TSTP Solution File: SWW180+1 by nanoCoP---2.0

View Problem - Process Solution 
%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWW180+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n027.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 12:25:43 EDT 2023

% Result   : Theorem 92.67s 90.37s
% Output   : Proof 92.67s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SWW180+1 : TPTP v8.1.2. Released v5.2.0.
% 0.06/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n027.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 22:50:35 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 92.67/90.37  
% 92.67/90.37  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 92.67/90.37  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 92.67/90.37  %-----------------------------------------------------
% 92.67/90.37  ncf(matrix, plain, [(12291 ^ _669506) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), v_r), v_m____)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____)), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), v_r), v_m____))))], !, (6404 ^ _224325) ^ [_446485, _446487] : [class_Groups_Ogroup__add(_446485), -(c_Groups_Ouminus__class_Ouminus(_446485, c_Groups_Ouminus__class_Ouminus(_446485, _446487)) = _446487)], (9239 ^ _224325) ^ [_543432, _543434] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _543432, c_Nat_OSuc(_543434)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _543432, _543434)))], (1910 ^ _224325) ^ [_285938, _285940, _285942] : [class_Orderings_Olinorder(_285938), 1913 ^ _224325 : [(1920 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_285938, _285942, _285940), c_Orderings_Oord__class_Oless(_285938, _285940, _285942)], (1914 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(_285938, _285940, _285942)), -(c_Orderings_Oord__class_Oless__eq(_285938, _285942, _285940))]]], (7282 ^ _224325) ^ [_475637, _475639, _475641, _475643] : [class_Groups_Ouminus(_475637), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_475639, _475637), _475641), _475643) = c_Groups_Ouminus__class_Ouminus(_475637, hAPP(_475641, _475643)))], (2943 ^ _224325) ^ [_322199, _322201, _322203, _322205] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_322199), 2946 ^ _224325 : [(2953 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_322199, _322201, _322205), -(c_Orderings_Oord__class_Oless__eq(_322199, c_Groups_Oplus__class_Oplus(_322199, _322201, _322203), c_Groups_Oplus__class_Oplus(_322199, _322205, _322203)))], (2947 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_322199, c_Groups_Oplus__class_Oplus(_322199, _322201, _322203), c_Groups_Oplus__class_Oplus(_322199, _322205, _322203)), -(c_Orderings_Oord__class_Oless__eq(_322199, _322201, _322205))]]], (10182 ^ _224325) ^ [_576384, _576386, _576388, _576390, _576392, _576394] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _576384), _576386), _576388) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _576390), _576392), _576394), 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), _576390), _576392), _576394), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _576388, _576384), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _576394), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _576390), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _576390, _576384), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _576392, _576386))], (3991 ^ _224325) ^ [_358791, _358793, _358795, _358797] : [class_Rings_Olinordered__ring__strict(_358791), c_Orderings_Oord__class_Oless(_358791, c_Groups_Ozero__class_Ozero(_358791), _358793), 3998 ^ _224325 : [(4005 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_358791, _358795, _358797), -(c_Orderings_Oord__class_Oless(_358791, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_358791), _358793), _358795), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_358791), _358793), _358797)))], (3999 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_358791, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_358791), _358793), _358795), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_358791), _358793), _358797)), -(c_Orderings_Oord__class_Oless(_358791, _358795, _358797))]]], (6536 ^ _224325) ^ [_450744, _450746] : [class_Groups_Oordered__ab__group__add(_450744), 6539 ^ _224325 : [(6546 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_450744, _450746, c_Groups_Ozero__class_Ozero(_450744)), -(c_Orderings_Oord__class_Oless__eq(_450744, c_Groups_Ozero__class_Ozero(_450744), c_Groups_Ouminus__class_Ouminus(_450744, _450746)))], (6540 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_450744, c_Groups_Ozero__class_Ozero(_450744), c_Groups_Ouminus__class_Ouminus(_450744, _450746)), -(c_Orderings_Oord__class_Oless__eq(_450744, _450746, c_Groups_Ozero__class_Ozero(_450744)))]]], (5775 ^ _224325) ^ [_423263] : [-(_423263 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _423263))], (9115 ^ _224325) ^ [_538650, _538652] : [9116 ^ _224325 : [(9119 ^ _224325) ^ [] : [_538650 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9117 ^ _224325) ^ [] : [_538652 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _538650), _538652) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (4409 ^ _224325) ^ [_372852, _372854, _372856, _372858] : [class_Rings_Olinordered__semiring__strict(_372852), c_Orderings_Oord__class_Oless__eq(_372852, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_372852), _372854), _372856), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_372852), _372854), _372858)), c_Orderings_Oord__class_Oless(_372852, c_Groups_Ozero__class_Ozero(_372852), _372854), -(c_Orderings_Oord__class_Oless__eq(_372852, _372856, _372858))], (2210 ^ _224325) ^ [_296187, _296189, _296191] : [class_Groups_Oordered__comm__monoid__add(_296187), c_Orderings_Oord__class_Oless(_296187, c_Groups_Ozero__class_Ozero(_296187), _296189), c_Orderings_Oord__class_Oless__eq(_296187, c_Groups_Ozero__class_Ozero(_296187), _296191), -(c_Orderings_Oord__class_Oless(_296187, c_Groups_Ozero__class_Ozero(_296187), c_Groups_Oplus__class_Oplus(_296187, _296189, _296191)))], (5683 ^ _224325) ^ [_420038, _420040, _420042] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _420038), _420040), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _420038), _420042)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _420038), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _420040, _420042))], (12243 ^ _224325) ^ [_648397] : [class_Rings_Ocomm__semiring__1(_648397), -(class_Power_Opower(tc_Polynomial_Opoly(_648397)))], (2456 ^ _224325) ^ [_304182, _304184, _304186, _304188, _304190] : [class_RealVector_Oreal__normed__vector(_304182), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_304182, _304184), _304186), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_304182, _304188), _304190), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_304182, c_Groups_Oplus__class_Oplus(_304182, _304184, _304188)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _304186, _304190)))], (7288 ^ _224325) ^ [_475901, _475903, _475905] : [class_Lattices_Oboolean__algebra(_475901), 7291 ^ _224325 : [(7298 ^ _224325) ^ [] : [_475903 = _475905, -(c_Groups_Ouminus__class_Ouminus(_475901, _475903) = c_Groups_Ouminus__class_Ouminus(_475901, _475905))], (7292 ^ _224325) ^ [] : [c_Groups_Ouminus__class_Ouminus(_475901, _475903) = c_Groups_Ouminus__class_Ouminus(_475901, _475905), -(_475903 = _475905)]]], (11611 ^ _224325) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (2532 ^ _224325) ^ [_306697, _306699, _306701] : [class_Orderings_Oorder(_306697), c_Orderings_Oord__class_Oless__eq(_306697, _306699, _306701), c_Orderings_Oord__class_Oless__eq(_306697, _306701, _306699), -(_306699 = _306701)], (10922 ^ _224325) ^ [_604988, _604990, _604992] : [class_Groups_Oab__group__add(_604988), 10925 ^ _224325 : [(10932 ^ _224325) ^ [] : [c_Groups_Ominus__class_Ominus(_604988, _604990, _604992) = c_Groups_Ozero__class_Ozero(_604988), -(_604990 = _604992)], (10926 ^ _224325) ^ [] : [_604990 = _604992, -(c_Groups_Ominus__class_Ominus(_604988, _604990, _604992) = c_Groups_Ozero__class_Ozero(_604988))]]], (4939 ^ _224325) ^ [_392533, _392535, _392537, _392539, _392541, _392543] : [class_Groups_Ozero(_392533), -(c_Polynomial_Opoly__rec(_392535, _392533, _392537, _392539, c_Polynomial_OpCons(_392533, _392541, _392543)) = hAPP(hAPP(hAPP(_392539, _392541), _392543), c_If(_392535, c_fequal(_392543, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_392533))), _392537, c_Polynomial_Opoly__rec(_392535, _392533, _392537, _392539, _392543))))], (11627 ^ _224325) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (6882 ^ _224325) ^ [_462001, _462003] : [class_Groups_Oordered__ab__group__add__abs(_462001), c_Orderings_Oord__class_Oless__eq(_462001, _462003, c_Groups_Ozero__class_Ozero(_462001)), -(c_Groups_Oabs__class_Oabs(_462001, _462003) = c_Groups_Ouminus__class_Ouminus(_462001, _462003))], (9569 ^ _224325) ^ [_554587] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _554587), _554587) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (12285 ^ _224325) ^ [_649747, _649749] : [_649747 = _649749, -(hBOOL(c_fequal(_649747, _649749)))], (6992 ^ _224325) ^ [_465854] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), c_RComplete_Onatfloor(_465854)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _465854))], (7372 ^ _224325) ^ [_478629] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _478629, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatfloor(_478629)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))], (970 ^ _224325) ^ [_255203, _255205, _255207, _255209] : [-(c_Groups_Ouminus__class_Ouminus(_255209, _255205) = c_Groups_Ouminus__class_Ouminus(_255207, _255203)), _255209 = _255207, _255205 = _255203], (11799 ^ _224325) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_RealDef_Oreal))], (2691 ^ _224325) ^ [_311866, _311868, _311870, _311872, _311874] : [class_Rings_Ocomm__semiring__1(_311866), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_311866), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_311866), _311868), _311870)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_311866), _311872), _311874)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_311866), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_311866), _311868), _311872)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_311866), _311870), _311874)))], (4753 ^ _224325) ^ [_385141, _385143] : [class_RealVector_Oreal__normed__algebra(_385141), 4757 ^ _224325 : [(4760 ^ _224325) ^ [_385440] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_385141, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_385141), _385440), _385143)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_385141, _385440)), 4756 ^ [_385141, _385143])))], (4758 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 4756 ^ [_385141, _385143]))]]], (3225 ^ _224325) ^ [_332962, _332964, _332966] : [class_Rings_Oordered__ring__abs(_332962), -(c_Groups_Oabs__class_Oabs(_332962, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_332962), _332964), _332966)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_332962), c_Groups_Oabs__class_Oabs(_332962, _332964)), c_Groups_Oabs__class_Oabs(_332962, _332966))), 3232 ^ _224325 : [(3235 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_332962, _332964, c_Groups_Ozero__class_Ozero(_332962))], (3233 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_332962, c_Groups_Ozero__class_Ozero(_332962), _332964)]], 3236 ^ _224325 : [(3239 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_332962, _332966, c_Groups_Ozero__class_Ozero(_332962))], (3237 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_332962, c_Groups_Ozero__class_Ozero(_332962), _332966)]]], (8431 ^ _224325) ^ [_514551, _514553, _514555] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _514551), c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _514551), _514553), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _514551), _514555)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _514553, _514555))], (8959 ^ _224325) ^ [_533494] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(_533494)))], (8085 ^ _224325) ^ [_503619, _503621] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _503619, _503621)), 8086 ^ _224325 : [(8087 ^ _224325) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _503619, _503621), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _503621, _503619))], (8093 ^ _224325) ^ [] : [_503619 = _503621]]], (7574 ^ _224325) ^ [_485730, _485732, _485734, _485736] : [class_Rings_Odvd(_485730), _485732 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_485730), _485734), _485736), -(c_Rings_Odvd__class_Odvd(_485730, _485734, _485732))], (11779 ^ _224325) ^ [] : [-(class_Rings_Olinordered__idom(tc_RealDef_Oreal))], (980 ^ _224325) ^ [_255534, _255536] : [_255536 = _255534, -(c_RComplete_Onatfloor(_255536) = c_RComplete_Onatfloor(_255534))], (5429 ^ _224325) ^ [_411060, _411062, _411064] : [class_Rings_Oidom(_411060), 5432 ^ _224325 : [(5433 ^ _224325) ^ [] : [c_Polynomial_Osmult(_411060, _411062, _411064) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_411060)), -(_411062 = c_Groups_Ozero__class_Ozero(_411060)), -(_411064 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_411060)))], (5443 ^ _224325) ^ [] : [5444 ^ _224325 : [(5447 ^ _224325) ^ [] : [_411064 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_411060))], (5445 ^ _224325) ^ [] : [_411062 = c_Groups_Ozero__class_Ozero(_411060)]], -(c_Polynomial_Osmult(_411060, _411062, _411064) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_411060)))]]], (9880 ^ _224325) ^ [_565460, _565462] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _565460), c_Nat_OSuc(_565462)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _565460, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _565460), _565462)))], (11567 ^ _224325) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (3327 ^ _224325) ^ [_336507, _336509] : [class_Rings_Omult__zero(_336507), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_336507), _336509), c_Groups_Ozero__class_Ozero(_336507)) = c_Groups_Ozero__class_Ozero(_336507))], (11901 ^ _224325) ^ [] : [-(class_Rings_Oring__1(tc_Complex_Ocomplex))], (7214 ^ _224325) ^ [_473029, _473031] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _473029, _473031), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _473029), c_RealDef_Oreal(tc_Nat_Onat, _473031)))], (7016 ^ _224325) ^ [_466625, _466627] : [class_Rings_Olinordered__idom(_466625), c_Orderings_Oord__class_Oless(_466625, _466627, c_Groups_Ozero__class_Ozero(_466625)), -(c_Groups_Osgn__class_Osgn(_466625, _466627) = c_Groups_Ouminus__class_Ouminus(_466625, c_Groups_Oone__class_Oone(_466625)))], (11637 ^ _224325) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (5527 ^ _224325) ^ [_414566] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _414566) = _414566)], (9413 ^ _224325) ^ [_549325, _549327] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _549325, _549327), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _549325, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _549327, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (11483 ^ _224325) ^ [_626385, _626387] : [class_Orderings_Oorder(_626385), -(class_Orderings_Oorder(tc_fun(_626387, _626385)))], (7883 ^ _224325) ^ [_496655, _496657, _496659, _496661] : [class_Rings_Ocomm__semiring__1(_496655), -(hAPP(hAPP(c_Power_Opower__class_Opower(_496655), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_496655), _496657), _496659)), _496661) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_496655), hAPP(hAPP(c_Power_Opower__class_Opower(_496655), _496657), _496661)), hAPP(hAPP(c_Power_Opower__class_Opower(_496655), _496659), _496661)))], (11785 ^ _224325) ^ [] : [-(class_Rings_Ocomm__semiring(tc_RealDef_Oreal))], (5757 ^ _224325) ^ [_422682, _422684] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _422682, _422684)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _422682)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _422684))], (9229 ^ _224325) ^ [_542985, _542987, _542989] : [_542987 = _542989, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_542985)), _542987) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_542985)), _542989))], (10624 ^ _224325) ^ [_592831, _592833, _592835] : [class_Groups_Ogroup__add(_592831), -(c_Groups_Ominus__class_Ominus(_592831, _592833, c_Groups_Ouminus__class_Ouminus(_592831, _592835)) = c_Groups_Oplus__class_Oplus(_592831, _592833, _592835))], (2815 ^ _224325) ^ [_317359, _317361, _317363, _317365] : [class_Rings_Ocomm__semiring__1(_317359), -(c_Groups_Oplus__class_Oplus(_317359, c_Groups_Oplus__class_Oplus(_317359, _317361, _317363), _317365) = c_Groups_Oplus__class_Oplus(_317359, c_Groups_Oplus__class_Oplus(_317359, _317361, _317365), _317363))], (10938 ^ _224325) ^ [_605480, _605482] : [class_Groups_Ogroup__add(_605480), -(c_Groups_Ominus__class_Ominus(_605480, _605482, _605482) = c_Groups_Ozero__class_Ozero(_605480))], (4251 ^ _224325) ^ [_367558, _367560, _367562, _367564, _367566] : [class_Rings_Olinordered__semiring__strict(_367558), c_Orderings_Oord__class_Oless(_367558, _367560, _367562), c_Orderings_Oord__class_Oless(_367558, _367564, _367566), c_Orderings_Oord__class_Oless(_367558, c_Groups_Ozero__class_Ozero(_367558), _367562), c_Orderings_Oord__class_Oless__eq(_367558, c_Groups_Ozero__class_Ozero(_367558), _367564), -(c_Orderings_Oord__class_Oless(_367558, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_367558), _367560), _367564), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_367558), _367562), _367566)))], (11489 ^ _224325) ^ [_626597, _626599] : [class_Orderings_Oord(_626597), -(class_Orderings_Oord(tc_fun(_626599, _626597)))], (2777 ^ _224325) ^ [_315973, _315975, _315977, _315979, _315981] : [class_Rings_Ocomm__semiring__1(_315973), -(c_Groups_Oplus__class_Oplus(_315973, c_Groups_Oplus__class_Oplus(_315973, _315975, _315977), c_Groups_Oplus__class_Oplus(_315973, _315979, _315981)) = c_Groups_Oplus__class_Oplus(_315973, c_Groups_Oplus__class_Oplus(_315973, _315975, _315979), c_Groups_Oplus__class_Oplus(_315973, _315977, _315981)))], (11613 ^ _224325) ^ [] : [-(class_Groups_Ominus(tc_Int_Oint))], (8517 ^ _224325) ^ [_517928, _517930, _517932, _517934] : [class_Groups_Omonoid__mult(_517928), -(hAPP(hAPP(c_Power_Opower__class_Opower(_517928), _517930), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _517932), _517934)) = hAPP(hAPP(c_Power_Opower__class_Opower(_517928), hAPP(hAPP(c_Power_Opower__class_Opower(_517928), _517930), _517932)), _517934))], (1092 ^ _224325) ^ [_259572, _259574] : [_259574 = _259572, -(c_Groups_Otimes__class_Otimes(_259574) = c_Groups_Otimes__class_Otimes(_259572))], (2851 ^ _224325) ^ [_318975, _318977] : [class_Groups_Oone(_318975), 2854 ^ _224325 : [(2861 ^ _224325) ^ [] : [_318977 = c_Groups_Oone__class_Oone(_318975), -(c_Groups_Oone__class_Oone(_318975) = _318977)], (2855 ^ _224325) ^ [] : [c_Groups_Oone__class_Oone(_318975) = _318977, -(_318977 = c_Groups_Oone__class_Oone(_318975))]]], (7907 ^ _224325) ^ [_497743, _497745, _497747, _497749] : [class_Rings_Ocomm__semiring__1(_497743), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_497743), hAPP(hAPP(c_Power_Opower__class_Opower(_497743), _497745), _497747)), hAPP(hAPP(c_Power_Opower__class_Opower(_497743), _497745), _497749)) = hAPP(hAPP(c_Power_Opower__class_Opower(_497743), _497745), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _497747, _497749)))], (11531 ^ _224325) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (4771 ^ _224325) ^ [_386031, _386033] : [class_Rings_Ocomm__semiring__0(_386031), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_386031)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_386031))), _386033) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_386031)))], (11525 ^ _224325) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (3113 ^ _224325) ^ [_329174, _329176, _329178, _329180, _329182, _329184] : [class_Rings_Olinordered__semiring__1__strict(_329174), c_Orderings_Oord__class_Oless(_329174, _329176, _329178), c_Orderings_Oord__class_Oless(_329174, _329180, _329178), c_Orderings_Oord__class_Oless__eq(_329174, c_Groups_Ozero__class_Ozero(_329174), _329182), c_Orderings_Oord__class_Oless__eq(_329174, c_Groups_Ozero__class_Ozero(_329174), _329184), c_Groups_Oplus__class_Oplus(_329174, _329182, _329184) = c_Groups_Oone__class_Oone(_329174), -(c_Orderings_Oord__class_Oless(_329174, c_Groups_Oplus__class_Oplus(_329174, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_329174), _329182), _329176), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_329174), _329184), _329180)), _329178))], (12069 ^ _224325) ^ [_642887] : [class_Rings_Olinordered__idom(_642887), -(class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(_642887)))], (9465 ^ _224325) ^ [_551142, _551144] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _551142), 9468 ^ _224325 : [(9477 ^ _224325) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _551142), _551144) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _551142 = c_Groups_Oone__class_Oone(tc_Int_Oint), _551144 = c_Groups_Oone__class_Oone(tc_Int_Oint)], (9469 ^ _224325) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _551142), _551144) = c_Groups_Oone__class_Oone(tc_Int_Oint), 9472 ^ _224325 : [(9475 ^ _224325) ^ [] : [-(_551144 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (9473 ^ _224325) ^ [] : [-(_551142 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]]]], (6166 ^ _224325) ^ [_437538, _437540, _437542] : [class_Groups_Oordered__ab__group__add(_437538), 6169 ^ _224325 : [(6176 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_437538, c_Groups_Ouminus__class_Ouminus(_437538, _437542), _437540), -(c_Orderings_Oord__class_Oless__eq(_437538, c_Groups_Ouminus__class_Ouminus(_437538, _437540), _437542))], (6170 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_437538, c_Groups_Ouminus__class_Ouminus(_437538, _437540), _437542), -(c_Orderings_Oord__class_Oless__eq(_437538, c_Groups_Ouminus__class_Ouminus(_437538, _437542), _437540))]]], (5923 ^ _224325) ^ [_428467, _428469] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _428467), _428469) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _428469), _428467))], (9075 ^ _224325) ^ [_537451, _537453, _537455] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _537451), _537453), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _537451), _537455)), -(_537451 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _537453, _537455))], (8375 ^ _224325) ^ [_512656, _512658, _512660] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _512656, _512658), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _512658, _512656)), 8390 ^ _224325 : [(8393 ^ _224325) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _512660, _512656)], (8391 ^ _224325) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _512656, _512660))]], c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _512658, _512660), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _512660, _512658))], (2747 ^ _224325) ^ [_314876, _314878, _314880, _314882] : [class_Groups_Ocancel__semigroup__add(_314876), c_Groups_Oplus__class_Oplus(_314876, _314878, _314880) = c_Groups_Oplus__class_Oplus(_314876, _314882, _314880), -(_314878 = _314882)], (1062 ^ _224325) ^ [_258543, _258545, _258547, _258549] : [-(c_RealVector_Onorm__class_Onorm(_258549, _258545) = c_RealVector_Onorm__class_Onorm(_258547, _258543)), _258549 = _258547, _258545 = _258543], (7196 ^ _224325) ^ [_472416, _472418] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _472416), c_RealDef_Oreal(tc_Nat_Onat, _472418)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _472416, _472418))], (9866 ^ _224325) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (11571 ^ _224325) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (1778 ^ _224325) ^ [_281890, _281892, _281894] : [class_Orderings_Olinorder(_281890), -(c_Orderings_Oord__class_Oless(_281890, _281892, _281894)), 1785 ^ _224325 : [(1792 ^ _224325) ^ [] : [_281892 = _281894, -(c_Orderings_Oord__class_Oless__eq(_281890, _281892, _281894))], (1786 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_281890, _281892, _281894), -(_281892 = _281894)]]], (11775 ^ _224325) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal))], (5177 ^ _224325) ^ [_401159, _401161] : [5178 ^ _224325 : [(5179 ^ _224325) ^ [_401234] : [_401161 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _401159, _401234)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _401159, _401161))], (5581 ^ _224325) ^ [_416441, _416443, _416445] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _416441), _416443) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _416441), _416445), -(_416443 = _416445), -(_416441 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11889 ^ _224325) ^ [] : [-(class_Groups_Ogroup__add(tc_Complex_Ocomplex))], (11665 ^ _224325) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (3455 ^ _224325) ^ [_341049] : [class_Rings_Olinordered__idom(_341049), -(c_Groups_Oabs__class_Oabs(_341049, c_Groups_Oone__class_Oone(_341049)) = c_Groups_Oone__class_Oone(_341049))], (6616 ^ _224325) ^ [_453171, _453173, _453175] : [class_Groups_Ogroup__add(_453171), 6619 ^ _224325 : [(6626 ^ _224325) ^ [] : [_453175 = c_Groups_Ouminus__class_Ouminus(_453171, _453173), -(c_Groups_Oplus__class_Oplus(_453171, _453173, _453175) = c_Groups_Ozero__class_Ozero(_453171))], (6620 ^ _224325) ^ [] : [c_Groups_Oplus__class_Oplus(_453171, _453173, _453175) = c_Groups_Ozero__class_Ozero(_453171), -(_453175 = c_Groups_Ouminus__class_Ouminus(_453171, _453173))]]], (5387 ^ _224325) ^ [_409184, _409186, _409188, _409190] : [class_Rings_Ocomm__semiring__0(_409184), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_409184)), _409186), c_Polynomial_Osmult(_409184, _409188, _409190)) = c_Polynomial_Osmult(_409184, _409188, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_409184)), _409186), _409190)))], (3579 ^ _224325) ^ [_345184, _345186, _345188] : [class_Rings_Oordered__cancel__semiring(_345184), c_Orderings_Oord__class_Oless__eq(_345184, c_Groups_Ozero__class_Ozero(_345184), _345186), c_Orderings_Oord__class_Oless__eq(_345184, c_Groups_Ozero__class_Ozero(_345184), _345188), -(c_Orderings_Oord__class_Oless__eq(_345184, c_Groups_Ozero__class_Ozero(_345184), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_345184), _345186), _345188)))], (334 ^ _224325) ^ [_234554, _234556] : [-(class_Groups_Ocancel__comm__monoid__add(_234554)), _234556 = _234554, class_Groups_Ocancel__comm__monoid__add(_234556)], (9123 ^ _224325) ^ [_538933, _538935] : [-(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, _538933)), _538935)))], (6822 ^ _224325) ^ [_460020, _460022] : [-(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _460020, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _460022))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _460022, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _460020))))], (9689 ^ _224325) ^ [_558974] : [_558974 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _558974, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (11603 ^ _224325) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (10856 ^ _224325) ^ [_602347, _602349, _602351, _602353] : [class_Rings_Ocomm__ring(_602347), -(c_Polynomial_Osmult(_602347, c_Groups_Ominus__class_Ominus(_602347, _602349, _602351), _602353) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_602347), c_Polynomial_Osmult(_602347, _602349, _602353), c_Polynomial_Osmult(_602347, _602351, _602353)))], (11595 ^ _224325) ^ [] : [-(class_Rings_Ocomm__ring(tc_Int_Oint))], (11689 ^ _224325) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (8179 ^ _224325) ^ [_506595, _506597, _506599] : [_506595 = _506597, c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _506597, _506599), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _506595, _506599))], (9860 ^ _224325) ^ [_564701, _564703] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_564701), _564703), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _564701, _564703))], (11451 ^ _224325) ^ [_625207, _625209, _625211] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _625207, _625209), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _625207, _625211)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _625209, _625211))], (6140 ^ _224325) ^ [_436689, _436691, _436693] : [class_Groups_Oordered__ab__group__add(_436689), c_Orderings_Oord__class_Oless__eq(_436689, _436691, _436693), -(c_Orderings_Oord__class_Oless__eq(_436689, c_Groups_Ouminus__class_Ouminus(_436689, _436693), c_Groups_Ouminus__class_Ouminus(_436689, _436691)))], (11537 ^ _224325) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (5617 ^ _224325) ^ [_417692, _417694] : [_417692 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _417692), _417694), -(_417694 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_417692 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10802 ^ _224325) ^ [_600107, _600109] : [class_Rings_Oring__1(_600107), -(c_Groups_Ominus__class_Ominus(_600107, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_600107), _600109), _600109), c_Groups_Oone__class_Oone(_600107)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_600107), c_Groups_Oplus__class_Oplus(_600107, _600109, c_Groups_Oone__class_Oone(_600107))), c_Groups_Ominus__class_Ominus(_600107, _600109, c_Groups_Oone__class_Oone(_600107))))], (10618 ^ _224325) ^ [_592561, _592563, _592565] : [class_RealVector_Oreal__normed__vector(_592561), -(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(_592561, _592563), c_RealVector_Onorm__class_Onorm(_592561, _592565))), c_RealVector_Onorm__class_Onorm(_592561, c_Groups_Ominus__class_Ominus(_592561, _592563, _592565))))], (2588 ^ _224325) ^ [_308467, _308469, _308471, _308473] : [class_Orderings_Oord(_308467), _308469 = _308471, c_Orderings_Oord__class_Oless__eq(_308467, _308471, _308473), -(c_Orderings_Oord__class_Oless__eq(_308467, _308469, _308473))], (6304 ^ _224325) ^ [_442439, _442441, _442443] : [class_Rings_Oring(_442439), -(c_Groups_Ouminus__class_Ouminus(_442439, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_442439), _442441), _442443)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_442439), c_Groups_Ouminus__class_Ouminus(_442439, _442441)), _442443))], (4111 ^ _224325) ^ [_362718] : [class_Rings_Olinordered__semidom(_362718), -(c_Orderings_Oord__class_Oless(_362718, c_Groups_Ozero__class_Ozero(_362718), c_Groups_Oone__class_Oone(_362718)))], (10832 ^ _224325) ^ [_601379, _601381, _601383, _601385] : [class_Rings_Ocomm__ring(_601379), class_Rings_Odvd(_601379), c_Rings_Odvd__class_Odvd(_601379, _601381, _601383), 10843 ^ _224325 : [(10850 ^ _224325) ^ [_602020, _602022] : [c_Rings_Odvd__class_Odvd(_601379, _601381, c_Groups_Oplus__class_Oplus(_601379, c_Groups_Ominus__class_Ominus(_601379, _602022, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_601379), _602020), _601383)), _601385)), -(c_Rings_Odvd__class_Odvd(_601379, _601381, c_Groups_Oplus__class_Oplus(_601379, _602022, _601385)))], (10844 ^ _224325) ^ [_601782, _601784] : [c_Rings_Odvd__class_Odvd(_601379, _601381, c_Groups_Oplus__class_Oplus(_601379, _601784, _601385)), -(c_Rings_Odvd__class_Odvd(_601379, _601381, c_Groups_Oplus__class_Oplus(_601379, c_Groups_Ominus__class_Ominus(_601379, _601784, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_601379), _601782), _601383)), _601385)))]]], (7122 ^ _224325) ^ [_469801] : [-(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, _469801)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _469801)))], (5265 ^ _224325) ^ [_404691, _404693, _404695] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _404691, _404693), _404695), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _404691, _404695))], (7634 ^ _224325) ^ [_487858, _487860, _487862, _487864] : [class_Rings_Ocomm__semiring__1(_487858), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_487858), _487860, _487862), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_487858), _487860, c_Polynomial_Osmult(_487858, _487864, _487862)))], (12207 ^ _224325) ^ [_647257] : [class_Rings_Olinordered__idom(_647257), -(class_Orderings_Oord(tc_Polynomial_Opoly(_647257)))], (6009 ^ _224325) ^ [_432054, _432056, _432058] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _432054, _432056), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _432054, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _432058, _432056)))], (7228 ^ _224325) ^ [_473635] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _473635), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(_473635 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11949 ^ _224325) ^ [_639087] : [class_Rings_Olinordered__idom(_639087), -(class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(_639087)))], (11671 ^ _224325) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (12201 ^ _224325) ^ [_647067] : [class_Rings_Ocomm__semiring__0(_647067), -(class_Rings_Osemiring(tc_Polynomial_Opoly(_647067)))], (6798 ^ _224325) ^ [_459206, _459208] : [_459208 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _459206), -(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _459206, _459208) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (11633 ^ _224325) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (9177 ^ _224325) ^ [_540912, _540914] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _540912, _540914), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_540912), c_Nat_OSuc(_540914)))], (6984 ^ _224325) ^ [_465450] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _465450, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), -(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _465450) = _465450)], (4527 ^ _224325) ^ [_376942] : [-(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), _376942), _376942))), -(_376942 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (11557 ^ _224325) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_Int_Oint))], (9683 ^ _224325) ^ [_558816] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _558816, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_558816 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (154 ^ _224325) ^ [_229244, _229246] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_229244)), _229246 = _229244, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_229246)], (5189 ^ _224325) ^ [_401634, _401636, _401638] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _401636, _401638), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _401634, _401636), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _401634, _401638)))], (1598 ^ _224325) ^ [_276332, _276334, _276336] : [class_Orderings_Olinorder(_276332), -(c_Orderings_Oord__class_Oless(_276332, _276334, _276336)), -(_276334 = _276336), -(c_Orderings_Oord__class_Oless(_276332, _276336, _276334))], (11563 ^ _224325) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (11911 ^ _224325) ^ [] : [-(class_Rings_Oring(tc_Complex_Ocomplex))], (11683 ^ _224325) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (5151 ^ _224325) ^ [_400087, _400089] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _400087, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _400089, _400087)))], (10590 ^ _224325) ^ [_591275, _591277, _591279, _591281, _591283, _591285] : [class_Rings_Oring(_591275), 10593 ^ _224325 : [(10600 ^ _224325) ^ [] : [c_Groups_Oplus__class_Oplus(_591275, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_591275), c_Groups_Ominus__class_Ominus(_591275, _591277, _591283)), _591279), _591281) = _591285, -(c_Groups_Oplus__class_Oplus(_591275, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_591275), _591277), _591279), _591281) = c_Groups_Oplus__class_Oplus(_591275, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_591275), _591283), _591279), _591285))], (10594 ^ _224325) ^ [] : [c_Groups_Oplus__class_Oplus(_591275, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_591275), _591277), _591279), _591281) = c_Groups_Oplus__class_Oplus(_591275, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_591275), _591283), _591279), _591285), -(c_Groups_Oplus__class_Oplus(_591275, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_591275), c_Groups_Ominus__class_Ominus(_591275, _591277, _591283)), _591279), _591281) = _591285)]]], (7208 ^ _224325) ^ [_472851, _472853] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _472851), c_RealDef_Oreal(tc_Nat_Onat, _472853)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _472851, _472853))], (11621 ^ _224325) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (11521 ^ _224325) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))], (5591 ^ _224325) ^ [_416727, _416729, _416731] : [5592 ^ _224325 : [(5595 ^ _224325) ^ [] : [_416727 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5593 ^ _224325) ^ [] : [_416729 = _416731]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _416727), _416729) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _416727), _416731))], (6756 ^ _224325) ^ [_457795, _457797, _457799] : [class_Rings_Olinordered__idom(_457795), 6759 ^ _224325 : [(6768 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(_457795, c_Groups_Oabs__class_Oabs(_457795, _457797), _457799)), c_Orderings_Oord__class_Oless(_457795, _457797, _457799), c_Orderings_Oord__class_Oless(_457795, c_Groups_Ouminus__class_Ouminus(_457795, _457797), _457799)], (6760 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_457795, c_Groups_Oabs__class_Oabs(_457795, _457797), _457799), 6763 ^ _224325 : [(6766 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(_457795, c_Groups_Ouminus__class_Ouminus(_457795, _457797), _457799))], (6764 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(_457795, _457797, _457799))]]]]], (9567 ^ _224325) ^ [] : [-(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (11517 ^ _224325) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (9593 ^ _224325) ^ [_555340, _555342] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_555340), c_Groups_Ozero__class_Ozero(_555340)), c_Nat_OSuc(_555342)) = c_Groups_Ozero__class_Ozero(_555340)), class_Power_Opower(_555340), class_Rings_Osemiring__0(_555340)], (11857 ^ _224325) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex))], (9882 ^ _224325) ^ [_565572, _565574] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_565572)), _565574) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _565574, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _565572), _565574)))], (11601 ^ _224325) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (8133 ^ _224325) ^ [_505138, _505140] : [_505138 = _505140, -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _505138, _505140))], (4683 ^ _224325) ^ [_381924, _381926, _381928, _381930, _381932] : [class_Groups_Ocomm__monoid__add(_381924), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_381924), c_Polynomial_OpCons(_381924, _381926, _381928), c_Polynomial_OpCons(_381924, _381930, _381932)) = c_Polynomial_OpCons(_381924, c_Groups_Oplus__class_Oplus(_381924, _381926, _381930), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_381924), _381928, _381932)))], (734 ^ _224325) ^ [_246354, _246356] : [-(class_Groups_Oone(_246354)), _246356 = _246354, class_Groups_Oone(_246356)], (11691 ^ _224325) ^ [] : [-(class_Groups_Ominus(tc_Nat_Onat))], (434 ^ _224325) ^ [_237504, _237506] : [-(class_Rings_Olinordered__ring(_237504)), _237506 = _237504, class_Rings_Olinordered__ring(_237506)], (11873 ^ _224325) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex))], (3593 ^ _224325) ^ [_345632, _345634, _345636] : [class_Rings_Oordered__cancel__semiring(_345632), c_Orderings_Oord__class_Oless__eq(_345632, c_Groups_Ozero__class_Ozero(_345632), _345634), c_Orderings_Oord__class_Oless__eq(_345632, _345636, c_Groups_Ozero__class_Ozero(_345632)), -(c_Orderings_Oord__class_Oless__eq(_345632, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_345632), _345634), _345636), c_Groups_Ozero__class_Ozero(_345632)))], (7800 ^ _224325) ^ [_493344, _493346, _493348] : [class_Rings_Odvd(_493344), class_Rings_Osemiring__0(_493344), 7807 ^ _224325 : [(7817 ^ _224325) ^ [] : [-(hBOOL(hAPP(_493346, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_493344), _493348), 7824 ^ [_493344, _493346, _493348])))), 7818 ^ _224325 : [(7819 ^ _224325) ^ [_493993] : [c_Rings_Odvd__class_Odvd(_493344, _493348, c_Groups_Oplus__class_Oplus(_493344, _493993, c_Groups_Ozero__class_Ozero(_493344))), hBOOL(hAPP(_493346, _493993))]]], (7808 ^ _224325) ^ [] : [7809 ^ _224325 : [(7810 ^ _224325) ^ [_493653] : [hBOOL(hAPP(_493346, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_493344), _493348), _493653)))]], 7812 ^ _224325 : [(7815 ^ _224325) ^ [] : [-(hBOOL(hAPP(_493346, 7811 ^ [_493344, _493346, _493348])))], (7813 ^ _224325) ^ [] : [-(c_Rings_Odvd__class_Odvd(_493344, _493348, c_Groups_Oplus__class_Oplus(_493344, 7811 ^ [_493344, _493346, _493348], c_Groups_Ozero__class_Ozero(_493344))))]]]]], (10124 ^ _224325) ^ [_574248] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _574248, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (7166 ^ _224325) ^ [_471379, _471381] : [c_RealDef_Oreal(tc_Nat_Onat, _471379) = c_RealDef_Oreal(tc_Nat_Onat, _471381), -(_471379 = _471381)], (5323 ^ _224325) ^ [_406940, _406942] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _406940, _406942), _406940)], (8909 ^ _224325) ^ [_531649, _531651, _531653, _531655] : [class_Rings_Olinordered__semidom(_531649), c_Orderings_Oord__class_Oless(_531649, c_Groups_Oone__class_Oone(_531649), _531651), c_Orderings_Oord__class_Oless__eq(_531649, hAPP(hAPP(c_Power_Opower__class_Opower(_531649), _531651), _531653), hAPP(hAPP(c_Power_Opower__class_Opower(_531649), _531651), _531655)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _531653, _531655))], (11389 ^ _224325) ^ [_622745, _622747, _622749] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _622745, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _622749, _622747)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _622745, _622747), _622749))], (10636 ^ _224325) ^ [_593331, _593333, _593335] : [class_Groups_Oab__group__add(_593331), -(c_Groups_Ominus__class_Ominus(_593331, _593333, _593335) = c_Groups_Oplus__class_Oplus(_593331, _593333, c_Groups_Ouminus__class_Ouminus(_593331, _593335)))], (9529 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (11559 ^ _224325) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (8319 ^ _224325) ^ [_510914, _510916] : [_510916 = _510914, c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _510914, _510916), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _510916, _510914))], (1612 ^ _224325) ^ [_276770, _276772, _276774, _276776] : [class_Orderings_Oorder(_276770), c_Orderings_Oord__class_Oless__eq(_276770, _276772, _276774), c_Orderings_Oord__class_Oless(_276770, _276776, _276772), -(c_Orderings_Oord__class_Oless(_276770, _276776, _276774))], (9407 ^ _224325) ^ [_549151, _549153] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _549151, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _549153, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _549151, _549153))], (10900 ^ _224325) ^ [_604202, _604204, _604206, _604208, _604210] : [class_Groups_Ominus(_604202), -(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_604204, _604202), _604206, _604208), _604210) = c_Groups_Ominus__class_Ominus(_604202, hAPP(_604206, _604210), hAPP(_604208, _604210)))], (11877 ^ _224325) ^ [] : [-(class_Groups_Oab__group__add(tc_Complex_Ocomplex))], (5861 ^ _224325) ^ [_426348, _426350] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _426348, _426350), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _426348, _426350))], (8295 ^ _224325) ^ [_510202, _510204] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _510202, _510204), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _510204, _510202)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _510204, _510202), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _510202, _510204))], (4997 ^ _224325) ^ [_394896, _394898] : [4998 ^ _224325 : [(5001 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _394898, _394896)], (4999 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _394896, _394898)]], _394896 = _394898], (624 ^ _224325) ^ [_243109, _243111] : [-(class_Rings_Olinordered__idom(_243109)), _243111 = _243109, class_Rings_Olinordered__idom(_243111)], (7516 ^ _224325) ^ [_483598, _483600, _483602] : [class_Rings_Olinordered__idom(_483598), c_Groups_Oabs__class_Oabs(_483598, _483600) = c_Groups_Oabs__class_Oabs(_483598, _483602), -(c_Rings_Odvd__class_Odvd(_483598, _483600, _483602))], (11793 ^ _224325) ^ [] : [-(class_Orderings_Opreorder(tc_RealDef_Oreal))], (11547 ^ _224325) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (1072 ^ _224325) ^ [_258902, _258904, _258906, _258908] : [-(c_Groups_Oabs__class_Oabs(_258908, _258904) = c_Groups_Oabs__class_Oabs(_258906, _258902)), _258908 = _258906, _258904 = _258902], (11467 ^ _224325) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat))], (9353 ^ _224325) ^ [_547287, _547289] : [9354 ^ _224325 : [(9357 ^ _224325) ^ [] : [_547287 = _547289], (9355 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _547287, _547289)]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _547287, c_Nat_OSuc(_547289)))], (10660 ^ _224325) ^ [_594359, _594361, _594363] : [class_Groups_Oordered__ab__group__add__abs(_594359), -(c_Orderings_Oord__class_Oless__eq(_594359, c_Groups_Oabs__class_Oabs(_594359, c_Groups_Ominus__class_Ominus(_594359, c_Groups_Oabs__class_Oabs(_594359, _594361), c_Groups_Oabs__class_Oabs(_594359, _594363))), c_Groups_Oabs__class_Oabs(_594359, c_Groups_Ominus__class_Ominus(_594359, _594361, _594363))))], (9337 ^ _224325) ^ [_546774, _546776] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _546774, _546776), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_546774), c_Nat_OSuc(_546776)))], (9615 ^ _224325) ^ [_556237, _556239, _556241] : [class_Rings_Ocomm__semiring__1(_556237), -(hAPP(hAPP(c_Power_Opower__class_Opower(_556237), _556239), c_Nat_OSuc(_556241)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_556237), _556239), hAPP(hAPP(c_Power_Opower__class_Opower(_556237), _556239), _556241)))], (5479 ^ _224325) ^ [_412993, _412995] : [class_Rings_Olinordered__idom(_412993), 5482 ^ _224325 : [(5489 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_412993, _412995, c_Groups_Ozero__class_Ozero(_412993)), -(c_Orderings_Oord__class_Oless(_412993, c_Groups_Osgn__class_Osgn(_412993, _412995), c_Groups_Ozero__class_Ozero(_412993)))], (5483 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_412993, c_Groups_Osgn__class_Osgn(_412993, _412995), c_Groups_Ozero__class_Ozero(_412993)), -(c_Orderings_Oord__class_Oless(_412993, _412995, c_Groups_Ozero__class_Ozero(_412993)))]]], (7340 ^ _224325) ^ [_477692, _477694] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _477692), 7343 ^ _224325 : [(7350 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _477694), _477692), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _477694, c_RComplete_Onatfloor(_477692)))], (7344 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _477694, c_RComplete_Onatfloor(_477692)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _477694), _477692))]]], (11471 ^ _224325) ^ [_625961, _625963] : [class_Lattices_Oboolean__algebra(_625961), -(class_Lattices_Oboolean__algebra(tc_fun(_625963, _625961)))], (11715 ^ _224325) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal))], (12075 ^ _224325) ^ [_643077] : [class_Rings_Oidom(_643077), -(class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(_643077)))], (6474 ^ _224325) ^ [] : [-(c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (1808 ^ _224325) ^ [_282807, _282809, _282811] : [class_Orderings_Olinorder(_282807), -(c_Orderings_Oord__class_Oless(_282807, _282809, _282811)), -(c_Orderings_Oord__class_Oless__eq(_282807, _282811, _282809))], (10230 ^ _224325) ^ [_578136, _578138, _578140] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _578136, _578138), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _578138, _578140), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _578136, _578140))], (11903 ^ _224325) ^ [] : [-(class_Groups_Ominus(tc_Complex_Ocomplex))], (4539 ^ _224325) ^ [_377350, _377352, _377354] : [class_Rings_Olinordered__ring__strict(_377350), 4542 ^ _224325 : [(4551 ^ _224325) ^ [] : [-(c_Groups_Oplus__class_Oplus(_377350, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_377350), _377352), _377352), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_377350), _377354), _377354)) = c_Groups_Ozero__class_Ozero(_377350)), _377352 = c_Groups_Ozero__class_Ozero(_377350), _377354 = c_Groups_Ozero__class_Ozero(_377350)], (4543 ^ _224325) ^ [] : [c_Groups_Oplus__class_Oplus(_377350, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_377350), _377352), _377352), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_377350), _377354), _377354)) = c_Groups_Ozero__class_Ozero(_377350), 4546 ^ _224325 : [(4549 ^ _224325) ^ [] : [-(_377354 = c_Groups_Ozero__class_Ozero(_377350))], (4547 ^ _224325) ^ [] : [-(_377352 = c_Groups_Ozero__class_Ozero(_377350))]]]]], (9549 ^ _224325) ^ [_553903] : [c_Nat_OSuc(_553903) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5909 ^ _224325) ^ [_427983, _427985] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _427983), _427985)), _427983 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _427985 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (9561 ^ _224325) ^ [_554346] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _554346, c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Groups_Oabs__class_Oabs(tc_Int_Oint, _554346) = _554346)], (8929 ^ _224325) ^ [_532365, _532367] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _532365), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _532367, _532365), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _532367))], (2414 ^ _224325) ^ [_302700, _302702] : [class_Groups_Oordered__ab__group__add__abs(_302700), 2417 ^ _224325 : [(2424 ^ _224325) ^ [] : [_302702 = c_Groups_Ozero__class_Ozero(_302700), -(c_Orderings_Oord__class_Oless__eq(_302700, c_Groups_Oabs__class_Oabs(_302700, _302702), c_Groups_Ozero__class_Ozero(_302700)))], (2418 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_302700, c_Groups_Oabs__class_Oabs(_302700, _302702), c_Groups_Ozero__class_Ozero(_302700)), -(_302702 = c_Groups_Ozero__class_Ozero(_302700))]]], (5701 ^ _224325) ^ [_420697, _420699, _420701] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _420697), _420699), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _420701), _420699)), 5704 ^ _224325 : [(5707 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _420697, _420701))], (5705 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _420699))]]], (5709 ^ _224325) ^ [_420972, _420974, _420976] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _420972), _420974), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _420976), _420974))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _420974), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _420972, _420976)], (2064 ^ _224325) ^ [_291366, _291368] : [class_Groups_Ocomm__monoid__add(_291366), -(c_Groups_Oplus__class_Oplus(_291366, _291368, c_Groups_Ozero__class_Ozero(_291366)) = _291368)], (12099 ^ _224325) ^ [_643837] : [class_Rings_Ocomm__semiring__1(_643837), -(class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(_643837)))], (5343 ^ _224325) ^ [_407794, _407796] : [class_Rings_Olinordered__idom(_407794), 5346 ^ _224325 : [(5353 ^ _224325) ^ [] : [_407796 = c_Groups_Ozero__class_Ozero(_407794), -(c_Groups_Osgn__class_Osgn(_407794, _407796) = c_Groups_Ozero__class_Ozero(_407794))], (5347 ^ _224325) ^ [] : [c_Groups_Osgn__class_Osgn(_407794, _407796) = c_Groups_Ozero__class_Ozero(_407794), -(_407796 = c_Groups_Ozero__class_Ozero(_407794))]]], (11575 ^ _224325) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (11659 ^ _224325) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (9455 ^ _224325) ^ [_550803, _550805, _550807] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _550803, _550805), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _550807), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _550807), _550803), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _550807), _550805)))], (1654 ^ _224325) ^ [_278114, _278116, _278118, _278120] : [class_Orderings_Opreorder(_278114), c_Orderings_Oord__class_Oless(_278114, _278116, _278118), c_Orderings_Oord__class_Oless__eq(_278114, _278118, _278120), -(c_Orderings_Oord__class_Oless(_278114, _278116, _278120))], (12009 ^ _224325) ^ [_640987] : [class_Rings_Olinordered__idom(_640987), -(class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(_640987)))], (11677 ^ _224325) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (11905 ^ _224325) ^ [] : [-(class_Fields_Ofield(tc_Complex_Ocomplex))], (774 ^ _224325) ^ [_247570, _247572, _247574, _247576, _247578, _247580] : [-(c_Orderings_Oord__class_Oless__eq(_247578, _247574, _247570)), c_Orderings_Oord__class_Oless__eq(_247580, _247576, _247572), _247580 = _247578, _247576 = _247574, _247572 = _247570], (10154 ^ _224325) ^ [_575338, _575340, _575342] : [class_Rings_Oidom(_575338), -(_575340 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_575338))), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_575338), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_575338)), c_Polynomial_OpCons(_575338, c_Groups_Ouminus__class_Ouminus(_575338, _575342), c_Polynomial_OpCons(_575338, c_Groups_Oone__class_Oone(_575338), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_575338))))), c_Nat_OSuc(c_Polynomial_Oorder(_575338, _575342, _575340))), _575340)], (948 ^ _224325) ^ [_254408, _254410, _254412, _254414] : [-(c_Nat__Transfer_Otsub(_254414, _254410) = c_Nat__Transfer_Otsub(_254412, _254408)), _254414 = _254412, _254410 = _254408], (3005 ^ _224325) ^ [_324853, _324855, _324857, _324859, _324861] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_324853), 3008 ^ _224325 : [(3009 ^ _224325) ^ [] : [c_Groups_Oplus__class_Oplus(_324853, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_324853), _324855), _324859), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_324853), _324857), _324861)) = c_Groups_Oplus__class_Oplus(_324853, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_324853), _324855), _324861), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_324853), _324857), _324859)), -(_324855 = _324857), -(_324859 = _324861)], (3019 ^ _224325) ^ [] : [-(c_Groups_Oplus__class_Oplus(_324853, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_324853), _324855), _324859), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_324853), _324857), _324861)) = c_Groups_Oplus__class_Oplus(_324853, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_324853), _324855), _324861), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_324853), _324857), _324859))), 3022 ^ _224325 : [(3025 ^ _224325) ^ [] : [_324859 = _324861], (3023 ^ _224325) ^ [] : [_324855 = _324857]]]]], (8569 ^ _224325) ^ [_519900, _519902, _519904] : [class_Rings_Olinordered__semidom(_519900), c_Orderings_Oord__class_Oless__eq(_519900, c_Groups_Oone__class_Oone(_519900), _519902), -(c_Orderings_Oord__class_Oless__eq(_519900, c_Groups_Oone__class_Oone(_519900), hAPP(hAPP(c_Power_Opower__class_Opower(_519900), _519902), _519904)))], (5375 ^ _224325) ^ [_408738] : [class_RealVector_Oreal__normed__vector(_408738), -(c_Groups_Osgn__class_Osgn(_408738, c_Groups_Ozero__class_Ozero(_408738)) = c_Groups_Ozero__class_Ozero(_408738))], (6058 ^ _224325) ^ [_434123] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _434123), -(c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _434123, c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatceiling(_434123), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (2518 ^ _224325) ^ [_306263, _306265, _306267, _306269] : [class_Orderings_Opreorder(_306263), c_Orderings_Oord__class_Oless__eq(_306263, _306265, _306267), c_Orderings_Oord__class_Oless__eq(_306263, _306267, _306269), -(c_Orderings_Oord__class_Oless__eq(_306263, _306265, _306269))], (11541 ^ _224325) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (1740 ^ _224325) ^ [_280722, _280724, _280726] : [class_Orderings_Olinorder(_280722), c_Orderings_Oord__class_Oless__eq(_280722, _280724, _280726), c_Orderings_Oord__class_Oless(_280722, _280726, _280724)], (11773 ^ _224325) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_RealDef_Oreal))], (1730 ^ _224325) ^ [_280397, _280399, _280401] : [class_Orderings_Opreorder(_280397), c_Orderings_Oord__class_Oless(_280397, _280399, _280401), -(c_Orderings_Oord__class_Oless__eq(_280397, _280399, _280401))], (11455 ^ _224325) ^ [_625445, _625447] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _625445, _625447), _625445))], (8713 ^ _224325) ^ [_524959, _524961, _524963] : [class_Rings_Olinordered__semidom(_524959), c_Orderings_Oord__class_Oless(_524959, c_Groups_Oone__class_Oone(_524959), _524961), -(c_Orderings_Oord__class_Oless(_524959, hAPP(hAPP(c_Power_Opower__class_Opower(_524959), _524961), _524963), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_524959), _524961), hAPP(hAPP(c_Power_Opower__class_Opower(_524959), _524961), _524963))))], (5899 ^ _224325) ^ [_427595] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _427595) = _427595)], (8189 ^ _224325) ^ [_506922, _506924, _506926] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _506922, _506924), _506924 = _506926, -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _506922, _506926))], (1682 ^ _224325) ^ [_278969, _278971, _278973] : [class_Orderings_Oorder(_278969), c_Orderings_Oord__class_Oless__eq(_278969, _278971, _278973), -(_278971 = _278973), -(c_Orderings_Oord__class_Oless(_278969, _278971, _278973))], (8009 ^ _224325) ^ [_501182, _501184, _501186, _501188] : [class_Rings_Olinordered__semidom(_501182), c_Orderings_Oord__class_Oless(_501182, _501184, _501186), c_Orderings_Oord__class_Oless__eq(_501182, c_Groups_Ozero__class_Ozero(_501182), _501184), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _501188), -(c_Orderings_Oord__class_Oless(_501182, hAPP(hAPP(c_Power_Opower__class_Opower(_501182), _501184), _501188), hAPP(hAPP(c_Power_Opower__class_Opower(_501182), _501186), _501188)))], (9269 ^ _224325) ^ [_544612, _544614] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _544612, c_Nat_OSuc(_544614)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _544612, _544614)), -(_544612 = _544614)], (11623 ^ _224325) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (5795 ^ _224325) ^ [_423909, _423911] : [class_Rings_Olinordered__idom(_423909), c_Orderings_Oord__class_Oless(_423909, c_Groups_Ozero__class_Ozero(_423909), _423911), -(c_Groups_Osgn__class_Osgn(_423909, _423911) = c_Groups_Oone__class_Oone(_423909))], (1960 ^ _224325) ^ [_287670, _287672, _287674, _287676] : [class_Groups_Oordered__cancel__ab__semigroup__add(_287670), c_Orderings_Oord__class_Oless(_287670, _287672, _287674), -(c_Orderings_Oord__class_Oless(_287670, c_Groups_Oplus__class_Oplus(_287670, _287676, _287672), c_Groups_Oplus__class_Oplus(_287670, _287676, _287674)))], (174 ^ _224325) ^ [_229834, _229836] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_229834)), _229836 = _229834, class_Groups_Oordered__ab__semigroup__add__imp__le(_229836)], (4339 ^ _224325) ^ [_370432, _370434, _370436, _370438] : [class_Rings_Olinordered__semiring(_370432), c_Orderings_Oord__class_Oless(_370432, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_370432), _370434), _370436), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_370432), _370438), _370436)), c_Orderings_Oord__class_Oless__eq(_370432, c_Groups_Ozero__class_Ozero(_370432), _370436), -(c_Orderings_Oord__class_Oless(_370432, _370434, _370438))], (11549 ^ _224325) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (8961 ^ _224325) ^ [_533575] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _533575))], (1105 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_z____), v_r))], (1178 ^ _224325) ^ [_263136] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _263136), v_r), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_cs____), _263136)), 1174 ^ []))], (7390 ^ _224325) ^ [_479303, _479305] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatfloor(_479303), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _479305), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _479303, c_RealDef_Oreal(tc_Nat_Onat, _479305)))], (11717 ^ _224325) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal))], (10894 ^ _224325) ^ [_603918, _603920, _603922] : [class_RealVector_Oreal__normed__vector(_603918), -(c_RealVector_Onorm__class_Onorm(_603918, c_Groups_Ominus__class_Ominus(_603918, _603920, _603922)) = c_RealVector_Onorm__class_Onorm(_603918, c_Groups_Ominus__class_Ominus(_603918, _603922, _603920)))], (4177 ^ _224325) ^ [_365015, _365017, _365019] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _365015), 4180 ^ _224325 : [(4187 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _365017, _365019), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _365017), _365015), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _365019), _365015)))], (4181 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _365017), _365015), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _365019), _365015)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _365017, _365019))]]], (3419 ^ _224325) ^ [_339938, _339940] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _339938, _339940), 3422 ^ _224325 : [(3425 ^ _224325) ^ [] : [_339938 = _339940], (3423 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _339938, _339940))]]], (9517 ^ _224325) ^ [_552807] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _552807), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _552807))], (7718 ^ _224325) ^ [_490684, _490686, _490688, _490690] : [class_Fields_Ofield(_490684), -(_490686 = c_Groups_Ozero__class_Ozero(_490684)), 7725 ^ _224325 : [(7732 ^ _224325) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_490684), _490688, _490690), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_490684), _490688, c_Polynomial_Osmult(_490684, _490686, _490690)))], (7726 ^ _224325) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_490684), _490688, c_Polynomial_Osmult(_490684, _490686, _490690)), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_490684), _490688, _490690))]]], (7895 ^ _224325) ^ [_497263, _497265] : [class_Rings_Ocomm__semiring__1(_497263), -(hAPP(hAPP(c_Power_Opower__class_Opower(_497263), _497265), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _497265)], (4701 ^ _224325) ^ [_382682, _382684, _382686, _382688] : [class_Rings_Ocomm__semiring__0(_382682), -(hAPP(c_Polynomial_Opoly(_382682, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_382682)), _382684), _382686)), _382688) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_382682), hAPP(c_Polynomial_Opoly(_382682, _382684), _382688)), hAPP(c_Polynomial_Opoly(_382682, _382686), _382688)))], (10434 ^ _224325) ^ [_584917] : [class_Power_Opower(_584917), -(c_Power_Opower__class_Opower(_584917) = c_Power_Opower_Opower(_584917, c_Groups_Oone__class_Oone(_584917), c_Groups_Otimes__class_Otimes(_584917)))], (10422 ^ _224325) ^ [] : [-(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)))], (6966 ^ _224325) ^ [_464887] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _464887, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _464887) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _464887))], (11837 ^ _224325) ^ [] : [-(class_Rings_Oidom(tc_RealDef_Oreal))], (4423 ^ _224325) ^ [_373322, _373324, _373326] : [class_Rings_Olinordered__idom(_373322), c_Orderings_Oord__class_Oless__eq(_373322, c_Groups_Ozero__class_Ozero(_373322), _373324), c_Orderings_Oord__class_Oless__eq(_373322, c_Groups_Ozero__class_Ozero(_373322), _373326), c_Orderings_Oord__class_Oless__eq(_373322, _373326, c_Groups_Oone__class_Oone(_373322)), -(c_Orderings_Oord__class_Oless__eq(_373322, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_373322), _373324), _373326), _373324))], (12087 ^ _224325) ^ [_643457] : [class_Rings_Olinordered__idom(_643457), -(class_Rings_Olinordered__ring(tc_Polynomial_Opoly(_643457)))], (5675 ^ _224325) ^ [_419670, _419672, _419674] : [5676 ^ _224325 : [(5679 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _419670, _419674)], (5677 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _419672))]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _419670), _419672), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _419674), _419672)))], (1884 ^ _224325) ^ [_285116, _285118, _285120] : [class_Orderings_Olinorder(_285116), -(c_Orderings_Oord__class_Oless__eq(_285116, _285118, _285120)), -(c_Orderings_Oord__class_Oless(_285116, _285120, _285118))], (9215 ^ _224325) ^ [_542229, _542231, _542233] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _542229, _542231)), _542233) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _542229), _542233), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _542231), _542233)))], (10712 ^ _224325) ^ [_596378, _596380] : [-(c_Groups_Ominus__class_Ominus(tc_Int_Oint, _596378, _596380) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _596378, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _596380)))], (11423 ^ _224325) ^ [_624213, _624215, _624217] : [class_Rings_Olinordered__idom(_624213), 11426 ^ _224325 : [(11427 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(_624213), _624215, _624217), -(_624215 = _624217), -(c_Polynomial_Opos__poly(_624213, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_624213), _624217, _624215)))], (11437 ^ _224325) ^ [] : [11438 ^ _224325 : [(11441 ^ _224325) ^ [] : [c_Polynomial_Opos__poly(_624213, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_624213), _624217, _624215))], (11439 ^ _224325) ^ [] : [_624215 = _624217]], -(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(_624213), _624215, _624217))]]], (9263 ^ _224325) ^ [_544394, _544396] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_544394), _544396), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _544394, _544396))], (1082 ^ _224325) ^ [_259261, _259263, _259265, _259267] : [-(hAPP(_259267, _259263) = hAPP(_259265, _259261)), _259267 = _259265, _259263 = _259261], (10070 ^ _224325) ^ [_572280, _572282] : [class_RealVector_Oreal__normed__vector(_572280), 10073 ^ _224325 : [(10074 ^ _224325) ^ [] : [10083 ^ _224325 : [(10084 ^ _224325) ^ [_572837] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_572280, hAPP(_572282, _572837)), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(10082 ^ [_572280, _572282]))))]], 10075 ^ _224325 : [(10076 ^ _224325) ^ [_572519] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _572519), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_572280, hAPP(_572282, 10079 ^ [_572280, _572282, _572519])), _572519)]]], (10086 ^ _224325) ^ [] : [10088 ^ _224325 : [(10089 ^ _224325) ^ [_573016] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_572280, hAPP(_572282, 10087 ^ [_572280, _572282, _573016])), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(_573016)))]], 10091 ^ _224325 : [(10094 ^ _224325) ^ [_573237] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_572280, hAPP(_572282, _573237)), 10090 ^ [_572280, _572282]))], (10092 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 10090 ^ [_572280, _572282]))]]]]], (8423 ^ _224325) ^ [_514228, _514230] : [8424 ^ _224325 : [(8427 ^ _224325) ^ [] : [_514230 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (8425 ^ _224325) ^ [] : [-(_514228 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), c_Groups_Oabs__class_Oabs(tc_Int_Oint, _514228)), _514230)))], (11807 ^ _224325) ^ [] : [-(class_Rings_Omult__zero(tc_RealDef_Oreal))], (4367 ^ _224325) ^ [_371400, _371402, _371404, _371406] : [class_Rings_Olinordered__semiring(_371400), c_Orderings_Oord__class_Oless(_371400, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_371400), _371402), _371404), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_371400), _371402), _371406)), c_Orderings_Oord__class_Oless__eq(_371400, c_Groups_Ozero__class_Ozero(_371400), _371402), -(c_Orderings_Oord__class_Oless(_371400, _371404, _371406))], (2076 ^ _224325) ^ [_291806, _291808] : [class_Groups_Omonoid__add(_291806), -(c_Groups_Oplus__class_Oplus(_291806, _291808, c_Groups_Ozero__class_Ozero(_291806)) = _291808)], (7042 ^ _224325) ^ [_467435, _467437] : [class_Groups_Osgn__if(_467435), 7045 ^ _224325 : [(7052 ^ _224325) ^ [] : [-(_467437 = c_Groups_Ozero__class_Ozero(_467435)), 7055 ^ _224325 : [(7062 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(_467435, c_Groups_Ozero__class_Ozero(_467435), _467437)), -(c_Groups_Osgn__class_Osgn(_467435, _467437) = c_Groups_Ouminus__class_Ouminus(_467435, c_Groups_Oone__class_Oone(_467435)))], (7056 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_467435, c_Groups_Ozero__class_Ozero(_467435), _467437), -(c_Groups_Osgn__class_Osgn(_467435, _467437) = c_Groups_Oone__class_Oone(_467435))]]], (7046 ^ _224325) ^ [] : [_467437 = c_Groups_Ozero__class_Ozero(_467435), -(c_Groups_Osgn__class_Osgn(_467435, _467437) = c_Groups_Ozero__class_Ozero(_467435))]]], (3621 ^ _224325) ^ [_346528, _346530, _346532] : [class_Rings_Oordered__cancel__semiring(_346528), c_Orderings_Oord__class_Oless__eq(_346528, _346530, c_Groups_Ozero__class_Ozero(_346528)), c_Orderings_Oord__class_Oless__eq(_346528, c_Groups_Ozero__class_Ozero(_346528), _346532), -(c_Orderings_Oord__class_Oless__eq(_346528, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_346528), _346530), _346532), c_Groups_Ozero__class_Ozero(_346528)))], (11457 ^ _224325) ^ [_625545] : [class_Groups_Ocancel__comm__monoid__add(_625545), -(class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(_625545)))], (9429 ^ _224325) ^ [_549842, _549844] : [9430 ^ _224325 : [(9433 ^ _224325) ^ [] : [_549842 = _549844], (9431 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _549842, _549844)]], -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _549842, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _549844, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (6698 ^ _224325) ^ [_455871, _455873] : [class_Rings_Ocomm__ring__1(_455871), -(c_Groups_Ouminus__class_Ouminus(_455871, _455873) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_455871), c_Groups_Ouminus__class_Ouminus(_455871, c_Groups_Oone__class_Oone(_455871))), _455873))], (11569 ^ _224325) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Int_Oint))], (2012 ^ _224325) ^ [_289468, _289470] : [class_RealVector_Oreal__normed__algebra(_289468), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_289468), _289470), c_Groups_Ozero__class_Ozero(_289468)) = c_Groups_Ozero__class_Ozero(_289468))], (8683 ^ _224325) ^ [_523832, _523834, _523836] : [class_Rings_Olinordered__idom(_523832), -(c_Groups_Oabs__class_Oabs(_523832, hAPP(hAPP(c_Power_Opower__class_Opower(_523832), c_Groups_Ouminus__class_Ouminus(_523832, _523834)), _523836)) = c_Groups_Oabs__class_Oabs(_523832, hAPP(hAPP(c_Power_Opower__class_Opower(_523832), _523834), _523836)))], (4477 ^ _224325) ^ [_375197, _375199, _375201] : [class_Rings_Olinordered__ring__strict(_375197), 4480 ^ _224325 : [(4481 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_375197, c_Groups_Ozero__class_Ozero(_375197), c_Groups_Oplus__class_Oplus(_375197, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_375197), _375199), _375199), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_375197), _375201), _375201))), _375199 = c_Groups_Ozero__class_Ozero(_375197), _375201 = c_Groups_Ozero__class_Ozero(_375197)], (4491 ^ _224325) ^ [] : [4492 ^ _224325 : [(4495 ^ _224325) ^ [] : [-(_375201 = c_Groups_Ozero__class_Ozero(_375197))], (4493 ^ _224325) ^ [] : [-(_375199 = c_Groups_Ozero__class_Ozero(_375197))]], -(c_Orderings_Oord__class_Oless(_375197, c_Groups_Ozero__class_Ozero(_375197), c_Groups_Oplus__class_Oplus(_375197, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_375197), _375199), _375199), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_375197), _375201), _375201))))]]], (11191 ^ _224325) ^ [_615588, _615590] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _615588, _615590), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_615590), _615588) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _615590, _615588)))], (3935 ^ _224325) ^ [_356985, _356987, _356989] : [class_Rings_Olinordered__semiring__strict(_356985), c_Orderings_Oord__class_Oless(_356985, c_Groups_Ozero__class_Ozero(_356985), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_356985), _356987), _356989)), c_Orderings_Oord__class_Oless(_356985, c_Groups_Ozero__class_Ozero(_356985), _356987), -(c_Orderings_Oord__class_Oless(_356985, c_Groups_Ozero__class_Ozero(_356985), _356989))], (1151 ^ _224325) ^ [_262116, _262118, _262120] : [class_Rings_Ocomm__semiring__1(_262116), -(c_Groups_Oplus__class_Oplus(_262116, _262118, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_262116), _262120), _262118)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_262116), c_Groups_Oplus__class_Oplus(_262116, _262120, c_Groups_Oone__class_Oone(_262116))), _262118))], (11831 ^ _224325) ^ [] : [-(class_Power_Opower(tc_RealDef_Oreal))], (12219 ^ _224325) ^ [_647637] : [class_Rings_Olinordered__idom(_647637), -(class_Groups_Osgn__if(tc_Polynomial_Opoly(_647637)))], (1330 ^ _224325) ^ [_267871, _267873] : [class_RealVector_Oreal__normed__vector(_267871), 1333 ^ _224325 : [(1340 ^ _224325) ^ [] : [_267873 = c_Groups_Ozero__class_Ozero(_267871), -(c_RealVector_Onorm__class_Onorm(_267871, _267873) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (1334 ^ _224325) ^ [] : [c_RealVector_Onorm__class_Onorm(_267871, _267873) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_267873 = c_Groups_Ozero__class_Ozero(_267871))]]], (9171 ^ _224325) ^ [_540738, _540740] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_540738), c_Nat_OSuc(_540740)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _540738, _540740))], (9658 ^ _224325) ^ [_557971] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _557971, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_557971 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11861 ^ _224325) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex))], (7594 ^ _224325) ^ [_486458, _486460, _486462, _486464] : [class_Rings_Ocomm__semiring__1(_486458), c_Rings_Odvd__class_Odvd(_486458, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_486458), _486460), _486462), _486464), -(c_Rings_Odvd__class_Odvd(_486458, _486462, _486464))], (1042 ^ _224325) ^ [_257837, _257839, _257841, _257843, _257845, _257847] : [-(c_Groups_Oplus__class_Oplus(_257847, _257843, _257839) = c_Groups_Oplus__class_Oplus(_257845, _257841, _257837)), _257847 = _257845, _257843 = _257841, _257839 = _257837], (9217 ^ _224325) ^ [_542365, _542367, _542369] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _542365), _542367)), _542369) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _542365), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _542367), _542369)))], (11765 ^ _224325) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal))], (9535 ^ _224325) ^ [_553366] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _553366, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _553366)], (7738 ^ _224325) ^ [_491336, _491338, _491340, _491342] : [class_Fields_Ofield(_491336), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_491336), _491338, _491340), -(_491342 = c_Groups_Ozero__class_Ozero(_491336)), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_491336), c_Polynomial_Osmult(_491336, _491342, _491338), _491340))], (524 ^ _224325) ^ [_240159, _240161] : [-(class_Rings_Osemiring__0(_240159)), _240161 = _240159, class_Rings_Osemiring__0(_240161)], (11417 ^ _224325) ^ [_623953, _623955] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _623953, _623955), -(c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _623955, _623953)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _623955), c_RealDef_Oreal(tc_Nat_Onat, _623953)))], (5529 ^ _224325) ^ [_414648] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _414648), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1588 ^ _224325) ^ [_276006, _276008, _276010] : [class_Orderings_Opreorder(_276006), c_Orderings_Oord__class_Oless(_276006, _276008, _276010), c_Orderings_Oord__class_Oless(_276006, _276010, _276008)], (11707 ^ _224325) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (6844 ^ _224325) ^ [_460751, _460753] : [class_Rings_Olinordered__idom(_460751), 6847 ^ _224325 : [(6854 ^ _224325) ^ [] : [-(_460753 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_460751))), 6857 ^ _224325 : [(6864 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_460751), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_460751)), _460753)), -(c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(_460751), _460753) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_460751), c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_460751))))], (6858 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_460751), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_460751)), _460753), -(c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(_460751), _460753) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_460751)))]]], (6848 ^ _224325) ^ [] : [_460753 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_460751)), -(c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(_460751), _460753) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_460751)))]]], (7374 ^ _224325) ^ [_478746, _478748] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _478746), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _478746, c_RealDef_Oreal(tc_Nat_Onat, _478748)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_RComplete_Onatfloor(_478746), _478748))], (6876 ^ _224325) ^ [_461775, _461777] : [class_Groups_Oordered__ab__group__add__abs(_461775), -(c_Orderings_Oord__class_Oless__eq(_461775, c_Groups_Ouminus__class_Ouminus(_461775, c_Groups_Oabs__class_Oabs(_461775, _461777)), c_Groups_Ozero__class_Ozero(_461775)))], (2470 ^ _224325) ^ [_304664, _304666, _304668] : [class_Orderings_Olinorder(_304664), -(c_Orderings_Oord__class_Oless__eq(_304664, _304666, _304668)), -(c_Orderings_Oord__class_Oless__eq(_304664, _304668, _304666))], (704 ^ _224325) ^ [_245469, _245471] : [-(class_Rings_Ocomm__ring(_245469)), _245471 = _245469, class_Rings_Ocomm__ring(_245471)], (7452 ^ _224325) ^ [_481586, _481588, _481590] : [class_Rings_Ocomm__ring__1(_481586), 7455 ^ _224325 : [(7462 ^ _224325) ^ [] : [c_Rings_Odvd__class_Odvd(_481586, _481588, _481590), -(c_Rings_Odvd__class_Odvd(_481586, _481588, c_Groups_Ouminus__class_Ouminus(_481586, _481590)))], (7456 ^ _224325) ^ [] : [c_Rings_Odvd__class_Odvd(_481586, _481588, c_Groups_Ouminus__class_Ouminus(_481586, _481590)), -(c_Rings_Odvd__class_Odvd(_481586, _481588, _481590))]]], (8951 ^ _224325) ^ [_533191] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _533191, c_Nat_OSuc(_533191)))], (404 ^ _224325) ^ [_236619, _236621] : [-(class_Rings_Oordered__semiring(_236619)), _236621 = _236619, class_Rings_Oordered__semiring(_236621)], (7240 ^ _224325) ^ [_473999] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _473999), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatfloor(_473999)), _473999))], (10142 ^ _224325) ^ [_574905, _574907, _574909] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _574905), _574907), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _574909), _574907)), -(_574907 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _574905, _574909))], (942 ^ _224325) ^ [_254162, _254164] : [_254164 = _254162, -(c_Power_Opower__class_Opower(_254164) = c_Power_Opower__class_Opower(_254162))], (12111 ^ _224325) ^ [_644217] : [class_Rings_Ocomm__semiring__0(_644217), -(class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(_644217)))], (11573 ^ _224325) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (1818 ^ _224325) ^ [_283135, _283137, _283139] : [class_Orderings_Oorder(_283135), 1821 ^ _224325 : [(1822 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_283135, _283137, _283139), -(c_Orderings_Oord__class_Oless(_283135, _283137, _283139)), -(_283137 = _283139)], (1832 ^ _224325) ^ [] : [1833 ^ _224325 : [(1836 ^ _224325) ^ [] : [_283137 = _283139], (1834 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_283135, _283137, _283139)]], -(c_Orderings_Oord__class_Oless__eq(_283135, _283137, _283139))]]], (5257 ^ _224325) ^ [_404366, _404368, _404370] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _404366, _404368), _404370), 5260 ^ _224325 : [(5263 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _404368, _404370))], (5261 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _404366, _404370))]]], (9289 ^ _224325) ^ [_545255, _545257] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _545255, _545257), -(c_Nat_OSuc(_545255) = _545257), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_545255), _545257))], (10126 ^ _224325) ^ [_574370, _574372, _574374] : [-(_574370 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 10129 ^ _224325 : [(10136 ^ _224325) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _574372, _574374), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _574372), _574370), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _574374), _574370)))], (10130 ^ _224325) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _574372), _574370), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _574374), _574370)), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _574372, _574374))]]], (8361 ^ _224325) ^ [_512237, _512239] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _512237, _512239), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _512239, _512237)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _512239, _512237), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _512237, _512239))], (11653 ^ _224325) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (11327 ^ _224325) ^ [_620520, _620522, _620524] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _620520, _620522), 11330 ^ _224325 : [(11337 ^ _224325) ^ [] : [_620522 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _620524, _620520), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _620522, _620520) = _620524)], (11331 ^ _224325) ^ [] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _620522, _620520) = _620524, -(_620522 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _620524, _620520))]]], (11170 ^ _224325) ^ [_614745, _614747, _614749] : [-(hBOOL(hAPP(_614745, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _614747, _614749)))), 11173 ^ _224325 : [(11176 ^ _224325) ^ [] : [hBOOL(hAPP(_614745, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (11174 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _614747, _614749))]], 11178 ^ _224325 : [(11181 ^ _224325) ^ [] : [hBOOL(hAPP(_614745, 11177 ^ [_614745, _614747, _614749]))], (11179 ^ _224325) ^ [] : [-(_614747 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _614749, 11177 ^ [_614745, _614747, _614749]))]]], (5245 ^ _224325) ^ [_403882, _403884, _403886] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _403882, _403884), _403886), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _403884, _403886))], (11847 ^ _224325) ^ [] : [-(class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex))], (244 ^ _224325) ^ [_231899, _231901] : [-(class_Groups_Olinordered__ab__group__add(_231899)), _231901 = _231899, class_Groups_Olinordered__ab__group__add(_231901)], (11605 ^ _224325) ^ [] : [-(class_Groups_Ouminus(tc_Int_Oint))], (6870 ^ _224325) ^ [_461565] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _461565, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_RComplete_Onatceiling(_461565) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5639 ^ _224325) ^ [_418431, _418433, _418435] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _418431, _418433), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _418435), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _418435), _418431), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _418435), _418433)))], (4695 ^ _224325) ^ [_382422, _382424] : [class_Rings_Ocomm__semiring__0(_382422), -(hAPP(c_Polynomial_Opoly(_382422, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_382422))), _382424) = c_Groups_Ozero__class_Ozero(_382422))], (3887 ^ _224325) ^ [_355414, _355416, _355418] : [class_Rings_Olinordered__semiring__strict(_355414), c_Orderings_Oord__class_Oless(_355414, _355416, c_Groups_Ozero__class_Ozero(_355414)), c_Orderings_Oord__class_Oless(_355414, c_Groups_Ozero__class_Ozero(_355414), _355418), -(c_Orderings_Oord__class_Oless(_355414, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_355414), _355416), _355418), c_Groups_Ozero__class_Ozero(_355414)))], (2703 ^ _224325) ^ [_312594, _312596, _312598, _312600, _312602] : [class_Rings_Ocomm__semiring__1(_312594), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_312594), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_312594), _312596), _312598)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_312594), _312600), _312602)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_312594), _312596), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_312594), _312598), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_312594), _312600), _312602))))], (8529 ^ _224325) ^ [_518480, _518482] : [class_Groups_Omonoid__mult(_518480), -(hAPP(hAPP(c_Power_Opower__class_Opower(_518480), _518482), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _518482)], (1946 ^ _224325) ^ [_287192, _287194, _287196, _287198, _287200] : [class_Groups_Oordered__cancel__ab__semigroup__add(_287192), c_Orderings_Oord__class_Oless(_287192, _287194, _287196), c_Orderings_Oord__class_Oless(_287192, _287198, _287200), -(c_Orderings_Oord__class_Oless(_287192, c_Groups_Oplus__class_Oplus(_287192, _287194, _287198), c_Groups_Oplus__class_Oplus(_287192, _287196, _287200)))], (384 ^ _224325) ^ [_236029, _236031] : [-(class_Groups_Ocomm__monoid__mult(_236029)), _236031 = _236029, class_Groups_Ocomm__monoid__mult(_236031)], (11789 ^ _224325) ^ [] : [-(class_Rings_Ozero__neq__one(tc_RealDef_Oreal))], (3319 ^ _224325) ^ [_336140, _336142, _336144] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _336140), _336142)), _336144) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _336140), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _336142), _336144)))], (754 ^ _224325) ^ [_246944, _246946] : [-(class_Rings_Odvd(_246944)), _246946 = _246944, class_Rings_Odvd(_246946)], (4639 ^ _224325) ^ [_380490, _380492] : [class_Groups_Olinordered__ab__group__add(_380490), 4642 ^ _224325 : [(4649 ^ _224325) ^ [] : [_380492 = c_Groups_Ozero__class_Ozero(_380490), -(c_Groups_Oplus__class_Oplus(_380490, _380492, _380492) = c_Groups_Ozero__class_Ozero(_380490))], (4643 ^ _224325) ^ [] : [c_Groups_Oplus__class_Oplus(_380490, _380492, _380492) = c_Groups_Ozero__class_Ozero(_380490), -(_380492 = c_Groups_Ozero__class_Ozero(_380490))]]], (5633 ^ _224325) ^ [_418208] : [-(_418208 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _418208))], (1464 ^ _224325) ^ [_272026, _272028, _272030] : [class_Orderings_Oorder(_272026), c_Orderings_Oord__class_Oless(_272026, _272028, _272030), _272028 = _272030], (8155 ^ _224325) ^ [_505815, _505817] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _505815, _505817), 8160 ^ _224325 : [(8163 ^ _224325) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _505817, _505815)], (8161 ^ _224325) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _505815, _505817))]], -(_505815 = _505817)], (9627 ^ _224325) ^ [_556797, _556799, _556801] : [class_Power_Opower(_556797), -(hAPP(hAPP(c_Power_Opower__class_Opower(_556797), _556799), c_Nat_OSuc(_556801)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_556797), _556799), hAPP(hAPP(c_Power_Opower__class_Opower(_556797), _556799), _556801)))], (7162 ^ _224325) ^ [_471155] : [-(c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat, _471155)) = _471155)], (11755 ^ _224325) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal))], (12117 ^ _224325) ^ [_644407] : [class_Groups_Oab__group__add(_644407), -(class_Groups_Oab__group__add(tc_Polynomial_Opoly(_644407)))], (2018 ^ _224325) ^ [_289700, _289702] : [class_RealVector_Oreal__normed__algebra(_289700), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_289700), _289702), c_Groups_Ozero__class_Ozero(_289700)) = c_Groups_Ozero__class_Ozero(_289700))], (11863 ^ _224325) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex))], (12159 ^ _224325) ^ [_645737] : [class_Groups_Ocomm__monoid__add(_645737), -(class_Groups_Omonoid__add(tc_Polynomial_Opoly(_645737)))], (4795 ^ _224325) ^ [_387003, _387005, _387007, _387009] : [class_Rings_Ocomm__semiring__0(_387003), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_387003)), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_387003), _387005, _387007)), _387009) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_387003), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_387003)), _387005), _387009), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_387003)), _387007), _387009)))], (11745 ^ _224325) ^ [] : [-(class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal))], (4985 ^ _224325) ^ [_394500] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _394500, _394500)], (7134 ^ _224325) ^ [_470267, _470269, _470271] : [class_Lattices_Oboolean__algebra(_470267), 7137 ^ _224325 : [(7144 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_470267, _470271, _470269), -(c_Orderings_Oord__class_Oless__eq(_470267, c_Groups_Ouminus__class_Ouminus(_470267, _470269), c_Groups_Ouminus__class_Ouminus(_470267, _470271)))], (7138 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_470267, c_Groups_Ouminus__class_Ouminus(_470267, _470269), c_Groups_Ouminus__class_Ouminus(_470267, _470271)), -(c_Orderings_Oord__class_Oless__eq(_470267, _470271, _470269))]]], (7618 ^ _224325) ^ [_487251, _487253] : [class_Rings_Ocomm__semiring__1(_487251), -(c_Rings_Odvd__class_Odvd(_487251, c_Groups_Oone__class_Oone(_487251), _487253))], (806 ^ _224325) ^ [_249163, _249165, _249167, _249169, _249171, _249173, _249175, _249177] : [-(c_If(_249177, _249173, _249169, _249165) = c_If(_249175, _249171, _249167, _249163)), _249177 = _249175, _249173 = _249171, _249169 = _249167, _249165 = _249163], (4381 ^ _224325) ^ [_371884, _371886, _371888, _371890] : [class_Rings_Olinordered__semiring__strict(_371884), c_Orderings_Oord__class_Oless(_371884, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_371884), _371886), _371888), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_371884), _371886), _371890)), c_Orderings_Oord__class_Oless__eq(_371884, c_Groups_Ozero__class_Ozero(_371884), _371886), -(c_Orderings_Oord__class_Oless(_371884, _371888, _371890))], (2893 ^ _224325) ^ [_320443, _320445, _320447, _320449, _320451] : [class_Groups_Oordered__ab__semigroup__add(_320443), c_Orderings_Oord__class_Oless__eq(_320443, _320445, _320447), c_Orderings_Oord__class_Oless__eq(_320443, _320449, _320451), -(c_Orderings_Oord__class_Oless__eq(_320443, c_Groups_Oplus__class_Oplus(_320443, _320445, _320449), c_Groups_Oplus__class_Oplus(_320443, _320447, _320451)))], (11589 ^ _224325) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (9898 ^ _224325) ^ [_566255] : [-(c_Nat_OSuc(_566255) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _566255, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (11695 ^ _224325) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (9868 ^ _224325) ^ [_565017, _565019, _565021] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_565017)), _565019), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_565017)), _565021)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _565019, _565021))], (2845 ^ _224325) ^ [_318745, _318747, _318749] : [class_Rings_Ocomm__semiring__1(_318745), -(c_Groups_Oplus__class_Oplus(_318745, _318747, _318749) = c_Groups_Oplus__class_Oplus(_318745, _318749, _318747))], (11405 ^ _224325) ^ [_623457, _623459] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _623457), _623459), -(c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _623459, c_RealDef_Oreal(tc_Nat_Onat, _623457))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_RComplete_Onatfloor(_623459), _623457))], (3091 ^ _224325) ^ [_328296, _328298] : [class_Groups_Oordered__ab__group__add__abs(_328296), -(c_Orderings_Oord__class_Oless__eq(_328296, _328298, c_Groups_Oabs__class_Oabs(_328296, _328298)))], (1474 ^ _224325) ^ [_272350, _272352, _272354] : [class_Orderings_Oorder(_272350), c_Orderings_Oord__class_Oless(_272350, _272352, _272354), _272354 = _272352], (4807 ^ _224325) ^ [_387641, _387643, _387645] : [class_Rings_Olinordered__idom(_387641), 4810 ^ _224325 : [(4823 ^ _224325) ^ [] : [-(c_Polynomial_Opos__poly(_387641, c_Polynomial_OpCons(_387641, _387643, _387645))), 4824 ^ _224325 : [(4827 ^ _224325) ^ [] : [_387645 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_387641)), c_Orderings_Oord__class_Oless(_387641, c_Groups_Ozero__class_Ozero(_387641), _387643)], (4825 ^ _224325) ^ [] : [c_Polynomial_Opos__poly(_387641, _387645)]]], (4811 ^ _224325) ^ [] : [c_Polynomial_Opos__poly(_387641, c_Polynomial_OpCons(_387641, _387643, _387645)), -(c_Polynomial_Opos__poly(_387641, _387645)), 4818 ^ _224325 : [(4821 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(_387641, c_Groups_Ozero__class_Ozero(_387641), _387643))], (4819 ^ _224325) ^ [] : [-(_387645 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_387641)))]]]]], (8261 ^ _224325) ^ [_509182, _509184] : [_509182 = _509184, c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _509182, _509184), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _509184, _509182))], (7164 ^ _224325) ^ [_471238] : [-(c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat, _471238)) = _471238)], (9984 ^ _224325) ^ [_569147, _569149] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _569147), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _569149), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _569147, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _569149), _569147)))], (2110 ^ _224325) ^ [_292948, _292950] : [class_Groups_Omonoid__add(_292948), -(c_Groups_Oplus__class_Oplus(_292948, c_Groups_Ozero__class_Ozero(_292948), _292950) = _292950)], (11221 ^ _224325) ^ [_616746, _616748] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _616746, _616748), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _616746, _616748) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4499 ^ _224325) ^ [_375934, _375936, _375938] : [class_Rings_Olinordered__ring(_375934), -(c_Orderings_Oord__class_Oless__eq(_375934, c_Groups_Ozero__class_Ozero(_375934), c_Groups_Oplus__class_Oplus(_375934, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_375934), _375936), _375936), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_375934), _375938), _375938))))], (890 ^ _224325) ^ [_252311, _252313, _252315, _252317, _252319, _252321] : [-(c_Power_Opower_Opower(_252321, _252317, _252313) = c_Power_Opower_Opower(_252319, _252315, _252311)), _252321 = _252319, _252317 = _252315, _252313 = _252311], (5359 ^ _224325) ^ [_408273, _408275] : [class_RealVector_Oreal__normed__vector(_408273), 5362 ^ _224325 : [(5369 ^ _224325) ^ [] : [_408275 = c_Groups_Ozero__class_Ozero(_408273), -(c_Groups_Osgn__class_Osgn(_408273, _408275) = c_Groups_Ozero__class_Ozero(_408273))], (5363 ^ _224325) ^ [] : [c_Groups_Osgn__class_Osgn(_408273, _408275) = c_Groups_Ozero__class_Ozero(_408273), -(_408275 = c_Groups_Ozero__class_Ozero(_408273))]]], (8963 ^ _224325) ^ [_533683, _533685] : [-(_533683 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Rings_Odvd__class_Odvd(tc_Int_Oint, _533685, _533683), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oabs__class_Oabs(tc_Int_Oint, _533685), c_Groups_Oabs__class_Oabs(tc_Int_Oint, _533683)))], (6632 ^ _224325) ^ [_453686, _453688, _453690] : [class_Groups_Ogroup__add(_453686), c_Groups_Oplus__class_Oplus(_453686, _453688, _453690) = c_Groups_Ozero__class_Ozero(_453686), -(c_Groups_Ouminus__class_Ouminus(_453686, _453688) = _453690)], (4459 ^ _224325) ^ [_374380] : [class_Rings_Olinordered__semidom(_374380), -(c_Orderings_Oord__class_Oless(_374380, c_Groups_Ozero__class_Ozero(_374380), c_Groups_Oplus__class_Oplus(_374380, c_Groups_Oone__class_Oone(_374380), c_Groups_Oone__class_Oone(_374380))))], (11757 ^ _224325) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal))], (11609 ^ _224325) ^ [] : [-(class_Groups_Oabs__if(tc_Int_Oint))], (1494 ^ _224325) ^ [_273000, _273002, _273004] : [class_Orderings_Oorder(_273000), c_Orderings_Oord__class_Oless(_273000, _273002, _273004), c_Orderings_Oord__class_Oless(_273000, _273004, _273002)], (1300 ^ _224325) ^ [_266963, _266965] : [class_Groups_Olinordered__ab__group__add(_266963), 1303 ^ _224325 : [(1310 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_266963, c_Groups_Ozero__class_Ozero(_266963), _266965), -(c_Orderings_Oord__class_Oless(_266963, c_Groups_Ozero__class_Ozero(_266963), c_Groups_Oplus__class_Oplus(_266963, _266965, _266965)))], (1304 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_266963, c_Groups_Ozero__class_Ozero(_266963), c_Groups_Oplus__class_Oplus(_266963, _266965, _266965)), -(c_Orderings_Oord__class_Oless(_266963, c_Groups_Ozero__class_Ozero(_266963), _266965))]]], (860 ^ _224325) ^ [_251162, _251164] : [_251164 = _251162, -(c_Complex_Oexpi(_251164) = c_Complex_Oexpi(_251162))], (3511 ^ _224325) ^ [_343086, _343088, _343090] : [class_Rings_Olinordered__ring__strict(_343086), 3514 ^ _224325 : [(3529 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_343086, c_Groups_Ozero__class_Ozero(_343086), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_343086), _343088), _343090))), 3530 ^ _224325 : [(3537 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_343086, _343088, c_Groups_Ozero__class_Ozero(_343086)), c_Orderings_Oord__class_Oless__eq(_343086, _343090, c_Groups_Ozero__class_Ozero(_343086))], (3531 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_343086, c_Groups_Ozero__class_Ozero(_343086), _343088), c_Orderings_Oord__class_Oless__eq(_343086, c_Groups_Ozero__class_Ozero(_343086), _343090)]]], (3515 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_343086, c_Groups_Ozero__class_Ozero(_343086), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_343086), _343088), _343090)), 3520 ^ _224325 : [(3523 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_343086, c_Groups_Ozero__class_Ozero(_343086), _343090))], (3521 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_343086, c_Groups_Ozero__class_Ozero(_343086), _343088))]], 3524 ^ _224325 : [(3527 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_343086, _343090, c_Groups_Ozero__class_Ozero(_343086)))], (3525 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_343086, _343088, c_Groups_Ozero__class_Ozero(_343086)))]]]]], (7444 ^ _224325) ^ [_481233, _481235] : [-(c_Complex_Oexpi(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, _481233, _481235)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Complex_Oexpi(_481233)), c_Complex_Oexpi(_481235)))], (11619 ^ _224325) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (9932 ^ _224325) ^ [_567465, _567467, _567469] : [class_Rings_Olinordered__semidom(_567465), c_Orderings_Oord__class_Oless(_567465, c_Groups_Oone__class_Oone(_567465), _567467), -(c_Orderings_Oord__class_Oless(_567465, c_Groups_Oone__class_Oone(_567465), hAPP(hAPP(c_Power_Opower__class_Opower(_567465), _567467), c_Nat_OSuc(_567469))))], (5719 ^ _224325) ^ [_421356, _421358, _421360] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _421356), _421358), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _421356), _421360)), 5722 ^ _224325 : [(5725 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _421358, _421360))], (5723 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _421356))]]], (2480 ^ _224325) ^ [_305020, _305022, _305024, _305026, _305028] : [class_Orderings_Oord(_305020), c_Orderings_Oord__class_Oless__eq(tc_fun(_305022, _305020), _305024, _305026), -(c_Orderings_Oord__class_Oless__eq(_305020, hAPP(_305024, _305028), hAPP(_305026, _305028)))], (9539 ^ _224325) ^ [_553529] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _553529), _553529) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (11841 ^ _224325) ^ [] : [-(class_Rings_Odvd(tc_RealDef_Oreal))], (7560 ^ _224325) ^ [_485236, _485238, _485240, _485242, _485244] : [class_Rings_Ocomm__semiring__1(_485236), c_Rings_Odvd__class_Odvd(_485236, _485238, _485240), c_Rings_Odvd__class_Odvd(_485236, _485242, _485244), -(c_Rings_Odvd__class_Odvd(_485236, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_485236), _485238), _485242), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_485236), _485240), _485244)))], (11687 ^ _224325) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (4783 ^ _224325) ^ [_386503, _386505] : [class_Rings_Ocomm__semiring__0(_386503), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_386503)), _386505), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_386503))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_386503)))], (5953 ^ _224325) ^ [_429880, _429882, _429884] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _429880, _429882) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _429880, _429884), -(_429882 = _429884)], (8559 ^ _224325) ^ [_519551, _519553, _519555] : [class_Rings_Olinordered__semidom(_519551), c_Orderings_Oord__class_Oless(_519551, c_Groups_Ozero__class_Ozero(_519551), _519553), -(c_Orderings_Oord__class_Oless(_519551, c_Groups_Ozero__class_Ozero(_519551), hAPP(hAPP(c_Power_Opower__class_Opower(_519551), _519553), _519555)))], (11667 ^ _224325) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Nat_Onat))], (11769 ^ _224325) ^ [] : [-(class_Rings_Oordered__semiring(tc_RealDef_Oreal))], (584 ^ _224325) ^ [_241929, _241931] : [-(class_Rings_Osemiring(_241929)), _241931 = _241929, class_Rings_Osemiring(_241931)], (11737 ^ _224325) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal))], (7993 ^ _224325) ^ [_500671, _500673] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _500671), 7996 ^ _224325 : [(8003 ^ _224325) ^ [] : [_500673 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _500671), _500673), _500671))], (7997 ^ _224325) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _500671), _500673), _500671), -(_500673 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (1574 ^ _224325) ^ [_275572, _275574, _275576, _275578] : [class_Orderings_Oorder(_275572), c_Orderings_Oord__class_Oless(_275572, _275574, _275576), c_Orderings_Oord__class_Oless(_275572, _275578, _275574), -(c_Orderings_Oord__class_Oless(_275572, _275578, _275576))], (6936 ^ _224325) ^ [_463773, _463775] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _463775, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _463773)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _463773, _463775), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (9874 ^ _224325) ^ [_565221, _565223, _565225] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _565223, _565225), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_565221)), _565223), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_565221)), _565225)))], (8229 ^ _224325) ^ [_508184, _508186, _508188] : [_508184 = _508186, 8240 ^ _224325 : [(8243 ^ _224325) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _508188, _508184)], (8241 ^ _224325) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _508184, _508188))]], c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _508186, _508188), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _508188, _508186))], (10606 ^ _224325) ^ [_591959, _591961, _591963, _591965, _591967] : [class_RealVector_Oreal__normed__algebra(_591959), -(c_Groups_Ominus__class_Ominus(_591959, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_591959), _591961), _591963), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_591959), _591965), _591967)) = c_Groups_Oplus__class_Oplus(_591959, c_Groups_Oplus__class_Oplus(_591959, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_591959), c_Groups_Ominus__class_Ominus(_591959, _591961, _591965)), c_Groups_Ominus__class_Ominus(_591959, _591963, _591967)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_591959), c_Groups_Ominus__class_Ominus(_591959, _591961, _591965)), _591967)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_591959), _591965), c_Groups_Ominus__class_Ominus(_591959, _591963, _591967))))], (4011 ^ _224325) ^ [_359466, _359468, _359470, _359472] : [class_Rings_Olinordered__ring__strict(_359466), 4014 ^ _224325 : [(4029 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(_359466, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_359466), _359468), _359470), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_359466), _359468), _359472))), 4030 ^ _224325 : [(4037 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_359466, _359468, c_Groups_Ozero__class_Ozero(_359466)), c_Orderings_Oord__class_Oless(_359466, _359472, _359470)], (4031 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_359466, c_Groups_Ozero__class_Ozero(_359466), _359468), c_Orderings_Oord__class_Oless(_359466, _359470, _359472)]]], (4015 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_359466, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_359466), _359468), _359470), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_359466), _359468), _359472)), 4020 ^ _224325 : [(4023 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(_359466, _359470, _359472))], (4021 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(_359466, c_Groups_Ozero__class_Ozero(_359466), _359468))]], 4024 ^ _224325 : [(4027 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(_359466, _359472, _359470))], (4025 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(_359466, _359468, c_Groups_Ozero__class_Ozero(_359466)))]]]]], (6334 ^ _224325) ^ [_443745, _443747, _443749] : [class_Groups_Oab__group__add(_443745), -(c_Groups_Ouminus__class_Ouminus(_443745, c_Groups_Oplus__class_Oplus(_443745, _443747, _443749)) = c_Groups_Oplus__class_Oplus(_443745, c_Groups_Ouminus__class_Ouminus(_443745, _443747), c_Groups_Ouminus__class_Ouminus(_443745, _443749)))], (164 ^ _224325) ^ [_229539, _229541] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_229539)), _229541 = _229539, class_Groups_Oordered__cancel__ab__semigroup__add(_229541)], (7068 ^ _224325) ^ [_468211, _468213] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _468211), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _468213), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_RComplete_Onatfloor(_468211)), c_RComplete_Onatfloor(_468213)), c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _468211), _468213))))], (11985 ^ _224325) ^ [_640227] : [class_Rings_Oidom(_640227), -(class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(_640227)))], (7100 ^ _224325) ^ [_469197] : [_469197 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, _469197) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (2697 ^ _224325) ^ [_312230, _312232, _312234, _312236, _312238] : [class_Rings_Ocomm__semiring__1(_312230), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_312230), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_312230), _312232), _312234)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_312230), _312236), _312238)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_312230), _312236), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_312230), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_312230), _312232), _312234)), _312238)))], (9511 ^ _224325) ^ [_552578] : [_552578 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oabs__class_Oabs(tc_Int_Oint, _552578), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (4201 ^ _224325) ^ [_365833, _365835] : [-(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _365833), _365833), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _365835), _365835)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _365833 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _365835 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)], (10404 ^ _224325) ^ [_583969, _583971] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _583969), -(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), _583969), _583971)))], (5399 ^ _224325) ^ [_409784, _409786, _409788, _409790] : [class_Rings_Ocomm__semiring__0(_409784), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_409784)), c_Polynomial_Osmult(_409784, _409786, _409788)), _409790) = c_Polynomial_Osmult(_409784, _409786, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_409784)), _409788), _409790)))], (5451 ^ _224325) ^ [_411768, _411770, _411772, _411774] : [class_Rings_Ocomm__semiring__0(_411768), -(c_Polynomial_Osmult(_411768, _411770, c_Polynomial_OpCons(_411768, _411772, _411774)) = c_Polynomial_OpCons(_411768, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_411768), _411770), _411772), c_Polynomial_Osmult(_411768, _411770, _411774)))], (7526 ^ _224325) ^ [] : [-(c_Complex_Oexpi(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))], (11753 ^ _224325) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal))], (10521 ^ _224325) ^ [_588360, _588362] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _588360), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _588362), 10529 ^ _224325 : [(10532 ^ _224325) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), 10528 ^ [_588360, _588362]), _588360) = _588362)], (10530 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 10528 ^ [_588360, _588362]))]]], (918 ^ _224325) ^ [_253315, _253317, _253319, _253321] : [-(c_Polynomial_Opoly(_253321, _253317) = c_Polynomial_Opoly(_253319, _253315)), _253321 = _253319, _253317 = _253315], (3253 ^ _224325) ^ [_333987, _333989, _333991, _333993] : [class_Orderings_Oord(_333987), 3256 ^ _224325 : [(3265 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_fun(_333989, _333987), _333991, _333993)), c_Orderings_Oord__class_Oless__eq(tc_fun(_333989, _333987), _333991, _333993), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_333989, _333987), _333993, _333991))], (3257 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(tc_fun(_333989, _333987), _333991, _333993), 3260 ^ _224325 : [(3263 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_333989, _333987), _333993, _333991)], (3261 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_fun(_333989, _333987), _333991, _333993))]]]]], (10214 ^ _224325) ^ [_577450, _577452] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _577450, _577452) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _577452, _577450))], (2827 ^ _224325) ^ [_317919, _317921, _317923, _317925] : [class_Rings_Ocomm__semiring__1(_317919), -(c_Groups_Oplus__class_Oplus(_317919, c_Groups_Oplus__class_Oplus(_317919, _317921, _317923), _317925) = c_Groups_Oplus__class_Oplus(_317919, _317921, c_Groups_Oplus__class_Oplus(_317919, _317923, _317925)))], (6252 ^ _224325) ^ [_440370, _440372, _440374] : [class_RealVector_Oreal__normed__algebra(_440370), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_440370), c_Groups_Ouminus__class_Ouminus(_440370, _440372)), _440374) = c_Groups_Ouminus__class_Ouminus(_440370, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_440370), _440372), _440374)))], (9127 ^ _224325) ^ [_539164, _539166] : [c_Nat_OSuc(_539164) = c_Nat_OSuc(_539166), -(_539164 = _539166)], (10264 ^ _224325) ^ [_579392, _579394] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _579392, _579394), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _579392), _579394))], (5495 ^ _224325) ^ [_413478, _413480] : [class_Rings_Olinordered__idom(_413478), 5498 ^ _224325 : [(5505 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_413478, c_Groups_Ozero__class_Ozero(_413478), _413480), -(c_Orderings_Oord__class_Oless(_413478, c_Groups_Ozero__class_Ozero(_413478), c_Groups_Osgn__class_Osgn(_413478, _413480)))], (5499 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_413478, c_Groups_Ozero__class_Ozero(_413478), c_Groups_Osgn__class_Osgn(_413478, _413480)), -(c_Orderings_Oord__class_Oless(_413478, c_Groups_Ozero__class_Ozero(_413478), _413480))]]], (11579 ^ _224325) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (11066 ^ _224325) ^ [_610677, _610679] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _610677, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _610679, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _610677, _610679))], (2386 ^ _224325) ^ [_301785, _301787, _301789, _301791, _301793, _301795] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_301785), -(_301787 = c_Groups_Ozero__class_Ozero(_301785)), c_Groups_Oplus__class_Oplus(_301785, _301789, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_301785), _301787), _301793)) = c_Groups_Oplus__class_Oplus(_301785, _301791, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_301785), _301787), _301795)), _301789 = _301791, -(_301793 = _301795)], (314 ^ _224325) ^ [_233964, _233966] : [-(class_Rings_Olinordered__semiring__1(_233964)), _233966 = _233964, class_Rings_Olinordered__semiring__1(_233966)], (11893 ^ _224325) ^ [] : [-(class_Rings_Ocomm__ring(tc_Complex_Ocomplex))], (5393 ^ _224325) ^ [_409488, _409490, _409492, _409494] : [class_Rings_Ocomm__semiring__0(_409488), -(c_Polynomial_Osmult(_409488, _409490, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_409488), _409492, _409494)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_409488), c_Polynomial_Osmult(_409488, _409490, _409492), c_Polynomial_Osmult(_409488, _409490, _409494)))], (11403 ^ _224325) ^ [_623337, _623339] : [-(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _623337, _623339) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _623337, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _623339)))], (10466 ^ _224325) ^ [_586203, _586205, _586207, _586209, _586211] : [-(hAPP(hAPP(c_Power_Opower_Opower(_586203, _586205, _586207), _586209), c_Nat_OSuc(_586211)) = hAPP(hAPP(_586207, _586209), hAPP(hAPP(c_Power_Opower_Opower(_586203, _586205, _586207), _586209), _586211)))], (4726 ^ _224325) ^ [_383783, _383785] : [class_RealVector_Oreal__normed__algebra(_383783), 4730 ^ _224325 : [(4733 ^ _224325) ^ [_384082] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_383783, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_383783), _384082), _383785)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_383783, _384082)), 4729 ^ [_383783, _383785])))], (4731 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 4729 ^ [_383783, _383785]))]]], (7334 ^ _224325) ^ [_477456, _477458] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _477456), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _477458), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _477456, _477458))], (2739 ^ _224325) ^ [_314490, _314492, _314494] : [class_Rings_Ocomm__semiring__1(_314490), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_314490), _314492), _314494) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_314490), _314494), _314492))], (8953 ^ _224325) ^ [_533301, _533303] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _533301, _533303), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_533301), c_Nat_OSuc(_533303)))], (6458 ^ _224325) ^ [_448237, _448239, _448241] : [class_Rings_Ocomm__ring(_448237), -(c_Polynomial_Osmult(_448237, c_Groups_Ouminus__class_Ouminus(_448237, _448239), _448241) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_448237), c_Polynomial_Osmult(_448237, _448239, _448241)))], (4883 ^ _224325) ^ [_390487] : [class_Rings_Olinordered__idom(_390487), c_Polynomial_Opos__poly(_390487, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_390487)))], (2098 ^ _224325) ^ [_292508, _292510] : [class_Groups_Ocomm__monoid__add(_292508), -(c_Groups_Oplus__class_Oplus(_292508, c_Groups_Ozero__class_Ozero(_292508), _292510) = _292510)], (11583 ^ _224325) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (12147 ^ _224325) ^ [_645357] : [class_Rings_Ocomm__semiring__1(_645357), -(class_Groups_Omonoid__mult(tc_Polynomial_Opoly(_645357)))], (8495 ^ _224325) ^ [_517009, _517011, _517013] : [class_Groups_Omonoid__mult(_517009), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_517009), hAPP(hAPP(c_Power_Opower__class_Opower(_517009), _517011), _517013)), _517011) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_517009), _517011), hAPP(hAPP(c_Power_Opower__class_Opower(_517009), _517011), _517013)))], (12255 ^ _224325) ^ [_648777] : [class_Rings_Ocomm__ring(_648777), -(class_Rings_Oring(tc_Polynomial_Opoly(_648777)))], (10424 ^ _224325) ^ [_584618, _584620] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _584618), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _584620), -(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, _584618, _584620)))], (7865 ^ _224325) ^ [_495795, _495797, _495799] : [class_RealVector_Oreal__normed__algebra__1(_495795), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_495795, hAPP(hAPP(c_Power_Opower__class_Opower(_495795), _495797), _495799)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_495795, _495797)), _495799)))], (3111 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, v_c____, v_cs____)), v_z____)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_z____), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_cs____), v_z____))))))], (8523 ^ _224325) ^ [_518222, _518224, _518226] : [class_Rings_Olinordered__idom(_518222), -(c_Groups_Oabs__class_Oabs(_518222, hAPP(hAPP(c_Power_Opower__class_Opower(_518222), _518224), _518226)) = hAPP(hAPP(c_Power_Opower__class_Opower(_518222), c_Groups_Oabs__class_Oabs(_518222, _518224)), _518226))], (10698 ^ _224325) ^ [_595788, _595790, _595792] : [class_RealVector_Oreal__normed__vector(_595788), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_595788, _595790), c_RealVector_Onorm__class_Onorm(_595788, _595792)), c_RealVector_Onorm__class_Onorm(_595788, c_Groups_Ominus__class_Ominus(_595788, _595790, _595792))))], (6039 ^ _224325) ^ [_433388, _433390] : [-(hBOOL(hAPP(_433388, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_433388, _433390)), 6047 ^ _224325 : [(6050 ^ _224325) ^ [_433824] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _433824, 6046 ^ [_433388, _433390]), hBOOL(hAPP(_433388, _433824))], (6056 ^ _224325) ^ [] : [-(hBOOL(hAPP(_433388, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, 6046 ^ [_433388, _433390], c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (6048 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, 6046 ^ [_433388, _433390], _433390))]]], (5563 ^ _224325) ^ [_415836, _415838] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _415836), _415838) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_415836 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_415838 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6478 ^ _224325) ^ [_448916] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_RComplete_Onatceiling(_448916)))], (11535 ^ _224325) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (11867 ^ _224325) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex))], (204 ^ _224325) ^ [_230719, _230721] : [-(class_Rings_Olinordered__semiring__strict(_230719)), _230721 = _230719, class_Rings_Olinordered__semiring__strict(_230721)], (2504 ^ _224325) ^ [_305831, _305833, _305835] : [class_Orderings_Oorder(_305831), c_Orderings_Oord__class_Oless__eq(_305831, _305833, _305835), c_Orderings_Oord__class_Oless__eq(_305831, _305835, _305833), -(_305835 = _305833)], (7178 ^ _224325) ^ [_471748] : [-(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _471748)) = c_RealDef_Oreal(tc_Nat_Onat, _471748))], (11909 ^ _224325) ^ [] : [-(class_Groups_Ozero(tc_Complex_Ocomplex))], (9545 ^ _224325) ^ [_553745] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_553745)], (5977 ^ _224325) ^ [_430772, _430774, _430776, _430778] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _430772), _430774), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _430776), _430774), _430778)) = 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, _430772, _430776)), _430774), _430778))], (11551 ^ _224325) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (1668 ^ _224325) ^ [_278548, _278550, _278552] : [class_Orderings_Oorder(_278548), c_Orderings_Oord__class_Oless__eq(_278548, _278550, _278552), -(_278552 = _278550), -(c_Orderings_Oord__class_Oless(_278548, _278550, _278552))], (5207 ^ _224325) ^ [_402370, _402372, _402374] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _402370, _402372), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _402370, _402374), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _402372, _402374)))], (10468 ^ _224325) ^ [_586360, _586362, _586364] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _586360), 10474 ^ _224325 : [(10477 ^ _224325) ^ [] : [hBOOL(hAPP(_586362, c_Groups_Oplus__class_Oplus(tc_Int_Oint, 10473 ^ [_586360, _586362, _586364], _586360)))], (10475 ^ _224325) ^ [] : [-(hBOOL(hAPP(_586362, 10473 ^ [_586360, _586362, _586364])))]], c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _586364), 10482 ^ _224325 : [(10483 ^ _224325) ^ [_586875] : [hBOOL(hAPP(_586362, _586875)), -(hBOOL(hAPP(_586362, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _586875, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _586364), _586360)))))]]], (2799 ^ _224325) ^ [_316817, _316819, _316821, _316823] : [class_Groups_Ocancel__semigroup__add(_316817), 2802 ^ _224325 : [(2809 ^ _224325) ^ [] : [_316821 = _316823, -(c_Groups_Oplus__class_Oplus(_316817, _316819, _316821) = c_Groups_Oplus__class_Oplus(_316817, _316819, _316823))], (2803 ^ _224325) ^ [] : [c_Groups_Oplus__class_Oplus(_316817, _316819, _316821) = c_Groups_Oplus__class_Oplus(_316817, _316819, _316823), -(_316821 = _316823)]]], (11585 ^ _224325) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (5959 ^ _224325) ^ [_430064, _430066, _430068] : [_430066 = _430068, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _430064, _430066) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _430064, _430068))], (7584 ^ _224325) ^ [_486093, _486095, _486097, _486099] : [class_Rings_Ocomm__semiring__1(_486093), c_Rings_Odvd__class_Odvd(_486093, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_486093), _486095), _486097), _486099), -(c_Rings_Odvd__class_Odvd(_486093, _486095, _486099))], (4876 ^ _224325) ^ [_390105] : [class_RealVector_Oreal__normed__algebra(_390105), 4880 ^ _224325 : [(4881 ^ _224325) ^ [_390350, _390352] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_390105, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_390105), _390352), _390350)), 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(_390105, _390352)), c_RealVector_Onorm__class_Onorm(_390105, _390350))), 4879 ^ [_390105])))]]], (10498 ^ _224325) ^ [_587502, _587504] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _587502), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _587504), 10506 ^ _224325 : [(10511 ^ _224325) ^ [_588006] : [-(_588006 = 10505 ^ [_587502, _587504]), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _588006), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _588006), _587502) = _587504], (10509 ^ _224325) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), 10505 ^ [_587502, _587504]), _587502) = _587504)], (10507 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 10505 ^ [_587502, _587504]))]]], (9373 ^ _224325) ^ [_548004, _548006] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _548004, _548006)), -(_548004 = _548006), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _548006, _548004))], (8345 ^ _224325) ^ [_511742, _511744, _511746] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _511742, _511744), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _511744, _511742)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _511744, _511746), 8356 ^ _224325 : [(8359 ^ _224325) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _511746, _511742)], (8357 ^ _224325) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _511742, _511746))]]], (7660 ^ _224325) ^ [_488740, _488742, _488744, _488746] : [class_Rings_Ocomm__semiring__1(_488740), c_Rings_Odvd__class_Odvd(_488740, _488742, _488744), c_Rings_Odvd__class_Odvd(_488740, _488744, _488746), -(c_Rings_Odvd__class_Odvd(_488740, _488742, _488746))], (11875 ^ _224325) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Complex_Ocomplex))], (11733 ^ _224325) ^ [] : [-(class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal))], (44 ^ _224325) ^ [_225868, _225870, _225872, _225874, _225876, _225878] : [-(c_Orderings_Oord__class_Oless(_225876, _225872, _225868)), c_Orderings_Oord__class_Oless(_225878, _225874, _225870), _225878 = _225876, _225874 = _225872, _225870 = _225868], (6230 ^ _224325) ^ [_439586, _439588, _439590] : [class_Groups_Oordered__ab__group__add(_439586), 6233 ^ _224325 : [(6240 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_439586, _439590, _439588), -(c_Orderings_Oord__class_Oless(_439586, c_Groups_Ouminus__class_Ouminus(_439586, _439588), c_Groups_Ouminus__class_Ouminus(_439586, _439590)))], (6234 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_439586, c_Groups_Ouminus__class_Ouminus(_439586, _439588), c_Groups_Ouminus__class_Ouminus(_439586, _439590)), -(c_Orderings_Oord__class_Oless(_439586, _439590, _439588))]]], (3401 ^ _224325) ^ [_339073, _339075, _339077, _339079, _339081] : [class_Rings_Osemiring(_339073), -(c_Groups_Oplus__class_Oplus(_339073, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_339073), _339075), _339077), c_Groups_Oplus__class_Oplus(_339073, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_339073), _339079), _339077), _339081)) = c_Groups_Oplus__class_Oplus(_339073, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_339073), c_Groups_Oplus__class_Oplus(_339073, _339075, _339079)), _339077), _339081))], (3333 ^ _224325) ^ [_336753, _336755, _336757] : [class_Rings_Oring__no__zero__divisors(_336753), 3336 ^ _224325 : [(3337 ^ _224325) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_336753), _336755), _336757) = c_Groups_Ozero__class_Ozero(_336753), -(_336755 = c_Groups_Ozero__class_Ozero(_336753)), -(_336757 = c_Groups_Ozero__class_Ozero(_336753))], (3347 ^ _224325) ^ [] : [3348 ^ _224325 : [(3351 ^ _224325) ^ [] : [_336757 = c_Groups_Ozero__class_Ozero(_336753)], (3349 ^ _224325) ^ [] : [_336755 = c_Groups_Ozero__class_Ozero(_336753)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_336753), _336755), _336757) = c_Groups_Ozero__class_Ozero(_336753))]]], (10714 ^ _224325) ^ [_596526, _596528, _596530, _596532] : [class_Rings_Ocomm__ring__1(_596526), c_Rings_Odvd__class_Odvd(_596526, _596528, _596530), c_Rings_Odvd__class_Odvd(_596526, _596528, _596532), -(c_Rings_Odvd__class_Odvd(_596526, _596528, c_Groups_Ominus__class_Ominus(_596526, _596530, _596532)))], (12165 ^ _224325) ^ [_645927] : [class_Rings_Ocomm__semiring__0(_645927), -(class_Rings_Osemiring__0(tc_Polynomial_Opoly(_645927)))], (2296 ^ _224325) ^ [_299001, _299003, _299005, _299007] : [class_Groups_Oordered__comm__monoid__add(_299001), c_Orderings_Oord__class_Oless__eq(_299001, c_Groups_Ozero__class_Ozero(_299001), _299003), c_Orderings_Oord__class_Oless__eq(_299001, _299005, _299007), -(c_Orderings_Oord__class_Oless__eq(_299001, _299005, c_Groups_Oplus__class_Oplus(_299001, _299003, _299007)))], (604 ^ _224325) ^ [_242519, _242521] : [-(class_Groups_Ouminus(_242519)), _242521 = _242519, class_Groups_Ouminus(_242521)], (6780 ^ _224325) ^ [_458599, _458601] : [c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _458599, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _458601)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_458599 = _458601)], (8849 ^ _224325) ^ [_529705, _529707, _529709, _529711] : [class_Rings_Olinordered__semidom(_529705), hAPP(hAPP(c_Power_Opower__class_Opower(_529705), _529707), _529709) = hAPP(hAPP(c_Power_Opower__class_Opower(_529705), _529711), _529709), c_Orderings_Oord__class_Oless__eq(_529705, c_Groups_Ozero__class_Ozero(_529705), _529707), c_Orderings_Oord__class_Oless__eq(_529705, c_Groups_Ozero__class_Ozero(_529705), _529711), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _529709), -(_529707 = _529711)], (10220 ^ _224325) ^ [_577819, _577821] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _577819, _577821), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _577821, _577819), -(_577819 = _577821)], (6812 ^ _224325) ^ [_459716, _459718] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _459716), _459718)), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _459718), _459716), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _459716, _459718)], (4917 ^ _224325) ^ [_391558, _391560] : [class_Rings_Ocomm__semiring__0(_391558), -(c_Polynomial_Opcompose(_391558, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_391558)), _391560) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_391558)))], (5545 ^ _224325) ^ [_415253, _415255] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _415253, _415255) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 5548 ^ _224325 : [(5551 ^ _224325) ^ [] : [-(_415255 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5549 ^ _224325) ^ [] : [-(_415253 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (986 ^ _224325) ^ [_255752, _255754] : [_255754 = _255752, -(c_RComplete_Onatceiling(_255754) = c_RComplete_Onatceiling(_255752))], (4956 ^ _224325) ^ [_393351, _393353] : [class_RealVector_Oreal__normed__algebra(_393351), 4960 ^ _224325 : [(4961 ^ _224325) ^ [_393562] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_393351, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_393351), _393353), _393562)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_393351, _393562)), 4959 ^ [_393351, _393353])))]]], (11447 ^ _224325) ^ [_624965, _624967] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _624965, _624967), _624965) = _624967)], (9577 ^ _224325) ^ [_554869] : [-(_554869 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 9580 ^ _224325 : [(9587 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _554869)), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _554869) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (9581 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _554869), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _554869) = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (11371 ^ _224325) ^ [_622036, _622038] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _622036, _622038), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _622036, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _622038, _622036)) = _622038)], (9125 ^ _224325) ^ [_539037, _539039] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _539037)), _539039) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _539037), _539039)))], (9493 ^ _224325) ^ [_551997] : [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), _551997), _551997), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _551997, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (4599 ^ _224325) ^ [_379316, _379318, _379320] : [class_Int_Oring__char__0(_379316), class_Rings_Oidom(_379316), 4606 ^ _224325 : [(4613 ^ _224325) ^ [] : [_379318 = _379320, -(c_Polynomial_Opoly(_379316, _379318) = c_Polynomial_Opoly(_379316, _379320))], (4607 ^ _224325) ^ [] : [c_Polynomial_Opoly(_379316, _379318) = c_Polynomial_Opoly(_379316, _379320), -(_379318 = _379320)]]], (10704 ^ _224325) ^ [_596052, _596054, _596056] : [class_Groups_Oab__group__add(_596052), -(c_Groups_Ouminus__class_Ouminus(_596052, c_Groups_Ominus__class_Ominus(_596052, _596054, _596056)) = c_Groups_Ominus__class_Ominus(_596052, _596056, _596054))], (11395 ^ _224325) ^ [_622997, _622999, _623001] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _622997, _622999), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _623001, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _622999, _622997)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _623001, _622997), _622999))], (6392 ^ _224325) ^ [_445961, _445963, _445965] : [class_Groups_Oab__group__add(_445961), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_445961), c_Polynomial_OpCons(_445961, _445963, _445965)) = c_Polynomial_OpCons(_445961, c_Groups_Ouminus__class_Ouminus(_445961, _445963), c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_445961), _445965)))], (2642 ^ _224325) ^ [_310199, _310201, _310203] : [class_Orderings_Oorder(_310199), 2645 ^ _224325 : [(2654 ^ _224325) ^ [] : [-(_310201 = _310203), c_Orderings_Oord__class_Oless__eq(_310199, _310201, _310203), c_Orderings_Oord__class_Oless__eq(_310199, _310203, _310201)], (2646 ^ _224325) ^ [] : [_310201 = _310203, 2649 ^ _224325 : [(2652 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_310199, _310203, _310201))], (2650 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_310199, _310201, _310203))]]]]], (10314 ^ _224325) ^ [_580962, _580964, _580966] : [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), _580962), _580964), _580966)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _580966, _580962), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _580962), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _580964))], (9725 ^ _224325) ^ [_560122, _560124] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _560122, _560124) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 9730 ^ _224325 : [(9733 ^ _224325) ^ [] : [-(_560124 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9731 ^ _224325) ^ [] : [-(_560122 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 9734 ^ _224325 : [(9737 ^ _224325) ^ [] : [-(_560124 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (9735 ^ _224325) ^ [] : [-(_560122 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (8923 ^ _224325) ^ [_532105, _532107] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _532105), -(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, _532107)), _532105), 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, _532105, c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), _532107)))], (9043 ^ _224325) ^ [_536332, _536334, _536336, _536338, _536340] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _536332, _536334), 9046 ^ _224325 : [(9053 ^ _224325) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _536332, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _536336, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _536340), _536334)), _536338)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _536332, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _536336, _536338)))], (9047 ^ _224325) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _536332, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _536336, _536338)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _536332, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _536336, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _536340), _536334)), _536338)))]]], (10992 ^ _224325) ^ [_607574, _607576, _607578, _607580] : [class_RealVector_Oreal__normed__algebra(_607574), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_607574), c_Groups_Ominus__class_Ominus(_607574, _607576, _607578)), _607580) = c_Groups_Ominus__class_Ominus(_607574, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_607574), _607576), _607580), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_607574), _607578), _607580)))], (12177 ^ _224325) ^ [_646307] : [class_Rings_Ocomm__semiring__0(_646307), -(class_Rings_Omult__zero(tc_Polynomial_Opoly(_646307)))], (7180 ^ _224325) ^ [_471879] : [c_RealDef_Oreal(tc_Nat_Onat, _471879) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_471879 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5979 ^ _224325) ^ [_430919, _430921] : [class_Rings_Ocomm__semiring__0(_430919), -(c_Polynomial_Osynthetic__div(_430919, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_430919)), _430921) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_430919)))], (11865 ^ _224325) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex))], (114 ^ _224325) ^ [_228064, _228066] : [-(class_RealVector_Oreal__normed__algebra__1(_228064)), _228066 = _228064, class_RealVector_Oreal__normed__algebra__1(_228066)], (1382 ^ _224325) ^ [_269437, _269439, _269441] : [class_Orderings_Olinorder(_269437), -(_269439 = _269441), -(c_Orderings_Oord__class_Oless(_269437, _269439, _269441)), -(c_Orderings_Oord__class_Oless(_269437, _269441, _269439))], (10956 ^ _224325) ^ [_606123, _606125] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _606123, _606125), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _606123, _606125))], (7186 ^ _224325) ^ [_472041] : [_472041 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_RealDef_Oreal(tc_Nat_Onat, _472041) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (2622 ^ _224325) ^ [_309513, _309515, _309517, _309519, _309521] : [class_Orderings_Oord(_309513), c_Orderings_Oord__class_Oless__eq(tc_fun(_309515, _309513), _309517, _309519), -(c_Orderings_Oord__class_Oless__eq(_309513, hAPP(_309517, _309521), hAPP(_309519, _309521)))], (1434 ^ _224325) ^ [_271050, _271052, _271054] : [class_Orderings_Oorder(_271050), c_Orderings_Oord__class_Oless(_271050, _271052, _271054), _271052 = _271054], (11727 ^ _224325) ^ [] : [-(class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal))], (12057 ^ _224325) ^ [_642507] : [class_Groups_Ocomm__monoid__add(_642507), -(class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(_642507)))], (6270 ^ _224325) ^ [_441186, _441188, _441190] : [class_Rings_Oidom(_441186), 6273 ^ _224325 : [(6274 ^ _224325) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_441186), _441188), _441188) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_441186), _441190), _441190), -(_441188 = _441190), -(_441188 = c_Groups_Ouminus__class_Ouminus(_441186, _441190))], (6284 ^ _224325) ^ [] : [6285 ^ _224325 : [(6288 ^ _224325) ^ [] : [_441188 = c_Groups_Ouminus__class_Ouminus(_441186, _441190)], (6286 ^ _224325) ^ [] : [_441188 = _441190]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_441186), _441188), _441188) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_441186), _441190), _441190))]]], (6924 ^ _224325) ^ [_463334, _463336] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _463334), _463336), -(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, _463334, _463336)))], (10990 ^ _224325) ^ [_607409, _607411, _607413] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Ominus__class_Ominus(tc_Int_Oint, _607409, _607411)), _607413) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _607409), _607413), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _607411), _607413)))], (9884 ^ _224325) ^ [_565742, _565744, _565746] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_565742)), _565744), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_565742)), _565746)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _565744, _565746))], (5149 ^ _224325) ^ [_399988] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _399988, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _399988), _399988)))], (11629 ^ _224325) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (1268 ^ _224325) ^ [_266001, _266003] : [class_Groups_Oordered__ab__group__add__abs(_266001), 1271 ^ _224325 : [(1278 ^ _224325) ^ [] : [-(_266003 = c_Groups_Ozero__class_Ozero(_266001)), -(c_Orderings_Oord__class_Oless(_266001, c_Groups_Ozero__class_Ozero(_266001), c_Groups_Oabs__class_Oabs(_266001, _266003)))], (1272 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_266001, c_Groups_Ozero__class_Ozero(_266001), c_Groups_Oabs__class_Oabs(_266001, _266003)), _266003 = c_Groups_Ozero__class_Ozero(_266001)]]], (5381 ^ _224325) ^ [_408940] : [class_Groups_Osgn__if(_408940), -(c_Groups_Osgn__class_Osgn(_408940, c_Groups_Ozero__class_Ozero(_408940)) = c_Groups_Ozero__class_Ozero(_408940))], (11871 ^ _224325) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex))], (1862 ^ _224325) ^ [_284456, _284458, _284460] : [class_Orderings_Oorder(_284456), 1865 ^ _224325 : [(1874 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(_284456, _284458, _284460)), c_Orderings_Oord__class_Oless__eq(_284456, _284458, _284460), -(_284458 = _284460)], (1866 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_284456, _284458, _284460), 1869 ^ _224325 : [(1872 ^ _224325) ^ [] : [_284458 = _284460], (1870 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_284456, _284458, _284460))]]]]], (2560 ^ _224325) ^ [_307575, _307577, _307579, _307581] : [class_Orderings_Oord(_307575), c_Orderings_Oord__class_Oless__eq(_307575, _307577, _307579), _307579 = _307581, -(c_Orderings_Oord__class_Oless__eq(_307575, _307577, _307581))], (12021 ^ _224325) ^ [_641367] : [class_Rings_Olinordered__idom(_641367), -(class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(_641367)))], (9541 ^ _224325) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (1113 ^ _224325) ^ [_260591, _260593, _260595] : [class_RealVector_Oreal__normed__algebra(_260591), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_260591, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_260591), _260593), _260595)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_260591, _260593)), c_RealVector_Onorm__class_Onorm(_260591, _260595))))], (9942 ^ _224325) ^ [_567818, _567820, _567822] : [class_Rings_Oidom(_567818), 9945 ^ _224325 : [(9946 ^ _224325) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_567818), _567820), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(_567818), _567822), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_567820 = _567822), -(_567820 = c_Groups_Ouminus__class_Ouminus(_567818, _567822))], (9956 ^ _224325) ^ [] : [9957 ^ _224325 : [(9960 ^ _224325) ^ [] : [_567820 = c_Groups_Ouminus__class_Ouminus(_567818, _567822)], (9958 ^ _224325) ^ [] : [_567820 = _567822]], -(hAPP(hAPP(c_Power_Opower__class_Opower(_567818), _567820), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(_567818), _567822), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))]]], (9419 ^ _224325) ^ [_549578, _549580] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _549578, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _549580, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _549578, _549580)), -(_549578 = _549580)], (7889 ^ _224325) ^ [_496983, _496985, _496987, _496989] : [class_Rings_Ocomm__semiring__1(_496983), -(hAPP(hAPP(c_Power_Opower__class_Opower(_496983), hAPP(hAPP(c_Power_Opower__class_Opower(_496983), _496985), _496987)), _496989) = hAPP(hAPP(c_Power_Opower__class_Opower(_496983), _496985), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _496987), _496989)))], (11915 ^ _224325) ^ [] : [-(class_Groups_Oone(tc_Complex_Ocomplex))], (3803 ^ _224325) ^ [_352560, _352562, _352564, _352566] : [class_Rings_Olinordered__ring__strict(_352560), c_Orderings_Oord__class_Oless(_352560, _352562, _352564), c_Orderings_Oord__class_Oless(_352560, _352566, c_Groups_Ozero__class_Ozero(_352560)), -(c_Orderings_Oord__class_Oless(_352560, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_352560), _352566), _352564), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_352560), _352566), _352562)))], (7220 ^ _224325) ^ [_473242, _473244] : [-(c_RealDef_Oreal(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _473242), _473244)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _473242)), c_RealDef_Oreal(tc_Nat_Onat, _473244)))], (7859 ^ _224325) ^ [_495573] : [_495573 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _495573, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (2767 ^ _224325) ^ [_315598, _315600, _315602, _315604] : [class_Groups_Ocancel__semigroup__add(_315598), c_Groups_Oplus__class_Oplus(_315598, _315600, _315602) = c_Groups_Oplus__class_Oplus(_315598, _315600, _315604), -(_315602 = _315604)], (2116 ^ _224325) ^ [_293139] : [-(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, _293139) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _293139))], (10988 ^ _224325) ^ [_607273, _607275, _607277] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _607273), c_Groups_Ominus__class_Ominus(tc_Int_Oint, _607275, _607277)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _607273), _607275), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _607273), _607277)))], (6442 ^ _224325) ^ [_447731, _447733, _447735] : [class_Groups_Ogroup__add(_447731), 6445 ^ _224325 : [(6452 ^ _224325) ^ [] : [_447733 = _447735, -(c_Groups_Ouminus__class_Ouminus(_447731, _447733) = c_Groups_Ouminus__class_Ouminus(_447731, _447735))], (6446 ^ _224325) ^ [] : [c_Groups_Ouminus__class_Ouminus(_447731, _447733) = c_Groups_Ouminus__class_Ouminus(_447731, _447735), -(_447733 = _447735)]]], (6786 ^ _224325) ^ [_458775, _458777] : [_458775 = _458777, -(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _458775, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _458777)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (11685 ^ _224325) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (5693 ^ _224325) ^ [_420329, _420331, _420333] : [5694 ^ _224325 : [(5697 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _420331, _420333)], (5695 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _420329))]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _420329), _420331), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _420329), _420333)))], (1484 ^ _224325) ^ [_272674, _272676, _272678] : [class_Orderings_Opreorder(_272674), c_Orderings_Oord__class_Oless(_272674, _272676, _272678), c_Orderings_Oord__class_Oless(_272674, _272678, _272676)], (2036 ^ _224325) ^ [_290396, _290398] : [class_RealVector_Oreal__normed__algebra(_290396), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_290396), c_Groups_Ozero__class_Ozero(_290396)), _290398) = c_Groups_Ozero__class_Ozero(_290396))], (11661 ^ _224325) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (6486 ^ _224325) ^ [] : [-(c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (9201 ^ _224325) ^ [_541756, _541758] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _541756, _541758)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_541758), _541756))], (9147 ^ _224325) ^ [_539850] : [_539850 = c_Nat_OSuc(_539850)], (11827 ^ _224325) ^ [] : [-(class_Groups_Ominus(tc_RealDef_Oreal))], (11883 ^ _224325) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex))], (3873 ^ _224325) ^ [_354966, _354968, _354970] : [class_Rings_Olinordered__ring__strict(_354966), c_Orderings_Oord__class_Oless(_354966, _354968, c_Groups_Ozero__class_Ozero(_354966)), c_Orderings_Oord__class_Oless(_354966, _354970, c_Groups_Ozero__class_Ozero(_354966)), -(c_Orderings_Oord__class_Oless(_354966, c_Groups_Ozero__class_Ozero(_354966), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_354966), _354968), _354970)))], (7246 ^ _224325) ^ [_474217, _474219] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _474217), _474219), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _474217, c_RComplete_Onatfloor(_474219)))], (9383 ^ _224325) ^ [_548338, _548340] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _548338, _548340), 9386 ^ _224325 : [(9389 ^ _224325) ^ [] : [_548338 = _548340], (9387 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _548338, _548340))]]], (6468 ^ _224325) ^ [_448617, _448619] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _448617, _448619), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatfloor(_448617), c_RComplete_Onatfloor(_448619)))], (11991 ^ _224325) ^ [_640417] : [class_Rings_Olinordered__idom(_640417), -(class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(_640417)))], (3193 ^ _224325) ^ [_331894, _331896, _331898] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _331894), 3196 ^ _224325 : [(3203 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _331896, _331898), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _331894), _331896), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _331894), _331898)))], (3197 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _331894), _331896), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _331894), _331898)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _331896, _331898))]]], (8983 ^ _224325) ^ [_534307, _534309] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _534307, _534309), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _534309), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _534307, _534309))], (11761 ^ _224325) ^ [] : [-(class_Rings_Olinordered__semidom(tc_RealDef_Oreal))], (12015 ^ _224325) ^ [_641177] : [class_Rings_Olinordered__idom(_641177), -(class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(_641177)))], (12063 ^ _224325) ^ [_642697] : [class_Rings_Olinordered__idom(_642697), -(class_Rings_Oordered__semiring(tc_Polynomial_Opoly(_642697)))], (8463 ^ _224325) ^ [_515713, _515715] : [_515713 = c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatfloor(_515713)), -(c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _515713), _515715)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_RComplete_Onatfloor(_515713)), _515715))], (6352 ^ _224325) ^ [_444445, _444447] : [class_Rings_Olinordered__idom(_444445), 6355 ^ _224325 : [(6362 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_444445), _444447, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_444445)))), -(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(_444445), _444447) = _444447)], (6356 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_444445), _444447, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_444445))), -(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(_444445), _444447) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_444445), _444447))]]], (9213 ^ _224325) ^ [_542120] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_542120), _542120)], (11835 ^ _224325) ^ [] : [-(class_Rings_Oring(tc_RealDef_Oreal))], (9896 ^ _224325) ^ [_566171] : [-(c_Nat_OSuc(_566171) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _566171))], (6746 ^ _224325) ^ [_457458, _457460, _457462] : [class_Groups_Oordered__ab__group__add__abs(_457458), c_Orderings_Oord__class_Oless__eq(_457458, c_Groups_Oabs__class_Oabs(_457458, _457460), _457462), -(c_Orderings_Oord__class_Oless__eq(_457458, c_Groups_Ouminus__class_Ouminus(_457458, _457460), _457462))], (5985 ^ _224325) ^ [_431194, _431196, _431198] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _431194), _431196) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _431194), _431198), -(_431194 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_431196 = _431198)], (7310 ^ _224325) ^ [_476574] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _476574), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _476574)))], (2867 ^ _224325) ^ [_319445, _319447] : [class_Groups_Oordered__ab__group__add__abs(_319445), -(c_Groups_Oabs__class_Oabs(_319445, c_Groups_Oabs__class_Oabs(_319445, _319447)) = c_Groups_Oabs__class_Oabs(_319445, _319447))], (3209 ^ _224325) ^ [_332428, _332430, _332432] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _332428), 3212 ^ _224325 : [(3219 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _332430, _332432), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _332430), _332428), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _332432), _332428)))], (3213 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _332430), _332428), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _332432), _332428)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _332430, _332432))]]], (6918 ^ _224325) ^ [_463154, _463156] : [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, _463154, _463156)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _463154), _463156))], (5405 ^ _224325) ^ [_410074, _410076, _410078] : [class_Rings_Olinordered__idom(_410074), -(c_Groups_Osgn__class_Osgn(_410074, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_410074), _410076), _410078)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_410074), c_Groups_Osgn__class_Osgn(_410074, _410076)), c_Groups_Osgn__class_Osgn(_410074, _410078)))], (12267 ^ _224325) ^ [_649157] : [class_Rings_Ocomm__semiring__1(_649157), -(class_Groups_Oone(tc_Polynomial_Opoly(_649157)))], (5071 ^ _224325) ^ [_397368, _397370] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _397368, _397370), -(_397368 = _397370), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _397368, _397370))], (11315 ^ _224325) ^ [_619992, _619994, _619996] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _619992, _619994), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _619994, _619992), _619996) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _619994, _619996), _619992))], (12129 ^ _224325) ^ [_644787] : [class_Rings_Olinordered__idom(_644787), -(class_Rings_Oordered__ring(tc_Polynomial_Opoly(_644787)))], (3275 ^ _224325) ^ [_334699, _334701, _334703] : [class_Rings_Olinordered__idom(_334699), -(_334701 = _334703), -(c_Orderings_Oord__class_Oless(_334699, _334701, _334703)), -(c_Orderings_Oord__class_Oless(_334699, _334703, _334701))], (7674 ^ _224325) ^ [_489188, _489190, _489192, _489194] : [class_Rings_Oidom(_489188), 7677 ^ _224325 : [(7678 ^ _224325) ^ [] : [c_Rings_Odvd__class_Odvd(_489188, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_489188), _489190), _489192), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_489188), _489190), _489194)), -(_489190 = c_Groups_Ozero__class_Ozero(_489188)), -(c_Rings_Odvd__class_Odvd(_489188, _489192, _489194))], (7688 ^ _224325) ^ [] : [7689 ^ _224325 : [(7692 ^ _224325) ^ [] : [c_Rings_Odvd__class_Odvd(_489188, _489192, _489194)], (7690 ^ _224325) ^ [] : [_489190 = c_Groups_Ozero__class_Ozero(_489188)]], -(c_Rings_Odvd__class_Odvd(_489188, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_489188), _489190), _489192), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_489188), _489190), _489194)))]]], (10276 ^ _224325) ^ [_579772] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _579772, c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_579772 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_579772 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (3321 ^ _224325) ^ [_336275, _336277] : [class_Rings_Omult__zero(_336275), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_336275), c_Groups_Ozero__class_Ozero(_336275)), _336277) = c_Groups_Ozero__class_Ozero(_336275))], (554 ^ _224325) ^ [_241044, _241046] : [-(class_Orderings_Oorder(_241044)), _241046 = _241044, class_Orderings_Oorder(_241046)], (11851 ^ _224325) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex))], (8055 ^ _224325) ^ [_502710, _502712] : [_502710 = _502712, 8058 ^ _224325 : [(8061 ^ _224325) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _502712, _502710))], (8059 ^ _224325) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _502710, _502712))]]], (4143 ^ _224325) ^ [_363841, _363843, _363845, _363847, _363849] : [class_Rings_Olinordered__idom(_363841), c_Orderings_Oord__class_Oless(_363841, c_Groups_Oabs__class_Oabs(_363841, _363843), _363845), c_Orderings_Oord__class_Oless(_363841, c_Groups_Oabs__class_Oabs(_363841, _363847), _363849), -(c_Orderings_Oord__class_Oless(_363841, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_363841), c_Groups_Oabs__class_Oabs(_363841, _363843)), c_Groups_Oabs__class_Oabs(_363841, _363847)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_363841), _363845), _363849)))], (8285 ^ _224325) ^ [_509894, _509896] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _509894, _509896)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _509894, _509896), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _509896, _509894))], (1504 ^ _224325) ^ [_273340, _273342, _273344, _273346] : [class_Orderings_Oord(_273340), _273342 = _273344, c_Orderings_Oord__class_Oless(_273340, _273344, _273346), -(c_Orderings_Oord__class_Oless(_273340, _273342, _273346))], (10738 ^ _224325) ^ [_597347, _597349, _597351, _597353, _597355, _597357] : [class_Rings_Oordered__ring(_597347), 10741 ^ _224325 : [(10748 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_597347, _597353, c_Groups_Oplus__class_Oplus(_597347, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_597347), c_Groups_Ominus__class_Ominus(_597347, _597355, _597349)), _597351), _597357)), -(c_Orderings_Oord__class_Oless__eq(_597347, c_Groups_Oplus__class_Oplus(_597347, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_597347), _597349), _597351), _597353), c_Groups_Oplus__class_Oplus(_597347, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_597347), _597355), _597351), _597357)))], (10742 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_597347, c_Groups_Oplus__class_Oplus(_597347, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_597347), _597349), _597351), _597353), c_Groups_Oplus__class_Oplus(_597347, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_597347), _597355), _597351), _597357)), -(c_Orderings_Oord__class_Oless__eq(_597347, _597353, c_Groups_Oplus__class_Oplus(_597347, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_597347), c_Groups_Ominus__class_Ominus(_597347, _597355, _597349)), _597351), _597357)))]]], (11723 ^ _224325) ^ [] : [-(class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal))], (11675 ^ _224325) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (11365 ^ _224325) ^ [_621786, _621788, _621790] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _621786, _621788), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _621790, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _621788, _621786)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _621790, _621788), _621786))], (10246 ^ _224325) ^ [_578637] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _578637, _578637))], (8411 ^ _224325) ^ [_513787, _513789, _513791] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _513787), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _513789, _513791)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _513787), _513789)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _513787), _513791)))], (7026 ^ _224325) ^ [_466944, _466946] : [class_Rings_Olinordered__idom(_466944), 7029 ^ _224325 : [(7036 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_466944, _466946, c_Groups_Ozero__class_Ozero(_466944)), -(c_Groups_Osgn__class_Osgn(_466944, _466946) = c_Groups_Ouminus__class_Ouminus(_466944, c_Groups_Oone__class_Oone(_466944)))], (7030 ^ _224325) ^ [] : [c_Groups_Osgn__class_Osgn(_466944, _466946) = c_Groups_Ouminus__class_Ouminus(_466944, c_Groups_Oone__class_Oone(_466944)), -(c_Orderings_Oord__class_Oless(_466944, _466946, c_Groups_Ozero__class_Ozero(_466944)))]]], (4577 ^ _224325) ^ [_378596, _378598, _378600, _378602, _378604] : [class_Groups_Ozero(_378596), 4580 ^ _224325 : [(4589 ^ _224325) ^ [] : [-(c_Polynomial_OpCons(_378596, _378598, _378600) = c_Polynomial_OpCons(_378596, _378602, _378604)), _378598 = _378602, _378600 = _378604], (4581 ^ _224325) ^ [] : [c_Polynomial_OpCons(_378596, _378598, _378600) = c_Polynomial_OpCons(_378596, _378602, _378604), 4584 ^ _224325 : [(4587 ^ _224325) ^ [] : [-(_378600 = _378604)], (4585 ^ _224325) ^ [] : [-(_378598 = _378602)]]]]], (846 ^ _224325) ^ [_250702, _250704, _250706, _250708, _250710, _250712] : [-(c_Polynomial_Osynthetic__div(_250712, _250708, _250704) = c_Polynomial_Osynthetic__div(_250710, _250706, _250702)), _250712 = _250710, _250708 = _250706, _250704 = _250702], (11617 ^ _224325) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (10786 ^ _224325) ^ [_599459, _599461, _599463, _599465, _599467, _599469] : [class_Rings_Oordered__ring(_599459), 10789 ^ _224325 : [(10796 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_599459, c_Groups_Oplus__class_Oplus(_599459, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_599459), c_Groups_Ominus__class_Ominus(_599459, _599461, _599467)), _599463), _599465), _599469), -(c_Orderings_Oord__class_Oless(_599459, c_Groups_Oplus__class_Oplus(_599459, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_599459), _599461), _599463), _599465), c_Groups_Oplus__class_Oplus(_599459, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_599459), _599467), _599463), _599469)))], (10790 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_599459, c_Groups_Oplus__class_Oplus(_599459, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_599459), _599461), _599463), _599465), c_Groups_Oplus__class_Oplus(_599459, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_599459), _599467), _599463), _599469)), -(c_Orderings_Oord__class_Oless(_599459, c_Groups_Oplus__class_Oplus(_599459, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_599459), c_Groups_Ominus__class_Ominus(_599459, _599461, _599467)), _599463), _599465), _599469))]]], (5051 ^ _224325) ^ [_396620] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _396620, _396620)], (11111 ^ _224325) ^ [_612601, _612603] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _612601, _612603), -(c_Nat__Transfer_Otsub(_612603, _612601) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, _612603, _612601))], (354 ^ _224325) ^ [_235144, _235146] : [-(class_Rings_Olinordered__semiring(_235144)), _235146 = _235144, class_Rings_Olinordered__semiring(_235146)], (464 ^ _224325) ^ [_238389, _238391] : [-(class_Rings_Oordered__ring(_238389)), _238391 = _238389, class_Rings_Oordered__ring(_238391)], (11587 ^ _224325) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (10386 ^ _224325) ^ [_583388, _583390, _583392, _583394, _583396] : [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), _583388), _583390), _583392), c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _583388), _583394), _583396)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _583396, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _583388, _583396), c_Orderings_Oord__class_Oless(tc_Int_Oint, _583388, _583392), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _583394, _583390))], (11349 ^ _224325) ^ [_621264, _621266, _621268] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _621264, _621266), 11352 ^ _224325 : [(11359 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _621268, _621264), _621266), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _621268, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _621266, _621264)))], (11353 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _621268, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _621266, _621264)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _621268, _621264), _621266))]]], (544 ^ _224325) ^ [_240749, _240751] : [-(class_Rings_Omult__zero(_240749)), _240751 = _240749, class_Rings_Omult__zero(_240751)], (10968 ^ _224325) ^ [_606645, _606647, _606649, _606651, _606653] : [class_Groups_Oordered__ab__group__add(_606645), c_Groups_Ominus__class_Ominus(_606645, _606647, _606649) = c_Groups_Ominus__class_Ominus(_606645, _606651, _606653), 10975 ^ _224325 : [(10982 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_606645, _606651, _606653), -(c_Orderings_Oord__class_Oless(_606645, _606647, _606649))], (10976 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_606645, _606647, _606649), -(c_Orderings_Oord__class_Oless(_606645, _606651, _606653))]]], (4689 ^ _224325) ^ [_382192] : [class_Rings_Ocomm__semiring__1(_382192), -(c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_382192)) = c_Polynomial_OpCons(_382192, c_Groups_Oone__class_Oone(_382192), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_382192))))], (514 ^ _224325) ^ [_239864, _239866] : [-(class_Groups_Omonoid__add(_239864)), _239866 = _239864, class_Groups_Omonoid__add(_239866)], (7951 ^ _224325) ^ [_499315, _499317, _499319] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _499315), 7954 ^ _224325 : [(7961 ^ _224325) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _499317, _499319), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _499315), _499317), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _499315), _499319)))], (7955 ^ _224325) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _499315), _499317), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _499315), _499319)), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _499317, _499319))]]], (2042 ^ _224325) ^ [_290628, _290630] : [class_Rings_Ocomm__semiring__1(_290628), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_290628), c_Groups_Ozero__class_Ozero(_290628)), _290630) = c_Groups_Ozero__class_Ozero(_290628))], (7078 ^ _224325) ^ [_468558] : [_468558 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, _468558) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (12279 ^ _224325) ^ [_649551, _649553] : [hBOOL(c_fequal(_649551, _649553)), -(_649551 = _649553)], (10360 ^ _224325) ^ [_582515, _582517, _582519, _582521, _582523, _582525] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _582515), _582517), _582519) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _582521), _582523), _582525), 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), _582521), _582523), _582525)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _582525, _582521), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _582519), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _582521), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _582521, _582515), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _582517, _582523))], (3039 ^ _224325) ^ [_326313, _326315, _326317, _326319] : [class_RealVector_Oreal__normed__algebra(_326313), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_326313), _326315), c_Groups_Oplus__class_Oplus(_326313, _326317, _326319)) = c_Groups_Oplus__class_Oplus(_326313, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_326313), _326315), _326317), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_326313), _326315), _326319)))], (5235 ^ _224325) ^ [_403519, _403521, _403523, _403525] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _403519, _403521), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _403523, _403525), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _403519), _403523), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _403521), _403525)))], (2340 ^ _224325) ^ [_300327, _300329, _300331] : [class_Groups_Oordered__comm__monoid__add(_300327), c_Orderings_Oord__class_Oless__eq(_300327, c_Groups_Ozero__class_Ozero(_300327), _300329), c_Orderings_Oord__class_Oless__eq(_300327, c_Groups_Ozero__class_Ozero(_300327), _300331), -(c_Orderings_Oord__class_Oless__eq(_300327, c_Groups_Ozero__class_Ozero(_300327), c_Groups_Oplus__class_Oplus(_300327, _300329, _300331)))], (5309 ^ _224325) ^ [_406432, _406434, _406436] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _406432, _406434), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _406432, _406436)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _406434, _406436))], (11463 ^ _224325) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex))], (6124 ^ _224325) ^ [_436202, _436204] : [class_Groups_Olinordered__ab__group__add(_436202), 6127 ^ _224325 : [(6134 ^ _224325) ^ [] : [_436204 = c_Groups_Ozero__class_Ozero(_436202), -(c_Groups_Ouminus__class_Ouminus(_436202, _436204) = _436204)], (6128 ^ _224325) ^ [] : [c_Groups_Ouminus__class_Ouminus(_436202, _436204) = _436204, -(_436204 = c_Groups_Ozero__class_Ozero(_436202))]]], (9994 ^ _224325) ^ [_569493, _569495] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _569493), _569495)), 9997 ^ _224325 : [(10000 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _569495))], (9998 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _569493))]]], (11711 ^ _224325) ^ [] : [-(class_Groups_Ominus(tc_HOL_Obool))], (144 ^ _224325) ^ [_228949, _228951] : [-(class_Fields_Ofield(_228949)), _228951 = _228949, class_Fields_Ofield(_228951)], (2783 ^ _224325) ^ [_316275, _316277, _316279, _316281] : [class_Groups_Ocancel__semigroup__add(_316275), 2786 ^ _224325 : [(2793 ^ _224325) ^ [] : [_316277 = _316281, -(c_Groups_Oplus__class_Oplus(_316275, _316277, _316279) = c_Groups_Oplus__class_Oplus(_316275, _316281, _316279))], (2787 ^ _224325) ^ [] : [c_Groups_Oplus__class_Oplus(_316275, _316277, _316279) = c_Groups_Oplus__class_Oplus(_316275, _316281, _316279), -(_316277 = _316281)]]], (11777 ^ _224325) ^ [] : [-(class_Rings_Olinordered__ring(tc_RealDef_Oreal))], (10016 ^ _224325) ^ [_570175] : [-(c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(_570175)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _570175), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (11771 ^ _224325) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_RealDef_Oreal))], (1926 ^ _224325) ^ [_286448, _286450, _286452, _286454] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_286448), c_Orderings_Oord__class_Oless(_286448, c_Groups_Oplus__class_Oplus(_286448, _286450, _286452), c_Groups_Oplus__class_Oplus(_286448, _286450, _286454)), -(c_Orderings_Oord__class_Oless(_286448, _286452, _286454))], (3901 ^ _224325) ^ [_355876, _355878, _355880, _355882] : [class_Rings_Olinordered__ring__strict(_355876), c_Orderings_Oord__class_Oless(_355876, _355878, c_Groups_Ozero__class_Ozero(_355876)), 3908 ^ _224325 : [(3915 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_355876, _355882, _355880), -(c_Orderings_Oord__class_Oless(_355876, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_355876), _355878), _355880), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_355876), _355878), _355882)))], (3909 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_355876, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_355876), _355878), _355880), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_355876), _355878), _355882)), -(c_Orderings_Oord__class_Oless(_355876, _355882, _355880))]]], (11725 ^ _224325) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal))], (12141 ^ _224325) ^ [_645167] : [class_Rings_Olinordered__idom(_645167), -(class_Orderings_Olinorder(tc_Polynomial_Opoly(_645167)))], (10574 ^ _224325) ^ [_590577, _590579, _590581, _590583, _590585, _590587] : [class_Rings_Oring(_590577), 10577 ^ _224325 : [(10584 ^ _224325) ^ [] : [_590583 = c_Groups_Oplus__class_Oplus(_590577, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_590577), c_Groups_Ominus__class_Ominus(_590577, _590585, _590579)), _590581), _590587), -(c_Groups_Oplus__class_Oplus(_590577, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_590577), _590579), _590581), _590583) = c_Groups_Oplus__class_Oplus(_590577, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_590577), _590585), _590581), _590587))], (10578 ^ _224325) ^ [] : [c_Groups_Oplus__class_Oplus(_590577, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_590577), _590579), _590581), _590583) = c_Groups_Oplus__class_Oplus(_590577, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_590577), _590585), _590581), _590587), -(_590583 = c_Groups_Oplus__class_Oplus(_590577, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_590577), c_Groups_Ominus__class_Ominus(_590577, _590585, _590579)), _590581), _590587))]]], (6824 ^ _224325) ^ [_460135] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _460135, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_RComplete_Onatfloor(_460135) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11123 ^ _224325) ^ [_613045, _613047, _613049] : [hBOOL(hAPP(_613045, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _613047, _613049))), 11126 ^ _224325 : [(11133 ^ _224325) ^ [_613383] : [_613047 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _613049, _613383), -(hBOOL(hAPP(_613045, _613383)))], (11127 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _613047, _613049), -(hBOOL(hAPP(_613045, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (10012 ^ _224325) ^ [_570038] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(_570038))))], (5533 ^ _224325) ^ [_414858] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _414858, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_414858 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2268 ^ _224325) ^ [_298087, _298089, _298091] : [class_Groups_Oordered__comm__monoid__add(_298087), c_Orderings_Oord__class_Oless__eq(_298087, _298089, c_Groups_Ozero__class_Ozero(_298087)), c_Orderings_Oord__class_Oless__eq(_298087, _298091, c_Groups_Ozero__class_Ozero(_298087)), -(c_Orderings_Oord__class_Oless__eq(_298087, c_Groups_Oplus__class_Oplus(_298087, _298089, _298091), c_Groups_Ozero__class_Ozero(_298087)))], (9085 ^ _224325) ^ [_537791, _537793] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _537791), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _537793), c_Rings_Odvd__class_Odvd(tc_Int_Oint, _537791, _537793), c_Rings_Odvd__class_Odvd(tc_Int_Oint, _537793, _537791), -(_537791 = _537793)], (11693 ^ _224325) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (9235 ^ _224325) ^ [_543220, _543222] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Nat_OSuc(_543220), _543222) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _543220, c_Nat_OSuc(_543222)))], (6972 ^ _224325) ^ [_465057] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _465057, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), -(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _465057) = _465057)], (8743 ^ _224325) ^ [_525937, _525939, _525941] : [class_Rings_Olinordered__idom(_525937), -(c_Orderings_Oord__class_Oless__eq(_525937, c_Groups_Ozero__class_Ozero(_525937), hAPP(hAPP(c_Power_Opower__class_Opower(_525937), c_Groups_Oabs__class_Oabs(_525937, _525939)), _525941)))], (6670 ^ _224325) ^ [_454978, _454980] : [class_Groups_Ogroup__add(_454978), -(c_Groups_Oplus__class_Oplus(_454978, _454980, c_Groups_Ouminus__class_Ouminus(_454978, _454980)) = c_Groups_Ozero__class_Ozero(_454978))], (9830 ^ _224325) ^ [_563693, _563695] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_563693), _563695), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _563693, _563695))], (3081 ^ _224325) ^ [_327979, _327981, _327983] : [class_Groups_Oordered__ab__group__add__abs(_327979), c_Orderings_Oord__class_Oless__eq(_327979, c_Groups_Oabs__class_Oabs(_327979, _327981), _327983), -(c_Orderings_Oord__class_Oless__eq(_327979, _327981, _327983))], (5325 ^ _224325) ^ [_407082, _407084, _407086, _407088] : [class_Rings_Ocomm__semiring__0(_407082), -(c_Polynomial_Osmult(_407082, _407084, c_Polynomial_Osmult(_407082, _407086, _407088)) = c_Polynomial_Osmult(_407082, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_407082), _407084), _407086), _407088))], (6464 ^ _224325) ^ [] : [-(c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11649 ^ _224325) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (11449 ^ _224325) ^ [_625081, _625083, _625085] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _625081, _625083), _625085) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _625081, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _625083, _625085)))], (7696 ^ _224325) ^ [_489936, _489938, _489940, _489942] : [class_Rings_Oidom(_489936), 7699 ^ _224325 : [(7700 ^ _224325) ^ [] : [c_Rings_Odvd__class_Odvd(_489936, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_489936), _489938), _489940), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_489936), _489942), _489940)), -(_489940 = c_Groups_Ozero__class_Ozero(_489936)), -(c_Rings_Odvd__class_Odvd(_489936, _489938, _489942))], (7710 ^ _224325) ^ [] : [7711 ^ _224325 : [(7714 ^ _224325) ^ [] : [c_Rings_Odvd__class_Odvd(_489936, _489938, _489942)], (7712 ^ _224325) ^ [] : [_489940 = c_Groups_Ozero__class_Ozero(_489936)]], -(c_Rings_Odvd__class_Odvd(_489936, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_489936), _489938), _489940), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_489936), _489942), _489940)))]]], (504 ^ _224325) ^ [_239569, _239571] : [-(class_Groups_Ocomm__monoid__add(_239569)), _239571 = _239569, class_Groups_Ocomm__monoid__add(_239571)], (6310 ^ _224325) ^ [_442711, _442713, _442715] : [class_Rings_Oring(_442711), -(c_Groups_Ouminus__class_Ouminus(_442711, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_442711), _442713), _442715)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_442711), _442713), c_Groups_Ouminus__class_Ouminus(_442711, _442715)))], (4353 ^ _224325) ^ [_370916, _370918, _370920, _370922] : [class_Rings_Olinordered__semiring__strict(_370916), c_Orderings_Oord__class_Oless(_370916, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_370916), _370918), _370920), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_370916), _370922), _370920)), c_Orderings_Oord__class_Oless__eq(_370916, c_Groups_Ozero__class_Ozero(_370916), _370920), -(c_Orderings_Oord__class_Oless(_370916, _370918, _370922))], (2490 ^ _224325) ^ [_305397, _305399, _305401, _305403] : [class_Orderings_Oorder(_305397), c_Orderings_Oord__class_Oless__eq(_305397, _305399, _305401), c_Orderings_Oord__class_Oless__eq(_305397, _305403, _305399), -(c_Orderings_Oord__class_Oless__eq(_305397, _305403, _305401))], (714 ^ _224325) ^ [_245764, _245766] : [-(class_Rings_Oring(_245764)), _245766 = _245764, class_Rings_Oring(_245766)], (8645 ^ _224325) ^ [_522463, _522465, _522467, _522469, _522471] : [class_Rings_Ocomm__semiring__1(_522463), c_Rings_Odvd__class_Odvd(_522463, hAPP(hAPP(c_Power_Opower__class_Opower(_522463), _522465), _522467), _522469), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _522471, _522467), -(c_Rings_Odvd__class_Odvd(_522463, hAPP(hAPP(c_Power_Opower__class_Opower(_522463), _522465), _522471), _522469))], (1936 ^ _224325) ^ [_286813, _286815, _286817, _286819] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_286813), c_Orderings_Oord__class_Oless(_286813, c_Groups_Oplus__class_Oplus(_286813, _286815, _286817), c_Groups_Oplus__class_Oplus(_286813, _286819, _286817)), -(c_Orderings_Oord__class_Oless(_286813, _286815, _286819))], (11731 ^ _224325) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal))], (8209 ^ _224325) ^ [_507538, _507540] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _507538, _507540), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _507540, _507538), -(_507538 = _507540)], (9449 ^ _224325) ^ [_550567, _550569] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _550567, _550569), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _550567, c_Groups_Oone__class_Oone(tc_Int_Oint)), _550569))], (3109 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, v_c____, v_cs____)), v_z____)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), v_r), v_m____))))], (304 ^ _224325) ^ [_233669, _233671] : [-(class_Rings_Oordered__comm__semiring(_233669)), _233671 = _233669, class_Rings_Oordered__comm__semiring(_233671)], (764 ^ _224325) ^ [_247239, _247241] : [-(hBOOL(_247239)), _247241 = _247239, hBOOL(_247241)], (11515 ^ _224325) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (4045 ^ _224325) ^ [_360569, _360571, _360573, _360575] : [class_Rings_Olinordered__ring__strict(_360569), 4048 ^ _224325 : [(4063 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(_360569, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_360569), _360571), _360573), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_360569), _360575), _360573))), 4064 ^ _224325 : [(4071 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_360569, _360573, c_Groups_Ozero__class_Ozero(_360569)), c_Orderings_Oord__class_Oless(_360569, _360575, _360571)], (4065 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_360569, c_Groups_Ozero__class_Ozero(_360569), _360573), c_Orderings_Oord__class_Oless(_360569, _360571, _360575)]]], (4049 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_360569, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_360569), _360571), _360573), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_360569), _360575), _360573)), 4054 ^ _224325 : [(4057 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(_360569, _360571, _360575))], (4055 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(_360569, c_Groups_Ozero__class_Ozero(_360569), _360573))]], 4058 ^ _224325 : [(4061 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(_360569, _360575, _360571))], (4059 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(_360569, _360573, c_Groups_Ozero__class_Ozero(_360569)))]]]]], (11979 ^ _224325) ^ [_640037] : [class_Groups_Ocancel__comm__monoid__add(_640037), -(class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(_640037)))], (5867 ^ _224325) ^ [_426576, _426578, _426580] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _426576), 5870 ^ _224325 : [(5877 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _426578, _426580), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _426576), _426578), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _426576), _426580)))], (5871 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _426576), _426578), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _426576), _426580)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _426578, _426580))]]], (7847 ^ _224325) ^ [_495176, _495178] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _495176, _495178), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _495176, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _495178, _495176)))], (5457 ^ _224325) ^ [_412064, _412066, _412068, _412070] : [class_Rings_Ocomm__semiring__0(_412064), -(hAPP(c_Polynomial_Opoly(_412064, c_Polynomial_Osmult(_412064, _412066, _412068)), _412070) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_412064), _412066), hAPP(c_Polynomial_Opoly(_412064, _412068), _412070)))], (6070 ^ _224325) ^ [_434555] : [class_Groups_Ogroup__add(_434555), -(c_Groups_Ouminus__class_Ouminus(_434555, c_Groups_Ozero__class_Ozero(_434555)) = c_Groups_Ozero__class_Ozero(_434555))], (3817 ^ _224325) ^ [_353044, _353046, _353048, _353050] : [class_Rings_Olinordered__ring__strict(_353044), c_Orderings_Oord__class_Oless(_353044, _353046, _353048), c_Orderings_Oord__class_Oless(_353044, _353050, c_Groups_Ozero__class_Ozero(_353044)), -(c_Orderings_Oord__class_Oless(_353044, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_353044), _353048), _353050), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_353044), _353046), _353050)))], (9551 ^ _224325) ^ [_553982] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_553982)], (2999 ^ _224325) ^ [_324527, _324529, _324531, _324533] : [class_Rings_Ocomm__semiring__1(_324527), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_324527), c_Groups_Oplus__class_Oplus(_324527, _324529, _324531)), _324533) = c_Groups_Oplus__class_Oplus(_324527, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_324527), _324529), _324533), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_324527), _324531), _324533)))], (11805 ^ _224325) ^ [] : [-(class_Groups_Ogroup__add(tc_RealDef_Oreal))], (7834 ^ _224325) ^ [_494660] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _494660), 7838 ^ _224325 : [(7839 ^ _224325) ^ [_494842] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _494842, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, 7837 ^ [_494660, _494842])), _494660)))]]], (3499 ^ _224325) ^ [] : [c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)], (8461 ^ _224325) ^ [_515586, _515588] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _515586)), _515588) = c_RealDef_Oreal(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _515586), _515588)))], (11669 ^ _224325) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (12225 ^ _224325) ^ [_647827] : [class_Rings_Olinordered__idom(_647827), -(class_Groups_Oabs__if(tc_Polynomial_Opoly(_647827)))], (3505 ^ _224325) ^ [_342842, _342844] : [class_Rings_Olinordered__ring(_342842), -(c_Orderings_Oord__class_Oless__eq(_342842, c_Groups_Ozero__class_Ozero(_342842), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_342842), _342844), _342844)))], (5929 ^ _224325) ^ [_428879, _428881] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _428879), _428881) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 5932 ^ _224325 : [(5935 ^ _224325) ^ [] : [-(_428881 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (5933 ^ _224325) ^ [] : [-(_428879 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (8507 ^ _224325) ^ [_517547, _517549, _517551, _517553] : [class_Rings_Ocomm__semiring__1(_517547), c_Rings_Odvd__class_Odvd(_517547, _517549, _517551), -(c_Rings_Odvd__class_Odvd(_517547, hAPP(hAPP(c_Power_Opower__class_Opower(_517547), _517549), _517553), hAPP(hAPP(c_Power_Opower__class_Opower(_517547), _517551), _517553)))], (11881 ^ _224325) ^ [] : [-(class_Groups_Omonoid__mult(tc_Complex_Ocomplex))], (8219 ^ _224325) ^ [_507855, _507857, _507859] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _507855, _507857), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _507857, _507859), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _507855, _507859))], (2873 ^ _224325) ^ [_319699, _319701, _319703, _319705] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_319699), c_Orderings_Oord__class_Oless__eq(_319699, c_Groups_Oplus__class_Oplus(_319699, _319701, _319703), c_Groups_Oplus__class_Oplus(_319699, _319701, _319705)), -(c_Orderings_Oord__class_Oless__eq(_319699, _319703, _319705))], (5473 ^ _224325) ^ [_412729, _412731, _412733, _412735] : [class_Rings_Ocomm__semiring__0(_412729), -(c_Polynomial_Osmult(_412729, c_Groups_Oplus__class_Oplus(_412729, _412731, _412733), _412735) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_412729), c_Polynomial_Osmult(_412729, _412731, _412735), c_Polynomial_Osmult(_412729, _412733, _412735)))], (7010 ^ _224325) ^ [_466411] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _466411, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_466411), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (1970 ^ _224325) ^ [_288035, _288037, _288039, _288041] : [class_Groups_Oordered__cancel__ab__semigroup__add(_288035), c_Orderings_Oord__class_Oless(_288035, _288037, _288039), -(c_Orderings_Oord__class_Oless(_288035, c_Groups_Oplus__class_Oplus(_288035, _288037, _288041), c_Groups_Oplus__class_Oplus(_288035, _288039, _288041)))], (9555 ^ _224325) ^ [_554176] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _554176, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Groups_Oabs__class_Oabs(tc_Int_Oint, _554176) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _554176))], (7901 ^ _224325) ^ [_497487, _497489] : [class_Rings_Ocomm__semiring__1(_497487), -(hAPP(hAPP(c_Power_Opower__class_Opower(_497487), _497489), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_497487))], (2168 ^ _224325) ^ [_294841, _294843, _294845, _294847] : [class_Groups_Oordered__comm__monoid__add(_294841), c_Orderings_Oord__class_Oless__eq(_294841, c_Groups_Ozero__class_Ozero(_294841), _294843), c_Orderings_Oord__class_Oless(_294841, _294845, _294847), -(c_Orderings_Oord__class_Oless(_294841, _294845, c_Groups_Oplus__class_Oplus(_294841, _294843, _294847)))], (11787 ^ _224325) ^ [] : [-(class_Groups_Oab__group__add(tc_RealDef_Oreal))], (10250 ^ _224325) ^ [_578814, _578816] : [-(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _578814, _578816)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _578814), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _578816)))], (6998 ^ _224325) ^ [_466018] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _466018), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), c_RComplete_Onatfloor(_466018)))], (30 ^ _224325) ^ [_225396, _225398, _225400, _225402] : [-(c_SEQ_Odecseq(_225400, _225396)), c_SEQ_Odecseq(_225402, _225398), _225402 = _225400, _225398 = _225396], (9633 ^ _224325) ^ [_557092, _557094] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _557092, c_Nat_OSuc(_557094)), -(_557092 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 9641 ^ _224325 : [(9644 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, 9640 ^ [_557092, _557094], _557094))], (9642 ^ _224325) ^ [] : [-(_557092 = c_Nat_OSuc(9640 ^ [_557092, _557094]))]]], (5013 ^ _224325) ^ [_395458, _395460] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _395458, _395460)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _395458, _395460), -(_395458 = _395460)], (8329 ^ _224325) ^ [_511235, _511237, _511239] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _511235, _511237), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _511237, _511235)), _511237 = _511239, 8340 ^ _224325 : [(8343 ^ _224325) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _511239, _511235)], (8341 ^ _224325) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _511235, _511239))]]], (684 ^ _224325) ^ [_244879, _244881] : [-(class_Power_Opower(_244879)), _244881 = _244879, class_Power_Opower(_244881)], (6027 ^ _224325) ^ [_432794, _432796, _432798, _432800] : [class_Rings_Ocomm__semiring__0(_432794), -(c_Polynomial_Osynthetic__div(_432794, c_Polynomial_OpCons(_432794, _432796, _432798), _432800) = c_Polynomial_OpCons(_432794, hAPP(c_Polynomial_Opoly(_432794, _432798), _432800), c_Polynomial_Osynthetic__div(_432794, _432798, _432800)))], (4561 ^ _224325) ^ [_378066, _378068] : [class_Rings_Olinordered__idom(_378066), 4564 ^ _224325 : [(4571 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_378066, _378068, c_Groups_Ozero__class_Ozero(_378066)), -(c_Orderings_Oord__class_Oless(_378066, c_Groups_Oplus__class_Oplus(_378066, _378068, _378068), c_Groups_Ozero__class_Ozero(_378066)))], (4565 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_378066, c_Groups_Oplus__class_Oplus(_378066, _378068, _378068), c_Groups_Ozero__class_Ozero(_378066)), -(c_Orderings_Oord__class_Oless(_378066, _378068, c_Groups_Ozero__class_Ozero(_378066)))]]], (12033 ^ _224325) ^ [_641747] : [class_Rings_Olinordered__idom(_641747), -(class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(_641747)))], (11207 ^ _224325) ^ [_616219, _616221] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _616219, _616221), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _616219, _616221))], (4 ^ _224325) ^ [_224556, _224558] : [_224558 = _224556, -(_224556 = _224558)], (4735 ^ _224325) ^ [_384228, _384230] : [class_RealVector_Oreal__normed__algebra(_384228), 4739 ^ _224325 : [(4742 ^ _224325) ^ [_384527] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_384228, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_384228), _384230), _384527)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_384228, _384527)), 4738 ^ [_384228, _384230])))], (4740 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 4738 ^ [_384228, _384230]))]]], (10962 ^ _224325) ^ [_606361, _606363, _606365] : [class_Groups_Oordered__ab__group__add__abs(_606361), -(c_Groups_Oabs__class_Oabs(_606361, c_Groups_Ominus__class_Ominus(_606361, _606363, _606365)) = c_Groups_Oabs__class_Oabs(_606361, c_Groups_Ominus__class_Ominus(_606361, _606365, _606363)))], (11271 ^ _224325) ^ [_618519, _618521, _618523] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _618519, _618521), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _618523, _618519), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _618519, _618523), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _618521, _618523)))], (7316 ^ _224325) ^ [_476819, _476821] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _476819, _476821), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _476819), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), c_RealDef_Oreal(tc_Nat_Onat, _476821)))], (10096 ^ _224325) ^ [_573391, _573393, _573395] : [class_Rings_Olinordered__semidom(_573391), c_Orderings_Oord__class_Oless__eq(_573391, c_Groups_Ozero__class_Ozero(_573391), _573393), c_Orderings_Oord__class_Oless__eq(_573391, _573393, c_Groups_Oone__class_Oone(_573391)), -(c_Orderings_Oord__class_Oless__eq(_573391, hAPP(hAPP(c_Power_Opower__class_Opower(_573391), _573393), c_Nat_OSuc(_573395)), _573393))], (9890 ^ _224325) ^ [_565946, _565948, _565950] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _565948, _565950), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_565946)), _565948), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_565946)), _565950)))], (10728 ^ _224325) ^ [_596968, _596970, _596972] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _596968, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _596970, _596972)), c_Rings_Odvd__class_Odvd(tc_Int_Oint, _596968, _596972), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _596968, _596970))], (3395 ^ _224325) ^ [_338747, _338749, _338751, _338753] : [class_Rings_Ocomm__semiring(_338747), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_338747), c_Groups_Oplus__class_Oplus(_338747, _338749, _338751)), _338753) = c_Groups_Oplus__class_Oplus(_338747, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_338747), _338749), _338753), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_338747), _338751), _338753)))], (344 ^ _224325) ^ [_234849, _234851] : [-(class_Groups_Ocancel__semigroup__add(_234849)), _234851 = _234849, class_Groups_Ocancel__semigroup__add(_234851)], (4945 ^ _224325) ^ [_392809] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _392809, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11967 ^ _224325) ^ [_639657] : [class_Rings_Olinordered__idom(_639657), -(class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(_639657)))], (958 ^ _224325) ^ [_254739, _254741] : [_254741 = _254739, -(c_Nat_OSuc(_254741) = c_Nat_OSuc(_254739))], (6520 ^ _224325) ^ [_450265, _450267] : [class_Groups_Olinordered__ab__group__add(_450265), 6523 ^ _224325 : [(6530 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_450265, _450267, c_Groups_Ozero__class_Ozero(_450265)), -(c_Orderings_Oord__class_Oless__eq(_450265, _450267, c_Groups_Ouminus__class_Ouminus(_450265, _450267)))], (6524 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_450265, _450267, c_Groups_Ouminus__class_Ouminus(_450265, _450267)), -(c_Orderings_Oord__class_Oless__eq(_450265, _450267, c_Groups_Ozero__class_Ozero(_450265)))]]], (2140 ^ _224325) ^ [_293947, _293949, _293951] : [class_Groups_Oordered__comm__monoid__add(_293947), c_Orderings_Oord__class_Oless__eq(_293947, _293949, c_Groups_Ozero__class_Ozero(_293947)), c_Orderings_Oord__class_Oless(_293947, _293951, c_Groups_Ozero__class_Ozero(_293947)), -(c_Orderings_Oord__class_Oless(_293947, c_Groups_Oplus__class_Oplus(_293947, _293949, _293951), c_Groups_Ozero__class_Ozero(_293947)))], (6264 ^ _224325) ^ [_440914, _440916, _440918] : [class_RealVector_Oreal__normed__algebra(_440914), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_440914), _440916), c_Groups_Ouminus__class_Ouminus(_440914, _440918)) = c_Groups_Ouminus__class_Ouminus(_440914, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_440914), _440916), _440918)))], (3649 ^ _224325) ^ [_347438, _347440, _347442, _347444] : [class_Rings_Oordered__semiring(_347438), c_Orderings_Oord__class_Oless__eq(_347438, _347440, _347442), c_Orderings_Oord__class_Oless__eq(_347438, c_Groups_Ozero__class_Ozero(_347438), _347444), -(c_Orderings_Oord__class_Oless__eq(_347438, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_347438), _347440), _347444), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_347438), _347442), _347444)))], (1532 ^ _224325) ^ [_274232, _274234, _274236, _274238] : [class_Orderings_Oord(_274232), c_Orderings_Oord__class_Oless(_274232, _274234, _274236), _274236 = _274238, -(c_Orderings_Oord__class_Oless(_274232, _274234, _274238))], (7412 ^ _224325) ^ [_480118, _480120, _480122] : [class_Rings_Oidom(_480118), 7415 ^ _224325 : [(7422 ^ _224325) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_480118), c_Polynomial_OpCons(_480118, c_Groups_Ouminus__class_Ouminus(_480118, _480122), c_Polynomial_OpCons(_480118, c_Groups_Oone__class_Oone(_480118), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_480118)))), _480120), -(hAPP(c_Polynomial_Opoly(_480118, _480120), _480122) = c_Groups_Ozero__class_Ozero(_480118))], (7416 ^ _224325) ^ [] : [hAPP(c_Polynomial_Opoly(_480118, _480120), _480122) = c_Groups_Ozero__class_Ozero(_480118), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_480118), c_Polynomial_OpCons(_480118, c_Groups_Ouminus__class_Ouminus(_480118, _480122), c_Polynomial_OpCons(_480118, c_Groups_Oone__class_Oone(_480118), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_480118)))), _480120))]]], (1163 ^ _224325) ^ [] : [-(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_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____)), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), v_r), v_m____)))))], (6316 ^ _224325) ^ [_442983, _442985, _442987] : [class_Groups_Ogroup__add(_442983), -(c_Groups_Oplus__class_Oplus(_442983, c_Groups_Ouminus__class_Ouminus(_442983, _442985), c_Groups_Oplus__class_Oplus(_442983, _442985, _442987)) = _442987)], (11997 ^ _224325) ^ [_640607] : [class_Rings_Olinordered__idom(_640607), -(class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(_640607)))], (7194 ^ _224325) ^ [_472276] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _472276), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (2048 ^ _224325) ^ [_290874, _290876, _290878] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_290874), 2051 ^ _224325 : [(2058 ^ _224325) ^ [] : [_290878 = c_Groups_Ozero__class_Ozero(_290874), -(_290876 = c_Groups_Oplus__class_Oplus(_290874, _290876, _290878))], (2052 ^ _224325) ^ [] : [_290876 = c_Groups_Oplus__class_Oplus(_290874, _290876, _290878), -(_290878 = c_Groups_Ozero__class_Ozero(_290874))]]], (10018 ^ _224325) ^ [_570308, _570310, _570312] : [-(_570308 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 10021 ^ _224325 : [(10028 ^ _224325) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _570310, _570312), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _570310), _570308), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _570312), _570308)))], (10022 ^ _224325) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _570310), _570308), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _570312), _570308)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _570310, _570312))]]], (6015 ^ _224325) ^ [_432296, _432298, _432300] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _432296, _432298), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _432296, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _432300, _432298)))], (5411 ^ _224325) ^ [_410352, _410354, _410356] : [class_RealVector_Oreal__normed__div__algebra(_410352), -(c_Groups_Osgn__class_Osgn(_410352, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_410352), _410354), _410356)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_410352), c_Groups_Osgn__class_Osgn(_410352, _410354)), c_Groups_Osgn__class_Osgn(_410352, _410356)))], (11401 ^ _224325) ^ [_623232, _623234] : [-(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _623232, _623234) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _623232, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _623234)))], (7528 ^ _224325) ^ [_483986, _483988, _483990] : [class_Rings_Ocomm__semiring__1(_483986), -(c_Rings_Odvd__class_Odvd(_483986, _483988, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_483986), _483988), _483990)))], (7224 ^ _224325) ^ [] : [-(c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (1230 ^ _224325) ^ [_264885, _264887, _264889] : [class_Orderings_Olinorder(_264885), 1233 ^ _224325 : [(1234 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(_264885, _264887, _264889)), -(c_Orderings_Oord__class_Oless(_264885, _264889, _264887)), -(_264887 = _264889)], (1244 ^ _224325) ^ [] : [1245 ^ _224325 : [(1248 ^ _224325) ^ [] : [_264887 = _264889], (1246 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_264885, _264889, _264887)]], c_Orderings_Oord__class_Oless(_264885, _264887, _264889)]]], (7160 ^ _224325) ^ [_471073] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _471073)))], (11925 ^ _224325) ^ [_638327] : [class_Rings_Olinordered__idom(_638327), -(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(_638327)))], (11199 ^ _224325) ^ [_615893, _615895] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _615893, c_Nat_OSuc(_615895)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _615893, c_Groups_Oone__class_Oone(tc_Nat_Onat)), _615895))], (11527 ^ _224325) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (3103 ^ _224325) ^ [_328786, _328788] : [class_RealVector_Oreal__normed__vector(_328786), -(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_328786, _328788)) = c_RealVector_Onorm__class_Onorm(_328786, _328788))], (7550 ^ _224325) ^ [_484857, _484859, _484861, _484863] : [class_Rings_Ocomm__semiring__1(_484857), c_Rings_Odvd__class_Odvd(_484857, _484859, _484861), -(c_Rings_Odvd__class_Odvd(_484857, _484859, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_484857), _484863), _484861)))], (5925 ^ _224325) ^ [_428587, _428589, _428591] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _428587, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _428589, _428591)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _428589, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _428587, _428591)))], (7604 ^ _224325) ^ [_486823, _486825, _486827, _486829] : [class_Rings_Ocomm__semiring__1(_486823), c_Rings_Odvd__class_Odvd(_486823, _486825, _486827), c_Rings_Odvd__class_Odvd(_486823, _486825, _486829), -(c_Rings_Odvd__class_Odvd(_486823, _486825, c_Groups_Oplus__class_Oplus(_486823, _486827, _486829)))], (10014 ^ _224325) ^ [] : [-(c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (9019 ^ _224325) ^ [_535435] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _535435, c_Groups_Oone__class_Oone(tc_Int_Oint)), -(c_Groups_Oabs__class_Oabs(tc_Int_Oint, _535435) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (11907 ^ _224325) ^ [] : [-(class_Power_Opower(tc_Complex_Ocomplex))], (12183 ^ _224325) ^ [_646497] : [class_Rings_Ocomm__ring(_646497), -(class_Rings_Ocomm__ring(tc_Polynomial_Opoly(_646497)))], (8139 ^ _224325) ^ [_505350, _505352] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _505350, _505352), 8142 ^ _224325 : [(8149 ^ _224325) ^ [] : [_505352 = _505350, -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _505352, _505350))], (8143 ^ _224325) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _505352, _505350), -(_505352 = _505350)]]], (1252 ^ _224325) ^ [_265531, _265533] : [class_Groups_Ozero(_265531), 1255 ^ _224325 : [(1262 ^ _224325) ^ [] : [_265533 = c_Groups_Ozero__class_Ozero(_265531), -(c_Groups_Ozero__class_Ozero(_265531) = _265533)], (1256 ^ _224325) ^ [] : [c_Groups_Ozero__class_Ozero(_265531) = _265533, -(_265533 = c_Groups_Ozero__class_Ozero(_265531))]]], (2602 ^ _224325) ^ [_308899, _308901, _308903] : [class_Orderings_Oorder(_308899), c_Orderings_Oord__class_Oless__eq(_308899, _308901, _308903), 2609 ^ _224325 : [(2616 ^ _224325) ^ [] : [_308903 = _308901, -(c_Orderings_Oord__class_Oless__eq(_308899, _308903, _308901))], (2610 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_308899, _308903, _308901), -(_308903 = _308901)]]], (2546 ^ _224325) ^ [_307129, _307131, _307133, _307135] : [class_Orderings_Oorder(_307129), c_Orderings_Oord__class_Oless__eq(_307129, _307131, _307133), _307131 = _307135, -(c_Orderings_Oord__class_Oless__eq(_307129, _307135, _307133))], (928 ^ _224325) ^ [_253702, _253704, _253706, _253708, _253710, _253712] : [-(c_Polynomial_OpCons(_253712, _253708, _253704) = c_Polynomial_OpCons(_253710, _253706, _253702)), _253712 = _253710, _253708 = _253706, _253704 = _253702], (7644 ^ _224325) ^ [_488195, _488197] : [class_Rings_Ocomm__semiring__1(_488195), c_Rings_Odvd__class_Odvd(_488195, c_Groups_Ozero__class_Ozero(_488195), _488197), -(_488197 = c_Groups_Ozero__class_Ozero(_488195))], (5883 ^ _224325) ^ [_427110, _427112, _427114] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _427110), 5886 ^ _224325 : [(5893 ^ _224325) ^ [] : [_427112 = _427114, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _427110), _427112) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _427110), _427114))], (5887 ^ _224325) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _427110), _427112) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _427110), _427114), -(_427112 = _427114)]]], (11663 ^ _224325) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (5805 ^ _224325) ^ [_424222, _424224] : [class_Rings_Olinordered__idom(_424222), 5808 ^ _224325 : [(5815 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_424222, c_Groups_Ozero__class_Ozero(_424222), _424224), -(c_Groups_Osgn__class_Osgn(_424222, _424224) = c_Groups_Oone__class_Oone(_424222))], (5809 ^ _224325) ^ [] : [c_Groups_Osgn__class_Osgn(_424222, _424224) = c_Groups_Oone__class_Oone(_424222), -(c_Orderings_Oord__class_Oless(_424222, c_Groups_Ozero__class_Ozero(_424222), _424224))]]], (5164 ^ _224325) ^ [_400653, _400655] : [5165 ^ _224325 : [(5166 ^ _224325) ^ [_400728] : [_400655 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _400653, _400728)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _400653, _400655))], (10152 ^ _224325) ^ [_575216] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _575216))], (4947 ^ _224325) ^ [_392888] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _392888))], (3291 ^ _224325) ^ [_335188, _335190] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _335188, _335190)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _335190, _335188))], (11495 ^ _224325) ^ [_626809, _626811] : [class_Groups_Ouminus(_626809), -(class_Groups_Ouminus(tc_fun(_626811, _626809)))], (10258 ^ _224325) ^ [_579141, _579143] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _579141, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _579143)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _579141, _579143))], (3845 ^ _224325) ^ [_354012, _354014, _354016, _354018] : [class_Rings_Olinordered__semiring__strict(_354012), c_Orderings_Oord__class_Oless(_354012, _354014, _354016), c_Orderings_Oord__class_Oless(_354012, c_Groups_Ozero__class_Ozero(_354012), _354018), -(c_Orderings_Oord__class_Oless(_354012, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_354012), _354018), _354014), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_354012), _354018), _354016)))], (5965 ^ _224325) ^ [_430341, _430343, _430345] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _430341, _430343) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _430345, _430343), -(_430341 = _430345)], (11701 ^ _224325) ^ [] : [-(class_Lattices_Oboolean__algebra(tc_HOL_Obool))], (3705 ^ _224325) ^ [_349374, _349376, _349378, _349380] : [class_Rings_Oordered__ring(_349374), c_Orderings_Oord__class_Oless__eq(_349374, _349376, _349378), c_Orderings_Oord__class_Oless__eq(_349374, _349380, c_Groups_Ozero__class_Ozero(_349374)), -(c_Orderings_Oord__class_Oless__eq(_349374, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_349374), _349380), _349378), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_349374), _349380), _349376)))], (11513 ^ _224325) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (5005 ^ _224325) ^ [_395216, _395218] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _395216, _395218), 5008 ^ _224325 : [(5011 ^ _224325) ^ [] : [_395216 = _395218], (5009 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _395216, _395218))]]], (9779 ^ _224325) ^ [_561806, _561808] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _561806, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _561806, _561808))))], (11781 ^ _224325) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal))], (9543 ^ _224325) ^ [_553666] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_553666)], (5201 ^ _224325) ^ [_402128, _402130, _402132] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _402128, _402130), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _402128, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _402132, _402130)))], (564 ^ _224325) ^ [_241339, _241341] : [-(class_Int_Oring__char__0(_241339)), _241341 = _241339, class_Int_Oring__char__0(_241341)], (12051 ^ _224325) ^ [_642317] : [class_Rings_Ocomm__semiring__1(_642317), -(class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(_642317)))], (3369 ^ _224325) ^ [_337896, _337898, _337900] : [class_Rings_Ono__zero__divisors(_337896), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_337896), _337898), _337900) = c_Groups_Ozero__class_Ozero(_337896), -(_337898 = c_Groups_Ozero__class_Ozero(_337896)), -(_337900 = c_Groups_Ozero__class_Ozero(_337896))], (11543 ^ _224325) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (7967 ^ _224325) ^ [_499849, _499851, _499853] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _499849), _499851), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _499849), _499853)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _499849), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _499851, _499853))], (3141 ^ _224325) ^ [_330115, _330117, _330119, _330121] : [class_RealVector_Oreal__normed__vector(_330115), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _330117, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_330115, _330119), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _330117), c_RealVector_Onorm__class_Onorm(_330115, _330121))), -(_330119 = c_Groups_Ozero__class_Ozero(_330115))], (5739 ^ _224325) ^ [_422079, _422081] : [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), _422079), _422081)), 5742 ^ _224325 : [(5745 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _422081))], (5743 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _422079))]]], (5041 ^ _224325) ^ [_396341, _396343] : [-(_396341 = _396343), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _396341, _396343)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _396343, _396341))], (9343 ^ _224325) ^ [_547027, _547029] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _547027, c_Nat_OSuc(_547029)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _547027, _547029)), -(_547027 = _547029)], (12027 ^ _224325) ^ [_641557] : [class_Groups_Ocancel__comm__monoid__add(_641557), -(class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(_641557)))], (7304 ^ _224325) ^ [_476408] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _476408)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _476408))], (5153 ^ _224325) ^ [_400186, _400188] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _400186, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _400186, _400188)))], (3075 ^ _224325) ^ [_327737, _327739] : [class_Groups_Omonoid__mult(_327737), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_327737), c_Groups_Oone__class_Oone(_327737)), _327739) = _327739)], (6948 ^ _224325) ^ [_464212, _464214] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _464214, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _464212)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _464212, _464214), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (1196 ^ _224325) ^ [_263796, _263798] : [class_RealVector_Oreal__normed__vector(_263796), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_263796, _263798), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (5921 ^ _224325) ^ [_428365, _428367] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _428365, _428367) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _428367, _428365))], (11859 ^ _224325) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex))], (594 ^ _224325) ^ [_242224, _242226] : [-(class_Orderings_Oord(_242224)), _242226 = _242224, class_Orderings_Oord(_242226)], (4762 ^ _224325) ^ [_385586, _385588] : [class_RealVector_Oreal__normed__algebra(_385586), 4766 ^ _224325 : [(4769 ^ _224325) ^ [_385885] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_385586, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_385586), _385588), _385885)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_385586, _385885)), 4765 ^ [_385586, _385588])))], (4767 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 4765 ^ [_385586, _385588]))]]], (2981 ^ _224325) ^ [_323591, _323593, _323595, _323597] : [class_Rings_Ocomm__semiring__1(_323591), -(c_Groups_Oplus__class_Oplus(_323591, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_323591), _323593), _323595), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_323591), _323597), _323595)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_323591), c_Groups_Oplus__class_Oplus(_323591, _323593, _323597)), _323595))], (10489 ^ _224325) ^ [_587131] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _587131), 10493 ^ _224325 : [(10496 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _587131, c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(10492 ^ [_587131]))))], (10494 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, 10492 ^ [_587131]), _587131))]]], (9709 ^ _224325) ^ [_559621, _559623] : [-(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _559621, _559623)), 9710 ^ _224325 : [(9717 ^ _224325) ^ [] : [_559621 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _559623 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9711 ^ _224325) ^ [] : [_559621 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _559623 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (9547 ^ _224325) ^ [_553824] : [c_Nat_OSuc(_553824) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (644 ^ _224325) ^ [_243699, _243701] : [-(class_Rings_Ocomm__ring__1(_243699)), _243701 = _243699, class_Rings_Ocomm__ring__1(_243701)], (3949 ^ _224325) ^ [_357433, _357435, _357437] : [class_Rings_Olinordered__semiring__strict(_357433), c_Orderings_Oord__class_Oless(_357433, c_Groups_Ozero__class_Ozero(_357433), _357435), c_Orderings_Oord__class_Oless(_357433, _357437, c_Groups_Ozero__class_Ozero(_357433)), -(c_Orderings_Oord__class_Oless(_357433, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_357433), _357437), _357435), c_Groups_Ozero__class_Ozero(_357433)))], (8479 ^ _224325) ^ [_516332, _516334, _516336] : [class_Rings_Oring__1__no__zero__divisors(_516332), -(_516334 = c_Groups_Ozero__class_Ozero(_516332)), hAPP(hAPP(c_Power_Opower__class_Opower(_516332), _516334), _516336) = c_Groups_Ozero__class_Ozero(_516332)], (7871 ^ _224325) ^ [_496065, _496067, _496069] : [class_RealVector_Oreal__normed__div__algebra(_496065), -(c_RealVector_Onorm__class_Onorm(_496065, hAPP(hAPP(c_Power_Opower__class_Opower(_496065), _496067), _496069)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_496065, _496067)), _496069))], (4295 ^ _224325) ^ [_369002, _369004, _369006, _369008, _369010] : [class_Rings_Olinordered__semiring__strict(_369002), c_Orderings_Oord__class_Oless(_369002, _369004, _369006), c_Orderings_Oord__class_Oless__eq(_369002, _369008, _369010), c_Orderings_Oord__class_Oless__eq(_369002, c_Groups_Ozero__class_Ozero(_369002), _369004), c_Orderings_Oord__class_Oless(_369002, c_Groups_Ozero__class_Ozero(_369002), _369008), -(c_Orderings_Oord__class_Oless(_369002, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_369002), _369004), _369008), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_369002), _369006), _369010)))], (8803 ^ _224325) ^ [_528158, _528160, _528162, _528164] : [class_Rings_Olinordered__semidom(_528158), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _528160, _528162), c_Orderings_Oord__class_Oless__eq(_528158, c_Groups_Oone__class_Oone(_528158), _528164), -(c_Orderings_Oord__class_Oless__eq(_528158, hAPP(hAPP(c_Power_Opower__class_Opower(_528158), _528164), _528160), hAPP(hAPP(c_Power_Opower__class_Opower(_528158), _528164), _528162)))], (8579 ^ _224325) ^ [_520249, _520251, _520253] : [class_Power_Opower(_520249), class_Rings_Omult__zero(_520249), class_Rings_Ono__zero__divisors(_520249), class_Rings_Ozero__neq__one(_520249), 8594 ^ _224325 : [(8603 ^ _224325) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_520249), _520251), _520253) = c_Groups_Ozero__class_Ozero(_520249)), _520251 = c_Groups_Ozero__class_Ozero(_520249), -(_520253 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8595 ^ _224325) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_520249), _520251), _520253) = c_Groups_Ozero__class_Ozero(_520249), 8598 ^ _224325 : [(8601 ^ _224325) ^ [] : [_520253 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (8599 ^ _224325) ^ [] : [-(_520251 = c_Groups_Ozero__class_Ozero(_520249))]]]]], (1026 ^ _224325) ^ [_257204, _257206] : [_257206 = _257204, -(tc_Polynomial_Opoly(_257206) = tc_Polynomial_Opoly(_257204))], (11647 ^ _224325) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (5747 ^ _224325) ^ [_422334, _422336] : [-(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), _422334), _422336))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _422334), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _422336)], (3033 ^ _224325) ^ [_326001, _326003, _326005, _326007] : [class_Rings_Ocomm__semiring__1(_326001), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_326001), _326003), c_Groups_Oplus__class_Oplus(_326001, _326005, _326007)) = c_Groups_Oplus__class_Oplus(_326001, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_326001), _326003), _326005), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_326001), _326003), _326007)))], (6830 ^ _224325) ^ [_460345, _460347] : [class_Rings_Olinordered__idom(_460345), -(_460347 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_460345))), -(c_Polynomial_Opos__poly(_460345, _460347)), -(c_Polynomial_Opos__poly(_460345, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_460345), _460347)))], (8749 ^ _224325) ^ [_526193, _526195, _526197] : [class_Rings_Oring__1(_526193), -(hAPP(hAPP(c_Power_Opower__class_Opower(_526193), c_Groups_Ouminus__class_Ouminus(_526193, _526195)), _526197) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_526193), hAPP(hAPP(c_Power_Opower__class_Opower(_526193), c_Groups_Ouminus__class_Ouminus(_526193, c_Groups_Oone__class_Oone(_526193))), _526197)), hAPP(hAPP(c_Power_Opower__class_Opower(_526193), _526195), _526197)))], (7192 ^ _224325) ^ [] : [-(c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (11553 ^ _224325) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (6340 ^ _224325) ^ [_443993, _443995] : [class_Groups_Oordered__ab__group__add__abs(_443993), -(c_Groups_Oabs__class_Oabs(_443993, c_Groups_Ouminus__class_Ouminus(_443993, _443995)) = c_Groups_Oabs__class_Oabs(_443993, _443995))], (4979 ^ _224325) ^ [_394230, _394232, _394234, _394236] : [class_Rings_Ocomm__semiring__0(_394230), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_394230)), c_Polynomial_OpCons(_394230, _394232, _394234)), _394236) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_394230), c_Polynomial_Osmult(_394230, _394232, _394236), c_Polynomial_OpCons(_394230, c_Groups_Ozero__class_Ozero(_394230), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_394230)), _394234), _394236))))], (294 ^ _224325) ^ [_233374, _233376] : [-(class_Rings_Oring__no__zero__divisors(_233374)), _233376 = _233374, class_Rings_Oring__no__zero__divisors(_233376)], (8613 ^ _224325) ^ [_521232, _521234, _521236, _521238] : [class_Rings_Olinordered__semidom(_521232), c_Orderings_Oord__class_Oless(_521232, c_Groups_Oone__class_Oone(_521232), _521234), 8620 ^ _224325 : [(8627 ^ _224325) ^ [] : [_521236 = _521238, -(hAPP(hAPP(c_Power_Opower__class_Opower(_521232), _521234), _521236) = hAPP(hAPP(c_Power_Opower__class_Opower(_521232), _521234), _521238))], (8621 ^ _224325) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_521232), _521234), _521236) = hAPP(hAPP(c_Power_Opower__class_Opower(_521232), _521234), _521238), -(_521236 = _521238)]]], (10286 ^ _224325) ^ [_580078, _580080, _580082] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _580078), _580078 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _580080, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _580078), _580082)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _580080), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _580082, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (5271 ^ _224325) ^ [_404947, _404949, _404951, _404953] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _404947, _404949), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _404951, _404949) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _404947, _404953), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _404951, _404953))], (3545 ^ _224325) ^ [_344135, _344137, _344139] : [class_Rings_Olinordered__ring__strict(_344135), 3548 ^ _224325 : [(3563 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_344135, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_344135), _344137), _344139), c_Groups_Ozero__class_Ozero(_344135))), 3564 ^ _224325 : [(3571 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_344135, _344137, c_Groups_Ozero__class_Ozero(_344135)), c_Orderings_Oord__class_Oless__eq(_344135, c_Groups_Ozero__class_Ozero(_344135), _344139)], (3565 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_344135, c_Groups_Ozero__class_Ozero(_344135), _344137), c_Orderings_Oord__class_Oless__eq(_344135, _344139, c_Groups_Ozero__class_Ozero(_344135))]]], (3549 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_344135, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_344135), _344137), _344139), c_Groups_Ozero__class_Ozero(_344135)), 3554 ^ _224325 : [(3557 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_344135, _344139, c_Groups_Ozero__class_Ozero(_344135)))], (3555 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_344135, c_Groups_Ozero__class_Ozero(_344135), _344137))]], 3558 ^ _224325 : [(3561 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_344135, c_Groups_Ozero__class_Ozero(_344135), _344139))], (3559 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_344135, _344137, c_Groups_Ozero__class_Ozero(_344135)))]]]]], (5059 ^ _224325) ^ [_396941, _396943] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _396941, _396943), _396941 = _396943], (5517 ^ _224325) ^ [_414199, _414201] : [class_Rings_Olinordered__idom(_414199), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_414199), c_Groups_Osgn__class_Osgn(_414199, _414201)), c_Groups_Oabs__class_Oabs(_414199, _414201)) = _414201)], (3501 ^ _224325) ^ [_342596] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _342596) = _342596)], (904 ^ _224325) ^ [_252827, _252829, _252831, _252833, _252835, _252837] : [-(c_Polynomial_Osmult(_252837, _252833, _252829) = c_Polynomial_Osmult(_252835, _252831, _252827)), _252837 = _252835, _252833 = _252831, _252829 = _252827], (264 ^ _224325) ^ [_232489, _232491] : [-(class_Rings_Oring__1__no__zero__divisors(_232489)), _232491 = _232489, class_Rings_Oring__1__no__zero__divisors(_232491)], (6600 ^ _224325) ^ [_452672, _452674] : [class_Groups_Oordered__ab__group__add(_452672), 6603 ^ _224325 : [(6610 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_452672, _452674, c_Groups_Ozero__class_Ozero(_452672)), -(c_Orderings_Oord__class_Oless(_452672, c_Groups_Ozero__class_Ozero(_452672), c_Groups_Ouminus__class_Ouminus(_452672, _452674)))], (6604 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_452672, c_Groups_Ozero__class_Ozero(_452672), c_Groups_Ouminus__class_Ouminus(_452672, _452674)), -(c_Orderings_Oord__class_Oless(_452672, _452674, c_Groups_Ozero__class_Ozero(_452672)))]]], (11545 ^ _224325) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (5665 ^ _224325) ^ [_419379, _419381, _419383] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _419379), _419381), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _419383), _419381)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _419381), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _419379, _419383))], (134 ^ _224325) ^ [_228654, _228656] : [-(class_RealVector_Oreal__normed__vector(_228654)), _228656 = _228654, class_RealVector_Oreal__normed__vector(_228656)], (11709 ^ _224325) ^ [] : [-(class_Groups_Ouminus(tc_HOL_Obool))], (1406 ^ _224325) ^ [_270170, _270172, _270174] : [class_Groups_Oordered__comm__monoid__add(_270170), c_Orderings_Oord__class_Oless(_270170, c_Groups_Ozero__class_Ozero(_270170), _270172), c_Orderings_Oord__class_Oless(_270170, c_Groups_Ozero__class_Ozero(_270170), _270174), -(c_Orderings_Oord__class_Oless(_270170, c_Groups_Ozero__class_Ozero(_270170), c_Groups_Oplus__class_Oplus(_270170, _270172, _270174)))], (7264 ^ _224325) ^ [_474941, _474943] : [class_Lattices_Oab__semigroup__idem__mult(_474941), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_474941), _474943), _474943) = _474943)], (11078 ^ _224325) ^ [_611117, _611119, _611121, _611123, _611125] : [class_RealVector_Oreal__normed__vector(_611117), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_611117, c_Groups_Ominus__class_Ominus(_611117, c_Groups_Oplus__class_Oplus(_611117, _611119, _611121), c_Groups_Oplus__class_Oplus(_611117, _611123, _611125))), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_611117, c_Groups_Ominus__class_Ominus(_611117, _611119, _611123)), c_RealVector_Onorm__class_Onorm(_611117, c_Groups_Ominus__class_Ominus(_611117, _611121, _611125)))))], (724 ^ _224325) ^ [_246059, _246061] : [-(class_Rings_Oidom(_246059)), _246061 = _246059, class_Rings_Oidom(_246061)], (7534 ^ _224325) ^ [_484232, _484234, _484236] : [class_Rings_Ocomm__semiring__1(_484232), -(c_Rings_Odvd__class_Odvd(_484232, _484234, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_484232), _484236), _484234)))], (7941 ^ _224325) ^ [_498996, _498998] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _498996, _498998), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _498998), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _498996, _498998))], (9299 ^ _224325) ^ [_545569, _545571] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _545569, _545571), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _545569, c_Nat_OSuc(_545571)))], (6258 ^ _224325) ^ [_440642, _440644, _440646] : [class_RealVector_Oreal__normed__algebra(_440642), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_440642), _440644), c_Groups_Ouminus__class_Ouminus(_440642, _440646)) = c_Groups_Ouminus__class_Ouminus(_440642, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_440642), _440644), _440646)))], (9105 ^ _224325) ^ [_538386, _538388] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _538386), _538388) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_538388 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_538386 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (11377 ^ _224325) ^ [_622278, _622280, _622282] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _622278, _622280), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _622282, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _622280, _622282), _622278)))], (5901 ^ _224325) ^ [_427734, _427736] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _427734), _427736), 5904 ^ _224325 : [(5907 ^ _224325) ^ [] : [-(_427736 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (5905 ^ _224325) ^ [] : [-(_427734 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (12273 ^ _224325) ^ [_649347] : [class_Rings_Ocomm__semiring__1(_649347), -(class_Rings_Odvd(tc_Polynomial_Opoly(_649347)))], (9523 ^ _224325) ^ [_552967] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _552967), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _552967))], (4655 ^ _224325) ^ [_380958] : [class_Groups_Ozero(_380958), -(c_Polynomial_OpCons(_380958, c_Groups_Ozero__class_Ozero(_380958), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_380958))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_380958)))], (11501 ^ _224325) ^ [_627021, _627023] : [class_Groups_Ominus(_627021), -(class_Groups_Ominus(tc_fun(_627023, _627021)))], (4211 ^ _224325) ^ [_366194, _366196, _366198, _366200] : [class_Rings_Olinordered__ring__strict(_366194), c_Orderings_Oord__class_Oless(_366194, c_Groups_Ozero__class_Ozero(_366194), _366196), 4218 ^ _224325 : [(4225 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_366194, _366198, _366200), -(c_Orderings_Oord__class_Oless__eq(_366194, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_366194), _366196), _366198), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_366194), _366196), _366200)))], (4219 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_366194, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_366194), _366196), _366198), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_366194), _366196), _366200)), -(c_Orderings_Oord__class_Oless__eq(_366194, _366198, _366200))]]], (8441 ^ _224325) ^ [_514919, _514921] : [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), _514919), _514921)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _514919)), -(_514921 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9487 ^ _224325) ^ [_551766] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _551766), -(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), _551766)))], (1626 ^ _224325) ^ [_277218, _277220, _277222, _277224] : [class_Orderings_Opreorder(_277218), c_Orderings_Oord__class_Oless__eq(_277218, _277220, _277222), c_Orderings_Oord__class_Oless(_277218, _277222, _277224), -(c_Orderings_Oord__class_Oless(_277218, _277220, _277224))], (224 ^ _224325) ^ [_231309, _231311] : [-(class_Groups_Oordered__ab__group__add__abs(_231309)), _231311 = _231309, class_Groups_Oordered__ab__group__add__abs(_231311)], (10888 ^ _224325) ^ [_603622, _603624, _603626, _603628, _603630] : [class_Groups_Oab__group__add(_603622), -(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_603622), c_Polynomial_OpCons(_603622, _603624, _603626), c_Polynomial_OpCons(_603622, _603628, _603630)) = c_Polynomial_OpCons(_603622, c_Groups_Ominus__class_Ominus(_603622, _603624, _603628), c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_603622), _603626, _603630)))], (8489 ^ _224325) ^ [_516695, _516697, _516699, _516701] : [class_Groups_Ocomm__monoid__mult(_516695), -(hAPP(hAPP(c_Power_Opower__class_Opower(_516695), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_516695), _516697), _516699)), _516701) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_516695), hAPP(hAPP(c_Power_Opower__class_Opower(_516695), _516697), _516701)), hAPP(hAPP(c_Power_Opower__class_Opower(_516695), _516699), _516701)))], (11751 ^ _224325) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal))], (11539 ^ _224325) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (11117 ^ _224325) ^ [_612779, _612781] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _612779, _612781)), -(c_Nat__Transfer_Otsub(_612781, _612779) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (2354 ^ _224325) ^ [_300753, _300755] : [class_Groups_Olinordered__ab__group__add(_300753), 2357 ^ _224325 : [(2364 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_300753, _300755, c_Groups_Ozero__class_Ozero(_300753)), -(c_Orderings_Oord__class_Oless__eq(_300753, c_Groups_Oplus__class_Oplus(_300753, _300755, _300755), c_Groups_Ozero__class_Ozero(_300753)))], (2358 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_300753, c_Groups_Oplus__class_Oplus(_300753, _300755, _300755), c_Groups_Ozero__class_Ozero(_300753)), -(c_Orderings_Oord__class_Oless__eq(_300753, _300755, c_Groups_Ozero__class_Ozero(_300753)))]]], (4867 ^ _224325) ^ [_389637] : [class_RealVector_Oreal__normed__algebra(_389637), 4871 ^ _224325 : [(4874 ^ _224325) ^ [_389966, _389968] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_389637, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_389637), _389968), _389966)), 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(_389637, _389968)), c_RealVector_Onorm__class_Onorm(_389637, _389966))), 4870 ^ [_389637])))], (4872 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 4870 ^ [_389637]))]]], (10808 ^ _224325) ^ [_600411, _600413, _600415, _600417] : [class_Rings_Ocomm__ring(_600411), class_Rings_Odvd(_600411), c_Rings_Odvd__class_Odvd(_600411, _600413, _600415), 10819 ^ _224325 : [(10826 ^ _224325) ^ [_601052, _601054] : [c_Rings_Odvd__class_Odvd(_600411, _600413, c_Groups_Oplus__class_Oplus(_600411, c_Groups_Ominus__class_Ominus(_600411, _601054, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_600411), _601052), _600415)), _600417)), -(c_Rings_Odvd__class_Odvd(_600411, _600413, c_Groups_Oplus__class_Oplus(_600411, _601054, _600417)))], (10820 ^ _224325) ^ [_600814, _600816] : [c_Rings_Odvd__class_Odvd(_600411, _600413, c_Groups_Oplus__class_Oplus(_600411, _600816, _600417)), -(c_Rings_Odvd__class_Odvd(_600411, _600413, c_Groups_Oplus__class_Oplus(_600411, c_Groups_Ominus__class_Ominus(_600411, _600816, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_600411), _600814), _600415)), _600417)))]]], (3243 ^ _224325) ^ [_333602, _333604, _333606] : [class_Rings_Olinordered__idom(_333602), c_Orderings_Oord__class_Oless__eq(_333602, c_Groups_Ozero__class_Ozero(_333602), _333604), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_333602), c_Groups_Oabs__class_Oabs(_333602, _333606)), _333604) = c_Groups_Oabs__class_Oabs(_333602, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_333602), _333606), _333604)))], (2757 ^ _224325) ^ [_315237, _315239, _315241, _315243] : [class_Groups_Ocancel__ab__semigroup__add(_315237), c_Groups_Oplus__class_Oplus(_315237, _315239, _315241) = c_Groups_Oplus__class_Oplus(_315237, _315239, _315243), -(_315241 = _315243)], (7084 ^ _224325) ^ [_468720] : [-(_468720 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 7087 ^ _224325 : [(7094 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _468720)), -(c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, _468720) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (7088 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _468720), -(c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, _468720) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))]]], (8993 ^ _224325) ^ [_534612, _534614] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _534612, _534614), c_Rings_Odvd__class_Odvd(tc_Int_Oint, _534614, _534612), -(c_Groups_Oabs__class_Oabs(tc_Int_Oint, _534612) = c_Groups_Oabs__class_Oabs(tc_Int_Oint, _534614))], (6426 ^ _224325) ^ [_447225, _447227, _447229] : [class_Groups_Ogroup__add(_447225), 6429 ^ _224325 : [(6436 ^ _224325) ^ [] : [c_Groups_Ouminus__class_Ouminus(_447225, _447229) = _447227, -(c_Groups_Ouminus__class_Ouminus(_447225, _447227) = _447229)], (6430 ^ _224325) ^ [] : [c_Groups_Ouminus__class_Ouminus(_447225, _447227) = _447229, -(c_Groups_Ouminus__class_Ouminus(_447225, _447229) = _447227)]]], (12189 ^ _224325) ^ [_646687] : [class_Rings_Olinordered__idom(_646687), -(class_Orderings_Oorder(tc_Polynomial_Opoly(_646687)))], (6214 ^ _224325) ^ [_439074, _439076, _439078] : [class_Groups_Oordered__ab__group__add(_439074), 6217 ^ _224325 : [(6224 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_439074, c_Groups_Ouminus__class_Ouminus(_439074, _439078), _439076), -(c_Orderings_Oord__class_Oless(_439074, c_Groups_Ouminus__class_Ouminus(_439074, _439076), _439078))], (6218 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_439074, c_Groups_Ouminus__class_Ouminus(_439074, _439076), _439078), -(c_Orderings_Oord__class_Oless(_439074, c_Groups_Ouminus__class_Ouminus(_439074, _439078), _439076))]]], (1145 ^ _224325) ^ [_261854, _261856] : [class_Rings_Ocomm__semiring__1(_261854), -(c_Groups_Oplus__class_Oplus(_261854, _261856, _261856) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_261854), c_Groups_Oplus__class_Oplus(_261854, c_Groups_Oone__class_Oone(_261854), c_Groups_Oone__class_Oone(_261854))), _261856))], (792 ^ _224325) ^ [_248619, _248621, _248623, _248625, _248627, _248629] : [-(c_Polynomial_Opcompose(_248629, _248625, _248621) = c_Polynomial_Opcompose(_248627, _248623, _248619)), _248629 = _248627, _248625 = _248623, _248621 = _248619], (5949 ^ _224325) ^ [_429566, _429568, _429570] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _429566), _429568)), _429570) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _429566), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _429568), _429570)))], (12135 ^ _224325) ^ [_644977] : [class_Rings_Olinordered__idom(_644977), -(class_Orderings_Opreorder(tc_Polynomial_Opoly(_644977)))], (11713 ^ _224325) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal))], (8395 ^ _224325) ^ [_513249, _513251] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _513249, _513251), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _513251, _513249)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _513251, _513249), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _513249, _513251))], (3139 ^ _224325) ^ [_329972] : [-(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, _329972))))], (4889 ^ _224325) ^ [_390712, _390714, _390716] : [class_Rings_Olinordered__idom(_390712), c_Polynomial_Opos__poly(_390712, _390714), c_Polynomial_Opos__poly(_390712, _390716), -(c_Polynomial_Opos__poly(_390712, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_390712)), _390714), _390716)))], (11897 ^ _224325) ^ [] : [-(class_Rings_Osemiring(tc_Complex_Ocomplex))], (7446 ^ _224325) ^ [_481358, _481360] : [class_Rings_Ocomm__semiring__1(_481358), -(c_Rings_Odvd__class_Odvd(_481358, _481360, c_Groups_Ozero__class_Ozero(_481358)))], (4099 ^ _224325) ^ [_362321] : [class_Rings_Olinordered__semidom(_362321), c_Orderings_Oord__class_Oless__eq(_362321, c_Groups_Oone__class_Oone(_362321), c_Groups_Ozero__class_Ozero(_362321))], (9505 ^ _224325) ^ [_552414] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oabs__class_Oabs(tc_Int_Oint, _552414), c_Groups_Oone__class_Oone(tc_Int_Oint)), -(_552414 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (6642 ^ _224325) ^ [_454011, _454013] : [class_Groups_Oab__group__add(_454011), -(c_Groups_Oplus__class_Oplus(_454011, c_Groups_Ouminus__class_Ouminus(_454011, _454013), _454013) = c_Groups_Ozero__class_Ozero(_454011))], (4273 ^ _224325) ^ [_368280, _368282, _368284, _368286, _368288] : [class_Rings_Olinordered__semiring__strict(_368280), c_Orderings_Oord__class_Oless(_368280, _368282, _368284), c_Orderings_Oord__class_Oless(_368280, _368286, _368288), c_Orderings_Oord__class_Oless__eq(_368280, c_Groups_Ozero__class_Ozero(_368280), _368282), c_Orderings_Oord__class_Oless__eq(_368280, c_Groups_Ozero__class_Ozero(_368280), _368286), -(c_Orderings_Oord__class_Oless(_368280, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_368280), _368282), _368286), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_368280), _368284), _368288)))], (11625 ^ _224325) ^ [] : [-(class_Rings_Odvd(tc_Int_Oint))], (11931 ^ _224325) ^ [_638517] : [class_Rings_Olinordered__idom(_638517), -(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(_638517)))], (3477 ^ _224325) ^ [_341808, _341810, _341812] : [-(_341808 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 3480 ^ _224325 : [(3487 ^ _224325) ^ [] : [_341810 = _341812, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _341808), _341810) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _341808), _341812))], (3481 ^ _224325) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _341808), _341810) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _341808), _341812), -(_341810 = _341812)]]], (1184 ^ _224325) ^ [_263364, _263366] : [class_Orderings_Opreorder(_263364), c_Orderings_Oord__class_Oless(_263364, _263366, _263366)], (2224 ^ _224325) ^ [_296613, _296615] : [class_RealVector_Oreal__normed__vector(_296613), 2227 ^ _224325 : [(2234 ^ _224325) ^ [] : [_296615 = c_Groups_Ozero__class_Ozero(_296613), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_296613, _296615), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (2228 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_296613, _296615), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(_296615 = c_Groups_Ozero__class_Ozero(_296613))]]], (3461 ^ _224325) ^ [_341279, _341281, _341283] : [-(_341279 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 3464 ^ _224325 : [(3471 ^ _224325) ^ [] : [_341281 = _341283, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _341281), _341279) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _341283), _341279))], (3465 ^ _224325) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _341281), _341279) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _341283), _341279), -(_341281 = _341283)]]], (6978 ^ _224325) ^ [_465280] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _465280, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _465280) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _465280))], (4231 ^ _224325) ^ [_366869, _366871, _366873, _366875] : [class_Rings_Olinordered__ring__strict(_366869), c_Orderings_Oord__class_Oless(_366869, _366871, c_Groups_Ozero__class_Ozero(_366869)), 4238 ^ _224325 : [(4245 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_366869, _366875, _366873), -(c_Orderings_Oord__class_Oless__eq(_366869, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_366869), _366871), _366873), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_366869), _366871), _366875)))], (4239 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_366869, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_366869), _366871), _366873), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_366869), _366871), _366875)), -(c_Orderings_Oord__class_Oless__eq(_366869, _366875, _366873))]]], (5649 ^ _224325) ^ [_418784, _418786, _418788] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _418784, _418786), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _418788), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _418784), _418788), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _418786), _418788)))], (4123 ^ _224325) ^ [_363143, _363145, _363147] : [class_Rings_Olinordered__semidom(_363143), c_Orderings_Oord__class_Oless(_363143, c_Groups_Oone__class_Oone(_363143), _363145), c_Orderings_Oord__class_Oless(_363143, c_Groups_Oone__class_Oone(_363143), _363147), -(c_Orderings_Oord__class_Oless(_363143, c_Groups_Oone__class_Oone(_363143), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_363143), _363145), _363147)))], (5511 ^ _224325) ^ [_413963, _413965] : [class_Rings_Olinordered__idom(_413963), -(c_Groups_Oabs__class_Oabs(_413963, _413965) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_413963), _413965), c_Groups_Osgn__class_Osgn(_413963, _413965)))], (3741 ^ _224325) ^ [_350594, _350596, _350598, _350600, _350602] : [class_Rings_Oordered__semiring(_350594), c_Orderings_Oord__class_Oless__eq(_350594, _350596, _350598), c_Orderings_Oord__class_Oless__eq(_350594, _350600, _350602), c_Orderings_Oord__class_Oless__eq(_350594, c_Groups_Ozero__class_Ozero(_350594), _350598), c_Orderings_Oord__class_Oless__eq(_350594, c_Groups_Ozero__class_Ozero(_350594), _350600), -(c_Orderings_Oord__class_Oless__eq(_350594, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_350594), _350596), _350600), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_350594), _350598), _350602)))], (12213 ^ _224325) ^ [_647447] : [class_Groups_Oab__group__add(_647447), -(class_Groups_Ouminus(tc_Polynomial_Opoly(_647447)))], (3155 ^ _224325) ^ [_330617, _330619, _330621, _330623, _330625, _330627] : [class_Rings_Olinordered__semiring__1(_330617), c_Orderings_Oord__class_Oless__eq(_330617, _330619, _330621), c_Orderings_Oord__class_Oless__eq(_330617, _330623, _330621), c_Orderings_Oord__class_Oless__eq(_330617, c_Groups_Ozero__class_Ozero(_330617), _330625), c_Orderings_Oord__class_Oless__eq(_330617, c_Groups_Ozero__class_Ozero(_330617), _330627), c_Groups_Oplus__class_Oplus(_330617, _330625, _330627) = c_Groups_Oone__class_Oone(_330617), -(c_Orderings_Oord__class_Oless__eq(_330617, c_Groups_Oplus__class_Oplus(_330617, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_330617), _330625), _330619), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_330617), _330627), _330623)), _330621))], (6292 ^ _224325) ^ [_441895, _441897, _441899] : [class_Rings_Oring(_441895), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_441895), c_Groups_Ouminus__class_Ouminus(_441895, _441897)), c_Groups_Ouminus__class_Ouminus(_441895, _441899)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_441895), _441897), _441899))], (11791 ^ _224325) ^ [] : [-(class_Rings_Oordered__ring(tc_RealDef_Oreal))], (7106 ^ _224325) ^ [_469359] : [-(_469359 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 7109 ^ _224325 : [(7116 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _469359)), -(c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, _469359) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (7110 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _469359), -(c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, _469359) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))]]], (6954 ^ _224325) ^ [_464471, _464473] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _464471, _464473)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _464471), _464473))], (9621 ^ _224325) ^ [_556517, _556519, _556521] : [class_Groups_Omonoid__mult(_556517), -(hAPP(hAPP(c_Power_Opower__class_Opower(_556517), _556519), c_Nat_OSuc(_556521)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_556517), hAPP(hAPP(c_Power_Opower__class_Opower(_556517), _556519), _556521)), _556519))], (8783 ^ _224325) ^ [_527483, _527485, _527487, _527489] : [class_Rings_Olinordered__semidom(_527483), c_Orderings_Oord__class_Oless(_527483, c_Groups_Oone__class_Oone(_527483), _527485), 8790 ^ _224325 : [(8797 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _527487, _527489), -(c_Orderings_Oord__class_Oless(_527483, hAPP(hAPP(c_Power_Opower__class_Opower(_527483), _527485), _527487), hAPP(hAPP(c_Power_Opower__class_Opower(_527483), _527485), _527489)))], (8791 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_527483, hAPP(hAPP(c_Power_Opower__class_Opower(_527483), _527485), _527487), hAPP(hAPP(c_Power_Opower__class_Opower(_527483), _527485), _527489)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _527487, _527489))]]], (6654 ^ _224325) ^ [_454477, _454479, _454481] : [class_Groups_Ogroup__add(_454477), 6657 ^ _224325 : [(6664 ^ _224325) ^ [] : [c_Groups_Oplus__class_Oplus(_454477, _454479, _454481) = c_Groups_Ozero__class_Ozero(_454477), -(_454479 = c_Groups_Ouminus__class_Ouminus(_454477, _454481))], (6658 ^ _224325) ^ [] : [_454479 = c_Groups_Ouminus__class_Ouminus(_454477, _454481), -(c_Groups_Oplus__class_Oplus(_454477, _454479, _454481) = c_Groups_Ozero__class_Ozero(_454477))]]], (5155 ^ _224325) ^ [_400271] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _400271, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _400271), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _400271), _400271))))], (9537 ^ _224325) ^ [_553448] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _553448) = _553448)], (7226 ^ _224325) ^ [_473507] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _473507, c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatceiling(_473507))))], (10252 ^ _224325) ^ [_578969, _578971] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _578969, _578971), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _578969, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _578971)))], (3181 ^ _224325) ^ [_331414] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _331414), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _331414)], (6648 ^ _224325) ^ [_454237, _454239] : [class_Groups_Ogroup__add(_454237), -(c_Groups_Oplus__class_Oplus(_454237, c_Groups_Ouminus__class_Ouminus(_454237, _454239), _454239) = c_Groups_Ozero__class_Ozero(_454237))], (7384 ^ _224325) ^ [_479061, _479063] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _479061), -(c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _479061, c_RealDef_Oreal(tc_Nat_Onat, _479063))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatfloor(_479061), _479063))], (11853 ^ _224325) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex))], (11759 ^ _224325) ^ [] : [-(class_Rings_Olinordered__semiring(tc_RealDef_Oreal))], (3289 ^ _224325) ^ [_335080] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _335080, _335080))], (10034 ^ _224325) ^ [_570843, _570845, _570847] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _570843), _570845), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _570847), _570845)), -(_570845 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _570843, _570847))], (6488 ^ _224325) ^ [_449301, _449303] : [class_Groups_Olinordered__ab__group__add(_449301), 6491 ^ _224325 : [(6498 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_449301, c_Groups_Ozero__class_Ozero(_449301), _449303), -(c_Orderings_Oord__class_Oless__eq(_449301, c_Groups_Ouminus__class_Ouminus(_449301, _449303), _449303))], (6492 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_449301, c_Groups_Ouminus__class_Ouminus(_449301, _449303), _449303), -(c_Orderings_Oord__class_Oless__eq(_449301, c_Groups_Ozero__class_Ozero(_449301), _449303))]]], (6732 ^ _224325) ^ [_457026, _457028, _457030] : [class_Groups_Oordered__ab__group__add__abs(_457026), c_Orderings_Oord__class_Oless__eq(_457026, _457028, _457030), c_Orderings_Oord__class_Oless__eq(_457026, c_Groups_Ouminus__class_Ouminus(_457026, _457028), _457030), -(c_Orderings_Oord__class_Oless__eq(_457026, c_Groups_Oabs__class_Oabs(_457026, _457028), _457030))], (6584 ^ _224325) ^ [_452187, _452189] : [class_Groups_Oordered__ab__group__add(_452187), 6587 ^ _224325 : [(6594 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_452187, c_Groups_Ozero__class_Ozero(_452187), _452189), -(c_Orderings_Oord__class_Oless(_452187, c_Groups_Ouminus__class_Ouminus(_452187, _452189), c_Groups_Ozero__class_Ozero(_452187)))], (6588 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_452187, c_Groups_Ouminus__class_Ouminus(_452187, _452189), c_Groups_Ozero__class_Ozero(_452187)), -(c_Orderings_Oord__class_Oless(_452187, c_Groups_Ozero__class_Ozero(_452187), _452189))]]], (4085 ^ _224325) ^ [_361903, _361905, _361907, _361909] : [class_Rings_Olinordered__semidom(_361903), c_Orderings_Oord__class_Oless(_361903, c_Groups_Ozero__class_Ozero(_361903), _361905), c_Orderings_Oord__class_Oless(_361903, _361907, _361909), -(c_Orderings_Oord__class_Oless(_361903, _361907, c_Groups_Oplus__class_Oplus(_361903, _361905, _361909)))], (2134 ^ _224325) ^ [_293717] : [class_Groups_Oordered__ab__group__add__abs(_293717), -(c_Groups_Oabs__class_Oabs(_293717, c_Groups_Ozero__class_Ozero(_293717)) = c_Groups_Ozero__class_Ozero(_293717))], (8413 ^ _224325) ^ [_513955, _513957] : [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, _513955)), _513957)), _513955 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_513957 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9670 ^ _224325) ^ [_558352] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _558352), -(_558352 = c_Nat_OSuc(9673 ^ [_558352]))], (5089 ^ _224325) ^ [_397976, _397978, _397980] : [5090 ^ _224325 : [(5093 ^ _224325) ^ [] : [hBOOL(hAPP(hAPP(_397980, _397978), _397976))], (5091 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _397976, _397978))]], 5096 ^ _224325 : [(5099 ^ _224325) ^ [] : [hBOOL(hAPP(hAPP(_397980, _397978), _397976))], (5097 ^ _224325) ^ [] : [-(_397976 = _397978)]], 5102 ^ _224325 : [(5105 ^ _224325) ^ [] : [hBOOL(hAPP(hAPP(_397980, _397978), _397976))], (5103 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _397978, _397976))]], -(hBOOL(hAPP(hAPP(_397980, _397978), _397976)))], (2430 ^ _224325) ^ [_303182, _303184] : [class_Groups_Oordered__ab__group__add__abs(_303182), -(c_Orderings_Oord__class_Oless__eq(_303182, c_Groups_Ozero__class_Ozero(_303182), c_Groups_Oabs__class_Oabs(_303182, _303184)))], (11811 ^ _224325) ^ [] : [-(class_Orderings_Oorder(tc_RealDef_Oreal))], (5115 ^ _224325) ^ [_398879, _398881] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _398879, _398881), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _398881, _398879), -(_398879 = _398881)], (3963 ^ _224325) ^ [_357881, _357883, _357885] : [class_Rings_Olinordered__semiring__strict(_357881), c_Orderings_Oord__class_Oless(_357881, c_Groups_Ozero__class_Ozero(_357881), _357883), c_Orderings_Oord__class_Oless(_357881, _357885, c_Groups_Ozero__class_Ozero(_357881)), -(c_Orderings_Oord__class_Oless(_357881, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_357881), _357883), _357885), c_Groups_Ozero__class_Ozero(_357881)))], (7004 ^ _224325) ^ [_466247] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_466247), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _466247, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (9003 ^ _224325) ^ [_534927, _534929] : [-(_534927 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 9006 ^ _224325 : [(9013 ^ _224325) ^ [] : [c_Groups_Oabs__class_Oabs(tc_Int_Oint, _534929) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _534927), _534929), _534927))], (9007 ^ _224325) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _534927), _534929), _534927), -(c_Groups_Oabs__class_Oabs(tc_Int_Oint, _534929) = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (2959 ^ _224325) ^ [_322761, _322763, _322765, _322767, _322769] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_322761), 2962 ^ _224325 : [(2963 ^ _224325) ^ [] : [c_Groups_Oplus__class_Oplus(_322761, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_322761), _322763), _322765), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_322761), _322767), _322769)) = c_Groups_Oplus__class_Oplus(_322761, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_322761), _322763), _322769), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_322761), _322767), _322765)), -(_322763 = _322767), -(_322765 = _322769)], (2973 ^ _224325) ^ [] : [2974 ^ _224325 : [(2977 ^ _224325) ^ [] : [_322765 = _322769], (2975 ^ _224325) ^ [] : [_322763 = _322767]], -(c_Groups_Oplus__class_Oplus(_322761, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_322761), _322763), _322765), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_322761), _322767), _322769)) = c_Groups_Oplus__class_Oplus(_322761, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_322761), _322763), _322769), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_322761), _322767), _322765)))]]], (9361 ^ _224325) ^ [_547610, _547612] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _547610, _547612)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _547612, c_Nat_OSuc(_547610)))], (3691 ^ _224325) ^ [_348890, _348892, _348894, _348896] : [class_Rings_Oordered__ring(_348890), c_Orderings_Oord__class_Oless__eq(_348890, _348892, _348894), c_Orderings_Oord__class_Oless__eq(_348890, _348896, c_Groups_Ozero__class_Ozero(_348890)), -(c_Orderings_Oord__class_Oless__eq(_348890, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_348890), _348894), _348896), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_348890), _348892), _348896)))], (8689 ^ _224325) ^ [_524124, _524126, _524128, _524130] : [class_Rings_Olinordered__semidom(_524124), c_Orderings_Oord__class_Oless(_524124, hAPP(hAPP(c_Power_Opower__class_Opower(_524124), _524126), _524128), hAPP(hAPP(c_Power_Opower__class_Opower(_524124), _524130), _524128)), c_Orderings_Oord__class_Oless__eq(_524124, c_Groups_Ozero__class_Ozero(_524124), _524130), -(c_Orderings_Oord__class_Oless(_524124, _524126, _524130))], (3297 ^ _224325) ^ [_335417, _335419, _335421] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _335417, _335419), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _335419, _335421), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _335417, _335421))], (11747 ^ _224325) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal))], (8659 ^ _224325) ^ [_522971, _522973, _522975, _522977, _522979] : [class_Rings_Ocomm__semiring__1(_522971), c_Rings_Odvd__class_Odvd(_522971, _522973, _522975), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _522977, _522979), -(c_Rings_Odvd__class_Odvd(_522971, hAPP(hAPP(c_Power_Opower__class_Opower(_522971), _522973), _522977), hAPP(hAPP(c_Power_Opower__class_Opower(_522971), _522975), _522979)))], (11705 ^ _224325) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (5081 ^ _224325) ^ [_397674, _397676] : [5082 ^ _224325 : [(5085 ^ _224325) ^ [] : [_397674 = _397676], (5083 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _397674, _397676)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _397674, _397676))], (4117 ^ _224325) ^ [_362916] : [class_Rings_Olinordered__semidom(_362916), c_Orderings_Oord__class_Oless(_362916, c_Groups_Oone__class_Oone(_362916), c_Groups_Ozero__class_Ozero(_362916))], (5627 ^ _224325) ^ [_418004, _418006] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _418004, _418006) = _418004, -(_418006 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11651 ^ _224325) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (5147 ^ _224325) ^ [_399909] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _399909, _399909))], (10464 ^ _224325) ^ [_586053, _586055, _586057, _586059] : [-(hAPP(hAPP(c_Power_Opower_Opower(_586053, _586055, _586057), _586059), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _586055)], (9824 ^ _224325) ^ [_563446, _563448] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _563446, _563448), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _563446, c_Nat_OSuc(_563448)))], (6092 ^ _224325) ^ [_435250, _435252] : [class_Groups_Olinordered__ab__group__add(_435250), 6095 ^ _224325 : [(6102 ^ _224325) ^ [] : [_435252 = c_Groups_Ozero__class_Ozero(_435250), -(_435252 = c_Groups_Ouminus__class_Ouminus(_435250, _435252))], (6096 ^ _224325) ^ [] : [_435252 = c_Groups_Ouminus__class_Ouminus(_435250, _435252), -(_435252 = c_Groups_Ozero__class_Ozero(_435250))]]], (11869 ^ _224325) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex))], (5737 ^ _224325) ^ [_421942] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _421942, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10648 ^ _224325) ^ [_593831, _593833, _593835] : [class_Groups_Oordered__ab__group__add__abs(_593831), -(c_Orderings_Oord__class_Oless__eq(_593831, c_Groups_Ominus__class_Ominus(_593831, c_Groups_Oabs__class_Oabs(_593831, _593833), c_Groups_Oabs__class_Oabs(_593831, _593835)), c_Groups_Oabs__class_Oabs(_593831, c_Groups_Ominus__class_Ominus(_593831, _593835, _593833))))], (1840 ^ _224325) ^ [_283793, _283795, _283797] : [class_Orderings_Opreorder(_283793), 1843 ^ _224325 : [(1852 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(_283793, _283795, _283797)), c_Orderings_Oord__class_Oless__eq(_283793, _283795, _283797), -(c_Orderings_Oord__class_Oless__eq(_283793, _283797, _283795))], (1844 