 = c_Groups_Ouminus__class_Ouminus(_330382, _330384))], (2200 ^ _257747) ^ [] : [_330386 = c_Groups_Ouminus__class_Ouminus(_330382, _330384), -(c_Groups_Oplus__class_Oplus(_330382, _330384, _330386) = c_Groups_Ozero__class_Ozero(_330382))]]], (9314 ^ _257747) ^ [_584867, _584869, _584871] : [class_Orderings_Opreorder(_584867), c_Orderings_Oord__class_Oless(_584867, _584869, _584871), c_Orderings_Oord__class_Oless(_584867, _584871, _584869)], (8155 ^ _257747) ^ [_543838, _543840, _543842, _543844] : [class_Rings_Ocomm__semiring__1(_543838), -(c_Groups_Oplus__class_Oplus(_543838, c_Groups_Oplus__class_Oplus(_543838, _543840, _543842), _543844) = c_Groups_Oplus__class_Oplus(_543838, _543840, c_Groups_Oplus__class_Oplus(_543838, _543842, _543844)))], (6231 ^ _257747) ^ [_475235, _475237, _475239] : [class_Int_Oring__char__0(_475235), class_Rings_Oidom(_475235), 6238 ^ _257747 : [(6239 ^ _257747) ^ [] : [c_Polynomial_Opoly(_475235, _475237) = c_Polynomial_Opoly(_475235, _475239), -(_475237 = _475239)], (6245 ^ _257747) ^ [] : [_475237 = _475239, -(c_Polynomial_Opoly(_475235, _475237) = c_Polynomial_Opoly(_475235, _475239))]]], (9610 ^ _257747) ^ [_594204, _594206, _594208] : [class_Orderings_Olinorder(_594204), -(c_Orderings_Oord__class_Oless(_594204, _594206, _594208)), 9617 ^ _257747 : [(9618 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_594204, _594206, _594208), -(_594206 = _594208)], (9624 ^ _257747) ^ [] : [_594206 = _594208, -(c_Orderings_Oord__class_Oless__eq(_594204, _594206, _594208))]]], (10730 ^ _257747) ^ [_633565, _633567] : [class_Rings_Olinordered__idom(_633565), c_Orderings_Oord__class_Oless(_633565, _633567, c_Groups_Ozero__class_Ozero(_633565)), -(c_Groups_Osgn__class_Osgn(_633565, _633567) = c_Groups_Ouminus__class_Ouminus(_633565, c_Groups_Oone__class_Oone(_633565)))], (6906 ^ _257747) ^ [_500597, _500599, _500601, _500603] : [class_Groups_Oordered__cancel__ab__semigroup__add(_500597), c_Orderings_Oord__class_Oless(_500597, _500599, _500601), -(c_Orderings_Oord__class_Oless(_500597, c_Groups_Oplus__class_Oplus(_500597, _500603, _500599), c_Groups_Oplus__class_Oplus(_500597, _500603, _500601)))], (6574 ^ _257747) ^ [_489180, _489182, _489184, _489186] : [class_Groups_Ocancel__semigroup__add(_489180), c_Groups_Oplus__class_Oplus(_489180, _489182, _489184) = c_Groups_Oplus__class_Oplus(_489180, _489186, _489184), -(_489182 = _489186)], (11198 ^ _257747) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (11540 ^ _257747) ^ [] : [-(class_Rings_Omult__zero(tc_Complex_Ocomplex))], (5878 ^ _257747) ^ [_462085, _462087] : [class_Fields_Ofield(_462085), -(_462087 = c_Groups_Ozero__class_Ozero(_462085)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_462085), c_Rings_Oinverse__class_Oinverse(_462085, _462087)), _462087) = c_Groups_Oone__class_Oone(_462085))], (772 ^ _257747) ^ [_280975, _280977] : [-(class_Groups_Ominus(_280975)), _280977 = _280975, class_Groups_Ominus(_280977)], (1777 ^ _257747) ^ [_316500, _316502, _316504, _316506] : [class_Rings_Olinordered__semidom(_316500), c_Orderings_Oord__class_Oless(_316500, c_Groups_Oone__class_Oone(_316500), _316502), 1784 ^ _257747 : [(1785 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_316500, hAPP(hAPP(c_Power_Opower__class_Opower(_316500), _316502), _316504), hAPP(hAPP(c_Power_Opower__class_Opower(_316500), _316502), _316506)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _316504, _316506))], (1791 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _316504, _316506), -(c_Orderings_Oord__class_Oless(_316500, hAPP(hAPP(c_Power_Opower__class_Opower(_316500), _316502), _316504), hAPP(hAPP(c_Power_Opower__class_Opower(_316500), _316502), _316506)))]]], (4191 ^ _257747) ^ [_401576, _401578] : [4192 ^ _257747 : [(4193 ^ _257747) ^ [] : [_401576 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (4195 ^ _257747) ^ [] : [_401578 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _401576), _401578) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5338 ^ _257747) ^ [_443887, _443889, _443891, _443893, _443895] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _443887, _443889), 5341 ^ _257747 : [(5342 ^ _257747) ^ [] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _443889), _443891), _443893) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _443887), _443891), _443895), -(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, _443889, _443887)), _443891), _443893) = _443895)], (5348 ^ _257747) ^ [] : [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, _443889, _443887)), _443891), _443893) = _443895, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _443889), _443891), _443893) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _443887), _443891), _443895))]]], (11264 ^ _257747) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (7990 ^ _257747) ^ [_536506, _536508] : [class_Groups_Oabs__if(_536506), 7993 ^ _257747 : [(7994 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_536506, _536508, c_Groups_Ozero__class_Ozero(_536506)), -(c_Groups_Oabs__class_Oabs(_536506, _536508) = c_Groups_Ouminus__class_Ouminus(_536506, _536508))], (8000 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(_536506, _536508, c_Groups_Ozero__class_Ozero(_536506))), -(c_Groups_Oabs__class_Oabs(_536506, _536508) = _536508)]]], (222 ^ _257747) ^ [_264750, _264752] : [-(class_Fields_Ofield__inverse__zero(_264750)), _264752 = _264750, class_Fields_Ofield__inverse__zero(_264752)], (11586 ^ _257747) ^ [_659596] : [class_Rings_Olinordered__idom(_659596), -(class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(_659596)))], (6694 ^ _257747) ^ [_493254, _493256, _493258] : [class_Groups_Ogroup__add(_493254), 6697 ^ _257747 : [(6698 ^ _257747) ^ [] : [c_Groups_Ouminus__class_Ouminus(_493254, _493256) = _493258, -(c_Groups_Ouminus__class_Ouminus(_493254, _493258) = _493256)], (6704 ^ _257747) ^ [] : [c_Groups_Ouminus__class_Ouminus(_493254, _493258) = _493256, -(c_Groups_Ouminus__class_Ouminus(_493254, _493256) = _493258)]]], (2113 ^ _257747) ^ [_327712, _327714, _327716, _327718] : [class_Rings_Olinordered__semiring__strict(_327712), c_Orderings_Oord__class_Oless__eq(_327712, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_327712), _327714), _327716), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_327712), _327714), _327718)), c_Orderings_Oord__class_Oless(_327712, c_Groups_Ozero__class_Ozero(_327712), _327714), -(c_Orderings_Oord__class_Oless__eq(_327712, _327716, _327718))], (11928 ^ _257747) ^ [] : [-(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), v_t____), 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(tc_Complex_Ocomplex, v_w____)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), v_k____))), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)))))))], (5842 ^ _257747) ^ [_461023, _461025] : [class_Fields_Olinordered__field(_461023), c_Orderings_Oord__class_Oless(_461023, c_Groups_Ozero__class_Ozero(_461023), _461025), c_Orderings_Oord__class_Oless(_461023, _461025, c_Groups_Oone__class_Oone(_461023)), -(c_Orderings_Oord__class_Oless(_461023, c_Groups_Oone__class_Oone(_461023), c_Rings_Oinverse__class_Oinverse(_461023, _461025)))], (11336 ^ _257747) ^ [] : [-(class_Groups_Ominus(tc_HOL_Obool))], (4285 ^ _257747) ^ [_405057, _405059, _405061] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _405057, _405059), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _405057, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _405061, _405059)))], (2141 ^ _257747) ^ [_328680, _328682, _328684, _328686] : [class_Rings_Olinordered__semiring__strict(_328680), c_Orderings_Oord__class_Oless(_328680, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_328680), _328682), _328684), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_328680), _328682), _328686)), c_Orderings_Oord__class_Oless__eq(_328680, c_Groups_Ozero__class_Ozero(_328680), _328682), -(c_Orderings_Oord__class_Oless(_328680, _328684, _328686))], (5961 ^ _257747) ^ [_464911, _464913] : [-(_464911 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _464911), _464913) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _464913, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _464911, c_Groups_Oone__class_Oone(tc_Nat_Onat))), _464913)))], (11240 ^ _257747) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (8179 ^ _257747) ^ [_544894, _544896] : [class_Rings_Ocomm__semiring__1(_544894), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_544894), c_Groups_Ozero__class_Ozero(_544894)), _544896) = c_Groups_Ozero__class_Ozero(_544894))], (8400 ^ _257747) ^ [_553761, _553763, _553765, _553767] : [class_Rings_Ocomm__semiring__0(_553761), -(hAPP(c_Polynomial_Opoly(_553761, c_Polynomial_Opcompose(_553761, _553763, _553765)), _553767) = hAPP(c_Polynomial_Opoly(_553761, _553763), hAPP(c_Polynomial_Opoly(_553761, _553765), _553767)))], (3266 ^ _257747) ^ [_367531, _367533, _367535, _367537, _367539] : [class_Rings_Olinordered__semiring__strict(_367531), c_Orderings_Oord__class_Oless(_367531, _367533, _367535), c_Orderings_Oord__class_Oless(_367531, _367537, _367539), c_Orderings_Oord__class_Oless__eq(_367531, c_Groups_Ozero__class_Ozero(_367531), _367533), c_Orderings_Oord__class_Oless__eq(_367531, c_Groups_Ozero__class_Ozero(_367531), _367537), -(c_Orderings_Oord__class_Oless(_367531, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_367531), _367533), _367537), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_367531), _367535), _367539)))], (3581 ^ _257747) ^ [_378383, _378385] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _378383), _378385), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _378383, _378385)))], (6880 ^ _257747) ^ [_499684, _499686, _499688, _499690] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_499684), 6883 ^ _257747 : [(6884 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_499684, c_Groups_Oplus__class_Oplus(_499684, _499686, _499688), c_Groups_Oplus__class_Oplus(_499684, _499686, _499690)), -(c_Orderings_Oord__class_Oless(_499684, _499688, _499690))], (6890 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_499684, _499688, _499690), -(c_Orderings_Oord__class_Oless(_499684, c_Groups_Oplus__class_Oplus(_499684, _499686, _499688), c_Groups_Oplus__class_Oplus(_499684, _499686, _499690)))]]], (302 ^ _257747) ^ [_267110, _267112] : [-(class_Rings_Olinordered__semiring__strict(_267110)), _267112 = _267110, class_Rings_Olinordered__semiring__strict(_267112)], (1685 ^ _257747) ^ [_313386, _313388, _313390] : [class_Rings_Olinordered__semidom(_313386), c_Orderings_Oord__class_Oless__eq(_313386, c_Groups_Ozero__class_Ozero(_313386), _313388), -(c_Orderings_Oord__class_Oless__eq(_313386, c_Groups_Ozero__class_Ozero(_313386), hAPP(hAPP(c_Power_Opower__class_Opower(_313386), _313388), _313390)))], (3635 ^ _257747) ^ [_380088, _380090] : [class_Rings_Odivision__ring__inverse__zero(_380088), 3638 ^ _257747 : [(3639 ^ _257747) ^ [] : [c_Rings_Oinverse__class_Oinverse(_380088, _380090) = c_Groups_Ozero__class_Ozero(_380088), -(_380090 = c_Groups_Ozero__class_Ozero(_380088))], (3645 ^ _257747) ^ [] : [_380090 = c_Groups_Ozero__class_Ozero(_380088), -(c_Rings_Oinverse__class_Oinverse(_380088, _380090) = c_Groups_Ozero__class_Ozero(_380088))]]], (11426 ^ _257747) ^ [] : [-(class_Groups_Oab__group__add(tc_RealDef_Oreal))], (11230 ^ _257747) ^ [] : [-(class_Groups_Ouminus(tc_Int_Oint))], (3346 ^ _257747) ^ [_370167, _370169, _370171, _370173] : [class_Rings_Olinordered__semiring__strict(_370167), c_Orderings_Oord__class_Oless(_370167, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_370167), _370169), _370171), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_370167), _370173), _370171)), c_Orderings_Oord__class_Oless__eq(_370167, c_Groups_Ozero__class_Ozero(_370167), _370171), -(c_Orderings_Oord__class_Oless(_370167, _370169, _370173))], (7264 ^ _257747) ^ [_512641, _512643, _512645] : [class_Groups_Oab__group__add(_512641), -(c_Groups_Ouminus__class_Ouminus(_512641, c_Groups_Oplus__class_Oplus(_512641, _512643, _512645)) = c_Groups_Oplus__class_Oplus(_512641, c_Groups_Ouminus__class_Ouminus(_512641, _512643), c_Groups_Ouminus__class_Ouminus(_512641, _512645)))], (8107 ^ _257747) ^ [_541214, _541216, _541218, _541220] : [class_Rings_Ocomm__semiring__1(_541214), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_541214), _541216), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_541214), _541218), _541220)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_541214), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_541214), _541216), _541218)), _541220))], (5888 ^ _257747) ^ [_462443, _462445, _462447, _462449] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _462443), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _462445), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _462445), _462447), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _462443), _462449)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, _462443)), _462447), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, _462445)), _462449)))], (7482 ^ _257747) ^ [_519769, _519771, _519773] : [class_Groups_Oordered__comm__monoid__add(_519769), c_Orderings_Oord__class_Oless(_519769, c_Groups_Ozero__class_Ozero(_519769), _519771), c_Orderings_Oord__class_Oless(_519769, c_Groups_Ozero__class_Ozero(_519769), _519773), -(c_Orderings_Oord__class_Oless(_519769, c_Groups_Ozero__class_Ozero(_519769), c_Groups_Oplus__class_Oplus(_519769, _519771, _519773)))], (3369 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)), c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, v_pa____)))], (4768 ^ _257747) ^ [_422321] : [-(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, _422321) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _422321))], (11322 ^ _257747) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (822 ^ _257747) ^ [_282450, _282452] : [-(class_Rings_Oidom(_282450)), _282452 = _282450, class_Rings_Oidom(_282452)], (5902 ^ _257747) ^ [_462955, _462957, _462959, _462961] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _462955), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _462957), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _462957), _462959), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _462955), _462961)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _462959), c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, _462955)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _462961), c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, _462957))))], (11416 ^ _257747) ^ [] : [-(class_Rings_Olinordered__idom(tc_RealDef_Oreal))], (8710 ^ _257747) ^ [_564750, _564752, _564754] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _564750, _564752), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _564754), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _564754), _564750), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _564754), _564752)))], (1913 ^ _257747) ^ [_320917, _320919] : [class_RealVector_Oreal__normed__vector(_320917), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_320917, _320919)))], (3587 ^ _257747) ^ [_378627, _378629, _378631] : [class_Rings_Odivision__ring(_378627), c_Rings_Oinverse__class_Oinverse(_378627, _378629) = c_Rings_Oinverse__class_Oinverse(_378627, _378631), -(_378629 = c_Groups_Ozero__class_Ozero(_378627)), -(_378631 = c_Groups_Ozero__class_Ozero(_378627)), -(_378629 = _378631)], (11694 ^ _257747) ^ [_663016] : [class_Rings_Ocomm__semiring__0(_663016), -(class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(_663016)))], (988 ^ _257747) ^ [_288683, _288685, _288687, _288689] : [-(c_Groups_Osgn__class_Osgn(_288689, _288685) = c_Groups_Osgn__class_Osgn(_288687, _288683)), _288689 = _288687, _288685 = _288683], (1465 ^ _257747) ^ [_305773, _305775] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _305773, _305775), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _305775, _305773), -(_305773 = _305775)], (512 ^ _257747) ^ [_273305, _273307] : [-(class_Rings_Oordered__ring__abs(_273305)), _273307 = _273305, class_Rings_Oordered__ring__abs(_273307)], (4331 ^ _257747) ^ [_406786, _406788] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _406786, _406788), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _406786, _406788))], (9444 ^ _257747) ^ [_589065, _589067, _589069, _589071] : [class_Orderings_Oorder(_589065), c_Orderings_Oord__class_Oless(_589065, _589067, _589069), c_Orderings_Oord__class_Oless(_589065, _589071, _589067), -(c_Orderings_Oord__class_Oless(_589065, _589071, _589069))], (10161 ^ _257747) ^ [_613513, _613515, _613517] : [class_Rings_Olinordered__idom(_613513), c_Polynomial_Opos__poly(_613513, _613515), c_Polynomial_Opos__poly(_613513, _613517), -(c_Polynomial_Opos__poly(_613513, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_613513), _613515, _613517)))], (10704 ^ _257747) ^ [_632770, _632772] : [class_Rings_Olinordered__idom(_632770), c_Orderings_Oord__class_Oless(_632770, c_Groups_Ozero__class_Ozero(_632770), _632772), -(c_Groups_Osgn__class_Osgn(_632770, _632772) = c_Groups_Oone__class_Oone(_632770))], (3967 ^ _257747) ^ [_393567, _393569, _393571] : [class_RealVector_Oreal__normed__vector(_393567), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_393567, _393569), c_RealVector_Onorm__class_Onorm(_393567, _393571)), c_RealVector_Onorm__class_Onorm(_393567, c_Groups_Oplus__class_Oplus(_393567, _393569, _393571))))], (8462 ^ _257747) ^ [_555922, _555924, _555926] : [class_Rings_Oidom(_555922), 8465 ^ _257747 : [(8476 ^ _257747) ^ [] : [8477 ^ _257747 : [(8478 ^ _257747) ^ [] : [_555924 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_555922))], (8480 ^ _257747) ^ [] : [-(c_Polynomial_Oorder(_555922, _555926, _555924) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], -(hAPP(c_Polynomial_Opoly(_555922, _555924), _555926) = c_Groups_Ozero__class_Ozero(_555922))], (8466 ^ _257747) ^ [] : [hAPP(c_Polynomial_Opoly(_555922, _555924), _555926) = c_Groups_Ozero__class_Ozero(_555922), -(_555924 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_555922))), c_Polynomial_Oorder(_555922, _555926, _555924) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (11390 ^ _257747) ^ [] : [-(class_Rings_Olinordered__semiring(tc_RealDef_Oreal))], (5750 ^ _257747) ^ [_458141, _458143, _458145] : [class_Fields_Olinordered__field(_458141), c_Orderings_Oord__class_Oless__eq(_458141, c_Rings_Oinverse__class_Oinverse(_458141, _458143), c_Rings_Oinverse__class_Oinverse(_458141, _458145)), c_Orderings_Oord__class_Oless(_458141, _458145, c_Groups_Ozero__class_Ozero(_458141)), -(c_Orderings_Oord__class_Oless__eq(_458141, _458145, _458143))], (8486 ^ _257747) ^ [_556666] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _556666), _556666) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (8006 ^ _257747) ^ [_537014, _537016, _537018] : [class_Rings_Ocomm__ring__1(_537014), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_537014), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_537014)), c_Polynomial_OpCons(_537014, c_Groups_Ouminus__class_Ouminus(_537014, _537016), c_Polynomial_OpCons(_537014, c_Groups_Oone__class_Oone(_537014), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_537014))))), c_Polynomial_Osynthetic__div(_537014, _537018, _537016)), c_Polynomial_OpCons(_537014, hAPP(c_Polynomial_Opoly(_537014, _537018), _537016), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_537014)))) = _537018)], (4703 ^ _257747) ^ [_420345] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, _420345), c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, v_pa____)), -(c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(tc_Complex_Ocomplex, _420345))), -(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, _420345), 4710 ^ [_420345]) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))], (932 ^ _257747) ^ [_286682, _286684, _286686, _286688, _286690, _286692] : [-(c_Power_Opower_Opower(_286692, _286688, _286684) = c_Power_Opower_Opower(_286690, _286686, _286682)), _286692 = _286690, _286688 = _286686, _286684 = _286682], (4502 ^ _257747) ^ [_413444, _413446] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _413444), _413446), 4505 ^ _257747 : [(4506 ^ _257747) ^ [] : [-(_413444 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (4508 ^ _257747) ^ [] : [-(_413446 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (3166 ^ _257747) ^ [_364161] : [class_Rings_Olinordered__semidom(_364161), c_Orderings_Oord__class_Oless__eq(_364161, c_Groups_Oone__class_Oone(_364161), c_Groups_Ozero__class_Ozero(_364161))], (9012 ^ _257747) ^ [_575384, _575386, _575388] : [class_Orderings_Oorder(_575384), 9015 ^ _257747 : [(9016 ^ _257747) ^ [] : [_575386 = _575388, 9019 ^ _257747 : [(9020 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_575384, _575386, _575388))], (9022 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_575384, _575388, _575386))]]], (9024 ^ _257747) ^ [] : [-(_575386 = _575388), c_Orderings_Oord__class_Oless__eq(_575384, _575386, _575388), c_Orderings_Oord__class_Oless__eq(_575384, _575388, _575386)]]], (11534 ^ _257747) ^ [] : [-(class_Groups_Omonoid__add(tc_Complex_Ocomplex))], (5426 ^ _257747) ^ [] : [-(c_RealVector_Oof__real(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))], (2316 ^ _257747) ^ [_335294, _335296, _335298] : [class_RealVector_Oreal__normed__algebra(_335294), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_335294), _335296), c_Groups_Ouminus__class_Ouminus(_335294, _335298)) = c_Groups_Ouminus__class_Ouminus(_335294, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_335294), _335296), _335298)))], (4466 ^ _257747) ^ [_412062, _412064, _412066] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _412062, _412064), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _412066), _412062), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _412066), _412064)))], (9430 ^ _257747) ^ [_588617, _588619, _588621, _588623] : [class_Orderings_Opreorder(_588617), c_Orderings_Oord__class_Oless(_588617, _588619, _588621), c_Orderings_Oord__class_Oless(_588617, _588621, _588623), -(c_Orderings_Oord__class_Oless(_588617, _588619, _588623))], (11538 ^ _257747) ^ [] : [-(class_Groups_Ogroup__add(tc_Complex_Ocomplex))], (4822 ^ _257747) ^ [_424481, _424483, _424485] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _424481, _424483), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _424481, _424485), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _424485, _424483), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _424485, _424481)))], (352 ^ _257747) ^ [_268585, _268587] : [-(class_Groups_Ocancel__ab__semigroup__add(_268585)), _268587 = _268585, class_Groups_Ocancel__ab__semigroup__add(_268587)], (11486 ^ _257747) ^ [] : [-(class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex))], (11450 ^ _257747) ^ [] : [-(class_Orderings_Oorder(tc_RealDef_Oreal))], (5316 ^ _257747) ^ [_442871, _442873, _442875, _442877, _442879] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _442871, _442873), -(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), _442871), _442875), _442877), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _442873), _442875), _442879)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _442877, 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, _442873, _442871)), _442875), _442879)))], (11396 ^ _257747) ^ [] : [-(class_Rings_Olinordered__semidom(tc_RealDef_Oreal))], (9590 ^ _257747) ^ [_593548, _593550, _593552] : [class_Orderings_Olinorder(_593548), -(c_Orderings_Oord__class_Oless(_593548, _593550, _593552)), -(c_Orderings_Oord__class_Oless__eq(_593548, _593552, _593550))], (6710 ^ _257747) ^ [_493760, _493762, _493764] : [class_Groups_Ogroup__add(_493760), 6713 ^ _257747 : [(6714 ^ _257747) ^ [] : [_493762 = c_Groups_Ouminus__class_Ouminus(_493760, _493764), -(_493764 = c_Groups_Ouminus__class_Ouminus(_493760, _493762))], (6720 ^ _257747) ^ [] : [_493764 = c_Groups_Ouminus__class_Ouminus(_493760, _493762), -(_493762 = c_Groups_Ouminus__class_Ouminus(_493760, _493764))]]], (4998 ^ _257747) ^ [_430914, _430916] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _430916, _430914), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _430914, _430916)))], (1409 ^ _257747) ^ [_303810, _303812, _303814] : [c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(_303810, _303812, _303814), 1412 ^ _257747 : [(1413 ^ _257747) ^ [_303957, _303959] : [-(hAPP(_303814, _303959) = hAPP(_303814, _303957))]]], (6542 ^ _257747) ^ [_488055, _488057] : [class_Groups_Oordered__ab__group__add__abs(_488055), c_Orderings_Oord__class_Oless(_488055, _488057, c_Groups_Ozero__class_Ozero(_488055)), -(c_Groups_Oabs__class_Oabs(_488055, _488057) = c_Groups_Ouminus__class_Ouminus(_488055, _488057))], (10281 ^ _257747) ^ [_617649, _617651] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _617649), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _617651), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _617649, _617651))], (7192 ^ _257747) ^ [_510099, _510101, _510103] : [class_Groups_Ogroup__add(_510099), -(c_Groups_Ominus__class_Ominus(_510099, c_Groups_Oplus__class_Oplus(_510099, _510101, _510103), _510103) = _510101)], (6033 ^ _257747) ^ [_467581, _467583, _467585] : [class_Rings_Olinordered__ring__strict(_467581), 6036 ^ _257747 : [(6047 ^ _257747) ^ [] : [6048 ^ _257747 : [(6049 ^ _257747) ^ [] : [-(_467583 = c_Groups_Ozero__class_Ozero(_467581))], (6051 ^ _257747) ^ [] : [-(_467585 = c_Groups_Ozero__class_Ozero(_467581))]], -(c_Orderings_Oord__class_Oless(_467581, c_Groups_Ozero__class_Ozero(_467581), c_Groups_Oplus__class_Oplus(_467581, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_467581), _467583), _467583), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_467581), _467585), _467585))))], (6037 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_467581, c_Groups_Ozero__class_Ozero(_467581), c_Groups_Oplus__class_Oplus(_467581, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_467581), _467583), _467583), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_467581), _467585), _467585))), _467583 = c_Groups_Ozero__class_Ozero(_467581), _467585 = c_Groups_Ozero__class_Ozero(_467581)]]], (8544 ^ _257747) ^ [_558968, _558970] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _558968, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _558970, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _558968, _558970)), -(_558968 = _558970)], (7408 ^ _257747) ^ [_517447, _517449, _517451, _517453] : [class_Groups_Oordered__comm__monoid__add(_517447), c_Orderings_Oord__class_Oless__eq(_517447, c_Groups_Ozero__class_Ozero(_517447), _517449), c_Orderings_Oord__class_Oless__eq(_517447, _517451, _517453), -(c_Orderings_Oord__class_Oless__eq(_517447, _517451, c_Groups_Oplus__class_Oplus(_517447, _517449, _517453)))], (7198 ^ _257747) ^ [_510343, _510345, _510347] : [class_Groups_Oordered__ab__group__add(_510343), 7201 ^ _257747 : [(7202 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_510343, _510345, c_Groups_Ouminus__class_Ouminus(_510343, _510347)), -(c_Orderings_Oord__class_Oless(_510343, _510347, c_Groups_Ouminus__class_Ouminus(_510343, _510345)))], (7208 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_510343, _510347, c_Groups_Ouminus__class_Ouminus(_510343, _510345)), -(c_Orderings_Oord__class_Oless(_510343, _510345, c_Groups_Ouminus__class_Ouminus(_510343, _510347)))]]], (9957 ^ _257747) ^ [_606297] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _606297, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_RComplete_Onatfloor(_606297) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3701 ^ _257747) ^ [_382790, _382792, _382794] : [class_RealVector_Oreal__normed__vector(_382790), -(c_RealVector_Onorm__class_Onorm(_382790, c_Groups_Ominus__class_Ominus(_382790, _382792, _382794)) = c_RealVector_Onorm__class_Onorm(_382790, c_Groups_Ominus__class_Ominus(_382790, _382794, _382792)))], (11254 ^ _257747) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (4892 ^ _257747) ^ [_426981, _426983] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _426981, _426983), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _426983, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _426983, _426981)) = _426981)], (2890 ^ _257747) ^ [_355091, _355093, _355095, _355097] : [class_Rings_Olinordered__ring__strict(_355091), 2893 ^ _257747 : [(2894 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_355091, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_355091), _355093), _355095), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_355091), _355097), _355095)), 2899 ^ _257747 : [(2900 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(_355091, c_Groups_Ozero__class_Ozero(_355091), _355095))], (2902 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(_355091, _355093, _355097))]], 2903 ^ _257747 : [(2904 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(_355091, _355095, c_Groups_Ozero__class_Ozero(_355091)))], (2906 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(_355091, _355097, _355093))]]], (2908 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(_355091, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_355091), _355093), _355095), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_355091), _355097), _355095))), 2909 ^ _257747 : [(2910 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_355091, c_Groups_Ozero__class_Ozero(_355091), _355095), c_Orderings_Oord__class_Oless(_355091, _355093, _355097)], (2916 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_355091, _355095, c_Groups_Ozero__class_Ozero(_355091)), c_Orderings_Oord__class_Oless(_355091, _355097, _355093)]]]]], (9116 ^ _257747) ^ [_578694, _578696, _578698, _578700] : [class_Orderings_Oorder(_578694), c_Orderings_Oord__class_Oless__eq(_578694, _578696, _578698), _578696 = _578700, -(c_Orderings_Oord__class_Oless__eq(_578694, _578700, _578698))], (11180 ^ _257747) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (9886 ^ _257747) ^ [_603277, _603279, _603281, _603283] : [class_RealVector_Oreal__normed__vector(_603277), class_Orderings_Oord(_603279), 9896 ^ _257747 : [(9897 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_603279, _603281, 9895 ^ [_603277, _603279, _603281, _603283]))], (9899 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_603277, c_Groups_Ominus__class_Ominus(_603277, hAPP(_603283, _603281), hAPP(_603283, 9895 ^ [_603277, _603279, _603281, _603283]))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))]], 9900 ^ _257747 : [(9901 ^ _257747) ^ [_603835] : [c_Orderings_Oord__class_Oless__eq(_603279, _603281, _603835), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_603277, hAPP(_603283, _603835)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_603277, hAPP(_603283, _603281)))))]]], (4 ^ _257747) ^ [_257978, _257980] : [_257980 = _257978, -(_257978 = _257980)], (11196 ^ _257747) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (11796 ^ _257747) ^ [_666246] : [class_Rings_Ocomm__semiring__1(_666246), -(class_Groups_Omonoid__mult(tc_Polynomial_Opoly(_666246)))], (4107 ^ _257747) ^ [_398714] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _398714, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (322 ^ _257747) ^ [_267700, _267702] : [-(class_Groups_Oordered__ab__group__add__abs(_267700)), _267702 = _267700, class_Groups_Oordered__ab__group__add__abs(_267702)], (11862 ^ _257747) ^ [_668336] : [class_Groups_Oab__group__add(_668336), -(class_Groups_Ouminus(tc_Polynomial_Opoly(_668336)))], (5546 ^ _257747) ^ [_451759, _451761] : [class_Fields_Ofield__inverse__zero(_451759), 5549 ^ _257747 : [(5550 ^ _257747) ^ [] : [c_Rings_Oinverse__class_Oinverse(_451759, _451761) = c_Groups_Oone__class_Oone(_451759), -(_451761 = c_Groups_Oone__class_Oone(_451759))], (5556 ^ _257747) ^ [] : [_451761 = c_Groups_Oone__class_Oone(_451759), -(c_Rings_Oinverse__class_Oinverse(_451759, _451761) = c_Groups_Oone__class_Oone(_451759))]]], (10424 ^ _257747) ^ [_622687, _622689] : [class_Orderings_Oorder(_622687), 10427 ^ _257747 : [(10438 ^ _257747) ^ [] : [10441 ^ _257747 : [(10442 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, 10439 ^ [_622687, _622689], 10440 ^ [_622687, _622689]))], (10444 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_622687, hAPP(_622689, 10440 ^ [_622687, _622689]), hAPP(_622689, 10439 ^ [_622687, _622689]))]], -(c_SEQ_Odecseq(_622687, _622689))], (10428 ^ _257747) ^ [] : [c_SEQ_Odecseq(_622687, _622689), 10431 ^ _257747 : [(10432 ^ _257747) ^ [_622963, _622965] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _622965, _622963), -(c_Orderings_Oord__class_Oless__eq(_622687, hAPP(_622689, _622963), hAPP(_622689, _622965)))]]]]], (2546 ^ _257747) ^ [_343870, _343872, _343874] : [class_Rings_Ono__zero__divisors(_343870), -(_343872 = c_Groups_Ozero__class_Ozero(_343870)), -(_343874 = c_Groups_Ozero__class_Ozero(_343870)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_343870), _343872), _343874) = c_Groups_Ozero__class_Ozero(_343870)], (2296 ^ _257747) ^ [_334520, _334522, _334524] : [class_RealVector_Oreal__normed__vector(_334520), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_334520, c_Groups_Oplus__class_Oplus(_334520, _334522, _334524)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_334520, _334522), c_RealVector_Onorm__class_Onorm(_334520, _334524))))], (5142 ^ _257747) ^ [_436223, _436225, _436227] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _436223, _436225), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _436227, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _436225, _436227), _436223)))], (3651 ^ _257747) ^ [_380553] : [class_Rings_Odivision__ring__inverse__zero(_380553), -(c_Rings_Oinverse__class_Oinverse(_380553, c_Groups_Ozero__class_Ozero(_380553)) = c_Groups_Ozero__class_Ozero(_380553))], (4390 ^ _257747) ^ [_408901, _408903, _408905] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _408901, _408903), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _408901, _408905)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _408903, _408905))], (1705 ^ _257747) ^ [_314070, _314072] : [class_Power_Opower(_314070), class_Rings_Osemiring__0(_314070), 1712 ^ _257747 : [(1713 ^ _257747) ^ [] : [_314072 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_314070), c_Groups_Ozero__class_Ozero(_314070)), _314072) = c_Groups_Oone__class_Oone(_314070))], (1719 ^ _257747) ^ [] : [-(_314072 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_314070), c_Groups_Ozero__class_Ozero(_314070)), _314072) = c_Groups_Ozero__class_Ozero(_314070))]]], (8656 ^ _257747) ^ [_563029, _563031] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _563029, _563031)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _563029, _563031), -(_563029 = _563031)], (392 ^ _257747) ^ [_269765, _269767] : [-(class_Rings_Oring__no__zero__divisors(_269765)), _269767 = _269765, class_Rings_Oring__no__zero__divisors(_269767)], (7308 ^ _257747) ^ [_514151, _514153] : [class_Groups_Oordered__ab__group__add__abs(_514151), -(c_Orderings_Oord__class_Oless__eq(_514151, _514153, c_Groups_Oabs__class_Oabs(_514151, _514153)))], (11512 ^ _257747) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex))], (1519 ^ _257747) ^ [_307677, _307679] : [class_RealVector_Oreal__normed__algebra(_307677), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_307677), _307679), c_Groups_Ozero__class_Ozero(_307677)) = c_Groups_Ozero__class_Ozero(_307677))], (11280 ^ _257747) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (11658 ^ _257747) ^ [_661876] : [class_Rings_Olinordered__idom(_661876), -(class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(_661876)))], (11212 ^ _257747) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (66 ^ _257747) ^ [_259992, _259994] : [-(class_Lattices_Oab__semigroup__idem__mult(_259992)), _259994 = _259992, class_Lattices_Oab__semigroup__idem__mult(_259994)], (7292 ^ _257747) ^ [_513604] : [class_Groups_Oordered__ab__group__add__abs(_513604), -(c_Groups_Oabs__class_Oabs(_513604, c_Groups_Ozero__class_Ozero(_513604)) = c_Groups_Ozero__class_Ozero(_513604))], (9925 ^ _257747) ^ [_605032, _605034] : [class_RealVector_Oreal__normed__algebra(_605032), 9929 ^ _257747 : [(9930 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 9928 ^ [_605032, _605034]))], (9932 ^ _257747) ^ [_605331] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_605032, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_605032), _605034), _605331)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_605032, _605331)), 9928 ^ [_605032, _605034])))]]], (4832 ^ _257747) ^ [_424811, _424813, _424815] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _424811, _424813), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _424815, _424813)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _424811, _424815))], (2222 ^ _257747) ^ [_331448, _331450, _331452] : [-(c_RealVector_Oof__real(_331448, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _331450, _331452)) = c_Groups_Oplus__class_Oplus(_331448, c_RealVector_Oof__real(_331448, _331450), c_RealVector_Oof__real(_331448, _331452))), class_RealVector_Oreal__algebra__1(_331448), class_RealVector_Oreal__normed__vector(_331448)], (5444 ^ _257747) ^ [_448207, _448209, _448211] : [class_Rings_Odivision__ring(_448207), -(_448209 = c_Groups_Ozero__class_Ozero(_448207)), -(_448211 = c_Groups_Ozero__class_Ozero(_448207)), -(c_Groups_Ominus__class_Ominus(_448207, c_Rings_Oinverse__class_Oinverse(_448207, _448209), c_Rings_Oinverse__class_Oinverse(_448207, _448211)) = c_Groups_Ouminus__class_Ouminus(_448207, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_448207), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_448207), c_Rings_Oinverse__class_Oinverse(_448207, _448209)), c_Groups_Ominus__class_Ominus(_448207, _448209, _448211))), c_Rings_Oinverse__class_Oinverse(_448207, _448211))))], (6511 ^ _257747) ^ [_486725, _486727, _486729, _486731] : [class_Rings_Ocomm__semiring__0(_486725), -(c_Polynomial_Osmult(_486725, _486727, c_Polynomial_OpCons(_486725, _486729, _486731)) = c_Polynomial_OpCons(_486725, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_486725), _486727), _486729), c_Polynomial_Osmult(_486725, _486727, _486731)))], (10101 ^ _257747) ^ [_611298] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _611298), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (7826 ^ _257747) ^ [_531101, _531103, _531105] : [class_Groups_Oordered__ab__group__add__abs(_531101), -(c_Orderings_Oord__class_Oless__eq(_531101, c_Groups_Ominus__class_Ominus(_531101, c_Groups_Oabs__class_Oabs(_531101, _531103), c_Groups_Oabs__class_Oabs(_531101, _531105)), c_Groups_Oabs__class_Oabs(_531101, c_Groups_Ominus__class_Ominus(_531101, _531103, _531105))))], (1725 ^ _257747) ^ [_314699, _314701, _314703, _314705] : [class_Rings_Olinordered__semidom(_314699), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _314701, _314703), c_Orderings_Oord__class_Oless__eq(_314699, c_Groups_Oone__class_Oone(_314699), _314705), -(c_Orderings_Oord__class_Oless__eq(_314699, hAPP(hAPP(c_Power_Opower__class_Opower(_314699), _314705), _314701), hAPP(hAPP(c_Power_Opower__class_Opower(_314699), _314705), _314703)))], (8958 ^ _257747) ^ [] : [-(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)))], (1531 ^ _257747) ^ [_308141, _308143] : [class_RealVector_Oreal__normed__algebra(_308141), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_308141), c_Groups_Ozero__class_Ozero(_308141)), _308143) = c_Groups_Ozero__class_Ozero(_308141))], (3681 ^ _257747) ^ [_381815, _381817, _381819, _381821] : [class_RealVector_Oreal__normed__algebra(_381815), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_381815), c_Groups_Ominus__class_Ominus(_381815, _381817, _381819)), _381821) = c_Groups_Ominus__class_Ominus(_381815, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_381815), _381817), _381821), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_381815), _381819), _381821)))], (472 ^ _257747) ^ [_272125, _272127] : [-(class_Groups_Oab__semigroup__mult(_272125)), _272127 = _272125, class_Groups_Oab__semigroup__mult(_272127)], (8768 ^ _257747) ^ [_567067, _567069, _567071] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _567067, _567069), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _567069, _567071), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _567067, _567071))], (11700 ^ _257747) ^ [_663206] : [class_Rings_Ocomm__semiring__1(_663206), -(class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(_663206)))], (3693 ^ _257747) ^ [_382439, _382441, _382443, _382445] : [class_RealVector_Oreal__normed__algebra(_382439), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_382439), _382441), c_Groups_Ominus__class_Ominus(_382439, _382443, _382445)) = c_Groups_Ominus__class_Ominus(_382439, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_382439), _382441), _382443), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_382439), _382441), _382445)))], (11874 ^ _257747) ^ [_668716] : [class_Rings_Olinordered__idom(_668716), -(class_Groups_Oabs__if(tc_Polynomial_Opoly(_668716)))], (5222 ^ _257747) ^ [_439209] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _439209, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _439209) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _439209))], (8359 ^ _257747) ^ [_552238, _552240, _552242, _552244] : [class_Rings_Ocomm__semiring__0(_552238), -(c_Polynomial_Opcompose(_552238, c_Polynomial_OpCons(_552238, _552240, _552242), _552244) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_552238), c_Polynomial_OpCons(_552238, _552240, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_552238))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_552238)), _552244), c_Polynomial_Opcompose(_552238, _552242, _552244))))], (8810 ^ _257747) ^ [_568546, _568548, _568550] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _568546), _568546 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _568548, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _568546), _568550)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _568548, _568546), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _568550))], (11742 ^ _257747) ^ [_664536] : [class_Rings_Olinordered__idom(_664536), -(class_Rings_Olinordered__idom(tc_Polynomial_Opoly(_664536)))], (9130 ^ _257747) ^ [_579126, _579128, _579130] : [class_Orderings_Oorder(_579126), c_Orderings_Oord__class_Oless__eq(_579126, _579128, _579130), c_Orderings_Oord__class_Oless__eq(_579126, _579130, _579128), -(_579128 = _579130)], (8444 ^ _257747) ^ [_555376] : [c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _555376) = 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, _555376, 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, _555376, 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, _555376, 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, _555376, c_Complex_Oii)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (11232 ^ _257747) ^ [] : [-(class_Groups_Osgn__if(tc_Int_Oint))], (5030 ^ _257747) ^ [_432114, _432116, _432118] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _432114, _432118), _432116), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _432114, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _432116, _432118)))], (432 ^ _257747) ^ [_270945, _270947] : [-(class_Groups_Ocancel__comm__monoid__add(_270945)), _270947 = _270945, class_Groups_Ocancel__comm__monoid__add(_270947)], (7682 ^ _257747) ^ [_526020, _526022] : [class_Groups_Ogroup__add(_526020), -(c_Groups_Oplus__class_Oplus(_526020, _526022, c_Groups_Ouminus__class_Ouminus(_526020, _526022)) = c_Groups_Ozero__class_Ozero(_526020))], (11288 ^ _257747) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (4674 ^ _257747) ^ [_419385, _419387, _419389] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _419385), _419387), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _419389), _419387)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _419387), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _419385, _419389))], (6738 ^ _257747) ^ [_494698, _494700] : [class_Groups_Omonoid__add(_494698), -(c_Groups_Oplus__class_Oplus(_494698, c_Groups_Ozero__class_Ozero(_494698), _494700) = _494700)], (11176 ^ _257747) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (11528 ^ _257747) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Complex_Ocomplex))], (3729 ^ _257747) ^ [_383910, _383912, _383914] : [class_Rings_Odivision__ring(_383910), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_383910), _383912), _383914) = c_Groups_Oone__class_Oone(_383910), -(c_Rings_Oinverse__class_Oinverse(_383910, _383912) = _383914)], (482 ^ _257747) ^ [_272420, _272422] : [-(class_Groups_Ocomm__monoid__mult(_272420)), _272422 = _272420, class_Groups_Ocomm__monoid__mult(_272422)], (5108 ^ _257747) ^ [_434967, _434969] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _434967, _434969), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _434969, _434967), _434967) = _434969)], (2688 ^ _257747) ^ [_348380, _348382, _348384] : [class_Rings_Oordered__cancel__semiring(_348380), c_Orderings_Oord__class_Oless__eq(_348380, c_Groups_Ozero__class_Ozero(_348380), _348382), c_Orderings_Oord__class_Oless__eq(_348380, _348384, c_Groups_Ozero__class_Ozero(_348380)), -(c_Orderings_Oord__class_Oless__eq(_348380, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_348380), _348384), _348382), c_Groups_Ozero__class_Ozero(_348380)))], (4321 ^ _257747) ^ [_406480, _406482] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _406480, _406482), -(_406480 = _406482), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _406480, _406482))], (10381 ^ _257747) ^ [_621045, _621047] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _621045), -(c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _621045, c_RealDef_Oreal(tc_Nat_Onat, _621047))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatceiling(_621045), _621047))], (11766 ^ _257747) ^ [_665296] : [class_Groups_Oab__group__add(_665296), -(class_Groups_Oab__group__add(tc_Polynomial_Opoly(_665296)))], (11352 ^ _257747) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal))], (4420 ^ _257747) ^ [_410089, _410091, _410093, _410095] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _410089, _410091), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _410093, _410095), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _410089, _410093), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _410091, _410095)))], (8682 ^ _257747) ^ [_563888] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _563888), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _563888))], (10509 ^ _257747) ^ [_626065, _626067] : [class_Lattices_Oab__semigroup__idem__mult(_626065), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_626065), _626067), _626067) = _626067)], (11506 ^ _257747) ^ [] : [-(class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex))], (3433 ^ _257747) ^ [_373062, _373064] : [-(c_RealVector_Onorm__class_Onorm(_373062, c_Rings_Oinverse__class_Oinverse(_373062, _373064)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_373062, _373064))), class_RealVector_Oreal__normed__div__algebra(_373062), class_Rings_Odivision__ring__inverse__zero(_373062)], (9937 ^ _257747) ^ [_605567] : [-(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, 9933 ^ []), _605567) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_c____, _605567)))], (11532 ^ _257747) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex))], (9270 ^ _257747) ^ [_583528, _583530, _583532] : [class_Orderings_Olinorder(_583528), -(c_Orderings_Oord__class_Oless(_583528, _583530, _583532)), 9277 ^ _257747 : [(9278 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(_583528, _583532, _583530)), -(_583532 = _583530)], (9284 ^ _257747) ^ [] : [_583532 = _583530, c_Orderings_Oord__class_Oless(_583528, _583532, _583530)]]], (8720 ^ _257747) ^ [] : [-(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (1667 ^ _257747) ^ [] : [c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)], (7918 ^ _257747) ^ [_534193, _534195, _534197, _534199] : [class_Groups_Oordered__comm__monoid__add(_534193), c_Orderings_Oord__class_Oless(_534193, c_Groups_Ozero__class_Ozero(_534193), _534195), c_Orderings_Oord__class_Oless__eq(_534193, _534197, _534199), -(c_Orderings_Oord__class_Oless(_534193, _534197, c_Groups_Oplus__class_Oplus(_534193, _534195, _534199)))], (3765 ^ _257747) ^ [_385349, _385351, _385353, _385355, _385357] : [class_RealVector_Oreal__normed__algebra(_385349), -(c_Groups_Ominus__class_Ominus(_385349, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_385349), _385351), _385353), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_385349), _385355), _385357)) = c_Groups_Oplus__class_Oplus(_385349, c_Groups_Oplus__class_Oplus(_385349, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_385349), c_Groups_Ominus__class_Ominus(_385349, _385351, _385355)), c_Groups_Ominus__class_Ominus(_385349, _385353, _385357)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_385349), c_Groups_Ominus__class_Ominus(_385349, _385351, _385355)), _385357)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_385349), _385355), c_Groups_Ominus__class_Ominus(_385349, _385353, _385357))))], (9865 ^ _257747) ^ [_602408] : [class_Power_Opower(_602408), -(c_Power_Opower__class_Opower(_602408) = c_Power_Opower_Opower(_602408, c_Groups_Oone__class_Oone(_602408), c_Groups_Otimes__class_Otimes(_602408)))], (11508 ^ _257747) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex))], (11174 ^ _257747) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (6065 ^ _257747) ^ [_468741, _468743, _468745, _468747] : [class_Rings_Olinordered__idom(_468741), 6068 ^ _257747 : [(6069 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_468741, c_Groups_Oabs__class_Oabs(_468741, c_Groups_Ominus__class_Ominus(_468741, _468743, _468745)), _468747), 6072 ^ _257747 : [(6073 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(_468741, c_Groups_Ominus__class_Ominus(_468741, _468745, _468747), _468743))], (6075 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(_468741, _468743, c_Groups_Oplus__class_Oplus(_468741, _468745, _468747)))]]], (6077 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(_468741, c_Groups_Oabs__class_Oabs(_468741, c_Groups_Ominus__class_Ominus(_468741, _468743, _468745)), _468747)), c_Orderings_Oord__class_Oless(_468741, c_Groups_Ominus__class_Ominus(_468741, _468745, _468747), _468743), c_Orderings_Oord__class_Oless(_468741, _468743, c_Groups_Oplus__class_Oplus(_468741, _468745, _468747))]]], (6916 ^ _257747) ^ [_500976, _500978, _500980, _500982, _500984] : [class_Groups_Oordered__cancel__ab__semigroup__add(_500976), c_Orderings_Oord__class_Oless(_500976, _500978, _500980), c_Orderings_Oord__class_Oless(_500976, _500982, _500984), -(c_Orderings_Oord__class_Oless(_500976, c_Groups_Oplus__class_Oplus(_500976, _500978, _500982), c_Groups_Oplus__class_Oplus(_500976, _500980, _500984)))], (10349 ^ _257747) ^ [_619929, _619931] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _619929), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _619929, c_RealDef_Oreal(tc_Nat_Onat, _619931)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_RComplete_Onatfloor(_619929), _619931))], (9839 ^ _257747) ^ [_601558, _601560] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _601558, _601560), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_601558), c_RComplete_Onatceiling(_601560)))], (5806 ^ _257747) ^ [_459871, _459873] : [class_Fields_Olinordered__field__inverse__zero(_459871), 5809 ^ _257747 : [(5820 ^ _257747) ^ [] : [5821 ^ _257747 : [(5822 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_459871, _459873, c_Groups_Ozero__class_Ozero(_459871))], (5824 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_459871, c_Groups_Oone__class_Oone(_459871), _459873)]], -(c_Orderings_Oord__class_Oless__eq(_459871, c_Rings_Oinverse__class_Oinverse(_459871, _459873), c_Groups_Oone__class_Oone(_459871)))], (5810 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_459871, c_Rings_Oinverse__class_Oinverse(_459871, _459873), c_Groups_Oone__class_Oone(_459871)), -(c_Orderings_Oord__class_Oless__eq(_459871, _459873, c_Groups_Ozero__class_Ozero(_459871))), -(c_Orderings_Oord__class_Oless__eq(_459871, c_Groups_Oone__class_Oone(_459871), _459873))]]], (6139 ^ _257747) ^ [_471751, _471753, _471755] : [class_Groups_Ozero(_471751), 6142 ^ _257747 : [(6143 ^ _257747) ^ [] : [c_Polynomial_Omonom(_471751, _471753, _471755) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_471751)), -(_471753 = c_Groups_Ozero__class_Ozero(_471751))], (6149 ^ _257747) ^ [] : [_471753 = c_Groups_Ozero__class_Ozero(_471751), -(c_Polynomial_Omonom(_471751, _471753, _471755) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_471751)))]]], (3949 ^ _257747) ^ [_392730, _392732] : [class_Rings_Oring__1(_392730), -(c_Groups_Ominus__class_Ominus(_392730, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_392730), _392732), _392732), c_Groups_Oone__class_Oone(_392730)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_392730), c_Groups_Oplus__class_Oplus(_392730, _392732, c_Groups_Oone__class_Oone(_392730))), c_Groups_Ominus__class_Ominus(_392730, _392732, c_Groups_Oone__class_Oone(_392730))))], (9568 ^ _257747) ^ [_592890, _592892, _592894] : [class_Orderings_Oorder(_592890), 9571 ^ _257747 : [(9582 ^ _257747) ^ [] : [9583 ^ _257747 : [(9584 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_592890, _592892, _592894)], (9586 ^ _257747) ^ [] : [_592892 = _592894]], -(c_Orderings_Oord__class_Oless__eq(_592890, _592892, _592894))], (9572 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_592890, _592892, _592894), -(c_Orderings_Oord__class_Oless(_592890, _592892, _592894)), -(_592892 = _592894)]]], (11152 ^ _257747) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (6994 ^ _257747) ^ [_503650, _503652, _503654, _503656, _503658] : [class_Groups_Oordered__ab__group__add(_503650), c_Groups_Ominus__class_Ominus(_503650, _503652, _503654) = c_Groups_Ominus__class_Ominus(_503650, _503656, _503658), 7001 ^ _257747 : [(7002 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_503650, _503652, _503654), -(c_Orderings_Oord__class_Oless__eq(_503650, _503656, _503658))], (7008 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_503650, _503656, _503658), -(c_Orderings_Oord__class_Oless__eq(_503650, _503652, _503654))]]], (5148 ^ _257747) ^ [_436502, _436504, _436506] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _436502, _436504), _436506), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _436502, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _436506, _436504)))], (7298 ^ _257747) ^ [_513834, _513836, _513838] : [class_Groups_Oordered__ab__group__add__abs(_513834), c_Orderings_Oord__class_Oless__eq(_513834, c_Groups_Oabs__class_Oabs(_513834, _513836), _513838), -(c_Orderings_Oord__class_Oless__eq(_513834, _513836, _513838))], (8536 ^ _257747) ^ [_558579, _558581] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _558579, _558581), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _558579, c_Groups_Oone__class_Oone(tc_Int_Oint)), _558581))], (6744 ^ _257747) ^ [_494918, _494920] : [class_Groups_Ocomm__monoid__add(_494918), -(c_Groups_Oplus__class_Oplus(_494918, c_Groups_Ozero__class_Ozero(_494918), _494920) = _494920)], (11488 ^ _257747) ^ [] : [-(class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex))], (4245 ^ _257747) ^ [_403497, _403499, _403501] : [4246 ^ _257747 : [(4247 ^ _257747) ^ [] : [_403497 = _403501], (4249 ^ _257747) ^ [] : [_403499 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _403497), _403499) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _403501), _403499))], (11190 ^ _257747) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (7326 ^ _257747) ^ [_514897, _514899] : [class_Groups_Oordered__ab__group__add__abs(_514897), -(c_Groups_Oabs__class_Oabs(_514897, c_Groups_Ouminus__class_Ouminus(_514897, _514899)) = c_Groups_Oabs__class_Oabs(_514897, _514899))], (8119 ^ _257747) ^ [_541838, _541840, _541842, _541844] : [class_Rings_Ocomm__semiring__1(_541838), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_541838), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_541838), _541840), _541842)), _541844) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_541838), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_541838), _541840), _541844)), _541842))], (11548 ^ _257747) ^ [] : [-(class_Groups_Ouminus(tc_Complex_Ocomplex))], (11246 ^ _257747) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (2560 ^ _257747) ^ [_344319, _344321, _344323] : [class_Rings_Ono__zero__divisors(_344319), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_344319), _344321), _344323) = c_Groups_Ozero__class_Ozero(_344319), -(_344321 = c_Groups_Ozero__class_Ozero(_344319)), -(_344323 = c_Groups_Ozero__class_Ozero(_344319))], (6387 ^ _257747) ^ [_482120, _482122, _482124, _482126] : [class_Rings_Ocomm__ring(_482120), -(c_Polynomial_Osmult(_482120, c_Groups_Ominus__class_Ominus(_482120, _482122, _482124), _482126) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_482120), c_Polynomial_Osmult(_482120, _482122, _482126), c_Polynomial_Osmult(_482120, _482124, _482126)))], (1026 ^ _257747) ^ [_290074, _290076, _290078, _290080] : [-(c_Groups_Ouminus__class_Ouminus(_290080, _290076) = c_Groups_Ouminus__class_Ouminus(_290078, _290074)), _290080 = _290078, _290076 = _290074], (402 ^ _257747) ^ [_270060, _270062] : [-(class_Rings_Oordered__comm__semiring(_270060)), _270062 = _270060, class_Rings_Oordered__comm__semiring(_270062)], (10019 ^ _257747) ^ [_608455, _608457, _608459] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _608455, _608457), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _608455, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _608457, _608459)))], (11470 ^ _257747) ^ [] : [-(class_Power_Opower(tc_RealDef_Oreal))], (3487 ^ _257747) ^ [_374929, _374931, _374933] : [class_RealVector_Oreal__algebra__1(_374929), -(c_RealVector_Oof__real(_374929, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _374931, _374933)) = c_Groups_Ominus__class_Ominus(_374929, c_RealVector_Oof__real(_374929, _374931), c_RealVector_Oof__real(_374929, _374933)))], (4115 ^ _257747) ^ [_398998] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _398998), _398998 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (7832 ^ _257747) ^ [_531365, _531367, _531369] : [class_Groups_Oordered__ab__group__add__abs(_531365), -(c_Orderings_Oord__class_Oless__eq(_531365, c_Groups_Ominus__class_Ominus(_531365, c_Groups_Oabs__class_Oabs(_531365, _531367), c_Groups_Oabs__class_Oabs(_531365, _531369)), c_Groups_Oabs__class_Oabs(_531365, c_Groups_Ominus__class_Ominus(_531365, _531369, _531367))))], (11688 ^ _257747) ^ [_662826] : [class_Rings_Olinordered__idom(_662826), -(class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(_662826)))], (10159 ^ _257747) ^ [] : [-(c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (5932 ^ _257747) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, v_pa____) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), 5935 ^ [])), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (8494 ^ _257747) ^ [_556971] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _556971, 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), _556971), _556971), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (9658 ^ _257747) ^ [_595635, _595637, _595639] : [class_Orderings_Olinorder(_595635), c_Orderings_Oord__class_Oless__eq(_595635, _595637, _595639), c_Orderings_Oord__class_Oless(_595635, _595639, _595637)], (9172 ^ _257747) ^ [_580424, _580426, _580428, _580430] : [class_Orderings_Oorder(_580424), c_Orderings_Oord__class_Oless__eq(_580424, _580426, _580428), c_Orderings_Oord__class_Oless__eq(_580424, _580430, _580426), -(c_Orderings_Oord__class_Oless__eq(_580424, _580430, _580428))], (11208 ^ _257747) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (10698 ^ _257747) ^ [_632538, _632540] : [class_RealVector_Oreal__normed__vector(_632538), -(c_Groups_Osgn__class_Osgn(_632538, c_Groups_Ouminus__class_Ouminus(_632538, _632540)) = c_Groups_Ouminus__class_Ouminus(_632538, c_Groups_Osgn__class_Osgn(_632538, _632540)))], (5400 ^ _257747) ^ [_446573, _446575, _446577, _446579, _446581] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _446573, _446575), 5403 ^ _257747 : [(5404 ^ _257747) ^ [] : [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), _446575), _446577), _446579), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _446573), _446577), _446581)), -(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, _446575, _446573)), _446577), _446579), _446581))], (5410 ^ _257747) ^ [] : [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, _446575, _446573)), _446577), _446579), _446581), -(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), _446575), _446577), _446579), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _446573), _446577), _446581)))]]], (11664 ^ _257747) ^ [_662066] : [class_Rings_Olinordered__idom(_662066), -(class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(_662066)))], (2238 ^ _257747) ^ [_332063, _332065, _332067] : [class_Rings_Oring(_332063), -(c_Groups_Ouminus__class_Ouminus(_332063, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_332063), _332065), _332067)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_332063), _332065), c_Groups_Ouminus__class_Ouminus(_332063, _332067)))], (1651 ^ _257747) ^ [_312240, _312242, _312244] : [-(_312240 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 1654 ^ _257747 : [(1655 ^ _257747) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _312242), _312240) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _312244), _312240), -(_312242 = _312244)], (1661 ^ _257747) ^ [] : [_312242 = _312244, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _312242), _312240) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _312244), _312240))]]], (2171 ^ _257747) ^ [_329643] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____), v_c____)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____), _329643))))], (1609 ^ _257747) ^ [_310828, _310830] : [1610 ^ _257747 : [(1611 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _310828, _310830)], (1613 ^ _257747) ^ [] : [_310828 = _310830]], -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _310828, _310830))], (2440 ^ _257747) ^ [_340256, _340258, _340260, _340262, _340264, _340266] : [class_Rings_Olinordered__semiring__1(_340256), c_Orderings_Oord__class_Oless__eq(_340256, _340258, _340260), c_Orderings_Oord__class_Oless__eq(_340256, _340262, _340260), c_Orderings_Oord__class_Oless__eq(_340256, c_Groups_Ozero__class_Ozero(_340256), _340264), c_Orderings_Oord__class_Oless__eq(_340256, c_Groups_Ozero__class_Ozero(_340256), _340266), c_Groups_Oplus__class_Oplus(_340256, _340264, _340266) = c_Groups_Oone__class_Oone(_340256), -(c_Orderings_Oord__class_Oless__eq(_340256, c_Groups_Oplus__class_Oplus(_340256, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_340256), _340264), _340258), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_340256), _340266), _340262)), _340260))], (4259 ^ _257747) ^ [_404085, _404087, _404089, _404091] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _404085, _404087), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _404089, _404087) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _404085, _404091), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _404089, _404091))], (4646 ^ _257747) ^ [_418371, _418373] : [_418371 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _418371), _418373), -(_418373 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_418371 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8394 ^ _257747) ^ [_553501, _553503] : [class_Rings_Ocomm__semiring__0(_553501), -(c_Polynomial_Opcompose(_553501, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_553501)), _553503) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_553501)))], (6309 ^ _257747) ^ [_478396, _478398, _478400, _478402] : [class_Rings_Ocomm__semiring__0(_478396), -(hAPP(c_Polynomial_Opoly(_478396, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_478396)), _478398), _478400)), _478402) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_478396), hAPP(c_Polynomial_Opoly(_478396, _478398), _478402)), hAPP(c_Polynomial_Opoly(_478396, _478400), _478402)))], (11546 ^ _257747) ^ [] : [-(class_Rings_Osemiring(tc_Complex_Ocomplex))], (1919 ^ _257747) ^ [_321133, _321135] : [class_RealVector_Oreal__normed__vector(_321133), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_321133, _321135), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (10365 ^ _257747) ^ [_620486, _620488] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatfloor(_620486), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _620488), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _620486, c_RealDef_Oreal(tc_Nat_Onat, _620488)))], (1485 ^ _257747) ^ [_306405, _306407] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _306405, _306407)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _306407, _306405))], (11132 ^ _257747) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (10756 ^ _257747) ^ [_634375, _634377] : [class_Groups_Osgn__if(_634375), 10759 ^ _257747 : [(10760 ^ _257747) ^ [] : [_634377 = c_Groups_Ozero__class_Ozero(_634375), -(c_Groups_Osgn__class_Osgn(_634375, _634377) = c_Groups_Ozero__class_Ozero(_634375))], (10766 ^ _257747) ^ [] : [-(_634377 = c_Groups_Ozero__class_Ozero(_634375)), 10769 ^ _257747 : [(10770 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_634375, c_Groups_Ozero__class_Ozero(_634375), _634377), -(c_Groups_Osgn__class_Osgn(_634375, _634377) = c_Groups_Oone__class_Oone(_634375))], (10776 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(_634375, c_Groups_Ozero__class_Ozero(_634375), _634377)), -(c_Groups_Osgn__class_Osgn(_634375, _634377) = c_Groups_Ouminus__class_Ouminus(_634375, c_Groups_Oone__class_Oone(_634375)))]]]]], (1140 ^ _257747) ^ [_294228, _294230, _294232, _294234] : [-(c_RealVector_Oof__real(_294234, _294230) = c_RealVector_Oof__real(_294232, _294228)), _294234 = _294232, _294230 = _294228], (11380 ^ _257747) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal))], (192 ^ _257747) ^ [_263865, _263867] : [-(class_RealVector_Oreal__normed__vector(_263865)), _263867 = _263865, class_RealVector_Oreal__normed__vector(_263867)], (9963 ^ _257747) ^ [_606522] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), c_RComplete_Onatfloor(_606522)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _606522))], (5200 ^ _257747) ^ [_438473, _438475, _438477] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _438473, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _438475), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _438473), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _438477))), -(_438475 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (5526 ^ _257747) ^ [_450836, _450838, _450840] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _450836, _450838), _450840) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _450836, _450840), _450838))], (4279 ^ _257747) ^ [_404807, _404809, _404811] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _404807, _404809), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _404807, _404811), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _404809, _404811)))], (10335 ^ _257747) ^ [_619345, _619347] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _619345), _619347), -(c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _619347, c_RealDef_Oreal(tc_Nat_Onat, _619345))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_RComplete_Onatfloor(_619347), _619345))], (1150 ^ _257747) ^ [_294559, _294561] : [_294561 = _294559, -(c_Groups_Otimes__class_Otimes(_294561) = c_Groups_Otimes__class_Otimes(_294559))], (3204 ^ _257747) ^ [_365445, _365447, _365449, _365451] : [class_Rings_Olinordered__ring__strict(_365445), c_Orderings_Oord__class_Oless(_365445, c_Groups_Ozero__class_Ozero(_365445), _365447), 3211 ^ _257747 : [(3212 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_365445, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_365445), _365447), _365449), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_365445), _365447), _365451)), -(c_Orderings_Oord__class_Oless__eq(_365445, _365449, _365451))], (3218 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_365445, _365449, _365451), -(c_Orderings_Oord__class_Oless__eq(_365445, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_365445), _365447), _365449), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_365445), _365447), _365451)))]]], (11096 ^ _257747) ^ [_646214, _646216] : [class_Lattices_Oboolean__algebra(_646214), -(class_Lattices_Oboolean__algebra(tc_fun(_646216, _646214)))], (3675 ^ _257747) ^ [_381503, _381505, _381507, _381509] : [class_RealVector_Oreal__normed__algebra(_381503), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_381503), c_Groups_Ominus__class_Ominus(_381503, _381505, _381507)), _381509) = c_Groups_Ominus__class_Ominus(_381503, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_381503), _381505), _381509), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_381503), _381507), _381509)))], (11220 ^ _257747) ^ [] : [-(class_Rings_Ocomm__ring(tc_Int_Oint))], (11334 ^ _257747) ^ [] : [-(class_Groups_Ouminus(tc_HOL_Obool))], (4695 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, 4691 ^ [], c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (11242 ^ _257747) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (7814 ^ _257747) ^ [_530567, _530569, _530571] : [class_Groups_Oordered__ab__group__add__abs(_530567), -(c_Orderings_Oord__class_Oless__eq(_530567, c_Groups_Oabs__class_Oabs(_530567, c_Groups_Oplus__class_Oplus(_530567, _530569, _530571)), c_Groups_Oplus__class_Oplus(_530567, c_Groups_Oabs__class_Oabs(_530567, _530569), c_Groups_Oabs__class_Oabs(_530567, _530571))))], (5568 ^ _257747) ^ [_452470, _452472] : [class_Fields_Olinordered__field__inverse__zero(_452470), 5571 ^ _257747 : [(5572 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_452470, c_Rings_Oinverse__class_Oinverse(_452470, _452472), c_Groups_Ozero__class_Ozero(_452470)), -(c_Orderings_Oord__class_Oless__eq(_452470, _452472, c_Groups_Ozero__class_Ozero(_452470)))], (5578 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_452470, _452472, c_Groups_Ozero__class_Ozero(_452470)), -(c_Orderings_Oord__class_Oless__eq(_452470, c_Rings_Oinverse__class_Oinverse(_452470, _452472), c_Groups_Ozero__class_Ozero(_452470)))]]], (10938 ^ _257747) ^ [_640911, _640913] : [class_Rings_Ocomm__semiring__1(_640911), -(c_Rings_Odvd__class_Odvd(_640911, c_Groups_Oone__class_Oone(_640911), _640913))], (11724 ^ _257747) ^ [_663966] : [class_Rings_Oidom(_663966), -(class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(_663966)))], (5136 ^ _257747) ^ [_435981, _435983] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _435981, _435983), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _435981, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _435983, _435981)) = _435983)], (7754 ^ _257747) ^ [_528480, _528482] : [class_Groups_Oordered__ab__group__add__abs(_528480), c_Orderings_Oord__class_Oless__eq(_528480, c_Groups_Ozero__class_Ozero(_528480), _528482), -(c_Groups_Oabs__class_Oabs(_528480, _528482) = _528482)], (8726 ^ _257747) ^ [] : [c_Complex_Oii = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)], (6339 ^ _257747) ^ [_479866, _479868, _479870] : [class_Rings_Ocomm__ring(_479866), -(hAPP(c_Polynomial_Opoly(_479866, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_479866), _479868)), _479870) = c_Groups_Ouminus__class_Ouminus(_479866, hAPP(c_Polynomial_Opoly(_479866, _479868), _479870)))], (10195 ^ _257747) ^ [_614609, _614611] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _614609, _614611), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _614609), c_RealDef_Oreal(tc_Nat_Onat, _614611)))], (542 ^ _257747) ^ [_274190, _274192] : [-(class_Rings_Ocomm__semiring(_274190)), _274192 = _274190, class_Rings_Ocomm__semiring(_274192)], (8299 ^ _257747) ^ [_549746, _549748, _549750, _549752] : [class_Rings_Ocomm__semiring__1(_549746), -(hAPP(hAPP(c_Power_Opower__class_Opower(_549746), hAPP(hAPP(c_Power_Opower__class_Opower(_549746), _549748), _549750)), _549752) = hAPP(hAPP(c_Power_Opower__class_Opower(_549746), _549748), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _549750), _549752)))], (2127 ^ _257747) ^ [_328196, _328198, _328200, _328202] : [class_Rings_Olinordered__semiring__strict(_328196), c_Orderings_Oord__class_Oless__eq(_328196, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_328196), _328198), _328200), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_328196), _328202), _328200)), c_Orderings_Oord__class_Oless(_328196, c_Groups_Ozero__class_Ozero(_328196), _328200), -(c_Orderings_Oord__class_Oless__eq(_328196, _328198, _328202))], (6552 ^ _257747) ^ [_488370, _488372] : [class_Groups_Ozero(_488370), 6555 ^ _257747 : [(6556 ^ _257747) ^ [] : [c_Groups_Ozero__class_Ozero(_488370) = _488372, -(_488372 = c_Groups_Ozero__class_Ozero(_488370))], (6562 ^ _257747) ^ [] : [_488372 = c_Groups_Ozero__class_Ozero(_488370), -(c_Groups_Ozero__class_Ozero(_488370) = _488372)]]], (2023 ^ _257747) ^ [_324825, _324827, _324829, _324831] : [class_Rings_Olinordered__semidom(_324825), c_Orderings_Oord__class_Oless(_324825, c_Groups_Oone__class_Oone(_324825), _324827), c_Orderings_Oord__class_Oless__eq(_324825, hAPP(hAPP(c_Power_Opower__class_Opower(_324825), _324827), _324829), hAPP(hAPP(c_Power_Opower__class_Opower(_324825), _324827), _324831)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _324829, _324831))], (4199 ^ _257747) ^ [_401917, _401919, _401921] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _401917), _401919) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _401917), _401921), -(_401917 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_401919 = _401921)], (1218 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 1216 ^ []))], (4930 ^ _257747) ^ [_428626, _428628, _428630] : [class_Rings_Olinordered__idom(_428626), 4933 ^ _257747 : [(4934 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_428626, c_Groups_Oabs__class_Oabs(_428626, _428628), _428630), 4937 ^ _257747 : [(4938 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(_428626, _428628, _428630))], (4940 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(_428626, c_Groups_Ouminus__class_Ouminus(_428626, _428628), _428630))]]], (4942 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(_428626, c_Groups_Oabs__class_Oabs(_428626, _428628), _428630)), c_Orderings_Oord__class_Oless(_428626, _428628, _428630), c_Orderings_Oord__class_Oless(_428626, c_Groups_Ouminus__class_Ouminus(_428626, _428628), _428630)]]], (10596 ^ _257747) ^ [_629003, _629005] : [class_Rings_Olinordered__idom(_629003), 10599 ^ _257747 : [(10600 