nanoCoP---2.0.THM-Prf.s

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%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWW181+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 192.54s 185.85s
% Output   : Proof 192.54s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SWW181+1 : TPTP v8.1.2. Released v5.2.0.
% 0.10/0.12  % Command  : nanocop.sh %s %d
% 0.13/0.33  % Computer : n027.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Thu May 18 23:01:35 EDT 2023
% 0.13/0.33  % CPUTime  : 
% 192.54/185.85  
% 192.54/185.85  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 192.54/185.85  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 192.54/185.85  %-----------------------------------------------------
% 192.54/185.85  ncf(matrix, plain, [(12363 ^ _668232) ^ [_668277] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _668277), 12367 ^ _668232 : [(12370 ^ _668232) ^ [] : [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____)), 12366 ^ [_668277])), _668277)], (12368 ^ _668232) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, 12366 ^ [_668277]), v_r))]]], !, (8973 ^ _221138) ^ [_529705] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_529705)], (11741 ^ _221138) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (12105 ^ _221138) ^ [_640735] : [class_Rings_Olinordered__idom(_640735), -(class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(_640735)))], (704 ^ _221138) ^ [_242266, _242268] : [-(class_Rings_Ocomm__ring(_242266)), _242268 = _242266, class_Rings_Ocomm__ring(_242268)], (11853 ^ _221138) ^ [] : [-(class_Rings_Olinordered__ring(tc_RealDef_Oreal))], (11773 ^ _221138) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (10225 ^ _221138) ^ [_573450, _573452] : [class_RealVector_Oreal__normed__vector(_573450), 10228 ^ _221138 : [(10236 ^ _221138) ^ [] : [10238 ^ _221138 : [(10239 ^ _221138) ^ [_573935] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_573450, hAPP(_573452, 10237 ^ [_573450, _573452, _573935])), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(_573935)))]], -(c_SEQ_OBseq(_573450, _573452))], (10229 ^ _221138) ^ [] : [c_SEQ_OBseq(_573450, _573452), 10233 ^ _221138 : [(10234 ^ _221138) ^ [_573757] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_573450, hAPP(_573452, _573757)), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(10232 ^ [_573450, _573452]))))]]]]], (11695 ^ _221138) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (12309 ^ _221138) ^ [_647195] : [class_Groups_Oab__group__add(_647195), -(class_Groups_Ominus(tc_Polynomial_Opoly(_647195)))], (2160 ^ _221138) ^ [_290405, _290407] : [2161 ^ _221138 : [(2164 ^ _221138) ^ [] : [_290405 = _290407], (2162 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _290405, _290407)]], -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _290405, _290407))], (8913 ^ _221138) ^ [_527278, _527280, _527282] : [_527280 = _527282, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_527278)), _527280) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_527278)), _527282))], (424 ^ _221138) ^ [_234006, _234008] : [-(class_Rings_Ono__zero__divisors(_234006)), _234008 = _234006, class_Rings_Ono__zero__divisors(_234008)], (11099 ^ _221138) ^ [_608033, _608035] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _608033, _608035), _608033) = _608035)], (3432 ^ _221138) ^ [_335655, _335657, _335659] : [class_Groups_Oordered__comm__monoid__add(_335655), c_Orderings_Oord__class_Oless(_335655, _335657, c_Groups_Ozero__class_Ozero(_335655)), c_Orderings_Oord__class_Oless(_335655, _335659, c_Groups_Ozero__class_Ozero(_335655)), -(c_Orderings_Oord__class_Oless(_335655, c_Groups_Oplus__class_Oplus(_335655, _335657, _335659), c_Groups_Ozero__class_Ozero(_335655)))], (7877 ^ _221138) ^ [_491539, _491541, _491543] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _491539, _491541), _491541 = _491543, -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _491539, _491543))], (11645 ^ _221138) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Int_Oint))], (7225 ^ _221138) ^ [_469192, _469194, _469196, _469198] : [class_Rings_Ocomm__semiring__1(_469192), c_Rings_Odvd__class_Odvd(_469192, _469194, _469196), c_Rings_Odvd__class_Odvd(_469192, _469194, _469198), -(c_Rings_Odvd__class_Odvd(_469192, _469194, c_Groups_Oplus__class_Oplus(_469192, _469196, _469198)))], (1878 ^ _221138) ^ [_281814, _281816, _281818, _281820] : [class_Orderings_Opreorder(_281814), c_Orderings_Oord__class_Oless(_281814, _281816, _281818), c_Orderings_Oord__class_Oless__eq(_281814, _281818, _281820), -(c_Orderings_Oord__class_Oless(_281814, _281816, _281820))], (7681 ^ _221138) ^ [_485525, _485527, _485529] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _485525, _485527), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _485527, _485525)), 7696 ^ _221138 : [(7699 ^ _221138) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _485529, _485525)], (7697 ^ _221138) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _485525, _485529))]], c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _485527, _485529), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _485529, _485527))], (9684 ^ _221138) ^ [_554397, _554399, _554401] : [-(_554397 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 9687 ^ _221138 : [(9694 ^ _221138) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _554399, _554401), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _554399), _554397), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _554401), _554397)))], (9688 ^ _221138) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _554399), _554397), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _554401), _554397)), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _554399, _554401))]]], (5179 ^ _221138) ^ [_397968, _397970] : [-(_397968 = _397970), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _397968, _397970)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _397970, _397968))], (5573 ^ _221138) ^ [_411652, _411654, _411656] : [class_Groups_Oab__group__add(_411652), -(c_Groups_Ouminus__class_Ouminus(_411652, c_Groups_Oplus__class_Oplus(_411652, _411654, _411656)) = c_Groups_Oplus__class_Oplus(_411652, c_Groups_Ouminus__class_Ouminus(_411652, _411654), c_Groups_Ouminus__class_Ouminus(_411652, _411656)))], (9570 ^ _221138) ^ [_550607, _550609] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _550607), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _550609), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _550607, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _550609), _550607)))], (3094 ^ _221138) ^ [_324570, _324572, _324574, _324576, _324578] : [class_RealVector_Oreal__normed__algebra(_324570), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_324570, _324572), _324574), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_324570, _324576), _324578), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_324570, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_324570), _324572), _324576)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _324574), _324578)))], (4664 ^ _221138) ^ [_377890, _377892, _377894, _377896, _377898] : [class_Rings_Ocomm__semiring__1(_377890), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_377890), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_377890), _377892), _377894)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_377890), _377896), _377898)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_377890), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_377890), _377892), _377896)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_377890), _377894), _377898)))], (2168 ^ _221138) ^ [_290681] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _290681), 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, c_Polynomial_OpCons(tc_Complex_Ocomplex, v_c____, v_cs____)), _290681)), 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____)))))], (9444 ^ _221138) ^ [_546108, _546110] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _546108, _546110), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_546108), _546110))], (10137 ^ _221138) ^ [_570323] : [_570323 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _570323), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (8823 ^ _221138) ^ [_524126, _524128] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _524126, _524128), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _524126, c_Groups_Oone__class_Oone(tc_Int_Oint)), _524128))], (2348 ^ _221138) ^ [_297181, _297183, _297185, _297187] : [class_RealVector_Oreal__normed__algebra(_297181), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_297181), _297183), c_Groups_Oplus__class_Oplus(_297181, _297185, _297187)) = c_Groups_Oplus__class_Oplus(_297181, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_297181), _297183), _297185), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_297181), _297183), _297187)))], (5315 ^ _221138) ^ [_402678, _402680] : [class_Groups_Ogroup__add(_402678), 5318 ^ _221138 : [(5325 ^ _221138) ^ [] : [c_Groups_Ozero__class_Ozero(_402678) = _402680, -(c_Groups_Ozero__class_Ozero(_402678) = c_Groups_Ouminus__class_Ouminus(_402678, _402680))], (5319 ^ _221138) ^ [] : [c_Groups_Ozero__class_Ozero(_402678) = c_Groups_Ouminus__class_Ouminus(_402678, _402680), -(c_Groups_Ozero__class_Ozero(_402678) = _402680)]]], (6373 ^ _221138) ^ [_438702, _438704, _438706] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _438702), 6376 ^ _221138 : [(6383 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _438704, _438706), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _438702), _438704), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _438702), _438706)))], (6377 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _438702), _438704), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _438702), _438706)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _438704, _438706))]]], (6747 ^ _221138) ^ [_452963] : [class_RealVector_Oreal__normed__vector(_452963), -(c_Groups_Osgn__class_Osgn(_452963, c_Groups_Ozero__class_Ozero(_452963)) = c_Groups_Ozero__class_Ozero(_452963))], (11273 ^ _221138) ^ [_614446, _614448, _614450] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _614446, _614448), 11276 ^ _221138 : [(11283 ^ _221138) ^ [] : [_614448 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _614450, _614446), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _614448, _614446) = _614450)], (11277 ^ _221138) ^ [] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _614448, _614446) = _614450, -(_614448 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _614450, _614446))]]], (1792 ^ _221138) ^ [_278987] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _278987, _278987))], (6461 ^ _221138) ^ [_442519, _442521, _442523] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _442519, _442521) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _442523, _442521), -(_442519 = _442523)], (6713 ^ _221138) ^ [_451754, _451756, _451758] : [class_RealVector_Oreal__normed__div__algebra(_451754), -(c_Groups_Osgn__class_Osgn(_451754, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_451754), _451756), _451758)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_451754), c_Groups_Osgn__class_Osgn(_451754, _451756)), c_Groups_Osgn__class_Osgn(_451754, _451758)))], (11565 ^ _221138) ^ [_625691, _625693] : [class_Orderings_Oord(_625691), -(class_Orderings_Oord(tc_fun(_625693, _625691)))], (1421 ^ _221138) ^ [_267186, _267188, _267190, _267192, _267194] : [class_Orderings_Oord(_267186), c_Orderings_Oord__class_Oless__eq(tc_fun(_267188, _267186), _267190, _267192), -(c_Orderings_Oord__class_Oless__eq(_267186, hAPP(_267190, _267194), hAPP(_267192, _267194)))], (4012 ^ _221138) ^ [_354674, _354676, _354678, _354680] : [class_Rings_Olinordered__comm__semiring__strict(_354674), c_Orderings_Oord__class_Oless(_354674, _354676, _354678), c_Orderings_Oord__class_Oless(_354674, c_Groups_Ozero__class_Ozero(_354674), _354680), -(c_Orderings_Oord__class_Oless(_354674, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_354674), _354680), _354676), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_354674), _354680), _354678)))], (9948 ^ _221138) ^ [_563463, _563465] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _563463), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _563465), -(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), _563463), _563465)))], (6017 ^ _221138) ^ [_426245, _426247] : [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, _426245, _426247)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _426245), _426247))], (7269 ^ _221138) ^ [_470755, _470757, _470759, _470761, _470763] : [class_Rings_Ocomm__semiring__1(_470755), c_Rings_Odvd__class_Odvd(_470755, _470757, _470759), c_Rings_Odvd__class_Odvd(_470755, _470761, _470763), -(c_Rings_Odvd__class_Odvd(_470755, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_470755), _470757), _470761), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_470755), _470759), _470763)))], (11197 ^ _221138) ^ [_611828, _611830, _611832] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _611828, _611830), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _611828, _611832), 11204 ^ _221138 : [(11211 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _611830, _611832), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _611830, _611828), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _611832, _611828)))], (11205 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _611830, _611828), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _611832, _611828)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _611830, _611832))]]], (7621 ^ _221138) ^ [_483607, _483609, _483611, _483613] : [class_Rings_Olinordered__semidom(_483607), c_Orderings_Oord__class_Oless(_483607, _483609, _483611), c_Orderings_Oord__class_Oless__eq(_483607, c_Groups_Ozero__class_Ozero(_483607), _483609), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _483613), -(c_Orderings_Oord__class_Oless(_483607, hAPP(hAPP(c_Power_Opower__class_Opower(_483607), _483609), _483613), hAPP(hAPP(c_Power_Opower__class_Opower(_483607), _483611), _483613)))], (8757 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (9752 ^ _221138) ^ [_556675, _556677] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _556675, _556677), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _556677, _556675), -(_556675 = _556677)], (104 ^ _221138) ^ [_224566, _224568] : [-(class_Lattices_Oboolean__algebra(_224566)), _224568 = _224566, class_Lattices_Oboolean__algebra(_224568)], (6843 ^ _221138) ^ [_456336, _456338, _456340] : [class_Lattices_Oboolean__algebra(_456336), 6846 ^ _221138 : [(6853 ^ _221138) ^ [] : [_456338 = _456340, -(c_Groups_Ouminus__class_Ouminus(_456336, _456338) = c_Groups_Ouminus__class_Ouminus(_456336, _456340))], (6847 ^ _221138) ^ [] : [c_Groups_Ouminus__class_Ouminus(_456336, _456338) = c_Groups_Ouminus__class_Ouminus(_456336, _456340), -(_456338 = _456340)]]], (10305 ^ _221138) ^ [_576468, _576470] : [class_RealVector_Oreal__normed__vector(_576468), 10308 ^ _221138 : [(10309 ^ _221138) ^ [] : [10318 ^ _221138 : [(10319 ^ _221138) ^ [_577025] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_576468, hAPP(_576470, _577025)), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(10317 ^ [_576468, _576470]))))]], 10310 ^ _221138 : [(10311 ^ _221138) ^ [_576707] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _576707), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_576468, hAPP(_576470, 10314 ^ [_576468, _576470, _576707])), _576707)]]], (10321 ^ _221138) ^ [] : [10323 ^ _221138 : [(10324 ^ _221138) ^ [_577204] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_576468, hAPP(_576470, 10322 ^ [_576468, _576470, _577204])), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(_577204)))]], 10326 ^ _221138 : [(10329 ^ _221138) ^ [_577425] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_576468, hAPP(_576470, _577425)), 10325 ^ [_576468, _576470]))], (10327 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 10325 ^ [_576468, _576470]))]]]]], (6029 ^ _221138) ^ [_426684, _426686] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _426684, _426686), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _426686, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _426684)))], (8829 ^ _221138) ^ [_524365] : [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), _524365), _524365), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _524365, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (7147 ^ _221138) ^ [_466644, _466646] : [class_Rings_Ocomm__semiring__1(_466644), c_Rings_Odvd__class_Odvd(_466644, c_Groups_Ozero__class_Ozero(_466644), _466646), -(_466646 = c_Groups_Ozero__class_Ozero(_466644))], (5173 ^ _221138) ^ [_397701, _397703, _397705] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _397703, _397705), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _397701, _397703), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _397701, _397705)))], (8241 ^ _221138) ^ [_504078, _504080, _504082, _504084] : [class_Groups_Omonoid__mult(_504078), -(hAPP(hAPP(c_Power_Opower__class_Opower(_504078), _504080), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _504082, _504084)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_504078), hAPP(hAPP(c_Power_Opower__class_Opower(_504078), _504080), _504082)), hAPP(hAPP(c_Power_Opower__class_Opower(_504078), _504080), _504084)))], (8505 ^ _221138) ^ [_513407, _513409, _513411, _513413] : [class_Rings_Olinordered__semidom(_513407), c_Orderings_Oord__class_Oless(_513407, c_Groups_Oone__class_Oone(_513407), _513409), 8512 ^ _221138 : [(8519 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _513411, _513413), -(c_Orderings_Oord__class_Oless__eq(_513407, hAPP(hAPP(c_Power_Opower__class_Opower(_513407), _513409), _513411), hAPP(hAPP(c_Power_Opower__class_Opower(_513407), _513409), _513413)))], (8513 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_513407, hAPP(hAPP(c_Power_Opower__class_Opower(_513407), _513409), _513411), hAPP(hAPP(c_Power_Opower__class_Opower(_513407), _513409), _513413)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _513411, _513413))]]], (2516 ^ _221138) ^ [_303953, _303955] : [class_Rings_Olinordered__idom(_303953), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_303953), c_Groups_Oabs__class_Oabs(_303953, _303955)), c_Groups_Oabs__class_Oabs(_303953, _303955)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_303953), _303955), _303955))], (11703 ^ _221138) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (11827 ^ _221138) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal))], (6589 ^ _221138) ^ [_447334, _447336, _447338] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _447334, _447336), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _447334, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _447338, _447336)))], (3120 ^ _221138) ^ [_325570, _325572] : [class_RealVector_Oreal__normed__algebra(_325570), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_325570), c_Groups_Ozero__class_Ozero(_325570)), _325572) = c_Groups_Ozero__class_Ozero(_325570))], (5985 ^ _221138) ^ [_425115, _425117] : [class_Groups_Oabs__if(_425115), 5988 ^ _221138 : [(5995 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(_425115, _425117, c_Groups_Ozero__class_Ozero(_425115))), -(c_Groups_Oabs__class_Oabs(_425115, _425117) = _425117)], (5989 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_425115, _425117, c_Groups_Ozero__class_Ozero(_425115)), -(c_Groups_Oabs__class_Oabs(_425115, _425117) = c_Groups_Ouminus__class_Ouminus(_425115, _425117))]]], (5115 ^ _221138) ^ [_395582, _395584, _395586, _395588] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _395582, _395584), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _395586, _395588), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _395582, _395586), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _395584, _395588)))], (1150 ^ _221138) ^ [_258426, _258428] : [class_RealVector_Oreal__normed__vector(_258426), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_258426, _258428), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (4246 ^ _221138) ^ [_362408, _362410, _362412, _362414, _362416] : [class_Rings_Olinordered__semiring__strict(_362408), c_Orderings_Oord__class_Oless(_362408, _362410, _362412), c_Orderings_Oord__class_Oless__eq(_362408, _362414, _362416), c_Orderings_Oord__class_Oless__eq(_362408, c_Groups_Ozero__class_Ozero(_362408), _362410), c_Orderings_Oord__class_Oless(_362408, c_Groups_Ozero__class_Ozero(_362408), _362414), -(c_Orderings_Oord__class_Oless(_362408, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_362408), _362410), _362414), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_362408), _362412), _362416)))], (11807 ^ _221138) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal))], (11931 ^ _221138) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex))], (11733 ^ _221138) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (11897 ^ _221138) ^ [] : [-(class_Groups_Osgn__if(tc_RealDef_Oreal))], (11671 ^ _221138) ^ [] : [-(class_Rings_Ocomm__ring(tc_Int_Oint))], (1974 ^ _221138) ^ [_284748, _284750, _284752] : [class_Orderings_Oorder(_284748), -(_284750 = _284752), c_Orderings_Oord__class_Oless__eq(_284748, _284752, _284750), -(c_Orderings_Oord__class_Oless(_284748, _284752, _284750))], (8947 ^ _221138) ^ [_528722, _528724] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _528722, c_Nat_OSuc(_528724)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _528722, _528724)))], (6731 ^ _221138) ^ [_452498, _452500] : [class_Rings_Olinordered__idom(_452498), 6734 ^ _221138 : [(6741 ^ _221138) ^ [] : [_452500 = c_Groups_Ozero__class_Ozero(_452498), -(c_Groups_Osgn__class_Osgn(_452498, _452500) = c_Groups_Ozero__class_Ozero(_452498))], (6735 ^ _221138) ^ [] : [c_Groups_Osgn__class_Osgn(_452498, _452500) = c_Groups_Ozero__class_Ozero(_452498), -(_452500 = c_Groups_Ozero__class_Ozero(_452498))]]], (11323 ^ _221138) ^ [_616204, _616206, _616208] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _616204, _616206), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _616208, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _616206, _616208), _616204)))], (10061 ^ _221138) ^ [_567455] : [-(c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat, _567455)) = _567455)], (11693 ^ _221138) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (1738 ^ _221138) ^ [_277312, _277314, _277316] : [class_Orderings_Olinorder(_277312), 1741 ^ _221138 : [(1742 ^ _221138) ^ [] : [-(_277314 = _277316), -(c_Orderings_Oord__class_Oless(_277312, _277314, _277316)), -(c_Orderings_Oord__class_Oless(_277312, _277316, _277314))], (1752 ^ _221138) ^ [] : [1753 ^ _221138 : [(1756 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_277312, _277316, _277314)], (1754 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_277312, _277314, _277316)]], _277314 = _277316]]], (10347 ^ _221138) ^ [_578122, _578124] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatfloor(_578122), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _578124), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _578122, c_RealDef_Oreal(tc_Nat_Onat, _578124)))], (9361 ^ _221138) ^ [_543098, _543100] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _543098), -(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), _543098), _543100)))], (1766 ^ _221138) ^ [_278169, _278171] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _278169, _278171), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _278171, _278169), -(_278169 = _278171)], (6133 ^ _221138) ^ [_430310] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _430310) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9480 ^ _221138) ^ [_547315, _547317, _547319] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _547317, _547319), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_547315)), _547317), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_547315)), _547319)))], (4438 ^ _221138) ^ [_368895, _368897, _368899] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _368895), 4441 ^ _221138 : [(4448 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _368897, _368899), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _368895), _368897), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _368895), _368899)))], (4442 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _368895), _368897), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _368895), _368899)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _368897, _368899))]]], (10420 ^ _221138) ^ [_580881, _580883, _580885] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _580881), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _580883, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _580885, 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, _580885, _580883)), c_Groups_Oone__class_Oone(tc_Int_Oint))), _580881))))], (7068 ^ _221138) ^ [_463835, _463837] : [class_RealVector_Oreal__normed__algebra(_463835), 7072 ^ _221138 : [(7075 ^ _221138) ^ [_464134] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_463835, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_463835), _463837), _464134)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_463835, _464134)), 7071 ^ [_463835, _463837])))], (7073 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 7071 ^ [_463835, _463837]))]]], (8081 ^ _221138) ^ [_498281, _498283, _498285] : [class_Rings_Oring__1__no__zero__divisors(_498281), -(_498283 = c_Groups_Ozero__class_Ozero(_498281)), hAPP(hAPP(c_Power_Opower__class_Opower(_498281), _498283), _498285) = c_Groups_Ozero__class_Ozero(_498281)], (8391 ^ _221138) ^ [_509623, _509625, _509627, _509629] : [class_Rings_Olinordered__semidom(_509623), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _509625, _509627), c_Orderings_Oord__class_Oless(_509623, c_Groups_Oone__class_Oone(_509623), _509629), -(c_Orderings_Oord__class_Oless(_509623, hAPP(hAPP(c_Power_Opower__class_Opower(_509623), _509629), _509625), hAPP(hAPP(c_Power_Opower__class_Opower(_509623), _509629), _509627)))], (2240 ^ _221138) ^ [] : [-(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____)))))], (5453 ^ _221138) ^ [_406981, _406983, _406985] : [class_Groups_Oordered__ab__group__add(_406981), 5456 ^ _221138 : [(5463 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_406981, c_Groups_Ouminus__class_Ouminus(_406981, _406985), _406983), -(c_Orderings_Oord__class_Oless(_406981, c_Groups_Ouminus__class_Ouminus(_406981, _406983), _406985))], (5457 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_406981, c_Groups_Ouminus__class_Ouminus(_406981, _406983), _406985), -(c_Orderings_Oord__class_Oless(_406981, c_Groups_Ouminus__class_Ouminus(_406981, _406985), _406983))]]], (5543 ^ _221138) ^ [_410346, _410348, _410350] : [class_Rings_Oring(_410346), -(c_Groups_Ouminus__class_Ouminus(_410346, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_410346), _410348), _410350)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_410346), c_Groups_Ouminus__class_Ouminus(_410346, _410348)), _410350))], (10081 ^ _221138) ^ [_568266, _568268] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _568266)), _568268) = c_RealDef_Oreal(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _568266), _568268)))], (6331 ^ _221138) ^ [_437367, _437369] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _437367, _437369) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _437367 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _437369 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (8535 ^ _221138) ^ [_514373, _514375, _514377] : [class_Rings_Oidom(_514373), -(_514375 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_514373))), 8542 ^ _221138 : [(8545 ^ _221138) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_514373), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_514373)), c_Polynomial_OpCons(_514373, c_Groups_Ouminus__class_Ouminus(_514373, _514377), c_Polynomial_OpCons(_514373, c_Groups_Oone__class_Oone(_514373), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_514373))))), c_Nat_OSuc(c_Polynomial_Oorder(_514373, _514377, _514375))), _514375)], (8543 ^ _221138) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_514373), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_514373)), c_Polynomial_OpCons(_514373, c_Groups_Ouminus__class_Ouminus(_514373, _514377), c_Polynomial_OpCons(_514373, c_Groups_Oone__class_Oone(_514373), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_514373))))), c_Polynomial_Oorder(_514373, _514377, _514375)), _514375))]]], (4060 ^ _221138) ^ [_356283] : [class_Rings_Olinordered__semidom(_356283), -(c_Orderings_Oord__class_Oless__eq(_356283, c_Groups_Ozero__class_Ozero(_356283), c_Groups_Oone__class_Oone(_356283)))], (10606 ^ _221138) ^ [_588701, _588703, _588705, _588707, _588709] : [class_RealVector_Oreal__normed__algebra(_588701), -(c_Groups_Ominus__class_Ominus(_588701, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_588701), _588703), _588705), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_588701), _588707), _588709)) = c_Groups_Oplus__class_Oplus(_588701, c_Groups_Oplus__class_Oplus(_588701, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_588701), c_Groups_Ominus__class_Ominus(_588701, _588703, _588707)), c_Groups_Ominus__class_Ominus(_588701, _588705, _588709)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_588701), c_Groups_Ominus__class_Ominus(_588701, _588703, _588707)), _588709)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_588701), _588707), c_Groups_Ominus__class_Ominus(_588701, _588705, _588709))))], (2550 ^ _221138) ^ [_305131, _305133] : [class_Groups_Ocomm__monoid__mult(_305131), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_305131), c_Groups_Oone__class_Oone(_305131)), _305133) = _305133)], (11619 ^ _221138) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (11103 ^ _221138) ^ [_608275, _608277, _608279] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _608275, _608277), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _608275, _608279)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _608277, _608279))], (4862 ^ _221138) ^ [_385920, _385922, _385924, _385926] : [class_Rings_Ocomm__semiring__0(_385920), -(c_Polynomial_Opcompose(_385920, c_Polynomial_OpCons(_385920, _385922, _385924), _385926) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_385920), c_Polynomial_OpCons(_385920, _385922, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_385920))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_385920)), _385926), c_Polynomial_Opcompose(_385920, _385924, _385926))))], (7115 ^ _221138) ^ [_465652, _465654, _465656] : [class_Rings_Ocomm__ring__1(_465652), 7118 ^ _221138 : [(7125 ^ _221138) ^ [] : [c_Rings_Odvd__class_Odvd(_465652, _465654, _465656), -(c_Rings_Odvd__class_Odvd(_465652, c_Groups_Ouminus__class_Ouminus(_465652, _465654), _465656))], (7119 ^ _221138) ^ [] : [c_Rings_Odvd__class_Odvd(_465652, c_Groups_Ouminus__class_Ouminus(_465652, _465654), _465656), -(c_Rings_Odvd__class_Odvd(_465652, _465654, _465656))]]], (12123 ^ _221138) ^ [_641305] : [class_Rings_Ocomm__semiring__1(_641305), -(class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(_641305)))], (6707 ^ _221138) ^ [_451524] : [class_RealVector_Oreal__normed__algebra__1(_451524), -(c_Groups_Osgn__class_Osgn(_451524, c_Groups_Oone__class_Oone(_451524)) = c_Groups_Oone__class_Oone(_451524))], (10656 ^ _221138) ^ [_590949, _590951, _590953] : [class_Rings_Ocomm__ring__1(_590949), -(c_Groups_Ominus__class_Ominus(_590949, _590951, _590953) = c_Groups_Oplus__class_Oplus(_590949, _590951, c_Groups_Ouminus__class_Ouminus(_590949, _590953)))], (8683 ^ _221138) ^ [_519559, _519561] : [-(_519559 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Rings_Odvd__class_Odvd(tc_Int_Oint, _519561, _519559), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oabs__class_Oabs(tc_Int_Oint, _519561), c_Groups_Oabs__class_Oabs(tc_Int_Oint, _519559)))], (744 ^ _221138) ^ [_243446, _243448] : [-(class_Rings_Ocomm__semiring__1(_243446)), _243448 = _243446, class_Rings_Ocomm__semiring__1(_243448)], (11805 ^ _221138) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal))], (9792 ^ _221138) ^ [_558234, _558236] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _558234, _558236), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _558234, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _558236)))], (11963 ^ _221138) ^ [] : [-(class_Groups_Ogroup__add(tc_Complex_Ocomplex))], (3590 ^ _221138) ^ [_340751, _340753, _340755] : [class_Rings_Oordered__cancel__semiring(_340751), c_Orderings_Oord__class_Oless__eq(_340751, _340753, c_Groups_Ozero__class_Ozero(_340751)), c_Orderings_Oord__class_Oless__eq(_340751, c_Groups_Ozero__class_Ozero(_340751), _340755), -(c_Orderings_Oord__class_Oless__eq(_340751, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_340751), _340753), _340755), c_Groups_Ozero__class_Ozero(_340751)))], (7979 ^ _221138) ^ [_494786, _494788] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _494786, _494788), 7984 ^ _221138 : [(7987 ^ _221138) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _494788, _494786)], (7985 ^ _221138) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _494786, _494788))]], -(_494786 = _494788)], (4634 ^ _221138) ^ [_376212, _376214, _376216, _376218] : [class_Rings_Ocomm__semiring__1(_376212), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_376212), _376214), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_376212), _376216), _376218)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_376212), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_376212), _376214), _376216)), _376218))], (2224 ^ _221138) ^ [_292514, _292516, _292518, _292520, _292522, _292524] : [class_Groups_Ozero(_292514), hAPP(hAPP(hAPP(_292516, c_Groups_Ozero__class_Ozero(_292514)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_292514))), _292518) = _292518, -(c_Polynomial_Opoly__rec(_292520, _292514, _292518, _292516, c_Polynomial_OpCons(_292514, _292522, _292524)) = hAPP(hAPP(hAPP(_292516, _292522), _292524), c_Polynomial_Opoly__rec(_292520, _292514, _292518, _292516, _292524)))], (504 ^ _221138) ^ [_236366, _236368] : [-(class_Groups_Ocomm__monoid__add(_236366)), _236368 = _236366, class_Groups_Ocomm__monoid__add(_236368)], (224 ^ _221138) ^ [_228106, _228108] : [-(class_Groups_Oordered__ab__group__add__abs(_228106)), _228108 = _228106, class_Groups_Oordered__ab__group__add__abs(_228108)], (7337 ^ _221138) ^ [_473219, _473221, _473223, _473225] : [class_Rings_Oidom(_473219), 7340 ^ _221138 : [(7341 ^ _221138) ^ [] : [c_Rings_Odvd__class_Odvd(_473219, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_473219), _473221), _473223), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_473219), _473225), _473223)), -(_473223 = c_Groups_Ozero__class_Ozero(_473219)), -(c_Rings_Odvd__class_Odvd(_473219, _473221, _473225))], (7351 ^ _221138) ^ [] : [7352 ^ _221138 : [(7355 ^ _221138) ^ [] : [c_Rings_Odvd__class_Odvd(_473219, _473221, _473225)], (7353 ^ _221138) ^ [] : [_473223 = c_Groups_Ozero__class_Ozero(_473219)]], -(c_Rings_Odvd__class_Odvd(_473219, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_473219), _473221), _473223), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_473219), _473225), _473223)))]]], (5285 ^ _221138) ^ [_401655, _401657, _401659] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _401655, _401657), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _401657, _401659), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _401655, _401659))], (8895 ^ _221138) ^ [_526551, _526553] : [c_Groups_Oabs__class_Oabs(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _526551), _526553)) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(c_Groups_Oabs__class_Oabs(tc_Int_Oint, _526551) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (2580 ^ _221138) ^ [_306351] : [class_Rings_Olinordered__idom(_306351), -(c_Groups_Oabs__class_Oabs(_306351, c_Groups_Oone__class_Oone(_306351)) = c_Groups_Oone__class_Oone(_306351))], (11631 ^ _221138) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (9035 ^ _221138) ^ [_531800, _531802] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _531800, _531802)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _531800, c_Nat_OSuc(_531802)), -(_531802 = _531800)], (11833 ^ _221138) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal))], (2574 ^ _221138) ^ [_306139, _306141] : [class_Groups_Oordered__ab__group__add__abs(_306139), -(c_Groups_Oabs__class_Oabs(_306139, c_Groups_Oabs__class_Oabs(_306139, _306141)) = c_Groups_Oabs__class_Oabs(_306139, _306141))], (12069 ^ _221138) ^ [_639595] : [class_Rings_Olinordered__idom(_639595), -(class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(_639595)))], (11317 ^ _221138) ^ [_615962, _615964] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _615962, _615964), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _615962, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _615964, _615962)) = _615964)], (6537 ^ _221138) ^ [_445501] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _445501) = _445501)], (3418 ^ _221138) ^ [_335209, _335211, _335213, _335215] : [class_Rings_Olinordered__semidom(_335209), c_Orderings_Oord__class_Oless(_335209, c_Groups_Ozero__class_Ozero(_335209), _335211), c_Orderings_Oord__class_Oless(_335209, _335213, _335215), -(c_Orderings_Oord__class_Oless(_335209, _335213, c_Groups_Oplus__class_Oplus(_335209, _335211, _335215)))], (4788 ^ _221138) ^ [_383242, _383244, _383246, _383248, _383250] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_383242), 4791 ^ _221138 : [(4792 ^ _221138) ^ [] : [c_Groups_Oplus__class_Oplus(_383242, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_383242), _383244), _383246), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_383242), _383248), _383250)) = c_Groups_Oplus__class_Oplus(_383242, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_383242), _383244), _383250), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_383242), _383248), _383246)), -(_383244 = _383248), -(_383246 = _383250)], (4802 ^ _221138) ^ [] : [4803 ^ _221138 : [(4806 ^ _221138) ^ [] : [_383246 = _383250], (4804 ^ _221138) ^ [] : [_383244 = _383248]], -(c_Groups_Oplus__class_Oplus(_383242, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_383242), _383244), _383246), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_383242), _383248), _383250)) = c_Groups_Oplus__class_Oplus(_383242, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_383242), _383244), _383250), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_383242), _383248), _383246)))]]], (8949 ^ _221138) ^ [_528843, _528845] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _528843, _528845)), -(_528843 = _528845), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _528845, _528843))], (5917 ^ _221138) ^ [_422817, _422819] : [c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _422817, _422819) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_422819 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _422817))], (4907 ^ _221138) ^ [_387801, _387803] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _387801, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _387801, _387803)))], (10363 ^ _221138) ^ [_578681, _578683] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _578681), -(c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _578681, c_RealDef_Oreal(tc_Nat_Onat, _578683))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatceiling(_578681), _578683))], (11723 ^ _221138) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (11879 ^ _221138) ^ [] : [-(class_Rings_Osemiring__0(tc_RealDef_Oreal))], (5567 ^ _221138) ^ [_411390, _411392, _411394] : [class_Groups_Ogroup__add(_411390), -(c_Groups_Ouminus__class_Ouminus(_411390, c_Groups_Oplus__class_Oplus(_411390, _411392, _411394)) = c_Groups_Oplus__class_Oplus(_411390, c_Groups_Ouminus__class_Ouminus(_411390, _411394), c_Groups_Ouminus__class_Ouminus(_411390, _411392)))], (1209 ^ _221138) ^ [_260475, _260477, _260479] : [class_Groups_Ozero(_260475), 1212 ^ _221138 : [(1221 ^ _221138) ^ [] : [-(c_Polynomial_OpCons(_260475, _260477, _260479) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_260475))), _260477 = c_Groups_Ozero__class_Ozero(_260475), _260479 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_260475))], (1213 ^ _221138) ^ [] : [c_Polynomial_OpCons(_260475, _260477, _260479) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_260475)), 1216 ^ _221138 : [(1219 ^ _221138) ^ [] : [-(_260479 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_260475)))], (1217 ^ _221138) ^ [] : [-(_260477 = c_Groups_Ozero__class_Ozero(_260475))]]]]], (194 ^ _221138) ^ [_227221, _227223] : [-(class_Rings_Olinordered__semiring__1__strict(_227221)), _227223 = _227221, class_Rings_Olinordered__semiring__1__strict(_227223)], (334 ^ _221138) ^ [_231351, _231353] : [-(class_Groups_Ocancel__comm__monoid__add(_231351)), _231353 = _231351, class_Groups_Ocancel__comm__monoid__add(_231353)], (11595 ^ _221138) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (8315 ^ _221138) ^ [_506908, _506910, _506912] : [class_Rings_Olinordered__semidom(_506908), c_Orderings_Oord__class_Oless(_506908, c_Groups_Oone__class_Oone(_506908), _506910), -(c_Orderings_Oord__class_Oless(_506908, hAPP(hAPP(c_Power_Opower__class_Opower(_506908), _506910), _506912), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_506908), _506910), hAPP(hAPP(c_Power_Opower__class_Opower(_506908), _506910), _506912))))], (11677 ^ _221138) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (9193 ^ _221138) ^ [_537217] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _537217, c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Groups_Oabs__class_Oabs(tc_Int_Oint, _537217) = _537217)], (8357 ^ _221138) ^ [_508464, _508466, _508468, _508470] : [class_Rings_Olinordered__semidom(_508464), c_Orderings_Oord__class_Oless(_508464, c_Groups_Oone__class_Oone(_508464), _508466), 8364 ^ _221138 : [(8371 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _508468, _508470), -(c_Orderings_Oord__class_Oless(_508464, hAPP(hAPP(c_Power_Opower__class_Opower(_508464), _508466), _508468), hAPP(hAPP(c_Power_Opower__class_Opower(_508464), _508466), _508470)))], (8365 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_508464, hAPP(hAPP(c_Power_Opower__class_Opower(_508464), _508466), _508468), hAPP(hAPP(c_Power_Opower__class_Opower(_508464), _508466), _508470)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _508468, _508470))]]], (7937 ^ _221138) ^ [_493410, _493412] : [_493410 = _493412, -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _493410, _493412))], (8841 ^ _221138) ^ [_524753] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _524753), -(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), _524753)))], (6321 ^ _221138) ^ [_436982] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _436982, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _436982)], (10063 ^ _221138) ^ [_567596, _567598] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _567596), c_RealDef_Oreal(tc_Nat_Onat, _567598)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _567596, _567598))], (4078 ^ _221138) ^ [_356906, _356908, _356910] : [class_Groups_Oordered__comm__monoid__add(_356906), c_Orderings_Oord__class_Oless(_356906, c_Groups_Ozero__class_Ozero(_356906), _356908), c_Orderings_Oord__class_Oless__eq(_356906, c_Groups_Ozero__class_Ozero(_356906), _356910), -(c_Orderings_Oord__class_Oless(_356906, c_Groups_Ozero__class_Ozero(_356906), c_Groups_Oplus__class_Oplus(_356906, _356908, _356910)))], (6509 ^ _221138) ^ [_444384, _444386, _444388] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _444384), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _444386, _444388)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _444384), _444386), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _444384), _444388)))], (144 ^ _221138) ^ [_225746, _225748] : [-(class_RealVector_Oreal__normed__vector(_225746)), _225748 = _225746, class_RealVector_Oreal__normed__vector(_225748)], (11923 ^ _221138) ^ [] : [-(class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex))], (5437 ^ _221138) ^ [_406469, _406471, _406473] : [class_Groups_Oordered__ab__group__add(_406469), 5440 ^ _221138 : [(5447 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_406469, _406473, c_Groups_Ouminus__class_Ouminus(_406469, _406471)), -(c_Orderings_Oord__class_Oless(_406469, _406471, c_Groups_Ouminus__class_Ouminus(_406469, _406473)))], (5441 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_406469, _406471, c_Groups_Ouminus__class_Ouminus(_406469, _406473)), -(c_Orderings_Oord__class_Oless(_406469, _406473, c_Groups_Ouminus__class_Ouminus(_406469, _406471)))]]], (9289 ^ _221138) ^ [_540910] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _540910, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_540910 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10197 ^ _221138) ^ [_572545, _572547] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _572545, _572547), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _572545), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _572547), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))], (11713 ^ _221138) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (7665 ^ _221138) ^ [_484998] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _484998, _484998))], (11947 ^ _221138) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex))], (10115 ^ _221138) ^ [] : [-(c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (10550 ^ _221138) ^ [_586521, _586523, _586525] : [class_Groups_Oordered__ab__group__add__abs(_586521), -(c_Orderings_Oord__class_Oless__eq(_586521, c_Groups_Oabs__class_Oabs(_586521, c_Groups_Ominus__class_Ominus(_586521, _586523, _586525)), c_Groups_Oplus__class_Oplus(_586521, c_Groups_Oabs__class_Oabs(_586521, _586523), c_Groups_Oabs__class_Oabs(_586521, _586525))))], (1185 ^ _221138) ^ [_259577] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _259577), 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____), _259577)), 1183 ^ []))], (10375 ^ _221138) ^ [_579169] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _579169), 10379 ^ _221138 : [(10382 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _579169, c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(10378 ^ [_579169]))))], (10380 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, 10378 ^ [_579169]), _579169))]]], (11731 ^ _221138) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (6199 ^ _221138) ^ [_432675, _432677, _432679] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _432675), _432677), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _432679), _432677))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _432677), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _432675, _432679)], (10991 ^ _221138) ^ [_604347, _604349] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _604347, _604349), -(c_Nat__Transfer_Otsub(_604349, _604347) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, _604349, _604347))], (10179 ^ _221138) ^ [_571849] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _571849), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _571849)))], (11639 ^ _221138) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (2952 ^ _221138) ^ [_319374, _319376, _319378, _319380] : [class_Rings_Ocomm__semiring__0(_319374), -(hAPP(c_Polynomial_Opoly(_319374, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_319374), _319376, _319378)), _319380) = c_Groups_Oplus__class_Oplus(_319374, hAPP(c_Polynomial_Opoly(_319374, _319376), _319380), hAPP(c_Polynomial_Opoly(_319374, _319378), _319380)))], (5561 ^ _221138) ^ [_411140, _411142, _411144] : [class_Groups_Ogroup__add(_411140), -(c_Groups_Oplus__class_Oplus(_411140, _411142, c_Groups_Oplus__class_Oplus(_411140, c_Groups_Ouminus__class_Ouminus(_411140, _411142), _411144)) = _411144)], (2834 ^ _221138) ^ [_315343, _315345, _315347, _315349] : [class_Groups_Oordered__cancel__ab__semigroup__add(_315343), c_Orderings_Oord__class_Oless(_315343, _315345, _315347), -(c_Orderings_Oord__class_Oless(_315343, c_Groups_Oplus__class_Oplus(_315343, _315349, _315345), c_Groups_Oplus__class_Oplus(_315343, _315349, _315347)))], (1239 ^ _221138) ^ [_261426, _261428] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _261426, _261428)), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _261426, _261428), -(_261426 = _261428)], (274 ^ _221138) ^ [_229581, _229583] : [-(class_Rings_Oordered__cancel__semiring(_229581)), _229583 = _229581, class_Rings_Oordered__cancel__semiring(_229583)], (10934 ^ _221138) ^ [_601868, _601870, _601872] : [class_RealVector_Oreal__normed__vector(_601868), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_601868, c_Groups_Ominus__class_Ominus(_601868, _601870, _601872)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_601868, _601870), c_RealVector_Onorm__class_Onorm(_601868, _601872))))], (12297 ^ _221138) ^ [_646815] : [class_Rings_Olinordered__idom(_646815), -(class_Groups_Oabs__if(tc_Polynomial_Opoly(_646815)))], (4886 ^ _221138) ^ [_386749] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _386749))], (8759 ^ _221138) ^ [_521946] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _521946) = _521946)], (3126 ^ _221138) ^ [_325802, _325804] : [class_RealVector_Oreal__normed__algebra(_325802), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_325802), c_Groups_Ozero__class_Ozero(_325802)), _325804) = c_Groups_Ozero__class_Ozero(_325802))], (6825 ^ _221138) ^ [_455562, _455564, _455566] : [class_Lattices_Oab__semigroup__idem__mult(_455562), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_455562), _455564), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_455562), _455564), _455566)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_455562), _455564), _455566))], (10770 ^ _221138) ^ [_595362, _595364] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _595362, _595364), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _595362, _595364))], (2118 ^ _221138) ^ [_289142, _289144, _289146] : [class_Orderings_Olinorder(_289142), 2121 ^ _221138 : [(2128 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_289142, _289146, _289144), c_Orderings_Oord__class_Oless__eq(_289142, _289144, _289146)], (2122 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_289142, _289144, _289146)), -(c_Orderings_Oord__class_Oless(_289142, _289146, _289144))]]], (11699 ^ _221138) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (4054 ^ _221138) ^ [_356084] : [class_Rings_Olinordered__semidom(_356084), c_Orderings_Oord__class_Oless__eq(_356084, c_Groups_Oone__class_Oone(_356084), c_Groups_Ozero__class_Ozero(_356084))], (11787 ^ _221138) ^ [] : [-(class_Groups_Ominus(tc_HOL_Obool))], (7493 ^ _221138) ^ [] : [-(c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (6557 ^ _221138) ^ [_446272, _446274, _446276] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _446272), 6560 ^ _221138 : [(6567 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _446274, _446276), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _446272), _446274), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _446272), _446276)))], (6561 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _446272), _446274), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _446272), _446276)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _446274, _446276))]]], (1668 ^ _221138) ^ [_275217, _275219, _275221] : [class_Orderings_Olinorder(_275217), -(_275219 = _275221), -(c_Orderings_Oord__class_Oless(_275217, _275219, _275221)), -(c_Orderings_Oord__class_Oless(_275217, _275221, _275219))], (9385 ^ _221138) ^ [_543944, _543946] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _543944, _543946), -(_543946 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _543944, 9388 ^ [_543944, _543946])))], (6191 ^ _221138) ^ [_432400, _432402, _432404] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _432400), _432402), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _432404), _432402)), 6194 ^ _221138 : [(6197 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _432400, _432404))], (6195 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _432402))]]], (364 ^ _221138) ^ [_232236, _232238] : [-(class_Rings_Olinordered__semidom(_232236)), _232238 = _232236, class_Rings_Olinordered__semidom(_232238)], (134 ^ _221138) ^ [_225451, _225453] : [-(class_RealVector_Oreal__normed__algebra(_225451)), _225453 = _225451, class_RealVector_Oreal__normed__algebra(_225453)], (44 ^ _221138) ^ [_222653, _222655, _222657, _222659] : [-(c_SEQ_Oincseq(_222657, _222653)), c_SEQ_Oincseq(_222659, _222655), _222659 = _222657, _222655 = _222653], (11637 ^ _221138) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (10279 ^ _221138) ^ [_575371, _575373] : [class_RealVector_Oreal__normed__vector(_575371), 10282 ^ _221138 : [(10283 ^ _221138) ^ [] : [10292 ^ _221138 : [(10293 ^ _221138) ^ [_575928] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_575371, hAPP(_575373, _575928)), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(10291 ^ [_575371, _575373]))))]], 10284 ^ _221138 : [(10285 ^ _221138) ^ [_575610] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _575610), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_575371, hAPP(_575373, 10288 ^ [_575371, _575373, _575610])), _575610)]]], (10295 ^ _221138) ^ [] : [10297 ^ _221138 : [(10298 ^ _221138) ^ [_576107] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_575371, hAPP(_575373, 10296 ^ [_575371, _575373, _576107])), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(_576107)))]], 10300 ^ _221138 : [(10303 ^ _221138) ^ [_576328] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_575371, hAPP(_575373, _576328)), 10299 ^ [_575371, _575373]))], (10301 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 10299 ^ [_575371, _575373]))]]]]], (1776 ^ _221138) ^ [_278486, _278488, _278490] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _278486, _278488), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _278488, _278490), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _278486, _278490))], (8125 ^ _221138) ^ [_500171, _500173, _500175] : [class_Rings_Olinordered__idom(_500171), -(c_Groups_Oabs__class_Oabs(_500171, hAPP(hAPP(c_Power_Opower__class_Opower(_500171), _500173), _500175)) = hAPP(hAPP(c_Power_Opower__class_Opower(_500171), c_Groups_Oabs__class_Oabs(_500171, _500173)), _500175))], (3674 ^ _221138) ^ [_343597, _343599, _343601, _343603] : [class_Rings_Oordered__ring(_343597), c_Orderings_Oord__class_Oless__eq(_343597, _343599, _343601), c_Orderings_Oord__class_Oless__eq(_343597, _343603, c_Groups_Ozero__class_Ozero(_343597)), -(c_Orderings_Oord__class_Oless__eq(_343597, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_343597), _343603), _343601), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_343597), _343603), _343599)))], (11605 ^ _221138) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (4148 ^ _221138) ^ [_359146, _359148, _359150] : [class_Groups_Oordered__comm__monoid__add(_359146), c_Orderings_Oord__class_Oless__eq(_359146, _359148, c_Groups_Ozero__class_Ozero(_359146)), c_Orderings_Oord__class_Oless(_359146, _359150, c_Groups_Ozero__class_Ozero(_359146)), -(c_Orderings_Oord__class_Oless(_359146, c_Groups_Oplus__class_Oplus(_359146, _359148, _359150), c_Groups_Ozero__class_Ozero(_359146)))], (8257 ^ _221138) ^ [_504793, _504795, _504797, _504799, _504801] : [class_Rings_Ocomm__semiring__1(_504793), c_Rings_Odvd__class_Odvd(_504793, _504795, _504797), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _504799, _504801), -(c_Rings_Odvd__class_Odvd(_504793, hAPP(hAPP(c_Power_Opower__class_Opower(_504793), _504795), _504799), hAPP(hAPP(c_Power_Opower__class_Opower(_504793), _504797), _504801)))], (9674 ^ _221138) ^ [_554043, _554045, _554047] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _554043), _554045), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _554047), _554045)), -(_554045 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _554043, _554047))], (1162 ^ _221138) ^ [_258845] : [class_RealVector_Oreal__normed__vector(_258845), -(c_RealVector_Onorm__class_Onorm(_258845, c_Groups_Ozero__class_Ozero(_258845)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (614 ^ _221138) ^ [_239611, _239613] : [-(class_Groups_Osgn__if(_239611)), _239613 = _239611, class_Groups_Osgn__if(_239613)], (5221 ^ _221138) ^ [_399600, _399602] : [class_Groups_Ogroup__add(_399600), -(c_Groups_Ouminus__class_Ouminus(_399600, c_Groups_Ouminus__class_Ouminus(_399600, _399602)) = _399602)], (5613 ^ _221138) ^ [_413088, _413090] : [class_Groups_Oordered__ab__group__add(_413088), 5616 ^ _221138 : [(5623 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_413088, _413090, c_Groups_Ozero__class_Ozero(_413088)), -(c_Orderings_Oord__class_Oless__eq(_413088, c_Groups_Ozero__class_Ozero(_413088), c_Groups_Ouminus__class_Ouminus(_413088, _413090)))], (5617 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_413088, c_Groups_Ozero__class_Ozero(_413088), c_Groups_Ouminus__class_Ouminus(_413088, _413090)), -(c_Orderings_Oord__class_Oless__eq(_413088, _413090, c_Groups_Ozero__class_Ozero(_413088)))]]], (11191 ^ _221138) ^ [_611583, _611585] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _611583, _611585)), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _611585, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _611583, _611585)) = _611583)], (10173 ^ _221138) ^ [_571683] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _571683)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _571683))], (2086 ^ _221138) ^ [_288156, _288158, _288160] : [class_Orderings_Oorder(_288156), 2089 ^ _221138 : [(2098 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(_288156, _288158, _288160)), c_Orderings_Oord__class_Oless__eq(_288156, _288158, _288160), -(_288158 = _288160)], (2090 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_288156, _288158, _288160), 2093 ^ _221138 : [(2096 ^ _221138) ^ [] : [_288158 = _288160], (2094 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_288156, _288158, _288160))]]]]], (8999 ^ _221138) ^ [_530605, _530607] : [9000 ^ _221138 : [(9003 ^ _221138) ^ [] : [_530605 = _530607], (9001 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _530605, _530607)]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _530605, c_Nat_OSuc(_530607)))], (5969 ^ _221138) ^ [_424574, _424576] : [class_Groups_Oordered__ab__group__add__abs(_424574), -(c_Orderings_Oord__class_Oless__eq(_424574, c_Groups_Ouminus__class_Ouminus(_424574, c_Groups_Oabs__class_Oabs(_424574, _424576)), c_Groups_Ozero__class_Ozero(_424574)))], (11939 ^ _221138) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex))], (12237 ^ _221138) ^ [_644915] : [class_Rings_Ocomm__semiring__0(_644915), -(class_Rings_Osemiring__0(tc_Polynomial_Opoly(_644915)))], (11649 ^ _221138) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (7831 ^ _221138) ^ [_490099, _490101, _490103] : [_490099 = _490101, 7842 ^ _221138 : [(7845 ^ _221138) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _490103, _490099)], (7843 ^ _221138) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _490099, _490103))]], c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _490101, _490103), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _490103, _490101))], (11641 ^ _221138) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (7791 ^ _221138) ^ [_488866, _488868] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _488866, _488868), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _488868, _488866)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _488868, _488866), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _488866, _488868))], (10113 ^ _221138) ^ [_569504] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _569504), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (11985 ^ _221138) ^ [] : [-(class_Rings_Oidom(tc_Complex_Ocomplex))], (2758 ^ _221138) ^ [_312674, _312676, _312678, _312680, _312682] : [class_Groups_Oordered__ab__semigroup__add(_312674), c_Orderings_Oord__class_Oless__eq(_312674, _312676, _312678), c_Orderings_Oord__class_Oless__eq(_312674, _312680, _312682), -(c_Orderings_Oord__class_Oless__eq(_312674, c_Groups_Oplus__class_Oplus(_312674, _312676, _312680), c_Groups_Oplus__class_Oplus(_312674, _312678, _312682)))], (9137 ^ _221138) ^ [_535246, _535248] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _535246, _535248), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _535246, c_Nat_OSuc(_535248)))], (7589 ^ _221138) ^ [_482613, _482615] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _482613), 7592 ^ _221138 : [(7599 ^ _221138) ^ [] : [_482615 = 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), _482613), _482615), _482613))], (7593 ^ _221138) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _482613), _482615), _482613), -(_482615 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (3576 ^ _221138) ^ [_340303, _340305, _340307] : [class_Rings_Oordered__cancel__semiring(_340303), c_Orderings_Oord__class_Oless__eq(_340303, c_Groups_Ozero__class_Ozero(_340303), _340305), c_Orderings_Oord__class_Oless__eq(_340303, _340307, c_Groups_Ozero__class_Ozero(_340303)), -(c_Orderings_Oord__class_Oless__eq(_340303, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_340303), _340307), _340305), c_Groups_Ozero__class_Ozero(_340303)))], (5975 ^ _221138) ^ [_424800, _424802] : [class_Groups_Oordered__ab__group__add__abs(_424800), c_Orderings_Oord__class_Oless__eq(_424800, _424802, c_Groups_Ozero__class_Ozero(_424800)), -(c_Groups_Oabs__class_Oabs(_424800, _424802) = c_Groups_Ouminus__class_Ouminus(_424800, _424802))], (9375 ^ _221138) ^ [_543602, _543604] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _543602), _543604) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _543602 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _543604 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10800 ^ _221138) ^ [_596820, _596822, _596824, _596826, _596828] : [class_Groups_Oab__group__add(_596820), c_Groups_Ominus__class_Ominus(_596820, _596822, _596824) = c_Groups_Ominus__class_Ominus(_596820, _596826, _596828), 10807 ^ _221138 : [(10814 ^ _221138) ^ [] : [_596826 = _596828, -(_596822 = _596824)], (10808 ^ _221138) ^ [] : [_596822 = _596824, -(_596826 = _596828)]]], (9600 ^ _221138) ^ [_551587, _551589] : [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), _551587), _551589)), 9603 ^ _221138 : [(9606 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _551589))], (9604 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _551587))]]], (3144 ^ _221138) ^ [_326498, _326500] : [class_RealVector_Oreal__normed__vector(_326498), -(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_326498, _326500)) = c_RealVector_Onorm__class_Onorm(_326498, _326500))], (11105 ^ _221138) ^ [_608401, _608403, _608405] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _608401, _608403), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _608405, _608403)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _608401, _608405))], (2792 ^ _221138) ^ [_313882, _313884, _313886, _313888] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_313882), 2795 ^ _221138 : [(2802 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_313882, _313884, _313888), -(c_Orderings_Oord__class_Oless(_313882, c_Groups_Oplus__class_Oplus(_313882, _313884, _313886), c_Groups_Oplus__class_Oplus(_313882, _313888, _313886)))], (2796 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_313882, c_Groups_Oplus__class_Oplus(_313882, _313884, _313886), c_Groups_Oplus__class_Oplus(_313882, _313888, _313886)), -(c_Orderings_Oord__class_Oless(_313882, _313884, _313888))]]], (12117 ^ _221138) ^ [_641115] : [class_Rings_Ocomm__semiring__0(_641115), -(class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(_641115)))], (8755 ^ _221138) ^ [_521807] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _521807), _521807) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (10038 ^ _221138) ^ [_566617, _566619, _566621] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _566617), 10044 ^ _221138 : [(10047 ^ _221138) ^ [] : [hBOOL(hAPP(_566619, c_Groups_Oplus__class_Oplus(tc_Int_Oint, 10043 ^ [_566617, _566619, _566621], _566617)))], (10045 ^ _221138) ^ [] : [-(hBOOL(hAPP(_566619, 10043 ^ [_566617, _566619, _566621])))]], c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _566621), 10052 ^ _221138 : [(10053 ^ _221138) ^ [_567132] : [hBOOL(hAPP(_566619, _567132)), -(hBOOL(hAPP(_566619, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _567132, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _566621), _566617)))))]]], (11675 ^ _221138) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (11261 ^ _221138) ^ [_613918, _613920, _613922] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _613918, _613920), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _613920, _613918), _613922) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _613920, _613922), _613918))], (8351 ^ _221138) ^ [_508142, _508144, _508146] : [class_Rings_Oring__1(_508142), -(hAPP(hAPP(c_Power_Opower__class_Opower(_508142), c_Groups_Ouminus__class_Ouminus(_508142, _508144)), _508146) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_508142), hAPP(hAPP(c_Power_Opower__class_Opower(_508142), c_Groups_Ouminus__class_Ouminus(_508142, c_Groups_Oone__class_Oone(_508142))), _508146)), hAPP(hAPP(c_Power_Opower__class_Opower(_508142), _508144), _508146)))], (6135 ^ _221138) ^ [_430449, _430451] : [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), _430449), _430451)), 6138 ^ _221138 : [(6141 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _430451))], (6139 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _430449))]]], (8103 ^ _221138) ^ [_499236, _499238] : [class_Groups_Omonoid__mult(_499236), -(hAPP(hAPP(c_Power_Opower__class_Opower(_499236), c_Groups_Oone__class_Oone(_499236)), _499238) = c_Groups_Oone__class_Oone(_499236))], (6807 ^ _221138) ^ [_454864, _454866] : [class_Rings_Olinordered__idom(_454864), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_454864), c_Groups_Osgn__class_Osgn(_454864, _454866)), c_Groups_Oabs__class_Oabs(_454864, _454866)) = _454866)], (6511 ^ _221138) ^ [_444520, _444522, _444524] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _444520, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _444522, _444524)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _444522, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _444520, _444524)))], (8793 ^ _221138) ^ [_523132, _523134] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _523132, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _523134, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _523132, _523134))], (9414 ^ _221138) ^ [_545081, _545083] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _545081, c_Nat_OSuc(_545083)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _545081, _545083))], (9986 ^ _221138) ^ [_564676, _564678] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _564676, _564678), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatfloor(_564676), c_RComplete_Onatfloor(_564678)))], (4955 ^ _221138) ^ [_389626, _389628] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _389626, _389628), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _389626, _389628)), -(_389626 = _389628)], (8721 ^ _221138) ^ [_520767, _520769] : [8722 ^ _221138 : [(8725 ^ _221138) ^ [] : [_520767 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8723 ^ _221138) ^ [] : [_520769 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _520767), _520769) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (2150 ^ _221138) ^ [_290149, _290151] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _290149, _290151), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _290149, _290151)), -(_290149 = _290151)], (9628 ^ _221138) ^ [_552529, _552531, _552533] : [-(_552529 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 9631 ^ _221138 : [(9638 ^ _221138) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _552531, _552533), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _552531), _552529), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _552533), _552529)))], (9632 ^ _221138) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _552531), _552529), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _552533), _552529)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _552531, _552533))]]], (9772 ^ _221138) ^ [_557307, _557309] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _557307, _557309)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _557309, _557307))], (6819 ^ _221138) ^ [_455324, _455326] : [class_Lattices_Oab__semigroup__idem__mult(_455324), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_455324), _455326), _455326) = _455326)], (9408 ^ _221138) ^ [_544832, _544834] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_544832), _544834), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _544832, _544834))], (11543 ^ _221138) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat))], (5661 ^ _221138) ^ [_414537, _414539] : [class_Groups_Olinordered__ab__group__add(_414537), 5664 ^ _221138 : [(5671 