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_283793, _283795, _283797), 1847 ^ _224325 : [(1850 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_283793, _283797, _283795)], (1848 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_283793, _283795, _283797))]]]]], (866 ^ _224325) ^ [_251408, _251410, _251412, _251414] : [-(c_Groups_Osgn__class_Osgn(_251414, _251410) = c_Groups_Osgn__class_Osgn(_251412, _251408)), _251414 = _251412, _251410 = _251408], (11561 ^ _224325) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (5827 ^ _224325) ^ [_425046, _425048, _425050] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _425046), 5830 ^ _224325 : [(5837 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _425048, _425050), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _425046), _425048), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _425046), _425050)))], (5831 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _425046), _425048), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _425046), _425050)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _425048, _425050))]]], (10270 ^ _224325) ^ [_579564, _579566] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _579564), _579566), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _579564, _579566))], (2030 ^ _224325) ^ [_290164, _290166] : [class_RealVector_Oreal__normed__algebra(_290164), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_290164), c_Groups_Ozero__class_Ozero(_290164)), _290166) = c_Groups_Ozero__class_Ozero(_290164))], (4713 ^ _224325) ^ [_383278, _383280] : [class_Rings_Ocomm__semiring__1(_383278), -(hAPP(c_Polynomial_Opoly(_383278, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_383278))), _383280) = c_Groups_Oone__class_Oone(_383278))], (9183 ^ _224325) ^ [_541165, _541167] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _541165, c_Nat_OSuc(_541167)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _541165, _541167)), -(_541165 = c_Nat_OSuc(_541167))], (484 ^ _224325) ^ [_238979, _238981] : [-(class_Orderings_Olinorder(_238979)), _238981 = _238979, class_Orderings_Olinorder(_238981)], (9609 ^ _224325) ^ [_555957, _555959, _555961] : [class_Rings_Ocomm__semiring__1(_555957), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_555957), _555959), hAPP(hAPP(c_Power_Opower__class_Opower(_555957), _555959), _555961)) = hAPP(hAPP(c_Power_Opower__class_Opower(_555957), _555959), c_Nat_OSuc(_555961)))], (9279 ^ _224325) ^ [_544936, _544938, _544940] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _544936, _544938), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _544938, _544940), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_544936), _544940))], (8167 ^ _224325) ^ [_506197, _506199] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _506197, _506199), -(_506197 = _506199), 8174 ^ _224325 : [(8177 ^ _224325) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _506199, _506197)], (8175 ^ _224325) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _506197, _506199))]]], (1750 ^ _224325) ^ [_281048, _281050, _281052] : [class_Orderings_Oorder(_281048), -(_281050 = _281052), c_Orderings_Oord__class_Oless__eq(_281048, _281052, _281050), -(c_Orderings_Oord__class_Oless(_281048, _281052, _281050))], (1056 ^ _224325) ^ [_258297, _258299] : [_258299 = _258297, -(c_Groups_Oone__class_Oone(_258299) = c_Groups_Oone__class_Oone(_258297))], (11821 ^ _224325) ^ [] : [-(class_Groups_Osgn__if(tc_RealDef_Oreal))], (9443 ^ _224325) ^ [_550343, _550345] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _550343, _550345), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _550343, c_Groups_Oone__class_Oone(tc_Int_Oint)), _550345))], (3307 ^ _224325) ^ [_335732, _335734] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _335732, _335734), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _335734, _335732), -(_335732 = _335734)], (4744 ^ _224325) ^ [_384659] : [class_RealVector_Oreal__normed__algebra(_384659), 4748 ^ _224325 : [(4751 ^ _224325) ^ [_384988, _384990] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_384659, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_384659), _384990), _384988)), 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(_384659, _384990)), c_RealVector_Onorm__class_Onorm(_384659, _384988))), 4747 ^ [_384659])))], (4749 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 4747 ^ [_384659]))]]], (964 ^ _224325) ^ [_254957, _254959] : [_254959 = _254957, -(c_Groups_Ozero__class_Ozero(_254959) = c_Groups_Ozero__class_Ozero(_254957))], (11631 ^ _224325) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (4079 ^ _224325) ^ [_361644, _361646] : [class_Rings_Olinordered__ring(_361644), c_Orderings_Oord__class_Oless(_361644, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_361644), _361646), _361646), c_Groups_Ozero__class_Ozero(_361644))], (11887 ^ _224325) ^ [] : [-(class_Rings_Osemiring__0(tc_Complex_Ocomplex))], (11801 ^ _224325) ^ [] : [-(class_Groups_Omonoid__add(tc_RealDef_Oreal))], (11839 ^ _224325) ^ [] : [-(class_Groups_Oone(tc_RealDef_Oreal))], (3447 ^ _224325) ^ [_340773, _340775] : [3448 ^ _224325 : [(3451 ^ _224325) ^ [] : [_340773 = _340775], (3449 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _340773, _340775)]], -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _340773, _340775))], (10216 ^ _224325) ^ [_577566, _577568, _577570] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _577566, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _577568, _577570)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _577568, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _577566, _577570)))], (7124 ^ _224325) ^ [_469918, _469920] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _469918), _469920), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _469920, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _469918), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_RComplete_Onatceiling(_469920) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _469918, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (11072 ^ _224325) ^ [_610851, _610853] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _610851, _610853), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _610851, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _610853, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (11937 ^ _224325) ^ [_638707] : [class_Rings_Olinordered__idom(_638707), -(class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(_638707)))], (9790 ^ _224325) ^ [_562291, _562293] : [9791 ^ _224325 : [(9792 ^ _224325) ^ [_562368] : [_562293 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _562291, _562368))]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _562291, _562293))], (1798 ^ _224325) ^ [_282479, _282481, _282483] : [class_Orderings_Olinorder(_282479), -(c_Orderings_Oord__class_Oless__eq(_282479, _282481, _282483)), -(c_Orderings_Oord__class_Oless(_282479, _282483, _282481))], (5141 ^ _224325) ^ [_399723, _399725] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _399723, _399725)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _399725, _399723))], (4193 ^ _224325) ^ [_365564, _365566] : [c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _365564), _365564), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _365566), _365566)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 4196 ^ _224325 : [(4199 ^ _224325) ^ [] : [-(_365566 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (4197 ^ _224325) ^ [] : [-(_365564 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))]]], (454 ^ _224325) ^ [_238094, _238096] : [-(class_Rings_Ozero__neq__one(_238094)), _238096 = _238094, class_Rings_Ozero__neq__one(_238096)], (5315 ^ _224325) ^ [_406620, _406622, _406624] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _406622, _406624), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _406620, _406622), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _406620, _406624)))], (10240 ^ _224325) ^ [_578451, _578453] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _578451, _578453)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _578453, _578451))], (9139 ^ _224325) ^ [_539581, _539583] : [_539581 = _539583, -(c_Nat_OSuc(_539581) = c_Nat_OSuc(_539583))], (9783 ^ _224325) ^ [_562052, _562054] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _562052, _562054), -(_562054 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _562052, 9786 ^ [_562052, _562054])))], (10998 ^ _224325) ^ [_607886, _607888, _607890, _607892] : [class_RealVector_Oreal__normed__algebra(_607886), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_607886), c_Groups_Ominus__class_Ominus(_607886, _607888, _607890)), _607892) = c_Groups_Ominus__class_Ominus(_607886, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_607886), _607888), _607892), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_607886), _607890), _607892)))], (7933 ^ _224325) ^ [_498674, _498676, _498678] : [7934 ^ _224325 : [(7937 ^ _224325) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _498676, _498678)], (7935 ^ _224325) ^ [] : [_498674 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _498674), _498676), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _498674), _498678)))], (11645 ^ _224325) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (11657 ^ _224325) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (11743 ^ _224325) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal))], (8063 ^ _224325) ^ [_502951, _502953] : [-(_502951 = _502953), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _502951, _502953), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _502953, _502951)], (12003 ^ _224325) ^ [_640797] : [class_Rings_Oidom(_640797), -(class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(_640797)))], (5321 ^ _224325) ^ [_406842, _406844] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _406842, _406844), _406844)], (10410 ^ _224325) ^ [_584195, _584197] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _584195), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _584197), -(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), _584195), _584197)))], (5821 ^ _224325) ^ [_424732, _424734, _424736, _424738] : [class_Rings_Ocomm__semiring__0(_424732), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_424732)), _424734), c_Polynomial_OpCons(_424732, _424736, _424738)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_424732), c_Polynomial_Osmult(_424732, _424736, _424734), c_Polynomial_OpCons(_424732, c_Groups_Ozero__class_Ozero(_424732), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_424732)), _424734), _424738))))], (11739 ^ _224325) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal))], (7624 ^ _224325) ^ [_487493, _487495, _487497, _487499] : [class_Rings_Ocomm__semiring__1(_487493), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_487493), c_Polynomial_Osmult(_487493, _487495, _487497), _487499), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_487493), _487497, _487499))], (1002 ^ _224325) ^ [_256385, _256387, _256389, _256391, _256393, _256395] : [-(c_Groups_Ominus__class_Ominus(_256395, _256391, _256387) = c_Groups_Ominus__class_Ominus(_256393, _256389, _256385)), _256395 = _256393, _256391 = _256389, _256387 = _256385], (10944 ^ _224325) ^ [_605700, _605702] : [class_Groups_Ogroup__add(_605700), -(c_Groups_Ominus__class_Ominus(_605700, _605702, c_Groups_Ozero__class_Ozero(_605700)) = _605702)], (824 ^ _224325) ^ [_249880, _249882, _249884, _249886, _249888, _249890, _249892, _249894, _249896, _249898] : [-(c_Polynomial_Opoly__rec(_249898, _249894, _249890, _249886, _249882) = c_Polynomial_Opoly__rec(_249896, _249892, _249888, _249884, _249880)), _249898 = _249896, _249894 = _249892, _249890 = _249888, _249886 = _249884, _249882 = _249880], (4707 ^ _224325) ^ [_383002, _383004, _383006, _383008] : [class_Rings_Ocomm__semiring__0(_383002), -(hAPP(c_Polynomial_Opoly(_383002, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_383002), _383004, _383006)), _383008) = c_Groups_Oplus__class_Oplus(_383002, hAPP(c_Polynomial_Opoly(_383002, _383004), _383008), hAPP(c_Polynomial_Opoly(_383002, _383006), _383008)))], (9499 ^ _224325) ^ [_552173] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _552173, 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), _552173), _552173), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (9133 ^ _224325) ^ [_539411, _539413] : [c_Nat_OSuc(_539411) = c_Nat_OSuc(_539413), -(_539411 = _539413)], (11090 ^ _224325) ^ [_611739, _611741, _611743, _611745] : [class_RealVector_Oreal__normed__vector(_611739), class_Orderings_Oord(_611741), 11100 ^ _224325 : [(11103 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_611739, c_Groups_Ominus__class_Ominus(_611739, hAPP(_611745, _611743), hAPP(_611745, 11099 ^ [_611739, _611741, _611743, _611745]))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (11101 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_611741, _611743, 11099 ^ [_611739, _611741, _611743, _611745]))]], 11104 ^ _224325 : [(11105 ^ _224325) ^ [_612297] : [c_Orderings_Oord__class_Oless__eq(_611741, _611743, _612297), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_611739, hAPP(_611745, _612297)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_611739, hAPP(_611745, _611743)))))]]], (12153 ^ _224325) ^ [_645547] : [class_Rings_Ocomm__ring__1(_645547), -(class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(_645547)))], (2082 ^ _224325) ^ [_292026, _292028] : [class_Groups_Olinordered__ab__group__add(_292026), 2085 ^ _224325 : [(2092 ^ _224325) ^ [] : [_292028 = c_Groups_Ozero__class_Ozero(_292026), -(c_Groups_Ozero__class_Ozero(_292026) = c_Groups_Oplus__class_Oplus(_292026, _292028, _292028))], (2086 ^ _224325) ^ [] : [c_Groups_Ozero__class_Ozero(_292026) = c_Groups_Oplus__class_Oplus(_292026, _292028, _292028), -(_292028 = c_Groups_Ozero__class_Ozero(_292026))]]], (11295 ^ _224325) ^ [_619296, _619298, _619300] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _619296, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _619298, _619300)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _619296, _619298), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _619300, _619298), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _619296, _619300))], (5919 ^ _224325) ^ [_428267] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _428267), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _428267)], (5951 ^ _224325) ^ [_429700, _429702, _429704] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _429700, _429702)), _429704) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _429700), _429704), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _429702), _429704)))], (9221 ^ _224325) ^ [_542621, _542623] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _542621), _542623) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _542623), _542621))], (5947 ^ _224325) ^ [_429440, _429442, _429444] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _429440, _429442), _429444) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _429440, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _429442, _429444)))], (4923 ^ _224325) ^ [_391818, _391820, _391822, _391824] : [class_Rings_Ocomm__semiring__0(_391818), -(hAPP(c_Polynomial_Opoly(_391818, c_Polynomial_Opcompose(_391818, _391820, _391822)), _391824) = hAPP(c_Polynomial_Opoly(_391818, _391820), hAPP(c_Polynomial_Opoly(_391818, _391822), _391824)))], (7396 ^ _224325) ^ [_479535, _479537] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _479535), _479537), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _479537, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _479535), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_RComplete_Onatfloor(_479537) = _479535)], (8053 ^ _224325) ^ [_502573] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _502573, _502573))], (5157 ^ _224325) ^ [_400420, _400422] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _400420, _400422), -(_400422 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _400420, 5160 ^ [_400420, _400422]))], (20 ^ _224325) ^ [_225073, _225075] : [-(class_Lattices_Oab__semigroup__idem__mult(_225073)), _225075 = _225073, class_Lattices_Oab__semigroup__idem__mult(_225075)], (9739 ^ _224325) ^ [_560532, _560534] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _560532, _560534) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 9740 ^ _224325 : [(9747 ^ _224325) ^ [] : [_560532 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _560534 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9741 ^ _224325) ^ [] : [_560532 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _560534 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (5053 ^ _224325) ^ [_396728, _396730] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _396728, _396730), _396730 = _396728], (7766 ^ _224325) ^ [_492274, _492276, _492278, _492280] : [class_Fields_Ofield(_492274), 7769 ^ _224325 : [(7770 ^ _224325) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_492274), c_Polynomial_Osmult(_492274, _492276, _492278), _492280), 7773 ^ _224325 : [(7780 ^ _224325) ^ [] : [-(_492276 = c_Groups_Ozero__class_Ozero(_492274)), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_492274), _492278, _492280))], (7774 ^ _224325) ^ [] : [_492276 = c_Groups_Ozero__class_Ozero(_492274), -(_492280 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_492274)))]]], (7786 ^ _224325) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_492274), c_Polynomial_Osmult(_492274, _492276, _492278), _492280)), 7789 ^ _224325 : [(7792 ^ _224325) ^ [] : [_492280 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_492274))], (7790 ^ _224325) ^ [] : [-(_492276 = c_Groups_Ozero__class_Ozero(_492274))]], 7793 ^ _224325 : [(7796 ^ _224325) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_492274), _492278, _492280)], (7794 ^ _224325) ^ [] : [_492276 = c_Groups_Ozero__class_Ozero(_492274)]]]]], (7654 ^ _224325) ^ [_488502, _488504] : [class_Rings_Ocomm__semiring__1(_488502), -(c_Rings_Odvd__class_Odvd(_488502, _488504, _488504))], (11823 ^ _224325) ^ [] : [-(class_Groups_Oabs__if(tc_RealDef_Oreal))], (6568 ^ _224325) ^ [_451708, _451710] : [class_Groups_Olinordered__ab__group__add(_451708), 6571 ^ _224325 : [(6578 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_451708, c_Groups_Ozero__class_Ozero(_451708), _451710), -(c_Orderings_Oord__class_Oless(_451708, c_Groups_Ouminus__class_Ouminus(_451708, _451710), _451710))], (6572 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_451708, c_Groups_Ouminus__class_Ouminus(_451708, _451710), _451710), -(c_Orderings_Oord__class_Oless(_451708, c_Groups_Ozero__class_Ozero(_451708), _451710))]]], (8703 ^ _224325) ^ [_524594, _524596, _524598] : [class_Rings_Olinordered__semidom(_524594), c_Orderings_Oord__class_Oless(_524594, c_Groups_Oone__class_Oone(_524594), _524596), -(c_Orderings_Oord__class_Oless(_524594, c_Groups_Oone__class_Oone(_524594), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_524594), _524596), hAPP(hAPP(c_Power_Opower__class_Opower(_524594), _524596), _524598))))], (11843 ^ _224325) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex))], (2404 ^ _224325) ^ [_302391, _302393] : [class_Groups_Oordered__ab__group__add__abs(_302391), c_Orderings_Oord__class_Oless__eq(_302391, c_Groups_Ozero__class_Ozero(_302391), _302393), -(c_Groups_Oabs__class_Oabs(_302391, _302393) = _302393)], (3413 ^ _224325) ^ [_339657, _339659] : [class_Rings_Olinordered__idom(_339657), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_339657), c_Groups_Oabs__class_Oabs(_339657, _339659)), c_Groups_Oabs__class_Oabs(_339657, _339659)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_339657), _339659), _339659))], (9219 ^ _224325) ^ [_542499, _542501, _542503] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _542499), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _542501, _542503)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _542499), _542501), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _542499), _542503)))], (9836 ^ _224325) ^ [_563863, _563865] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _563863, _563865), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_563863), _563865))], (7853 ^ _224325) ^ [_495415] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _495415, c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_495415 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (3407 ^ _224325) ^ [_339393, _339395, _339397] : [class_Rings_Olinordered__idom(_339393), -(c_Groups_Oabs__class_Oabs(_339393, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_339393), _339395), _339397)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_339393), c_Groups_Oabs__class_Oabs(_339393, _339395)), c_Groups_Oabs__class_Oabs(_339393, _339397)))], (5927 ^ _224325) ^ [_428713, _428715, _428717] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _428713), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _428715, _428717)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _428713), _428715), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _428713), _428717)))], (4317 ^ _224325) ^ [_369724, _369726, _369728, _369730, _369732] : [class_Rings_Olinordered__semiring__strict(_369724), c_Orderings_Oord__class_Oless__eq(_369724, _369726, _369728), c_Orderings_Oord__class_Oless(_369724, _369730, _369732), c_Orderings_Oord__class_Oless(_369724, c_Groups_Ozero__class_Ozero(_369724), _369726), c_Orderings_Oord__class_Oless__eq(_369724, c_Groups_Ozero__class_Ozero(_369724), _369730), -(c_Orderings_Oord__class_Oless(_369724, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_369724), _369726), _369730), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_369724), _369728), _369732)))], (6246 ^ _224325) ^ [_440098, _440100, _440102] : [class_RealVector_Oreal__normed__algebra(_440098), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_440098), c_Groups_Ouminus__class_Ouminus(_440098, _440100)), _440102) = c_Groups_Ouminus__class_Ouminus(_440098, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_440098), _440100), _440102)))], (94 ^ _224325) ^ [_227474, _227476] : [-(class_Lattices_Oboolean__algebra(_227474)), _227476 = _227474, class_Lattices_Oboolean__algebra(_227476)], (6930 ^ _224325) ^ [_463593, _463595] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _463593, _463595), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _463595, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _463593)))], (11803 ^ _224325) ^ [] : [-(class_Rings_Osemiring__0(tc_RealDef_Oreal))], (5033 ^ _224325) ^ [_396051, _396053] : [5034 ^ _224325 : [(5037 ^ _224325) ^ [] : [_396051 = _396053], (5035 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _396051, _396053)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _396051, _396053))], (8633 ^ _224325) ^ [_521873, _521875] : [class_Power_Opower(_521873), -(hAPP(hAPP(c_Power_Opower__class_Opower(_521873), _521875), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_521873))], (12039 ^ _224325) ^ [_641937] : [class_Rings_Olinordered__idom(_641937), -(class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(_641937)))], (234 ^ _224325) ^ [_231604, _231606] : [-(class_Groups_Oordered__comm__monoid__add(_231604)), _231606 = _231604, class_Groups_Oordered__comm__monoid__add(_231606)], (11655 ^ _224325) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (9437 ^ _224325) ^ [_550169, _550171] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _550169, c_Groups_Oone__class_Oone(tc_Int_Oint)), _550171), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _550169, _550171))], (12123 ^ _224325) ^ [_644597] : [class_Rings_Ocomm__semiring__1(_644597), -(class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(_644597)))], (5553 ^ _224325) ^ [_415498, _415500] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _415498, _415500) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _415498 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _415500 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (11529 ^ _224325) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (5170 ^ _224325) ^ [_400926, _400928] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _400926, _400928), -(_400928 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _400926, 5173 ^ [_400926, _400928]))], (7222 ^ _224325) ^ [_473357, _473359] : [-(c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _473357, _473359)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _473357), c_RealDef_Oreal(tc_Nat_Onat, _473359)))], (80 ^ _224325) ^ [_227058, _227060, _227062, _227064] : [-(c_Polynomial_Opos__poly(_227062, _227058)), c_Polynomial_Opos__poly(_227064, _227060), _227064 = _227062, _227060 = _227058], (274 ^ _224325) ^ [_232784, _232786] : [-(class_Rings_Oordered__cancel__semiring(_232784)), _232786 = _232784, class_Rings_Oordered__cancel__semiring(_232786)], (4720 ^ _224325) ^ [_383557] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _383557), v_r), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_cs____), _383557)), 4718 ^ []))], (6150 ^ _224325) ^ [_437026, _437028, _437030] : [class_Groups_Oordered__ab__group__add(_437026), 6153 ^ _224325 : [(6160 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_437026, _437030, _437028), -(c_Orderings_Oord__class_Oless__eq(_437026, c_Groups_Ouminus__class_Ouminus(_437026, _437028), c_Groups_Ouminus__class_Ouminus(_437026, _437030)))], (6154 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_437026, c_Groups_Ouminus__class_Ouminus(_437026, _437028), c_Groups_Ouminus__class_Ouminus(_437026, _437030)), -(c_Orderings_Oord__class_Oless__eq(_437026, _437030, _437028))]]], (8817 ^ _224325) ^ [_528628, _528630, _528632] : [class_Rings_Olinordered__semidom(_528628), c_Orderings_Oord__class_Oless(_528628, c_Groups_Ozero__class_Ozero(_528628), _528630), c_Orderings_Oord__class_Oless(_528628, _528630, c_Groups_Oone__class_Oone(_528628)), -(c_Orderings_Oord__class_Oless(_528628, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_528628), _528630), hAPP(hAPP(c_Power_Opower__class_Opower(_528628), _528630), _528632)), hAPP(hAPP(c_Power_Opower__class_Opower(_528628), _528630), _528632)))], (8723 ^ _224325) ^ [_525322, _525324] : [class_Power_Opower(_525322), class_Rings_Osemiring__0(_525322), 8730 ^ _224325 : [(8737 ^ _224325) ^ [] : [-(_525324 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_525322), c_Groups_Ozero__class_Ozero(_525322)), _525324) = c_Groups_Ozero__class_Ozero(_525322))], (8731 ^ _224325) ^ [] : [_525324 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_525322), c_Groups_Ozero__class_Ozero(_525322)), _525324) = c_Groups_Oone__class_Oone(_525322))]]], (284 ^ _224325) ^ [_233079, _233081] : [-(class_Rings_Olinordered__ring__strict(_233079)), _233081 = _233079, class_Rings_Olinordered__ring__strict(_233081)], (8097 ^ _224325) ^ [_504032, _504034] : [8104 ^ _224325 : [(8107 ^ _224325) ^ [] : [_504032 = _504034], (8105 ^ _224325) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _504032, _504034))]], c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _504032, _504034), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _504034, _504032))], (11060 ^ _224325) ^ [_610354, _610356, _610358, _610360, _610362] : [class_Groups_Oordered__ab__group__add__abs(_610354), -(c_Orderings_Oord__class_Oless__eq(_610354, c_Groups_Oabs__class_Oabs(_610354, c_Groups_Ominus__class_Ominus(_610354, c_Groups_Oplus__class_Oplus(_610354, _610356, _610358), c_Groups_Oplus__class_Oplus(_610354, _610360, _610362))), c_Groups_Oplus__class_Oplus(_610354, c_Groups_Oabs__class_Oabs(_610354, c_Groups_Ominus__class_Ominus(_610354, _610356, _610360)), c_Groups_Oabs__class_Oabs(_610354, c_Groups_Ominus__class_Ominus(_610354, _610358, _610362)))))], (11507 ^ _224325) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (10164 ^ _224325) ^ [_575758, _575760] : [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), _575758), _575760)), -(_575760 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _575758))], (6033 ^ _224325) ^ [_433072, _433074, _433076] : [class_Rings_Ocomm__ring__1(_433072), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_433072), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_433072)), c_Polynomial_OpCons(_433072, c_Groups_Ouminus__class_Ouminus(_433072, _433074), c_Polynomial_OpCons(_433072, c_Groups_Oone__class_Oone(_433072), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_433072))))), c_Polynomial_Osynthetic__div(_433072, _433076, _433074)), c_Polynomial_OpCons(_433072, hAPP(c_Polynomial_Opoly(_433072, _433076), _433074), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_433072)))) = _433076)], (11643 ^ _224325) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (11032 ^ _224325) ^ [_609334, _609336, _609338, _609340] : [class_Rings_Olinordered__idom(_609334), 11035 ^ _224325 : [(11044 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(_609334, c_Groups_Oabs__class_Oabs(_609334, c_Groups_Ominus__class_Ominus(_609334, _609336, _609338)), _609340)), c_Orderings_Oord__class_Oless(_609334, c_Groups_Ominus__class_Ominus(_609334, _609338, _609340), _609336), c_Orderings_Oord__class_Oless(_609334, _609336, c_Groups_Oplus__class_Oplus(_609334, _609338, _609340))], (11036 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_609334, c_Groups_Oabs__class_Oabs(_609334, c_Groups_Ominus__class_Ominus(_609334, _609336, _609338)), _609340), 11039 ^ _224325 : [(11042 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(_609334, _609336, c_Groups_Oplus__class_Oplus(_609334, _609338, _609340)))], (11040 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(_609334, c_Groups_Ominus__class_Ominus(_609334, _609338, _609340), _609336))]]]]], (534 ^ _224325) ^ [_240454, _240456] : [-(class_Groups_Ogroup__add(_240454)), _240456 = _240454, class_Groups_Ogroup__add(_240456)], (11607 ^ _224325) ^ [] : [-(class_Groups_Osgn__if(tc_Int_Oint))], (11251 ^ _224325) ^ [_617902, _617904, _617906] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _617902, _617904), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _617902, _617906), 11258 ^ _224325 : [(11265 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _617904, _617906), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _617904, _617902), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _617906, _617902)))], (11259 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _617904, _617902), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _617906, _617902)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _617904, _617906))]]], (8271 ^ _224325) ^ [_509489, _509491] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _509489, _509491), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _509491, _509489)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _509491, _509489), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _509489, _509491))], (6021 ^ _224325) ^ [_432538, _432540, _432542] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _432538, _432540), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _432538, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _432540, _432542)))], (9695 ^ _224325) ^ [_559211, _559213] : [c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _559211, _559213), 9700 ^ _224325 : [(9703 ^ _224325) ^ [] : [-(_559213 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9701 ^ _224325) ^ [] : [-(_559211 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 9704 ^ _224325 : [(9707 ^ _224325) ^ [] : [-(_559213 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (9705 ^ _224325) ^ [] : [-(_559211 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (7252 ^ _224325) ^ [_474441, _474443] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _474441, c_RealDef_Oreal(tc_Nat_Onat, _474443)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_474441), _474443))], (124 ^ _224325) ^ [_228359, _228361] : [-(class_RealVector_Oreal__normed__algebra(_228359)), _228361 = _228359, class_RealVector_Oreal__normed__algebra(_228361)], (10642 ^ _224325) ^ [_593581, _593583, _593585] : [class_Groups_Ogroup__add(_593581), -(c_Groups_Ominus__class_Ominus(_593581, _593583, _593585) = c_Groups_Oplus__class_Oplus(_593581, _593583, c_Groups_Ouminus__class_Ouminus(_593581, _593585)))], (9251 ^ _224325) ^ [_543936, _543938, _543940] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _543936, _543938), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _543936, _543940), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _543938, _543940)))], (9305 ^ _224325) ^ [_545787, _545789] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _545787, _545789)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _545787, c_Nat_OSuc(_545789)), -(_545789 = _545787)], (9193 ^ _224325) ^ [_541429, _541431] : [9194 ^ _224325 : [(9197 ^ _224325) ^ [] : [_541429 = c_Nat_OSuc(_541431)], (9195 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _541429, _541431)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _541429, c_Nat_OSuc(_541431)))], (11943 ^ _224325) ^ [_638897] : [class_Rings_Olinordered__idom(_638897), -(class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(_638897)))], (11961 ^ _224325) ^ [_639467] : [class_Rings_Olinordered__idom(_639467), -(class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(_639467)))], (8535 ^ _224325) ^ [_518718, _518720, _518722] : [class_Rings_Olinordered__semidom(_518718), c_Orderings_Oord__class_Oless__eq(_518718, c_Groups_Ozero__class_Ozero(_518718), _518720), -(c_Orderings_Oord__class_Oless__eq(_518718, c_Groups_Ozero__class_Ozero(_518718), hAPP(hAPP(c_Power_Opower__class_Opower(_518718), _518720), _518722)))], (6380 ^ _224325) ^ [_445445, _445447] : [class_RealVector_Oreal__normed__vector(_445445), -(c_Groups_Osgn__class_Osgn(_445445, c_Groups_Ouminus__class_Ouminus(_445445, _445447)) = c_Groups_Ouminus__class_Ouminus(_445445, c_Groups_Osgn__class_Osgn(_445445, _445447)))], (9391 ^ _224325) ^ [_548580, _548582] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _548580, _548582)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _548580, _548582), -(_548580 = _548582)], (11703 ^ _224325) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (5023 ^ _224325) ^ [_395795, _395797] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _395795, _395797), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _395795, _395797)), -(_395795 = _395797)], (11955 ^ _224325) ^ [_639277] : [class_Rings_Olinordered__idom(_639277), -(class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(_639277)))], (1208 ^ _224325) ^ [_264225, _264227, _264229] : [class_Orderings_Olinorder(_264225), 1211 ^ _224325 : [(1212 ^ _224325) ^ [] : [-(_264227 = _264229), -(c_Orderings_Oord__class_Oless(_264225, _264227, _264229)), -(c_Orderings_Oord__class_Oless(_264225, _264229, _264227))], (1222 ^ _224325) ^ [] : [1223 ^ _224325 : [(1226 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_264225, _264229, _264227)], (1224 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_264225, _264227, _264229)]], _264227 = _264229]]], (11635 ^ _224325) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (254 ^ _224325) ^ [_232194, _232196] : [-(class_Groups_Ocancel__ab__semigroup__add(_232194)), _232196 = _232194, class_Groups_Ocancel__ab__semigroup__add(_232196)], (9761 ^ _224325) ^ [_561259, _561261] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _561259), _561261) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 9764 ^ _224325 : [(9767 ^ _224325) ^ [] : [-(_561261 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (9765 ^ _224325) ^ [] : [-(_561259 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (9964 ^ _224325) ^ [_568513, _568515] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _568513), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _568515), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _568515), _568513)))], (11819 ^ _224325) ^ [] : [-(class_Groups_Ouminus(tc_RealDef_Oreal))], (10612 ^ _224325) ^ [_592321, _592323] : [class_Groups_Ogroup__add(_592321), -(c_Groups_Ominus__class_Ominus(_592321, c_Groups_Ozero__class_Ozero(_592321), _592323) = c_Groups_Ouminus__class_Ouminus(_592321, _592323))], (10686 ^ _224325) ^ [_595300, _595302, _595304] : [class_Groups_Ogroup__add(_595300), -(c_Groups_Ominus__class_Ominus(_595300, c_Groups_Oplus__class_Oplus(_595300, _595302, _595304), _595304) = _595302)], (3783 ^ _224325) ^ [_351917, _351919, _351921] : [class_Rings_Oordered__cancel__semiring(_351917), -(c_Orderings_Oord__class_Oless__eq(_351917, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_351917), _351919), _351921), c_Groups_Ozero__class_Ozero(_351917))), 3788 ^ _224325 : [(3795 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_351917, _351919, c_Groups_Ozero__class_Ozero(_351917)), c_Orderings_Oord__class_Oless__eq(_351917, c_Groups_Ozero__class_Ozero(_351917), _351921)], (3789 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_351917, c_Groups_Ozero__class_Ozero(_351917), _351919), c_Orderings_Oord__class_Oless__eq(_351917, _351921, c_Groups_Ozero__class_Ozero(_351917))]]], (11855 ^ _224325) ^ [] : [-(class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex))], (1202 ^ _224325) ^ [_263999] : [class_RealVector_Oreal__normed__vector(_263999), -(c_RealVector_Onorm__class_Onorm(_263999, c_Groups_Ozero__class_Ozero(_263999)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (7258 ^ _224325) ^ [_474679, _474681, _474683] : [class_Lattices_Oab__semigroup__idem__mult(_474679), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_474679), _474681), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_474679), _474681), _474683)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_474679), _474681), _474683))], (6108 ^ _224325) ^ [_435723, _435725] : [class_Groups_Ogroup__add(_435723), 6111 ^ _224325 : [(6118 ^ _224325) ^ [] : [_435725 = c_Groups_Ozero__class_Ozero(_435723), -(c_Groups_Ouminus__class_Ouminus(_435723, _435725) = c_Groups_Ozero__class_Ozero(_435723))], (6112 ^ _224325) ^ [] : [c_Groups_Ouminus__class_Ouminus(_435723, _435725) = c_Groups_Ozero__class_Ozero(_435723), -(_435725 = c_Groups_Ozero__class_Ozero(_435723))]]], (12171 ^ _224325) ^ [_646117] : [class_Groups_Oab__group__add(_646117), -(class_Groups_Ogroup__add(tc_Polynomial_Opoly(_646117)))], (8469 ^ _224325) ^ [_515979, _515981, _515983] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _515979), _515981), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _515979), _515983)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _515979), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _515981, _515983))], (2917 ^ _224325) ^ [_321286, _321288, _321290, _321292] : [class_Groups_Oordered__ab__semigroup__add(_321286), c_Orderings_Oord__class_Oless__eq(_321286, _321288, _321290), -(c_Orderings_Oord__class_Oless__eq(_321286, c_Groups_Oplus__class_Oplus(_321286, _321288, _321292), c_Groups_Oplus__class_Oplus(_321286, _321290, _321292)))], (11673 ^ _224325) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (3977 ^ _224325) ^ [_358329, _358331, _358333] : [class_Rings_Olinordered__semiring__strict(_358329), c_Orderings_Oord__class_Oless(_358329, c_Groups_Ozero__class_Ozero(_358329), _358331), c_Orderings_Oord__class_Oless(_358329, c_Groups_Ozero__class_Ozero(_358329), _358333), -(c_Orderings_Oord__class_Oless(_358329, c_Groups_Ozero__class_Ozero(_358329), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_358329), _358331), _358333)))], (8027 ^ _224325) ^ [_501751, _501753, _501755] : [class_Rings_Ocomm__semiring__1(_501751), 8032 ^ _224325 : [(8035 ^ _224325) ^ [] : [_501755 = c_Groups_Oone__class_Oone(_501751)], (8033 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _501753)]], -(c_Rings_Odvd__class_Odvd(_501751, _501755, hAPP(hAPP(c_Power_Opower__class_Opower(_501751), _501755), _501753)))], (7913 ^ _224325) ^ [_498035, _498037] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _498035), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _498035, _498037), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _498037, _498035)], (9165 ^ _224325) ^ [_540491, _540493] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _540491, _540493), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _540491, c_Nat_OSuc(_540493)))], (6792 ^ _224325) ^ [_459030, _459032] : [c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _459030, _459032) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_459032 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _459030))], (424 ^ _224325) ^ [_237209, _237211] : [-(class_Rings_Ono__zero__divisors(_237209)), _237211 = _237209, class_Rings_Ono__zero__divisors(_237211)], (364 ^ _224325) ^ [_235439, _235441] : [-(class_Rings_Olinordered__semidom(_235439)), _235441 = _235439, class_Rings_Olinordered__semidom(_235441)], (2715 ^ _224325) ^ [_313256, _313258, _313260, _313262] : [class_Rings_Ocomm__semiring__1(_313256), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_313256), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_313256), _313258), _313260)), _313262) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_313256), _313258), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_313256), _313260), _313262)))], (12195 ^ _224325) ^ [_646877] : [class_Rings_Olinordered__idom(_646877), -(class_Int_Oring__char__0(tc_Polynomial_Opoly(_646877)))], (1420 ^ _224325) ^ [_270610, _270612, _270614] : [class_Groups_Oordered__comm__monoid__add(_270610), c_Orderings_Oord__class_Oless(_270610, _270612, c_Groups_Ozero__class_Ozero(_270610)), c_Orderings_Oord__class_Oless(_270610, _270614, c_Groups_Ozero__class_Ozero(_270610)), -(c_Orderings_Oord__class_Oless(_270610, c_Groups_Oplus__class_Oplus(_270610, _270612, _270614), c_Groups_Ozero__class_Ozero(_270610)))], (9802 ^ _224325) ^ [_562757, _562759] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _562757, _562759), 9805 ^ _224325 : [(9812 ^ _224325) ^ [] : [_562759 = _562757, -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _562759, c_Nat_OSuc(_562757)))], (9806 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _562759, c_Nat_OSuc(_562757)), -(_562759 = _562757)]]], (11215 ^ _224325) ^ [_616574, _616576] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _616574, _616576) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _616574, _616576))], (9854 ^ _224325) ^ [_564531, _564533] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _564531, _564533), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_564531), _564533))], (6710 ^ _224325) ^ [_456347, _456349, _456351] : [class_Groups_Oordered__ab__group__add__abs(_456347), 6713 ^ _224325 : [(6722 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_456347, c_Groups_Oabs__class_Oabs(_456347, _456349), _456351)), c_Orderings_Oord__class_Oless__eq(_456347, _456349, _456351), c_Orderings_Oord__class_Oless__eq(_456347, c_Groups_Ouminus__class_Ouminus(_456347, _456349), _456351)], (6714 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_456347, c_Groups_Oabs__class_Oabs(_456347, _456349), _456351), 6717 ^ _224325 : [(6720 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_456347, c_Groups_Ouminus__class_Ouminus(_456347, _456349), _456351))], (6718 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_456347, _456349, _456351))]]]]], (7172 ^ _224325) ^ [_471553, _471555] : [_471553 = _471555, -(c_RealDef_Oreal(tc_Nat_Onat, _471553) = c_RealDef_Oreal(tc_Nat_Onat, _471555))], (11533 ^ _224325) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (1396 ^ _224325) ^ [_269847, _269849] : [class_Groups_Oordered__ab__group__add__abs(_269847), c_Orderings_Oord__class_Oless(_269847, c_Groups_Ozero__class_Ozero(_269847), _269849), -(c_Groups_Oabs__class_Oabs(_269847, _269849) = _269849)], (6076 ^ _224325) ^ [_434771, _434773] : [class_Groups_Ogroup__add(_434771), 6079 ^ _224325 : [(6086 ^ _224325) ^ [] : [c_Groups_Ozero__class_Ozero(_434771) = _434773, -(c_Groups_Ozero__class_Ozero(_434771) = c_Groups_Ouminus__class_Ouminus(_434771, _434773))], (6080 ^ _224325) ^ [] : [c_Groups_Ozero__class_Ozero(_434771) = c_Groups_Ouminus__class_Ouminus(_434771, _434773), -(c_Groups_Ozero__class_Ozero(_434771) = _434773)]]], (1119 ^ _224325) ^ [_260839] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _260839), v_r), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_cs____), _260839)), v_m____))], (11197 ^ _224325) ^ [_615795] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_615795), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _615795)], (12081 ^ _224325) ^ [_643267] : [class_Groups_Ocomm__monoid__add(_643267), -(class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(_643267)))], (3183 ^ _224325) ^ [_331543, _331545, _331547] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _331543, 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, _331545), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _331543), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _331547))), -(_331545 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (4963 ^ _224325) ^ [_393706, _393708] : [class_RealVector_Oreal__normed__vector(_393706), 4966 ^ _224325 : [(4973 ^ _224325) ^ [] : [-(_393708 = c_Groups_Ozero__class_Ozero(_393706)), -(c_RealVector_Onorm__class_Onorm(_393706, c_Groups_Osgn__class_Osgn(_393706, _393708)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (4967 ^ _224325) ^ [] : [_393708 = c_Groups_Ozero__class_Ozero(_393706), -(c_RealVector_Onorm__class_Onorm(_393706, c_Groups_Osgn__class_Osgn(_393706, _393708)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))]]], (9677 ^ _224325) ^ [_558567] : [9678 ^ _224325 : [(9679 ^ _224325) ^ [_558638] : [_558567 = c_Nat_OSuc(_558638)]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _558567))], (7276 ^ _224325) ^ [_475389, _475391] : [class_Lattices_Oboolean__algebra(_475389), -(c_Groups_Ouminus__class_Ouminus(_475389, c_Groups_Ouminus__class_Ouminus(_475389, _475391)) = _475391)], (8039 ^ _224325) ^ [_502172, _502174, _502176] : [class_Rings_Olinordered__semidom(_502172), c_Orderings_Oord__class_Oless(_502172, c_Groups_Oone__class_Oone(_502172), _502174), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _502176), -(c_Orderings_Oord__class_Oless(_502172, c_Groups_Oone__class_Oone(_502172), hAPP(hAPP(c_Power_Opower__class_Opower(_502172), _502174), _502176)))], (9257 ^ _224325) ^ [_544172, _544174] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_544172), c_Nat_OSuc(_544174)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _544172, _544174))], (11895 ^ _224325) ^ [] : [-(class_Int_Oring__char__0(tc_Complex_Ocomplex))], (3045 ^ _224325) ^ [_326597, _326599] : [class_Groups_Ocomm__monoid__mult(_326597), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_326597), _326599), c_Groups_Oone__class_Oone(_326597)) = _326599)], (11227 ^ _224325) ^ [_616968, _616970] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _616968, _616970), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _616968, _616970) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5523 ^ _224325) ^ [_414406] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _414406) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2927 ^ _224325) ^ [_321651, _321653, _321655, _321657] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_321651), 2930 ^ _224325 : [(2937 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_321651, _321655, _321657), -(c_Orderings_Oord__class_Oless__eq(_321651, c_Groups_Oplus__class_Oplus(_321651, _321653, _321655), c_Groups_Oplus__class_Oplus(_321651, _321653, _321657)))], (2931 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_321651, c_Groups_Oplus__class_Oplus(_321651, _321653, _321655), c_Groups_Oplus__class_Oplus(_321651, _321653, _321657)), -(c_Orderings_Oord__class_Oless__eq(_321651, _321655, _321657))]]], (5937 ^ _224325) ^ [_429128, _429130] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _429128), _429130) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _429128 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _429130 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (6480 ^ _224325) ^ [_449026, _449028] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _449026, _449028), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_449026), c_RComplete_Onatceiling(_449028)))], (3831 ^ _224325) ^ [_353528, _353530, _353532, _353534] : [class_Rings_Olinordered__comm__semiring__strict(_353528), c_Orderings_Oord__class_Oless(_353528, _353530, _353532), c_Orderings_Oord__class_Oless(_353528, c_Groups_Ozero__class_Ozero(_353528), _353534), -(c_Orderings_Oord__class_Oless(_353528, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_353528), _353534), _353530), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_353528), _353534), _353532)))], (9974 ^ _224325) ^ [_568830, _568832] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _568830), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _568832), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _568830, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _568830), _568832)))], (1316 ^ _224325) ^ [_267465, _267467, _267469] : [class_Orderings_Olinorder(_267465), -(c_Orderings_Oord__class_Oless(_267465, _267467, _267469)), -(_267467 = _267469), -(c_Orderings_Oord__class_Oless(_267465, _267469, _267467))], (374 ^ _224325) ^ [_235734, _235736] : [-(class_Groups_Oab__semigroup__mult(_235734)), _235736 = _235734, class_Groups_Oab__semigroup__mult(_235736)], (876 ^ _224325) ^ [_251795, _251797, _251799, _251801, _251803, _251805] : [-(c_Polynomial_Oorder(_251805, _251801, _251797) = c_Polynomial_Oorder(_251803, _251799, _251795)), _251805 = _251803, _251801 = _251799, _251797 = _251795], (7828 ^ _224325) ^ [_494392, _494394, _494396] : [class_Rings_Oidom(_494392), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_494392), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_494392)), c_Polynomial_OpCons(_494392, c_Groups_Ouminus__class_Ouminus(_494392, _494394), c_Polynomial_OpCons(_494392, c_Groups_Oone__class_Oone(_494392), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_494392))))), c_Polynomial_Oorder(_494392, _494394, _494396)), _494396))], (6990 ^ _224325) ^ [_465680, _465682, _465684, _465686] : [-(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, _465680, _465682), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _465684), c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _465686)))), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _465680, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _465684))), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _465682, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _465686))))))], (11511 ^ _224325) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (4137 ^ _224325) ^ [_363577, _363579] : [class_Rings_Olinordered__semidom(_363577), -(c_Orderings_Oord__class_Oless(_363577, _363579, c_Groups_Oplus__class_Oplus(_363577, _363579, c_Groups_Oone__class_Oone(_363577))))], (3921 ^ _224325) ^ [_356537, _356539, _356541] : [class_Rings_Olinordered__semiring__strict(_356537), c_Orderings_Oord__class_Oless(_356537, c_Groups_Ozero__class_Ozero(_356537), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_356537), _356539), _356541)), c_Orderings_Oord__class_Oless(_356537, c_Groups_Ozero__class_Ozero(_356537), _356541), -(c_Orderings_Oord__class_Oless(_356537, c_Groups_Ozero__class_Ozero(_356537), _356539))], (4929 ^ _224325) ^ [_392110, _392112, _392114, _392116] : [class_Groups_Ozero(_392110), hAPP(hAPP(hAPP(_392112, c_Groups_Ozero__class_Ozero(_392110)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_392110))), _392114) = _392114, -(c_Polynomial_Opoly__rec(_392116, _392110, _392114, _392112, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_392110))) = _392114)], (1176 