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_629003, c_Groups_Ozero__class_Ozero(_629003), c_Groups_Osgn__class_Osgn(_629003, _629005)), -(c_Orderings_Oord__class_Oless(_629003, c_Groups_Ozero__class_Ozero(_629003), _629005))], (10606 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_629003, c_Groups_Ozero__class_Ozero(_629003), _629005), -(c_Orderings_Oord__class_Oless(_629003, c_Groups_Ozero__class_Ozero(_629003), c_Groups_Osgn__class_Osgn(_629003, _629005)))]]], (2358 ^ _257747) ^ [_337332, _337334, _337336, _337338] : [class_RealVector_Oreal__normed__algebra(_337332), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_337332), c_Groups_Oplus__class_Oplus(_337332, _337334, _337336)), _337338) = c_Groups_Oplus__class_Oplus(_337332, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_337332), _337334), _337338), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_337332), _337336), _337338)))], (11342 ^ _257747) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal))], (7314 ^ _257747) ^ [_514381, _514383, _514385] : [class_Groups_Oordered__ab__group__add__abs(_514381), -(c_Groups_Oabs__class_Oabs(_514381, c_Groups_Oplus__class_Oplus(_514381, c_Groups_Oabs__class_Oabs(_514381, _514383), c_Groups_Oabs__class_Oabs(_514381, _514385))) = c_Groups_Oplus__class_Oplus(_514381, c_Groups_Oabs__class_Oabs(_514381, _514383), c_Groups_Oabs__class_Oabs(_514381, _514385)))], (3493 ^ _257747) ^ [_375191, _375193, _375195] : [class_Rings_Odivision__ring(_375191), -(_375193 = c_Groups_Ozero__class_Ozero(_375191)), -(_375195 = c_Groups_Ozero__class_Ozero(_375191)), -(c_Groups_Ominus__class_Ominus(_375191, c_Rings_Oinverse__class_Oinverse(_375191, _375193), c_Rings_Oinverse__class_Oinverse(_375191, _375195)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_375191), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_375191), c_Rings_Oinverse__class_Oinverse(_375191, _375193)), c_Groups_Ominus__class_Ominus(_375191, _375195, _375193))), c_Rings_Oinverse__class_Oinverse(_375191, _375195)))], (5778 ^ _257747) ^ [_459013, _459015, _459017] : [class_Fields_Olinordered__field(_459013), c_Orderings_Oord__class_Oless__eq(_459013, _459015, _459017), c_Orderings_Oord__class_Oless(_459013, _459017, c_Groups_Ozero__class_Ozero(_459013)), -(c_Orderings_Oord__class_Oless__eq(_459013, c_Rings_Oinverse__class_Oinverse(_459013, _459017), c_Rings_Oinverse__class_Oinverse(_459013, _459015)))], (11294 ^ _257747) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (6820 ^ _257747) ^ [_497549, _497551, _497553, _497555] : [class_Groups_Oordered__ab__semigroup__add(_497549), c_Orderings_Oord__class_Oless__eq(_497549, _497551, _497553), -(c_Orderings_Oord__class_Oless__eq(_497549, c_Groups_Oplus__class_Oplus(_497549, _497555, _497551), c_Groups_Oplus__class_Oplus(_497549, _497555, _497553)))], (11442 ^ _257747) ^ [] : [-(class_Rings_Osemiring__0(tc_RealDef_Oreal))], (11172 ^ _257747) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (11364 ^ _257747) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal))], (7040 ^ _257747) ^ [_505178, _505180] : [class_Groups_Ocomm__monoid__mult(_505178), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_505178), c_Groups_Oone__class_Oone(_505178)), _505180) = _505180)], (11238 ^ _257747) ^ [] : [-(class_Groups_Ominus(tc_Int_Oint))], (4456 ^ _257747) ^ [_411699, _411701, _411703, _411705] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _411699, _411701), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _411703, _411705), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _411699), _411703), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _411701), _411705)))], (10129 ^ _257747) ^ [_612358] : [-(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _612358)) = c_RealDef_Oreal(tc_Nat_Onat, _612358))], (11522 ^ _257747) ^ [] : [-(class_Rings_Odivision__ring(tc_Complex_Ocomplex))], (972 ^ _257747) ^ [_288078, _288080] : [_288080 = _288078, -(c_RComplete_Onatceiling(_288080) = c_RComplete_Onatceiling(_288078))], (11158 ^ _257747) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (2884 ^ _257747) ^ [_354832, _354834] : [class_Rings_Olinordered__ring(_354832), c_Orderings_Oord__class_Oless(_354832, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_354832), _354834), _354834), c_Groups_Ozero__class_Ozero(_354832))], (6121 ^ _257747) ^ [_470909, _470911, _470913, _470915] : [class_Groups_Oab__group__add(_470909), -(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_470909), c_Polynomial_Omonom(_470909, _470911, _470913), c_Polynomial_Omonom(_470909, _470915, _470913)) = c_Polynomial_Omonom(_470909, c_Groups_Ominus__class_Ominus(_470909, _470911, _470915), _470913))], (1763 ^ _257747) ^ [_316016, _316018, _316020, _316022] : [class_Rings_Olinordered__semidom(_316016), c_Orderings_Oord__class_Oless(_316016, c_Groups_Oone__class_Oone(_316016), _316018), c_Orderings_Oord__class_Oless(_316016, hAPP(hAPP(c_Power_Opower__class_Opower(_316016), _316018), _316020), hAPP(hAPP(c_Power_Opower__class_Opower(_316016), _316018), _316022)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _316020, _316022))], (2580 ^ _257747) ^ [_344931] : [class_Rings_Ozero__neq__one(_344931), c_Groups_Ozero__class_Ozero(_344931) = c_Groups_Oone__class_Oone(_344931)], (2512 ^ _257747) ^ [_342698, _342700] : [class_Rings_Omult__zero(_342698), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_342698), c_Groups_Ozero__class_Ozero(_342698)), _342700) = c_Groups_Ozero__class_Ozero(_342698))], (11504 ^ _257747) ^ [] : [-(class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex))], (4337 ^ _257747) ^ [_407029, _407031] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _407029, _407031), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _407029, _407031)), -(_407029 = _407031)], (10341 ^ _257747) ^ [_619564] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _619564, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatfloor(_619564))))], (11168 ^ _257747) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (3669 ^ _257747) ^ [_381217, _381219, _381221] : [class_Rings_Odivision__ring__inverse__zero(_381217), -(c_Rings_Oinverse__class_Oinverse(_381217, hAPP(hAPP(c_Power_Opower__class_Opower(_381217), _381219), _381221)) = hAPP(hAPP(c_Power_Opower__class_Opower(_381217), c_Rings_Oinverse__class_Oinverse(_381217, _381219)), _381221))], (10245 ^ _257747) ^ [_616334, _616336] : [_616334 = c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatfloor(_616334)), -(c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _616334), _616336)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_RComplete_Onatfloor(_616334)), _616336))], (11270 ^ _257747) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (242 ^ _257747) ^ [_265340, _265342] : [-(class_Fields_Ofield(_265340)), _265342 = _265340, class_Fields_Ofield(_265342)], (8341 ^ _257747) ^ [_551454, _551456, _551458] : [class_Rings_Ocomm__semiring__1(_551454), -(c_Groups_Oplus__class_Oplus(_551454, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_551454), _551456), _551458), _551458) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_551454), c_Groups_Oplus__class_Oplus(_551454, _551456, c_Groups_Oone__class_Oone(_551454))), _551458))], (562 ^ _257747) ^ [_274780, _274782] : [-(class_Rings_Oordered__ring(_274780)), _274782 = _274780, class_Rings_Oordered__ring(_274782)], (7230 ^ _257747) ^ [_511367, _511369, _511371] : [class_Groups_Oordered__ab__group__add(_511367), 7233 ^ _257747 : [(7234 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_511367, c_Groups_Ouminus__class_Ouminus(_511367, _511369), c_Groups_Ouminus__class_Ouminus(_511367, _511371)), -(c_Orderings_Oord__class_Oless(_511367, _511371, _511369))], (7240 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_511367, _511371, _511369), -(c_Orderings_Oord__class_Oless(_511367, c_Groups_Ouminus__class_Ouminus(_511367, _511369), c_Groups_Ouminus__class_Ouminus(_511367, _511371)))]]], (8620 ^ _257747) ^ [_561725] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oabs__class_Oabs(tc_Int_Oint, _561725), c_Groups_Oone__class_Oone(tc_Int_Oint)), -(_561725 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (4043 ^ _257747) ^ [_396317, _396319, _396321] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _396317, _396319), _396321) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _396317, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _396319, _396321)))], (11258 ^ _257747) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (11856 ^ _257747) ^ [_668146] : [class_Rings_Olinordered__idom(_668146), -(class_Orderings_Oord(tc_Polynomial_Opoly(_668146)))], (1695 ^ _257747) ^ [_313735, _313737, _313739] : [class_Rings_Olinordered__semidom(_313735), c_Orderings_Oord__class_Oless(_313735, c_Groups_Ozero__class_Ozero(_313735), _313737), -(c_Orderings_Oord__class_Oless(_313735, c_Groups_Ozero__class_Ozero(_313735), hAPP(hAPP(c_Power_Opower__class_Opower(_313735), _313737), _313739)))], (10640 ^ _257747) ^ [_630425] : [class_RealVector_Oreal__normed__vector(_630425), -(c_Groups_Osgn__class_Osgn(_630425, c_Groups_Ozero__class_Ozero(_630425)) = c_Groups_Ozero__class_Ozero(_630425))], (9186 ^ _257747) ^ [_580886, _580888, _580890, _580892, _580894] : [class_Orderings_Oord(_580886), c_Orderings_Oord__class_Oless__eq(tc_fun(_580888, _580886), _580890, _580892), -(c_Orderings_Oord__class_Oless__eq(_580886, hAPP(_580890, _580894), hAPP(_580892, _580894)))], (8311 ^ _257747) ^ [_550306, _550308, _550310, _550312, _550314, _550316] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_550306), -(_550308 = c_Groups_Ozero__class_Ozero(_550306)), c_Groups_Oplus__class_Oplus(_550306, _550310, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_550306), _550308), _550314)) = c_Groups_Oplus__class_Oplus(_550306, _550312, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_550306), _550308), _550316)), _550310 = _550312, -(_550314 = _550316)], (8143 ^ _257747) ^ [_543256, _543258, _543260, _543262, _543264] : [class_Rings_Ocomm__semiring__1(_543256), -(c_Groups_Oplus__class_Oplus(_543256, c_Groups_Oplus__class_Oplus(_543256, _543258, _543260), c_Groups_Oplus__class_Oplus(_543256, _543262, _543264)) = c_Groups_Oplus__class_Oplus(_543256, c_Groups_Oplus__class_Oplus(_543256, _543258, _543262), c_Groups_Oplus__class_Oplus(_543256, _543260, _543264)))], (3138 ^ _257747) ^ [_363235, _363237, _363239, _363241] : [class_Rings_Olinordered__ring__strict(_363235), c_Orderings_Oord__class_Oless(_363235, _363237, _363239), c_Orderings_Oord__class_Oless(_363235, _363241, c_Groups_Ozero__class_Ozero(_363235)), -(c_Orderings_Oord__class_Oless(_363235, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_363235), _363239), _363241), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_363235), _363237), _363241)))], (1845 ^ _257747) ^ [_318761, _318763] : [class_RealVector_Oreal__algebra__1(_318761), 1848 ^ _257747 : [(1849 ^ _257747) ^ [] : [c_RealVector_Oof__real(_318761, _318763) = c_Groups_Ozero__class_Ozero(_318761), -(_318763 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (1855 ^ _257747) ^ [] : [_318763 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(c_RealVector_Oof__real(_318761, _318763) = c_Groups_Ozero__class_Ozero(_318761))]]], (8568 ^ _257747) ^ [_559733, _559735] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _559733, _559735), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _559733, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _559735, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (10497 ^ _257747) ^ [_625579, _625581, _625583] : [class_Lattices_Oab__semigroup__idem__mult(_625579), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_625579), _625581), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_625579), _625581), _625583)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_625579), _625581), _625583))], (8554 ^ _257747) ^ [_559232, _559234] : [8555 ^ _257747 : [(8556 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _559232, _559234)], (8558 ^ _257747) ^ [] : [_559232 = _559234]], -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _559232, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _559234, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (11844 ^ _257747) ^ [_667766] : [class_Rings_Olinordered__idom(_667766), -(class_Int_Oring__char__0(tc_Polynomial_Opoly(_667766)))], (6103 ^ _257747) ^ [_470011, _470013, _470015] : [class_Groups_Oab__group__add(_470011), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_470011), c_Polynomial_Omonom(_470011, _470013, _470015)) = c_Polynomial_Omonom(_470011, c_Groups_Ouminus__class_Ouminus(_470011, _470013), _470015))], (3224 ^ _257747) ^ [_366120, _366122, _366124, _366126] : [class_Rings_Olinordered__ring__strict(_366120), c_Orderings_Oord__class_Oless(_366120, _366122, c_Groups_Ozero__class_Ozero(_366120)), 3231 ^ _257747 : [(3232 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_366120, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_366120), _366122), _366124), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_366120), _366122), _366126)), -(c_Orderings_Oord__class_Oless__eq(_366120, _366126, _366124))], (3238 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_366120, _366126, _366124), -(c_Orderings_Oord__class_Oless__eq(_366120, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_366120), _366122), _366124), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_366120), _366122), _366126)))]]], (462 ^ _257747) ^ [_271830, _271832] : [-(class_Rings_Olinordered__semidom(_271830)), _271832 = _271830, class_Rings_Olinordered__semidom(_271832)], (1861 ^ _257747) ^ [_319220] : [-(c_RealVector_Oof__real(_319220, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(_319220)), class_RealVector_Oreal__algebra__1(_319220), class_RealVector_Oreal__normed__vector(_319220)], (1387 ^ _257747) ^ [_302896, _302898, _302900] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _302896), c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _302896), _302898), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _302896), _302900)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _302898, _302900))], (1877 ^ _257747) ^ [_319727, _319729, _319731] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _319727), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _319729, _319731), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _319727), _319729), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _319727), _319731)))], (2574 ^ _257747) ^ [_344734] : [class_Rings_Ozero__neq__one(_344734), c_Groups_Oone__class_Oone(_344734) = c_Groups_Ozero__class_Ozero(_344734)], (2177 ^ _257747) ^ [_329891, _329893] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _329891, _329893), -(_329893 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _329891, 2180 ^ [_329891, _329893]))], (11832 ^ _257747) ^ [_667386] : [class_Rings_Ocomm__ring(_667386), -(class_Rings_Ocomm__ring(tc_Polynomial_Opoly(_667386)))], (10175 ^ _257747) ^ [_613940] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _613940), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(_613940 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8674 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (7144 ^ _257747) ^ [_508494, _508496, _508498] : [class_Groups_Oordered__ab__group__add(_508494), 7147 ^ _257747 : [(7148 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_508494, c_Groups_Ouminus__class_Ouminus(_508494, _508496), _508498), -(c_Orderings_Oord__class_Oless__eq(_508494, c_Groups_Ouminus__class_Ouminus(_508494, _508498), _508496))], (7154 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_508494, c_Groups_Ouminus__class_Ouminus(_508494, _508498), _508496), -(c_Orderings_Oord__class_Oless__eq(_508494, c_Groups_Ouminus__class_Ouminus(_508494, _508496), _508498))]]], (10782 ^ _257747) ^ [_635151, _635153] : [class_RealVector_Oreal__normed__vector(_635151), 10785 ^ _257747 : [(10786 ^ _257747) ^ [] : [_635153 = c_Groups_Ozero__class_Ozero(_635151), -(c_RealVector_Onorm__class_Onorm(_635151, c_Groups_Osgn__class_Osgn(_635151, _635153)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (10792 ^ _257747) ^ [] : [-(_635153 = c_Groups_Ozero__class_Ozero(_635151)), -(c_RealVector_Onorm__class_Onorm(_635151, c_Groups_Osgn__class_Osgn(_635151, _635153)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))]]], (7364 ^ _257747) ^ [_516113, _516115, _516117] : [class_Groups_Oordered__comm__monoid__add(_516113), c_Orderings_Oord__class_Oless__eq(_516113, c_Groups_Ozero__class_Ozero(_516113), _516115), c_Orderings_Oord__class_Oless__eq(_516113, c_Groups_Ozero__class_Ozero(_516113), _516117), -(c_Orderings_Oord__class_Oless__eq(_516113, c_Groups_Ozero__class_Ozero(_516113), c_Groups_Oplus__class_Oplus(_516113, _516115, _516117)))], (922 ^ _257747) ^ [_286295, _286297, _286299, _286301] : [-(c_Rings_Oinverse__class_Oinverse(_286301, _286297) = c_Rings_Oinverse__class_Oinverse(_286299, _286295)), _286301 = _286299, _286297 = _286295], (8638 ^ _257747) ^ [_562453, _562455] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _562453, _562455)), -(_562453 = _562455), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _562455, _562453))], (1365 ^ _257747) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____))], (6333 ^ _257747) ^ [_479570, _479572, _479574, _479576, _479578] : [class_Groups_Ocomm__monoid__add(_479570), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_479570), c_Polynomial_OpCons(_479570, _479572, _479574), c_Polynomial_OpCons(_479570, _479576, _479578)) = c_Polynomial_OpCons(_479570, c_Groups_Oplus__class_Oplus(_479570, _479572, _479576), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_479570), _479574, _479578)))], (1339 ^ _257747) ^ [_301337, _301339] : [class_RealVector_Oreal__normed__vector(_301337), 1342 ^ _257747 : [(1343 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_301337, _301339), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(_301339 = c_Groups_Ozero__class_Ozero(_301337))], (1349 ^ _257747) ^ [] : [_301339 = c_Groups_Ozero__class_Ozero(_301337), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_301337, _301339), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))]]], (8089 ^ _257747) ^ [_540386, _540388] : [class_Rings_Ocomm__semiring__1(_540386), -(hAPP(hAPP(c_Power_Opower__class_Opower(_540386), _540388), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_540386))], (9206 ^ _257747) ^ [_581563, _581565] : [class_Orderings_Opreorder(_581563), c_Orderings_Oord__class_Oless(_581563, _581565, _581565)], (8012 ^ _257747) ^ [_537330, _537332] : [-(_537330 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), -(_537332 = 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), _537330), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), 8019 ^ [_537330, _537332]), _537332)))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (4311 ^ _257747) ^ [_406078, _406080] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _406078, _406080), _406078)], (6189 ^ _257747) ^ [_473597, _473599] : [class_Rings_Ocomm__semiring__0(_473597), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_473597)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_473597))), _473599) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_473597)))], (9304 ^ _257747) ^ [_584543, _584545, _584547] : [class_Orderings_Oorder(_584543), c_Orderings_Oord__class_Oless(_584543, _584545, _584547), _584545 = _584547], (7820 ^ _257747) ^ [_530831, _530833, _530835] : [class_Groups_Oordered__ab__group__add__abs(_530831), -(c_Orderings_Oord__class_Oless__eq(_530831, c_Groups_Oabs__class_Oabs(_530831, c_Groups_Ominus__class_Ominus(_530831, c_Groups_Oabs__class_Oabs(_530831, _530833), c_Groups_Oabs__class_Oabs(_530831, _530835))), c_Groups_Oabs__class_Oabs(_530831, c_Groups_Ominus__class_Ominus(_530831, _530833, _530835))))], (11228 ^ _257747) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (6375 ^ _257747) ^ [_481566, _481568, _481570] : [class_Groups_Oab__group__add(_481566), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_481566), c_Polynomial_OpCons(_481566, _481568, _481570)) = c_Polynomial_OpCons(_481566, c_Groups_Ouminus__class_Ouminus(_481566, _481568), c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_481566), _481570)))], (7808 ^ _257747) ^ [_530317, _530319, _530321] : [class_Groups_Ogroup__add(_530317), -(c_Groups_Ominus__class_Ominus(_530317, _530319, _530321) = c_Groups_Oplus__class_Oplus(_530317, _530319, c_Groups_Ouminus__class_Ouminus(_530317, _530321)))], (9782 ^ _257747) ^ [_599493, _599495, _599497, _599499] : [class_Orderings_Oorder(_599493), c_Orderings_Oord__class_Oless__eq(_599493, _599495, _599497), c_Orderings_Oord__class_Oless(_599493, _599499, _599495), -(c_Orderings_Oord__class_Oless(_599493, _599499, _599497))], (4510 ^ _257747) ^ [_413693, _413695] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _413693), _413695)), _413693 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _413695 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (9054 ^ _257747) ^ [_576756, _576758, _576760] : [class_Orderings_Oorder(_576756), c_Orderings_Oord__class_Oless__eq(_576756, _576758, _576760), 9061 ^ _257747 : [(9062 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_576756, _576760, _576758), -(_576760 = _576758)], (9068 ^ _257747) ^ [] : [_576760 = _576758, -(c_Orderings_Oord__class_Oless__eq(_576756, _576760, _576758))]]], (10025 ^ _257747) ^ [_608697, _608699, _608701] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _608697, _608699), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _608697, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _608701, _608699)))], (2352 ^ _257747) ^ [_337020, _337022, _337024, _337026] : [class_RealVector_Oreal__normed__algebra(_337020), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_337020), c_Groups_Oplus__class_Oplus(_337020, _337022, _337024)), _337026) = c_Groups_Oplus__class_Oplus(_337020, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_337020), _337022), _337026), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_337020), _337024), _337026)))], (11186 ^ _257747) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (3955 ^ _257747) ^ [_393048, _393050, _393052, _393054, _393056] : [class_RealVector_Oreal__normed__vector(_393048), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_393048, c_Groups_Ominus__class_Ominus(_393048, c_Groups_Oplus__class_Oplus(_393048, _393050, _393052), c_Groups_Oplus__class_Oplus(_393048, _393054, _393056))), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_393048, c_Groups_Ominus__class_Ominus(_393048, _393050, _393054)), c_RealVector_Onorm__class_Onorm(_393048, c_Groups_Ominus__class_Ominus(_393048, _393052, _393056)))))], (10131 ^ _257747) ^ [_612488, _612490, _612492] : [class_Rings_Olinordered__idom(_612488), c_Polynomial_Opos__poly(_612488, _612490), c_Polynomial_Opos__poly(_612488, _612492), -(c_Polynomial_Opos__poly(_612488, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_612488)), _612490), _612492)))], (502 ^ _257747) ^ [_273010, _273012] : [-(class_Rings_Oordered__semiring(_273010)), _273012 = _273010, class_Rings_Oordered__semiring(_273012)], (3310 ^ _257747) ^ [_368975, _368977, _368979, _368981, _368983] : [class_Rings_Olinordered__semiring__strict(_368975), c_Orderings_Oord__class_Oless__eq(_368975, _368977, _368979), c_Orderings_Oord__class_Oless(_368975, _368981, _368983), c_Orderings_Oord__class_Oless(_368975, c_Groups_Ozero__class_Ozero(_368975), _368977), c_Orderings_Oord__class_Oless__eq(_368975, c_Groups_Ozero__class_Ozero(_368975), _368981), -(c_Orderings_Oord__class_Oless(_368975, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_368975), _368977), _368981), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_368975), _368979), _368983)))], (8668 ^ _257747) ^ [_563414] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _563414), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _563414)], (10990 ^ _257747) ^ [_642730, _642732, _642734, _642736] : [class_Rings_Ocomm__semiring__1(_642730), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_642730), _642732, _642734), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_642730), _642732, c_Polynomial_Osmult(_642730, _642736, _642734)))], (4728 ^ _257747) ^ [_421155, _421157, _421159] : [class_RealVector_Oreal__normed__div__algebra(_421155), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _421157, c_RealVector_Onorm__class_Onorm(_421155, _421159)), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _421157), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_421155, c_Rings_Oinverse__class_Oinverse(_421155, _421159)), c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, _421157)))], (1191 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, v_t____, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (11414 ^ _257747) ^ [] : [-(class_Rings_Olinordered__ring(tc_RealDef_Oreal))], (11868 ^ _257747) ^ [_668526] : [class_Rings_Olinordered__idom(_668526), -(class_Groups_Osgn__if(tc_Polynomial_Opoly(_668526)))], (5024 ^ _257747) ^ [_431926, _431928, _431930] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _431926, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _431928, _431930)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _431926, _431930), _431928))], (4540 ^ _257747) ^ [_414711, _414713] : [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), _414711), _414713)), 4543 ^ _257747 : [(4544 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _414711))], (4546 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _414713))]]], (10980 ^ _257747) ^ [_642365, _642367, _642369, _642371] : [class_Rings_Ocomm__semiring__1(_642365), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_642365), c_Polynomial_Osmult(_642365, _642367, _642369), _642371), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_642365), _642369, _642371))], (11292 ^ _257747) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Nat_Onat))], (7112 ^ _257747) ^ [_507495, _507497] : [class_Groups_Olinordered__ab__group__add(_507495), 7115 ^ _257747 : [(7116 ^ _257747) ^ [] : [c_Groups_Ouminus__class_Ouminus(_507495, _507497) = _507497, -(_507497 = c_Groups_Ozero__class_Ozero(_507495))], (7122 ^ _257747) ^ [] : [_507497 = c_Groups_Ozero__class_Ozero(_507495), -(c_Groups_Ouminus__class_Ouminus(_507495, _507497) = _507497)]]], (1379 ^ _257747) ^ [_302580, _302582] : [1380 ^ _257747 : [(1381 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _302580)], (1383 ^ _257747) ^ [] : [_302582 = 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), _302580), _302582)))], (11778 ^ _257747) ^ [_665676] : [class_Rings_Olinordered__idom(_665676), -(class_Rings_Oordered__ring(tc_Polynomial_Opoly(_665676)))], (3961 ^ _257747) ^ [_393328] : [-(_393328 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, _393328)), _393328) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (4480 ^ _257747) ^ [_412626] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _412626, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _412626), _412626)))], (7586 ^ _257747) ^ [_523128, _523130] : [class_Groups_Olinordered__ab__group__add(_523128), 7589 ^ _257747 : [(7590 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_523128, _523130, c_Groups_Ouminus__class_Ouminus(_523128, _523130)), -(c_Orderings_Oord__class_Oless__eq(_523128, _523130, c_Groups_Ozero__class_Ozero(_523128)))], (7596 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_523128, _523130, c_Groups_Ozero__class_Ozero(_523128)), -(c_Orderings_Oord__class_Oless__eq(_523128, _523130, c_Groups_Ouminus__class_Ouminus(_523128, _523130)))]]], (9354 ^ _257747) ^ [_586167, _586169, _586171] : [class_Orderings_Opreorder(_586167), c_Orderings_Oord__class_Oless(_586167, _586169, _586171), c_Orderings_Oord__class_Oless(_586167, _586171, _586169)], (11448 ^ _257747) ^ [] : [-(class_Rings_Ocomm__ring(tc_RealDef_Oreal))], (5562 ^ _257747) ^ [_452238, _452240] : [class_Fields_Olinordered__field__inverse__zero(_452238), -(c_Groups_Oabs__class_Oabs(_452238, c_Rings_Oinverse__class_Oinverse(_452238, _452240)) = c_Rings_Oinverse__class_Oinverse(_452238, c_Groups_Oabs__class_Oabs(_452238, _452240)))], (3975 ^ _257747) ^ [_393943, _393945, _393947] : [3976 ^ _257747 : [(3977 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _393943, _393945))], (3979 ^ _257747) ^ [] : [hBOOL(hAPP(hAPP(_393947, _393945), _393943))]], 3982 ^ _257747 : [(3983 ^ _257747) ^ [] : [-(_393943 = _393945)], (3985 ^ _257747) ^ [] : [hBOOL(hAPP(hAPP(_393947, _393945), _393943))]], 3988 ^ _257747 : [(3989 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _393945, _393943))], (3991 ^ _257747) ^ [] : [hBOOL(hAPP(hAPP(_393947, _393945), _393943))]], -(hBOOL(hAPP(hAPP(_393947, _393945), _393943)))], (11094 ^ _257747) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint))], (2095 ^ _257747) ^ [_327155, _327157, _327159] : [class_Rings_Olinordered__idom(_327155), c_Orderings_Oord__class_Oless__eq(_327155, c_Groups_Ozero__class_Ozero(_327155), _327157), c_Orderings_Oord__class_Oless__eq(_327155, c_Groups_Ozero__class_Ozero(_327155), _327159), c_Orderings_Oord__class_Oless__eq(_327155, _327159, c_Groups_Oone__class_Oone(_327155)), -(c_Orderings_Oord__class_Oless__eq(_327155, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_327155), _327157), _327159), _327157))], (11338 ^ _257747) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal))], (11126 ^ _257747) ^ [_647274, _647276] : [class_Groups_Ominus(_647274), -(class_Groups_Ominus(tc_fun(_647276, _647274)))], (5285 ^ _257747) ^ [_441596, _441598, _441600] : [-(hBOOL(hAPP(_441596, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _441598, _441600)))), 5288 ^ _257747 : [(5289 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _441598, _441600))], (5291 ^ _257747) ^ [] : [hBOOL(hAPP(_441596, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 5293 ^ _257747 : [(5294 ^ _257747) ^ [] : [-(_441598 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _441600, 5292 ^ [_441596, _441598, _441600]))], (5296 ^ _257747) ^ [] : [hBOOL(hAPP(_441596, 5292 ^ [_441596, _441598, _441600]))]]], (8732 ^ _257747) ^ [] : [-(c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, c_Complex_Oii) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, c_Complex_Oii))], (3809 ^ _257747) ^ [_387310, _387312] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _387310, _387312), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _387310, _387312))], (11640 ^ _257747) ^ [_661306] : [class_Rings_Olinordered__idom(_661306), -(class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(_661306)))], (8247 ^ _257747) ^ [_547494, _547496, _547498, _547500] : [class_Rings_Ocomm__semiring__1(_547494), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_547494), c_Groups_Oplus__class_Oplus(_547494, _547496, _547498)), _547500) = c_Groups_Oplus__class_Oplus(_547494, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_547494), _547496), _547500), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_547494), _547498), _547500)))], (7618 ^ _257747) ^ [_524092, _524094] : [class_Groups_Olinordered__ab__group__add(_524092), 7621 ^ _257747 : [(7622 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_524092, c_Groups_Ouminus__class_Ouminus(_524092, _524094), _524094), -(c_Orderings_Oord__class_Oless__eq(_524092, c_Groups_Ozero__class_Ozero(_524092), _524094))], (7628 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_524092, c_Groups_Ozero__class_Ozero(_524092), _524094), -(c_Orderings_Oord__class_Oless__eq(_524092, c_Groups_Ouminus__class_Ouminus(_524092, _524094), _524094))]]], (11282 ^ _257747) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (11384 ^ _257747) ^ [] : [-(class_RealVector_Oreal__div__algebra(tc_RealDef_Oreal))], (5004 ^ _257747) ^ [_431123, _431125] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _431123, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _431123, _431125)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11566 ^ _257747) ^ [] : [-(class_Rings_Odvd(tc_Complex_Ocomplex))], (4814 ^ _257747) ^ [_424114] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _424114) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1182 ^ _257747) ^ [_295879, _295881] : [hAPP(_295879, 1183 ^ [_295879, _295881]) = hAPP(_295881, 1183 ^ [_295879, _295881]), -(_295879 = _295881)], (1084 ^ _257747) ^ [_292171, _292173] : [_292173 = _292171, -(c_Groups_Ozero__class_Ozero(_292173) = c_Groups_Ozero__class_Ozero(_292171))], (2169 ^ _257747) ^ [] : [hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____), v_c____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)], (11484 ^ _257747) ^ [] : [-(class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex))], (4594 ^ _257747) ^ [_416617, _416619, _416621] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _416617), 4597 ^ _257747 : [(4598 ^ _257747) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _416617), _416619) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _416617), _416621), -(_416619 = _416621)], (4604 ^ _257747) ^ [] : [_416619 = _416621, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _416617), _416619) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _416617), _416621))]]], (4373 ^ _257747) ^ [_408139, _408141] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _408139, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _408141, _408139)))], (8047 ^ _257747) ^ [_538611, _538613, _538615, _538617] : [class_Rings_Ocomm__semiring__0(_538611), -(c_Polynomial_Osynthetic__div(_538611, c_Polynomial_OpCons(_538611, _538613, _538615), _538617) = c_Polynomial_OpCons(_538611, hAPP(c_Polynomial_Opoly(_538611, _538615), _538617), c_Polynomial_Osynthetic__div(_538611, _538615, _538617)))], (1220 ^ _257747) ^ [_297126] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _297126), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), _297126)), 1216 ^ []))], (532 ^ _257747) ^ [_273895, _273897] : [-(class_Rings_Olinordered__ring(_273895)), _273897 = _273895, class_Rings_Olinordered__ring(_273897)], (908 ^ _257747) ^ [_285807, _285809, _285811, _285813, _285815, _285817] : [-(c_Polynomial_Opcompose(_285817, _285813, _285809) = c_Polynomial_Opcompose(_285815, _285811, _285807)), _285817 = _285815, _285813 = _285811, _285809 = _285807], (10333 ^ _257747) ^ [_619228] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _619228, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatfloor(_619228)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))], (1581 ^ _257747) ^ [_309719, _309721, _309723, _309725] : [class_Groups_Ocomm__monoid__mult(_309719), -(hAPP(hAPP(c_Power_Opower__class_Opower(_309719), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_309719), _309721), _309723)), _309725) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_309719), hAPP(hAPP(c_Power_Opower__class_Opower(_309719), _309721), _309725)), hAPP(hAPP(c_Power_Opower__class_Opower(_309719), _309723), _309725)))], (11564 ^ _257747) ^ [] : [-(class_Groups_Oone(tc_Complex_Ocomplex))], (8219 ^ _257747) ^ [_546332, _546334, _546336, _546338] : [class_Rings_Ocomm__semiring__1(_546332), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_546332), _546334), c_Groups_Oplus__class_Oplus(_546332, _546336, _546338)) = c_Groups_Oplus__class_Oplus(_546332, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_546332), _546334), _546336), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_546332), _546334), _546338)))], (6844 ^ _257747) ^ [_498406, _498408, _498410, _498412] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_498406), c_Orderings_Oord__class_Oless__eq(_498406, c_Groups_Oplus__class_Oplus(_498406, _498408, _498410), c_Groups_Oplus__class_Oplus(_498406, _498412, _498410)), -(c_Orderings_Oord__class_Oless__eq(_498406, _498408, _498412))], (9949 ^ _257747) ^ [_606008, _606010] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _606008, _606010), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatfloor(_606008), c_RComplete_Onatfloor(_606010)))], (4069 ^ _257747) ^ [_397337] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _397337, _397337))], (8592 ^ _257747) ^ [_560553, _560555] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _560553, _560555), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _560553, _560555))], (9630 ^ _257747) ^ [_594793, _594795, _594797] : [class_Orderings_Oorder(_594793), -(_594795 = _594797), c_Orderings_Oord__class_Oless__eq(_594793, _594795, _594797), -(c_Orderings_Oord__class_Oless(_594793, _594795, _594797))], (7046 ^ _257747) ^ [_505406, _505408] : [class_Groups_Omonoid__mult(_505406), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_505406), _505408), c_Groups_Oone__class_Oone(_505406)) = _505408)], (8636 ^ _257747) ^ [_562318, _562320, _562322] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _562318), _562320)), _562322) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _562318), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _562320), _562322)))], (1949 ^ _257747) ^ [_322302, _322304, _322306] : [class_RealVector_Oreal__algebra__1(_322302), -(c_RealVector_Oof__real(_322302, hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _322304), _322306)) = hAPP(hAPP(c_Power_Opower__class_Opower(_322302), c_RealVector_Oof__real(_322302, _322304)), _322306))], (11412 ^ _257747) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal))], (11252 ^ _257747) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (11400 ^ _257747) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal))], (9698 ^ _257747) ^ [_596874, _596876, _596878] : [class_Orderings_Oorder(_596874), c_Orderings_Oord__class_Oless__eq(_596874, _596876, _596878), -(c_Orderings_Oord__class_Oless(_596874, _596876, _596878)), -(_596876 = _596878)], (1367 ^ _257747) ^ [] : [-(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), v_w____), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))], (11930 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), v_m____))], (2328 ^ _257747) ^ [_335838, _335840, _335842] : [class_RealVector_Oreal__normed__algebra(_335838), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_335838), c_Groups_Ouminus__class_Ouminus(_335838, _335840)), _335842) = c_Groups_Ouminus__class_Ouminus(_335838, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_335838), _335840), _335842)))], (752 ^ _257747) ^ [_280385, _280387] : [-(class_Rings_Oring__1(_280385)), _280387 = _280385, class_Rings_Oring__1(_280387)], (9768 ^ _257747) ^ [_599045, _599047, _599049, _599051] : [class_Orderings_Opreorder(_599045), c_Orderings_Oord__class_Oless__eq(_599045, _599047, _599049), c_Orderings_Oord__class_Oless(_599045, _599049, _599051), -(c_Orderings_Oord__class_Oless(_599045, _599047, _599051))], (11114 ^ _257747) ^ [_646850, _646852] : [class_Orderings_Oord(_646850), -(class_Orderings_Oord(tc_fun(_646852, _646850)))], (11370 ^ _257747) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal))], (11420 ^ _257747) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal))], (4093 ^ _257747) ^ [_398201, _398203] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _398201, _398203), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _398203, _398201), -(_398201 = _398203)], (10317 ^ _257747) ^ [_618774, _618776] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _618774), 10320 ^ _257747 : [(10321 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_618774), _618776), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _618774, c_RealDef_Oreal(tc_Nat_Onat, _618776)))], (10327 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _618774, c_RealDef_Oreal(tc_Nat_Onat, _618776)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_618774), _618776))]]], (9498 ^ _257747) ^ [_590745, _590747, _590749] : [class_Orderings_Olinorder(_590745), 9501 ^ _257747 : [(9502 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_590745, _590747, _590749)), -(c_Orderings_Oord__class_Oless(_590745, _590749, _590747))], (9508 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_590745, _590749, _590747), c_Orderings_Oord__class_Oless__eq(_590745, _590747, _590749)]]], (5228 ^ _257747) ^ [_439379] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _439379, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), -(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _439379) = _439379)], (9997 ^ _257747) ^ [_607676, _607678, _607680] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _607676, _607678), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _607676, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _607678, _607680)))], (3288 ^ _257747) ^ [_368253, _368255, _368257, _368259, _368261] : [class_Rings_Olinordered__semiring__strict(_368253), c_Orderings_Oord__class_Oless(_368253, _368255, _368257), c_Orderings_Oord__class_Oless__eq(_368253, _368259, _368261), c_Orderings_Oord__class_Oless__eq(_368253, c_Groups_Ozero__class_Ozero(_368253), _368255), c_Orderings_Oord__class_Oless(_368253, c_Groups_Ozero__class_Ozero(_368253), _368259), -(c_Orderings_Oord__class_Oless(_368253, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_368253), _368255), _368259), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_368253), _368257), _368261)))], (2992 ^ _257747) ^ [_358406, _358408, _358410] : [class_Rings_Olinordered__semiring__strict(_358406), c_Orderings_Oord__class_Oless(_358406, c_Groups_Ozero__class_Ozero(_358406), _358408), c_Orderings_Oord__class_Oless(_358406, _358410, c_Groups_Ozero__class_Ozero(_358406)), -(c_Orderings_Oord__class_Oless(_358406, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_358406), _358408), _358410), c_Groups_Ozero__class_Ozero(_358406)))], (10714 ^ _257747) ^ [_633083, _633085] : [class_Rings_Olinordered__idom(_633083), 10717 ^ _257747 : [(10718 ^ _257747) ^ [] : [c_Groups_Osgn__class_Osgn(_633083, _633085) = c_Groups_Oone__class_Oone(_633083), -(c_Orderings_Oord__class_Oless(_633083, c_Groups_Ozero__class_Ozero(_633083), _633085))], (10724 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_633083, c_Groups_Ozero__class_Ozero(_633083), _633085), -(c_Groups_Osgn__class_Osgn(_633083, _633085) = c_Groups_Oone__class_Oone(_633083))]]], (7980 ^ _257747) ^ [_536191, _536193] : [class_Groups_Oordered__ab__group__add__abs(_536191), c_Orderings_Oord__class_Oless__eq(_536191, _536193, c_Groups_Ozero__class_Ozero(_536191)), -(c_Groups_Oabs__class_Oabs(_536191, _536193) = c_Groups_Ouminus__class_Ouminus(_536191, _536193))], (5999 ^ _257747) ^ [_466299, _466301, _466303] : [class_Rings_Olinordered__ring(_466299), -(c_Orderings_Oord__class_Oless__eq(_466299, c_Groups_Ozero__class_Ozero(_466299), c_Groups_Oplus__class_Oplus(_466299, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_466299), _466301), _466301), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_466299), _466303), _466303))))], (7688 ^ _257747) ^ [_526260, _526262, _526264] : [class_Groups_Ogroup__add(_526260), 7691 ^ _257747 : [(7692 ^ _257747) ^ [] : [_526262 = c_Groups_Ouminus__class_Ouminus(_526260, _526264), -(c_Groups_Oplus__class_Oplus(_526260, _526262, _526264) = c_Groups_Ozero__class_Ozero(_526260))], (7698 ^ _257747) ^ [] : [c_Groups_Oplus__class_Oplus(_526260, _526262, _526264) = c_Groups_Ozero__class_Ozero(_526260), -(_526262 = c_Groups_Ouminus__class_Ouminus(_526260, _526264))]]], (4181 ^ _257747) ^ [_401312, _401314] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _401312), _401314) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_401312 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_401314 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11296 ^ _257747) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (5376 ^ _257747) ^ [_445529, _445531, _445533] : [class_RealVector_Oreal__normed__vector(_445529), -(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(_445529, _445531), c_RealVector_Onorm__class_Onorm(_445529, _445533))), c_RealVector_Onorm__class_Onorm(_445529, c_Groups_Ominus__class_Ominus(_445529, _445531, _445533))))], (8381 ^ _257747) ^ [_553004] : [8389 ^ _257747 : [(8390 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 8388 ^ [_553004]))], (8392 ^ _257747) ^ [_553364] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_553004, c_RealVector_Oof__real(_553004, _553364)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, _553364)), 8388 ^ [_553004])))]], class_RealVector_Oreal__algebra__1(_553004), class_RealVector_Oreal__normed__vector(_553004)], (11904 ^ _257747) ^ [_669666] : [class_Rings_Ocomm__ring(_669666), -(class_Rings_Oring(tc_Polynomial_Opoly(_669666)))], (11250 ^ _257747) ^ [] : [-(class_Rings_Odvd(tc_Int_Oint))], (1166 ^ _257747) ^ [_295136, _295138] : [_295138 = _295136, -(c_Power_Opower__class_Opower(_295138) = c_Power_Opower__class_Opower(_295136))], (880 ^ _257747) ^ [_284775, _284777, _284779, _284781, _284783, _284785] : [-(c_Polynomial_Omonom(_284785, _284781, _284777) = c_Polynomial_Omonom(_284783, _284779, _284775)), _284785 = _284783, _284781 = _284779, _284777 = _284775], (4766 ^ _257747) ^ [] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, v_s____), v_k____), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)))], (11892 ^ _257747) ^ [_669286] : [class_Rings_Ocomm__semiring__1(_669286), -(class_Power_Opower(tc_Polynomial_Opoly(_669286)))], (3427 ^ _257747) ^ [_372842, _372844] : [class_Rings_Odivision__ring__inverse__zero(_372842), -(c_Rings_Oinverse__class_Oinverse(_372842, c_Rings_Oinverse__class_Oinverse(_372842, _372844)) = _372844)], (11366 ^ _257747) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal))], (4291 ^ _257747) ^ [_405299, _405301, _405303] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _405299, _405301), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _405299, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _405301, _405303)))], (832 ^ _257747) ^ [_282745, _282747] : [-(class_Groups_Oone(_282745)), _282747 = _282745, class_Groups_Oone(_282747)], (11820 ^ _257747) ^ [_667006] : [class_Groups_Oab__group__add(_667006), -(class_Groups_Ogroup__add(tc_Polynomial_Opoly(_667006)))], (1823 ^ _257747) ^ [_318014, _318016] : [class_RealVector_Oreal__normed__vector(_318014), 1826 ^ _257747 : [(1827 ^ _257747) ^ [] : [c_RealVector_Onorm__class_Onorm(_318014, _318016) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_318016 = c_Groups_Ozero__class_Ozero(_318014))], (1833 ^ _257747) ^ [] : [_318016 = c_Groups_Ozero__class_Ozero(_318014), -(c_RealVector_Onorm__class_Onorm(_318014, _318016) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))]]], (642 ^ _257747) ^ [_277140, _277142] : [-(class_Rings_Omult__zero(_277140)), _277142 = _277140, class_Rings_Omult__zero(_277142)], (2322 ^ _257747) ^ [_335566, _335568, _335570] : [class_RealVector_Oreal__normed__algebra(_335566), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_335566), _335568), c_Groups_Ouminus__class_Ouminus(_335566, _335570)) = c_Groups_Ouminus__class_Ouminus(_335566, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_335566), _335568), _335570)))], (11274 ^ _257747) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (4450 ^ _257747) ^ [_411252, _411254, _411256, _411258] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _411252), _411254), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _411256), _411254), _411258)) = 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, _411252, _411256)), _411254), _411258))], (3377 ^ _257747) ^ [_371098] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _371098, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10109 ^ _257747) ^ [_611701] : [c_RealDef_Oreal(tc_Nat_Onat, _611701) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_611701 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7738 ^ _257747) ^ [_527998, _528000] : [class_Groups_Oordered__ab__group__add__abs(_527998), 7741 ^ _257747 : [(7742 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_527998, c_Groups_Oabs__class_Oabs(_527998, _528000), c_Groups_Ozero__class_Ozero(_527998)), -(_528000 = c_Groups_Ozero__class_Ozero(_527998))], (7748 ^ _257747) ^ [] : [_528000 = c_Groups_Ozero__class_Ozero(_527998), -(c_Orderings_Oord__class_Oless__eq(_527998, c_Groups_Oabs__class_Oabs(_527998, _528000), c_Groups_Ozero__class_Ozero(_527998)))]]], (2 ^ _257747) ^ [_257871] : [-(_257871 = _257871)], (252 ^ _257747) ^ [_265635, _265637] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_265635)), _265637 = _265635, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_265637)], (4363 ^ _257747) ^ [_407846, _407848] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _407846, _407848)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _407846, _407848), -(_407846 = _407848)], (4912 ^ _257747) ^ [_427807, _427809, _427811] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _427807), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _427809, _427811)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _427807), _427809), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _427807), _427811)))], (4442 ^ _257747) ^ [_410928, _410930, _410932] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _410928, _410930), _410932), 4445 ^ _257747 : [(4446 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _410928, _410932))], (4448 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _410930, _410932))]]], (4717 ^ _257747) ^ [_420810] : [-(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, 4713 ^ []), _420810) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_c____, _420810)))], (662 ^ _257747) ^ [_277730, _277732] : [-(class_Int_Oring__char__0(_277730)), _277732 = _277730, class_Int_Oring__char__0(_277732)], (4699 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(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), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_a____, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))))))), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____))), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)))))))], (582 ^ _257747) ^ [_275370, _275372] : [-(class_Orderings_Olinorder(_275370)), _275372 = _275370, class_Orderings_Olinorder(_275372)], (10187 ^ _257747) ^ [_614289] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _614289, c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatceiling(_614289))))], (7666 ^ _257747) ^ [_525541, _525543] : [class_Groups_Olinordered__ab__group__add(_525541), 7669 ^ _257747 : [(7670 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_525541, c_Groups_Ouminus__class_Ouminus(_525541, _525543), _525543), -(c_Orderings_Oord__class_Oless(_525541, c_Groups_Ozero__class_Ozero(_525541), _525543))], (7676 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_525541, c_Groups_Ozero__class_Ozero(_525541), _525543), -(c_Orderings_Oord__class_Oless(_525541, c_Groups_Ouminus__class_Ouminus(_525541, _525543), _525543))]]], (4810 ^ _257747) ^ [_423950] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _423950, _423950) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6487 ^ _257747) ^ [_485515] : [class_Rings_Ocomm__semiring__1(_485515), -(c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_485515)) = c_Polynomial_OpCons(_485515, c_Groups_Oone__class_Oone(_485515), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_485515))))], (11298 ^ _257747) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (4904 ^ _257747) ^ [_427473, _427475, _427477] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _427473, _427475), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _427477, _427475), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _427477, _427473)))], (5600 ^ _257747) ^ [_453454, _453456, _453458] : [class_Fields_Olinordered__field(_453454), c_Orderings_Oord__class_Oless(_453454, c_Rings_Oinverse__class_Oinverse(_453454, _453456), c_Rings_Oinverse__class_Oinverse(_453454, _453458)), c_Orderings_Oord__class_Oless(_453454, _453458, c_Groups_Ozero__class_Ozero(_453454)), -(c_Orderings_Oord__class_Oless(_453454, _453458, _453456))], (8754 ^ _257747) ^ [_566523, _566525, _566527] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _566523, _566525), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _566527, _566523), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _566527, _566525)))], (8426 ^ _257747) ^ [_554773, _554775, _554777] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _554773), _554775)), _554777) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _554773), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _554775), _554777)))], (4548 ^ _257747) ^ [_414966, _414968] : [-(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), _414966), _414968))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _414966), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _414968)], (5540 ^ _257747) ^ [_451495, _451497, _451499] : [class_Fields_Ofield__inverse__zero(_451495), -(c_Rings_Oinverse__class_Oinverse(_451495, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_451495), _451497), _451499)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_451495), c_Rings_Oinverse__class_Oinverse(_451495, _451497)), c_Rings_Oinverse__class_Oinverse(_451495, _451499)))], (5012 ^ _257747) ^ [_431441, _431443] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _431441, _431443), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _431441, _431443) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9290 ^ _257747) ^ [_584119, _584121, _584123] : [class_Orderings_Olinorder(_584119), -(_584121 = _584123), -(c_Orderings_Oord__class_Oless(_584119, _584121, _584123)), -(c_Orderings_Oord__class_Oless(_584119, _584123, _584121))], (4297 ^ _257747) ^ [_405570, _405572, _405574] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _405570, _405572), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _405570, _405574)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _405572, _405574))], (1593 ^ _257747) ^ [_310311, _310313] : [class_Groups_Omonoid__mult(_310311), -(hAPP(hAPP(c_Power_Opower__class_Opower(_310311), c_Groups_Oone__class_Oone(_310311)), _310313) = c_Groups_Oone__class_Oone(_310311))], (11314 ^ _257747) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (10083 ^ _257747) ^ [_610647, _610649] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _610647, _610649), -(c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _610649, _610647)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _610649), c_RealDef_Oreal(tc_Nat_Onat, _610647)))], (10003 ^ _257747) ^ [_607904, _607906] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _607904), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _607906), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Nat__Transfer_Otsub(_607904, _607906)))], (11006 ^ _257747) ^ [_643305, _643307, _643309, _643311] : [class_Rings_Ocomm__semiring__1(_643305), c_Rings_Odvd__class_Odvd(_643305, _643307, _643309), c_Rings_Odvd__class_Odvd(_643305, _643309, _643311), -(c_Rings_Odvd__class_Odvd(_643305, _643307, _643311))], (9196 ^ _257747) ^ [_581249, _581251, _581253] : [class_Orderings_Olinorder(_581249), -(c_Orderings_Oord__class_Oless__eq(_581249, _581251, _581253)), -(c_Orderings_Oord__class_Oless__eq(_581249, _581253, _581251))], (8416 ^ _257747) ^ [_554327, _554329] : [8417 ^ _257747 : [(8418 ^ _257747) ^ [] : [-(_554327 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (8420 ^ _257747) ^ [] : [_554329 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), c_Groups_Oabs__class_Oabs(tc_Int_Oint, _554327)), _554329)))], (11278 ^ _257747) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (11272 ^ _257747) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (4414 ^ _257747) ^ [_409825, _409827, _409829] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _409825, _409827), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _409825, _409829), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _409827, _409829)))], (10680 ^ _257747) ^ [_631878, _631880] : [class_Rings_Olinordered__idom(_631878), -(c_Groups_Osgn__class_Osgn(_631878, c_Groups_Osgn__class_Osgn(_631878, _631880)) = c_Groups_Osgn__class_Osgn(_631878, _631880))], (5216 ^ _257747) ^ [_438986] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _438986, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), -(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _438986) = _438986)], (11446 ^ _257747) ^ [] : [-(class_Rings_Omult__zero(tc_RealDef_Oreal))], (4532 ^ _257747) ^ [_414382, _414384] : [4533 ^ _257747 : [(4534 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _414382)], (4536 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _414384)]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _414382, _414384)))], (4163 ^ _257747) ^ [_400629] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _400629))], (3533 ^ _257747) ^ [_376622, _376624] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _376622, _376624), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _376624, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _376622)))], (11178 ^ _257747) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (7838 ^ _257747) ^ [_531629, _531631, _531633] : [class_Groups_Oordered__ab__group__add__abs(_531629), c_Orderings_Oord__class_Oless__eq(_531629, c_Groups_Oabs__class_Oabs(_531629, _531631), _531633), -(c_Orderings_Oord__class_Oless__eq(_531629, c_Groups_Ouminus__class_Ouminus(_531629, _531631), _531633))], (8528 ^ _257747) ^ [_558239, _558241, _558243] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _558239, _558241)), _558243) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _558239), _558243), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _558241), _558243)))], (5382 ^ _257747) ^ [_445756] : [-(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, _445756))))], (7570 ^ _257747) ^ [_522643, _522645] : [class_Groups_Oordered__ab__group__add(_522643), 7573 ^ _257747 : [(7574 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_522643, c_Groups_Ozero__class_Ozero(_522643), c_Groups_Ouminus__class_Ouminus(_522643, _522645)), -(c_Orderings_Oord__class_Oless__eq(_522643, _522645, c_Groups_Ozero__class_Ozero(_522643)))], (7580 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_522643, _522645, c_Groups_Ozero__class_Ozero(_522643)), -(c_Orderings_Oord__class_Oless__eq(_522643, c_Groups_Ozero__class_Ozero(_522643), c_Groups_Ouminus__class_Ouminus(_522643, _522645)))]]], (5512 ^ _257747) ^ [_450319] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), _450319)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), _450319)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))))], (572 ^ _257747) ^ [_275075, _275077] : [-(class_Orderings_Opreorder(_275075)), _275077 = _275075, class_Orderings_Opreorder(_275077)], (8742 ^ _257747) ^ [_565893, _565895, _565897] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _565893), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _565895, 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, _565895, _565897)), c_Groups_Oone__class_Oone(tc_Int_Oint))), _565893)), _565897))], (4313 ^ _257747) ^ [_406192, _406194] : [4314 ^ _257747 : [(4315 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _406192, _406194)], (4317 ^ _257747) ^ [] : [_406192 = _406194]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _406192, _406194))], (3459 ^ _257747) ^ [_373905, _373907] : [_373905 = _373907, -(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _373905, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _373907)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (8736 ^ _257747) ^ [_565617, _565619, _565621] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _565617), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _565619, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _565621, 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, _565621, _565619)), c_Groups_Oone__class_Oone(tc_Int_Oint))), _565617))))], (3411 ^ _257747) ^ [_372350, _372352, _372354] : [class_Rings_Odivision__ring__inverse__zero(_372350), 3414 ^ _257747 : [(3415 ^ _257747) ^ [] : [c_Rings_Oinverse__class_Oinverse(_372350, _372352) = c_Rings_Oinverse__class_Oinverse(_372350, _372354), -(_372352 = _372354)], (3421 ^ _257747) ^ [] : [_372352 = _372354, -(c_Rings_Oinverse__class_Oinverse(_372350, _372352) = c_Rings_Oinverse__class_Oinverse(_372350, _372354))]]], (8053 ^ _257747) ^ [_538917, _538919, _538921, _538923, _538925] : [class_Rings_Ocomm__semiring__0(_538917), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_538917), _538919, c_Polynomial_Osmult(_538917, _538921, _538923)) = c_Polynomial_OpCons(_538917, _538925, _538923), 8060 ^ _257747 : [(8061 ^ _257747) ^ [] : [-(_538925 = hAPP(c_Polynomial_Opoly(_538917, _538919), _538921))], (8063 ^ _257747) ^ [] : [-(_538923 = c_Polynomial_Osynthetic__div(_538917, _538919, _538921))]]], (652 ^ _257747) ^ [_277435, _277437] : [-(class_Orderings_Oorder(_277435)), _277437 = _277435, class_Orderings_Oorder(_277437)], (1265 ^ _257747) ^ [_298737, _298739, _298741] : [class_RealVector_Oreal__normed__algebra__1(_298737), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_298737, hAPP(hAPP(c_Power_Opower__class_Opower(_298737), _298739), _298741)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_298737, _298739)), _298741)))], (6315 ^ _257747) ^ [_478716, _478718, _478720, _478722] : [class_Rings_Ocomm__semiring__0(_478716), -(hAPP(c_Polynomial_Opoly(_478716, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_478716), _478718, _478720)), _478722) = c_Groups_Oplus__class_Oplus(_478716, hAPP(c_Polynomial_Opoly(_478716, _478718), _478722), hAPP(c_Polynomial_Opoly(_478716, _478720), _478722)))], (8071 ^ _257747) ^ [_539672] : [-(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), _539672), _539672))), -(_539672 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (2716 ^ _257747) ^ [_349276, _349278, _349280] : [class_Rings_Oordered__ring(_349276), c_Orderings_Oord__class_Oless__eq(_349276, _349278, c_Groups_Ozero__class_Ozero(_349276)), c_Orderings_Oord__class_Oless__eq(_349276, _349280, c_Groups_Ozero__class_Ozero(_349276)), -(c_Orderings_Oord__class_Oless__eq(_349276, c_Groups_Ozero__class_Ozero(_349276), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_349276), _349278), _349280)))], (9088 ^ _257747) ^ [_577802, _577804, _577806, _577808] : [class_Orderings_Oorder(_577802), _577804 = _577806, c_Orderings_Oord__class_Oless__eq(_577802, _577808, _577806), -(c_Orderings_Oord__class_Oless__eq(_577802, _577808, _577804))], (8329 ^ _257747) ^ [_550912, _550914] : [class_Rings_Ocomm__semiring__1(_550912), -(c_Groups_Oplus__class_Oplus(_550912, _550914, _550914) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_550912), c_Groups_Oplus__class_Oplus(_550912, c_Groups_Oone__class_Oone(_550912), c_Groups_Oone__class_Oone(_550912))), _550914))], (11790 ^ _257747) ^ [_666056] : [class_Rings_Olinordered__idom(_666056), -(class_Orderings_Olinorder(tc_Polynomial_Opoly(_666056)))], (11214 ^ _257747) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (9416 ^ _257747) ^ [_588171, _588173, _588175, _588177] : [class_Orderings_Oorder(_588171), c_Orderings_Oord__class_Oless(_588171, _588173, _588175), _588173 = _588177, -(c_Orderings_Oord__class_Oless(_588171, _588177, _588175))], (172 ^ _257747) ^ [_263275, _263277] : [-(class_RealVector_Oreal__normed__algebra__1(_263275)), _263277 = _263275, class_RealVector_Oreal__normed__algebra__1(_263277)], (3771 ^ _257747) ^ [_385767, _385769, _385771, _385773, _385775, _385777] : [class_Rings_Oring(_385767), 3774 ^ _257747 : [(3775 ^ _257747) ^ [] : [c_Groups_Oplus__class_Oplus(_385767, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_385767), _385769), _385771), _385773) = c_Groups_Oplus__class_Oplus(_385767, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_385767), _385775), _385771), _385777), -(c_Groups_Oplus__class_Oplus(_385767, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_385767), c_Groups_Ominus__class_Ominus(_385767, _385769, _385775)), _385771), _385773) = _385777)], (3781 ^ _257747) ^ [] : [c_Groups_Oplus__class_Oplus(_385767, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_385767), c_Groups_Ominus__class_Ominus(_385767, _385769, _385775)), _385771), _385773) = _385777, -(c_Groups_Oplus__class_Oplus(_385767, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_385767), _385769), _385771), _385773) = c_Groups_Oplus__class_Oplus(_385767, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_385767), _385775), _385771), _385777))]]], (6219 ^ _257747) ^ [_474779, _474781] : [class_Groups_Ocomm__monoid__add(_474779), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_474779), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_474779)), _474781) = _474781)], (8287 ^ _257747) ^ [_549162, _549164] : [class_Rings_Ocomm__semiring__1(_549162), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_549162), _549164), c_Groups_Oone__class_Oone(_549162)) = _549164)], (11482 ^ _257747) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex))], (10624 ^ _257747) ^ [_629960, _629962] : [class_RealVector_Oreal__normed__vector(_629960), 10627 ^ _257747 : [(10628 ^ _257747) ^ [] : [c_Groups_Osgn__class_Osgn(_629960, _629962) = c_Groups_Ozero__class_Ozero(_629960), -(_629962 = c_Groups_Ozero__class_Ozero(_629960))], (10634 ^ _257747) ^ [] : [_629962 = c_Groups_Ozero__class_Ozero(_629960), -(c_Groups_Osgn__class_Osgn(_629960, _629962) = c_Groups_Ozero__class_Ozero(_629960))]]], (7946 ^ _257747) ^ [_535099, _535101, _535103] : [class_Groups_Oordered__comm__monoid__add(_535099), c_Orderings_Oord__class_Oless(_535099, _535101, c_Groups_Ozero__class_Ozero(_535099)), c_Orderings_Oord__class_Oless__eq(_535099, _535103, c_Groups_Ozero__class_Ozero(_535099)), -(c_Orderings_Oord__class_Oless(_535099, c_Groups_Oplus__class_Oplus(_535099, _535101, _535103), c_Groups_Ozero__class_Ozero(_535099)))], (5480 ^ _257747) ^ [_449351, _449353] : [class_Fields_Olinordered__field__inverse__zero(_449351), 5483 ^ _257747 : [(5494 ^ _257747) ^ [] : [5495 ^ _257747 : [(5496 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_449351, _449353, c_Groups_Ozero__class_Ozero(_449351))], (5498 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_449351, c_Groups_Oone__class_Oone(_449351), _449353)]], -(c_Orderings_Oord__class_Oless(_449351, c_Rings_Oinverse__class_Oinverse(_449351, _449353), c_Groups_Oone__class_Oone(_449351)))], (5484 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_449351, c_Rings_Oinverse__class_Oinverse(_449351, _449353), c_Groups_Oone__class_Oone(_449351)), -(c_Orderings_Oord__class_Oless__eq(_449351, _449353, c_Groups_Ozero__class_Ozero(_449351))), -(c_Orderings_Oord__class_Oless(_449351, c_Groups_Oone__class_Oone(_449351), _449353))]]], (10359 ^ _257747) ^ [_620244, _620246] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _620244), -(c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _620244, c_RealDef_Oreal(tc_Nat_Onat, _620246))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatfloor(_620244), _620246))], (2364 ^ _257747) ^ [_337616, _337618] : [class_RealVector_Oreal__normed__vector(_337616), -(c_RealVector_Onorm__class_Onorm(_337616, c_Groups_Ouminus__class_Ouminus(_337616, _337618)) = c_RealVector_Onorm__class_Onorm(_337616, _337618))], (2250 ^ _257747) ^ [_332607, _332609, _332611] : [class_Rings_Oring(_332607), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_332607), c_Groups_Ouminus__class_Ouminus(_332607, _332609)), _332611) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_332607), _332609), c_Groups_Ouminus__class_Ouminus(_332607, _332611)))], (5176 ^ _257747) ^ [_437577, _437579, _437581] : [class_Rings_Oordered__ring__abs(_437577), -(c_Groups_Oabs__class_Oabs(_437577, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_437577), _437579), _437581)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_437577), c_Groups_Oabs__class_Oabs(_437577, _437579)), c_Groups_Oabs__class_Oabs(_437577, _437581))), 5183 ^ _257747 : [(5184 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_437577, c_Groups_Ozero__class_Ozero(_437577), _437579)], (5186 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_437577, _437579, c_Groups_Ozero__class_Ozero(_437577))]], 5187 ^ _257747 : [(5188 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_437577, c_Groups_Ozero__class_Ozero(_437577), _437581)], (5190 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_437577, _437581, c_Groups_Ozero__class_Ozero(_437577))]]], (4105 ^ _257747) ^ [_398623, _398625] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _398623), _398625) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _398625), _398623))], (6794 ^ _257747) ^ [_496636, _496638, _496640, _496642] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_496636), 6797 ^ _257747 : [(6798 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_496636, c_Groups_Oplus__class_Oplus(_496636, _496638, _496640), c_Groups_Oplus__class_Oplus(_496636, _496638, _496642)), -(c_Orderings_Oord__class_Oless__eq(_496636, _496640, _496642))], (6804 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_496636, _496640, _496642), -(c_Orderings_Oord__class_Oless__eq(_496636, c_Groups_Oplus__class_Oplus(_496636, _496638, _496640), c_Groups_Oplus__class_Oplus(_496636, _496638, _496642)))]]], (3551 ^ _257747) ^ [_377241, _377243] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _377241), _377243), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _377241, _377243)))], (8973 ^ _257747) ^ [_573951] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _573951), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), _573951)), 8969 ^ []))], (7704 ^ _257747) ^ [_526761, _526763] : [class_Groups_Ogroup__add(_526761), -(c_Groups_Oplus__class_Oplus(_526761, c_Groups_Ouminus__class_Ouminus(_526761, _526763), _526763) = c_Groups_Ozero__class_Ozero(_526761))], (7960 ^ _257747) ^ [_535539, _535541, _535543] : [class_Groups_Oordered__comm__monoid__add(_535539), c_Orderings_Oord__class_Oless__eq(_535539, _535541, c_Groups_Ozero__class_Ozero(_535539)), c_Orderings_Oord__class_Oless(_535539, _535543, c_Groups_Ozero__class_Ozero(_535539)), -(c_Orderings_Oord__class_Oless(_535539, c_Groups_Oplus__class_Oplus(_535539, _535541, _535543), c_Groups_Ozero__class_Ozero(_535539)))], (3803 ^ _257747) ^ [_387136, _387138] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _387136, _387138), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _387136, _387138), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (11622 ^ _257747) ^ [_660736] : [class_Rings_Olinordered__idom(_660736), -(class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(_660736)))], (632 ^ _257747) ^ [_276845, _276847] : [-(class_Groups_Ogroup__add(_276845)), _276847 = _276845, class_Groups_Ogroup__add(_276847)], (11808 ^ _257747) ^ [_666626] : [class_Groups_Ocomm__monoid__add(_666626), -(class_Groups_Omonoid__add(tc_Polynomial_Opoly(_666626)))], (3517 ^ _257747) ^ [_376005, _376007] : [class_RealVector_Oreal__div__algebra(_376005), -(_376007 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_RealVector_Oof__real(_376005, c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, _376007)) = c_Rings_Oinverse__class_Oinverse(_376005, c_RealVector_Oof__real(_376005, _376007)))], (11748 ^ _257747) ^ [_664726] : [class_Rings_Ocomm__semiring__1(_664726), -(class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(_664726)))], (522 ^ _257747) ^ [_273600, _273602] : [-(class_Rings_Ono__zero__divisors(_273600)), _273602 = _273600, class_Rings_Ono__zero__divisors(_273602)], (9234 ^ _257747) ^ [_582448, _582450, _582452] : [class_Orderings_Olinorder(_582448), 9237 ^ _257747 : [(9248 ^ _257747) ^ [] : [9249 ^ _257747 : [(9250 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_582448, _582452, _582450)], (9252 ^ _257747) ^ [] : [_582450 = _582452]], c_Orderings_Oord__class_Oless(_582448, _582450, _582452)], (9238 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(_582448, _582450, _582452)), -(c_Orderings_Oord__class_Oless(_582448, _582452, _582450)), -(_582450 = _582452)]]], (4976 ^ _257747) ^ [_430172, _430174] : [class_RealVector_Oreal__normed__algebra__1(_430172), -(c_RealVector_Onorm__class_Onorm(_430172, c_RealVector_Oof__real(_430172, _430174)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _430174))], (6059 ^ _257747) ^ [_468437, _468439, _468441, _468443] : [class_Rings_Ocomm__semiring__0(_468437), -(hAPP(c_Polynomial_Opoly(_468437, c_Polynomial_OpCons(_468437, _468439, _468441)), _468443) = c_Groups_Oplus__class_Oplus(_468437, _468439, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_468437), _468443), hAPP(c_Polynomial_Opoly(_468437, _468441), _468443))))], (6620 ^ _257747) ^ [_490805, _490807, _490809, _490811] : [class_Groups_Ocancel__semigroup__add(_490805), 6623 ^ _257747 : [(6624 ^ _257747) ^ [] : [c_Groups_Oplus__class_Oplus(_490805, _490807, _490809) = c_Groups_Oplus__class_Oplus(_490805, _490807, _490811), -(_490809 = _490811)], (6630 ^ _257747) ^ [] : [_490809 = _490811, -(c_Groups_Oplus__class_Oplus(_490805, _490807, _490809) = c_Groups_Oplus__class_Oplus(_490805, _490807, _490811))]]], (9074 ^ _257747) ^ [_577356, _577358, _577360, _577362] : [class_Orderings_Oord(_577356), _577358 = _577360, c_Orderings_Oord__class_Oless__eq(_577356, _577360, _577362), -(c_Orderings_Oord__class_Oless__eq(_577356, _577358, _577362))], (10554 ^ _257747) ^ [_627690, _627692] : [class_Rings_Olinordered__idom(_627690), 10557 ^ _257747 : [(10558 ^ _257747) ^ [] : [_627692 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_627690)), -(c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(_627690), _627692) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_627690)))], (10564 ^ _257747) ^ [] : [-(_627692 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_627690))), 10567 ^ _257747 : [(10568 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_627690), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_627690)), _627692), -(c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(_627690), _627692) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_627690)))], (10574 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_627690), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_627690)), _627692)), -(c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(_627690), _627692) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_627690), c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_627690))))]]]]], (4522 ^ _257747) ^ [_414116, _414118] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _414116, _414118)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _414116)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _414118))], (4436 ^ _257747) ^ [_410686, _410688, _410690] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _410686, _410688), _410690), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _410686, _410690))], (6982 ^ _257747) ^ [_503168, _503170] : [class_Groups_Ogroup__add(_503168), -(c_Groups_Ominus__class_Ominus(_503168, _503170, _503170) = c_Groups_Ozero__class_Ozero(_503168))], (4636 ^ _257747) ^ [_418032, _418034, _418036] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _418032, _418034), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _418036), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _418036), _418032), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _418036), _418034)))], (11480 ^ _257747) ^ [] : [-(class_Rings_Odvd(tc_RealDef_Oreal))], (11402 ^ _257747) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_RealDef_Oreal))], (5656 ^ _257747) ^ [_455173, _455175, _455177] : [class_Fields_Olinordered__field(_455173), c_Orderings_Oord__class_Oless(_455173, _455175, _455177), c_Orderings_Oord__class_Oless(_455173, c_Groups_Ozero__class_Ozero(_455173), _455175), -(c_Orderings_Oord__class_Oless(_455173, c_Rings_Oinverse__class_Oinverse(_455173, _455177), c_Rings_Oinverse__class_Oinverse(_455173, _455175)))], (6055 ^ _257747) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Polynomial_Omonom(tc_Complex_Ocomplex, v_a____, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))], (1943 ^ _257747) ^ [_322076] : [class_RealVector_Oreal__algebra__1(_322076), -(c_RealVector_Oof__real(_322076, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(_322076))], (9916 ^ _257747) ^ [_604587, _604589] : [class_RealVector_Oreal__normed__algebra(_604587), 9920 ^ _257747 : [(9921 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 9919 ^ [_604587, _604589]))], (9923 ^ _257747) ^ [_604886] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_604587, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_604587), _604886), _604589)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_604587, _604886)), 9919 ^ [_604587, _604589])))]]], (6321 ^ _257747) ^ [_478992, _478994] : [class_Rings_Ocomm__semiring__1(_478992), -(hAPP(c_Polynomial_Opoly(_478992, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_478992))), _478994) = c_Groups_Oone__class_Oone(_478992))], (9985 ^ _257747) ^ [_607261, _607263] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _607261, _607263), -(c_Nat__Transfer_Otsub(_607263, _607261) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, _607263, _607261))], (8670 ^ _257747) ^ [_563498] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _563498) = _563498)], (10123 ^ _257747) ^ [_612176] : [class_Rings_Olinordered__idom(_612176), c_Polynomial_Opos__poly(_612176, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_612176)))], (11194 ^ _257747) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Int_Oint))], (5828 ^ _257747) ^ [_460537, _460539, _460541] : [class_Fields_Ofield(_460537), -(_460539 = c_Groups_Ozero__class_Ozero(_460537)), -(_460541 = c_Groups_Ozero__class_Ozero(_460537)), -(c_Groups_Oplus__class_Oplus(_460537, c_Rings_Oinverse__class_Oinverse(_460537, _460539), c_Rings_Oinverse__class_Oinverse(_460537, _460541)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_460537), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_460537), c_Groups_Oplus__class_Oplus(_460537, _460539, _460541)), c_Rings_Oinverse__class_Oinverse(_460537, _460539))), c_Rings_Oinverse__class_Oinverse(_460537, _460541)))], (11218 ^ _257747) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (9975 ^ _257747) ^ [_606900, _606902] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _606900), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _606902), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_RComplete_Onatfloor(_606900)), c_RComplete_Onatfloor(_606902)), c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _606900), _606902))))], (1897 ^ _257747) ^ [_320397, _320399, _320401] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _320397), 1900 ^ _257747 : [(1901 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _320399), _320397), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _320401), _320397)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _320399, _320401))], (1907 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _320399, _320401), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _320399), _320397), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _320401), _320397)))]]], (6778 ^ _257747) ^ [_496088, _496090, _496092, _496094] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_496088), 6781 ^ _257747 : [(6782 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_496088, c_Groups_Oplus__class_Oplus(_496088, _496090, _496092), c_Groups_Oplus__class_Oplus(_496088, _496094, _496092)), -(c_Orderings_Oord__class_Oless__eq(_496088, _496090, _496094))], (6788 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_496088, _496090, _496094), -(c_Orderings_Oord__class_Oless__eq(_496088, c_Groups_Oplus__class_Oplus(_496088, _496090, _496092), c_Groups_Oplus__class_Oplus(_496088, _496094, _496092)))]]], (9546 ^ _257747) ^ [_592227, _592229, _592231] : [class_Orderings_Opreorder(_592227), 9549 ^ _257747 : [(9550 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_592227, _592229, _592231), 9553 ^ _257747 : [(9554 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_592227, _592229, _592231))], (9556 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_592227, _592231, _592229)]]], (9558 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(_592227, _592229, _592231)), c_Orderings_Oord__class_Oless__eq(_592227, _592229, _592231), -(c_Orderings_Oord__class_Oless__eq(_592227, _592231, _592229))]]], (894 ^ _257747) ^ [_285291, _285293, _285295, _285297, _285299, _285301] : [-(c_Polynomial_Osynthetic__div(_285301, _285297, _285293) = c_Polynomial_Osynthetic__div(_285299, _285295, _285291)), _285301 = _285299, _285297 = _285295, _285293 = _285291], (4478 ^ _257747) ^ [_412535] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _412535, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _412535), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _412535), _412535))))], (5528 ^ _257747) ^ [_451005, _451007, _451009, _451011, _451013] : [class_Groups_Oab__group__add(_451005), -(c_Groups_Ominus__class_Ominus(_451005, c_Groups_Oplus__class_Oplus(_451005, _451007, _451009), c_Groups_Oplus__class_Oplus(_451005, _451011, _451013)) = c_Groups_Oplus__class_Oplus(_451005, c_Groups_Ominus__class_Ominus(_451005, _451007, _451011), c_Groups_Ominus__class_Ominus(_451005, _451009, _451013)))], (5428 ^ _257747) ^ [_447637, _447639, _447641] : [class_Power_Opower(_447637), 5431 ^ _257747 : [(5432 ^ _257747) ^ [] : [_447639 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_447637), _447641), _447639) = c_Groups_Oone__class_Oone(_447637))], (5438 ^ _257747) ^ [] : [-(_447639 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_447637), _447641), _447639) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_447637), _447641), hAPP(hAPP(c_Power_Opower__class_Opower(_447637), _447641), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _447639, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (9644 ^ _257747) ^ [_595214, _595216, _595218] : [class_Orderings_Oorder(_595214), -(_595216 = _595218), c_Orderings_Oord__class_Oless__eq(_595214, _595218, _595216), -(c_Orderings_Oord__class_Oless(_595214, _595218, _595216))], (3739 ^ _257747) ^ [_384243, _384245] : [class_Rings_Odivision__ring(_384243), -(_384245 = c_Groups_Ozero__class_Ozero(_384243)), -(c_Rings_Oinverse__class_Oinverse(_384243, c_Groups_Ouminus__class_Ouminus(_384243, _384245)) = c_Groups_Ouminus__class_Ouminus(_384243, c_Rings_Oinverse__class_Oinverse(_384243, _384245)))], (4135 ^ _257747) ^ [_399664] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _399664) = _399664)], (11526 ^ _257747) ^ [] : [-(class_Groups_Oab__group__add(tc_Complex_Ocomplex))], (11224 ^ _257747) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (1403 ^ _257747) ^ [_303543, _303545] : [class_Groups_Omonoid__mult(_303543), -(hAPP(hAPP(c_Power_Opower__class_Opower(_303543), _303545), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _303545)], (8850 ^ _257747) ^ [_569903, _569905, _569907, _569909, _569911] : [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), _569903), _569905), _569907), c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _569903), _569909), _569911)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _569911, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _569903, _569911), c_Orderings_Oord__class_Oless(tc_Int_Oint, _569903, _569907), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _569909, _569905))], (1397 ^ _257747) ^ [_303263, _303265, _303267, _303269] : [class_Groups_Omonoid__mult(_303263), -(hAPP(hAPP(c_Power_Opower__class_Opower(_303263), _303265), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _303267), _303269)) = hAPP(hAPP(c_Power_Opower__class_Opower(_303263), hAPP(hAPP(c_Power_Opower__class_Opower(_303263), _303265), _303267)), _303269))], (842 ^ _257747) ^ [_283040, _283042] : [-(class_Rings_Ocomm__semiring__1(_283040)), _283042 = _283040, class_Rings_Ocomm__semiring__1(_283042)], (8614 ^ _257747) ^ [_561476, _561478] : [c_Groups_Oabs__class_Oabs(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _561476), _561478)) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(c_Groups_Oabs__class_Oabs(tc_Int_Oint, _561476) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (1969 ^ _257747) ^ [_323068, _323070, _323072, _323074] : [class_Rings_Olinordered__semidom(_323068), c_Orderings_Oord__class_Oless(_323068, _323070, _323072), c_Orderings_Oord__class_Oless__eq(_323068, c_Groups_Ozero__class_Ozero(_323068), _323070), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _323074), -(c_Orderings_Oord__class_Oless(_323068, hAPP(hAPP(c_Power_Opower__class_Opower(_323068), _323070), _323074), hAPP(hAPP(c_Power_Opower__class_Opower(_323068), _323072), _323074)))], (8083 ^ _257747) ^ [_540094, _540096, _540098, _540100] : [class_Rings_Ocomm__semiring__1(_540094), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_540094), hAPP(hAPP(c_Power_Opower__class_Opower(_540094), _540096), _540098)), hAPP(hAPP(c_Power_Opower__class_Opower(_540094), _540096), _540100)) = hAPP(hAPP(c_Power_Opower__class_Opower(_540094), _540096), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _540098, _540100)))], (978 ^ _257747) ^ [_288324, _288326, _288328, _288330] : [-(c_RealDef_Oreal(_288330, _288326) = c_RealDef_Oreal(_288328, _288324)), _288330 = _288328, _288326 = _288324], (2422 ^ _257747) ^ [_339448, _339450] : [class_Rings_Olinordered__semidom(_339448), -(c_Orderings_Oord__class_Oless(_339448, _339450, c_Groups_Oplus__class_Oplus(_339448, _339450, c_Groups_Oone__class_Oone(_339448))))], (1193 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), v_m____))], (5130 ^ _257747) ^ [_435731, _435733, _435735] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _435731, _435733), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _435735, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _435733, _435731)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _435735, _435733), _435731))], (5092 ^ _257747) ^ [_434465, _434467, _434469] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _434465, _434467), 5095 ^ _257747 : [(5096 ^ _257747) ^ [] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _434467, _434465) = _434469, -(_434467 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _434469, _434465))], (5102 ^ _257747) ^ [] : [_434467 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _434469, _434465), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _434467, _434465) = _434469)]]], (6505 ^ _257747) ^ [_486397, _486399, _486401, _486403] : [class_Rings_Ocomm__semiring__0(_486397), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_486397)), _486399), c_Polynomial_OpCons(_486397, _486401, _486403)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_486397), c_Polynomial_Osmult(_486397, _486401, _486399), c_Polynomial_OpCons(_486397, c_Groups_Ozero__class_Ozero(_486397), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_486397)), _486399), _486403))))], (4834 ^ _257747) ^ [_424937, _424939, _424941] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _424937, _424939), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _424937, _424941)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _424939, _424941))], (8748 ^ _257747) ^ [_566140, _566142] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _566140, _566142) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _566142, _566140))], (11754 ^ _257747) ^ [_664916] : [class_Rings_Ocomm__semiring__0(_664916), -(class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(_664916)))], (7332 ^ _257747) ^ [_515123, _515125] : [class_Groups_Olinordered__ab__group__add(_515123), 7335 ^ _257747 : [(7336 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_515123, c_Groups_Ozero__class_Ozero(_515123), c_Groups_Oplus__class_Oplus(_515123, _515125, _515125)), -(c_Orderings_Oord__class_Oless__eq(_515123, c_Groups_Ozero__class_Ozero(_515123), _515125))], (7342 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_515123, c_Groups_Ozero__class_Ozero(_515123), _515125), -(c_Orderings_Oord__class_Oless__eq(_515123, c_Groups_Ozero__class_Ozero(_515123), c_Groups_Oplus__class_Oplus(_515123, _515125, _515125)))]]], (11052 ^ _257747) ^ [_644745, _644747, _644749] : [class_Rings_Olinordered__idom(_644745), c_Groups_Oabs__class_Oabs(_644745, _644747) = c_Groups_Oabs__class_Oabs(_644745, _644749), -(c_Rings_Odvd__class_Odvd(_644745, _644747, _644749))], (11410 ^ _257747) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_RealDef_Oreal))], (5670 ^ _257747) ^ [_455595, _455597] : [class_Fields_Olinordered__field(_455595), c_Orderings_Oord__class_Oless(_455595, _455597, c_Groups_Ozero__class_Ozero(_455595)), -(c_Orderings_Oord__class_Oless(_455595, c_Rings_Oinverse__class_Oinverse(_455595, _455597), c_Groups_Ozero__class_Ozero(_455595)))], (8648 ^ _257747) ^ [_562787, _562789] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _562787, _562789), 8651 ^ _257747 : [(8652 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _562787, _562789))], (8654 ^ _257747) ^ [] : [_562787 = _562789]]], (7726 ^ _257747) ^ [_527552, _527554] : [class_Groups_Ogroup__add(_527552), -(c_Groups_Ominus__class_Ominus(_527552, c_Groups_Ozero__class_Ozero(_527552), _527554) = c_Groups_Ouminus__class_Ouminus(_527552, _527554))], (4762 ^ _257747) ^ [_422130] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____), _422130))))], (702 ^ _257747) ^ [_278910, _278912] : [-(class_Groups_Ouminus(_278910)), _278912 = _278910, class_Groups_Ouminus(_278912)], (4800 ^ _257747) ^ [_423664, _423666] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _423664, _423666) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _423666, _423664) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_423664 = _423666)], (998 ^ _257747) ^ [_289070, _289072, _289074, _289076, _289078, _289080] : [-(c_Polynomial_Oorder(_289080, _289076, _289072) = c_Polynomial_Oorder(_289078, _289074, _289070)), _289080 = _289078, _289076 = _289074, _289072 = _289070], (11290 ^ _257747) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (10053 ^ _257747) ^ [_609730, _609732, _609734] : [class_Rings_Olinordered__idom(_609730), 10056 ^ _257747 : [(10057 ^ _257747) ^ [] : [c_Polynomial_Opos__poly(_609730, c_Polynomial_OpCons(_609730, _609732, _609734)), -(c_Polynomial_Opos__poly(_609730, _609734)), 10064 ^ _257747 : [(10065 ^ _257747) ^ [] : [-(_609734 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_609730)))], (10067 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(_609730, c_Groups_Ozero__class_Ozero(_609730), _609732))]]], (10069 ^ _257747) ^ [] : [-(c_Polynomial_Opos__poly(_609730, c_Polynomial_OpCons(_609730, _609732, _609734))), 10070 ^ _257747 : [(10071 ^ _257747) ^ [] : [c_Polynomial_Opos__poly(_609730, _609734)], (10073 ^ _257747) ^ [] : [_609734 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_609730)), c_Orderings_Oord__class_Oless(_609730, c_Groups_Ozero__class_Ozero(_609730), _609732)]]]]], (1189 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), v_t____))], (5236 ^ _257747) ^ [_439694, _439696, _439698, _439700] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _439694, _439696), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _439698), c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _439700)))), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _439694, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _439698))), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _439696, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _439700))))))], (3699 ^ _257747) ^ [] : [-(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (1050 ^ _257747) ^ [_290921, _290923] : [_290923 = _290921, -(c_Groups_Oone__class_Oone(_290923) = c_Groups_Oone__class_Oone(_290921))], (3395 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_RealVector_Oof__real(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))))), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_RealVector_Oof__real(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____)))), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)))))))], (11418 ^ _257747) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal))], (10157 ^ _257747) ^ [_613320, _613322] : [-(c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _613320, _613322)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _613320), c_RealDef_Oreal(tc_Nat_Onat, _613322)))], (8173 ^ _257747) ^ [_544664, _544666, _544668] : [class_Rings_Ocomm__semiring__1(_544664), -(c_Groups_Oplus__class_Oplus(_544664, _544666, _544668) = c_Groups_Oplus__class_Oplus(_544664, _544668, _544666))], (11562 ^ _257747) ^ [] : [-(class_Rings_Oidom(tc_Complex_Ocomplex))], (8095 ^ _257747) ^ [_540628, _540630, _540632] : [class_Rings_Ocomm__semiring__1(_540628), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_540628), _540630), _540632) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_540628), _540632), _540630))], (11308 ^ _257747) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (6830 ^ _257747) ^ [_497928, _497930, _497932, _497934, _497936] : [class_Groups_Oordered__ab__semigroup__add(_497928), c_Orderings_Oord__class_Oless__eq(_497928, _497930, _497932), c_Orderings_Oord__class_Oless__eq(_497928, _497934, _497936), -(c_Orderings_Oord__class_Oless__eq(_497928, c_Groups_Oplus__class_Oplus(_497928, _497930, _497934), c_Groups_Oplus__class_Oplus(_497928, _497932, _497936)))], (1070 ^ _257747) ^ [_291711, _291713, _291715, _291717, _291719, _291721] : [-(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_291721, _291717, _291713) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_291719, _291715, _291711)), _291721 = _291719, _291717 = _291715, _291713 = _291711], (11156 ^ _257747) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (4788 ^ _257747) ^ [_423180, _423182, _423184] : [class_Rings_Olinordered__idom(_423180), -(c_Groups_Oabs__class_Oabs(_423180, hAPP(hAPP(c_Power_Opower__class_Opower(_423180), _423182), _423184)) = hAPP(hAPP(c_Power_Opower__class_Opower(_423180), c_Groups_Oabs__class_Oabs(_423180, _423182)), _423184))], (11388 ^ _257747) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal))], (11382 ^ _257747) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal))], (6896 ^ _257747) ^ [_500232, _500234, _500236, _500238] : [class_Groups_Oordered__cancel__ab__semigroup__add(_500232), c_Orderings_Oord__class_Oless(_500232, _500234, _500236), -(c_Orderings_Oord__class_Oless(_500232, c_Groups_Oplus__class_Oplus(_500232, _500234, _500238), c_Groups_Oplus__class_Oplus(_500232, _500236, _500238)))], (8672 ^ _257747) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (11516 ^ _257747) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex))], (11556 ^ _257747) ^ [] : [-(class_Power_Opower(tc_Complex_Ocomplex))], (9212 ^ _257747) ^ [_581788, _581790, _581792] : [class_Orderings_Olinorder(_581788), 9215 ^ _257747 : [(9226 ^ _257747) ^ [] : [9227 ^ _257747 : [(9228 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_581788, _581790, _581792)], (9230 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_581788, _581792, _581790)]], _581790 = _581792], (9216 ^ _257747) ^ [] : [-(_581790 = _581792), -(c_Orderings_Oord__class_Oless(_581788, _581790, _581792)), -(c_Orderings_Oord__class_Oless(_581788, _581792, _581790))]]], (1415 ^ _257747) ^ [_304035, _304037, _304039] : [hAPP(_304039, 1416 ^ [_304035, _304037, _304039]) = hAPP(_304039, 1417 ^ [_304035, _304037, _304039]), -(c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(_304035, _304037, _304039))], (6303 ^ _257747) ^ [_478060, _478062, _478064, _478066] : [class_Rings_Ocomm__ring__1(_478060), -(hAPP(c_Polynomial_Opoly(_478060, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_478060)), c_Polynomial_Omonom(_478060, c_Groups_Oone__class_Oone(_478060), _478062)), _478064)), _478066) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_478060), hAPP(hAPP(c_Power_Opower__class_Opower(_478060), _478066), _478062)), hAPP(c_Polynomial_Opoly(_478060, _478064), _478066)))], (6057 ^ _257747) ^ [] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Polynomial_Omonom(tc_Complex_Ocomplex, v_a____, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))))))], (10371 ^ _257747) ^ [_620718, _620720] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _620718), _620720), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _620720, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _620718), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_RComplete_Onatfloor(_620720) = _620718)], (9853 ^ _257747) ^ [_602044] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_602044), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _602044, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (3096 ^ _257747) ^ [_361783, _361785, _361787, _361789] : [class_Rings_Olinordered__semiring__strict(_361783), c_Orderings_Oord__class_Oless(_361783, _361785, _361787), c_Orderings_Oord__class_Oless(_361783, c_Groups_Ozero__class_Ozero(_361783), _361789), -(c_Orderings_Oord__class_Oless(_361783, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_361783), _361785), _361789), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_361783), _361787), _361789)))], (2057 ^ _257747) ^ [_325970, _325972, _325974] : [class_Rings_Olinordered__semidom(_325970), c_Orderings_Oord__class_Oless(_325970, c_Groups_Oone__class_Oone(_325970), _325972), -(c_Orderings_Oord__class_Oless(_325970, hAPP(hAPP(c_Power_Opower__class_Opower(_325970), _325972), _325974), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_325970), _325972), hAPP(hAPP(c_Power_Opower__class_Opower(_325970), _325972), _325974))))], (11236 ^ _257747) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (5628 ^ _257747) ^ [_454312, _454314] : [class_Fields_Olinordered__field(_454312), c_Orderings_Oord__class_Oless(_454312, c_Rings_Oinverse__class_Oinverse(_454312, _454314), c_Groups_Ozero__class_Ozero(_454312)), -(_454314 = c_Groups_Ozero__class_Ozero(_454312)), -(c_Orderings_Oord__class_Oless(_454312, _454314, c_Groups_Ozero__class_Ozero(_454312)))], (8586 ^ _257747) ^ [_560379, _560381] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _560379, _560381), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _560379, _560381), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (10287 ^ _257747) ^ [_617885, _617887] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _617885), 10290 ^ _257747 : [(10291 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _617887, c_RComplete_Onatfloor(_617885)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _617887), _617885))], (10297 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _617887), _617885), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _617887, c_RComplete_Onatfloor(_617885)))]]], (11500 ^ _257747) ^ [] : [-(class_RealVector_Oreal__div__algebra(tc_Complex_Ocomplex))], (8912 ^ _257747) ^ [_572008, _572010, _572012] : [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), _572008), _572010), _572012), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _572012), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _572008), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _572010, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (2256 ^ _257747) ^ [_332879, _332881, _332883] : [class_Rings_Oring(_332879), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_332879), c_Groups_Ouminus__class_Ouminus(_332879, _332881)), c_Groups_Ouminus__class_Ouminus(_332879, _332883)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_332879), _332881), _332883))], (11406 ^ _257747) ^ [] : [-(class_Rings_Oordered__semiring(tc_RealDef_Oreal))], (3657 ^ _257747) ^ [_380755] : [class_Rings_Odivision__ring(_380755), -(c_Rings_Oinverse__class_Oinverse(_380755, c_Groups_Oone__class_Oone(_380755)) = c_Groups_Oone__class_Oone(_380755))], (6636 ^ _257747) ^ [_491347, _491349, _491351, _491353] : [class_Groups_Oab__semigroup__add(_491347), -(c_Groups_Oplus__class_Oplus(_491347, c_Groups_Oplus__class_Oplus(_491347, _491349, _491351), _491353) = c_Groups_Oplus__class_Oplus(_491347, _491349, c_Groups_Oplus__class_Oplus(_491347, _491351, _491353)))], (8730 ^ _257747) ^ [_565381] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Complex_Oii), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Complex_Oii), _565381)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, _565381))], (11262 ^ _257747) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (5518 ^ _257747) ^ [_450503] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), _450503)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)), _450503)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (11670 ^ _257747) ^ [_662256] : [class_Rings_Olinordered__idom(_662256), -(class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(_662256)))], (4520 ^ _257747) ^ [_413977] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _413977) = _413977)], (3663 ^ _257747) ^ [_380971, _380973] : [class_Rings_Odivision__ring__inverse__zero(_380971), -(c_Rings_Oinverse__class_Oinverse(_380971, c_Groups_Ouminus__class_Ouminus(_380971, _380973)) = c_Groups_Ouminus__class_Ouminus(_380971, c_Rings_Oinverse__class_Oinverse(_380971, _380973)))], (7128 ^ _257747) ^ [_507982, _507984, _507986] : [class_Groups_Oordered__ab__group__add(_507982), 7131 ^ _257747 : [(7132 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_507982, _507984, c_Groups_Ouminus__class_Ouminus(_507982, _507986)), -(c_Orderings_Oord__class_Oless__eq(_507982, _507986, c_Groups_Ouminus__class_Ouminus(_507982, _507984)))], (7138 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_507982, _507986, c_Groups_Ouminus__class_Ouminus(_507982, _507984)), -(c_Orderings_Oord__class_Oless__eq(_507982, _507984, c_Groups_Ouminus__class_Ouminus(_507982, _507986)))]]], (6291 ^ _257747) ^ [_477486, _477488, _477490] : [class_Rings_Ocomm__ring(_477486), -(c_Polynomial_Osmult(_477486, _477488, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_477486), _477490)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_477486), c_Polynomial_Osmult(_477486, _477488, _477490)))], (1056 ^ _257747) ^ [_291195, _291197, _291199, _291201, _291203, _291205] : [-(c_Groups_Oplus__class_Oplus(_291205, _291201, _291197) = c_Groups_Oplus__class_Oplus(_291203, _291199, _291195)), _291205 = _291203, _291201 = _291199, _291197 = _291195], (2428 ^ _257747) ^ [_339656] : [class_Rings_Olinordered__semidom(_339656), -(c_Orderings_Oord__class_Oless(_339656, c_Groups_Ozero__class_Ozero(_339656), c_Groups_Oplus__class_Oplus(_339656, c_Groups_Oone__class_Oone(_339656), c_Groups_Oone__class_Oone(_339656))))], (11466 ^ _257747) ^ [] : [-(class_Groups_Ominus(tc_RealDef_Oreal))], (3545 ^ _257747) ^ [_377061, _377063] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _377061, _377063)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _377061), _377063))], (2744 ^ _257747) ^ [_350222, _350224, _350226, _350228] : [class_Rings_Oordered__semiring(_350222), c_Orderings_Oord__class_Oless__eq(_350222, _350224, _350226), c_Orderings_Oord__class_Oless__eq(_350222, c_Groups_Ozero__class_Ozero(_350222), _350228), -(c_Orderings_Oord__class_Oless__eq(_350222, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_350222), _350228), _350224), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_350222), _350228), _350226)))], (11502 ^ _257747) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex))], (11090 ^ _257747) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal))], (10089 ^ _257747) ^ [_610922, _610924] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _610922), c_RealDef_Oreal(tc_Nat_Onat, _610924)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _610922, _610924))], (4051 ^ _257747) ^ [_396671, _396673, _396675] : [_396673 = _396675, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _396671, _396673) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _396671, _396675))], (1739 ^ _257747) ^ [_315169, _315171, _315173] : [class_Rings_Olinordered__semidom(_315169), c_Orderings_Oord__class_Oless__eq(_315169, c_Groups_Oone__class_Oone(_315169), _315171), -(c_Orderings_Oord__class_Oless__eq(_315169, c_Groups_Oone__class_Oone(_315169), hAPP(hAPP(c_Power_Opower__class_Opower(_315169), _315171), _315173)))], (1429 ^ _257747) ^ [_304675, _304677, _304679, _304681] : [class_Rings_Olinordered__semidom(_304675), hAPP(hAPP(c_Power_Opower__class_Opower(_304675), _304677), _304679) = hAPP(hAPP(c_Power_Opower__class_Opower(_304675), _304681), _304679), c_Orderings_Oord__class_Oless__eq(_304675, c_Groups_Ozero__class_Ozero(_304675), _304677), c_Orderings_Oord__class_Oless__eq(_304675, c_Groups_Ozero__class_Ozero(_304675), _304681), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _304679), -(_304677 = _304681)], (3749 ^ _257747) ^ [_384585, _384587, _384589] : [class_Rings_Odivision__ring(_384585), -(_384587 = c_Groups_Ozero__class_Ozero(_384585)), -(c_Rings_Oinverse__class_Oinverse(_384585, hAPP(hAPP(c_Power_Opower__class_Opower(_384585), _384587), _384589)) = hAPP(hAPP(c_Power_Opower__class_Opower(_384585), c_Rings_Oinverse__class_Oinverse(_384585, _384587)), _384589))], (11372 ^ _257747) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal))], (4227 ^ _257747) ^ [_402850, _402852, _402854] : [4228 ^ _257747 : [(4229 ^ _257747) ^ [] : [_402852 = _402854], (4231 ^ _257747) ^ [] : [_402850 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _402850), _402852) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _402850), _402854))], (3397 ^ _257747) ^ [_371778, _371780] : [-(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _371778, _371780) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _371778, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _371780)))], (4408 ^ _257747) ^ [_409583, _409585, _409587] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _409583, _409585), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _409583, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _409587, _409585)))], (1955 ^ _257747) ^ [_322584, _322586, _322588, _322590] : [class_Rings_Olinordered__semidom(_322584), c_Orderings_Oord__class_Oless(_322584, hAPP(hAPP(c_Power_Opower__class_Opower(_322584), _322586), _322588), hAPP(hAPP(c_Power_Opower__class_Opower(_322584), _322590), _322588)), c_Orderings_Oord__class_Oless__eq(_322584, c_Groups_Ozero__class_Ozero(_322584), _322590), -(c_Orderings_Oord__class_Oless(_322584, _322586, _322590))], (8666 ^ _257747) ^ [_563322, _563324] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _563322), _563324) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _563324), _563322))], (2216 ^ _257747) ^ [_331202, _331204] : [class_RealVector_Oreal__algebra__1(_331202), -(c_RealVector_Oof__real(_331202, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _331204)) = c_Groups_Ouminus__class_Ouminus(_331202, c_RealVector_Oof__real(_331202, _331204)))], (8484 ^ _257747) ^ [_556580] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _556580), _556580) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (3917 ^ _257747) ^ [_391378, _391380, _391382, _391384, _391386, _391388] : [class_Rings_Oordered__ring(_391378), 3920 ^ _257747 : [(3921 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_391378, c_Groups_Oplus__class_Oplus(_391378, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_391378), _391380), _391382), _391384), c_Groups_Oplus__class_Oplus(_391378, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_391378), _391386), _391382), _391388)), -(c_Orderings_Oord__class_Oless(_391378, c_Groups_Oplus__class_Oplus(_391378, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_391378), c_Groups_Ominus__class_Ominus(_391378, _391380, _391386)), _391382), _391384), _391388))], (3927 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_391378, c_Groups_Oplus__class_Oplus(_391378, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_391378), c_Groups_Ominus__class_Ominus(_391378, _391380, _391386)), _391382), _391384), _391388), -(c_Orderings_Oord__class_Oless(_391378, c_Groups_Oplus__class_Oplus(_391378, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_391378), _391380), _391382), _391384), c_Groups_Oplus__class_Oplus(_391378, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_391378), _391386), _391382), _391388)))]]], (1104 ^ _257747) ^ [_292933, _292935, _292937, _292939] : [-(c_Groups_Oabs__class_Oabs(_292939, _292935) = c_Groups_Oabs__class_Oabs(_292937, _292933)), _292939 = _292937, _292935 = _292933], (372 ^ _257747) ^ [_269175, _269177] : [-(class_Rings_Oordered__cancel__semiring(_269175)), _269177 = _269175, class_Rings_Oordered__cancel__semiring(_269177)], (10181 ^ _257747) ^ [_614104] : [_614104 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _614104), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (38 ^ _257747) ^ [_259132, _259134, _259136, _259138] : [-(c_Polynomial_Opos__poly(_259136, _259132)), c_Polynomial_Opos__poly(_259138, _259134), _259138 = _259136, _259134 = _259132], (2434 ^ _257747) ^ [_339908, _339910, _339912, _339914] : [class_Groups_Omonoid__mult(_339908), -(hAPP(hAPP(c_Power_Opower__class_Opower(_339908), _339910), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _339912, _339914)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_339908), hAPP(hAPP(c_Power_Opower__class_Opower(_339908), _339910), _339912)), hAPP(hAPP(c_Power_Opower__class_Opower(_339908), _339910), _339914)))], (3048 ^ _257747) ^ [_360212, _360214, _360216, _360218] : [class_Rings_Olinordered__ring__strict(_360212), c_Orderings_Oord__class_Oless(_360212, _360214, c_Groups_Ozero__class_Ozero(_360212)), 3055 ^ _257747 : [(3056 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_360212, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_360212), _360214), _360216), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_360212), _360214), _360218)), -(c_Orderings_Oord__class_Oless(_360212, _360218, _360216))], (3062 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_360212, _360218, _360216), -(c_Orderings_Oord__class_Oless(_360212, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_360212), _360214), _360216), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_360212), _360214), _360218)))]]], (9102 ^ _257747) ^ [_578248, _578250, _578252, _578254] : [class_Orderings_Oord(_578248), c_Orderings_Oord__class_Oless__eq(_578248, _578250, _578252), _578252 = _578254, -(c_Orderings_Oord__class_Oless__eq(_578248, _578250, _578254))], (1599 ^ _257747) ^ [_310572, _310574] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _310572, _310574), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _310572, _310574)), -(_310572 = _310574)], (11302 ^ _257747) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (6213 ^ _257747) ^ [_474541, _474543] : [class_Groups_Oab__group__add(_474541), -(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_474541), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_474541)), _474543) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_474541), _474543))], (4063 ^ _257747) ^ [_397132, _397134, _397136] : [_397132 = _397136, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _397132, _397134) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _397136, _397134))], (11244 ^ _257747) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (7064 ^ _257747) ^ [_506064, _506066] : [class_Groups_Ogroup__add(_506064), 7067 ^ _257747 : [(7068 ^ _257747) ^ [] : [c_Groups_Ozero__class_Ozero(_506064) = c_Groups_Ouminus__class_Ouminus(_506064, _506066), -(c_Groups_Ozero__class_Ozero(_506064) = _506066)], (7074 ^ _257747) ^ [] : [c_Groups_Ozero__class_Ozero(_506064) = _506066, -(c_Groups_Ozero__class_Ozero(_506064) = c_Groups_Ouminus__class_Ouminus(_506064, _506066))]]], (3020 ^ _257747) ^ [_359302, _359304, _359306] : [class_Rings_Olinordered__semiring__strict(_359302), c_Orderings_Oord__class_Oless(_359302, c_Groups_Ozero__class_Ozero(_359302), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_359302), _359304), _359306)), c_Orderings_Oord__class_Oless(_359302, c_Groups_Ozero__class_Ozero(_359302), _359304), -(c_Orderings_Oord__class_Oless(_359302, c_Groups_Ozero__class_Ozero(_359302), _359306))], (6658 ^ _257747) ^ [_492111, _492113, _492115, _492117, _492119] : [class_Groups_Oab__group__add(_492111), c_Groups_Ominus__class_Ominus(_492111, _492113, _492115) = c_Groups_Ominus__class_Ominus(_492111, _492117, _492119), 6665 ^ _257747 : [(6666 ^ _257747) ^ [] : [_492113 = _492115, -(_492117 = _492119)], (6672 ^ _257747) ^ [] : [_492117 = _492119, -(_492113 = _492115)]]], (4303 ^ _257747) ^ [_405758, _405760, _405762] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _405760, _405762), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _405758, _405760), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _405758, _405762)))], (8033 ^ _257747) ^ [_538049, _538051] : [8034 ^ _257747 : [(8035 ^ _257747) ^ [] : [_538051 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (8037 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _538049)]], -(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), _538049), _538051)))], (2400 ^ _257747) ^ [_338781, _338783] : [class_Rings_Oring__1__no__zero__divisors(_338781), 2403 ^ _257747 : [(2414 ^ _257747) ^ [] : [2415 ^ _257747 : [(2416 ^ _257747) ^ [] : [_338783 = c_Groups_Oone__class_Oone(_338781)], (2418 ^ _257747) ^ [] : [_338783 = c_Groups_Ouminus__class_Ouminus(_338781, c_Groups_Oone__class_Oone(_338781))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_338781), _338783), _338783) = c_Groups_Oone__class_Oone(_338781))], (2404 ^ _257747) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_338781), _338783), _338783) = c_Groups_Oone__class_Oone(_338781), -(_338783 = c_Groups_Oone__class_Oone(_338781)), -(_338783 = c_Groups_Ouminus__class_Ouminus(_338781, c_Groups_Oone__class_Oone(_338781)))]]], (1749 ^ _257747) ^ [_315532, _315534, _315536, _315538] : [class_Rings_Olinordered__semidom(_315532), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _315534, _315536), c_Orderings_Oord__class_Oless(_315532, c_Groups_Oone__class_Oone(_315532), _315538), -(c_Orderings_Oord__class_Oless(_315532, hAPP(hAPP(c_Power_Opower__class_Opower(_315532), _315538), _315534), hAPP(hAPP(c_Power_Opower__class_Opower(_315532), _315538), _315536)))], (5160 ^ _257747) ^ [_436942, _436944, _436946] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _436942, _436944), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _436946, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _436944, _436942)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _436946, _436942), _436944))], (8926 ^ _257747) ^ [_572452, _572454, _572456] : [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), _572452), _572454), _572456)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _572456, _572452), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _572452), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _572454))], (3625 ^ _257747) ^ [_379773, _379775] : [class_Rings_Odivision__ring(_379773), -(_379775 = c_Groups_Ozero__class_Ozero(_379773)), c_Rings_Oinverse__class_Oinverse(_379773, _379775) = c_Groups_Ozero__class_Ozero(_379773)], (10958 ^ _257747) ^ [_641595, _641597, _641599] : [class_Rings_Ocomm__semiring__0(_641595), 10961 ^ _257747 : [(10962 ^ _257747) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_641595, _641597, _641599) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_641595)), -(_641597 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_641595)))], (10968 ^ _257747) ^ [] : [_641597 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_641595)), -(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_641595, _641597, _641599) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_641595)))]]], (3082 ^ _257747) ^ [_361321, _361323, _361325] : [class_Rings_Olinordered__ring__strict(_361321), c_Orderings_Oord__class_Oless(_361321, _361323, c_Groups_Ozero__class_Ozero(_361321)), c_Orderings_Oord__class_Oless(_361321, _361325, c_Groups_Ozero__class_Ozero(_361321)), -(c_Orderings_Oord__class_Oless(_361321, c_Groups_Ozero__class_Ozero(_361321), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_361321), _361323), _361325)))], (8161 ^ _257747) ^ [_544118, _544120, _544122, _544124] : [class_Rings_Ocomm__semiring__1(_544118), -(c_Groups_Oplus__class_Oplus(_544118, _544120, c_Groups_Oplus__class_Oplus(_544118, _544122, _544124)) = c_Groups_Oplus__class_Oplus(_544118, c_Groups_Oplus__class_Oplus(_544118, _544120, _544122), _544124))], (4217 ^ _257747) ^ [_402564, _402566, _402568] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _402564), _402566) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _402564), _402568), -(_402566 = _402568), -(_402564 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4764 ^ _257747) ^ [] : [-(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____), v_c____) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))], (1537 ^ _257747) ^ [_308387, _308389, _308391] : [class_Rings_Oring__1__no__zero__divisors(_308387), -(_308389 = c_Groups_Ozero__class_Ozero(_308387)), hAPP(hAPP(c_Power_Opower__class_Opower(_308387), _308389), _308391) = c_Groups_Ozero__class_Ozero(_308387)], (11092 ^ _257747) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat))], (11468 ^ _257747) ^ [] : [-(class_Fields_Ofield(tc_RealDef_Oreal))], (7176 ^ _257747) ^ [_509518, _509520, _509522] : [class_Groups_Oordered__ab__group__add(_509518), c_Orderings_Oord__class_Oless__eq(_509518, _509520, _509522), -(c_Orderings_Oord__class_Oless__eq(_509518, c_Groups_Ouminus__class_Ouminus(_509518, _509522), c_Groups_Ouminus__class_Ouminus(_509518, _509520)))], (3885 ^ _257747) ^ [_389970, _389972, _389974, _389976, _389978, _389980] : [class_Rings_Oordered__ring(_389970), 3888 ^ _257747 : [(3889 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_389970, c_Groups_Oplus__class_Oplus(_389970, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_389970), _389972), _389974), _389976), c_Groups_Oplus__class_Oplus(_389970, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_389970), _389978), _389974), _389980)), -(c_Orderings_Oord__class_Oless__eq(_389970, c_Groups_Oplus__class_Oplus(_389970, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_389970), c_Groups_Ominus__class_Ominus(_389970, _389972, _389978)), _389974), _389976), _389980))], (3895 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_389970, c_Groups_Oplus__class_Oplus(_389970, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_389970), c_Groups_Ominus__class_Ominus(_389970, _389972, _389978)), _389974), _389976), _389980), -(c_Orderings_Oord__class_Oless__eq(_389970, c_Groups_Oplus__class_Oplus(_389970, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_389970), _389972), _389974), _389976), c_Groups_Oplus__class_Oplus(_389970, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_389970), _389978), _389974), _389980)))]]], (10227 ^ _257747) ^ [_615668] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _615668), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatfloor(_615668)), _615668))], (1925 ^ _257747) ^ [_321336] : [class_RealVector_Oreal__normed__algebra__1(_321336), -(c_RealVector_Onorm__class_Onorm(_321336, c_Groups_Oone__class_Oone(_321336)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (8522 ^ _257747) ^ [_558018, _558020] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _558018, _558020), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _558018, c_Groups_Oone__class_Oone(tc_Int_Oint)), _558020))], (11558 ^ _257747) ^ [] : [-(class_Groups_Ozero(tc_Complex_Ocomplex))], (672 ^ _257747) ^ [_278025, _278027] : [-(class_Rings_Ocomm__semiring__0(_278025)), _278027 = _278025, class_Rings_Ocomm__semiring__0(_278027)], (4402 ^ _257747) ^ [_409341, _409343, _409345] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _409341, _409343), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _409341, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _409343, _409345)))], (852 ^ _257747) ^ [_283335, _283337] : [-(class_Rings_Odvd(_283335)), _283337 = _283335, class_Rings_Odvd(_283337)], (10475 ^ _257747) ^ [_624759, _624761, _624763] : [class_Lattices_Oboolean__algebra(_624759), 10478 ^ _257747 : [(10479 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_624759, c_Groups_Ouminus__class_Ouminus(_624759, _624761), c_Groups_Ouminus__class_Ouminus(_624759, _624763)), -(c_Orderings_Oord__class_Oless__eq(_624759, _624763, _624761))], (10485 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_624759, _624763, _624761), -(c_Orderings_Oord__class_Oless__eq(_624759, c_Groups_Ouminus__class_Ouminus(_624759, _624761), c_Groups_Ouminus__class_Ouminus(_624759, _624763)))]]], (4139 ^ _257747) ^ [_399886, _399888] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _399886, _399888) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 4142 ^ _257747 : [(4143 ^ _257747) ^ [] : [-(_399886 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4145 ^ _257747) ^ [] : [-(_399888 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (5534 ^ _257747) ^ [_451265] : [class_Fields_Ofield__inverse__zero(_451265), -(c_Rings_Oinverse__class_Oinverse(_451265, c_Groups_Ozero__class_Ozero(_451265)) = c_Groups_Ozero__class_Ozero(_451265))], (3034 ^ _257747) ^ [_359750, _359752, _359754] : [class_Rings_Olinordered__semiring__strict(_359750), c_Orderings_Oord__class_Oless(_359750, c_Groups_Ozero__class_Ozero(_359750), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_359750), _359752), _359754)), c_Orderings_Oord__class_Oless(_359750, c_Groups_Ozero__class_Ozero(_359750), _359754), -(c_Orderings_Oord__class_Oless(_359750, c_Groups_Ozero__class_Ozero(_359750), _359752))], (11634 ^ _257747) ^ [_661116] : [class_Rings_Oidom(_661116), -(class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(_661116)))], (4610 ^ _257747) ^ [_417145, _417147, _417149] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _417145), 4613 ^ _257747 : [(4614 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _417145), _417147), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _417145), _417149)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _417147, _417149))], (4620 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _417147, _417149), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _417145), _417147), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _417145), _417149)))]]], (212 ^ _257747) ^ [_264455, _264457] : [-(class_RealVector_Oreal__algebra__1(_264455)), _264457 = _264455, class_RealVector_Oreal__algebra__1(_264457)], (1525 ^ _257747) ^ [_307909, _307911] : [class_RealVector_Oreal__normed__algebra(_307909), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_307909), c_Groups_Ozero__class_Ozero(_307909)), _307911) = c_Groups_Ozero__class_Ozero(_307909))], (1199 ^ _257747) ^ [] : [v_a____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)], (10257 ^ _257747) ^ [_616767] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _616767), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _616767)))], (1547 ^ _257747) ^ [_308736, _308738, _308740] : [class_Power_Opower(_308736), class_Rings_Omult__zero(_308736), class_Rings_Ono__zero__divisors(_308736), class_Rings_Ozero__neq__one(_308736), 1562 ^ _257747 : [(1563 ^ _257747) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_308736), _308738), _308740) = c_Groups_Ozero__class_Ozero(_308736), 1566 ^ _257747 : [(1567 ^ _257747) ^ [] : [-(_308738 = c_Groups_Ozero__class_Ozero(_308736))], (1569 ^ _257747) ^ [] : [_308740 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (1571 ^ _257747) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_308736), _308738), _308740) = c_Groups_Ozero__class_Ozero(_308736)), _308738 = c_Groups_Ozero__class_Ozero(_308736), -(_308740 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (4862 ^ _257747) ^ [_426025, _426027, _426029] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _426025, _426027), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _426025, _426029), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _426027, _426025), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _426029, _426025)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _426027, _426029))], (8516 ^ _257747) ^ [_557782, _557784, _557786] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _557782, _557784), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _557782, _557786), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _557784, _557786)))], (8259 ^ _257747) ^ [_548132, _548134, _548136, _548138, _548140] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_548132), 8262 ^ _257747 : [(8273 ^ _257747) ^ [] : [8274 ^ _257747 : [(8275 ^ _257747) ^ [] : [_548134 = _548138], (8277 ^ _257747) ^ [] : [_548136 = _548140]], -(c_Groups_Oplus__class_Oplus(_548132, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_548132), _548134), _548136), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_548132), _548138), _548140)) = c_Groups_Oplus__class_Oplus(_548132, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_548132), _548134), _548140), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_548132), _548138), _548136)))], (8263 ^ _257747) ^ [] : [c_Groups_Oplus__class_Oplus(_548132, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_548132), _548134), _548136), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_548132), _548138), _548140)) = c_Groups_Oplus__class_Oplus(_548132, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_548132), _548134), _548140), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_548132), _548138), _548136)), -(_548134 = _548138), -(_548136 = _548140)]]], (5234 ^ _257747) ^ [_439566] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _439566), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _439566)], (1254 ^ _257747) ^ [_298290] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _298290), 1258 ^ _257747 : [(1263 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, 1257 ^ [_298290], _298290))], (1261 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, 1257 ^ [_298290], c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (1259 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 1257 ^ [_298290]))]]], (6604 ^ _257747) ^ [_490263, _490265, _490267, _490269] : [class_Groups_Ocancel__semigroup__add(_490263), 6607 ^ _257747 : [(6608 ^ _257747) ^ [] : [c_Groups_Oplus__class_Oplus(_490263, _490265, _490267) = c_Groups_Oplus__class_Oplus(_490263, _490269, _490267), -(_490265 = _490269)], (6614 ^ _257747) ^ [] : [_490265 = _490269, -(c_Groups_Oplus__class_Oplus(_490263, _490265, _490267) = c_Groups_Oplus__class_Oplus(_490263, _490269, _490267))]]], (7014 ^ _257747) ^ [_504321, _504323, _504325, _504327, _504329] : [class_Groups_Oordered__ab__group__add(_504321), c_Groups_Ominus__class_Ominus(_504321, _504323, _504325) = c_Groups_Ominus__class_Ominus(_504321, _504327, _504329), 7021 ^ _257747 : [(7022 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_504321, _504323, _504325), -(c_Orderings_Oord__class_Oless(_504321, _504327, _504329))], (7028 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_504321, _504327, _504329), -(c_Orderings_Oord__class_Oless(_504321, _504323, _504325))]]], (5918 ^ _257747) ^ [_463551, _463553] : [class_Fields_Olinordered__field(_463551), c_Orderings_Oord__class_Oless(_463551, c_Groups_Ozero__class_Ozero(_463551), _463553), c_Orderings_Oord__class_Oless__eq(_463551, _463553, c_Groups_Oone__class_Oone(_463551)), -(c_Orderings_Oord__class_Oless__eq(_463551, c_Groups_Oone__class_Oone(_463551), c_Rings_Oinverse__class_Oinverse(_463551, _463553)))], (946 ^ _257747) ^ [_287170, _287172, _287174, _287176] : [-(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_287176, _287172) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_287174, _287170)), _287176 = _287174, _287172 = _287170], (4165 ^ _257747) ^ [_400752] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _400752, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_400752 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1323 ^ _257747) ^ [_300859, _300861] : [class_RealVector_Oreal__normed__vector(_300859), 1326 ^ _257747 : [(1327 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_300859, _300861)), _300861 = c_Groups_Ozero__class_Ozero(_300859)], (1333 ^ _257747) ^ [] : [-(_300861 = c_Groups_Ozero__class_Ozero(_300859)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_300859, _300861)))]]], (3875 ^ _257747) ^ [_389584, _389586] : [class_Rings_Odivision__ring(_389584), -(_389586 = c_Groups_Ozero__class_Ozero(_389584)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_389584), _389586), c_Rings_Oinverse__class_Oinverse(_389584, _389586)) = c_Groups_Oone__class_Oone(_389584))], (9991 ^ _257747) ^ [_607439, _607441] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _607439, _607441)), -(c_Nat__Transfer_Otsub(_607441, _607439) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (5943 ^ _257747) ^ [_464284, _464286] : [_464284 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _464286), _464284) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (10612 ^ _257747) ^ [_629488, _629490] : [class_Rings_Olinordered__idom(_629488), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_629488), c_Groups_Osgn__class_Osgn(_629488, _629490)), c_Groups_Oabs__class_Oabs(_629488, _629490)) = _629490)], (5416 ^ _257747) ^ [_447205, _447207, _447209] : [class_Groups_Omonoid__mult(_447205), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _447207), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_447205), hAPP(hAPP(c_Power_Opower__class_Opower(_447205), _447209), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _447207, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _447209) = hAPP(hAPP(c_Power_Opower__class_Opower(_447205), _447209), _447207))], (11760 ^ _257747) ^ [_665106] : [class_Rings_Ocomm__semiring__0(_665106), -(class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(_665106)))], (9600 ^ _257747) ^ [_593876, _593878, _593880] : [class_Orderings_Olinorder(_593876), -(c_Orderings_Oord__class_Oless__eq(_593876, _593878, _593880)), -(c_Orderings_Oord__class_Oless(_593876, _593880, _593878))], (2772 ^ _257747) ^ [_351190, _351192, _351194, _351196] : [class_Rings_Oordered__ring(_351190), c_Orderings_Oord__class_Oless__eq(_351190, _351192, _351194), c_Orderings_Oord__class_Oless__eq(_351190, _351196, c_Groups_Ozero__class_Ozero(_351190)), -(c_Orderings_Oord__class_Oless__eq(_351190, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_351190), _351194), _351196), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_351190), _351192), _351196)))], (11162 ^ _257747) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (1839 ^ _257747) ^ [_318501, _318503, _318505] : [class_RealVector_Oreal__normed__div__algebra(_318501), -(c_RealVector_Onorm__class_Onorm(_318501, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_318501), _318503), _318505)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_318501, _318503)), c_RealVector_Onorm__class_Onorm(_318501, _318505)))], (11430 ^ _257747) ^ [] : [-(class_Rings_Oordered__ring(tc_RealDef_Oreal))], (7186 ^ _257747) ^ [_509855, _509857, _509859] : [class_Groups_Ogroup__add(_509855), -(c_Groups_Oplus__class_Oplus(_509855, c_Groups_Ominus__class_Ominus(_509855, _509857, _509859), _509859) = _509857)], (11592 ^ _257747) ^ [_659786] : [class_Rings_Olinordered__idom(_659786), -(class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(_659786)))], (4490 ^ _257747) ^ [_413018, _413020] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _413018), _413020) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _413018 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _413020 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (20 ^ _257747) ^ [_258551, _258553, _258555, _258557, _258559, _258561] : [-(c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(_258559, _258555, _258551)), c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(_258561, _258557, _258553), _258561 = _258559, _258557 = _258555, _258553 = _258551], (9668 ^ _257747) ^ [_595961, _595963, _595965] : [class_Orderings_Opreorder(_595961), c_Orderings_Oord__class_Oless(_595961, _595963, _595965), -(c_Orderings_Oord__class_Oless__eq(_595961, _595963, _595965))], (52 ^ _257747) ^ [_259576, _259578, _259580, _259582] : [-(c_SEQ_Odecseq(_259580, _259576)), c_SEQ_Odecseq(_259582, _259578), _259582 = _259580, _259578 = _259576], (4430 ^ _257747) ^ [_410444, _410446, _410448] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _410444, _410446), _410448), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _410446, _410448))], (6369 ^ _257747) ^ [_481332, _481334] : [class_Rings_Ocomm__semiring__1(_481332), -(c_Polynomial_Osmult(_481332, c_Groups_Oone__class_Oone(_481332), _481334) = _481334)], (2184 ^ _257747) ^ [_330124, _330126] : [2185 ^ _257747 : [(2186 ^ _257747) ^ [_330199] : [_330126 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _330124, _330199)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _330124, _330126))], (5792 ^ _257747) ^ [_459449, _459451, _459453] : [class_Fields_Olinordered__field(_459449), c_Orderings_Oord__class_Oless__eq(_459449, _459451, _459453), c_Orderings_Oord__class_Oless(_459449, c_Groups_Ozero__class_Ozero(_459449), _459451), -(c_Orderings_Oord__class_Oless__eq(_459449, c_Rings_Oinverse__class_Oinverse(_459449, _459453), c_Rings_Oinverse__class_Oinverse(_459449, _459451)))], (4770 ^ _257747) ^ [_422448, _422450, _422452] : [class_Rings_Olinordered__idom(_422448), -(c_Groups_Oabs__class_Oabs(_422448, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_422448), _422450), _422452)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_422448), c_Groups_Oabs__class_Oabs(_422448, _422450)), c_Groups_Oabs__class_Oabs(_422448, _422452)))], (6161 ^ _257747) ^ [_472571, _472573, _472575, _472577] : [class_Rings_Ocomm__semiring__1(_472571), -(hAPP(c_Polynomial_Opoly(_472571, c_Polynomial_Omonom(_472571, _472573, _472575)), _472577) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_472571), _472573), hAPP(hAPP(c_Power_Opower__class_Opower(_472571), _472577), _472575)))], (11316 ^ _257747) ^ [] : [-(class_Groups_Ominus(tc_Nat_Onat))], (11082 ^ _257747) ^ [_645798] : [class_Groups_Ocancel__comm__monoid__add(_645798), -(class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(_645798)))], (1987 ^ _257747) ^ [_323651, _323653, _323655, _323657] : [class_Rings_Olinordered__semidom(_323651), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _323653, _323655), c_Orderings_Oord__class_Oless__eq(_323651, c_Groups_Ozero__class_Ozero(_323651), _323657), c_Orderings_Oord__class_Oless__eq(_323651, _323657, c_Groups_Oone__class_Oone(_323651)), -(c_Orderings_Oord__class_Oless__eq(_323651, hAPP(hAPP(c_Power_Opower__class_Opower(_323651), _323657), _323655), hAPP(hAPP(c_Power_Opower__class_Opower(_323651), _323657), _323653)))], (4347 ^ _257747) ^ [_407285, _407287] : [4348 ^ _257747 : [(4349 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _407285, _407287)], (4351 ^ _257747) ^ [] : [_407285 = _407287]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _407285, _407287))], (9334 ^ _257747) ^ [_585519, _585521, _585523] : [class_Orderings_Oorder(_585519), c_Orderings_Oord__class_Oless(_585519, _585521, _585523), _585521 = _585523], (8065 ^ _257747) ^ [_539387, _539389, _539391] : [class_Rings_Ocomm__semiring__0(_539387), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_539387), _539389, c_Polynomial_Osmult(_539387, _539391, c_Polynomial_Osynthetic__div(_539387, _539389, _539391))) = c_Polynomial_OpCons(_539387, hAPP(c_Polynomial_Opoly(_539387, _539389), _539391), c_Polynomial_Osynthetic__div(_539387, _539389, _539391)))], (11268 ^ _257747) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (11020 ^ _257747) ^ [_643739, _643741, _643743] : [class_Rings_Olinordered__idom(_643739), 11023 ^ _257747 : [(11024 ^ _257747) ^ [] : [c_Rings_Odvd__class_Odvd(_643739, _643741, c_Groups_Oabs__class_Oabs(_643739, _643743)), -(c_Rings_Odvd__class_Odvd(_643739, _643741, _643743))], (11030 ^ _257747) ^ [] : [c_Rings_Odvd__class_Odvd(_643739, _643741, _643743), -(c_Rings_Odvd__class_Odvd(_643739, _643741, c_Groups_Oabs__class_Oabs(_643739, _643743)))]]], (104 ^ _257747) ^ [_261247, _261249, _261251, _261253, _261255, _261257] : [-(c_Rings_Odvd__class_Odvd(_261255, _261251, _261247)), c_Rings_Odvd__class_Odvd(_261257, _261253, _261249), _261257 = _261255, _261253 = _261251, _261249 = _261247], (7802 ^ _257747) ^ [_530067, _530069, _530071] : [class_Groups_Oab__group__add(_530067), -(c_Groups_Ominus__class_Ominus(_530067, _530069, _530071) = c_Groups_Oplus__class_Oplus(_530067, _530069, c_Groups_Ouminus__class_Ouminus(_530067, _530071)))], (1012 ^ _257747) ^ [_289586, _289588, _289590, _289592, _289594, _289596] : [-(c_Polynomial_OpCons(_289596, _289592, _289588) = c_Polynomial_OpCons(_289594, _289590, _289586)), _289596 = _289594, _289592 = _289590, _289588 = _289586], (11550 ^ _257747) ^ [] : [-(class_Rings_Oring__1(tc_Complex_Ocomplex))], (11552 ^ _257747) ^ [] : [-(class_Groups_Ominus(tc_Complex_Ocomplex))], (3901 ^ _257747) ^ [_390674, _390676, _390678, _390680, _390682, _390684] : [class_Rings_Oordered__ring(_390674), 3904 ^ _257747 : [(3905 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_390674, c_Groups_Oplus__class_Oplus(_390674, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_390674), _390676), _390678), _390680), c_Groups_Oplus__class_Oplus(_390674, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_390674), _390682), _390678), _390684)), -(c_Orderings_Oord__class_Oless__eq(_390674, _390680, c_Groups_Oplus__class_Oplus(_390674, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_390674), c_Groups_Ominus__class_Ominus(_390674, _390682, _390676)), _390678), _390684)))], (3911 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_390674, _390680, c_Groups_Oplus__class_Oplus(_390674, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_390674), c_Groups_Ominus__class_Ominus(_390674, _390682, _390676)), _390678), _390684)), -(c_Orderings_Oord__class_Oless__eq(_390674, c_Groups_Oplus__class_Oplus(_390674, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_390674), _390676), _390678), _390680), c_Groups_Oplus__class_Oplus(_390674, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_390674), _390682), _390678), _390684)))]]], (11374 ^ _257747) ^ [] : [-(class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal))], (3569 ^ _257747) ^ [_377944, _377946] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _377946, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _377944)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _377944, _377946), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (10910 ^ _257747) ^ [_639877, _639879, _639881] : [class_Rings_Odvd(_639877), class_Rings_Osemiring__0(_639877), 10917 ^ _257747 : [(10918 ^ _257747) ^ [] : [10919 ^ _257747 : [(10920 ^ _257747) ^ [_640186] : [hBOOL(hAPP(_639879, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_639877), _639881), _640186)))]], 10922 ^ _257747 : [(10923 ^ _257747) ^ [] : [-(c_Rings_Odvd__class_Odvd(_639877, _639881, c_Groups_Oplus__class_Oplus(_639877, 10921 ^ [_639877, _639879, _639881], c_Groups_Ozero__class_Ozero(_639877))))], (10925 ^ _257747) ^ [] : [-(hBOOL(hAPP(_639879, 10921 ^ [_639877, _639879, _639881])))]]], (10927 ^ _257747) ^ [] : [-(hBOOL(hAPP(_639879, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_639877), _639881), 10934 ^ [_639877, _639879, _639881])))), 10928 ^ _257747 : [(10929 ^ _257747) ^ [_640526] : [c_Rings_Odvd__class_Odvd(_639877, _639881, c_Groups_Oplus__class_Oplus(_639877, _640526, c_Groups_Ozero__class_Ozero(_639877))), hBOOL(hAPP(_639879, _640526))]]]]], (4001 ^ _257747) ^ [_394833, _394835] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _394833, _394835), _394835 = _394833], (2730 ^ _257747) ^ [_349738, _349740, _349742, _349744] : [class_Rings_Oordered__semiring(_349738), c_Orderings_Oord__class_Oless__eq(_349738, _349740, _349742), c_Orderings_Oord__class_Oless__eq(_349738, c_Groups_Ozero__class_Ozero(_349738), _349744), -(c_Orderings_Oord__class_Oless__eq(_349738, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_349738), _349740), _349744), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_349738), _349742), _349744)))], (10515 ^ _257747) ^ [_626303, _626305, _626307] : [class_Lattices_Oboolean__algebra(_626303), 10518 ^ _257747 : [(10519 ^ _257747) ^ [] : [c_Groups_Ouminus__class_Ouminus(_626303, _626305) = c_Groups_Ouminus__class_Ouminus(_626303, _626307), -(_626305 = _626307)], (10525 ^ _257747) ^ [] : [_626305 = _626307, -(c_Groups_Ouminus__class_Ouminus(_626303, _626305) = c_Groups_Ouminus__class_Ouminus(_626303, _626307))]]], (6399 ^ _257747) ^ [_482644, _482646] : [class_Int_Oring__char__0(_482644), class_Rings_Oidom(_482644), 6406 ^ _257747 : [(6407 ^ _257747) ^ [] : [c_Polynomial_Opoly(_482644, _482646) = c_Polynomial_Opoly(_482644, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_482644))), -(_482646 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_482644)))], (6413 ^ _257747) ^ [] : [_482646 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_482644)), -(c_Polynomial_Opoly(_482644, _482646) = c_Polynomial_Opoly(_482644, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_482644))))]]], (7320 ^ _257747) ^ [_514655, _514657, _514659] : [class_Groups_Oordered__ab__group__add__abs(_514655), -(c_Groups_Oabs__class_Oabs(_514655, c_Groups_Ominus__class_Ominus(_514655, _514657, _514659)) = c_Groups_Oabs__class_Oabs(_514655, c_Groups_Ominus__class_Ominus(_514655, _514659, _514657)))], (11438 ^ _257747) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_RealDef_Oreal))], (1513 ^ _257747) ^ [_307445, _307447] : [class_RealVector_Oreal__normed__algebra(_307445), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_307445), _307447), c_Groups_Ozero__class_Ozero(_307445)) = c_Groups_Ozero__class_Ozero(_307445))], (11394 ^ _257747) ^ [] : [-(class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal))], (4377 ^ _257747) ^ [_408381, _408383] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _408381, _408383), -(_408383 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _408381, 4380 ^ [_408381, _408383]))], (4355 ^ _257747) ^ [_407604, _407606] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _407604, _407606), 4358 ^ _257747 : [(4359 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _407604, _407606))], (4361 ^ _257747) ^ [] : [_407604 = _407606]]], (11458 ^ _257747) ^ [] : [-(class_Groups_Ouminus(tc_RealDef_Oreal))], (452 ^ _257747) ^ [_271535, _271537] : [-(class_Rings_Olinordered__semiring(_271535)), _271537 = _271535, class_Rings_Olinordered__semiring(_271537)], (422 ^ _257747) ^ [_270650, _270652] : [-(class_Groups_Oordered__ab__group__add(_270650)), _270652 = _270650, class_Groups_Oordered__ab__group__add(_270652)], (11216 ^ _257747) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (2232 ^ _257747) ^ [_331801, _331803, _331805] : [class_RealVector_Oreal__algebra__1(_331801), -(c_RealVector_Oof__real(_331801, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _331803, _331805)) = c_Groups_Oplus__class_Oplus(_331801, c_RealVector_Oof__real(_331801, _331803), c_RealVector_Oof__real(_331801, _331805)))], (6810 ^ _257747) ^ [_497184, _497186, _497188, _497190] : [class_Groups_Oordered__ab__semigroup__add(_497184), c_Orderings_Oord__class_Oless__eq(_497184, _497186, _497188), -(c_Orderings_Oord__class_Oless__eq(_497184, c_Groups_Oplus__class_Oplus(_497184, _497186, _497190), c_Groups_Oplus__class_Oplus(_497184, _497188, _497190)))], (11910 ^ _257747) ^ [_669856] : [class_Rings_Oidom(_669856), -(class_Rings_Oidom(tc_Polynomial_Opoly(_669856)))], (9726 ^ _257747) ^ [_597714, _597716, _597718] : [class_Orderings_Oorder(_597714), c_Orderings_Oord__class_Oless__eq(_597714, _597716, _597718), -(_597718 = _597716), -(c_Orderings_Oord__class_Oless(_597714, _597716, _597718))], (4500 ^ _257747) ^ [_413302] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _413302), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _413302)], (11072 ^ _257747) ^ [_645475, _645477, _645479, _645481] : [class_Rings_Ocomm__semiring__1(_645475), c_Rings_Odvd__class_Odvd(_645475, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_645475), _645477), _645479), _645481), -(c_Rings_Odvd__class_Odvd(_645475, _645479, _645481))], (7058 ^ _257747) ^ [_505848] : [class_Groups_Ogroup__add(_505848), -(c_Groups_Ouminus__class_Ouminus(_505848, c_Groups_Ozero__class_Ozero(_505848)) = c_Groups_Ozero__class_Ozero(_505848))], (1497 ^ _257747) ^ [_306953, _306955, _306957] : [class_RealVector_Oreal__algebra__1(_306953), 1500 ^ _257747 : [(1501 ^ _257747) ^ [] : [c_RealVector_Oof__real(_306953, _306955) = c_RealVector_Oof__real(_306953, _306957), -(_306955 = _306957)], (1507 ^ _257747) ^ [] : [_306955 = _306957, -(c_RealVector_Oof__real(_306953, _306955) = c_RealVector_Oof__real(_306953, _306957))]]], (3851 ^ _257747) ^ [_388768, _388770, _388772] : [class_Rings_Odivision__ring(_388768), -(_388770 = c_Groups_Ozero__class_Ozero(_388768)), -(_388772 = c_Groups_Ozero__class_Ozero(_388768)), -(c_Groups_Oplus__class_Oplus(_388768, c_Rings_Oinverse__class_Oinverse(_388768, _388770), c_Rings_Oinverse__class_Oinverse(_388768, _388772)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_388768), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_388768), c_Rings_Oinverse__class_Oinverse(_388768, _388770)), c_Groups_Oplus__class_Oplus(_388768, _388770, _388772))), c_Rings_Oinverse__class_Oinverse(_388768, _388772)))], (8191 ^ _257747) ^ [_545358, _545360] : [class_Rings_Ocomm__semiring__1(_545358), -(c_Groups_Oplus__class_Oplus(_545358, c_Groups_Ozero__class_Ozero(_545358), _545360) = _545360)], (4838 ^ _257747) ^ [_425175, _425177] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _425175, _425177), _425175) = _425177)], (6201 ^ _257747) ^ [_474085, _474087] : [class_Groups_Oab__group__add(_474085), -(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_474085), _474087, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_474085))) = _474087)], (2206 ^ _257747) ^ [_330883, _330885] : [-(c_RealVector_Oof__real(_330883, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _330885)) = c_Groups_Ouminus__class_Ouminus(_330883, c_RealVector_Oof__real(_330883, _330885))), class_RealVector_Oreal__algebra__1(_330883), class_RealVector_Oreal__normed__vector(_330883)], (4666 ^ _257747) ^ [_419017, _419019, _419021] : [4667 ^ _257747 : [(4668 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _419017))], (4670 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _419019, _419021)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _419017), _419019), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _419017), _419021)))], (10944 ^ _257747) ^ [_641153, _641155, _641157, _641159] : [class_Rings_Ocomm__semiring__1(_641153), c_Rings_Odvd__class_Odvd(_641153, _641155, _641157), c_Rings_Odvd__class_Odvd(_641153, _641155, _641159), -(c_Rings_Odvd__class_Odvd(_641153, _641155, c_Groups_Oplus__class_Oplus(_641153, _641157, _641159)))], (722 ^ _257747) ^ [_279500, _279502] : [-(class_Rings_Olinordered__idom(_279500)), _279502 = _279500, class_Rings_Olinordered__idom(_279502)], (1423 ^ _257747) ^ [_304419, _304421] : [class_Power_Opower(_304419), -(hAPP(hAPP(c_Power_Opower__class_Opower(_304419), _304421), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_304419))], (7466 ^ _257747) ^ [_519267, _519269] : [class_Groups_Olinordered__ab__group__add(_519267), 7469 ^ _257747 : [(7470 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_519267, c_Groups_Oplus__class_Oplus(_519267, _519269, _519269), c_Groups_Ozero__class_Ozero(_519267)), -(c_Orderings_Oord__class_Oless(_519267, _519269, c_Groups_Ozero__class_Ozero(_519267)))], (7476 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_519267, _519269, c_Groups_Ozero__class_Ozero(_519267)), -(c_Orderings_Oord__class_Oless(_519267, c_Groups_Oplus__class_Oplus(_519267, _519269, _519269), c_Groups_Ozero__class_Ozero(_519267)))]]], (9002 ^ _257747) ^ [_575058, _575060, _575062] : [class_Orderings_Olinorder(_575058), -(c_Orderings_Oord__class_Oless__eq(_575058, _575060, _575062)), -(c_Orderings_Oord__class_Oless__eq(_575058, _575062, _575060))], (10816 ^ _257747) ^ [_636479, _636481, _636483] : [class_Rings_Ocomm__ring__1(_636479), 10819 ^ _257747 : [(10820 ^ _257747) ^ [] : [c_Rings_Odvd__class_Odvd(_636479, c_Groups_Ouminus__class_Ouminus(_636479, _636481), _636483), -(c_Rings_Odvd__class_Odvd(_636479, _636481, _636483))], (10826 ^ _257747) ^ [] : [c_Rings_Odvd__class_Odvd(_636479, _636481, _636483), -(c_Rings_Odvd__class_Odvd(_636479, c_Groups_Ouminus__class_Ouminus(_636479, _636481), _636483))]]], (4746 ^ _257747) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____))], (11682 ^ _257747) ^ [_662636] : [class_Rings_Olinordered__idom(_662636), -(class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(_662636)))], (11148 ^ _257747) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (1195 ^ _257747) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p))], (4626 ^ _257747) ^ [_417679, _417681, _417683] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _417679, _417681), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _417683), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _417679), _417683), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _417681), _417683)))], (2924 ^ _257747) ^ [_356194, _356196, _356198, _356200] : [class_Rings_Olinordered__ring__strict(_356194), 2927 ^ _257747 : [(2928 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_356194, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_356194), _356196), _356198), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_356194), _356196), _356200)), 2933 ^ _257747 : [(2934 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(_356194, c_Groups_Ozero__class_Ozero(_356194), _356196))], (2936 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(_356194, _356198, _356200))]], 2937 ^ _257747 : [(2938 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(_356194, _356196, c_Groups_Ozero__class_Ozero(_356194)))], (2940 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(_356194, _356200, _356198))]]], (2942 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(_356194, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_356194), _356196), _356198), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_356194), _356196), _356200))), 2943 ^ _257747 : [(2944 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_356194, c_Groups_Ozero__class_Ozero(_356194), _356196), c_Orderings_Oord__class_Oless(_356194, _356198, _356200)], (2950 