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 1174 ^ []))], (2182 ^ _224325) ^ [_295301, _295303, _295305, _295307] : [class_Groups_Oordered__comm__monoid__add(_295301), c_Orderings_Oord__class_Oless(_295301, c_Groups_Ozero__class_Ozero(_295301), _295303), c_Orderings_Oord__class_Oless__eq(_295301, _295305, _295307), -(c_Orderings_Oord__class_Oless(_295301, _295305, c_Groups_Oplus__class_Oplus(_295301, _295303, _295307)))], (9533 ^ _224325) ^ [_553282] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _553282), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _553282)], (11201 ^ _224325) ^ [_616045, _616047] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _616045, _616047), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _616045, _616047), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (11641 ^ _224325) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (5297 ^ _224325) ^ [_405919, _405921, _405923] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _405919, _405921), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _405919, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _405923, _405921)))], (2070 ^ _224325) ^ [_291586, _291588] : [class_Rings_Ocomm__semiring__1(_291586), -(c_Groups_Oplus__class_Oplus(_291586, _291588, c_Groups_Ozero__class_Ozero(_291586)) = _291588)], (6466 ^ _224325) ^ [_448507] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_RComplete_Onatfloor(_448507)))], (5135 ^ _224325) ^ [_399511, _399513] : [_399511 = _399513, -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _399511, _399513))], (992 ^ _224325) ^ [_255998, _256000, _256002, _256004] : [-(c_RealDef_Oreal(_256004, _256000) = c_RealDef_Oreal(_256002, _255998)), _256004 = _256002, _256000 = _255998], (6504 ^ _224325) ^ [_449780, _449782] : [class_Groups_Oordered__ab__group__add(_449780), 6507 ^ _224325 : [(6514 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_449780, c_Groups_Ozero__class_Ozero(_449780), _449782), -(c_Orderings_Oord__class_Oless__eq(_449780, c_Groups_Ouminus__class_Ouminus(_449780, _449782), c_Groups_Ozero__class_Ozero(_449780)))], (6508 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_449780, c_Groups_Ouminus__class_Ouminus(_449780, _449782), c_Groups_Ozero__class_Ozero(_449780)), -(c_Orderings_Oord__class_Oless__eq(_449780, c_Groups_Ozero__class_Ozero(_449780), _449782))]]], (6804 ^ _224325) ^ [_459461, _459463] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _459461), _459463), 6807 ^ _224325 : [(6810 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _459461, _459463))], (6808 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _459463), _459461))]]], (6942 ^ _224325) ^ [_464032, _464034] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _464032, _464034), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _464034, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _464032)))], (5781 ^ _224325) ^ [_423424] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _423424), _423424 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (8545 ^ _224325) ^ [_519081, _519083, _519085, _519087] : [class_Rings_Olinordered__semidom(_519081), c_Orderings_Oord__class_Oless__eq(_519081, _519083, _519085), c_Orderings_Oord__class_Oless__eq(_519081, c_Groups_Ozero__class_Ozero(_519081), _519083), -(c_Orderings_Oord__class_Oless__eq(_519081, hAPP(hAPP(c_Power_Opower__class_Opower(_519081), _519083), _519087), hAPP(hAPP(c_Power_Opower__class_Opower(_519081), _519085), _519087)))], (5609 ^ _224325) ^ [_417374, _417376, _417378] : [5610 ^ _224325 : [(5613 ^ _224325) ^ [] : [_417376 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5611 ^ _224325) ^ [] : [_417374 = _417378]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _417374), _417376) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _417378), _417376))], (11919 ^ _224325) ^ [_638137] : [class_Rings_Oidom(_638137), -(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(_638137)))], (574 ^ _224325) ^ [_241634, _241636] : [-(class_Rings_Ocomm__semiring__0(_241634)), _241636 = _241634, class_Rings_Ocomm__semiring__0(_241636)], (10546 ^ _224325) ^ [_589395, _589397, _589399] : [class_RealVector_Oreal__normed__vector(_589395), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_589395, c_Groups_Ominus__class_Ominus(_589395, _589397, _589399)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_589395, _589397), c_RealVector_Onorm__class_Onorm(_589395, _589399))))], (1016 ^ _224325) ^ [_256873, _256875, _256877, _256879] : [-(tc_fun(_256879, _256875) = tc_fun(_256877, _256873)), _256879 = _256877, _256875 = _256873], (2436 ^ _224325) ^ [_303402, _303404] : [class_RealVector_Oreal__normed__vector(_303402), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_303402, _303404)))], (5787 ^ _224325) ^ [_423603] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _423603, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (324 ^ _224325) ^ [_234259, _234261] : [-(class_Groups_Oordered__ab__group__add(_234259)), _234261 = _234259, class_Groups_Oordered__ab__group__add(_234261)], (11749 ^ _224325) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal))], (10630 ^ _224325) ^ [_593081, _593083, _593085] : [class_Rings_Ocomm__ring__1(_593081), -(c_Groups_Ominus__class_Ominus(_593081, _593083, _593085) = c_Groups_Oplus__class_Oplus(_593081, _593083, c_Groups_Ouminus__class_Ouminus(_593081, _593085)))], (1996 ^ _224325) ^ [_288948, _288950, _288952, _288954] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_288948), 1999 ^ _224325 : [(2006 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_288948, _288950, _288954), -(c_Orderings_Oord__class_Oless(_288948, c_Groups_Oplus__class_Oplus(_288948, _288950, _288952), c_Groups_Oplus__class_Oplus(_288948, _288954, _288952)))], (2000 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_288948, c_Groups_Oplus__class_Oplus(_288948, _288950, _288952), c_Groups_Oplus__class_Oplus(_288948, _288954, _288952)), -(c_Orderings_Oord__class_Oless(_288948, _288950, _288954))]]], (9103 ^ _224325) ^ [_538247] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _538247) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (11849 ^ _224325) ^ [] : [-(class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex))], (11054 ^ _224325) ^ [_610062, _610064, _610066] : [class_Groups_Oordered__ab__group__add__abs(_610062), -(c_Orderings_Oord__class_Oless__eq(_610062, c_Groups_Oabs__class_Oabs(_610062, c_Groups_Ominus__class_Ominus(_610062, _610064, _610066)), c_Groups_Oplus__class_Oplus(_610062, c_Groups_Oabs__class_Oabs(_610062, _610064), c_Groups_Oabs__class_Oabs(_610062, _610066))))], (10692 ^ _224325) ^ [_595544, _595546, _595548] : [class_Groups_Ogroup__add(_595544), -(c_Groups_Oplus__class_Oplus(_595544, c_Groups_Ominus__class_Ominus(_595544, _595546, _595548), _595548) = _595546)], (4801 ^ _224325) ^ [_387335, _387337, _387339, _387341] : [class_Rings_Ocomm__semiring__0(_387335), -(c_Polynomial_Opcompose(_387335, c_Polynomial_OpCons(_387335, _387337, _387339), _387341) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_387335), c_Polynomial_OpCons(_387335, _387337, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_387335))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_387335)), _387341), c_Polynomial_Opcompose(_387335, _387339, _387341))))], (7484 ^ _224325) ^ [_482592, _482594, _482596] : [class_Rings_Olinordered__idom(_482592), 7487 ^ _224325 : [(7494 ^ _224325) ^ [] : [c_Rings_Odvd__class_Odvd(_482592, _482594, _482596), -(c_Rings_Odvd__class_Odvd(_482592, _482594, c_Groups_Oabs__class_Oabs(_482592, _482596)))], (7488 ^ _224325) ^ [] : [c_Rings_Odvd__class_Odvd(_482592, _482594, c_Groups_Oabs__class_Oabs(_482592, _482596)), -(c_Rings_Odvd__class_Odvd(_482592, _482594, _482596))]]], (9553 ^ _224325) ^ [_554061] : [c_Nat_OSuc(_554061) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (1362 ^ _224325) ^ [_268846, _268848, _268850] : [class_Orderings_Olinorder(_268846), -(c_Orderings_Oord__class_Oless(_268846, _268848, _268850)), 1369 ^ _224325 : [(1376 ^ _224325) ^ [] : [_268850 = _268848, c_Orderings_Oord__class_Oless(_268846, _268850, _268848)], (1370 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(_268846, _268850, _268848)), -(_268850 = _268848)]]], (11591 ^ _224325) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (4789 ^ _224325) ^ [_386747, _386749] : [class_Groups_Ocomm__monoid__add(_386747), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_386747), _386749, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_386747))) = _386749)], (1346 ^ _224325) ^ [_268344, _268346] : [class_Groups_Olinordered__ab__group__add(_268344), 1349 ^ _224325 : [(1356 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_268344, _268346, c_Groups_Ozero__class_Ozero(_268344)), -(c_Orderings_Oord__class_Oless(_268344, c_Groups_Oplus__class_Oplus(_268344, _268346, _268346), c_Groups_Ozero__class_Ozero(_268344)))], (1350 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_268344, c_Groups_Oplus__class_Oplus(_268344, _268346, _268346), c_Groups_Ozero__class_Ozero(_268344)), -(c_Orderings_Oord__class_Oless(_268344, _268346, c_Groups_Ozero__class_Ozero(_268344)))]]], (11185 ^ _224325) ^ [_615338, _615340, _615342] : [class_RealVector_Oreal__normed__vector(_615338), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_615338, _615340), c_RealVector_Onorm__class_Onorm(_615338, _615342)), c_RealVector_Onorm__class_Onorm(_615338, c_Groups_Oplus__class_Oplus(_615338, _615340, _615342))))], (1454 ^ _224325) ^ [_271700, _271702, _271704] : [class_Orderings_Opreorder(_271700), c_Orderings_Oord__class_Oless(_271700, _271702, _271704), c_Orderings_Oord__class_Oless(_271700, _271704, _271702)], (4167 ^ _224325) ^ [_364684, _364686] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _364684), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _364686), -(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), _364684), _364686)))], (11697 ^ _224325) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (9059 ^ _224325) ^ [_536916, _536918, _536920] : [-(_536916 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 9062 ^ _224325 : [(9069 ^ _224325) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _536916), _536918), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _536916), _536920)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _536918, _536920))], (9063 ^ _224325) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _536918, _536920), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _536916), _536918), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _536916), _536920)))]]], (10342 ^ _224325) ^ [_581878, _581880, _581882, _581884, _581886] : [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), _581878), _581880), _581882), c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _581878), _581884), _581886)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _581882), c_Orderings_Oord__class_Oless(tc_Int_Oint, _581882, _581878), c_Orderings_Oord__class_Oless(tc_Int_Oint, _581886, _581878), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _581880, _581884))], (5971 ^ _224325) ^ [_430525, _430527, _430529] : [_430525 = _430529, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _430525, _430527) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _430529, _430527))], (11453 ^ _224325) ^ [_625333, _625335, _625337] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _625333, _625335), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _625337, _625335)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _625333, _625337))], (7406 ^ _224325) ^ [_479862, _479864] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _479862), -(c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _479862, c_RealDef_Oreal(tc_Nat_Onat, _479864))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatceiling(_479862), _479864))], (3493 ^ _224325) ^ [_342337, _342339, _342341] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _342337, _342339), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _342341, _342337), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _342341, _342339)))], (8121 ^ _224325) ^ [_504754, _504756] : [-(_504754 = _504756), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _504754, _504756), 8128 ^ _224325 : [(8131 ^ _224325) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _504756, _504754)], (8129 ^ _224325) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _504754, _504756))]]], (3383 ^ _224325) ^ [_338311] : [class_Rings_Ozero__neq__one(_338311), c_Groups_Oone__class_Oone(_338311) = c_Groups_Ozero__class_Ozero(_338311)], (10328 ^ _224325) ^ [_581406, _581408, _581410] : [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), _581406), _581408), _581410), 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), _581410), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _581406), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _581408, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (5125 ^ _224325) ^ [_399196, _399198, _399200] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _399196, _399198), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _399198, _399200), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _399196, _399200))], (6476 ^ _224325) ^ [] : [-(c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3317 ^ _224325) ^ [_336020, _336022] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _336020), _336022) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _336022), _336020))], (1640 ^ _224325) ^ [_277666, _277668, _277670, _277672] : [class_Orderings_Oorder(_277666), c_Orderings_Oord__class_Oless(_277666, _277668, _277670), c_Orderings_Oord__class_Oless__eq(_277666, _277672, _277668), -(c_Orderings_Oord__class_Oless(_277666, _277672, _277670))], (3663 ^ _224325) ^ [_347922, _347924, _347926, _347928] : [class_Rings_Oordered__semiring(_347922), c_Orderings_Oord__class_Oless__eq(_347922, _347924, _347926), c_Orderings_Oord__class_Oless__eq(_347922, c_Groups_Ozero__class_Ozero(_347922), _347928), -(c_Orderings_Oord__class_Oless__eq(_347922, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_347922), _347928), _347924), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_347922), _347928), _347926)))], (104 ^ _224325) ^ [_227769, _227771] : [-(class_RealVector_Oreal__normed__div__algebra(_227769)), _227771 = _227769, class_RealVector_Oreal__normed__div__algebra(_227771)], (11465 ^ _224325) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal))], (11477 ^ _224325) ^ [_626173, _626175] : [class_Orderings_Opreorder(_626173), -(class_Orderings_Opreorder(tc_fun(_626175, _626173)))], (414 ^ _224325) ^ [_236914, _236916] : [-(class_Rings_Oordered__ring__abs(_236914)), _236916 = _236914, class_Rings_Oordered__ring__abs(_236916)], (8501 ^ _224325) ^ [_517287, _517289] : [class_Groups_Omonoid__mult(_517287), -(hAPP(hAPP(c_Power_Opower__class_Opower(_517287), c_Groups_Oone__class_Oone(_517287)), _517289) = c_Groups_Oone__class_Oone(_517287))], (11845 ^ _224325) ^ [] : [-(class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex))], (2987 ^ _224325) ^ [_323903, _323905, _323907, _323909] : [class_RealVector_Oreal__normed__algebra(_323903), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_323903), c_Groups_Oplus__class_Oplus(_323903, _323905, _323907)), _323909) = c_Groups_Oplus__class_Oplus(_323903, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_323903), _323905), _323909), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_323903), _323907), _323909)))], (694 ^ _224325) ^ [_245174, _245176] : [-(class_Groups_Ozero(_245174)), _245176 = _245174, class_Groups_Ozero(_245176)], (10552 ^ _224325) ^ [_589659, _589661, _589663] : [class_Groups_Oordered__ab__group__add(_589659), 10555 ^ _224325 : [(10562 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_589659, c_Groups_Ominus__class_Ominus(_589659, _589661, _589663), c_Groups_Ozero__class_Ozero(_589659)), -(c_Orderings_Oord__class_Oless__eq(_589659, _589661, _589663))], (10556 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_589659, _589661, _589663), -(c_Orderings_Oord__class_Oless__eq(_589659, c_Groups_Ominus__class_Ominus(_589659, _589661, _589663), c_Groups_Ozero__class_Ozero(_589659)))]]], (1546 ^ _224325) ^ [_274678, _274680, _274682, _274684] : [class_Orderings_Oorder(_274678), c_Orderings_Oord__class_Oless(_274678, _274680, _274682), _274680 = _274684, -(c_Orderings_Oord__class_Oless(_274678, _274684, _274682))], (11729 ^ _224325) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal))], (2282 ^ _224325) ^ [_298541, _298543, _298545, _298547] : [class_Groups_Oordered__comm__monoid__add(_298541), c_Orderings_Oord__class_Oless__eq(_298541, c_Groups_Ozero__class_Ozero(_298541), _298543), c_Orderings_Oord__class_Oless__eq(_298541, _298545, _298547), -(c_Orderings_Oord__class_Oless__eq(_298541, _298545, c_Groups_Oplus__class_Oplus(_298541, _298547, _298543)))], (9603 ^ _224325) ^ [_555677, _555679, _555681] : [class_Rings_Ocomm__semiring__1(_555677), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_555677), hAPP(hAPP(c_Power_Opower__class_Opower(_555677), _555679), _555681)), _555679) = hAPP(hAPP(c_Power_Opower__class_Opower(_555677), _555679), c_Nat_OSuc(_555681)))], (6410 ^ _224325) ^ [_446719, _446721, _446723] : [class_Groups_Ogroup__add(_446719), 6413 ^ _224325 : [(6420 ^ _224325) ^ [] : [_446723 = c_Groups_Ouminus__class_Ouminus(_446719, _446721), -(_446721 = c_Groups_Ouminus__class_Ouminus(_446719, _446723))], (6414 ^ _224325) ^ [] : [_446721 = c_Groups_Ouminus__class_Ouminus(_446719, _446723), -(_446723 = c_Groups_Ouminus__class_Ouminus(_446719, _446721))]]], (8973 ^ _224325) ^ [_534001, _534003] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _534001), c_Orderings_Oord__class_Oless(tc_Int_Oint, _534001, _534003), c_Rings_Odvd__class_Odvd(tc_Int_Oint, _534003, _534001)], (3635 ^ _224325) ^ [_346976, _346978, _346980] : [class_Rings_Oordered__ring(_346976), c_Orderings_Oord__class_Oless__eq(_346976, _346978, c_Groups_Ozero__class_Ozero(_346976)), c_Orderings_Oord__class_Oless__eq(_346976, _346980, c_Groups_Ozero__class_Ozero(_346976)), -(c_Orderings_Oord__class_Oless__eq(_346976, c_Groups_Ozero__class_Ozero(_346976), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_346976), _346978), _346980)))], (3427 ^ _224325) ^ [_340180, _340182] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _340180, _340182)), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _340180, _340182), -(_340180 = _340182)], (9818 ^ _224325) ^ [_563228, _563230] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _563228, _563230), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_563228), _563230))], (3097 ^ _224325) ^ [_328526, _328528, _328530] : [class_Groups_Oordered__ab__group__add__abs(_328526), -(c_Groups_Oabs__class_Oabs(_328526, c_Groups_Oplus__class_Oplus(_328526, c_Groups_Oabs__class_Oabs(_328526, _328528), c_Groups_Oabs__class_Oabs(_328526, _328530))) = c_Groups_Oplus__class_Oplus(_328526, c_Groups_Oabs__class_Oabs(_328526, _328528), c_Groups_Oabs__class_Oabs(_328526, _328530)))], (2839 ^ _224325) ^ [_318479, _318481, _318483, _318485] : [class_Rings_Ocomm__semiring__1(_318479), -(c_Groups_Oplus__class_Oplus(_318479, _318481, c_Groups_Oplus__class_Oplus(_318479, _318483, _318485)) = c_Groups_Oplus__class_Oplus(_318479, _318483, c_Groups_Oplus__class_Oplus(_318479, _318481, _318485)))], (5767 ^ _224325) ^ [_422948, _422950] : [5768 ^ _224325 : [(5771 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _422950)], (5769 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _422948)]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _422948, _422950)))], (9223 ^ _224325) ^ [_542785, _542787, _542789] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_542785)), _542787) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_542785)), _542789), -(_542787 = _542789)], (10 ^ _224325) ^ [_224760, _224762, _224764] : [-(_224764 = _224760), _224764 = _224762, _224762 = _224760], (12231 ^ _224325) ^ [_648017] : [class_Rings_Ocomm__ring__1(_648017), -(class_Rings_Oring__1(tc_Polynomial_Opoly(_648017)))], (11445 ^ _224325) ^ [_624863, _624865] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _624863, _624865), _624865) = _624863)], (4835 ^ _224325) ^ [_388490, _388492, _388494] : [class_Rings_Oidom(_388490), 4838 ^ _224325 : [(4839 ^ _224325) ^ [] : [hAPP(c_Polynomial_Opoly(_388490, _388492), _388494) = c_Groups_Ozero__class_Ozero(_388490), -(_388492 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_388490))), c_Polynomial_Oorder(_388490, _388494, _388492) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (4849 ^ _224325) ^ [] : [4850 ^ _224325 : [(4853 ^ _224325) ^ [] : [-(c_Polynomial_Oorder(_388490, _388494, _388492) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4851 ^ _224325) ^ [] : [_388492 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_388490))]], -(hAPP(c_Polynomial_Opoly(_388490, _388492), _388494) = c_Groups_Ozero__class_Ozero(_388490))]]], (3437 ^ _224325) ^ [_340517, _340519] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _340517, _340519), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _340517, _340519)), -(_340517 = _340519)], (1107 ^ _224325) ^ [_260327, _260329, _260331] : [class_RealVector_Oreal__normed__vector(_260327), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_260327, c_Groups_Oplus__class_Oplus(_260327, _260329, _260331)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_260327, _260329), c_RealVector_Onorm__class_Onorm(_260327, _260331))))], (6398 ^ _224325) ^ [_446231, _446233, _446235] : [class_Rings_Ocomm__ring(_446231), -(hAPP(c_Polynomial_Opoly(_446231, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_446231), _446233)), _446235) = c_Groups_Ouminus__class_Ouminus(_446231, hAPP(c_Polynomial_Opoly(_446231, _446233), _446235)))], (214 ^ _224325) ^ [_231014, _231016] : [-(class_Groups_Oordered__ab__semigroup__add(_231014)), _231016 = _231014, class_Groups_Oordered__ab__semigroup__add(_231016)], (5599 ^ _224325) ^ [_417088, _417090, _417092] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _417088), _417090) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _417092), _417090), -(_417088 = _417092), -(_417090 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6704 ^ _224325) ^ [_456111, _456113] : [class_Groups_Oordered__ab__group__add__abs(_456111), -(c_Orderings_Oord__class_Oless__eq(_456111, c_Groups_Ouminus__class_Ouminus(_456111, _456113), c_Groups_Oabs__class_Oabs(_456111, _456113)))], (11519 ^ _224325) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (9145 ^ _224325) ^ [_539771] : [c_Nat_OSuc(_539771) = _539771], (5331 ^ _224325) ^ [_407342, _407344] : [class_Rings_Ocomm__semiring__1(_407342), -(c_Polynomial_Osmult(_407342, c_Groups_Oone__class_Oone(_407342), _407344) = _407344)], (3027 ^ _224325) ^ [_325689, _325691, _325693, _325695] : [class_RealVector_Oreal__normed__algebra(_325689), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_325689), _325691), c_Groups_Oplus__class_Oplus(_325689, _325693, _325695)) = c_Groups_Oplus__class_Oplus(_325689, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_325689), _325691), _325693), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_325689), _325691), _325695)))], (4471 ^ _224325) ^ [_374922, _374924, _374926] : [class_Rings_Olinordered__ring(_374922), c_Orderings_Oord__class_Oless(_374922, c_Groups_Oplus__class_Oplus(_374922, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_374922), _374924), _374924), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_374922), _374926), _374926)), c_Groups_Ozero__class_Ozero(_374922))], (6064 ^ _224325) ^ [_434339] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _434339), -(c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _434339, c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatfloor(_434339), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (2733 ^ _224325) ^ [_314192, _314194, _314196, _314198] : [class_Rings_Ocomm__semiring__1(_314192), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_314192), _314194), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_314192), _314196), _314198)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_314192), _314196), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_314192), _314194), _314198)))], (9571 ^ _224325) ^ [_554707] : [_554707 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _554707) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (2745 ^ _224325) ^ [_314721, _314723] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _314721), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, _314721, _314723)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _314723))))], (5843 ^ _224325) ^ [_425580, _425582, _425584] : [class_Rings_Ocomm__semiring__0(_425580), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_425580), _425582, c_Polynomial_Osmult(_425580, _425584, c_Polynomial_Osynthetic__div(_425580, _425582, _425584))) = c_Polynomial_OpCons(_425580, hAPP(c_Polynomial_Opoly(_425580, _425582), _425584), c_Polynomial_Osynthetic__div(_425580, _425582, _425584)))], (11719 ^ _224325) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal))], (4619 ^ _224325) ^ [_379901, _379903] : [class_Int_Oring__char__0(_379901), class_Rings_Oidom(_379901), 4626 ^ _224325 : [(4633 ^ _224325) ^ [] : [_379903 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_379901)), -(c_Polynomial_Opoly(_379901, _379903) = c_Polynomial_Opoly(_379901, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_379901))))], (4627 ^ _224325) ^ [] : [c_Polynomial_Opoly(_379901, _379903) = c_Polynomial_Opoly(_379901, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_379901))), -(_379903 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_379901)))]]], (5065 ^ _224325) ^ [_397154, _397156] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _397154, _397156), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _397154, _397156))], (5303 ^ _224325) ^ [_406161, _406163, _406165] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _406161, _406163), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _406161, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _406163, _406165)))], (11004 ^ _224325) ^ [_608198, _608200, _608202, _608204] : [class_RealVector_Oreal__normed__algebra(_608198), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_608198), _608200), c_Groups_Ominus__class_Ominus(_608198, _608202, _608204)) = c_Groups_Ominus__class_Ominus(_608198, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_608198), _608200), _608202), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_608198), _608200), _608204)))], (11016 ^ _224325) ^ [_608808, _608810, _608812] : [class_Groups_Oordered__ab__group__add(_608808), 11019 ^ _224325 : [(11026 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_608808, c_Groups_Ominus__class_Ominus(_608808, _608810, _608812), c_Groups_Ozero__class_Ozero(_608808)), -(c_Orderings_Oord__class_Oless(_608808, _608810, _608812))], (11020 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_608808, _608810, _608812), -(c_Orderings_Oord__class_Oless(_608808, c_Groups_Ominus__class_Ominus(_608808, _608810, _608812), c_Groups_Ozero__class_Ozero(_608808)))]]], (8639 ^ _224325) ^ [_522129, _522131, _522133, _522135] : [class_Groups_Omonoid__mult(_522129), -(hAPP(hAPP(c_Power_Opower__class_Opower(_522129), _522131), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _522133, _522135)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_522129), hAPP(hAPP(c_Power_Opower__class_Opower(_522129), _522131), _522133)), hAPP(hAPP(c_Power_Opower__class_Opower(_522129), _522131), _522135)))], (6198 ^ _224325) ^ [_438562, _438564, _438566] : [class_Groups_Oordered__ab__group__add(_438562), 6201 ^ _224325 : [(6208 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_438562, _438566, c_Groups_Ouminus__class_Ouminus(_438562, _438564)), -(c_Orderings_Oord__class_Oless(_438562, _438564, c_Groups_Ouminus__class_Ouminus(_438562, _438566)))], (6202 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_438562, _438564, c_Groups_Ouminus__class_Ouminus(_438562, _438566)), -(c_Orderings_Oord__class_Oless(_438562, _438566, c_Groups_Ouminus__class_Ouminus(_438562, _438564)))]]], (2709 ^ _224325) ^ [_312944, _312946, _312948, _312950] : [class_Rings_Ocomm__semiring__1(_312944), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_312944), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_312944), _312946), _312948)), _312950) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_312944), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_312944), _312946), _312950)), _312948))], (11523 ^ _224325) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (11639 ^ _224325) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (2721 ^ _224325) ^ [_313568, _313570, _313572, _313574] : [class_Groups_Oab__semigroup__mult(_313568), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_313568), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_313568), _313570), _313572)), _313574) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_313568), _313570), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_313568), _313572), _313574)))], (11343 ^ _224325) ^ [_621022, _621024] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _621022, _621024), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _621024, _621022), _621022) = _621024)], (10654 ^ _224325) ^ [_594095, _594097, _594099] : [class_Groups_Oordered__ab__group__add__abs(_594095), -(c_Orderings_Oord__class_Oless__eq(_594095, c_Groups_Ominus__class_Ominus(_594095, c_Groups_Oabs__class_Oabs(_594095, _594097), c_Groups_Oabs__class_Oabs(_594095, _594099)), c_Groups_Oabs__class_Oabs(_594095, c_Groups_Ominus__class_Ominus(_594095, _594097, _594099))))], (12237 ^ _224325) ^ [_648207] : [class_Groups_Oab__group__add(_648207), -(class_Groups_Ominus(tc_Polynomial_Opoly(_648207)))], (11679 ^ _224325) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (7328 ^ _224325) ^ [_477270, _477272] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _477270, _477272), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _477270), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _477272), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))], (394 ^ _224325) ^ [_236324, _236326] : [-(class_Groups_Oab__semigroup__add(_236324)), _236326 = _236324, class_Groups_Oab__semigroup__add(_236326)], (184 ^ _224325) ^ [_230129, _230131] : [-(class_Rings_Olinordered__comm__semiring__strict(_230129)), _230131 = _230129, class_Rings_Olinordered__comm__semiring__strict(_230131)], (7270 ^ _224325) ^ [_475165, _475167] : [class_Lattices_Oab__semigroup__idem__mult(_475165), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_475165), _475167), _475167) = _475167)], (2632 ^ _224325) ^ [_309876, _309878, _309880] : [class_Orderings_Opreorder(_309876), _309878 = _309880, -(c_Orderings_Oord__class_Oless__eq(_309876, _309878, _309880))], (9664 ^ _224325) ^ [_558129] : [_558129 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _558129, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (11813 ^ _224325) ^ [] : [-(class_Int_Oring__char__0(tc_RealDef_Oreal))], (2674 ^ _224325) ^ [_311197, _311199, _311201, _311203] : [class_Orderings_Oord(_311197), 2677 ^ _224325 : [(2684 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_311197, hAPP(_311201, 2685 ^ [_311197, _311199, _311201, _311203]), hAPP(_311203, 2685 ^ [_311197, _311199, _311201, _311203])), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_311199, _311197), _311201, _311203))], (2678 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_311199, _311197), _311201, _311203), 2681 ^ _224325 : [(2682 ^ _224325) ^ [_311456] : [-(c_Orderings_Oord__class_Oless__eq(_311197, hAPP(_311201, _311456), hAPP(_311203, _311456)))]]]]], (4533 ^ _224325) ^ [_377115] : [_377115 = 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), _377115), _377115))], (8939 ^ _224325) ^ [_532684, _532686, _532688] : [class_Rings_Oidom(_532684), -(_532686 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_532684))), 8946 ^ _224325 : [(8949 ^ _224325) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_532684), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_532684)), c_Polynomial_OpCons(_532684, c_Groups_Ouminus__class_Ouminus(_532684, _532688), c_Polynomial_OpCons(_532684, c_Groups_Oone__class_Oone(_532684), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_532684))))), c_Nat_OSuc(c_Polynomial_Oorder(_532684, _532688, _532686))), _532686)], (8947 ^ _224325) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_532684), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_532684)), c_Polynomial_OpCons(_532684, c_Groups_Ouminus__class_Ouminus(_532684, _532688), c_Polynomial_OpCons(_532684, c_Groups_Oone__class_Oone(_532684), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_532684))))), c_Polynomial_Oorder(_532684, _532688, _532686)), _532686))]]], (6892 ^ _224325) ^ [_462316, _462318] : [class_Groups_Oordered__ab__group__add__abs(_462316), c_Orderings_Oord__class_Oless(_462316, _462318, c_Groups_Ozero__class_Ozero(_462316)), -(c_Groups_Oabs__class_Oabs(_462316, _462318) = c_Groups_Ouminus__class_Ouminus(_462316, _462318))], (10420 ^ _224325) ^ [] : [-(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)))], (10174 ^ _224325) ^ [_576026, _576028] : [10175 ^ _224325 : [(10178 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _576026)], (10176 ^ _224325) ^ [] : [_576028 = 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), _576026), _576028)))], (11809 ^ _224325) ^ [] : [-(class_Rings_Ocomm__ring(tc_RealDef_Oreal))], (10710 ^ _224325) ^ [_596273, _596275] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _596273, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _596275)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, _596273, _596275))], (10568 ^ _224325) ^ [_590199, _590201, _590203, _590205, _590207] : [class_Rings_Oring(_590199), -(c_Groups_Ominus__class_Ominus(_590199, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_590199), _590201), _590203), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_590199), _590205), _590207)) = c_Groups_Oplus__class_Oplus(_590199, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_590199), _590201), c_Groups_Ominus__class_Ominus(_590199, _590203, _590207)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_590199), c_Groups_Ominus__class_Ominus(_590199, _590201, _590205)), _590207)))], (8073 ^ _224325) ^ [_503285, _503287] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _503285, _503287), 8078 ^ _224325 : [(8081 ^ _224325) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _503287, _503285)], (8079 ^ _224325) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _503285, _503287))]], -(_503285 = _503287)], (11783 ^ _224325) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal))], (11599 ^ _224325) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (5219 ^ _224325) ^ [_402878, _402880, _402882] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _402878, _402880), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _402882), _402878), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _402882), _402880)))], (11825 ^ _224325) ^ [] : [-(class_Rings_Oring__1(tc_RealDef_Oreal))], (11213 ^ _224325) ^ [_616428, _616430] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _616428, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _616428, _616430)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4505 ^ _224325) ^ [_376208, _376210, _376212] : [class_Rings_Olinordered__ring__strict(_376208), 4508 ^ _224325 : [(4517 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_376208, c_Groups_Oplus__class_Oplus(_376208, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_376208), _376210), _376210), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_376208), _376212), _376212)), c_Groups_Ozero__class_Ozero(_376208))), _376210 = c_Groups_Ozero__class_Ozero(_376208), _376212 = c_Groups_Ozero__class_Ozero(_376208)], (4509 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_376208, c_Groups_Oplus__class_Oplus(_376208, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_376208), _376210), _376210), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_376208), _376212), _376212)), c_Groups_Ozero__class_Ozero(_376208)), 4512 ^ _224325 : [(4515 ^ _224325) ^ [] : [-(_376212 = c_Groups_Ozero__class_Ozero(_376208))], (4513 ^ _224325) ^ [] : [-(_376210 = c_Groups_Ozero__class_Ozero(_376208))]]]]], (10044 ^ _224325) ^ [_571183, _571185] : [class_RealVector_Oreal__normed__vector(_571183), 10047 ^ _224325 : [(10048 ^ _224325) ^ [] : [10057 ^ _224325 : [(10058 ^ _224325) ^ [_571740] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_571183, hAPP(_571185, _571740)), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(10056 ^ [_571183, _571185]))))]], 10049 ^ _224325 : [(10050 ^ _224325) ^ [_571422] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _571422), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_571183, hAPP(_571185, 10053 ^ [_571183, _571185, _571422])), _571422)]]], (10060 ^ _224325) ^ [] : [10062 ^ _224325 : [(10063 ^ _224325) ^ [_571919] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_571183, hAPP(_571185, 10061 ^ [_571183, _571185, _571919])), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(_571919)))]], 10065 ^ _224325 : [(10068 ^ _224325) ^ [_572140] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_571183, hAPP(_571185, _572140)), 10064 ^ [_571183, _571185]))], (10066 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 10064 ^ [_571183, _571185]))]]]]], (4857 ^ _224325) ^ [_389234, _389236, _389238, _389240, _389242, _389244] : [class_Groups_Ozero(_389234), hAPP(hAPP(hAPP(_389236, c_Groups_Ozero__class_Ozero(_389234)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_389234))), _389238) = _389238, -(c_Polynomial_Opoly__rec(_389240, _389234, _389238, _389236, c_Polynomial_OpCons(_389234, _389242, _389244)) = hAPP(hAPP(hAPP(_389236, _389242), _389244), c_Polynomial_Opoly__rec(_389240, _389234, _389238, _389236, _389244)))], (9025 ^ _224325) ^ [_535599] : [c_Groups_Oabs__class_Oabs(tc_Int_Oint, _535599) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _535599, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (7428 ^ _224325) ^ [_480690, _480692, _480694] : [class_Rings_Oidom(_480690), 7431 ^ _224325 : [(7438 ^ _224325) ^ [] : [hAPP(c_Polynomial_Opoly(_480690, _480694), c_Groups_Ouminus__class_Ouminus(_480690, _480692)) = c_Groups_Ozero__class_Ozero(_480690), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_480690), c_Polynomial_OpCons(_480690, _480692, c_Polynomial_OpCons(_480690, c_Groups_Oone__class_Oone(_480690), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_480690)))), _480694))], (7432 ^ _224325) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_480690), c_Polynomial_OpCons(_480690, _480692, c_Polynomial_OpCons(_480690, c_Groups_Oone__class_Oone(_480690), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_480690)))), _480694), -(hAPP(c_Polynomial_Opoly(_480690, _480694), c_Groups_Ouminus__class_Ouminus(_480690, _480692)) = c_Groups_Ozero__class_Ozero(_480690))]]], (10208 ^ _224325) ^ [_577229, _577231, _577233] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _577229, _577231), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _577233, _577229), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _577233, _577231)))], (494 ^ _224325) ^ [_239274, _239276] : [-(class_Groups_Omonoid__mult(_239274)), _239276 = _239274, class_Groups_Omonoid__mult(_239276)], (11509 ^ _224325) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (4987 ^ _224325) ^ [_394637, _394639] : [-(_394637 = _394639), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _394637, _394639)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _394639, _394637))], (10770 ^ _224325) ^ [_598755, _598757, _598759, _598761, _598763, _598765] : [class_Rings_Oordered__ring(_598755), 10773 ^ _224325 : [(10780 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_598755, _598761, c_Groups_Oplus__class_Oplus(_598755, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_598755), c_Groups_Ominus__class_Ominus(_598755, _598763, _598757)), _598759), _598765)), -(c_Orderings_Oord__class_Oless(_598755, c_Groups_Oplus__class_Oplus(_598755, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_598755), _598757), _598759), _598761), c_Groups_Oplus__class_Oplus(_598755, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_598755), _598763), _598759), _598765)))], (10774 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_598755, c_Groups_Oplus__class_Oplus(_598755, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_598755), _598757), _598759), _598761), c_Groups_Oplus__class_Oplus(_598755, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_598755), _598763), _598759), _598765)), -(c_Orderings_Oord__class_Oless(_598755, _598761, c_Groups_Oplus__class_Oplus(_598755, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_598755), c_Groups_Ominus__class_Ominus(_598755, _598763, _598757)), _598759), _598765)))]]], (3503 ^ _224325) ^ [_342705, _342707, _342709] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _342705, _342707)), _342709) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _342705), _342709), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _342707), _342709)))], (5281 ^ _224325) ^ [_405314, _405316, _405318, _405320] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _405314, _405316), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _405318, _405320), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _405314, _405318), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _405316, _405320)))], (674 ^ _224325) ^ [_244584, _244586] : [-(class_Groups_Ominus(_244584)), _244586 = _244584, class_Groups_Ominus(_244586)], (5251 ^ _224325) ^ [_404124, _404126, _404128] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _404124, _404126), _404128), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _404124, _404128))], (1133 ^ _224325) ^ [_261330, _261332, _261334] : [class_RealVector_Oreal__normed__div__algebra(_261330), -(c_RealVector_Onorm__class_Onorm(_261330, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_261330), _261332), _261334)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_261330, _261332)), c_RealVector_Onorm__class_Onorm(_261330, _261334)))], (2254 ^ _224325) ^ [_297623, _297625, _297627, _297629, _297631] : [class_Groups_Oordered__cancel__ab__semigroup__add(_297623), c_Orderings_Oord__class_Oless(_297623, _297625, _297627), c_Orderings_Oord__class_Oless__eq(_297623, _297629, _297631), -(c_Orderings_Oord__class_Oless(_297623, c_Groups_Oplus__class_Oplus(_297623, _297625, _297629), c_Groups_Oplus__class_Oplus(_297623, _297627, _297631)))], (1894 ^ _224325) ^ [_285442, _285444, _285446] : [class_Orderings_Olinorder(_285442), 1897 ^ _224325 : [(1904 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_285442, _285446, _285444), c_Orderings_Oord__class_Oless__eq(_285442, _285444, _285446)], (1898 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_285442, _285444, _285446)), -(c_Orderings_Oord__class_Oless(_285442, _285446, _285444))]]], (11084 ^ _224325) ^ [_611425, _611427, _611429] : [class_Rings_Ocomm__ring__1(_611425), -(c_Groups_Ominus__class_Ominus(_611425, hAPP(hAPP(c_Power_Opower__class_Opower(_611425), _611427), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(hAPP(c_Power_Opower__class_Opower(_611425), _611429), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_611425), c_Groups_Ominus__class_Ominus(_611425, _611427, _611429)), c_Groups_Oplus__class_Oplus(_611425, _611427, _611429)))], (9646 ^ _224325) ^ [_557504, _557506] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _557504, c_Nat_OSuc(_557506))), 9647 ^ _224325 : [(9650 ^ _224325) ^ [_557673] : [_557504 = c_Nat_OSuc(_557673), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _557673, _557506)], (9648 ^ _224325) ^ [] : [_557504 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (6328 ^ _224325) ^ [_443483, _443485, _443487] : [class_Groups_Ogroup__add(_443483), -(c_Groups_Ouminus__class_Ouminus(_443483, c_Groups_Oplus__class_Oplus(_443483, _443485, _443487)) = c_Groups_Oplus__class_Oplus(_443483, c_Groups_Ouminus__class_Ouminus(_443483, _443487), c_Groups_Ouminus__class_Ouminus(_443483, _443485)))], (9842 ^ _224325) ^ [_564112, _564114] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _564112, c_Nat_OSuc(_564114)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _564112, _564114))], (614 ^ _224325) ^ [_242814, _242816] : [-(class_Groups_Osgn__if(_242814)), _242816 = _242814, class_Groups_Osgn__if(_242816)], (1131 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), v_r))], (5659 ^ _224325) ^ [_419123, _419125] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _419123, _419125), _419125 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (3063 ^ _224325) ^ [_327281, _327283] : [class_Groups_Ocomm__monoid__mult(_327281), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_327281), c_Groups_Oone__class_Oone(_327281)), _327283) = _327283)], (2240 ^ _224325) ^ [_297131, _297133, _297135, _297137, _297139] : [class_Groups_Oordered__cancel__ab__semigroup__add(_297131), c_Orderings_Oord__class_Oless__eq(_297131, _297133, _297135), c_Orderings_Oord__class_Oless(_297131, _297137, _297139), -(c_Orderings_Oord__class_Oless(_297131, c_Groups_Oplus__class_Oplus(_297131, _297133, _297137), c_Groups_Oplus__class_Oplus(_297131, _297135, _297139)))], (6182 ^ _224325) ^ [_438050, _438052, _438054] : [class_Groups_Oordered__ab__group__add(_438050), 6185 ^ _224325 : [(6192 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_438050, _438054, c_Groups_Ouminus__class_Ouminus(_438050, _438052)), -(c_Orderings_Oord__class_Oless__eq(_438050, _438052, c_Groups_Ouminus__class_Ouminus(_438050, _438054)))], (6186 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_438050, _438052, c_Groups_Ouminus__class_Ouminus(_438050, _438054)), -(c_Orderings_Oord__class_Oless__eq(_438050, _438054, c_Groups_Ouminus__class_Ouminus(_438050, _438052)))]]], (11411 ^ _224325) ^ [_623705, _623707] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _623705), _623707), -(c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _623707, c_RealDef_Oreal(tc_Nat_Onat, _623705))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_RComplete_Onatceiling(_623707), _623705))], (7322 ^ _224325) ^ [_477005, _477007] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _477005), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), c_RealDef_Oreal(tc_Nat_Onat, _477007)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _477005, _477007))], (11973 ^ _224325) ^ [_639847] : [class_Rings_Olinordered__idom(_639847), -(class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(_639847)))], (7841 ^ _224325) ^ [_495002, _495004] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _495002, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _495004, _495002)), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _495002, _495004))], (11891 ^ _224325) ^ [] : [-(class_Rings_Omult__zero(tc_Complex_Ocomplex))], (11767 ^ _224325) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_RealDef_Oreal))], (6676 ^ _224325) ^ [_455204, _455206] : [class_Rings_Oring__1__no__zero__divisors(_455204), 6679 ^ _224325 : [(6680 ^ _224325) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_455204), _455206), _455206) = c_Groups_Oone__class_Oone(_455204), -(_455206 = c_Groups_Oone__class_Oone(_455204)), -(_455206 = c_Groups_Ouminus__class_Ouminus(_455204, c_Groups_Oone__class_Oone(_455204)))], (6690 ^ _224325) ^ [] : [6691 ^ _224325 : [(6694 ^ _224325) ^ [] : [_455206 = c_Groups_Ouminus__class_Ouminus(_455204, c_Groups_Oone__class_Oone(_455204))], (6692 ^ _224325) ^ [] : [_455206 = c_Groups_Oone__class_Oone(_455204)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_455204), _455206), _455206) = c_Groups_Oone__class_Oone(_455204))]]], (1284 ^ _224325) ^ [_266485, _266487] : [class_RealVector_Oreal__normed__vector(_266485), 1287 ^ _224325 : [(1294 ^ _224325) ^ [] : [-(_266487 = c_Groups_Ozero__class_Ozero(_266485)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_266485, _266487)))], (1288 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_266485, _266487)), _266487 = c_Groups_Ozero__class_Ozero(_266485)]]], (8755 ^ _224325) ^ [_526515, _526517, _526519, _526521] : [class_Rings_Olinordered__semidom(_526515), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _526517, _526519), c_Orderings_Oord__class_Oless(_526515, c_Groups_Oone__class_Oone(_526515), _526521), -(c_Orderings_Oord__class_Oless(_526515, hAPP(hAPP(c_Power_Opower__class_Opower(_526515), _526521), _526517), hAPP(hAPP(c_Power_Opower__class_Opower(_526515), _526521), _526519)))], (11899 ^ _224325) ^ [] : [-(class_Groups_Ouminus(tc_Complex_Ocomplex))], (9401 ^ _224325) ^ [_548888, _548890] : [c_Groups_Oabs__class_Oabs(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _548888), _548890)) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(c_Groups_Oabs__class_Oabs(tc_Int_Oint, _548888) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (8459 ^ _224325) ^ [_515474, _515476] : [-(c_RealDef_Oreal(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _515474), _515476)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _515474)), _515476))], (8309 ^ _224325) ^ [_510607, _510609] : [_510607 = _510609, c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _510607, _510609), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _510609, _510607))], (5531 ^ _224325) ^ [_414732] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _414732, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _414732)], (4949 ^ _224325) ^ [_392996, _392998] : [class_RealVector_Oreal__normed__algebra(_392996), 4953 ^ _224325 : [(4954 ^ _224325) ^ [_393207] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_392996, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_392996), _393207), _392998)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_392996, _393207)), 4952 ^ [_392996, _392998])))]]], (3057 ^ _224325) ^ [_327053, _327055] : [class_Groups_Omonoid__mult(_327053), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_327053), _327055), c_Groups_Oone__class_Oone(_327053)) = _327055)], (12105 ^ _224325) ^ [_644027] : [class_Rings_Ocomm__semiring__0(_644027), -(class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(_644027)))], (1171 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_cs____), v_z____)), v_m____))], (9796 ^ _224325) ^ [_562539, _562541] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_562539), _562541), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _562539, _562541))], (8889 ^ _224325) ^ [_530974, _530976, _530978, _530980] : [class_Rings_Olinordered__semidom(_530974), c_Orderings_Oord__class_Oless(_530974, c_Groups_Oone__class_Oone(_530974), _530976), 8896 ^ _224325 : [(8903 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _530978, _530980), -(c_Orderings_Oord__class_Oless__eq(_530974, hAPP(hAPP(c_Power_Opower__class_Opower(_530974), _530976), _530978), hAPP(hAPP(c_Power_Opower__class_Opower(_530974), _530976), _530980)))], (8897 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_530974, hAPP(hAPP(c_Power_Opower__class_Opower(_530974), _530976), _530978), hAPP(hAPP(c_Power_Opower__class_Opower(_530974), _530976), _530980)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _530978, _530980))]]], (5291 ^ _224325) ^ [_405669, _405671, _405673] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _405669, _405671), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _405669, _405673), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _405671, _405673)))], (11721 ^ _224325) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal))], (11879 ^ _224325) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Complex_Ocomplex))], (11555 ^ _224325) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (10666 ^ _224325) ^ [_594657, _594659, _594661, _594663, _594665] : [class_Groups_Oordered__ab__group__add(_594657), c_Groups_Ominus__class_Ominus(_594657, _594659, _594661) = c_Groups_Ominus__class_Ominus(_594657, _594663, _594665), 10673 ^ _224325 : [(10680 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_594657, _594663, _594665), -(c_Orderings_Oord__class_Oless__eq(_594657, _594659, _594661))], (10674 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_594657, _594659, _594661), -(c_Orderings_Oord__class_Oless__eq(_594657, _594663, _594665))]]], (6902 ^ _224325) ^ [_462631, _462633] : [class_Groups_Oabs__if(_462631), 6905 ^ _224325 : [(6912 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(_462631, _462633, c_Groups_Ozero__class_Ozero(_462631))), -(c_Groups_Oabs__class_Oabs(_462631, _462633) = _462633)], (6906 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_462631, _462633, c_Groups_Ozero__class_Ozero(_462631)), -(c_Groups_Oabs__class_Oabs(_462631, _462633) = c_Groups_Ouminus__class_Ouminus(_462631, _462633))]]], (1764 ^ _224325) ^ [_281469, _281471, _281473] : [class_Orderings_Oorder(_281469), -(_281471 = _281473), c_Orderings_Oord__class_Oless__eq(_281469, _281471, _281473), -(c_Orderings_Oord__class_Oless(_281469, _281471, _281473))], (3607 ^ _224325) ^ [_346080, _346082, _346084] : [class_Rings_Oordered__cancel__semiring(_346080), c_Orderings_Oord__class_Oless__eq(_346080, c_Groups_Ozero__class_Ozero(_346080), _346082), c_Orderings_Oord__class_Oless__eq(_346080, _346084, c_Groups_Ozero__class_Ozero(_346080)), -(c_Orderings_Oord__class_Oless__eq(_346080, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_346080), _346084), _346082), c_Groups_Ozero__class_Ozero(_346080)))], (8831 ^ _224325) ^ [_529118, _529120, _529122, _529124] : [class_Rings_Olinordered__semidom(_529118), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _529120, _529122), c_Orderings_Oord__class_Oless(_529118, c_Groups_Ozero__class_Ozero(_529118), _529124), c_Orderings_Oord__class_Oless(_529118, _529124, c_Groups_Oone__class_Oone(_529118)), -(c_Orderings_Oord__class_Oless(_529118, hAPP(hAPP(c_Power_Opower__class_Opower(_529118), _529124), _529122), hAPP(hAPP(c_Power_Opower__class_Opower(_529118), _529124), _529120)))], (1173 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_z____), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_cs____), v_z____)))), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), v_r), v_m____))))], (9531 ^ _224325) ^ [_553201] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _553201) = _553201)], (10300 ^ _224325) ^ [_580520, _580522, _580524] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _580520), _580520 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _580522, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _580520), _580524)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _580522, _580520), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _580524))], (1696 ^ _224325) ^ [_279390, _279392, _279394] : [class_Orderings_Oorder(_279390), c_Orderings_Oord__class_Oless__eq(_279390, _279392, _279394), -(c_Orderings_Oord__class_Oless(_279390, _279392, _279394)), -(_279392 = _279394)], (10110 ^ _224325) ^ [_573839, _573841, _573843] : [class_Rings_Olinordered__semidom(_573839), c_Orderings_Oord__class_Oless(_573839, c_Groups_Ozero__class_Ozero(_573839), _573841), c_Orderings_Oord__class_Oless(_573839, _573841, c_Groups_Oone__class_Oone(_573839)), -(c_Orderings_Oord__class_Oless(_573839, hAPP(hAPP(c_Power_Opower__class_Opower(_573839), _573841), c_Nat_OSuc(_573843)), c_Groups_Oone__class_Oone(_573839)))], (10218 ^ _224325) ^ [_577692, _577694, _577696] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _577692, _577694), _577696) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _577692, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _577694, _577696)))], (11763 ^ _224325) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal))], (10882 ^ _224325) ^ [_603304, _603306, _603308, _603310] : [class_Rings_Ocomm__ring(_603304), -(hAPP(c_Polynomial_Opoly(_603304, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_603304), _603306, _603308)), _603310) = c_Groups_Ominus__class_Ominus(_603304, hAPP(c_Polynomial_Opoly(_603304, _603306), _603310), hAPP(c_Polynomial_Opoly(_603304, _603308), _603310)))], (5525 ^ _224325) ^ [_414487] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _414487))], (2370 ^ _224325) ^ [_301241, _301243] : [class_Groups_Olinordered__ab__group__add(_301241), 2373 ^ _224325 : [(2380 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_301241, c_Groups_Ozero__class_Ozero(_301241), _301243), -(c_Orderings_Oord__class_Oless__eq(_301241, c_Groups_Ozero__class_Ozero(_301241), c_Groups_Oplus__class_Oplus(_301241, _301243, _301243)))], (2374 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_301241, c_Groups_Ozero__class_Ozero(_301241), c_Groups_Oplus__class_Oplus(_301241, _301243, _301243)), -(c_Orderings_Oord__class_Oless__eq(_301241, c_Groups_Ozero__class_Ozero(_301241), _301243))]]], (6368 ^ _224325) ^ [_444953] : [class_Groups_Oab__group__add(_444953), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_444953), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_444953))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_444953)))], (3389 ^ _224325) ^ [_338508] : [class_Rings_Ozero__neq__one(_338508), c_Groups_Ozero__class_Ozero(_338508) = c_Groups_Oone__class_Oone(_338508)], (4395 ^ _224325) ^ [_372368, _372370, _372372, _372374] : [class_Rings_Olinordered__semiring__strict(_372368), c_Orderings_Oord__class_Oless__eq(_372368, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_372368), _372370), _372372), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_372368), _372374), _372372)), c_Orderings_Oord__class_Oless(_372368, c_Groups_Ozero__class_Ozero(_372368), _372372), -(c_Orderings_Oord__class_Oless__eq(_372368, _372370, _372374))], (9781 ^ _224325) ^ [_561907, _561909] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _561907, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _561909, _561907))))], (7977 ^ _224325) ^ [_500188, _500190] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _500188), 7980 ^ _224325 : [(7987 ^ _224325) ^ [] : [_500190 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _500190), _500188), _500188))], (7981 ^ _224325) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _500190), _500188), _500188), -(_500190 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (10002 ^ _224325) ^ [_569748, _569750] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _569748), _569750))), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _569748), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _569750)], (11565 ^ _224325) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (11309 ^ _224325) ^ [_619728, _619730, _619732] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _619728, _619730), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _619730, _619732), _619728) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _619730, _619728), _619732))], (5195 ^ _224325) ^ [_401886, _401888, _401890] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _401886, _401888), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _401886, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _401888, _401890)))], (1125 ^ _224325) ^ [_261051] : [class_RealVector_Oreal__normed__algebra__1(_261051), -(c_RealVector_Onorm__class_Onorm(_261051, c_Groups_Oone__class_Oone(_261051)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (9367 ^ _224325) ^ [_547783, _547785] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _547785, c_Nat_OSuc(_547783)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _547783, _547785)], (4157 ^ _224325) ^ [_364345, _364347, _364349] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _364345), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _364347, _364349), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _364345), _364347), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _364345), _364349)))], (10754 ^ _224325) ^ [_598051, _598053, _598055, _598057, _598059, _598061] : [class_Rings_Oordered__ring(_598051), 10757 ^ _224325 : [(10764 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_598051, c_Groups_Oplus__class_Oplus(_598051, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_598051), c_Groups_Ominus__class_Ominus(_598051, _598053, _598059)), _598055), _598057), _598061), -(c_Orderings_Oord__class_Oless__eq(_598051, c_Groups_Oplus__class_Oplus(_598051, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_598051), _598053), _598055), _598057), c_Groups_Oplus__class_Oplus(_598051, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_598051), _598059), _598055), _598061)))], (10758 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_598051, c_Groups_Oplus__class_Oplus(_598051, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_598051), _598053), _598055), _598057), c_Groups_Oplus__class_Oplus(_598051, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_598051), _598059), _598055), _598061)), -(c_Orderings_Oord__class_Oless__eq(_598051, c_Groups_Oplus__class_Oplus(_598051, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_598051), c_Groups_Ominus__class_Ominus(_598051, _598053, _598059)), _598055), _598057), _598061))]]], (1560 ^ _224325) ^ [_275124, _275126, _275128, _275130] : [class_Orderings_Opreorder(_275124), c_Orderings_Oord__class_Oless(_275124, _275126, _275128), c_Orderings_Oord__class_Oless(_275124, _275128, _275130), -(c_Orderings_Oord__class_Oless(_275124, _275126, _275130))], (1518 ^ _224325) ^ [_273786, _273788, _273790, _273792] : [class_Orderings_Oorder(_273786), _273788 = _273790, c_Orderings_Oord__class_Oless(_273786, _273792, _273790), -(c_Orderings_Oord__class_Oless(_273786, _273792, _273788))], (9848 ^ _224325) ^ [_564282, _564284] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _564282, _564284), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _564282, c_Nat_OSuc(_564284)))], (6552 ^ _224325) ^ [_451229, _451231] : [class_Rings_Olinordered__idom(_451229), 6555 ^ _224325 : [(6562 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_451229, _451231, c_Groups_Ozero__class_Ozero(_451229)), -(c_Orderings_Oord__class_Oless(_451229, _451231, c_Groups_Ouminus__class_Ouminus(_451229, _451231)))], (6556 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_451229, _451231, c_Groups_Ouminus__class_Ouminus(_451229, _451231)), -(c_Orderings_Oord__class_Oless(_451229, _451231, c_Groups_Ozero__class_Ozero(_451229)))]]], (10534 ^ _224325) ^ [_588843, _588845, _588847] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _588843), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _588845, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _588847, 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, _588847, _588845)), c_Groups_Oone__class_Oone(tc_Int_Oint))), _588843))))], (11239 ^ _224325) ^ [_617419, _617421, _617423] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _617419, _617423), _617421), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _617419, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _617421, _617423)))], (11795 ^ _224325) ^ [] : [-(class_Orderings_Olinorder(tc_RealDef_Oreal))], (7356 ^ _224325) ^ [_478175, _478177] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _478175), 7359 ^ _224325 : [(7366 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _478175, c_RealDef_Oreal(tc_Nat_Onat, _478177)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_478175), _478177))], (7360 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_478175), _478177), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _478175, c_RealDef_Oreal(tc_Nat_Onat, _478177)))]]], (7202 ^ _224325) ^ [_472594, _472596] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _472594, _472596), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _472594), c_RealDef_Oreal(tc_Nat_Onat, _472596)))], (2118 ^ _224325) ^ [_293252, _293254] : [class_Groups_Oordered__ab__group__add__abs(_293252), 2121 ^ _224325 : [(2128 ^ _224325) ^ [] : [_293254 = c_Groups_Ozero__class_Ozero(_293252), -(c_Groups_Oabs__class_Oabs(_293252, _293254) = c_Groups_Ozero__class_Ozero(_293252))], (2122 ^ _224325) ^ [] : [c_Groups_Oabs__class_Oabs(_293252, _293254) = c_Groups_Ozero__class_Ozero(_293252), -(_293254 = c_Groups_Ozero__class_Ozero(_293252))]]], (2196 ^ _224325) ^ [_295747, _295749, _295751] : [class_Groups_Oordered__comm__monoid__add(_295747), c_Orderings_Oord__class_Oless__eq(_295747, c_Groups_Ozero__class_Ozero(_295747), _295749), c_Orderings_Oord__class_Oless(_295747, c_Groups_Ozero__class_Ozero(_295747), _295751), -(c_Orderings_Oord__class_Oless(_295747, c_Groups_Ozero__class_Ozero(_295747), c_Groups_Oplus__class_Oplus(_295747, _295749, _295751)))], (474 ^ _224325) ^ [_238684, _238686] : [-(class_Orderings_Opreorder(_238684)), _238686 = _238684, class_Orderings_Opreorder(_238686)], (9149 ^ _224325) ^ [_539959, _539961] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_539959), _539961), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _539959, _539961))], (5789 ^ _224325) ^ [_423697] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _423697), -(c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, _423697) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (11245 ^ _224325) ^ [_617657, _617659] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _617657, _617659)), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _617659, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _617657, _617659)) = _617657)], (5225 ^ _224325) ^ [_403150, _403152, _403154, _403156] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _403150, _403152), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _403154, _403156), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _403150, _403154), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _403152, _403156)))], (634 ^ _224325) ^ [_243404, _243406] : [-(class_Groups_Oabs__if(_243404)), _243406 = _243404, class_Groups_Oabs__if(_243406)], (11383 ^ _224325) ^ [_622557, _622559, _622561] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _622557, _622559), _622561), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _622557, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _622561, _622559)))], (11321 ^ _224325) ^ [_620256, _620258, _620260] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _620256, _620258), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _620260, _620258), _620256) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _620260, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _620258, _620256)))], (11815 ^ _224325) ^ [] : [-(class_Rings_Osemiring(tc_RealDef_Oreal))], (11917 ^ _224325) ^ [] : [-(class_Rings_Odvd(tc_Complex_Ocomplex))], (11154 ^ _224325) ^ [_614214, _614216, _614218] : [hBOOL(hAPP(_614214, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _614216, _614218))), 11157 ^ _224325 : [(11164 ^ _224325) ^ [_614546] : [_614216 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _614218, _614546), -(hBOOL(hAPP(_614214, _614546)))], (11158 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _614216, _614218), -(hBOOL(hAPP(_614214, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (11469 ^ _224325) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint))], (664 ^ _224325) ^ [_244289, _244291] : [-(class_Groups_Oab__group__add(_244289)), _244291 = _244289, class_Groups_Oab__group__add(_244291)], (62 ^ _224325) ^ [_226477, _226479, _226481, _226483, _226485, _226487] : [-(c_Rings_Odvd__class_Odvd(_226485, _226481, _226477)), c_Rings_Odvd__class_Odvd(_226487, _226483, _226479), _226487 = _226485, _226483 = _226481, _226479 = _226477], (9155 ^ _224325) ^ [_540177, _540179] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _540177, c_Nat_OSuc(_540179)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _540177, _540179)), -(_540177 = c_Nat_OSuc(_540179))], (5213 ^ _224325) ^ [_402620, _402622, _402624] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _402620, _402622), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _402620), _402624), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _402622), _402624)))], (4441 ^ _224325) ^ [_373865, _373867, _373869] : [class_Rings_Olinordered__idom(_373865), c_Orderings_Oord__class_Oless__eq(_373865, c_Groups_Ozero__class_Ozero(_373865), _373867), c_Orderings_Oord__class_Oless__eq(_373865, c_Groups_Ozero__class_Ozero(_373865), _373869), c_Orderings_Oord__class_Oless__eq(_373865, _373869, c_Groups_Oone__class_Oone(_373865)), -(c_Orderings_Oord__class_Oless__eq(_373865, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_373865), _373869), _373867), _373867))], (744 ^ _224325) ^ [_246649, _246651] : [-(class_Rings_Ocomm__semiring__1(_246649)), _246651 = _246649, class_Rings_Ocomm__semiring__1(_246651)], (4903 ^ _224325) ^ [_391146, _391148, _391150] : [class_Rings_Olinordered__idom(_391146), c_Polynomial_Opos__poly(_391146, _391148), c_Polynomial_Opos__poly(_391146, _391150), -(c_Polynomial_Opos__poly(_391146, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_391146), _391148, _391150)))], (3355 ^ _224325) ^ [_337447, _337449, _337451] : [class_Rings_Ono__zero__divisors(_337447), -(_337449 = c_Groups_Ozero__class_Ozero(_337447)), -(_337451 = c_Groups_Ozero__class_Ozero(_337447)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_337447), _337449), _337451) = c_Groups_Ozero__class_Ozero(_337447)], (2442 ^ _224325) ^ [_303660, _303662, _303664, _303666, _303668] : [class_RealVector_Oreal__normed__algebra(_303660), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_303660, _303662), _303664), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_303660, _303666), _303668), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_303660, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_303660), _303662), _303666)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _303664), _303668)))], (8769 ^ _224325) ^ [_526999, _527001, _527003, _527005] : [class_Rings_Olinordered__semidom(_526999), c_Orderings_Oord__class_Oless(_526999, c_Groups_Oone__class_Oone(_526999), _527001), c_Orderings_Oord__class_Oless(_526999, hAPP(hAPP(c_Power_Opower__class_Opower(_526999), _527001), _527003), hAPP(hAPP(c_Power_Opower__class_Opower(_526999), _527001), _527005)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _527003, _527005))], (8109 ^ _224325) ^ [_504368, _504370] : [8116 ^ _224325 : [(8119 ^ _224325) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _504370, _504368)], (8117 ^ _224325) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _504368, _504370))]], c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _504368, _504370), -(_504368 = _504370)], (8199 ^ _224325) ^ [_507235, _507237] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _507235, _507237), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _507237, _507235), -(_507235 = _507237)], (3069 ^ _224325) ^ [_327509, _327511] : [class_Rings_Ocomm__semiring__1(_327509), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_327509), c_Groups_Oone__class_Oone(_327509)), _327511) = _327511)], (12045 ^ _224325) ^ [_642127] : [class_Rings_Ocomm__semiring__0(_642127), -(class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(_642127)))], (5727 ^ _224325) ^ [_421631, _421633, _421635] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _421631), _421633), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _421631), _421635))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _421631), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _421633, _421635)], (10540 ^ _224325) ^ [_589119, _589121, _589123] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _589119), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _589121, 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, _589121, _589123)), c_Groups_Oone__class_Oone(tc_Int_Oint))), _589119)), _589123))], (5109 ^ _224325) ^ [_398653, _398655] : [class_Rings_Olinordered__idom(_398653), -(c_Groups_Osgn__class_Osgn(_398653, c_Groups_Osgn__class_Osgn(_398653, _398655)) = c_Groups_Osgn__class_Osgn(_398653, _398655))], (7500 ^ _224325) ^ [_483095, _483097, _483099] : [class_Rings_Olinordered__idom(_483095), 7503 ^ _224325 : [(7510 ^ _224325) ^ [] : [c_Rings_Odvd__class_Odvd(_483095, _483097, _483099), -(c_Rings_Odvd__class_Odvd(_483095, c_Groups_Oabs__class_Oabs(_483095, _483097), _483099))], (7504 ^ _224325) ^ [] : [c_Rings_Odvd__class_Odvd(_483095, c_Groups_Oabs__class_Oabs(_483095, _483097), _483099), -(c_Rings_Odvd__class_Odvd(_483095, _483097, _483099))]]], (7468 ^ _224325) ^ [_482089, _482091, _482093] : [class_Rings_Ocomm__ring__1(_482089), 7471 ^ _224325 : [(7478 ^ _224325) ^ [] : [c_Rings_Odvd__class_Odvd(_482089, _482091, _482093), -(c_Rings_Odvd__class_Odvd(_482089, c_Groups_Ouminus__class_Ouminus(_482089, _482091), _482093))], (7472 ^ _224325) ^ [] : [c_Rings_Odvd__class_Odvd(_482089, c_Groups_Ouminus__class_Ouminus(_482089, _482091), _482093), -(c_Rings_Odvd__class_Odvd(_482089, _482091, _482093))]]], (2833 ^ _224325) ^ [_318199, _318201, _318203, _318205] : [class_Rings_Ocomm__semiring__1(_318199), -(c_Groups_Oplus__class_Oplus(_318199, _318201, c_Groups_Oplus__class_Oplus(_318199, _318203, _318205)) = c_Groups_Oplus__class_Oplus(_318199, c_Groups_Oplus__class_Oplus(_318199, _318201, _318203), _318205))], (11829 ^ _224325) ^ [] : [-(class_Fields_Ofield(tc_RealDef_Oreal))], (6322 ^ _224325) ^ [_443233, _443235, _443237] : [class_Groups_Ogroup__add(_443233), -(c_Groups_Oplus__class_Oplus(_443233, _443235, c_Groups_Oplus__class_Oplus(_443233, c_Groups_Ouminus__class_Ouminus(_443233, _443235), _443237)) = _443237)], (2154 ^ _224325) ^ [_294387, _294389, _294391] : [class_Groups_Oordered__comm__monoid__add(_294387), c_Orderings_Oord__class_Oless(_294387, _294389, c_Groups_Ozero__class_Ozero(_294387)), c_Orderings_Oord__class_Oless__eq(_294387, _294391, c_Groups_Ozero__class_Ozero(_294387)), -(c_Orderings_Oord__class_Oless(_294387, c_Groups_Oplus__class_Oplus(_294387, _294389, _294391), c_Groups_Ozero__class_Ozero(_294387)))], (12093 ^ _224325) ^ [_643647] : [class_Rings_Olinordered__idom(_643647), -(class_Rings_Olinordered__idom(tc_Polynomial_Opoly(_643647)))], (10950 ^ _224325) ^ [_605949, _605951] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _605949, _605951), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _605949, _605951), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (9914 ^ _224325) ^ [_566888, _566890, _566892, _566894] : [class_Rings_Olinordered__semidom(_566888), hAPP(hAPP(c_Power_Opower__class_Opower(_566888), _566890), c_Nat_OSuc(_566892)) = hAPP(hAPP(c_Power_Opower__class_Opower(_566888), _566894), c_Nat_OSuc(_566892)), c_Orderings_Oord__class_Oless__eq(_566888, c_Groups_Ozero__class_Ozero(_566888), _566890), c_Orderings_Oord__class_Oless__eq(_566888, c_Groups_Ozero__class_Ozero(_566888), _566894), -(_566890 = _566894)], (5417 ^ _224325) ^ [_410602] : [class_RealVector_Oreal__normed__algebra__1(_410602), -(c_Groups_Osgn__class_Osgn(_410602, c_Groups_Oone__class_Oone(_410602)) = c_Groups_Oone__class_Oone(_410602))], (11010 ^ _224325) ^ [_608510, _608512, _608514, _608516] : [class_RealVector_Oreal__normed__algebra(_608510), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_608510), _608512), c_Groups_Ominus__class_Ominus(_608510, _608514, _608516)) = c_Groups_Ominus__class_Ominus(_608510, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_608510), _608512), _608514), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_608510), _608512), _608516)))], (3051 ^ _224325) ^ [_326825, _326827] : [class_Rings_Ocomm__semiring__1(_326825), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_326825), _326827), c_Groups_Oone__class_Oone(_326825)) = _326827)], (5337 ^ _224325) ^ [_407562, _407564] : [class_Rings_Ocomm__semiring__0(_407562), -(c_Polynomial_Osmult(_407562, _407564, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_407562))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_407562)))], (4777 ^ _224325) ^ [_386275, _386277] : [class_Groups_Ocomm__monoid__add(_386275), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_386275), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_386275)), _386277) = _386277)], (2907 ^ _224325) ^ [_320921, _320923, _320925, _320927] : [class_Groups_Oordered__ab__semigroup__add(_320921), c_Orderings_Oord__class_Oless__eq(_320921, _320923, _320925), -(c_Orderings_Oord__class_Oless__eq(_320921, c_Groups_Oplus__class_Oplus(_320921, _320927, _320923), c_Groups_Oplus__class_Oplus(_320921, _320927, _320925)))], (1165 ^ _224325) ^ [_262715, _262717] : [class_Orderings_Opreorder(_262715), -(c_Orderings_Oord__class_Oless__eq(_262715, _262717, _262717))], (1139 ^ _224325) ^ [_261604, _261606, _261608] : [class_Groups_Oordered__ab__group__add__abs(_261604), -(c_Orderings_Oord__class_Oless__eq(_261604, c_Groups_Oabs__class_Oabs(_261604, c_Groups_Oplus__class_Oplus(_261604, _261606, _261608)), c_Groups_Oplus__class_Oplus(_261604, c_Groups_Oabs__class_Oabs(_261604, _261606), c_Groups_Oabs__class_Oabs(_261604, _261608))))], (9037 ^ _224325) ^ [_536048, _536050, _536052] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _536048, _536050), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _536048, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _536050, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _536048), _536052))))], (3763 ^ _224325) ^ [_351288, _351290, _351292] : [class_Rings_Oordered__ring(_351288), -(c_Orderings_Oord__class_Oless__eq(_351288, c_Groups_Ozero__class_Ozero(_351288), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_351288), _351290), _351292))), 3768 ^ _224325 : [(3775 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_351288, _351290, c_Groups_Ozero__class_Ozero(_351288)), c_Orderings_Oord__class_Oless__eq(_351288, _351292, c_Groups_Ozero__class_Ozero(_351288))], (3769 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_351288, c_Groups_Ozero__class_Ozero(_351288), _351290), c_Orderings_Oord__class_Oless__eq(_351288, c_Groups_Ozero__class_Ozero(_351288), _351292)]]], (11681 ^ _224325) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (9755 ^ _224325) ^ [_561004, _561006] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _561004), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _561004), _561006)))], (194 ^ _224325) ^ [_230424, _230426] : [-(class_Rings_Olinordered__semiring__1__strict(_230424)), _230426 = _230424, class_Rings_Olinordered__semiring__1__strict(_230426)], (6374 ^ _224325) ^ [_445195, _445197, _445199] : [class_Rings_Ocomm__ring(_445195), -(c_Polynomial_Osmult(_445195, _445197, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_445195), _445199)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_445195), c_Polynomial_Osmult(_445195, _445197, _445199)))], (8245 ^ _224325) ^ [_508689, _508691, _508693] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _508689, _508691), 8256 ^ _224325 : [(8259 ^ _224325) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _508693, _508689)], (8257 ^ _224325) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _508689, _508693))]], c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _508691, _508693), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _508693, _508691))], (1098 ^ _224325) ^ [_259968, _259970] : [hAPP(_259968, 1099 ^ [_259968, _259970]) = hAPP(_259970, 1099 ^ [_259968, _259970]), -(_259968 = _259970)], (11817 ^ _224325) ^ [] : [-(class_Orderings_Oord(tc_RealDef_Oreal))], (1157 ^ _224325) ^ [_262396, _262398, _262400] : [class_Rings_Ocomm__semiring__1(_262396), -(c_Groups_Oplus__class_Oplus(_262396, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_262396), _262398), _262400), _262400) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_262396), c_Groups_Oplus__class_Oplus(_262396, _262398, c_Groups_Oone__class_Oone(_262396))), _262400))], (11581 ^ _224325) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (3859 ^ _224325) ^ [_354496, _354498, _354500, _354502] : [class_Rings_Olinordered__semiring__strict(_354496), c_Orderings_Oord__class_Oless(_354496, _354498, _354500), c_Orderings_Oord__class_Oless(_354496, c_Groups_Ozero__class_Ozero(_354496), _354502), -(c_Orderings_Oord__class_Oless(_354496, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_354496), _354498), _354502), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_354496), _354500), _354502)))], (7877 ^ _224325) ^ [_496347, _496349, _496351, _496353] : [class_Rings_Ocomm__semiring__1(_496347), -(hAPP(c_Polynomial_Opoly(_496347, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_496347)), _496349), _496351)), _496353) = hAPP(hAPP(c_Power_Opower__class_Opower(_496347), hAPP(c_Polynomial_Opoly(_496347, _496349), _496353)), _496351))], (2993 ^ _224325) ^ [_324215, _324217, _324219, _324221] : [class_RealVector_Oreal__normed__algebra(_324215), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_324215), c_Groups_Oplus__class_Oplus(_324215, _324217, _324219)), _324221) = c_Groups_Oplus__class_Oplus(_324215, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_324215), _324217), _324221), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_324215), _324219), _324221)))], (9207 ^ _224325) ^ [_541929, _541931] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_541931), _541929), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _541929, _541931)], (12249 ^ _224325) ^ [_648587] : [class_Groups_Ozero(_648587), -(class_Groups_Ozero(tc_Polynomial_Opoly(_648587)))], (11913 ^ _224325) ^ [] : [-(class_Rings_Oidom(tc_Complex_Ocomplex))], (3719 ^ _224325) ^ [_349872, _349874, _349876, _349878, _349880] : [class_Rings_Oordered__semiring(_349872), c_Orderings_Oord__class_Oless__eq(_349872, _349874, _349876), c_Orderings_Oord__class_Oless__eq(_349872, _349878, _349880), c_Orderings_Oord__class_Oless__eq(_349872, c_Groups_Ozero__class_Ozero(_349872), _349874), c_Orderings_Oord__class_Oless__eq(_349872, c_Groups_Ozero__class_Ozero(_349872), _349878), -(c_Orderings_Oord__class_Oless__eq(_349872, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_349872), _349874), _349878), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_349872), _349876), _349880)))], (1190 ^ _224325) ^ [_263575, _263577] : [class_Groups_Oordered__ab__group__add__abs(_263575), c_Orderings_Oord__class_Oless(_263575, c_Groups_Oabs__class_Oabs(_263575, _263577), c_Groups_Ozero__class_Ozero(_263575))], (444 ^ _224325) ^ [_237799, _237801] : [-(class_Rings_Ocomm__semiring(_237799)), _237801 = _237799, class_Rings_Ocomm__semiring(_237801)], (11577 ^ _224325) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (5849 ^ _224325) ^ [_425892, _425894, _425896, _425898, _425900] : [class_Rings_Ocomm__semiring__0(_425892), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_425892), _425894, c_Polynomial_Osmult(_425892, _425896, _425898)) = c_Polynomial_OpCons(_425892, _425900, _425898), 5856 ^ _224325 : [(5859 ^ _224325) ^ [] : [-(_425898 = c_Polynomial_Osynthetic__div(_425892, _425894, _425896))], (5857 ^ _224325) ^ [] : [-(_425900 = hAPP(c_Polynomial_Opoly(_425892, _425894), _425896))]]], (654 ^ _224325) ^ [_243994, _243996] : [-(class_Rings_Oring__1(_243994)), _243996 = _243994, class_Rings_Oring__1(_243996)], (11833 ^ _224325) ^ [] : [-(class_Groups_Ozero(tc_RealDef_Oreal))], (11797 ^ _224325) ^ [] : [-(class_Groups_Omonoid__mult(tc_RealDef_Oreal))], (7234 ^ _224325) ^ [_473799] : [_473799 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _473799), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (8451 ^ _224325) ^ [_515187, _515189] : [8452 ^ _224325 : [(8455 ^ _224325) ^ [] : [_515189 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (8453 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _515187)]], -(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), _515187), _515189)))], (5463 ^ _224325) ^ [_412360, _412362, _412364, _412366] : [class_Rings_Ocomm__semiring__0(_412360), c_Polynomial_Osmult(_412360, _412362, _412364) = c_Polynomial_OpCons(_412360, _412366, _412364), -(_412364 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_412360)))], (11615 ^ _224325) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (1032 ^ _224325) ^ [_257450, _257452, _257454, _257456] : [-(c_fequal(_257456, _257452) = c_fequal(_257454, _257450)), _257456 = _257454, _257452 = _257450], (1980 ^ _224325) ^ [_288400, _288402, _288404, _288406] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_288400), 1983 ^ _224325 : [(1990 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_288400, _288404, _288406), -(c_Orderings_Oord__class_Oless(_288400, c_Groups_Oplus__class_Oplus(_288400, _288402, _288404), c_Groups_Oplus__class_Oplus(_288400, _288402, _288406)))], (1984 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(_288400, c_Groups_Oplus__class_Oplus(_288400, _288402, _288404), c_Groups_Oplus__class_Oplus(_288400, _288402, _288406)), -(c_Orderings_Oord__class_Oless(_288400, _288404, _288406))]]], (11735 ^ _224325) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal))], (7923 ^ _224325) ^ [_498384, _498386, _498388] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _498384), _498386), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _498384), _498388)), -(_498384 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _498386, _498388))], (2883 ^ _224325) ^ [_320064, _320066, _320068, _320070] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_320064), c_Orderings_Oord__class_Oless__eq(_320064, c_Groups_Oplus__class_Oplus(_320064, _320066, _320068), c_Groups_Oplus__class_Oplus(_320064, _320070, _320068)), -(c_Orderings_Oord__class_Oless__eq(_320064, _320066, _320070))], (11281 ^ _224325) ^ [_618864, _618866, _618868] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _618864, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _618866, _618868)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _618864, _618868), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _618868, _618866), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _618864, _618866))], (5183 ^ _224325) ^ [_401446, _401448, _401450] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _401446, _401448), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _401446, _401450)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _401448, _401450))], (8673 ^ _224325) ^ [_523465, _523467, _523469, _523471] : [class_Rings_Ocomm__semiring__1(_523465), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _523467, _523469), -(c_Rings_Odvd__class_Odvd(_523465, hAPP(hAPP(c_Power_Opower__class_Opower(_523465), _523471), _523467), hAPP(hAPP(c_Power_Opower__class_Opower(_523465), _523471), _523469)))], (9315 ^ _224325) ^ [_546097, _546099] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _546097, _546099)), 9318 ^ _224325 : [(9325 ^ _224325) ^ [] : [_546097 = _546099, -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _546097, c_Nat_OSuc(_546099)))], (9319 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _546097, c_Nat_OSuc(_546099)), -(_546097 = _546099)]]], (10862 ^ _224325) ^ [_602653, _602655, _602657, _602659, _602661] : [class_Groups_Oab__group__add(_602653), c_Groups_Ominus__class_Ominus(_602653, _602655, _602657) = c_Groups_Ominus__class_Ominus(_602653, _602659, _602661), 10869 ^ _224325 : [(10876 ^ _224325) ^ [] : [_602659 = _602661, -(_602655 = _602657)], (10870 ^ _224325) ^ [] : [_602655 = _602657, -(_602659 = _602661)]]], (2104 ^ _224325) ^ [_292728, _292730] : [class_Rings_Ocomm__semiring__1(_292728), -(c_Groups_Oplus__class_Oplus(_292728, c_Groups_Ozero__class_Ozero(_292728), _292730) = _292730)], (7150 ^ _224325) ^ [_470779, _470781, _470783] : [class_Lattices_Oboolean__algebra(_470779), c_Orderings_Oord__class_Oless__eq(_470779, _470781, _470783), -(c_Orderings_Oord__class_Oless__eq(_470779, c_Groups_Ouminus__class_Ouminus(_470779, _470783), c_Groups_Ouminus__class_Ouminus(_470779, _470781)))], (8409 ^ _224325) ^ [_513653, _513655, _513657] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _513653), _513655)), _513657) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _513653), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _513655), _513657)))], (5573 ^ _224325) ^ [_416100, _416102] : [5574 ^ _224325 : [(5577 ^ _224325) ^ [] : [_416102 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5575 ^ _224325) ^ [] : [_416100 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _416100), _416102) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6960 ^ _224325) ^ [_464651, _464653] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _464651), _464653), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _464651, _464653)))], (7540 ^ _224325) ^ [_484492, _484494, _484496, _484498] : [class_Rings_Ocomm__semiring__1(_484492), c_Rings_Odvd__class_Odvd(_484492, _484494, _484496), -(c_Rings_Odvd__class_Odvd(_484492, _484494, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_484492), _484496), _484498)))], (8871 ^ _224325) ^ [_530387, _530389, _530391, _530393] : [class_Rings_Olinordered__semidom(_530387), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _530389, _530391), c_Orderings_Oord__class_Oless__eq(_530387, c_Groups_Ozero__class_Ozero(_530387), _530393), c_Orderings_Oord__class_Oless__eq(_530387, _530393, c_Groups_Oone__class_Oone(_530387)), -(c_Orderings_Oord__class_Oless__eq(_530387, hAPP(hAPP(c_Power_Opower__class_Opower(_530387), _530393), _530391), hAPP(hAPP(c_Power_Opower__class_Opower(_530387), _530393), _530389)))], (2664 ^ _224325) ^ [_310857, _310859, _310861] : [class_Orderings_Olinorder(_310857), -(c_Orderings_Oord__class_Oless__eq(_310857, _310859, _310861)), -(c_Orderings_Oord__class_Oless__eq(_310857, _310861, _310859))], (9237 ^ _224325) ^ [_543326, _543328] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Nat_OSuc(_543326), _543328) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _543326, _543328)))], (4661 ^ _224325) ^ [_381202, _381204, _381206] : [class_Groups_Ozero(_381202), 4664 ^ _224325 : [(4673 ^ _224325) ^ [] : [-(c_Polynomial_OpCons(_381202, _381204, _381206) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_381202))), _381204 = c_Groups_Ozero__class_Ozero(_381202), _381206 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_381202))], (4665 ^ _224325) ^ [] : [c_Polynomial_OpCons(_381202, _381204, _381206) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_381202)), 4668 ^ _224325 : [(4671 ^ _224325) ^ [] : [-(_381206 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_381202)))], (4669 ^ _224325) ^ [] : [-(_381204 = c_Groups_Ozero__class_Ozero(_381202))]]]]], (7752 ^ _224325) ^ [_491805, _491807, _491809, _491811] : [class_Fields_Ofield(_491805), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_491805), _491807, c_Polynomial_Osmult(_491805, _491809, _491811)), -(_491809 = c_Groups_Ozero__class_Ozero(_491805)), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_491805), _491807, _491811))], (2310 ^ _224325) ^ [_299447, _299449, _299451] : [class_Groups_Oordered__comm__monoid__add(_299447), c_Orderings_Oord__class_Oless__eq(_299447, c_Groups_Ozero__class_Ozero(_299447), _299449), c_Orderings_Oord__class_Oless__eq(_299447, c_Groups_Ozero__class_Ozero(_299447), _299451), 2321 ^ _224325 : [(2330 ^ _224325) ^ [] : [-(c_Groups_Oplus__class_Oplus(_299447, _299449, _299451) = c_Groups_Ozero__class_Ozero(_299447)), _299449 = c_Groups_Ozero__class_Ozero(_299447), _299451 = c_Groups_Ozero__class_Ozero(_299447)], (2322 ^ _224325) ^ [] : [c_Groups_Oplus__class_Oplus(_299447, _299449, _299451) = c_Groups_Ozero__class_Ozero(_299447), 2325 ^ _224325 : [(2328 ^ _224325) ^ [] : [-(_299451 = c_Groups_Ozero__class_Ozero(_299447))], (2326 ^ _224325) ^ [] : [-(_299449 = c_Groups_Ozero__class_Ozero(_299447))]]]]], (12261 ^ _224325) ^ [_648967] : [class_Rings_Oidom(_648967), -(class_Rings_Oidom(tc_Polynomial_Opoly(_648967)))], (10248 ^ _224325) ^ [_578716] : [-(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _578716)) = _578716)], (6386 ^ _224325) ^ [_445691, _445693, _445695] : [class_Groups_Oab__group__add(_445691), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_445691), c_Polynomial_OpCons(_445691, _445693, _445695)) = c_Polynomial_OpCons(_445691, c_Groups_Ouminus__class_Ouminus(_445691, _445693), c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_445691), _445695)))], (9241 ^ _224325) ^ [_543581, _543583, _543585, _543587] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _543581, _543583), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _543585, _543587), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _543581, _543585), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _543583, _543587)))], (3677 ^ _224325) ^ [_348406, _348408, _348410, _348412] : [class_Rings_Oordered__comm__semiring(_348406), c_Orderings_Oord__class_Oless__eq(_348406, _348408, _348410), c_Orderings_Oord__class_Oless__eq(_348406, c_Groups_Ozero__class_Ozero(_348406), _348412), -(c_Orderings_Oord__class_Oless__eq(_348406, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_348406), _348412), _348408), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_348406), _348412), _348410)))], (5995 ^ _224325) ^ [_431480, _431482, _431484] : [5996 ^ _224325 : [(5999 ^ _224325) ^ [] : [_431482 = _431484], (5997 ^ _224325) ^ [] : [_431480 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _431480), _431482) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _431480), _431484))], (6003 ^ _224325) ^ [_431812, _431814, _431816] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _431812, _431814), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _431812, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _431814, _431816)))], (5423 ^ _224325) ^ [_410818, _410820] : [class_Rings_Ocomm__semiring__0(_410818), -(c_Polynomial_Osmult(_410818, c_Groups_Ozero__class_Ozero(_410818), _410820) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_410818)))], (10440 ^ _224325) ^ [_585139, _585141] : [class_Orderings_Oorder(_585139), 10443 ^ _224325 : [(10444 ^ _224325) ^ [] : [c_SEQ_Odecseq(_585139, _585141), 10447 ^ _224325 : [(10448 ^ _224325) ^ [_585415, _585417] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _585417, _585415), -(c_Orderings_Oord__class_Oless__eq(_585139, hAPP(_585141, _585415), hAPP(_585141, _585417)))]]], (10454 ^ _224325) ^ [] : [10457 ^ _224325 : [(10460 ^ _224325) ^ [] : [c_Orderings_Oord__class_Oless__eq(_585139, hAPP(_585141, 10456 ^ [_585139, _585141]), hAPP(_585141, 10455 ^ [_585139, _585141]))], (10458 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, 10455 ^ [_585139, _585141], 10456 ^ [_585139, _585141]))]], -(c_SEQ_Odecseq(_585139, _585141))]]], (11139 ^ _224325) ^ [_613584, _613586, _613588] : [-(hBOOL(hAPP(_613584, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _613586, _613588)))), 11142 ^ _224325 : [(11145 ^ _224325) ^ [] : [hBOOL(hAPP(_613584, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (11143 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _613586, _613588))]], 11147 ^ _224325 : [(11150 ^ _224325) ^ [] : [hBOOL(hAPP(_613584, 11146 ^ [_613584, _613586, _613588]))], (11148 ^ _224325) ^ [] : [-(_613586 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _613588, 11146 ^ [_613584, _613586, _613588]))]]], (2821 ^ _224325) ^ [_317639, _317641, _317643, _317645] : [class_Groups_Oab__semigroup__add(_317639), -(c_Groups_Oplus__class_Oplus(_317639, c_Groups_Oplus__class_Oplus(_317639, _317641, _317643), _317645) = c_Groups_Oplus__class_Oplus(_317639, _317641, c_Groups_Oplus__class_Oplus(_317639, _317643, _317645)))], (9031 ^ _224325) ^ [_535856, _535858, _535860] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _535856, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _535858, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _535856), _535860))), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _535856, _535858))], (2 ^ _224325) ^ [_224449] : [-(_224449 = _224449)], (6298 ^ _224325) ^ [_442167, _442169, _442171] : [class_Rings_Oring(_442167), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_442167), c_Groups_Ouminus__class_Ouminus(_442167, _442169)), _442171) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_442167), _442169), c_Groups_Ouminus__class_Ouminus(_442167, _442171)))], (9769 ^ _224325) ^ [_561508, _561510] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _561508), _561510) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _561508 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _561510 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11597 ^ _224325) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (2024 ^ _224325) ^ [_289932, _289934] : [class_Rings_Ocomm__semiring__1(_289932), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_289932), _289934), c_Groups_Ozero__class_Ozero(_289932)) = c_Groups_Ozero__class_Ozero(_289932))], (11699 ^ _224325) ^ [] : [-(class_Rings_Odvd(tc_Nat_Onat))], (5539 ^ _224325) ^ [_415016] : [_415016 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _415016, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (1444 ^ _224325) ^ [_271374, _271376, _271378] : [class_Orderings_Opreorder(_271374), c_Orderings_Oord__class_Oless(_271374, _271376, _271378), c_Orderings_Oord__class_Oless(_271374, _271378, _271376)], (11593 ^ _224325) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (4105 ^ _224325) ^ [_362520] : [class_Rings_Olinordered__semidom(_362520), -(c_Orderings_Oord__class_Oless__eq(_362520, c_Groups_Ozero__class_Ozero(_362520), c_Groups_Oone__class_Oone(_362520)))], (11885 ^ _224325) ^ [] : [-(class_Groups_Omonoid__add(tc_Complex_Ocomplex))], (6778 ^ _224325) ^ [_458445, _458447] : [-(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), _458445), _458445)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _458447), _458447)))], (2574 ^ _224325) ^ [_308021, _308023, _308025, _308027] : [class_Orderings_Oorder(_308021), _308023 = _308025, c_Orderings_Oord__class_Oless__eq(_308021, _308027, _308025), -(c_Orderings_Oord__class_Oless__eq(_308021, _308027, _308023))], (4465 ^ _224325) ^ [_374632, _374634, _374636, _374638] : [class_Rings_Ocomm__semiring__0(_374632), -(hAPP(c_Polynomial_Opoly(_374632, c_Polynomial_OpCons(_374632, _374634, _374636)), _374638) = c_Groups_Oplus__class_Oplus(_374632, _374634, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_374632), _374638), hAPP(c_Polynomial_Opoly(_374632, _374636), _374638))))], (6346 ^ _224325) ^ [_444219, _444221] : [class_RealVector_Oreal__normed__vector(_444219), -(c_RealVector_Onorm__class_Onorm(_444219, c_Groups_Ouminus__class_Ouminus(_444219, _444221)) = c_RealVector_Onorm__class_Onorm(_444219, _444221))], (2727 ^ _224325) ^ [_313880, _313882, _313884, _313886] : [class_Rings_Ocomm__semiring__1(_313880), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_313880), _313882), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_313880), _313884), _313886)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_313880), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_313880), _313882), _313884)), _313886))], (11233 ^ _224325) ^ [_617231, _617233, _617235] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _617231, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _617233, _617235)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _617231, _617235), _617233))], (9331 ^ _224325) ^ [_546600, _546602] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_546600), c_Nat_OSuc(_546602)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _546600, _546602))], (9900 ^ _224325) ^ [_566396, _566398, _566400, _566402] : [class_Rings_Olinordered__semidom(_566396), c_Orderings_Oord__class_Oless__eq(_566396, hAPP(hAPP(c_Power_Opower__class_Opower(_566396), _566398), c_Nat_OSuc(_566400)), hAPP(hAPP(c_Power_Opower__class_Opower(_566396), _566402), c_Nat_OSuc(_566400))), c_Orderings_Oord__class_Oless__eq(_566396, c_Groups_Ozero__class_Ozero(_566396), _566402), -(c_Orderings_Oord__class_Oless__eq(_566396, _566398, _566402))], (10906 ^ _224325) ^ [_604482, _604484, _604486] : [class_Groups_Ogroup__add(_604482), 10909 ^ _224325 : [(10916 ^ _224325) ^ [] : [_604484 = _604486, -(c_Groups_Ominus__class_Ominus(_604482, _604484, _604486) = c_Groups_Ozero__class_Ozero(_604482))], (10910 ^ _224325) ^ [] : [c_Groups_Ominus__class_Ominus(_604482, _604484, _604486) = c_Groups_Ozero__class_Ozero(_604482), -(_604484 = _604486)]]], (1710 ^ _224325) ^ [_279809, _279811, _279813] : [class_Orderings_Olinorder(_279809), c_Orderings_Oord__class_Oless__eq(_279809, _279811, _279813), 1717 ^ _224325 : [(1724 ^ _224325) ^ [] : [_279811 = _279813, c_Orderings_Oord__class_Oless(_279809, _279811, _279813)], (1718 ^ _224325) ^ [] : [-(c_Orderings_Oord__class_Oless(_279809, _279811, _279813)), -(_279811 = _279813)]]], (11741 ^ _224325) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal))]], input).
% 92.67/90.38  ncf('1',plain,[c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), v_r), v_m____)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____)), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), v_r), v_m____))))],start(12291 ^ 0)).
% 92.67/90.38  ncf('1.1',plain,[-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), v_r), v_m____)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____)), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), v_r), v_m____))))), class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____))), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), v_r), v_m____), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), v_r), v_m____)))],extension(2893 ^ 1,bind([[_320443, _320445, _320447, _320449, _320451], [tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), v_r), v_m____), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), v_r), v_m____))]]))).
% 92.67/90.38  ncf('1.1.1',plain,[-(class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal))],extension(11729 ^ 2)).
% 92.67/90.38  ncf('1.1.2',plain,[-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____)))), class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____))],extension(2296 ^ 2,bind([[_299001, _299003, _299005, _299007], [tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____)]]))).
% 92.67/90.38  ncf('1.1.2.1',plain,[-(class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal))],extension(11735 ^ 3)).
% 92.67/90.38  ncf('1.1.2.2',plain,[-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), class_Rings_Olinordered__semidom(tc_RealDef_Oreal)],extension(4105 ^ 3,bind([[_362520], [tc_RealDef_Oreal]]))).
% 92.67/90.38  ncf('1.1.2.2.1',plain,[-(class_Rings_Olinordered__semidom(tc_RealDef_Oreal))],extension(11761 ^ 4)).
% 92.67/90.38  ncf('1.1.2.3',plain,[-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____))), class_Orderings_Olinorder(tc_RealDef_Oreal), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____)))],extension(2470 ^ 3,bind([[_304664, _304666, _304668], [tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____)]]))).
% 92.67/90.38  ncf('1.1.2.3.1',plain,[-(class_Orderings_Olinorder(tc_RealDef_Oreal))],extension(11795 ^ 4)).
% 92.67/90.38  ncf('1.1.2.3.2',plain,[c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____))],reduction('1.1.2')).
% 92.67/90.38  ncf('1.1.3',plain,[-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), v_r), v_m____), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), v_r), v_m____)))), class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)],extension(3091 ^ 2,bind([[_328296, _328298], [tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), v_r), v_m____)]]))).
% 92.67/90.38  ncf('1.1.3.1',plain,[-(class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal))],extension(11731 ^ 3)).
% 92.67/90.38  %-----------------------------------------------------
% 92.67/90.38  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------