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_356194, _356196, c_Groups_Ozero__class_Ozero(_356194)), c_Orderings_Oord__class_Oless(_356194, _356200, _356198)]]]]], (11514 ^ _257747) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex))], (8734 ^ _257747) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Complex_Oii), c_Complex_Oii) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))], (11248 ^ _257747) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (7436 ^ _257747) ^ [_518353, _518355, _518357] : [class_Groups_Oordered__comm__monoid__add(_518353), c_Orderings_Oord__class_Oless__eq(_518353, _518355, c_Groups_Ozero__class_Ozero(_518353)), c_Orderings_Oord__class_Oless__eq(_518353, _518357, c_Groups_Ozero__class_Ozero(_518353)), -(c_Orderings_Oord__class_Oless__eq(_518353, c_Groups_Oplus__class_Oplus(_518353, _518355, _518357), c_Groups_Ozero__class_Ozero(_518353)))], (9798 ^ _257747) ^ [] : [9796 ^ [] = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)], (6297 ^ _257747) ^ [_477764, _477766, _477768, _477770] : [class_Rings_Ocomm__semiring__0(_477764), -(c_Polynomial_Osmult(_477764, _477766, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_477764), _477768, _477770)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_477764), c_Polynomial_Osmult(_477764, _477766, _477768), c_Polynomial_Osmult(_477764, _477766, _477770)))], (10810 ^ _257747) ^ [_636251, _636253] : [class_Rings_Ocomm__semiring__1(_636251), -(c_Rings_Odvd__class_Odvd(_636251, _636253, c_Groups_Ozero__class_Ozero(_636251)))], (3124 ^ _257747) ^ [_362751, _362753, _362755, _362757] : [class_Rings_Olinordered__comm__semiring__strict(_362751), c_Orderings_Oord__class_Oless(_362751, _362753, _362755), c_Orderings_Oord__class_Oless(_362751, c_Groups_Ozero__class_Ozero(_362751), _362757), -(c_Orderings_Oord__class_Oless(_362751, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_362751), _362757), _362753), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_362751), _362757), _362755)))], (5949 ^ _257747) ^ [_464458, _464460] : [-(_464458 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _464460), _464458) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _464460), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _464460), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _464458, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (3759 ^ _257747) ^ [_384985, _384987, _384989, _384991, _384993] : [class_Rings_Oring(_384985), -(c_Groups_Ominus__class_Ominus(_384985, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_384985), _384987), _384989), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_384985), _384991), _384993)) = c_Groups_Oplus__class_Oplus(_384985, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_384985), _384987), c_Groups_Ominus__class_Ominus(_384985, _384989, _384993)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_384985), c_Groups_Ominus__class_Ominus(_384985, _384987, _384991)), _384993)))], (9939 ^ _257747) ^ [_605672] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _605672), -(c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _605672, c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatfloor(_605672), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (11312 ^ _257747) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (10343 ^ _257747) ^ [_619681, _619683] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _619681), _619683), -(c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _619683, c_RealDef_Oreal(tc_Nat_Onat, _619681))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_RComplete_Onatceiling(_619683), _619681))], (10303 ^ _257747) ^ [_618368, _618370] : [class_Rings_Olinordered__idom(_618368), -(_618370 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_618368))), -(c_Polynomial_Opos__poly(_618368, _618370)), -(c_Polynomial_Opos__poly(_618368, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_618368), _618370)))], (5018 ^ _257747) ^ [_431663, _431665] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _431663, _431665), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _431663, _431665) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (342 ^ _257747) ^ [_268290, _268292] : [-(class_Groups_Olinordered__ab__group__add(_268290)), _268292 = _268290, class_Groups_Olinordered__ab__group__add(_268292)], (2386 ^ _257747) ^ [_338349, _338351, _338353, _338355] : [class_Rings_Olinordered__semidom(_338349), c_Orderings_Oord__class_Oless(_338349, c_Groups_Ozero__class_Ozero(_338349), _338351), c_Orderings_Oord__class_Oless(_338349, _338353, _338355), -(c_Orderings_Oord__class_Oless(_338349, _338353, c_Groups_Oplus__class_Oplus(_338349, _338351, _338355)))], (11730 ^ _257747) ^ [_664156] : [class_Groups_Ocomm__monoid__add(_664156), -(class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(_664156)))], (10804 ^ _257747) ^ [_635971, _635973, _635975, _635977] : [class_Rings_Ocomm__semiring__0(_635971), -(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_635971, c_Polynomial_OpCons(_635971, _635973, _635975), _635977) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_635971), c_Polynomial_Osmult(_635971, _635977, c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_635971, _635975, _635977)), c_Polynomial_OpCons(_635971, _635973, c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_635971, _635975, _635977))))], (11146 ^ _257747) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))], (2173 ^ _257747) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, v_pa____) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone(tc_Nat_Onat))], (8506 ^ _257747) ^ [_557427, _557429, _557431, _557433] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _557427, _557429), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _557431, _557433), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _557427, _557431), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _557429, _557433)))], (9344 ^ _257747) ^ [_585843, _585845, _585847] : [class_Orderings_Oorder(_585843), c_Orderings_Oord__class_Oless(_585843, _585845, _585847), _585847 = _585845], (11476 ^ _257747) ^ [] : [-(class_Rings_Oidom(tc_RealDef_Oreal))], (6499 ^ _257747) ^ [_486069, _486071, _486073, _486075] : [class_Rings_Ocomm__semiring__0(_486069), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_486069)), c_Polynomial_OpCons(_486069, _486071, _486073)), _486075) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_486069), c_Polynomial_Osmult(_486069, _486071, _486075), c_Polynomial_OpCons(_486069, c_Groups_Ozero__class_Ozero(_486069), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_486069)), _486073), _486075))))], (5967 ^ _257747) ^ [_465194, _465196, _465198, _465200] : [class_Rings_Ocomm__semiring__0(_465194), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_465194), c_Polynomial_Osmult(_465194, _465196, _465198), c_Polynomial_OpCons(_465194, _465200, _465198)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_465194)), -(_465198 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_465194)))], (9374 ^ _257747) ^ [_586833, _586835, _586837, _586839] : [class_Orderings_Oord(_586833), _586835 = _586837, c_Orderings_Oord__class_Oless(_586833, _586837, _586839), -(c_Orderings_Oord__class_Oless(_586833, _586835, _586839))], (11354 ^ _257747) ^ [] : [-(class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal))], (6465 ^ _257747) ^ [_484849, _484851, _484853] : [class_Rings_Oidom(_484849), 6468 ^ _257747 : [(6479 ^ _257747) ^ [] : [6480 ^ _257747 : [(6481 ^ _257747) ^ [] : [_484851 = c_Groups_Ozero__class_Ozero(_484849)], (6483 ^ _257747) ^ [] : [_484853 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_484849))]], -(c_Polynomial_Osmult(_484849, _484851, _484853) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_484849)))], (6469 ^ _257747) ^ [] : [c_Polynomial_Osmult(_484849, _484851, _484853) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_484849)), -(_484851 = c_Groups_Ozero__class_Ozero(_484849)), -(_484853 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_484849)))]]], (11598 ^ _257747) ^ [_659976] : [class_Rings_Olinordered__idom(_659976), -(class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(_659976)))], (11188 ^ _257747) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (10081 ^ _257747) ^ [_610536] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _610536)))], (11524 ^ _257747) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Complex_Ocomplex))], (7904 ^ _257747) ^ [_533739, _533741, _533743] : [class_Groups_Oordered__comm__monoid__add(_533739), c_Orderings_Oord__class_Oless__eq(_533739, c_Groups_Ozero__class_Ozero(_533739), _533741), c_Orderings_Oord__class_Oless(_533739, c_Groups_Ozero__class_Ozero(_533739), _533743), -(c_Orderings_Oord__class_Oless(_533739, c_Groups_Ozero__class_Ozero(_533739), c_Groups_Oplus__class_Oplus(_533739, _533741, _533743)))], (5736 ^ _257747) ^ [_457606, _457608] : [class_Fields_Olinordered__field(_457606), -(_457608 = c_Groups_Ozero__class_Ozero(_457606)), -(c_Groups_Oabs__class_Oabs(_457606, c_Rings_Oinverse__class_Oinverse(_457606, _457608)) = c_Rings_Oinverse__class_Oinverse(_457606, c_Groups_Oabs__class_Oabs(_457606, _457608)))], (812 ^ _257747) ^ [_282155, _282157] : [-(class_Rings_Oring(_282155)), _282157 = _282155, class_Rings_Oring(_282157)], (8778 ^ _257747) ^ [_567382, _567384] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _567382, _567384), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _567384, _567382), -(_567382 = _567384)], (5044 ^ _257747) ^ [_432711, _432713, _432715] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _432711, _432713), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _432715, _432711), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _432711, _432715), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _432713, _432715)))], (2660 ^ _257747) ^ [_347484, _347486, _347488] : [class_Rings_Oordered__cancel__semiring(_347484), c_Orderings_Oord__class_Oless__eq(_347484, c_Groups_Ozero__class_Ozero(_347484), _347486), c_Orderings_Oord__class_Oless__eq(_347484, c_Groups_Ozero__class_Ozero(_347484), _347488), -(c_Orderings_Oord__class_Oless__eq(_347484, c_Groups_Ozero__class_Ozero(_347484), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_347484), _347486), _347488)))], (6988 ^ _257747) ^ [_503388, _503390] : [class_Groups_Ogroup__add(_503388), -(c_Groups_Ominus__class_Ominus(_503388, _503390, c_Groups_Ozero__class_Ozero(_503388)) = _503390)], (3190 ^ _257747) ^ [_364983, _364985, _364987] : [class_Rings_Olinordered__semidom(_364983), c_Orderings_Oord__class_Oless(_364983, c_Groups_Oone__class_Oone(_364983), _364985), c_Orderings_Oord__class_Oless(_364983, c_Groups_Oone__class_Oone(_364983), _364987), -(c_Orderings_Oord__class_Oless(_364983, c_Groups_Oone__class_Oone(_364983), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_364983), _364985), _364987)))], (8041 ^ _257747) ^ [_538351, _538353] : [class_Rings_Ocomm__semiring__0(_538351), -(c_Polynomial_Osynthetic__div(_538351, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_538351)), _538353) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_538351)))], (2800 ^ _257747) ^ [_352172, _352174, _352176, _352178, _352180] : [class_Rings_Oordered__semiring(_352172), c_Orderings_Oord__class_Oless__eq(_352172, _352174, _352176), c_Orderings_Oord__class_Oless__eq(_352172, _352178, _352180), c_Orderings_Oord__class_Oless__eq(_352172, c_Groups_Ozero__class_Ozero(_352172), _352174), c_Orderings_Oord__class_Oless__eq(_352172, c_Groups_Ozero__class_Ozero(_352172), _352178), -(c_Orderings_Oord__class_Oless__eq(_352172, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_352172), _352174), _352178), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_352172), _352176), _352180)))], (7764 ^ _257747) ^ [_528789, _528791] : [class_Groups_Oordered__ab__group__add__abs(_528789), c_Orderings_Oord__class_Oless(_528789, c_Groups_Oabs__class_Oabs(_528789, _528791), c_Groups_Ozero__class_Ozero(_528789))], (1207 ^ _257747) ^ [] : [v_k____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10403 ^ _257747) ^ [_621802, _621804] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _621802), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _621804)), _621802), 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, _621802, c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), _621804)))], (8113 ^ _257747) ^ [_541526, _541528, _541530, _541532] : [class_Rings_Ocomm__semiring__1(_541526), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_541526), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_541526), _541528), _541530)), _541532) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_541526), _541528), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_541526), _541530), _541532)))], (4039 ^ _257747) ^ [_396075, _396077] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _396075, _396077) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _396077, _396075))], (262 ^ _257747) ^ [_265930, _265932] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_265930)), _265932 = _265930, class_Groups_Oordered__cancel__ab__semigroup__add(_265932)], (4109 ^ _257747) ^ [_398837] : [-(_398837 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _398837))], (2978 ^ _257747) ^ [_357958, _357960, _357962] : [class_Rings_Olinordered__semiring__strict(_357958), c_Orderings_Oord__class_Oless(_357958, c_Groups_Ozero__class_Ozero(_357958), _357960), c_Orderings_Oord__class_Oless(_357958, c_Groups_Ozero__class_Ozero(_357958), _357962), -(c_Orderings_Oord__class_Oless(_357958, c_Groups_Ozero__class_Ozero(_357958), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_357958), _357960), _357962)))], (11444 ^ _257747) ^ [] : [-(class_Groups_Ogroup__add(tc_RealDef_Oreal))], (1491 ^ _257747) ^ [_306591] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _306591, _306591))], (5680 ^ _257747) ^ [_455910, _455912] : [class_Fields_Olinordered__field(_455910), c_Orderings_Oord__class_Oless(_455910, c_Groups_Ozero__class_Ozero(_455910), c_Rings_Oinverse__class_Oinverse(_455910, _455912)), -(_455912 = c_Groups_Ozero__class_Ozero(_455910)), -(c_Orderings_Oord__class_Oless(_455910, c_Groups_Ozero__class_Ozero(_455910), _455912))], (1124 ^ _257747) ^ [_293623, _293625] : [_293625 = _293623, -(tc_Polynomial_Opoly(_293625) = tc_Polynomial_Opoly(_293623))], (1156 ^ _257747) ^ [_294805, _294807, _294809, _294811] : [-(hAPP(_294811, _294807) = hAPP(_294809, _294805)), _294811 = _294809, _294807 = _294805], (4719 ^ _257747) ^ [] : [hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____), v_c____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), -(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____), 4722 ^ []) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))], (4253 ^ _257747) ^ [_403829, _403831, _403833] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _403829, _403831), _403833), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _403829, _403833))], (4147 ^ _257747) ^ [_400131, _400133] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _400131, _400133) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _400131 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _400133 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (4794 ^ _257747) ^ [_423438, _423440] : [class_RealVector_Oreal__normed__vector(_423438), -(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_423438, _423440)) = c_RealVector_Onorm__class_Onorm(_423438, _423440))], (3152 ^ _257747) ^ [_363719, _363721, _363723, _363725] : [class_Rings_Olinordered__ring__strict(_363719), c_Orderings_Oord__class_Oless(_363719, _363721, _363723), c_Orderings_Oord__class_Oless(_363719, _363725, c_Groups_Ozero__class_Ozero(_363719)), -(c_Orderings_Oord__class_Oless(_363719, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_363719), _363725), _363723), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_363719), _363725), _363721)))], (8610 ^ _257747) ^ [_561203, _561205, _561207] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _561203), c_Groups_Ominus__class_Ominus(tc_Int_Oint, _561205, _561207)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _561203), _561205), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _561203), _561207)))], (10115 ^ _257747) ^ [_611863] : [_611863 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_RealDef_Oreal(tc_Nat_Onat, _611863) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (11332 ^ _257747) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (3615 ^ _257747) ^ [_379457, _379459] : [class_Rings_Odivision__ring(_379457), -(_379459 = c_Groups_Ozero__class_Ozero(_379457)), -(c_Rings_Oinverse__class_Oinverse(_379457, c_Rings_Oinverse__class_Oinverse(_379457, _379459)) = _379459)], (6453 ^ _257747) ^ [_484377] : [class_Groups_Ozero(_484377), -(c_Polynomial_OpCons(_484377, c_Groups_Ozero__class_Ozero(_484377), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_484377))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_484377)))], (11276 ^ _257747) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (7160 ^ _257747) ^ [_509006, _509008, _509010] : [class_Groups_Oordered__ab__group__add(_509006), 7163 ^ _257747 : [(7164 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_509006, c_Groups_Ouminus__class_Ouminus(_509006, _509008), c_Groups_Ouminus__class_Ouminus(_509006, _509010)), -(c_Orderings_Oord__class_Oless__eq(_509006, _509010, _509008))], (7170 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_509006, _509010, _509008), -(c_Orderings_Oord__class_Oless__eq(_509006, c_Groups_Ouminus__class_Ouminus(_509006, _509008), c_Groups_Ouminus__class_Ouminus(_509006, _509010)))]]], (8752 ^ _257747) ^ [_566382, _566384, _566386] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _566382, _566384), _566386) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _566382, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _566384, _566386)))], (10103 ^ _257747) ^ [_611394, _611396] : [-(c_RealDef_Oreal(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _611394), _611396)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _611394)), _611396))], (8960 ^ _257747) ^ [_573531, _573533] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _573531), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _573533), -(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, _573531, _573533)))], (8724 ^ _257747) ^ [_565195] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _565195) = _565195)], (8688 ^ _257747) ^ [_564098, _564100] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _564098), 8691 ^ _257747 : [(8692 ^ _257747) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _564098), _564100) = c_Groups_Oone__class_Oone(tc_Int_Oint), 8695 ^ _257747 : [(8696 ^ _257747) ^ [] : [-(_564098 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (8698 ^ _257747) ^ [] : [-(_564100 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (8700 ^ _257747) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _564098), _564100) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _564098 = c_Groups_Oone__class_Oone(tc_Int_Oint), _564100 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (1226 ^ _257747) ^ [_297382, _297384, _297386, _297388] : [class_RealVector_Oreal__normed__vector(_297382), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _297384, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_297382, _297386), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _297384), c_RealVector_Onorm__class_Onorm(_297382, _297388))), -(_297386 = c_Groups_Ozero__class_Ozero(_297382))], (862 ^ _257747) ^ [_283666, _283668, _283670, _283672, _283674, _283676] : [-(c_Orderings_Oord__class_Oless__eq(_283674, _283670, _283666)), c_Orderings_Oord__class_Oless__eq(_283676, _283672, _283668), _283676 = _283674, _283672 = _283670, _283668 = _283666], (10974 ^ _257747) ^ [_642105, _642107] : [class_Rings_Ocomm__semiring__0(_642105), -(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_642105, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_642105)), _642107) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_642105)))], (3713 ^ _257747) ^ [_383281, _383283, _383285] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _383281, _383283)), _383285) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _383281), _383285), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _383283), _383285)))], (7096 ^ _257747) ^ [_507016, _507018] : [class_Groups_Ogroup__add(_507016), 7099 ^ _257747 : [(7100 ^ _257747) ^ [] : [c_Groups_Ouminus__class_Ouminus(_507016, _507018) = c_Groups_Ozero__class_Ozero(_507016), -(_507018 = c_Groups_Ozero__class_Ozero(_507016))], (7106 ^ _257747) ^ [] : [_507018 = c_Groups_Ozero__class_Ozero(_507016), -(c_Groups_Ouminus__class_Ouminus(_507016, _507018) = c_Groups_Ozero__class_Ozero(_507016))]]], (11456 ^ _257747) ^ [] : [-(class_Orderings_Oord(tc_RealDef_Oreal))], (8760 ^ _257747) ^ [_566730] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _566730, _566730))], (1209 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____)))], (6393 ^ _257747) ^ [_482398, _482400, _482402] : [class_Rings_Ocomm__ring(_482398), -(c_Polynomial_Osmult(_482398, c_Groups_Ouminus__class_Ouminus(_482398, _482400), _482402) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_482398), c_Polynomial_Osmult(_482398, _482400, _482402)))], (3605 ^ _257747) ^ [_379146, _379148] : [class_Rings_Odivision__ring(_379146), c_Rings_Oinverse__class_Oinverse(_379146, _379148) = c_Groups_Ozero__class_Ozero(_379146), -(_379148 = c_Groups_Ozero__class_Ozero(_379146))], (11568 ^ _257747) ^ [_659026] : [class_Rings_Oidom(_659026), -(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(_659026)))], (5955 ^ _257747) ^ [_464737, _464739] : [_464737 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _464737), _464739) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4872 ^ _257747) ^ [_426384, _426386, _426388] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _426384, _426386), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _426384, _426388), 4879 ^ _257747 : [(4880 ^ _257747) ^ [] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _426386, _426384) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _426388, _426384), -(_426386 = _426388)], (4886 ^ _257747) ^ [] : [_426386 = _426388, -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _426386, _426384) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _426388, _426384))]]], (142 ^ _257747) ^ [_262390, _262392] : [-(class_Fields_Olinordered__field(_262390)), _262392 = _262390, class_Fields_Olinordered__field(_262392)], (7796 ^ _257747) ^ [_529817, _529819, _529821] : [class_Groups_Ogroup__add(_529817), -(c_Groups_Ominus__class_Ominus(_529817, _529819, c_Groups_Ouminus__class_Ouminus(_529817, _529821)) = c_Groups_Oplus__class_Oplus(_529817, _529819, _529821))], (5269 ^ _257747) ^ [_441065, _441067, _441069] : [hBOOL(hAPP(_441065, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _441067, _441069))), 5272 ^ _257747 : [(5273 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _441067, _441069), -(hBOOL(hAPP(_441065, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (5279 ^ _257747) ^ [_441397] : [_441067 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _441069, _441397), -(hBOOL(hAPP(_441065, _441397)))]]], (10465 ^ _257747) ^ [_624422, _624424, _624426] : [class_Lattices_Oboolean__algebra(_624422), c_Orderings_Oord__class_Oless__eq(_624422, _624424, _624426), -(c_Orderings_Oord__class_Oless__eq(_624422, c_Groups_Ouminus__class_Ouminus(_624422, _624426), c_Groups_Ouminus__class_Ouminus(_624422, _624424)))], (2340 ^ _257747) ^ [_336396, _336398, _336400, _336402] : [class_RealVector_Oreal__normed__algebra(_336396), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_336396), _336398), c_Groups_Oplus__class_Oplus(_336396, _336400, _336402)) = c_Groups_Oplus__class_Oplus(_336396, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_336396), _336398), _336400), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_336396), _336398), _336402)))], (9324 ^ _257747) ^ [_585193, _585195, _585197] : [class_Orderings_Opreorder(_585193), c_Orderings_Oord__class_Oless(_585193, _585195, _585197), c_Orderings_Oord__class_Oless(_585193, _585197, _585195)], (122 ^ _257747) ^ [_261800, _261802] : [-(class_Lattices_Oboolean__algebra(_261800)), _261802 = _261800, class_Lattices_Oboolean__algebra(_261802)], (5746 ^ _257747) ^ [_457905] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _457905)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _457905)))], (2674 ^ _257747) ^ [_347932, _347934, _347936] : [class_Rings_Oordered__cancel__semiring(_347932), c_Orderings_Oord__class_Oless__eq(_347932, c_Groups_Ozero__class_Ozero(_347932), _347934), c_Orderings_Oord__class_Oless__eq(_347932, _347936, c_Groups_Ozero__class_Ozero(_347932)), -(c_Orderings_Oord__class_Oless__eq(_347932, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_347932), _347934), _347936), c_Groups_Ozero__class_Ozero(_347932)))], (3471 ^ _257747) ^ [_374336, _374338] : [_374338 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _374336), -(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _374336, _374338) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (2822 ^ _257747) ^ [_352894, _352896, _352898, _352900, _352902] : [class_Rings_Oordered__semiring(_352894), c_Orderings_Oord__class_Oless__eq(_352894, _352896, _352898), c_Orderings_Oord__class_Oless__eq(_352894, _352900, _352902), c_Orderings_Oord__class_Oless__eq(_352894, c_Groups_Ozero__class_Ozero(_352894), _352898), c_Orderings_Oord__class_Oless__eq(_352894, c_Groups_Ozero__class_Ozero(_352894), _352900), -(c_Orderings_Oord__class_Oless__eq(_352894, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_352894), _352896), _352900), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_352894), _352898), _352902)))], (11204 ^ _257747) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (272 ^ _257747) ^ [_266225, _266227] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_266225)), _266227 = _266225, class_Groups_Oordered__ab__semigroup__add__imp__le(_266227)], (4816 ^ _257747) ^ [_424239, _424241, _424243] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _424239, _424241), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _424239, _424243), _424241))], (7716 ^ _257747) ^ [_527227, _527229, _527231] : [class_Groups_Ogroup__add(_527227), c_Groups_Oplus__class_Oplus(_527227, _527229, _527231) = c_Groups_Ozero__class_Ozero(_527227), -(c_Groups_Ouminus__class_Ouminus(_527227, _527229) = _527231)], (7890 ^ _257747) ^ [_533299, _533301, _533303] : [class_Groups_Oordered__comm__monoid__add(_533299), c_Orderings_Oord__class_Oless(_533299, c_Groups_Ozero__class_Ozero(_533299), _533301), c_Orderings_Oord__class_Oless__eq(_533299, c_Groups_Ozero__class_Ozero(_533299), _533303), -(c_Orderings_Oord__class_Oless(_533299, c_Groups_Ozero__class_Ozero(_533299), c_Groups_Oplus__class_Oplus(_533299, _533301, _533303)))], (11454 ^ _257747) ^ [] : [-(class_Rings_Osemiring(tc_RealDef_Oreal))], (5154 ^ _257747) ^ [_436690, _436692, _436694] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _436690, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _436694, _436692)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _436690, _436692), _436694))], (5720 ^ _257747) ^ [_457121, _457123] : [class_Fields_Olinordered__field__inverse__zero(_457121), 5723 ^ _257747 : [(5724 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_457121, c_Groups_Ozero__class_Ozero(_457121), c_Rings_Oinverse__class_Oinverse(_457121, _457123)), -(c_Orderings_Oord__class_Oless(_457121, c_Groups_Ozero__class_Ozero(_457121), _457123))], (5730 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_457121, c_Groups_Ozero__class_Ozero(_457121), _457123), -(c_Orderings_Oord__class_Oless(_457121, c_Groups_Ozero__class_Ozero(_457121), c_Rings_Oinverse__class_Oinverse(_457121, _457123)))]]], (3363 ^ _257747) ^ [] : [-(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), 3361 ^ []), v_k____)), v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))], (6127 ^ _257747) ^ [_471215, _471217, _471219, _471221, _471223] : [class_Rings_Ocomm__semiring__0(_471215), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_471215)), c_Polynomial_Omonom(_471215, _471217, _471219)), c_Polynomial_Omonom(_471215, _471221, _471223)) = c_Polynomial_Omonom(_471215, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_471215), _471217), _471221), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _471219, _471223)))], (8101 ^ _257747) ^ [_540902, _540904, _540906, _540908] : [class_Rings_Ocomm__semiring__1(_540902), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_540902), _540904), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_540902), _540906), _540908)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_540902), _540906), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_540902), _540904), _540908)))], (4037 ^ _257747) ^ [_395982] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _395982, _395982)], (8956 ^ _257747) ^ [] : [-(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)))], (7862 ^ _257747) ^ [_532398, _532400, _532402] : [class_Groups_Oordered__ab__group__add__abs(_532398), 7865 ^ _257747 : [(7866 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_532398, c_Groups_Oabs__class_Oabs(_532398, _532400), _532402), 7869 ^ _257747 : [(7870 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_532398, _532400, _532402))], (7872 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_532398, c_Groups_Ouminus__class_Ouminus(_532398, _532400), _532402))]]], (7874 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_532398, c_Groups_Oabs__class_Oabs(_532398, _532400), _532402)), c_Orderings_Oord__class_Oless__eq(_532398, _532400, _532402), c_Orderings_Oord__class_Oless__eq(_532398, c_Groups_Ouminus__class_Ouminus(_532398, _532400), _532402)]]], (5977 ^ _257747) ^ [_465569, _465571, _465573] : [class_Rings_Olinordered__ring__strict(_465569), 5980 ^ _257747 : [(5981 ^ _257747) ^ [] : [c_Groups_Oplus__class_Oplus(_465569, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_465569), _465571), _465571), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_465569), _465573), _465573)) = c_Groups_Ozero__class_Ozero(_465569), 5984 ^ _257747 : [(5985 ^ _257747) ^ [] : [-(_465571 = c_Groups_Ozero__class_Ozero(_465569))], (5987 ^ _257747) ^ [] : [-(_465573 = c_Groups_Ozero__class_Ozero(_465569))]]], (5989 ^ _257747) ^ [] : [-(c_Groups_Oplus__class_Oplus(_465569, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_465569), _465571), _465571), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_465569), _465573), _465573)) = c_Groups_Ozero__class_Ozero(_465569)), _465571 = c_Groups_Ozero__class_Ozero(_465569), _465573 = c_Groups_Ozero__class_Ozero(_465569)]]], (7246 ^ _257747) ^ [_511879, _511881, _511883] : [class_Groups_Ogroup__add(_511879), -(c_Groups_Oplus__class_Oplus(_511879, c_Groups_Ouminus__class_Ouminus(_511879, _511881), c_Groups_Oplus__class_Oplus(_511879, _511881, _511883)) = _511883)], (4077 ^ _257747) ^ [_397660, _397662] : [_397660 = _397662, -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _397660, _397662))], (11460 ^ _257747) ^ [] : [-(class_Groups_Osgn__if(tc_RealDef_Oreal))], (8424 ^ _257747) ^ [_554635, _554637, _554639] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _554635), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _554637, _554639)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _554635), _554637)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _554635), _554639)))], (9364 ^ _257747) ^ [_586493, _586495, _586497] : [class_Orderings_Oorder(_586493), c_Orderings_Oord__class_Oless(_586493, _586495, _586497), c_Orderings_Oord__class_Oless(_586493, _586497, _586495)], (9678 ^ _257747) ^ [_596286, _596288, _596290] : [class_Orderings_Olinorder(_596286), c_Orderings_Oord__class_Oless__eq(_596286, _596288, _596290), 9685 ^ _257747 : [(9686 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(_596286, _596288, _596290)), -(_596288 = _596290)], (9692 ^ _257747) ^ [] : [_596288 = _596290, c_Orderings_Oord__class_Oless(_596286, _596288, _596290)]]], (11718 ^ _257747) ^ [_663776] : [class_Rings_Olinordered__idom(_663776), -(class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(_663776)))], (5036 ^ _257747) ^ [_432352, _432354] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _432352, _432354)), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _432354, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _432352, _432354)) = _432352)], (11304 ^ _257747) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (232 ^ _257747) ^ [_265045, _265047] : [-(class_Rings_Odivision__ring(_265045)), _265047 = _265045, class_Rings_Odivision__ring(_265047)], (10686 ^ _257747) ^ [_632104, _632106] : [class_RealVector_Oreal__normed__algebra__1(_632104), -(c_Groups_Osgn__class_Osgn(_632104, c_RealVector_Oof__real(_632104, _632106)) = c_RealVector_Oof__real(_632104, c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, _632106)))], (1114 ^ _257747) ^ [_293292, _293294, _293296, _293298] : [-(tc_fun(_293298, _293294) = tc_fun(_293296, _293292)), _293298 = _293296, _293294 = _293292], (8794 ^ _257747) ^ [_567964, _567966] : [-(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _567964, _567966)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _567964), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _567966)))], (8281 ^ _257747) ^ [_548934, _548936] : [class_Rings_Ocomm__semiring__1(_548934), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_548934), c_Groups_Oone__class_Oone(_548934)), _548936) = _548936)], (6115 ^ _257747) ^ [_470577, _470579, _470581, _470583] : [class_Rings_Ocomm__semiring__0(_470577), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_470577)), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_470577), _470579, _470581)), _470583) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_470577), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_470577)), _470579), _470583), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_470577)), _470581), _470583)))], (4566 ^ _257747) ^ [_415603, _415605, _415607] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _415603), _415605), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _415603), _415607))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _415603), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _415605, _415607)], (3973 ^ _257747) ^ [_393802, _393804] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _393802), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, _393802, _393804)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _393804))))], (9712 ^ _257747) ^ [_597293, _597295, _597297] : [class_Orderings_Oorder(_597293), c_Orderings_Oord__class_Oless__eq(_597293, _597295, _597297), -(_597295 = _597297), -(c_Orderings_Oord__class_Oless(_597293, _597295, _597297))], (6133 ^ _257747) ^ [_471509, _471511] : [class_Groups_Ozero(_471509), -(c_Polynomial_Omonom(_471509, c_Groups_Ozero__class_Ozero(_471509), _471511) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_471509)))], (11736 ^ _257747) ^ [_664346] : [class_Rings_Olinordered__idom(_664346), -(class_Rings_Olinordered__ring(tc_Polynomial_Opoly(_664346)))], (6594 ^ _257747) ^ [_489902, _489904, _489906, _489908] : [class_Groups_Ocancel__semigroup__add(_489902), c_Groups_Oplus__class_Oplus(_489902, _489904, _489906) = c_Groups_Oplus__class_Oplus(_489902, _489904, _489908), -(_489906 = _489908)], (3006 ^ _257747) ^ [_358854, _358856, _358858] : [class_Rings_Olinordered__semiring__strict(_358854), c_Orderings_Oord__class_Oless(_358854, c_Groups_Ozero__class_Ozero(_358854), _358856), c_Orderings_Oord__class_Oless(_358854, _358858, c_Groups_Ozero__class_Ozero(_358854)), -(c_Orderings_Oord__class_Oless(_358854, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_358854), _358858), _358856), c_Groups_Ozero__class_Ozero(_358854)))], (6173 ^ _257747) ^ [_473075, _473077] : [class_Rings_Olinordered__idom(_473075), 6176 ^ _257747 : [(6177 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_473075), _473077, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_473075))), -(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(_473075), _473077) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_473075), _473077))], (6183 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_473075), _473077, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_473075)))), -(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(_473075), _473077) = _473077)]]], (3995 ^ _257747) ^ [_394620, _394622] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _394620, _394622), _394620 = _394622], (10275 ^ _257747) ^ [_617463, _617465] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _617463, _617465), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _617463), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _617465), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))], (5458 ^ _257747) ^ [_448699, _448701] : [class_Fields_Olinordered__field__inverse__zero(_448699), 5461 ^ _257747 : [(5462 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_448699, c_Groups_Oone__class_Oone(_448699), c_Rings_Oinverse__class_Oinverse(_448699, _448701)), 5465 ^ _257747 : [(5466 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(_448699, c_Groups_Ozero__class_Ozero(_448699), _448701))], (5468 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_448699, _448701, c_Groups_Oone__class_Oone(_448699)))]]], (5470 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_448699, c_Groups_Oone__class_Oone(_448699), c_Rings_Oinverse__class_Oinverse(_448699, _448701))), c_Orderings_Oord__class_Oless(_448699, c_Groups_Ozero__class_Ozero(_448699), _448701), c_Orderings_Oord__class_Oless__eq(_448699, _448701, c_Groups_Oone__class_Oone(_448699))]]], (4558 ^ _257747) ^ [_415328, _415330, _415332] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _415328), _415330), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _415328), _415332)), 4561 ^ _257747 : [(4562 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _415328))], (4564 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _415330, _415332))]]], (712 ^ _257747) ^ [_279205, _279207] : [-(class_Groups_Osgn__if(_279205)), _279207 = _279205, class_Groups_Osgn__if(_279207)], (7052 ^ _257747) ^ [_505634, _505636] : [class_Groups_Ocomm__monoid__mult(_505634), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_505634), _505636), c_Groups_Oone__class_Oone(_505634)) = _505636)], (11164 ^ _257747) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (11036 ^ _257747) ^ [_644242, _644244, _644246] : [class_Rings_Olinordered__idom(_644242), 11039 ^ _257747 : [(11040 ^ _257747) ^ [] : [c_Rings_Odvd__class_Odvd(_644242, c_Groups_Oabs__class_Oabs(_644242, _644244), _644246), -(c_Rings_Odvd__class_Odvd(_644242, _644244, _644246))], (11046 ^ _257747) ^ [] : [c_Rings_Odvd__class_Odvd(_644242, _644244, _644246), -(c_Rings_Odvd__class_Odvd(_644242, c_Groups_Oabs__class_Oabs(_644242, _644244), _644246))]]], (10740 ^ _257747) ^ [_633884, _633886] : [class_Rings_Olinordered__idom(_633884), 10743 ^ _257747 : [(10744 ^ _257747) ^ [] : [c_Groups_Osgn__class_Osgn(_633884, _633886) = c_Groups_Ouminus__class_Ouminus(_633884, c_Groups_Oone__class_Oone(_633884)), -(c_Orderings_Oord__class_Oless(_633884, _633886, c_Groups_Ozero__class_Ozero(_633884)))], (10750 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_633884, _633886, c_Groups_Ozero__class_Ozero(_633884)), -(c_Groups_Osgn__class_Osgn(_633884, _633886) = c_Groups_Ouminus__class_Ouminus(_633884, c_Groups_Oone__class_Oone(_633884)))]]], (11386 ^ _257747) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal))], (11356 ^ _257747) ^ [] : [-(class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal))], (8676 ^ _257747) ^ [_563728] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _563728), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _563728))], (7634 ^ _257747) ^ [_524571, _524573] : [class_Groups_Oordered__ab__group__add(_524571), 7637 ^ _257747 : [(7638 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_524571, c_Groups_Ozero__class_Ozero(_524571), c_Groups_Ouminus__class_Ouminus(_524571, _524573)), -(c_Orderings_Oord__class_Oless(_524571, _524573, c_Groups_Ozero__class_Ozero(_524571)))], (7644 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_524571, _524573, c_Groups_Ozero__class_Ozero(_524571)), -(c_Orderings_Oord__class_Oless(_524571, c_Groups_Ozero__class_Ozero(_524571), c_Groups_Ouminus__class_Ouminus(_524571, _524573)))]]], (6642 ^ _257747) ^ [_491599, _491601] : [class_Groups_Oone(_491599), 6645 ^ _257747 : [(6646 ^ _257747) ^ [] : [c_Groups_Oone__class_Oone(_491599) = _491601, -(_491601 = c_Groups_Oone__class_Oone(_491599))], (6652 ^ _257747) ^ [] : [_491601 = c_Groups_Oone__class_Oone(_491599), -(c_Groups_Oone__class_Oone(_491599) = _491601)]]], (1317 ^ _257747) ^ [_300597, _300599, _300601] : [class_RealVector_Oreal__normed__algebra(_300597), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_300597, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_300597), _300599), _300601)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_300597, _300599)), c_RealVector_Onorm__class_Onorm(_300597, _300601))))], (5916 ^ _257747) ^ [_463424, _463426] : [-(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, _463424, _463426)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _463424)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _463426)))], (1197 ^ _257747) ^ [] : [v_w____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)], (11318 ^ _257747) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (5054 ^ _257747) ^ [_433056, _433058, _433060] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _433056, _433058), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _433056, _433060), 5061 ^ _257747 : [(5062 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _433058, _433056), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _433060, _433056)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _433058, _433060))], (5068 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _433058, _433060), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _433058, _433056), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _433060, _433056)))]]], (4209 ^ _257747) ^ [_402203, _402205, _402207] : [4210 ^ _257747 : [(4211 ^ _257747) ^ [] : [_402203 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (4213 ^ _257747) ^ [] : [_402205 = _402207]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _402203), _402205) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _402203), _402207))], (3557 ^ _257747) ^ [_377485, _377487, _377489] : [class_RealVector_Oreal__normed__vector(_377485), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_377485, c_Groups_Ominus__class_Ominus(_377485, _377487, _377489)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_377485, _377487), c_RealVector_Onorm__class_Onorm(_377485, _377489))))], (8353 ^ _257747) ^ [_551974, _551976, _551978] : [class_Rings_Ocomm__ring__1(_551974), -(c_Groups_Ominus__class_Ominus(_551974, _551976, _551978) = c_Groups_Oplus__class_Oplus(_551974, _551976, c_Groups_Ouminus__class_Ouminus(_551974, _551978)))], (4137 ^ _257747) ^ [_399746] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _399746, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _399746)], (3707 ^ _257747) ^ [_383046, _383048, _383050] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _383046, _383048), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _383050, _383046), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _383050, _383048)))], (6027 ^ _257747) ^ [_467306, _467308, _467310] : [class_Rings_Olinordered__ring(_467306), c_Orderings_Oord__class_Oless(_467306, c_Groups_Oplus__class_Oplus(_467306, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_467306), _467308), _467308), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_467306), _467310), _467310)), c_Groups_Ozero__class_Ozero(_467306))], (9144 ^ _257747) ^ [_579558, _579560, _579562, _579564] : [class_Orderings_Opreorder(_579558), c_Orderings_Oord__class_Oless__eq(_579558, _579560, _579562), c_Orderings_Oord__class_Oless__eq(_579558, _579562, _579564), -(c_Orderings_Oord__class_Oless__eq(_579558, _579560, _579564))], (11200 ^ _257747) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (2958 ^ _257747) ^ [_357297, _357299, _357301, _357303] : [class_Rings_Olinordered__ring__strict(_357297), c_Orderings_Oord__class_Oless(_357297, c_Groups_Ozero__class_Ozero(_357297), _357299), 2965 ^ _257747 : [(2966 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_357297, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_357297), _357299), _357301), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_357297), _357299), _357303)), -(c_Orderings_Oord__class_Oless(_357297, _357301, _357303))], (2972 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_357297, _357301, _357303), -(c_Orderings_Oord__class_Oless(_357297, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_357297), _357299), _357301), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_357297), _357299), _357303)))]]], (4235 ^ _257747) ^ [_403211, _403213, _403215] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _403211), _403213) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _403215), _403213), -(_403211 = _403215), -(_403213 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1211 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), v_t____), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____))))], (11160 ^ _257747) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (7538 ^ _257747) ^ [_521633, _521635, _521637] : [class_Groups_Oordered__ab__group__add(_521633), 7541 ^ _257747 : [(7542 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_521633, _521635, _521637), -(c_Orderings_Oord__class_Oless__eq(_521633, c_Groups_Ominus__class_Ominus(_521633, _521635, _521637), c_Groups_Ozero__class_Ozero(_521633)))], (7548 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_521633, c_Groups_Ominus__class_Ominus(_521633, _521635, _521637), c_Groups_Ozero__class_Ozero(_521633)), -(c_Orderings_Oord__class_Oless__eq(_521633, _521635, _521637))]]], (1172 ^ _257747) ^ [_295362, _295364, _295366, _295368] : [-(c_RealVector_Onorm__class_Onorm(_295368, _295364) = c_RealVector_Onorm__class_Onorm(_295366, _295362)), _295368 = _295366, _295364 = _295362], (10448 ^ _257747) ^ [_623602, _623604, _623606] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _623602), 10452 ^ _257747 : [(10453 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 10451 ^ [_623602, _623604, _623606]))], (10455 ^ _257747) ^ [_623986] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, _623606), _623986), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, _623606), _623604))), _623602)), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, _623986, _623604))), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, _623986, _623604)), 10451 ^ [_623602, _623604, _623606])]]], (8788 ^ _257747) ^ [_567656] : [-(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _567656)) = _567656)], (592 ^ _257747) ^ [_275665, _275667] : [-(class_Groups_Omonoid__mult(_275665)), _275667 = _275665, class_Groups_Omonoid__mult(_275667)], (11652 ^ _257747) ^ [_661686] : [class_Rings_Oidom(_661686), -(class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(_661686)))], (5642 ^ _257747) ^ [_454737, _454739, _454741] : [class_Fields_Olinordered__field(_454737), c_Orderings_Oord__class_Oless(_454737, _454739, _454741), c_Orderings_Oord__class_Oless(_454737, _454741, c_Groups_Ozero__class_Ozero(_454737)), -(c_Orderings_Oord__class_Oless(_454737, c_Rings_Oinverse__class_Oinverse(_454737, _454741), c_Rings_Oinverse__class_Oinverse(_454737, _454739)))], (6864 ^ _257747) ^ [_499136, _499138, _499140, _499142] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_499136), 6867 ^ _257747 : [(6868 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_499136, c_Groups_Oplus__class_Oplus(_499136, _499138, _499140), c_Groups_Oplus__class_Oplus(_499136, _499142, _499140)), -(c_Orderings_Oord__class_Oless(_499136, _499138, _499142))], (6874 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_499136, _499138, _499142), -(c_Orderings_Oord__class_Oless(_499136, c_Groups_Oplus__class_Oplus(_499136, _499138, _499140), c_Groups_Oplus__class_Oplus(_499136, _499142, _499140)))]]], (1493 ^ _257747) ^ [_306698, _306700, _306702] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _306698), _306700)), _306702) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _306698), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _306700), _306702)))], (2037 ^ _257747) ^ [_325309, _325311, _325313, _325315] : [class_Rings_Olinordered__semidom(_325309), c_Orderings_Oord__class_Oless(_325309, c_Groups_Oone__class_Oone(_325309), _325311), 2044 ^ _257747 : [(2045 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_325309, hAPP(hAPP(c_Power_Opower__class_Opower(_325309), _325311), _325313), hAPP(hAPP(c_Power_Opower__class_Opower(_325309), _325311), _325315)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _325313, _325315))], (2051 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _325313, _325315), -(c_Orderings_Oord__class_Oless__eq(_325309, hAPP(hAPP(c_Power_Opower__class_Opower(_325309), _325311), _325313), hAPP(hAPP(c_Power_Opower__class_Opower(_325309), _325311), _325315)))]]], (4029 ^ _257747) ^ [_395721, _395723] : [4030 ^ _257747 : [(4031 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _395721, _395723)], (4033 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _395723, _395721)]], _395721 = _395723], (3539 ^ _257747) ^ [_376802, _376804] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _376804, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _376802)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _376802, _376804), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (7080 ^ _257747) ^ [_506543, _506545] : [class_Groups_Olinordered__ab__group__add(_506543), 7083 ^ _257747 : [(7084 ^ _257747) ^ [] : [_506545 = c_Groups_Ouminus__class_Ouminus(_506543, _506545), -(_506545 = c_Groups_Ozero__class_Ozero(_506543))], (7090 ^ _257747) ^ [] : [_506545 = c_Groups_Ozero__class_Ozero(_506543), -(_506545 = c_Groups_Ouminus__class_Ouminus(_506543, _506545))]]], (3367 ^ _257747) ^ [] : [-(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), v_w____), v_k____)), v_a____))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)))) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_RealVector_Oof__real(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)))))], (4396 ^ _257747) ^ [_409089, _409091, _409093] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _409091, _409093), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _409089, _409091), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _409089, _409093)))], (1931 ^ _257747) ^ [_321562, _321564, _321566] : [class_RealVector_Oreal__algebra__1(_321562), -(c_RealVector_Oof__real(_321562, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _321564), _321566)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_321562), c_RealVector_Oof__real(_321562, _321564)), c_RealVector_Oof__real(_321562, _321566)))], (442 ^ _257747) ^ [_271240, _271242] : [-(class_Groups_Ocancel__semigroup__add(_271240)), _271242 = _271240, class_Groups_Ocancel__semigroup__add(_271242)], (11408 ^ _257747) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_RealDef_Oreal))], (10201 ^ _257747) ^ [_614851, _614853, _614855] : [class_Rings_Olinordered__idom(_614851), 10204 ^ _257747 : [(10215 ^ _257747) ^ [] : [10216 ^ _257747 : [(10217 ^ _257747) ^ [] : [_614853 = _614855], (10219 ^ _257747) ^ [] : [c_Polynomial_Opos__poly(_614851, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_614851), _614855, _614853))]], -(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(_614851), _614853, _614855))], (10205 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(_614851), _614853, _614855), -(_614853 = _614855), -(c_Polynomial_Opos__poly(_614851, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_614851), _614855, _614853)))]]], (10107 ^ _257747) ^ [] : [-(c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (4384 ^ _257747) ^ [_408614, _408616] : [4385 ^ _257747 : [(4386 ^ _257747) ^ [_408689] : [_408616 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _408614, _408689)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _408614, _408616))], (10491 ^ _257747) ^ [_625299, _625301, _625303, _625305, _625307] : [class_Groups_Ominus(_625299), -(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_625301, _625299), _625303, _625305), _625307) = c_Groups_Ominus__class_Ominus(_625299, hAPP(_625303, _625307), hAPP(_625305, _625307)))], (6966 ^ _257747) ^ [_502676, _502678, _502680] : [class_Groups_Oab__group__add(_502676), 6969 ^ _257747 : [(6970 ^ _257747) ^ [] : [_502678 = _502680, -(c_Groups_Ominus__class_Ominus(_502676, _502678, _502680) = c_Groups_Ozero__class_Ozero(_502676))], (6976 ^ _257747) ^ [] : [c_Groups_Ominus__class_Ominus(_502676, _502678, _502680) = c_Groups_Ozero__class_Ozero(_502676), -(_502678 = _502680)]]], (3365 ^ _257747) ^ [] : [-(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_a____, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)))))) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_RealVector_Oof__real(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), v_t____), v_k____))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)), v_k____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)))))], (1355 ^ _257747) ^ [_301827, _301829, _301831] : [class_Rings_Olinordered__semidom(_301827), c_Orderings_Oord__class_Oless(_301827, c_Groups_Oone__class_Oone(_301827), _301829), -(c_Orderings_Oord__class_Oless(_301827, c_Groups_Oone__class_Oone(_301827), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_301827), _301829), hAPP(hAPP(c_Power_Opower__class_Opower(_301827), _301829), _301831))))], (7034 ^ _257747) ^ [_504950, _504952] : [class_Groups_Omonoid__mult(_504950), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_504950), c_Groups_Oone__class_Oone(_504950)), _504952) = _504952)], (3563 ^ _257747) ^ [_377764, _377766] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _377764, _377766), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _377766, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _377764)))], (10043 ^ _257747) ^ [_609381, _609383] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _609381), _609383), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _609383, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _609381), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_RComplete_Onatceiling(_609383) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _609381, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (11310 ^ _257747) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (2077 ^ _257747) ^ [_326612, _326614, _326616] : [class_Rings_Olinordered__idom(_326612), c_Orderings_Oord__class_Oless__eq(_326612, c_Groups_Ozero__class_Ozero(_326612), _326614), c_Orderings_Oord__class_Oless__eq(_326612, c_Groups_Ozero__class_Ozero(_326612), _326616), c_Orderings_Oord__class_Oless__eq(_326612, _326616, c_Groups_Oone__class_Oone(_326612)), -(c_Orderings_Oord__class_Oless__eq(_326612, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_326612), _326616), _326614), _326614))], (11202 ^ _257747) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (6285 ^ _257747) ^ [_477196, _477198, _477200, _477202] : [class_Rings_Ocomm__semiring__0(_477196), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_477196)), c_Polynomial_Osmult(_477196, _477198, _477200)), _477202) = c_Polynomial_Osmult(_477196, _477198, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_477196)), _477200), _477202)))], (3815 ^ _257747) ^ [_387519, _387521] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _387519), _387519)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _387521), _387521)))], (4123 ^ _257747) ^ [_399285, _399287] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _399285, _399287), _399287 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (9969 ^ _257747) ^ [_606686] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _606686), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), c_RComplete_Onatfloor(_606686)))], (11346 ^ _257747) ^ [] : [-(class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal))], (7524 ^ _257747) ^ [_521169, _521171, _521173, _521175, _521177] : [class_Groups_Oordered__cancel__ab__semigroup__add(_521169), c_Orderings_Oord__class_Oless__eq(_521169, _521171, _521173), c_Orderings_Oord__class_Oless(_521169, _521175, _521177), -(c_Orderings_Oord__class_Oless(_521169, c_Groups_Oplus__class_Oplus(_521169, _521171, _521175), c_Groups_Oplus__class_Oplus(_521169, _521173, _521177)))], (3110 ^ _257747) ^ [_362267, _362269, _362271, _362273] : [class_Rings_Olinordered__semiring__strict(_362267), c_Orderings_Oord__class_Oless(_362267, _362269, _362271), c_Orderings_Oord__class_Oless(_362267, c_Groups_Ozero__class_Ozero(_362267), _362273), -(c_Orderings_Oord__class_Oless(_362267, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_362267), _362273), _362269), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_362267), _362273), _362271)))], (1201 ^ _257747) ^ [_296472] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _296472), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), _296472)), v_m____))], (5254 ^ _257747) ^ [_440435, _440437, _440439] : [-(hBOOL(hAPP(_440435, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _440437, _440439)))), 5257 ^ _257747 : [(5258 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _440437, _440439))], (5260 ^ _257747) ^ [] : [hBOOL(hAPP(_440435, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 5262 ^ _257747 : [(5263 ^ _257747) ^ [] : [-(_440437 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _440439, 5261 ^ [_440435, _440437, _440439]))], (5265 ^ _257747) ^ [] : [hBOOL(hAPP(_440435, 5261 ^ [_440435, _440437, _440439]))]]], (8946 ^ _257747) ^ [_573108, _573110] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _573108), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _573110), -(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), _573108), _573110)))], (9482 ^ _257747) ^ [_590249, _590251, _590253] : [class_Orderings_Olinorder(_590249), 9485 ^ _257747 : [(9486 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless(_590249, _590251, _590253)), -(c_Orderings_Oord__class_Oless__eq(_590249, _590253, _590251))], (9492 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_590249, _590253, _590251), c_Orderings_Oord__class_Oless(_590249, _590251, _590253)]]], (10668 ^ _257747) ^ [_631412, _631414, _631416] : [class_RealVector_Oreal__normed__div__algebra(_631412), -(c_Groups_Osgn__class_Osgn(_631412, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_631412), _631414), _631416)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_631412), c_Groups_Osgn__class_Osgn(_631412, _631414)), c_Groups_Osgn__class_Osgn(_631412, _631416)))], (11300 ^ _257747) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (11368 ^ _257747) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal))], (11210 ^ _257747) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (4910 ^ _257747) ^ [_427694, _427696] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _427694, _427696), _427694))], (11320 ^ _257747) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (5300 ^ _257747) ^ [_442217, _442219, _442221, _442223, _442225] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _442217, _442219), 5303 ^ _257747 : [(5304 ^ _257747) ^ [] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _442217), _442221), _442223) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _442219), _442221), _442225), -(_442223 = 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, _442219, _442217)), _442221), _442225))], (5310 ^ _257747) ^ [] : [_442223 = 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, _442219, _442217)), _442221), _442225), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _442217), _442221), _442223) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _442219), _442221), _442225))]]], (10798 ^ _257747) ^ [_635661, _635663, _635665] : [class_Rings_Oidom(_635661), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_635661), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_635661)), c_Polynomial_OpCons(_635661, c_Groups_Ouminus__class_Ouminus(_635661, _635663), c_Polynomial_OpCons(_635661, c_Groups_Oone__class_Oone(_635661), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_635661))))), c_Polynomial_Oorder(_635661, _635663, _635665)), _635665))], (8894 ^ _257747) ^ [_571413, _571415, _571417, _571419, _571421] : [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), _571413), _571415), _571417), c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _571413), _571419), _571421)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _571417), c_Orderings_Oord__class_Oless(tc_Int_Oint, _571417, _571413), c_Orderings_Oord__class_Oless(tc_Int_Oint, _571421, _571413), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _571415, _571419))], (4472 ^ _257747) ^ [_412320, _412322, _412324] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _412320, _412322), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _412320), _412324), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _412322), _412324)))], (11328 ^ _257747) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (4157 ^ _257747) ^ [_400440, _400442] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _400440, _400442) = _400440, -(_400442 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10223 ^ _257747) ^ [_615487] : [-(c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat, _615487)) = _615487)], (5764 ^ _257747) ^ [_458577, _458579, _458581] : [class_Fields_Olinordered__field(_458577), c_Orderings_Oord__class_Oless__eq(_458577, c_Rings_Oinverse__class_Oinverse(_458577, _458579), c_Rings_Oinverse__class_Oinverse(_458577, _458581)), c_Orderings_Oord__class_Oless(_458577, c_Groups_Ozero__class_Ozero(_458577), _458579), -(c_Orderings_Oord__class_Oless__eq(_458577, _458581, _458579))], (1495 ^ _257747) ^ [_306818, _306820] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _306818), _306820) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _306820), _306818))], (2244 ^ _257747) ^ [_332335, _332337, _332339] : [class_Rings_Oring(_332335), -(c_Groups_Ouminus__class_Ouminus(_332335, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_332335), _332337), _332339)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_332335), c_Groups_Ouminus__class_Ouminus(_332335, _332337)), _332339))], (11088 ^ _257747) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex))], (4776 ^ _257747) ^ [_422712, _422714] : [class_Rings_Olinordered__idom(_422712), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_422712), c_Groups_Oabs__class_Oabs(_422712, _422714)), c_Groups_Oabs__class_Oabs(_422712, _422714)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_422712), _422714), _422714))], (11234 ^ _257747) ^ [] : [-(class_Groups_Oabs__if(tc_Int_Oint))], (8149 ^ _257747) ^ [_543558, _543560, _543562, _543564] : [class_Rings_Ocomm__semiring__1(_543558), -(c_Groups_Oplus__class_Oplus(_543558, c_Groups_Oplus__class_Oplus(_543558, _543560, _543562), _543564) = c_Groups_Oplus__class_Oplus(_543558, c_Groups_Oplus__class_Oplus(_543558, _543560, _543564), _543562))], (2702 ^ _257747) ^ [_348828, _348830, _348832] : [class_Rings_Oordered__cancel__semiring(_348828), c_Orderings_Oord__class_Oless__eq(_348828, _348830, c_Groups_Ozero__class_Ozero(_348828)), c_Orderings_Oord__class_Oless__eq(_348828, c_Groups_Ozero__class_Ozero(_348828), _348832), -(c_Orderings_Oord__class_Oless__eq(_348828, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_348828), _348830), _348832), c_Groups_Ozero__class_Ozero(_348828)))], (11518 ^ _257747) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex))], (10848 ^ _257747) ^ [_637499, _637501, _637503, _637505] : [class_Rings_Ocomm__ring__1(_637499), c_Rings_Odvd__class_Odvd(_637499, _637501, _637503), c_Rings_Odvd__class_Odvd(_637499, _637501, _637505), -(c_Rings_Odvd__class_Odvd(_637499, _637501, c_Groups_Ominus__class_Ominus(_637499, _637503, _637505)))], (5384 ^ _257747) ^ [_445913, _445915, _445917, _445919, _445921] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _445913, _445915), 5387 ^ _257747 : [(5388 ^ _257747) ^ [] : [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), _445913), _445917), _445919), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _445915), _445917), _445921)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _445919, 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, _445915, _445913)), _445917), _445921)))], (5394 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _445919, 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, _445915, _445913)), _445917), _445921)), -(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), _445913), _445917), _445919), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _445915), _445917), _445921)))]]], (3825 ^ _257747) ^ [_387942, _387944] : [-(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _387942), _387942), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _387944), _387944)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _387942 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _387944 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)], (8347 ^ _257747) ^ [_551720, _551722] : [class_Rings_Ocomm__ring__1(_551720), -(c_Groups_Ouminus__class_Ouminus(_551720, _551722) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_551720), c_Groups_Ouminus__class_Ouminus(_551720, c_Groups_Oone__class_Oone(_551720))), _551722))], (11452 ^ _257747) ^ [] : [-(class_Int_Oring__char__0(tc_RealDef_Oreal))], (3373 ^ _257747) ^ [] : [-(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), v_w____), v_k____)), v_a____)), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))], (10618 ^ _257747) ^ [_629724, _629726] : [class_Rings_Olinordered__idom(_629724), -(c_Groups_Oabs__class_Oabs(_629724, _629726) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_629724), _629726), c_Groups_Osgn__class_Osgn(_629724, _629726)))], (3401 ^ _257747) ^ [_372017, _372019, _372021] : [class_Rings_Odivision__ring__inverse__zero(_372017), c_Rings_Oinverse__class_Oinverse(_372017, _372019) = c_Rings_Oinverse__class_Oinverse(_372017, _372021), -(_372019 = _372021)], (8167 ^ _257747) ^ [_544398, _544400, _544402, _544404] : [class_Rings_Ocomm__semiring__1(_544398), -(c_Groups_Oplus__class_Oplus(_544398, _544400, c_Groups_Oplus__class_Oplus(_544398, _544402, _544404)) = c_Groups_Oplus__class_Oplus(_544398, _544402, c_Groups_Oplus__class_Oplus(_544398, _544400, _544404)))], (10503 ^ _257747) ^ [_625841, _625843] : [class_Lattices_Oab__semigroup__idem__mult(_625841), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_625841), _625843), _625843) = _625843)], (9845 ^ _257747) ^ [] : [-(c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (11102 ^ _257747) ^ [_646426, _646428] : [class_Orderings_Opreorder(_646426), -(class_Orderings_Opreorder(tc_fun(_646428, _646426)))], (6568 ^ _257747) ^ [_488868, _488870, _488872, _488874] : [class_Groups_Oab__semigroup__mult(_488868), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_488868), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_488868), _488870), _488872)), _488874) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_488868), _488870), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_488868), _488872), _488874)))], (4840 ^ _257747) ^ [_425277, _425279] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _425277, _425279), _425279) = _425277)], (7378 ^ _257747) ^ [_516553, _516555, _516557] : [class_Groups_Oordered__comm__monoid__add(_516553), c_Orderings_Oord__class_Oless__eq(_516553, c_Groups_Ozero__class_Ozero(_516553), _516555), c_Orderings_Oord__class_Oless__eq(_516553, c_Groups_Ozero__class_Ozero(_516553), _516557), 7389 ^ _257747 : [(7390 ^ _257747) ^ [] : [c_Groups_Oplus__class_Oplus(_516553, _516555, _516557) = c_Groups_Ozero__class_Ozero(_516553), 7393 ^ _257747 : [(7394 ^ _257747) ^ [] : [-(_516555 = c_Groups_Ozero__class_Ozero(_516553))], (7396 ^ _257747) ^ [] : [-(_516557 = c_Groups_Ozero__class_Ozero(_516553))]]], (7398 ^ _257747) ^ [] : [-(c_Groups_Oplus__class_Oplus(_516553, _516555, _516557) = c_Groups_Ozero__class_Ozero(_516553)), _516555 = c_Groups_Ozero__class_Ozero(_516553), _516557 = c_Groups_Ozero__class_Ozero(_516553)]]], (4454 ^ _257747) ^ [_411534, _411536, _411538] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _411534), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _411536, _411538)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _411534), _411536), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _411534), _411538)))], (11260 ^ _257747) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (7450 ^ _257747) ^ [_518779, _518781] : [class_Groups_Olinordered__ab__group__add(_518779), 7453 ^ _257747 : [(7454 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_518779, c_Groups_Ozero__class_Ozero(_518779), c_Groups_Oplus__class_Oplus(_518779, _518781, _518781)), -(c_Orderings_Oord__class_Oless(_518779, c_Groups_Ozero__class_Ozero(_518779), _518781))], (7460 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless(_518779, c_Groups_Ozero__class_Ozero(_518779), _518781), -(c_Orderings_Oord__class_Oless(_518779, c_Groups_Ozero__class_Ozero(_518779), c_Groups_Oplus__class_Oplus(_518779, _518781, _518781)))]]], (6109 ^ _257747) ^ [_470285, _470287, _470289, _470291] : [class_Groups_Ocomm__monoid__add(_470285), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_470285), c_Polynomial_Omonom(_470285, _470287, _470289), c_Polynomial_Omonom(_470285, _470291, _470289)) = c_Polynomial_Omonom(_470285, c_Groups_Oplus__class_Oplus(_470285, _470287, _470291), _470289))], (5510 ^ _257747) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_Osmult(tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q____), c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))), v_q____)))], (11464 ^ _257747) ^ [] : [-(class_Rings_Oring__1(tc_RealDef_Oreal))], (6005 ^ _257747) ^ [_466573, _466575, _466577] : [class_Rings_Olinordered__ring__strict(_466573), 6008 ^ _257747 : [(6009 ^ _257747) ^ [] : [c_Orderings_Oord__class_Oless__eq(_466573, c_Groups_Oplus__class_Oplus(_466573, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_466573), _466575), _466575), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_466573), _466577), _466577)), c_Groups_Ozero__class_Ozero(_466573)), 6012 ^ _257747 : [(6013 ^ _257747) ^ [] : [-(_466575 = c_Groups_Ozero__class_Ozero(_466573))], (6015 ^ _257747) ^ [] : [-(_466577 = c_Groups_Ozero__class_Ozero(_466573))]]], (6017 ^ _257747) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_466573, c_Groups_Oplus__class_Oplus(_466573, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_466573), _466575), _466575), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_466573), _466577), _466577)), c_Groups_Ozero__class_Ozero(_466573))), _466575 = c_Groups_Ozero__class_Ozero(_466573), _466577 = c_Groups_Ozero__class_Ozero(_466573)]]], (7270 ^ _257747) ^ [_512903, _512905, _512907] : [class_Groups_Oab__group__add(_512903), -(c_Groups_Ouminus__class_Ouminus(_512903, c_Groups_Ominus__class_Ominus(_512903, _512905, _512907)) = c_Groups_Ominus__class_Ominus(_512903, _512907, _512905))], (3453 ^ _257747) ^ [_373729, _373731] : [c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _373729, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _373731)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_373729 = _373731)]], input).
% 170.86/164.92  ncf('1',plain,[c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, 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(tc_Complex_Ocomplex, v_w____)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), v_k____))), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)))), 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(tc_Complex_Ocomplex, v_w____)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), v_k____))), v_m____))],start(11932 ^ 0)).
% 170.86/164.92  ncf('1.1',plain,[-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, 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(tc_Complex_Ocomplex, v_w____)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), v_k____))), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____)))), 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(tc_Complex_Ocomplex, v_w____)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), v_k____))), v_m____))), 1297 : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), v_m____), 1297 : 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), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), v_k____)))],extension(1287 ^ 1,bind([[_299541, _299543, _299545], [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), v_k____)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), v_m____]]))).
% 170.86/164.92  ncf('1.1.1',plain,[-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_RealVector_Oof__real(tc_Complex_Ocomplex, v_t____)), v_w____))), v_m____))],extension(11930 ^ 4)).
% 170.86/164.92  ncf('1.1.2',plain,[-(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), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), v_k____)))), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), v_k____))],extension(1887 ^ 2,bind([[_320066, _320068], [c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), v_k____)]]))).
% 170.86/164.92  ncf('1.1.2.1',plain,[-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____))), 1333 : -(v_w____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), 1333 : class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)],extension(1323 ^ 3,bind([[_300859, _300861], [tc_Complex_Ocomplex, v_w____]]))).
% 170.86/164.92  ncf('1.1.2.1.1',plain,[v_w____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)],extension(1197 ^ 6)).
% 170.86/164.92  ncf('1.1.2.1.2',plain,[-(class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex))],extension(11496 ^ 4)).
% 170.86/164.92  ncf('1.1.2.2',plain,[-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)), v_k____))), class_Rings_Olinordered__semidom(tc_RealDef_Oreal), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____))],extension(1695 ^ 3,bind([[_313735, _313737, _313739], [tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____), v_k____]]))).
% 170.86/164.92  ncf('1.1.2.2.1',plain,[-(class_Rings_Olinordered__semidom(tc_RealDef_Oreal))],extension(11396 ^ 4)).
% 170.86/164.92  ncf('1.1.2.2.2',plain,[-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_w____)))],lemmata('[1, 1].x')).
% 170.86/164.92  %-----------------------------------------------------
% 170.86/164.92  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------