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_414537, c_Groups_Ozero__class_Ozero(_414537), _414539), -(c_Orderings_Oord__class_Oless__eq(_414537, c_Groups_Ouminus__class_Ouminus(_414537, _414539), _414539))], (5665 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_414537, c_Groups_Ouminus__class_Ouminus(_414537, _414539), _414539), -(c_Orderings_Oord__class_Oless__eq(_414537, c_Groups_Ozero__class_Ozero(_414537), _414539))]]], (7043 ^ _221138) ^ [_462896] : [-(_462896 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 7046 ^ _221138 : [(7053 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _462896)), -(c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, _462896) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (7047 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _462896), -(c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, _462896) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))]]], (6968 ^ _221138) ^ [_460205, _460207] : [class_RealVector_Oreal__normed__vector(_460205), c_SEQ_OBseq(_460205, _460207), 6976 ^ _221138 : [(6979 ^ _221138) ^ [_460561] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_460205, hAPP(_460207, _460561)), 6975 ^ [_460205, _460207]))], (6977 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 6975 ^ [_460205, _460207]))]]], (11983 ^ _221138) ^ [] : [-(class_Rings_Oring(tc_Complex_Ocomplex))], (3688 ^ _221138) ^ [_344095, _344097, _344099, _344101, _344103] : [class_Rings_Oordered__semiring(_344095), c_Orderings_Oord__class_Oless__eq(_344095, _344097, _344099), c_Orderings_Oord__class_Oless__eq(_344095, _344101, _344103), c_Orderings_Oord__class_Oless__eq(_344095, c_Groups_Ozero__class_Ozero(_344095), _344097), c_Orderings_Oord__class_Oless__eq(_344095, c_Groups_Ozero__class_Ozero(_344095), _344101), -(c_Orderings_Oord__class_Oless__eq(_344095, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_344095), _344097), _344101), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_344095), _344099), _344103)))], (6613 ^ _221138) ^ [_448274, _448276, _448278] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _448274, _448276), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _448274, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _448278, _448276)))], (2360 ^ _221138) ^ [_297776, _297778, _297780] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _297776), _297778)), _297780) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _297776), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _297778), _297780)))], (7459 ^ _221138) ^ [_477768, _477770, _477772, _477774] : [class_Rings_Ocomm__semiring__1(_477768), -(hAPP(hAPP(c_Power_Opower__class_Opower(_477768), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_477768), _477770), _477772)), _477774) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_477768), hAPP(hAPP(c_Power_Opower__class_Opower(_477768), _477770), _477774)), hAPP(hAPP(c_Power_Opower__class_Opower(_477768), _477772), _477774)))], (9209 ^ _221138) ^ [_537771, _537773, _537775] : [class_Rings_Ocomm__semiring__1(_537771), -(hAPP(hAPP(c_Power_Opower__class_Opower(_537771), _537773), c_Nat_OSuc(_537775)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_537771), _537773), hAPP(hAPP(c_Power_Opower__class_Opower(_537771), _537773), _537775)))], (4546 ^ _221138) ^ [_372682, _372684, _372686] : [class_Rings_Ocomm__semiring__1(_372682), -(c_Groups_Oplus__class_Oplus(_372682, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_372682), _372684), _372686), _372686) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_372682), c_Groups_Oplus__class_Oplus(_372682, _372684, c_Groups_Oone__class_Oone(_372682))), _372686))], (11969 ^ _221138) ^ [] : [-(class_Int_Oring__char__0(tc_Complex_Ocomplex))], (6869 ^ _221138) ^ [_457141, _457143] : [class_Rings_Olinordered__idom(_457141), 6872 ^ _221138 : [(6879 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_457141, c_Groups_Ozero__class_Ozero(_457141), _457143), -(c_Groups_Osgn__class_Osgn(_457141, _457143) = c_Groups_Oone__class_Oone(_457141))], (6873 ^ _221138) ^ [] : [c_Groups_Osgn__class_Osgn(_457141, _457143) = c_Groups_Oone__class_Oone(_457141), -(c_Orderings_Oord__class_Oless(_457141, c_Groups_Ozero__class_Ozero(_457141), _457143))]]], (11517 ^ _221138) ^ [_624041, _624043, _624045, _624047, _624049] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _624041, _624043), 11520 ^ _221138 : [(11527 ^ _221138) ^ [] : [_624047 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _624043, _624041)), _624045), _624049), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _624041), _624045), _624047) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _624043), _624045), _624049))], (11521 ^ _221138) ^ [] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _624041), _624045), _624047) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _624043), _624045), _624049), -(_624047 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _624043, _624041)), _624045), _624049))]]], (6549 ^ _221138) ^ [_445940, _445942, _445944] : [6550 ^ _221138 : [(6553 ^ _221138) ^ [] : [_445942 = _445944], (6551 ^ _221138) ^ [] : [_445940 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _445940), _445942) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _445940), _445944))], (10203 ^ _221138) ^ [_572731, _572733] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _572731), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _572733), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _572731, _572733))], (1168 ^ _221138) ^ [_259057, _259059] : [class_RealVector_Oreal__normed__vector(_259057), 1171 ^ _221138 : [(1178 ^ _221138) ^ [] : [_259059 = c_Groups_Ozero__class_Ozero(_259057), -(c_RealVector_Onorm__class_Onorm(_259057, _259059) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (1172 ^ _221138) ^ [] : [c_RealVector_Onorm__class_Onorm(_259057, _259059) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_259059 = c_Groups_Ozero__class_Ozero(_259057))]]], (5579 ^ _221138) ^ [_411900, _411902] : [class_Groups_Oordered__ab__group__add__abs(_411900), -(c_Groups_Oabs__class_Oabs(_411900, c_Groups_Ouminus__class_Ouminus(_411900, _411902)) = c_Groups_Oabs__class_Oabs(_411900, _411902))], (11533 ^ _221138) ^ [_624639] : [class_Groups_Ocancel__comm__monoid__add(_624639), -(class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(_624639)))], (1716 ^ _221138) ^ [_276652, _276654, _276656] : [class_Orderings_Olinorder(_276652), 1719 ^ _221138 : [(1720 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(_276652, _276654, _276656)), -(c_Orderings_Oord__class_Oless(_276652, _276656, _276654)), -(_276654 = _276656)], (1730 ^ _221138) ^ [] : [1731 ^ _221138 : [(1734 ^ _221138) ^ [] : [_276654 = _276656], (1732 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_276652, _276656, _276654)]], c_Orderings_Oord__class_Oless(_276652, _276654, _276656)]]], (8711 ^ _221138) ^ [_520503, _520505] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _520503), _520505) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_520505 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_520503 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (304 ^ _221138) ^ [_230466, _230468] : [-(class_Rings_Oordered__comm__semiring(_230466)), _230468 = _230466, class_Rings_Oordered__comm__semiring(_230468)], (10131 ^ _221138) ^ [_570159] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _570159), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(_570159 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5677 ^ _221138) ^ [_415016, _415018] : [class_Groups_Oordered__ab__group__add(_415016), 5680 ^ _221138 : [(5687 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_415016, _415018, c_Groups_Ozero__class_Ozero(_415016)), -(c_Orderings_Oord__class_Oless(_415016, c_Groups_Ozero__class_Ozero(_415016), c_Groups_Ouminus__class_Ouminus(_415016, _415018)))], (5681 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_415016, c_Groups_Ozero__class_Ozero(_415016), c_Groups_Ouminus__class_Ouminus(_415016, _415018)), -(c_Orderings_Oord__class_Oless(_415016, _415018, c_Groups_Ozero__class_Ozero(_415016)))]]], (9502 ^ _221138) ^ [_548265] : [-(c_Nat_OSuc(_548265) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _548265))], (11387 ^ _221138) ^ [_618864, _618866] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _618864, _618866) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _618866, _618864) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_618864 = _618866)], (394 ^ _221138) ^ [_233121, _233123] : [-(class_Groups_Oab__semigroup__add(_233121)), _233123 = _233121, class_Groups_Oab__semigroup__add(_233123)], (2354 ^ _221138) ^ [_297493, _297495, _297497, _297499] : [class_RealVector_Oreal__normed__algebra(_297493), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_297493), _297495), c_Groups_Oplus__class_Oplus(_297493, _297497, _297499)) = c_Groups_Oplus__class_Oplus(_297493, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_297493), _297495), _297497), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_297493), _297495), _297499)))], (12219 ^ _221138) ^ [_644345] : [class_Rings_Ocomm__semiring__1(_644345), -(class_Groups_Omonoid__mult(tc_Polynomial_Opoly(_644345)))], (5347 ^ _221138) ^ [_403630, _403632] : [class_Groups_Ogroup__add(_403630), 5350 ^ _221138 : [(5357 ^ _221138) ^ [] : [_403632 = c_Groups_Ozero__class_Ozero(_403630), -(c_Groups_Ouminus__class_Ouminus(_403630, _403632) = c_Groups_Ozero__class_Ozero(_403630))], (5351 ^ _221138) ^ [] : [c_Groups_Ouminus__class_Ouminus(_403630, _403632) = c_Groups_Ozero__class_Ozero(_403630), -(_403632 = c_Groups_Ozero__class_Ozero(_403630))]]], (5497 ^ _221138) ^ [_408549, _408551, _408553] : [class_RealVector_Oreal__normed__algebra(_408549), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_408549), c_Groups_Ouminus__class_Ouminus(_408549, _408551)), _408553) = c_Groups_Ouminus__class_Ouminus(_408549, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_408549), _408551), _408553)))], (11603 ^ _221138) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (9181 ^ _221138) ^ [] : [-(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (6573 ^ _221138) ^ [_446806, _446808, _446810] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _446806), 6576 ^ _221138 : [(6583 ^ _221138) ^ [] : [_446808 = _446810, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _446806), _446808) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _446806), _446810))], (6577 ^ _221138) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _446806), _446808) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _446806), _446810), -(_446808 = _446810)]]], (11895 ^ _221138) ^ [] : [-(class_Groups_Ouminus(tc_RealDef_Oreal))], (5769 ^ _221138) ^ [_417911, _417913] : [class_Groups_Oab__group__add(_417911), -(c_Groups_Oplus__class_Oplus(_417911, c_Groups_Ouminus__class_Ouminus(_417911, _417913), _417913) = c_Groups_Ozero__class_Ozero(_417911))], (7485 ^ _221138) ^ [_478938] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_RComplete_Onatceiling(_478938)))], (11793 ^ _221138) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal))], (1289 ^ _221138) ^ [_263070, _263072, _263074, _263076] : [class_Orderings_Oorder(_263070), c_Orderings_Oord__class_Oless__eq(_263070, _263072, _263074), c_Orderings_Oord__class_Oless__eq(_263070, _263076, _263072), -(c_Orderings_Oord__class_Oless__eq(_263070, _263076, _263074))], (11817 ^ _221138) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal))], (6065 ^ _221138) ^ [_427978] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _427978, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _427978) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _427978))], (7583 ^ _221138) ^ [_482399] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _482399, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_482399), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (4106 ^ _221138) ^ [_357800, _357802, _357804, _357806] : [class_Groups_Oordered__comm__monoid__add(_357800), c_Orderings_Oord__class_Oless(_357800, c_Groups_Ozero__class_Ozero(_357800), _357802), c_Orderings_Oord__class_Oless__eq(_357800, _357804, _357806), -(c_Orderings_Oord__class_Oless(_357800, _357804, c_Groups_Oplus__class_Oplus(_357800, _357802, _357806)))], (11027 ^ _221138) ^ [_605546, _605548, _605550] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _605546, _605548), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _605546, _605550), 11034 ^ _221138 : [(11041 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _605548, _605550), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _605548, _605546), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _605550, _605546)))], (11035 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _605548, _605546), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _605550, _605546)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _605548, _605550))]]], (8959 ^ _221138) ^ [_529133, _529135] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _529133), _529135) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _529135), _529133))], (4534 ^ _221138) ^ [_372274] : [-(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), _372274), _372274))), -(_372274 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (12351 ^ _221138) ^ [_648539, _648541] : [hBOOL(c_fequal(_648539, _648541)), -(_648539 = _648541)], (86 ^ _221138) ^ [_224013, _224015, _224017, _224019, _224021, _224023] : [-(c_Rings_Odvd__class_Odvd(_224021, _224017, _224013)), c_Rings_Odvd__class_Odvd(_224023, _224019, _224015), _224023 = _224021, _224019 = _224017, _224015 = _224013], (5099 ^ _221138) ^ [_394959, _394961, _394963] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _394959, _394961), _394963), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _394959, _394963))], (2248 ^ _221138) ^ [_293666, _293668, _293670, _293672] : [class_Groups_Ozero(_293666), hAPP(hAPP(hAPP(_293668, c_Groups_Ozero__class_Ozero(_293666)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_293666))), _293670) = _293670, -(c_Polynomial_Opoly__rec(_293672, _293666, _293670, _293668, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_293666))) = _293670)], (9159 ^ _221138) ^ [_535966] : [_535966 = c_Nat_OSuc(_535966)], (2748 ^ _221138) ^ [_312295, _312297, _312299, _312301] : [class_Groups_Oordered__ab__semigroup__add(_312295), c_Orderings_Oord__class_Oless__eq(_312295, _312297, _312299), -(c_Orderings_Oord__class_Oless__eq(_312295, c_Groups_Oplus__class_Oplus(_312295, _312301, _312297), c_Groups_Oplus__class_Oplus(_312295, _312301, _312299)))], (2522 ^ _221138) ^ [_304205, _304207] : [class_Groups_Ocomm__monoid__mult(_304205), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_304205), _304207), c_Groups_Oone__class_Oone(_304205)) = _304207)], (8643 ^ _221138) ^ [_518279, _518281] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _518279, _518281), c_Rings_Odvd__class_Odvd(tc_Int_Oint, _518281, _518279), -(c_Groups_Oabs__class_Oabs(tc_Int_Oint, _518279) = c_Groups_Oabs__class_Oabs(tc_Int_Oint, _518281))], (810 ^ _221138) ^ [_246064, _246066, _246068, _246070, _246072, _246074, _246076, _246078] : [-(c_If(_246078, _246074, _246070, _246066) = c_If(_246076, _246072, _246068, _246064)), _246078 = _246076, _246074 = _246072, _246070 = _246068, _246066 = _246064], (7059 ^ _221138) ^ [_463353] : [class_RealVector_Oreal__normed__algebra(_463353), 7063 ^ _221138 : [(7066 ^ _221138) ^ [_463682, _463684] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_463353, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_463353), _463684), _463682)), 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(_463353, _463684)), c_RealVector_Onorm__class_Onorm(_463353, _463682))), 7062 ^ [_463353])))], (7064 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 7062 ^ [_463353]))]]], (2242 ^ _221138) ^ [_293374, _293376, _293378, _293380] : [class_Rings_Ocomm__semiring__0(_293374), -(c_Polynomial_Osynthetic__div(_293374, c_Polynomial_OpCons(_293374, _293376, _293378), _293380) = c_Polynomial_OpCons(_293374, hAPP(c_Polynomial_Opoly(_293374, _293378), _293380), c_Polynomial_Osynthetic__div(_293374, _293378, _293380)))], (4985 ^ _221138) ^ [_390641, _390643] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _390641, _390643), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _390641, _390643))], (11341 ^ _221138) ^ [_616923, _616925, _616927] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _616923, _616925), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _616927, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _616925, _616923)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _616927, _616923), _616925))], (9185 ^ _221138) ^ [_536927] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _536927), _536927) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (8621 ^ _221138) ^ [_517425, _517427, _517429] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _517425, _517427), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _517425, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _517427, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _517425), _517429))))], (10075 ^ _221138) ^ [_567987, _567989] : [-(c_RealDef_Oreal(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _567987), _567989)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _567987)), c_RealDef_Oreal(tc_Nat_Onat, _567989)))], (9778 ^ _221138) ^ [_557493] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _557493, _557493))], (554 ^ _221138) ^ [_237841, _237843] : [-(class_Orderings_Oorder(_237841)), _237843 = _237841, class_Orderings_Oorder(_237843)], (4658 ^ _221138) ^ [_377526, _377528, _377530, _377532, _377534] : [class_Rings_Ocomm__semiring__1(_377526), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_377526), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_377526), _377528), _377530)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_377526), _377532), _377534)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_377526), _377532), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_377526), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_377526), _377528), _377530)), _377534)))], (11755 ^ _221138) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (4628 ^ _221138) ^ [_375900, _375902, _375904, _375906] : [class_Rings_Ocomm__semiring__1(_375900), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_375900), _375902), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_375900), _375904), _375906)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_375900), _375904), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_375900), _375902), _375906)))], (10261 ^ _221138) ^ [_574800, _574802] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _574800), 10264 ^ _221138 : [(10271 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _574800, c_RealDef_Oreal(tc_Nat_Onat, _574802)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_574800), _574802))], (10265 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_574800), _574802), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _574800, c_RealDef_Oreal(tc_Nat_Onat, _574802)))]]], (2174 ^ _221138) ^ [_290921, _290923, _290925] : [class_Rings_Olinordered__idom(_290921), 2177 ^ _221138 : [(2190 ^ _221138) ^ [] : [-(c_Polynomial_Opos__poly(_290921, c_Polynomial_OpCons(_290921, _290923, _290925))), 2191 ^ _221138 : [(2194 ^ _221138) ^ [] : [_290925 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_290921)), c_Orderings_Oord__class_Oless(_290921, c_Groups_Ozero__class_Ozero(_290921), _290923)], (2192 ^ _221138) ^ [] : [c_Polynomial_Opos__poly(_290921, _290925)]]], (2178 ^ _221138) ^ [] : [c_Polynomial_Opos__poly(_290921, c_Polynomial_OpCons(_290921, _290923, _290925)), -(c_Polynomial_Opos__poly(_290921, _290925)), 2185 ^ _221138 : [(2188 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(_290921, c_Groups_Ozero__class_Ozero(_290921), _290923))], (2186 ^ _221138) ^ [] : [-(_290925 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_290921)))]]]]], (5835 ^ _221138) ^ [_420134, _420136, _420138] : [class_Groups_Oordered__ab__group__add__abs(_420134), 5838 ^ _221138 : [(5847 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_420134, c_Groups_Oabs__class_Oabs(_420134, _420136), _420138)), c_Orderings_Oord__class_Oless__eq(_420134, _420136, _420138), c_Orderings_Oord__class_Oless__eq(_420134, c_Groups_Ouminus__class_Ouminus(_420134, _420136), _420138)], (5839 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_420134, c_Groups_Oabs__class_Oabs(_420134, _420136), _420138), 5842 ^ _221138 : [(5845 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_420134, c_Groups_Ouminus__class_Ouminus(_420134, _420136), _420138))], (5843 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_420134, _420136, _420138))]]]]], (5903 ^ _221138) ^ [_422232, _422234] : [-(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), _422232), _422232)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _422234), _422234)))], (1191 ^ _221138) ^ [_259803, _259805] : [class_Orderings_Opreorder(_259803), -(c_Orderings_Oord__class_Oless__eq(_259803, _259805, _259805))], (9227 ^ _221138) ^ [_538611, _538613, _538615] : [class_Groups_Omonoid__mult(_538611), -(hAPP(hAPP(c_Power_Opower__class_Opower(_538611), _538613), c_Nat_OSuc(_538615)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_538611), hAPP(hAPP(c_Power_Opower__class_Opower(_538611), _538613), _538615)), _538613))], (8811 ^ _221138) ^ [_523709] : [_523709 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oabs__class_Oabs(tc_Int_Oint, _523709), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (3846 ^ _221138) ^ [_349220, _349222, _349224, _349226] : [class_Rings_Olinordered__ring__strict(_349220), c_Orderings_Oord__class_Oless(_349220, c_Groups_Ozero__class_Ozero(_349220), _349222), 3853 ^ _221138 : [(3860 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_349220, _349224, _349226), -(c_Orderings_Oord__class_Oless(_349220, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_349220), _349222), _349224), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_349220), _349222), _349226)))], (3854 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_349220, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_349220), _349222), _349224), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_349220), _349222), _349226)), -(c_Orderings_Oord__class_Oless(_349220, _349224, _349226))]]], (11617 ^ _221138) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (5829 ^ _221138) ^ [_419898, _419900] : [class_Groups_Oordered__ab__group__add__abs(_419898), -(c_Orderings_Oord__class_Oless__eq(_419898, c_Groups_Ouminus__class_Ouminus(_419898, _419900), c_Groups_Oabs__class_Oabs(_419898, _419900)))], (8557 ^ _221138) ^ [_515285] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _515285, c_Nat_OSuc(_515285)))], (10708 ^ _221138) ^ [_593221, _593223, _593225] : [class_Groups_Ogroup__add(_593221), -(c_Groups_Ominus__class_Ominus(_593221, c_Groups_Oplus__class_Oplus(_593221, _593223, _593225), _593225) = _593223)], (2824 ^ _221138) ^ [_314978, _314980, _314982, _314984] : [class_Groups_Oordered__cancel__ab__semigroup__add(_314978), c_Orderings_Oord__class_Oless(_314978, _314980, _314982), -(c_Orderings_Oord__class_Oless(_314978, c_Groups_Oplus__class_Oplus(_314978, _314980, _314984), c_Groups_Oplus__class_Oplus(_314978, _314982, _314984)))], (5585 ^ _221138) ^ [_412126, _412128] : [class_RealVector_Oreal__normed__vector(_412126), -(c_RealVector_Onorm__class_Onorm(_412126, c_Groups_Ouminus__class_Ouminus(_412126, _412128)) = c_RealVector_Onorm__class_Onorm(_412126, _412128))], (11227 ^ _221138) ^ [_612790, _612792, _612794] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _612790, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _612792, _612794)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _612790, _612794), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _612794, _612792), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _612790, _612792))], (7447 ^ _221138) ^ [_477208, _477210] : [class_Rings_Ocomm__semiring__1(_477208), -(hAPP(hAPP(c_Power_Opower__class_Opower(_477208), _477210), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _477210)], (11877 ^ _221138) ^ [] : [-(class_Groups_Omonoid__add(tc_RealDef_Oreal))], (4672 ^ _221138) ^ [_378338, _378340, _378342] : [class_Rings_Ocomm__semiring__1(_378338), -(c_Groups_Oplus__class_Oplus(_378338, _378340, _378342) = c_Groups_Oplus__class_Oplus(_378338, _378342, _378340))], (7239 ^ _221138) ^ [_469648, _469650, _469652, _469654] : [class_Rings_Ocomm__semiring__1(_469648), c_Rings_Odvd__class_Odvd(_469648, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_469648), _469650), _469652), _469654), -(c_Rings_Odvd__class_Odvd(_469648, _469652, _469654))], (5275 ^ _221138) ^ [_401338, _401340] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _401338, _401340), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _401340, _401338), -(_401338 = _401340)], (6105 ^ _221138) ^ [_429364] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _429364))], (4506 ^ _221138) ^ [_371266, _371268, _371270] : [class_Rings_Olinordered__ring(_371266), -(c_Orderings_Oord__class_Oless__eq(_371266, c_Groups_Ozero__class_Ozero(_371266), c_Groups_Oplus__class_Oplus(_371266, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_371266), _371268), _371268), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_371266), _371270), _371270))))], (2296 ^ _221138) ^ [_295337, _295339] : [class_Groups_Ozero(_295337), 2299 ^ _221138 : [(2306 ^ _221138) ^ [] : [_295339 = c_Groups_Ozero__class_Ozero(_295337), -(c_Groups_Ozero__class_Ozero(_295337) = _295339)], (2300 ^ _221138) ^ [] : [c_Groups_Ozero__class_Ozero(_295337) = _295339, -(_295339 = c_Groups_Ozero__class_Ozero(_295337))]]], (9488 ^ _221138) ^ [_547666, _547668] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_547666)), _547668) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _547668, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _547666), _547668)))], (6165 ^ _221138) ^ [_431400, _431402] : [6166 ^ _221138 : [(6169 ^ _221138) ^ [] : [_431402 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (6167 ^ _221138) ^ [] : [_431400 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _431400), _431402) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2374 ^ _221138) ^ [_298534, _298536, _298538] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _298534, _298536)), _298538) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _298534), _298538), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _298536), _298538)))], (11735 ^ _221138) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (5741 ^ _221138) ^ [_416944, _416946] : [class_Groups_Ogroup__add(_416944), -(c_Groups_Oplus__class_Oplus(_416944, _416946, c_Groups_Ouminus__class_Ouminus(_416944, _416946)) = c_Groups_Ozero__class_Ozero(_416944))], (5725 ^ _221138) ^ [_416465, _416467] : [class_Groups_Olinordered__ab__group__add(_416465), 5728 ^ _221138 : [(5735 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_416465, c_Groups_Ozero__class_Ozero(_416465), _416467), -(c_Orderings_Oord__class_Oless(_416465, c_Groups_Ouminus__class_Ouminus(_416465, _416467), _416467))], (5729 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_416465, c_Groups_Ouminus__class_Ouminus(_416465, _416467), _416467), -(c_Orderings_Oord__class_Oless(_416465, c_Groups_Ozero__class_Ozero(_416465), _416467))]]], (58 ^ _221138) ^ [_223097, _223099, _223101, _223103] : [-(c_SEQ_OBseq(_223101, _223097)), c_SEQ_OBseq(_223103, _223099), _223103 = _223101, _223099 = _223097], (11403 ^ _221138) ^ [_619424, _619426, _619428] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _619424), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _619426, _619428)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _619424), _619426), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _619424), _619428)))], (5509 ^ _221138) ^ [_409093, _409095, _409097] : [class_Rings_Oidom(_409093), 5512 ^ _221138 : [(5513 ^ _221138) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_409093), _409095), _409095) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_409093), _409097), _409097), -(_409095 = _409097), -(_409095 = c_Groups_Ouminus__class_Ouminus(_409093, _409097))], (5523 ^ _221138) ^ [] : [5524 ^ _221138 : [(5527 ^ _221138) ^ [] : [_409095 = c_Groups_Ouminus__class_Ouminus(_409093, _409097)], (5525 ^ _221138) ^ [] : [_409095 = _409097]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_409093), _409095), _409095) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_409093), _409097), _409097))]]], (12249 ^ _221138) ^ [_645295] : [class_Rings_Ocomm__semiring__0(_645295), -(class_Rings_Omult__zero(tc_Polynomial_Opoly(_645295)))], (10584 ^ _221138) ^ [_587797, _587799, _587801] : [class_Groups_Oordered__ab__group__add(_587797), 10587 ^ _221138 : [(10594 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_587797, c_Groups_Ominus__class_Ominus(_587797, _587799, _587801), c_Groups_Ozero__class_Ozero(_587797)), -(c_Orderings_Oord__class_Oless__eq(_587797, _587799, _587801))], (10588 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_587797, _587799, _587801), -(c_Orderings_Oord__class_Oless__eq(_587797, c_Groups_Ominus__class_Ominus(_587797, _587799, _587801), c_Groups_Ozero__class_Ozero(_587797)))]]], (12135 ^ _221138) ^ [_641685] : [class_Rings_Olinordered__idom(_641685), -(class_Rings_Oordered__semiring(tc_Polynomial_Opoly(_641685)))], (4640 ^ _221138) ^ [_376524, _376526, _376528, _376530] : [class_Rings_Ocomm__semiring__1(_376524), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_376524), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_376524), _376526), _376528)), _376530) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_376524), _376526), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_376524), _376528), _376530)))], (644 ^ _221138) ^ [_240496, _240498] : [-(class_Rings_Ocomm__ring__1(_240496)), _240498 = _240496, class_Rings_Ocomm__ring__1(_240498)], (34 ^ _221138) ^ [_222330, _222332] : [-(class_Lattices_Oab__semigroup__idem__mult(_222330)), _222332 = _222330, class_Lattices_Oab__semigroup__idem__mult(_222332)], (2808 ^ _221138) ^ [_314430, _314432, _314434, _314436] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_314430), 2811 ^ _221138 : [(2818 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_314430, _314434, _314436), -(c_Orderings_Oord__class_Oless(_314430, c_Groups_Oplus__class_Oplus(_314430, _314432, _314434), c_Groups_Oplus__class_Oplus(_314430, _314432, _314436)))], (2812 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_314430, c_Groups_Oplus__class_Oplus(_314430, _314432, _314434), c_Groups_Oplus__class_Oplus(_314430, _314432, _314436)), -(c_Orderings_Oord__class_Oless(_314430, _314434, _314436))]]], (3344 ^ _221138) ^ [_332893, _332895, _332897, _332899] : [class_Groups_Oordered__comm__monoid__add(_332893), c_Orderings_Oord__class_Oless__eq(_332893, c_Groups_Ozero__class_Ozero(_332893), _332895), c_Orderings_Oord__class_Oless__eq(_332893, _332897, _332899), -(c_Orderings_Oord__class_Oless__eq(_332893, _332897, c_Groups_Oplus__class_Oplus(_332893, _332899, _332895)))], (12057 ^ _221138) ^ [_639215] : [class_Rings_Oidom(_639215), -(class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(_639215)))], (5143 ^ _221138) ^ [_396657, _396659] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _396657, _396659), _396657 = _396659], (1786 ^ _221138) ^ [_278801, _278803] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _278801, _278803)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _278803, _278801))], (5395 ^ _221138) ^ [_405108, _405110, _405112] : [class_Groups_Oordered__ab__group__add(_405108), 5398 ^ _221138 : [(5405 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_405108, c_Groups_Ouminus__class_Ouminus(_405108, _405112), _405110), -(c_Orderings_Oord__class_Oless__eq(_405108, c_Groups_Ouminus__class_Ouminus(_405108, _405110), _405112))], (5399 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_405108, c_Groups_Ouminus__class_Ouminus(_405108, _405110), _405112), -(c_Orderings_Oord__class_Oless__eq(_405108, c_Groups_Ouminus__class_Ouminus(_405108, _405112), _405110))]]], (4396 ^ _221138) ^ [_367445, _367447] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _367445), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _367447), -(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), _367445), _367447)))], (5693 ^ _221138) ^ [_415501, _415503] : [class_Rings_Olinordered__idom(_415501), 5696 ^ _221138 : [(5703 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_415501, _415503, c_Groups_Ozero__class_Ozero(_415501)), -(c_Orderings_Oord__class_Oless(_415501, _415503, c_Groups_Ouminus__class_Ouminus(_415501, _415503)))], (5697 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_415501, _415503, c_Groups_Ouminus__class_Ouminus(_415501, _415503)), -(c_Orderings_Oord__class_Oless(_415501, _415503, c_Groups_Ozero__class_Ozero(_415501)))]]], (8053 ^ _221138) ^ [_497259, _497261] : [8054 ^ _221138 : [(8057 ^ _221138) ^ [] : [_497261 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (8055 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _497259)]], -(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), _497259), _497261)))], (7541 ^ _221138) ^ [_481028, _481030] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _481028, _481030), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _481030), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _481028, _481030))], (4702 ^ _221138) ^ [_379730, _379732, _379734, _379736, _379738] : [class_Rings_Ocomm__semiring__1(_379730), -(c_Groups_Oplus__class_Oplus(_379730, c_Groups_Oplus__class_Oplus(_379730, _379732, _379734), c_Groups_Oplus__class_Oplus(_379730, _379736, _379738)) = c_Groups_Oplus__class_Oplus(_379730, c_Groups_Oplus__class_Oplus(_379730, _379732, _379736), c_Groups_Oplus__class_Oplus(_379730, _379734, _379738)))], (4576 ^ _221138) ^ [_374036, _374038] : [class_Groups_Ocomm__monoid__add(_374036), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_374036), _374038, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_374036))) = _374038)], (7021 ^ _221138) ^ [_462257] : [-(_462257 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 7024 ^ _221138 : [(7031 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _462257)), -(c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, _462257) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (7025 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _462257), -(c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, _462257) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))]]], (10930 ^ _221138) ^ [_601581, _601583, _601585] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _601581), c_Groups_Ominus__class_Ominus(tc_Int_Oint, _601583, _601585)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _601581), _601583), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _601581), _601585)))], (4512 ^ _221138) ^ [_371540, _371542, _371544] : [class_Rings_Olinordered__ring__strict(_371540), 4515 ^ _221138 : [(4524 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_371540, c_Groups_Oplus__class_Oplus(_371540, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_371540), _371542), _371542), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_371540), _371544), _371544)), c_Groups_Ozero__class_Ozero(_371540))), _371542 = c_Groups_Ozero__class_Ozero(_371540), _371544 = c_Groups_Ozero__class_Ozero(_371540)], (4516 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_371540, c_Groups_Oplus__class_Oplus(_371540, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_371540), _371542), _371542), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_371540), _371544), _371544)), c_Groups_Ozero__class_Ozero(_371540)), 4519 ^ _221138 : [(4522 ^ _221138) ^ [] : [-(_371544 = c_Groups_Ozero__class_Ozero(_371540))], (4520 ^ _221138) ^ [] : [-(_371542 = c_Groups_Ozero__class_Ozero(_371540))]]]]], (11811 ^ _221138) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal))], (9400 ^ _221138) ^ [_544517, _544519] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _544517, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _544517, _544519))))], (574 ^ _221138) ^ [_238431, _238433] : [-(class_Rings_Ocomm__semiring__0(_238431)), _238433 = _238431, class_Rings_Ocomm__semiring__0(_238433)], (6127 ^ _221138) ^ [_430130] : [-(_430130 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _430130))], (5531 ^ _221138) ^ [_409802, _409804, _409806] : [class_Rings_Oring(_409802), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_409802), c_Groups_Ouminus__class_Ouminus(_409802, _409804)), c_Groups_Ouminus__class_Ouminus(_409802, _409806)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_409802), _409804), _409806))], (1648 ^ _221138) ^ [_274567, _274569, _274571] : [class_Orderings_Opreorder(_274567), c_Orderings_Oord__class_Oless(_274567, _274569, _274571), c_Orderings_Oord__class_Oless(_274567, _274571, _274569)], (4422 ^ _221138) ^ [_368361, _368363, _368365] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _368361), 4425 ^ _221138 : [(4432 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _368363, _368365), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _368363), _368361), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _368365), _368361)))], (4426 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _368363), _368361), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _368365), _368361)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _368363, _368365))]]], (8753 ^ _221138) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (8137 ^ _221138) ^ [_500667, _500669, _500671] : [class_Rings_Olinordered__semidom(_500667), c_Orderings_Oord__class_Oless__eq(_500667, c_Groups_Ozero__class_Ozero(_500667), _500669), -(c_Orderings_Oord__class_Oless__eq(_500667, c_Groups_Ozero__class_Ozero(_500667), hAPP(hAPP(c_Power_Opower__class_Opower(_500667), _500669), _500671)))], (6479 ^ _221138) ^ [_443164, _443166, _443168] : [_443166 = _443168, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _443164, _443166) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _443164, _443168))], (10099 ^ _221138) ^ [_568987] : [-(c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat, _568987)) = _568987)], (11831 ^ _221138) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal))], (11801 ^ _221138) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal))], (8271 ^ _221138) ^ [_505301, _505303, _505305, _505307, _505309] : [class_Rings_Ocomm__semiring__1(_505301), c_Rings_Odvd__class_Odvd(_505301, hAPP(hAPP(c_Power_Opower__class_Opower(_505301), _505303), _505305), _505307), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _505309, _505305), -(c_Rings_Odvd__class_Odvd(_505301, hAPP(hAPP(c_Power_Opower__class_Opower(_505301), _505303), _505309), _505307))], (3300 ^ _221138) ^ [_331539, _331541, _331543] : [class_Groups_Oordered__comm__monoid__add(_331539), c_Orderings_Oord__class_Oless__eq(_331539, c_Groups_Ozero__class_Ozero(_331539), _331541), c_Orderings_Oord__class_Oless__eq(_331539, c_Groups_Ozero__class_Ozero(_331539), _331543), 3311 ^ _221138 : [(3320 ^ _221138) ^ [] : [-(c_Groups_Oplus__class_Oplus(_331539, _331541, _331543) = c_Groups_Ozero__class_Ozero(_331539)), _331541 = c_Groups_Ozero__class_Ozero(_331539), _331543 = c_Groups_Ozero__class_Ozero(_331539)], (3312 ^ _221138) ^ [] : [c_Groups_Oplus__class_Oplus(_331539, _331541, _331543) = c_Groups_Ozero__class_Ozero(_331539), 3315 ^ _221138 : [(3318 ^ _221138) ^ [] : [-(_331543 = c_Groups_Ozero__class_Ozero(_331539))], (3316 ^ _221138) ^ [] : [-(_331541 = c_Groups_Ozero__class_Ozero(_331539))]]]]], (11663 ^ _221138) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (2868 ^ _221138) ^ [_316565, _316567, _316569, _316571] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_316565), c_Orderings_Oord__class_Oless(_316565, c_Groups_Oplus__class_Oplus(_316565, _316567, _316569), c_Groups_Oplus__class_Oplus(_316565, _316567, _316571)), -(c_Orderings_Oord__class_Oless(_316565, _316569, _316571))], (8971 ^ _221138) ^ [_529626] : [c_Nat_OSuc(_529626) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (11351 ^ _221138) ^ [_617350, _617352] : [-(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _617350, _617352) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _617350, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _617352)))], (10702 ^ _221138) ^ [_592957, _592959, _592961] : [class_RealVector_Oreal__normed__vector(_592957), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_592957, _592959), c_RealVector_Onorm__class_Onorm(_592957, _592961)), c_RealVector_Onorm__class_Onorm(_592957, c_Groups_Ominus__class_Ominus(_592957, _592959, _592961))))], (8901 ^ _221138) ^ [_526799, _526801, _526803] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _526799, _526801), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _526799, _526803), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _526801, _526803)))], (4979 ^ _221138) ^ [_390403, _390405, _390407] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _390405, _390407), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _390403, _390405), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _390403, _390407)))], (4720 ^ _221138) ^ [_380482, _380484, _380486] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_380482), 4723 ^ _221138 : [(4730 ^ _221138) ^ [] : [_380486 = c_Groups_Ozero__class_Ozero(_380482), -(_380484 = c_Groups_Oplus__class_Oplus(_380482, _380484, _380486))], (4724 ^ _221138) ^ [] : [_380484 = c_Groups_Oplus__class_Oplus(_380482, _380484, _380486), -(_380486 = c_Groups_Ozero__class_Ozero(_380482))]]], (7259 ^ _221138) ^ [_470378, _470380, _470382, _470384] : [class_Rings_Odvd(_470378), _470380 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_470378), _470382), _470384), -(c_Rings_Odvd__class_Odvd(_470378, _470382, _470380))], (8673 ^ _221138) ^ [_519253, _519255] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _519253), c_Orderings_Oord__class_Oless(tc_Int_Oint, _519253, _519255), c_Rings_Odvd__class_Odvd(tc_Int_Oint, _519255, _519253)], (11825 ^ _221138) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal))], (5537 ^ _221138) ^ [_410074, _410076, _410078] : [class_Rings_Oring(_410074), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_410074), c_Groups_Ouminus__class_Ouminus(_410074, _410076)), _410078) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_410074), _410076), c_Groups_Ouminus__class_Ouminus(_410074, _410078)))], (5259 ^ _221138) ^ [_400846, _400848, _400850] : [class_Groups_Ogroup__add(_400846), 5262 ^ _221138 : [(5269 ^ _221138) ^ [] : [_400848 = _400850, -(c_Groups_Ouminus__class_Ouminus(_400846, _400848) = c_Groups_Ouminus__class_Ouminus(_400846, _400850))], (5263 ^ _221138) ^ [] : [c_Groups_Ouminus__class_Ouminus(_400846, _400848) = c_Groups_Ouminus__class_Ouminus(_400846, _400850), -(_400848 = _400850)]]], (6227 ^ _221138) ^ [_433718, _433720, _433722] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _433718), _433720), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _433722), _433720)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _433720), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _433718, _433722))], (5597 ^ _221138) ^ [_412566, _412568] : [class_Rings_Olinordered__idom(_412566), 5600 ^ _221138 : [(5607 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_412566), _412568, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_412566)))), -(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(_412566), _412568) = _412568)], (5601 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_412566), _412568, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_412566))), -(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(_412566), _412568) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_412566), _412568))]]], (11647 ^ _221138) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (4 ^ _221138) ^ [_221369, _221371] : [_221371 = _221369, -(_221369 = _221371)], (5469 ^ _221138) ^ [_407493, _407495, _407497] : [class_Groups_Oordered__ab__group__add(_407493), 5472 ^ _221138 : [(5479 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_407493, _407497, _407495), -(c_Orderings_Oord__class_Oless(_407493, c_Groups_Ouminus__class_Ouminus(_407493, _407495), c_Groups_Ouminus__class_Ouminus(_407493, _407497)))], (5473 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_407493, c_Groups_Ouminus__class_Ouminus(_407493, _407495), c_Groups_Ouminus__class_Ouminus(_407493, _407497)), -(c_Orderings_Oord__class_Oless(_407493, _407497, _407495))]]], (12267 ^ _221138) ^ [_645865] : [class_Rings_Olinordered__idom(_645865), -(class_Int_Oring__char__0(tc_Polynomial_Opoly(_645865)))], (9081 ^ _221138) ^ [_533285, _533287] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_533285), _533287), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _533285, _533287))], (2700 ^ _221138) ^ [_310586, _310588] : [class_Groups_Ocomm__monoid__add(_310586), -(c_Groups_Oplus__class_Oplus(_310586, _310588, c_Groups_Ozero__class_Ozero(_310586)) = _310588)], (1528 ^ _221138) ^ [_270723, _270725, _270727, _270729] : [class_Orderings_Opreorder(_270723), c_Orderings_Oord__class_Oless(_270723, _270725, _270727), c_Orderings_Oord__class_Oless(_270723, _270727, _270729), -(c_Orderings_Oord__class_Oless(_270723, _270725, _270729))], (10341 ^ _221138) ^ [_577880, _577882] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _577880), -(c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _577880, c_RealDef_Oreal(tc_Nat_Onat, _577882))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatfloor(_577880), _577882))], (11845 ^ _221138) ^ [] : [-(class_Rings_Oordered__semiring(tc_RealDef_Oreal))], (7715 ^ _221138) ^ [_486537, _486539, _486541] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _486537, _486539), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _486539, _486537)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _486539, _486541), 7726 ^ _221138 : [(7729 ^ _221138) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _486541, _486537)], (7727 ^ _221138) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _486537, _486541))]]], (6719 ^ _221138) ^ [_452032, _452034, _452036] : [class_Rings_Olinordered__idom(_452032), -(c_Groups_Osgn__class_Osgn(_452032, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_452032), _452034), _452036)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_452032), c_Groups_Osgn__class_Osgn(_452032, _452034)), c_Groups_Osgn__class_Osgn(_452032, _452036)))], (8929 ^ _221138) ^ [_528175, _528177] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _528175, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _528177, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _528175, _528177)), -(_528175 = _528177)], (8161 ^ _221138) ^ [_501500, _501502, _501504] : [class_Rings_Olinordered__semidom(_501500), c_Orderings_Oord__class_Oless(_501500, c_Groups_Ozero__class_Ozero(_501500), _501502), -(c_Orderings_Oord__class_Oless(_501500, c_Groups_Ozero__class_Ozero(_501500), hAPP(hAPP(c_Power_Opower__class_Opower(_501500), _501502), _501504)))], (10185 ^ _221138) ^ [_572094, _572096] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _572094, _572096), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _572094), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), c_RealDef_Oreal(tc_Nat_Onat, _572096)))], (8547 ^ _221138) ^ [_514923, _514925, _514927] : [class_Rings_Oidom(_514923), -(_514925 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_514923))), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_514923), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_514923)), c_Polynomial_OpCons(_514923, c_Groups_Ouminus__class_Ouminus(_514923, _514927), c_Polynomial_OpCons(_514923, c_Groups_Oone__class_Oone(_514923), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_514923))))), c_Nat_OSuc(c_Polynomial_Oorder(_514923, _514927, _514925))), _514925)], (414 ^ _221138) ^ [_233711, _233713] : [-(class_Rings_Oordered__ring__abs(_233711)), _233713 = _233711, class_Rings_Oordered__ring__abs(_233713)], (754 ^ _221138) ^ [_243741, _243743] : [-(class_Rings_Odvd(_243741)), _243743 = _243741, class_Rings_Odvd(_243743)], (11971 ^ _221138) ^ [] : [-(class_Rings_Osemiring(tc_Complex_Ocomplex))], (8119 ^ _221138) ^ [_499877, _499879, _499881, _499883] : [class_Groups_Omonoid__mult(_499877), -(hAPP(hAPP(c_Power_Opower__class_Opower(_499877), _499879), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _499881), _499883)) = hAPP(hAPP(c_Power_Opower__class_Opower(_499877), hAPP(hAPP(c_Power_Opower__class_Opower(_499877), _499879), _499881)), _499883))], (3752 ^ _221138) ^ [_346140, _346142, _346144] : [class_Rings_Oordered__cancel__semiring(_346140), -(c_Orderings_Oord__class_Oless__eq(_346140, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_346140), _346142), _346144), c_Groups_Ozero__class_Ozero(_346140))), 3757 ^ _221138 : [(3764 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_346140, _346142, c_Groups_Ozero__class_Ozero(_346140)), c_Orderings_Oord__class_Oless__eq(_346140, c_Groups_Ozero__class_Ozero(_346140), _346144)], (3758 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_346140, c_Groups_Ozero__class_Ozero(_346140), _346142), c_Orderings_Oord__class_Oless__eq(_346140, _346144, c_Groups_Ozero__class_Ozero(_346140))]]], (11951 ^ _221138) ^ [] : [-(class_Groups_Oab__group__add(tc_Complex_Ocomplex))], (10696 ^ _221138) ^ [_592707, _592709, _592711] : [class_Groups_Oab__group__add(_592707), -(c_Groups_Ouminus__class_Ouminus(_592707, c_Groups_Ominus__class_Ominus(_592707, _592709, _592711)) = c_Groups_Ominus__class_Ominus(_592707, _592711, _592709))], (8869 ^ _221138) ^ [_525607, _525609] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _525607, _525609), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _525607, c_Groups_Oone__class_Oone(tc_Int_Oint)), _525609))], (11459 ^ _221138) ^ [_621707, _621709, _621711] : [-(hBOOL(hAPP(_621707, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _621709, _621711)))), 11462 ^ _221138 : [(11465 ^ _221138) ^ [] : [hBOOL(hAPP(_621707, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (11463 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _621709, _621711))]], 11467 ^ _221138 : [(11470 ^ _221138) ^ [] : [hBOOL(hAPP(_621707, 11466 ^ [_621707, _621709, _621711]))], (11468 ^ _221138) ^ [] : [-(_621709 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _621711, 11466 ^ [_621707, _621709, _621711]))]]], (10079 ^ _221138) ^ [] : [-(c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (1431 ^ _221138) ^ [_267549, _267551, _267553] : [class_Orderings_Opreorder(_267549), _267551 = _267553, -(c_Orderings_Oord__class_Oless__eq(_267549, _267551, _267553))], (8325 ^ _221138) ^ [_507271, _507273] : [class_Power_Opower(_507271), class_Rings_Osemiring__0(_507271), 8332 ^ _221138 : [(8339 ^ _221138) ^ [] : [-(_507273 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_507271), c_Groups_Ozero__class_Ozero(_507271)), _507273) = c_Groups_Ozero__class_Ozero(_507271))], (8333 ^ _221138) ^ [] : [_507273 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_507271), c_Groups_Ozero__class_Ozero(_507271)), _507273) = c_Groups_Oone__class_Oone(_507271))]]], (11791 ^ _221138) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal))], (1279 ^ _221138) ^ [_262693, _262695, _262697, _262699, _262701] : [class_Orderings_Oord(_262693), c_Orderings_Oord__class_Oless__eq(tc_fun(_262695, _262693), _262697, _262699), -(c_Orderings_Oord__class_Oless__eq(_262693, hAPP(_262697, _262701), hAPP(_262699, _262701)))], (1373 ^ _221138) ^ [_265694, _265696, _265698, _265700] : [class_Orderings_Oorder(_265694), _265696 = _265698, c_Orderings_Oord__class_Oless__eq(_265694, _265700, _265698), -(c_Orderings_Oord__class_Oless__eq(_265694, _265700, _265696))], (1906 ^ _221138) ^ [_282669, _282671, _282673] : [class_Orderings_Oorder(_282669), c_Orderings_Oord__class_Oless__eq(_282669, _282671, _282673), -(_282671 = _282673), -(c_Orderings_Oord__class_Oless(_282669, _282671, _282673))], (5763 ^ _221138) ^ [_417685, _417687] : [class_Groups_Ogroup__add(_417685), -(c_Groups_Oplus__class_Oplus(_417685, c_Groups_Ouminus__class_Ouminus(_417685, _417687), _417687) = c_Groups_Ozero__class_Ozero(_417685))], (4945 ^ _221138) ^ [_389289, _389291] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _389289, _389291)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _389289, _389291), -(_389289 = _389291)], (11855 ^ _221138) ^ [] : [-(class_Rings_Olinordered__idom(tc_RealDef_Oreal))], (9367 ^ _221138) ^ [_543353, _543355] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _543353), _543355) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 9370 ^ _221138 : [(9373 ^ _221138) ^ [] : [-(_543355 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (9371 ^ _221138) ^ [] : [-(_543353 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (7887 ^ _221138) ^ [_491866, _491868, _491870] : [_491866 = _491868, c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _491868, _491870), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _491866, _491870))], (10544 ^ _221138) ^ [_586213, _586215, _586217, _586219, _586221] : [class_Groups_Oordered__ab__group__add__abs(_586213), -(c_Orderings_Oord__class_Oless__eq(_586213, c_Groups_Oabs__class_Oabs(_586213, c_Groups_Ominus__class_Ominus(_586213, c_Groups_Oplus__class_Oplus(_586213, _586215, _586217), c_Groups_Oplus__class_Oplus(_586213, _586219, _586221))), c_Groups_Oplus__class_Oplus(_586213, c_Groups_Oabs__class_Oabs(_586213, c_Groups_Ominus__class_Ominus(_586213, _586215, _586219)), c_Groups_Oabs__class_Oabs(_586213, c_Groups_Ominus__class_Ominus(_586213, _586217, _586221)))))], (10012 ^ _221138) ^ [_565713] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _565713), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), c_RComplete_Onatfloor(_565713)))], (7857 ^ _221138) ^ [_490919, _490921] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _490919, _490921), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _490921, _490919), -(_490919 = _490921)], (11715 ^ _221138) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (6181 ^ _221138) ^ [_432016, _432018, _432020] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _432016), _432018), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _432016), _432020))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _432016), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _432018, _432020)], (11977 ^ _221138) ^ [] : [-(class_Groups_Ominus(tc_Complex_Ocomplex))], (4564 ^ _221138) ^ [_373504, _373506, _373508, _373510] : [class_Rings_Ocomm__semiring__0(_373504), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_373504)), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_373504), _373506, _373508)), _373510) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_373504), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_373504)), _373506), _373510), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_373504)), _373508), _373510)))], (10650 ^ _221138) ^ [_590699, _590701, _590703] : [class_Groups_Ogroup__add(_590699), -(c_Groups_Ominus__class_Ominus(_590699, _590701, c_Groups_Ouminus__class_Ouminus(_590699, _590703)) = c_Groups_Oplus__class_Oplus(_590699, _590701, _590703))], (12225 ^ _221138) ^ [_644535] : [class_Rings_Ocomm__ring__1(_644535), -(class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(_644535)))], (5149 ^ _221138) ^ [_396870, _396872] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _396870, _396872), _396872 = _396870], (12003 ^ _221138) ^ [_637505] : [class_Rings_Olinordered__idom(_637505), -(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(_637505)))], (5309 ^ _221138) ^ [_402462] : [class_Groups_Ogroup__add(_402462), -(c_Groups_Ouminus__class_Ouminus(_402462, c_Groups_Ozero__class_Ozero(_402462)) = c_Groups_Ozero__class_Ozero(_402462))], (2678 ^ _221138) ^ [_309884, _309886] : [class_Groups_Olinordered__ab__group__add(_309884), 2681 ^ _221138 : [(2688 ^ _221138) ^ [] : [_309886 = c_Groups_Ozero__class_Ozero(_309884), -(c_Groups_Ozero__class_Ozero(_309884) = c_Groups_Oplus__class_Oplus(_309884, _309886, _309886))], (2682 ^ _221138) ^ [] : [c_Groups_Ozero__class_Ozero(_309884) = c_Groups_Oplus__class_Oplus(_309884, _309886, _309886), -(_309886 = c_Groups_Ozero__class_Ozero(_309884))]]], (8091 ^ _221138) ^ [_498630, _498632, _498634] : [class_Groups_Omonoid__mult(_498630), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_498630), hAPP(hAPP(c_Power_Opower__class_Opower(_498630), _498632), _498634)), _498632) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_498630), _498632), hAPP(hAPP(c_Power_Opower__class_Opower(_498630), _498632), _498634)))], (6669 ^ _221138) ^ [_450252, _450254] : [class_Rings_Olinordered__idom(_450252), 6672 ^ _221138 : [(6679 ^ _221138) ^ [] : [-(_450254 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_450252))), 6682 ^ _221138 : [(6689 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_450252), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_450252)), _450254)), -(c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(_450252), _450254) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_450252), c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_450252))))], (6683 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_450252), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_450252)), _450254), -(c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(_450252), _450254) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_450252)))]]], (6673 ^ _221138) ^ [] : [_450254 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_450252)), -(c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(_450252), _450254) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_450252)))]]], (1331 ^ _221138) ^ [_264370, _264372, _264374] : [class_Orderings_Oorder(_264370), c_Orderings_Oord__class_Oless__eq(_264370, _264372, _264374), c_Orderings_Oord__class_Oless__eq(_264370, _264374, _264372), -(_264372 = _264374)], (2632 ^ _221138) ^ [_308101, _308103] : [class_Groups_Oordered__ab__group__add__abs(_308101), -(c_Orderings_Oord__class_Oless__eq(_308101, _308103, c_Groups_Oabs__class_Oabs(_308101, _308103)))], (3068 ^ _221138) ^ [_323492, _323494, _323496] : [class_RealVector_Oreal__normed__vector(_323492), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_323492, c_Groups_Oplus__class_Oplus(_323492, _323494, _323496)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_323492, _323494), c_RealVector_Onorm__class_Onorm(_323492, _323496))))], (9252 ^ _221138) ^ [_539598, _539600] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _539598, c_Nat_OSuc(_539600))), 9253 ^ _221138 : [(9256 ^ _221138) ^ [_539767] : [_539598 = c_Nat_OSuc(_539767), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _539767, _539600)], (9254 ^ _221138) ^ [] : [_539598 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (2638 ^ _221138) ^ [_308331, _308333, _308335] : [class_Groups_Oordered__ab__group__add__abs(_308331), c_Orderings_Oord__class_Oless__eq(_308331, c_Groups_Oabs__class_Oabs(_308331, _308333), _308335), -(c_Orderings_Oord__class_Oless__eq(_308331, _308333, _308335))], (11329 ^ _221138) ^ [_616483, _616485, _616487] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _616483, _616485), _616487), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _616483, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _616487, _616485)))], (7303 ^ _221138) ^ [_471965, _471967, _471969] : [class_Rings_Ocomm__semiring__1(_471965), -(c_Rings_Odvd__class_Odvd(_471965, _471967, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_471965), _471969), _471967)))], (3922 ^ _221138) ^ [_351673, _351675, _351677] : [class_Rings_Olinordered__semiring__strict(_351673), c_Orderings_Oord__class_Oless(_351673, c_Groups_Ozero__class_Ozero(_351673), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_351673), _351675), _351677)), c_Orderings_Oord__class_Oless(_351673, c_Groups_Ozero__class_Ozero(_351673), _351677), -(c_Orderings_Oord__class_Oless(_351673, c_Groups_Ozero__class_Ozero(_351673), _351675))], (4937 ^ _221138) ^ [_389047, _389049] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _389047, _389049), 4940 ^ _221138 : [(4943 ^ _221138) ^ [] : [_389047 = _389049], (4941 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _389047, _389049))]]], (584 ^ _221138) ^ [_238726, _238728] : [-(class_Rings_Osemiring(_238726)), _238728 = _238726, class_Rings_Osemiring(_238728)], (11941 ^ _221138) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex))], (6753 ^ _221138) ^ [_453179, _453181] : [class_RealVector_Oreal__normed__vector(_453179), 6756 ^ _221138 : [(6763 ^ _221138) ^ [] : [_453181 = c_Groups_Ozero__class_Ozero(_453179), -(c_Groups_Osgn__class_Osgn(_453179, _453181) = c_Groups_Ozero__class_Ozero(_453179))], (6757 ^ _221138) ^ [] : [c_Groups_Osgn__class_Osgn(_453179, _453181) = c_Groups_Ozero__class_Ozero(_453179), -(_453181 = c_Groups_Ozero__class_Ozero(_453179))]]], (11141 ^ _221138) ^ [_609719, _609721] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _609719), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _609721), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _609721, _609719), _609721))], (4092 ^ _221138) ^ [_357346, _357348, _357350] : [class_Groups_Oordered__comm__monoid__add(_357346), c_Orderings_Oord__class_Oless__eq(_357346, c_Groups_Ozero__class_Ozero(_357346), _357348), c_Orderings_Oord__class_Oless(_357346, c_Groups_Ozero__class_Ozero(_357346), _357350), -(c_Orderings_Oord__class_Oless(_357346, c_Groups_Ozero__class_Ozero(_357346), c_Groups_Oplus__class_Oplus(_357346, _357348, _357350)))], (7701 ^ _221138) ^ [_486118, _486120] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _486118, _486120), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _486120, _486118)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _486120, _486118), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _486118, _486120))], (3908 ^ _221138) ^ [_351225, _351227, _351229] : [class_Rings_Olinordered__semiring__strict(_351225), c_Orderings_Oord__class_Oless(_351225, c_Groups_Ozero__class_Ozero(_351225), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_351225), _351227), _351229)), c_Orderings_Oord__class_Oless(_351225, c_Groups_Ozero__class_Ozero(_351225), _351227), -(c_Orderings_Oord__class_Oless(_351225, c_Groups_Ozero__class_Ozero(_351225), _351229))], (10087 ^ _221138) ^ [_568618, _568620] : [c_RealDef_Oreal(tc_Nat_Onat, _568618) = c_RealDef_Oreal(tc_Nat_Onat, _568620), -(_568618 = _568620)], (1231 ^ _221138) ^ [_261184, _261186] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _261184, _261186), 1234 ^ _221138 : [(1237 ^ _221138) ^ [] : [_261184 = _261186], (1235 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _261184, _261186))]]], (4810 ^ _221138) ^ [_384044, _384046] : [class_Rings_Ocomm__semiring__1(_384044), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_384044), c_Groups_Oone__class_Oone(_384044)), _384046) = _384046)], (5295 ^ _221138) ^ [_401970, _401972] : [_401970 = _401972, -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _401970, _401972))], (10886 ^ _221138) ^ [_600130, _600132] : [class_Groups_Ogroup__add(_600130), -(c_Groups_Ominus__class_Ominus(_600130, _600132, c_Groups_Ozero__class_Ozero(_600130)) = _600132)], (2568 ^ _221138) ^ [_305875, _305877, _305879] : [class_Rings_Olinordered__idom(_305875), -(c_Groups_Oabs__class_Oabs(_305875, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_305875), _305877), _305879)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_305875), c_Groups_Oabs__class_Oabs(_305875, _305877)), c_Groups_Oabs__class_Oabs(_305875, _305879)))], (8921 ^ _221138) ^ [_527663, _527665, _527667] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _527663), _527665)), _527667) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _527663), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _527665), _527667)))], (264 ^ _221138) ^ [_229286, _229288] : [-(class_Rings_Oring__1__no__zero__divisors(_229286)), _229288 = _229286, class_Rings_Oring__1__no__zero__divisors(_229288)], (6515 ^ _221138) ^ [_444738, _444740] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _444738, _444740) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _444740, _444738))], (11425 ^ _221138) ^ [_620453, _620455, _620457] : [class_RealVector_Oreal__normed__vector(_620453), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_620453, _620455), c_RealVector_Onorm__class_Onorm(_620453, _620457)), c_RealVector_Onorm__class_Onorm(_620453, c_Groups_Oplus__class_Oplus(_620453, _620455, _620457))))], (5063 ^ _221138) ^ [_393655, _393657, _393659] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _393655, _393657), _393659), 5066 ^ _221138 : [(5069 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _393657, _393659))], (5067 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _393655, _393659))]]], (11405 ^ _221138) ^ [_619560, _619562, _619564] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _619560, _619562)), _619564) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _619560), _619564), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _619562), _619564)))], (6341 ^ _221138) ^ [_437676, _437678] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _437676, _437678) = _437676, -(_437678 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4182 ^ _221138) ^ [_360275, _360277, _360279, _360281] : [class_Rings_Olinordered__ring__strict(_360275), c_Orderings_Oord__class_Oless(_360275, _360277, c_Groups_Ozero__class_Ozero(_360275)), 4189 ^ _221138 : [(4196 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_360275, _360281, _360279), -(c_Orderings_Oord__class_Oless__eq(_360275, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_360275), _360277), _360279), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_360275), _360277), _360281)))], (4190 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_360275, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_360275), _360277), _360279), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_360275), _360277), _360281)), -(c_Orderings_Oord__class_Oless__eq(_360275, _360281, _360279))]]], (11365 ^ _221138) ^ [_618049, _618051] : [class_Groups_Oab__group__add(_618049), -(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_618049), _618051, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_618049))) = _618051)], (5137 ^ _221138) ^ [_396429, _396431, _396433] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _396429, _396431), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _396429, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _396431, _396433)))], (5243 ^ _221138) ^ [_400340, _400342, _400344] : [class_Groups_Ogroup__add(_400340), 5246 ^ _221138 : [(5253 ^ _221138) ^ [] : [c_Groups_Ouminus__class_Ouminus(_400340, _400344) = _400342, -(c_Groups_Ouminus__class_Ouminus(_400340, _400342) = _400344)], (5247 ^ _221138) ^ [] : [c_Groups_Ouminus__class_Ouminus(_400340, _400342) = _400344, -(c_Groups_Ouminus__class_Ouminus(_400340, _400344) = _400342)]]], (9215 ^ _221138) ^ [_538051, _538053, _538055] : [class_Rings_Ocomm__semiring__1(_538051), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_538051), _538053), hAPP(hAPP(c_Power_Opower__class_Opower(_538051), _538053), _538055)) = hAPP(hAPP(c_Power_Opower__class_Opower(_538051), _538053), c_Nat_OSuc(_538055)))], (4360 ^ _221138) ^ [_366258, _366260, _366262, _366264] : [class_Rings_Olinordered__semiring__strict(_366258), c_Orderings_Oord__class_Oless__eq(_366258, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_366258), _366260), _366262), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_366258), _366260), _366264)), c_Orderings_Oord__class_Oless(_366258, c_Groups_Ozero__class_Ozero(_366258), _366260), -(c_Orderings_Oord__class_Oless__eq(_366258, _366262, _366264))], (11623 ^ _221138) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (11571 ^ _221138) ^ [_625903, _625905] : [class_Groups_Ouminus(_625903), -(class_Groups_Ouminus(tc_fun(_625905, _625903)))], (11591 ^ _221138) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (8939 ^ _221138) ^ [_528439, _528441] : [8940 ^ _221138 : [(8943 ^ _221138) ^ [] : [_528439 = _528441], (8941 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _528439, _528441)]], -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _528439, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _528441, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (4816 ^ _221138) ^ [_384272, _384274] : [class_Rings_Ocomm__semiring__1(_384272), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_384272), _384274), c_Groups_Oone__class_Oone(_384272)) = _384274)], (8473 ^ _221138) ^ [_512336, _512338, _512340, _512342] : [class_Rings_Olinordered__semidom(_512336), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _512338, _512340), c_Orderings_Oord__class_Oless__eq(_512336, c_Groups_Ozero__class_Ozero(_512336), _512342), c_Orderings_Oord__class_Oless__eq(_512336, _512342, c_Groups_Oone__class_Oone(_512336)), -(c_Orderings_Oord__class_Oless__eq(_512336, hAPP(hAPP(c_Power_Opower__class_Opower(_512336), _512342), _512340), hAPP(hAPP(c_Power_Opower__class_Opower(_512336), _512342), _512338)))], (2432 ^ _221138) ^ [_300679, _300681, _300683, _300685, _300687] : [class_Rings_Olinordered__idom(_300679), c_Orderings_Oord__class_Oless(_300679, c_Groups_Oabs__class_Oabs(_300679, _300681), _300683), c_Orderings_Oord__class_Oless(_300679, c_Groups_Oabs__class_Oabs(_300679, _300685), _300687), -(c_Orderings_Oord__class_Oless(_300679, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_300679), c_Groups_Oabs__class_Oabs(_300679, _300681)), c_Groups_Oabs__class_Oabs(_300679, _300685)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_300679), _300683), _300687)))], (6485 ^ _221138) ^ [_443397, _443399, _443401] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _443397, _443399)), _443401) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _443397), _443401), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _443399), _443401)))], (764 ^ _221138) ^ [_244036, _244038] : [-(hBOOL(_244036)), _244038 = _244036, hBOOL(_244038)], (4304 ^ _221138) ^ [_364322, _364324, _364326, _364328] : [class_Rings_Olinordered__semiring__strict(_364322), c_Orderings_Oord__class_Oless(_364322, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_364322), _364324), _364326), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_364322), _364328), _364326)), c_Orderings_Oord__class_Oless__eq(_364322, c_Groups_Ozero__class_Ozero(_364322), _364326), -(c_Orderings_Oord__class_Oless(_364322, _364324, _364328))], (1359 ^ _221138) ^ [_265248, _265250, _265252, _265254] : [class_Orderings_Oord(_265248), c_Orderings_Oord__class_Oless__eq(_265248, _265250, _265252), _265252 = _265254, -(c_Orderings_Oord__class_Oless__eq(_265248, _265250, _265254))], (9780 ^ _221138) ^ [_557586, _557588] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _557586, _557588) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _557588, _557586))], (5775 ^ _221138) ^ [_418151, _418153, _418155] : [class_Groups_Ogroup__add(_418151), c_Groups_Oplus__class_Oplus(_418151, _418153, _418155) = c_Groups_Ozero__class_Ozero(_418151), -(c_Groups_Ouminus__class_Ouminus(_418151, _418153) = _418155)], (10932 ^ _221138) ^ [_601717, _601719, _601721] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Ominus__class_Ominus(tc_Int_Oint, _601717, _601719)), _601721) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _601717), _601721), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _601719), _601721)))], (11945 ^ _221138) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex))], (11705 ^ _221138) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (11599 ^ _221138) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (9804 ^ _221138) ^ [_558657, _558659] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _558657, _558659), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _558657), _558659))], (1303 ^ _221138) ^ [_263504, _263506, _263508] : [class_Orderings_Oorder(_263504), c_Orderings_Oord__class_Oless__eq(_263504, _263506, _263508), c_Orderings_Oord__class_Oless__eq(_263504, _263508, _263506), -(_263508 = _263506)], (6653 ^ _221138) ^ [_449754, _449756, _449758] : [class_Lattices_Oboolean__algebra(_449754), 6656 ^ _221138 : [(6663 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_449754, _449758, _449756), -(c_Orderings_Oord__class_Oless__eq(_449754, c_Groups_Ouminus__class_Ouminus(_449754, _449756), c_Groups_Ouminus__class_Ouminus(_449754, _449758)))], (6657 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_449754, c_Groups_Ouminus__class_Ouminus(_449754, _449756), c_Groups_Ouminus__class_Ouminus(_449754, _449758)), -(c_Orderings_Oord__class_Oless__eq(_449754, _449758, _449756))]]], (6209 ^ _221138) ^ [_433059, _433061, _433063] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _433059), _433061), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _433059), _433063)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _433059), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _433061, _433063))], (10069 ^ _221138) ^ [_567774, _567776] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _567774, _567776), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _567774), c_RealDef_Oreal(tc_Nat_Onat, _567776)))], (8731 ^ _221138) ^ [_521152] : [_521152 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _521152) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (12093 ^ _221138) ^ [_640355] : [class_Rings_Olinordered__idom(_640355), -(class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(_640355)))], (664 ^ _221138) ^ [_241086, _241088] : [-(class_Groups_Oab__group__add(_241086)), _241088 = _241086, class_Groups_Oab__group__add(_241088)], (9748 ^ _221138) ^ [_556465, _556467] : [-(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _556465, _556467)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _556465), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _556467)))], (12033 ^ _221138) ^ [_638455] : [class_Rings_Olinordered__idom(_638455), -(class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(_638455)))], (922 ^ _221138) ^ [_250216, _250218, _250220, _250222] : [-(c_Groups_Oabs__class_Oabs(_250222, _250218) = c_Groups_Oabs__class_Oabs(_250220, _250216)), _250222 = _250220, _250218 = _250216], (11997 ^ _221138) ^ [_637315] : [class_Rings_Olinordered__idom(_637315), -(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(_637315)))], (1514 ^ _221138) ^ [_270275, _270277, _270279, _270281] : [class_Orderings_Oorder(_270275), c_Orderings_Oord__class_Oless(_270275, _270277, _270279), c_Orderings_Oord__class_Oless(_270275, _270281, _270277), -(c_Orderings_Oord__class_Oless(_270275, _270281, _270279))], (9702 ^ _221138) ^ [_555026, _555028] : [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), _555026), _555028)), -(_555028 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _555026))], (11589 ^ _221138) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (10243 ^ _221138) ^ [_574125, _574127] : [class_RealVector_Oreal__normed__vector(_574125), 10246 ^ _221138 : [(10254 ^ _221138) ^ [] : [10256 ^ _221138 : [(10257 ^ _221138) ^ [_574610] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_574125, hAPP(_574127, 10255 ^ [_574125, _574127, _574610])), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(_574610)))]], -(c_SEQ_OBseq(_574125, _574127))], (10247 ^ _221138) ^ [] : [c_SEQ_OBseq(_574125, _574127), 10251 ^ _221138 : [(10252 ^ _221138) ^ [_574432] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_574125, hAPP(_574127, _574432)), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(10250 ^ [_574125, _574127]))))]]]]], (10059 ^ _221138) ^ [_567373] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _567373)))], (6115 ^ _221138) ^ [_429723] : [_429723 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _429723, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (9045 ^ _221138) ^ [_532110, _532112] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _532110, _532112), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _532110, c_Nat_OSuc(_532112)))], (11829 ^ _221138) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal))], (3632 ^ _221138) ^ [_342145, _342147, _342149, _342151] : [class_Rings_Oordered__semiring(_342145), c_Orderings_Oord__class_Oless__eq(_342145, _342147, _342149), c_Orderings_Oord__class_Oless__eq(_342145, c_Groups_Ozero__class_Ozero(_342145), _342151), -(c_Orderings_Oord__class_Oless__eq(_342145, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_342145), _342151), _342147), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_342145), _342151), _342149)))], (9450 ^ _221138) ^ [_546326, _546328] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _546326, _546328), 9453 ^ _221138 : [(9460 ^ _221138) ^ [] : [_546328 = _546326, -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _546328, c_Nat_OSuc(_546326)))], (9454 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _546328, c_Nat_OSuc(_546326)), -(_546328 = _546326)]]], (2534 ^ _221138) ^ [_304661, _304663] : [class_Groups_Oone(_304661), 2537 ^ _221138 : [(2544 ^ _221138) ^ [] : [_304663 = c_Groups_Oone__class_Oone(_304661), -(c_Groups_Oone__class_Oone(_304661) = _304663)], (2538 ^ _221138) ^ [] : [c_Groups_Oone__class_Oone(_304661) = _304663, -(_304663 = c_Groups_Oone__class_Oone(_304661))]]], (10474 ^ _221138) ^ [_583311, _583313, _583315, _583317, _583319, _583321] : [class_Rings_Oordered__ring(_583311), 10477 ^ _221138 : [(10484 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_583311, c_Groups_Oplus__class_Oplus(_583311, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_583311), c_Groups_Ominus__class_Ominus(_583311, _583313, _583319)), _583315), _583317), _583321), -(c_Orderings_Oord__class_Oless(_583311, c_Groups_Oplus__class_Oplus(_583311, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_583311), _583313), _583315), _583317), c_Groups_Oplus__class_Oplus(_583311, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_583311), _583319), _583315), _583321)))], (10478 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_583311, c_Groups_Oplus__class_Oplus(_583311, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_583311), _583313), _583315), _583317), c_Groups_Oplus__class_Oplus(_583311, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_583311), _583319), _583315), _583321)), -(c_Orderings_Oord__class_Oless(_583311, c_Groups_Oplus__class_Oplus(_583311, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_583311), c_Groups_Ominus__class_Ominus(_583311, _583313, _583319)), _583315), _583317), _583321))]]], (6487 ^ _221138) ^ [_443533, _443535, _443537] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _443533), _443535)), _443537) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _443533), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _443535), _443537)))], (2654 ^ _221138) ^ [_308908] : [class_RealVector_Oreal__normed__algebra__1(_308908), -(c_RealVector_Onorm__class_Onorm(_308908, c_Groups_Oone__class_Oone(_308908)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (2202 ^ _221138) ^ [_291770, _291772, _291774] : [class_Rings_Oidom(_291770), 2205 ^ _221138 : [(2206 ^ _221138) ^ [] : [hAPP(c_Polynomial_Opoly(_291770, _291772), _291774) = c_Groups_Ozero__class_Ozero(_291770), -(_291772 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_291770))), c_Polynomial_Oorder(_291770, _291774, _291772) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (2216 ^ _221138) ^ [] : [2217 ^ _221138 : [(2220 ^ _221138) ^ [] : [-(c_Polynomial_Oorder(_291770, _291774, _291772) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2218 ^ _221138) ^ [] : [_291772 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_291770))]], -(hAPP(c_Polynomial_Opoly(_291770, _291772), _291774) = c_Groups_Ozero__class_Ozero(_291770))]]], (10694 ^ _221138) ^ [_592573, _592575] : [-(c_Groups_Ominus__class_Ominus(tc_Int_Oint, _592573, _592575) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _592573, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _592575)))], (8559 ^ _221138) ^ [_515395, _515397] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _515395, _515397), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_515395), c_Nat_OSuc(_515397)))], (5131 ^ _221138) ^ [_396187, _396189, _396191] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _396187, _396189), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _396187, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _396191, _396189)))], (11949 ^ _221138) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Complex_Ocomplex))], (7009 ^ _221138) ^ [_461877] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _461877), -(c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, _461877) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (7093 ^ _221138) ^ [_464866, _464868, _464870] : [class_Rings_Oidom(_464866), 7096 ^ _221138 : [(7103 ^ _221138) ^ [] : [hAPP(c_Polynomial_Opoly(_464866, _464870), c_Groups_Ouminus__class_Ouminus(_464866, _464868)) = c_Groups_Ozero__class_Ozero(_464866), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_464866), c_Polynomial_OpCons(_464866, _464868, c_Polynomial_OpCons(_464866, c_Groups_Oone__class_Oone(_464866), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_464866)))), _464870))], (7097 ^ _221138) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_464866), c_Polynomial_OpCons(_464866, _464868, c_Polynomial_OpCons(_464866, c_Groups_Oone__class_Oone(_464866), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_464866)))), _464870), -(hAPP(c_Polynomial_Opoly(_464866, _464870), c_Groups_Ouminus__class_Ouminus(_464866, _464868)) = c_Groups_Ozero__class_Ozero(_464866))]]], (11155 ^ _221138) ^ [_610264, _610266] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _610264, _610266) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _610264, _610266))], (164 ^ _221138) ^ [_226336, _226338] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_226336)), _226338 = _226336, class_Groups_Oordered__cancel__ab__semigroup__add(_226338)], (2412 ^ _221138) ^ [_299943, _299945, _299947, _299949] : [class_Groups_Ocancel__ab__semigroup__add(_299943), c_Groups_Oplus__class_Oplus(_299943, _299945, _299947) = c_Groups_Oplus__class_Oplus(_299943, _299945, _299949), -(_299947 = _299949)], (4622 ^ _221138) ^ [_375626, _375628, _375630] : [class_Rings_Ocomm__semiring__1(_375626), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_375626), _375628), _375630) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_375626), _375630), _375628))], (7517 ^ _221138) ^ [_480220, _480222, _480224] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _480220), _480222), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _480220), _480224)), -(_480220 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _480222, _480224))], (8773 ^ _221138) ^ [_522413] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _522413, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _522413)], (5155 ^ _221138) ^ [_397053] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _397053, _397053)], (8035 ^ _221138) ^ [_496653, _496655] : [8036 ^ _221138 : [(8039 ^ _221138) ^ [] : [_496655 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (8037 ^ _221138) ^ [] : [-(_496653 = 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, _496653)), _496655)))], (7867 ^ _221138) ^ [_491222, _491224] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _491222, _491224), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _491224, _491222), -(_491222 = _491224)], (5379 ^ _221138) ^ [_404596, _404598, _404600] : [class_Groups_Oordered__ab__group__add(_404596), 5382 ^ _221138 : [(5389 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_404596, _404600, c_Groups_Ouminus__class_Ouminus(_404596, _404598)), -(c_Orderings_Oord__class_Oless__eq(_404596, _404598, c_Groups_Ouminus__class_Ouminus(_404596, _404600)))], (5383 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_404596, _404598, c_Groups_Ouminus__class_Ouminus(_404596, _404600)), -(c_Orderings_Oord__class_Oless__eq(_404596, _404600, c_Groups_Ouminus__class_Ouminus(_404596, _404598)))]]], (9019 ^ _221138) ^ [_531326, _531328] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _531326, _531328)), 9022 ^ _221138 : [(9029 ^ _221138) ^ [] : [_531326 = _531328, -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _531326, c_Nat_OSuc(_531328)))], (9023 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _531326, c_Nat_OSuc(_531328)), -(_531326 = _531328)]]], (11541 ^ _221138) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal))], (7815 ^ _221138) ^ [_489592, _489594, _489596] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _489592, _489594), 7826 ^ _221138 : [(7829 ^ _221138) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _489596, _489592)], (7827 ^ _221138) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _489592, _489596))]], c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _489594, _489596), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _489596, _489594))], (3866 ^ _221138) ^ [_349881, _349883, _349885] : [class_Rings_Olinordered__semiring__strict(_349881), c_Orderings_Oord__class_Oless(_349881, c_Groups_Ozero__class_Ozero(_349881), _349883), c_Orderings_Oord__class_Oless(_349881, c_Groups_Ozero__class_Ozero(_349881), _349885), -(c_Orderings_Oord__class_Oless(_349881, c_Groups_Ozero__class_Ozero(_349881), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_349881), _349883), _349885)))], (792 ^ _221138) ^ [_244976, _244978, _244980, _244982, _244984, _244986] : [-(c_Orderings_Oord__class_Oless__eq(_244984, _244980, _244976)), c_Orderings_Oord__class_Oless__eq(_244986, _244982, _244978), _244986 = _244984, _244982 = _244980, _244978 = _244976], (244 ^ _221138) ^ [_228696, _228698] : [-(class_Groups_Olinordered__ab__group__add(_228696)), _228698 = _228696, class_Groups_Olinordered__ab__group__add(_228698)], (9870 ^ _221138) ^ [_560895, _560897, _560899, _560901, _560903, _560905] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _560895), _560897), _560899) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _560901), _560903), _560905), 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), _560901), _560903), _560905)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _560905, _560901), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _560899), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _560901), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _560901, _560895), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _560897, _560903))], (11739 ^ _221138) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (11933 ^ _221138) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex))], (6109 ^ _221138) ^ [_429565] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _429565, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_429565 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9345 ^ _221138) ^ [_542626, _542628] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _542626, _542628) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 9346 ^ _221138 : [(9353 ^ _221138) ^ [] : [_542626 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _542628 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9347 ^ _221138) ^ [] : [_542626 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _542628 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (11611 ^ _221138) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (494 ^ _221138) ^ [_236071, _236073] : [-(class_Groups_Omonoid__mult(_236071)), _236073 = _236071, class_Groups_Omonoid__mult(_236073)], (2782 ^ _221138) ^ [_313517, _313519, _313521, _313523] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_313517), c_Orderings_Oord__class_Oless__eq(_313517, c_Groups_Oplus__class_Oplus(_313517, _313519, _313521), c_Groups_Oplus__class_Oplus(_313517, _313519, _313523)), -(c_Orderings_Oord__class_Oless__eq(_313517, _313521, _313523))], (9426 ^ _221138) ^ [_545500, _545502] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_545500), _545502), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _545500, _545502))], (8799 ^ _221138) ^ [_523306, _523308] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _523306, _523308), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _523306, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _523308, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (2498 ^ _221138) ^ [_303077, _303079, _303081, _303083] : [class_Rings_Ocomm__semiring(_303077), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_303077), c_Groups_Oplus__class_Oplus(_303077, _303079, _303081)), _303083) = c_Groups_Oplus__class_Oplus(_303077, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_303077), _303079), _303083), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_303077), _303081), _303083)))], (6489 ^ _221138) ^ [_443667, _443669, _443671] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _443667, _443669), _443671) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _443667, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _443669, _443671)))], (1112 ^ _221138) ^ [_257244] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _257244), 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____), _257244)), 1108 ^ []))], (9472 ^ _221138) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (154 ^ _221138) ^ [_226041, _226043] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_226041)), _226043 = _226041, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_226043)], (9644 ^ _221138) ^ [_553064, _553066, _553068] : [class_Rings_Olinordered__semidom(_553064), c_Orderings_Oord__class_Oless__eq(_553064, c_Groups_Ozero__class_Ozero(_553064), _553066), c_Orderings_Oord__class_Oless__eq(_553064, _553066, c_Groups_Oone__class_Oone(_553064)), -(c_Orderings_Oord__class_Oless__eq(_553064, hAPP(hAPP(c_Power_Opower__class_Opower(_553064), _553066), c_Nat_OSuc(_553068)), _553066))], (11399 ^ _221138) ^ [_619232] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _619232, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _619232)], (9734 ^ _221138) ^ [_556052, _556054, _556056] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _556052), _556052 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _556054, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _556052), _556056)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _556054, _556052), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _556056))], (9175 ^ _221138) ^ [_536573, _536575] : [c_Nat_OSuc(_536573) = c_Nat_OSuc(_536575), -(_536573 = _536575)], (11701 ^ _221138) ^ [] : [-(class_Rings_Odvd(tc_Int_Oint))], (8737 ^ _221138) ^ [_521314] : [-(_521314 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 8740 ^ _221138 : [(8747 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _521314)), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _521314) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (8741 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _521314), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _521314) = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (10143 ^ _221138) ^ [_570508] : [-(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(_570508))))], (10692 ^ _221138) ^ [_592468, _592470] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _592468, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _592470)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, _592468, _592470))], (11937 ^ _221138) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex))], (3108 ^ _221138) ^ [_325036] : [class_Rings_Ocomm__semiring__1(_325036), -(c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_325036)) = c_Polynomial_OpCons(_325036, c_Groups_Oone__class_Oone(_325036), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_325036))))], (8021 ^ _221138) ^ [_496078, _496080, _496082] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _496078), _496080)), _496082) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _496078), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _496080), _496082)))], (11615 ^ _221138) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (12339 ^ _221138) ^ [_648145] : [class_Rings_Ocomm__semiring__1(_648145), -(class_Groups_Oone(tc_Polynomial_Opoly(_648145)))], (8003 ^ _221138) ^ [_495533, _495535] : [_495533 = _495535, 8006 ^ _221138 : [(8009 ^ _221138) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _495535, _495533))], (8007 ^ _221138) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _495533, _495535))]]], (8983 ^ _221138) ^ [_530095, _530097] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _530097, c_Nat_OSuc(_530095)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _530095, _530097)], (7781 ^ _221138) ^ [_488558, _488560] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _488558, _488560)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _488558, _488560), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _488560, _488558))], (8761 ^ _221138) ^ [_522072] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _522072), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _522072))], (10820 ^ _221138) ^ [_597457, _597459, _597461] : [class_Groups_Oordered__ab__group__add(_597457), 10823 ^ _221138 : [(10830 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_597457, c_Groups_Ominus__class_Ominus(_597457, _597459, _597461), c_Groups_Ozero__class_Ozero(_597457)), -(c_Orderings_Oord__class_Oless(_597457, _597459, _597461))], (10824 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_597457, _597459, _597461), -(c_Orderings_Oord__class_Oless(_597457, c_Groups_Ominus__class_Ominus(_597457, _597459, _597461), c_Groups_Ozero__class_Ozero(_597457)))]]], (4268 ^ _221138) ^ [_363130, _363132, _363134, _363136, _363138] : [class_Rings_Olinordered__semiring__strict(_363130), c_Orderings_Oord__class_Oless__eq(_363130, _363132, _363134), c_Orderings_Oord__class_Oless(_363130, _363136, _363138), c_Orderings_Oord__class_Oless(_363130, c_Groups_Ozero__class_Ozero(_363130), _363132), c_Orderings_Oord__class_Oless__eq(_363130, c_Groups_Ozero__class_Ozero(_363130), _363136), -(c_Orderings_Oord__class_Oless(_363130, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_363130), _363132), _363136), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_363130), _363134), _363138)))], (5785 ^ _221138) ^ [_418490, _418492, _418494] : [class_Groups_Ogroup__add(_418490), 5788 ^ _221138 : [(5795 ^ _221138) ^ [] : [_418494 = c_Groups_Ouminus__class_Ouminus(_418490, _418492), -(c_Groups_Oplus__class_Oplus(_418490, _418492, _418494) = c_Groups_Ozero__class_Ozero(_418490))], (5789 ^ _221138) ^ [] : [c_Groups_Oplus__class_Oplus(_418490, _418492, _418494) = c_Groups_Ozero__class_Ozero(_418490), -(_418494 = c_Groups_Ouminus__class_Ouminus(_418490, _418492))]]], (11893 ^ _221138) ^ [] : [-(class_Orderings_Oord(tc_RealDef_Oreal))], (2722 ^ _221138) ^ [_311382, _311384, _311386, _311388] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_311382), 2725 ^ _221138 : [(2732 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_311382, _311386, _311388), -(c_Orderings_Oord__class_Oless__eq(_311382, c_Groups_Oplus__class_Oplus(_311382, _311384, _311386), c_Groups_Oplus__class_Oplus(_311382, _311384, _311388)))], (2726 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_311382, c_Groups_Oplus__class_Oplus(_311382, _311384, _311386), c_Groups_Oplus__class_Oplus(_311382, _311384, _311388)), -(c_Orderings_Oord__class_Oless__eq(_311382, _311386, _311388))]]], (11179 ^ _221138) ^ [_611157, _611159, _611161] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _611157, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _611159, _611161)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _611157, _611161), _611159))], (2972 ^ _221138) ^ [_320302, _320304, _320306] : [class_Rings_Olinordered__idom(_320302), c_Orderings_Oord__class_Oless__eq(_320302, c_Groups_Ozero__class_Ozero(_320302), _320304), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_320302), c_Groups_Oabs__class_Oabs(_320302, _320306)), _320304) = c_Groups_Oabs__class_Oabs(_320302, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_320302), _320306), _320304)))], (9270 ^ _221138) ^ [_540223] : [_540223 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _540223, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (11865 ^ _221138) ^ [] : [-(class_Rings_Ozero__neq__one(tc_RealDef_Oreal))], (484 ^ _221138) ^ [_235776, _235778] : [-(class_Orderings_Olinorder(_235776)), _235778 = _235776, class_Orderings_Olinorder(_235778)], (734 ^ _221138) ^ [_243151, _243153] : [-(class_Groups_Oone(_243151)), _243153 = _243151, class_Groups_Oone(_243153)], (6459 ^ _221138) ^ [_442329, _442331, _442333, _442335] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _442329), _442331), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _442333), _442331), _442335)) = 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, _442329, _442333)), _442331), _442335))], (6785 ^ _221138) ^ [_454143, _454145] : [class_Rings_Olinordered__idom(_454143), 6788 ^ _221138 : [(6795 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_454143, c_Groups_Ozero__class_Ozero(_454143), _454145), -(c_Orderings_Oord__class_Oless(_454143, c_Groups_Ozero__class_Ozero(_454143), c_Groups_Osgn__class_Osgn(_454143, _454145)))], (6789 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_454143, c_Groups_Ozero__class_Ozero(_454143), c_Groups_Osgn__class_Osgn(_454143, _454145)), -(c_Orderings_Oord__class_Oless(_454143, c_Groups_Ozero__class_Ozero(_454143), _454145))]]], (384 ^ _221138) ^ [_232826, _232828] : [-(class_Groups_Ocomm__monoid__mult(_232826)), _232828 = _232826, class_Groups_Ocomm__monoid__mult(_232828)], (10674 ^ _221138) ^ [_591699, _591701, _591703] : [class_Groups_Oordered__ab__group__add__abs(_591699), -(c_Orderings_Oord__class_Oless__eq(_591699, c_Groups_Oabs__class_Oabs(_591699, c_Groups_Ominus__class_Ominus(_591699, c_Groups_Oabs__class_Oabs(_591699, _591701), c_Groups_Oabs__class_Oabs(_591699, _591703))), c_Groups_Oabs__class_Oabs(_591699, c_Groups_Ominus__class_Ominus(_591699, _591701, _591703))))], (11643 ^ _221138) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (11867 ^ _221138) ^ [] : [-(class_Rings_Oordered__ring(tc_RealDef_Oreal))], (2622 ^ _221138) ^ [_307768, _307770] : [-(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _307768), _307768), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _307770), _307770)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _307768 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _307770 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)], (9958 ^ _221138) ^ [] : [-(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)))], (6701 ^ _221138) ^ [_451306, _451308] : [class_RealVector_Oreal__normed__vector(_451306), -(c_Groups_Osgn__class_Osgn(_451306, c_Groups_Ouminus__class_Ouminus(_451306, _451308)) = c_Groups_Ouminus__class_Ouminus(_451306, c_Groups_Osgn__class_Osgn(_451306, _451308)))], (11785 ^ _221138) ^ [] : [-(class_Groups_Ouminus(tc_HOL_Obool))], (2884 ^ _221138) ^ [_317134, _317136] : [class_Rings_Omult__zero(_317134), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_317134), _317136), c_Groups_Ozero__class_Ozero(_317134)) = c_Groups_Ozero__class_Ozero(_317134))], (5227 ^ _221138) ^ [_399834, _399836, _399838] : [class_Groups_Ogroup__add(_399834), 5230 ^ _221138 : [(5237 ^ _221138) ^ [] : [_399838 = c_Groups_Ouminus__class_Ouminus(_399834, _399836), -(_399836 = c_Groups_Ouminus__class_Ouminus(_399834, _399838))], (5231 ^ _221138) ^ [] : [_399836 = c_Groups_Ouminus__class_Ouminus(_399834, _399838), -(_399838 = c_Groups_Ouminus__class_Ouminus(_399834, _399836))]]], (11353 ^ _221138) ^ [_617455, _617457] : [-(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _617455, _617457) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _617455, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _617457)))], (11709 ^ _221138) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (11371 ^ _221138) ^ [_618291, _618293, _618295] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _618291, _618293), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _618291, _618295), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _618295, _618293), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _618295, _618291)))], (1020 ^ _221138) ^ [_253774, _253776, _253778, _253780] : [-(tc_fun(_253780, _253776) = tc_fun(_253778, _253774)), _253780 = _253778, _253776 = _253774], (3006 ^ _221138) ^ [_321523, _321525, _321527] : [class_Rings_Olinordered__idom(_321523), c_Orderings_Oord__class_Oless__eq(_321523, c_Groups_Ozero__class_Ozero(_321523), _321525), c_Orderings_Oord__class_Oless__eq(_321523, c_Groups_Ozero__class_Ozero(_321523), _321527), c_Orderings_Oord__class_Oless__eq(_321523, _321527, c_Groups_Oone__class_Oone(_321523)), -(c_Orderings_Oord__class_Oless__eq(_321523, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_321523), _321525), _321527), _321525))], (10490 ^ _221138) ^ [_583959, _583961] : [class_Rings_Oring__1(_583959), -(c_Groups_Ominus__class_Ominus(_583959, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_583959), _583961), _583961), c_Groups_Oone__class_Oone(_583959)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_583959), c_Groups_Oplus__class_Oplus(_583959, _583961, c_Groups_Oone__class_Oone(_583959))), c_Groups_Ominus__class_Ominus(_583959, _583961, c_Groups_Oone__class_Oone(_583959))))], (902 ^ _221138) ^ [_249510, _249512, _249514, _249516, _249518, _249520] : [-(c_Power_Opower_Opower(_249520, _249516, _249512) = c_Power_Opower_Opower(_249518, _249514, _249510)), _249520 = _249518, _249516 = _249514, _249512 = _249510], (10077 ^ _221138) ^ [_568102, _568104] : [-(c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _568102, _568104)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _568102), c_RealDef_Oreal(tc_Nat_Onat, _568104)))], (11679 ^ _221138) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (12045 ^ _221138) ^ [_638835] : [class_Rings_Olinordered__idom(_638835), -(class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(_638835)))], (11673 ^ _221138) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (3252 ^ _221138) ^ [] : [c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)], (11875 ^ _221138) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_RealDef_Oreal))], (2460 ^ _221138) ^ [_301659, _301661, _301663, _301665, _301667] : [class_Rings_Osemiring(_301659), -(c_Groups_Oplus__class_Oplus(_301659, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_301659), _301661), _301663), c_Groups_Oplus__class_Oplus(_301659, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_301659), _301665), _301663), _301667)) = c_Groups_Oplus__class_Oplus(_301659, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_301659), c_Groups_Oplus__class_Oplus(_301659, _301661, _301665)), _301663), _301667))], (11763 ^ _221138) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (7453 ^ _221138) ^ [_477460, _477462, _477464, _477466] : [class_Rings_Ocomm__semiring__1(_477460), -(hAPP(hAPP(c_Power_Opower__class_Opower(_477460), hAPP(hAPP(c_Power_Opower__class_Opower(_477460), _477462), _477464)), _477466) = hAPP(hAPP(c_Power_Opower__class_Opower(_477460), _477462), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _477464), _477466)))], (11707 ^ _221138) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (10407 ^ _221138) ^ [_580398, _580400] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _580398), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _580400), 10415 ^ _221138 : [(10418 ^ _221138) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), 10414 ^ [_580398, _580400]), _580398) = _580400)], (10416 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 10414 ^ [_580398, _580400]))]]], (564 ^ _221138) ^ [_238136, _238138] : [-(class_Int_Oring__char__0(_238136)), _238138 = _238136, class_Int_Oring__char__0(_238138)], (3042 ^ _221138) ^ [_322651, _322653, _322655, _322657, _322659, _322661] : [class_Rings_Olinordered__semiring__1__strict(_322651), c_Orderings_Oord__class_Oless(_322651, _322653, _322655), c_Orderings_Oord__class_Oless(_322651, _322657, _322655), c_Orderings_Oord__class_Oless__eq(_322651, c_Groups_Ozero__class_Ozero(_322651), _322659), c_Orderings_Oord__class_Oless__eq(_322651, c_Groups_Ozero__class_Ozero(_322651), _322661), c_Groups_Oplus__class_Oplus(_322651, _322659, _322661) = c_Groups_Oone__class_Oone(_322651), -(c_Orderings_Oord__class_Oless(_322651, c_Groups_Oplus__class_Oplus(_322651, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_322651), _322659), _322653), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_322651), _322661), _322657)), _322655))], (828 ^ _221138) ^ [_246781, _246783, _246785, _246787, _246789, _246791, _246793, _246795, _246797, _246799] : [-(c_Polynomial_Opoly__rec(_246799, _246795, _246791, _246787, _246783) = c_Polynomial_Opoly__rec(_246797, _246793, _246789, _246785, _246781)), _246799 = _246797, _246795 = _246793, _246791 = _246789, _246787 = _246785, _246783 = _246781], (11767 ^ _221138) ^ [] : [-(class_Groups_Ominus(tc_Nat_Onat))], (10155 ^ _221138) ^ [_570968, _570970] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _570968), _570970), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _570968, c_RComplete_Onatfloor(_570970)))], (10129 ^ _221138) ^ [_570028] : [-(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _570028)) = c_RealDef_Oreal(tc_Nat_Onat, _570028))], (7495 ^ _221138) ^ [_479323, _479325] : [class_Rings_Ocomm__semiring__1(_479323), -(hAPP(hAPP(c_Power_Opower__class_Opower(_479323), _479325), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_479323))], (10892 ^ _221138) ^ [_600350, _600352] : [class_Groups_Ogroup__add(_600350), -(c_Groups_Ominus__class_Ominus(_600350, _600352, _600352) = c_Groups_Ozero__class_Ozero(_600350))], (6121 ^ _221138) ^ [_429931, _429933] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _429931, _429933), _429933 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (11685 ^ _221138) ^ [] : [-(class_Groups_Oabs__if(tc_Int_Oint))], (4134 ^ _221138) ^ [_358706, _358708, _358710] : [class_Groups_Oordered__comm__monoid__add(_358706), c_Orderings_Oord__class_Oless(_358706, _358708, c_Groups_Ozero__class_Ozero(_358706)), c_Orderings_Oord__class_Oless__eq(_358706, _358710, c_Groups_Ozero__class_Ozero(_358706)), -(c_Orderings_Oord__class_Oless(_358706, c_Groups_Oplus__class_Oplus(_358706, _358708, _358710), c_Groups_Ozero__class_Ozero(_358706)))], (7943 ^ _221138) ^ [_493622, _493624] : [-(_493622 = _493624), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _493622, _493624), 7950 ^ _221138 : [(7953 ^ _221138) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _493624, _493622)], (7951 ^ _221138) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _493622, _493624))]]], (11633 ^ _221138) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_Int_Oint))], (4040 ^ _221138) ^ [_355642, _355644, _355646, _355648] : [class_Rings_Olinordered__ring__strict(_355642), c_Orderings_Oord__class_Oless(_355642, _355644, _355646), c_Orderings_Oord__class_Oless(_355642, _355648, c_Groups_Ozero__class_Ozero(_355642)), -(c_Orderings_Oord__class_Oless(_355642, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_355642), _355648), _355646), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_355642), _355648), _355644)))], (11349 ^ _221138) ^ [_617252] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_617252), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _617252)], (4558 ^ _221138) ^ [_373228, _373230] : [class_Rings_Ocomm__semiring__1(_373228), -(c_Groups_Oplus__class_Oplus(_373228, _373230, _373230) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_373228), c_Groups_Oplus__class_Oplus(_373228, c_Groups_Oone__class_Oone(_373228), c_Groups_Oone__class_Oone(_373228))), _373230))], (6441 ^ _221138) ^ [_441389] : [class_RealVector_Oreal__normed__algebra(_441389), 6445 ^ _221138 : [(6448 ^ _221138) ^ [_441718, _441720] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_441389, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_441389), _441720), _441718)), 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(_441389, _441720)), c_RealVector_Onorm__class_Onorm(_441389, _441718))), 6444 ^ [_441389])))], (6446 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 6444 ^ [_441389]))]]], (6323 ^ _221138) ^ [_437122, _437124] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _437122, _437124) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 6326 ^ _221138 : [(6329 ^ _221138) ^ [] : [-(_437124 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6327 ^ _221138) ^ [] : [-(_437122 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (6595 ^ _221138) ^ [_447576, _447578, _447580] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _447576, _447578), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _447576, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _447578, _447580)))], (8969 ^ _221138) ^ [_529547] : [c_Nat_OSuc(_529547) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (4696 ^ _221138) ^ [_379436, _379438, _379440, _379442] : [class_Rings_Ocomm__semiring__1(_379436), -(c_Groups_Oplus__class_Oplus(_379436, c_Groups_Oplus__class_Oplus(_379436, _379438, _379440), _379442) = c_Groups_Oplus__class_Oplus(_379436, c_Groups_Oplus__class_Oplus(_379436, _379438, _379442), _379440))], (8247 ^ _221138) ^ [_504398, _504400, _504402, _504404] : [class_Rings_Ocomm__semiring__1(_504398), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _504400, _504402), -(c_Rings_Odvd__class_Odvd(_504398, hAPP(hAPP(c_Power_Opower__class_Opower(_504398), _504404), _504400), hAPP(hAPP(c_Power_Opower__class_Opower(_504398), _504404), _504402)))], (6281 ^ _221138) ^ [_435642, _435644, _435646] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _435642, _435644), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _435646), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _435642), _435646), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _435644), _435646)))], (12081 ^ _221138) ^ [_639975] : [class_Rings_Olinordered__idom(_639975), -(class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(_639975)))], (2660 ^ _221138) ^ [_309162, _309164, _309166, _309168, _309170] : [class_Groups_Ocomm__monoid__add(_309162), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_309162), c_Polynomial_OpCons(_309162, _309164, _309166), c_Polynomial_OpCons(_309162, _309168, _309170)) = c_Polynomial_OpCons(_309162, c_Groups_Oplus__class_Oplus(_309162, _309164, _309168), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_309162), _309166, _309170)))], (2368 ^ _221138) ^ [_298251, _298253, _298255, _298257] : [class_RealVector_Oreal__normed__algebra(_298251), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_298251), c_Groups_Oplus__class_Oplus(_298251, _298253, _298255)), _298257) = c_Groups_Oplus__class_Oplus(_298251, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_298251), _298253), _298257), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_298251), _298255), _298257)))], (6801 ^ _221138) ^ [_454628, _454630] : [class_Rings_Olinordered__idom(_454628), -(c_Groups_Oabs__class_Oabs(_454628, _454630) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_454628), _454630), c_Groups_Osgn__class_Osgn(_454628, _454630)))], (8603 ^ _221138) ^ [_516812] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _516812, c_Groups_Oone__class_Oone(tc_Int_Oint)), -(c_Groups_Oabs__class_Oabs(tc_Int_Oint, _516812) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (11915 ^ _221138) ^ [] : [-(class_Rings_Odvd(tc_RealDef_Oreal))], (5003 ^ _221138) ^ [_391353, _391355, _391357] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _391353, _391355), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _391353, _391357), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _391355, _391357)))], (12087 ^ _221138) ^ [_640165] : [class_Rings_Olinordered__idom(_640165), -(class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(_640165)))], (2890 ^ _221138) ^ [_317380, _317382, _317384] : [class_Rings_Oring__no__zero__divisors(_317380), 2893 ^ _221138 : [(2894 ^ _221138) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_317380), _317382), _317384) = c_Groups_Ozero__class_Ozero(_317380), -(_317382 = c_Groups_Ozero__class_Ozero(_317380)), -(_317384 = c_Groups_Ozero__class_Ozero(_317380))], (2904 ^ _221138) ^ [] : [2905 ^ _221138 : [(2908 ^ _221138) ^ [] : [_317384 = c_Groups_Ozero__class_Ozero(_317380)], (2906 ^ _221138) ^ [] : [_317382 = c_Groups_Ozero__class_Ozero(_317380)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_317380), _317382), _317384) = c_Groups_Ozero__class_Ozero(_317380))]]], (9712 ^ _221138) ^ [_555294, _555296] : [9713 ^ _221138 : [(9716 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _555294)], (9714 ^ _221138) ^ [] : [_555296 = 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), _555294), _555296)))], (11505 ^ _221138) ^ [_623469, _623471, _623473] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _623469, _623471), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _623471, _623469)), _623473) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_623471), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _623469, _623473)))], (3562 ^ _221138) ^ [_339855, _339857, _339859] : [class_Rings_Oordered__cancel__semiring(_339855), c_Orderings_Oord__class_Oless__eq(_339855, c_Groups_Ozero__class_Ozero(_339855), _339857), c_Orderings_Oord__class_Oless__eq(_339855, _339859, c_Groups_Ozero__class_Ozero(_339855)), -(c_Orderings_Oord__class_Oless__eq(_339855, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_339855), _339857), _339859), c_Groups_Ozero__class_Ozero(_339855)))], (6885 ^ _221138) ^ [_457623, _457625] : [class_Rings_Olinordered__idom(_457623), c_Orderings_Oord__class_Oless(_457623, _457625, c_Groups_Ozero__class_Ozero(_457623)), -(c_Groups_Osgn__class_Osgn(_457623, _457625) = c_Groups_Ouminus__class_Ouminus(_457623, c_Groups_Oone__class_Oone(_457623)))], (3404 ^ _221138) ^ [_334755, _334757, _334759] : [class_Groups_Oordered__comm__monoid__add(_334755), c_Orderings_Oord__class_Oless(_334755, c_Groups_Ozero__class_Ozero(_334755), _334757), c_Orderings_Oord__class_Oless(_334755, c_Groups_Ozero__class_Ozero(_334755), _334759), -(c_Orderings_Oord__class_Oless(_334755, c_Groups_Ozero__class_Ozero(_334755), c_Groups_Oplus__class_Oplus(_334755, _334757, _334759)))], (12255 ^ _221138) ^ [_645485] : [class_Rings_Ocomm__ring(_645485), -(class_Rings_Ocomm__ring(tc_Polynomial_Opoly(_645485)))], (5905 ^ _221138) ^ [_422386, _422388] : [c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _422386, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _422388)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_422386 = _422388)], (4652 ^ _221138) ^ [_377162, _377164, _377166, _377168, _377170] : [class_Rings_Ocomm__semiring__1(_377162), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_377162), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_377162), _377164), _377166)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_377162), _377168), _377170)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_377162), _377164), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_377162), _377166), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_377162), _377168), _377170))))], (6263 ^ _221138) ^ [_435024, _435026, _435028] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _435024), _435026) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _435028), _435026), -(_435024 = _435028), -(_435026 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11821 ^ _221138) ^ [] : [-(class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal))], (1570 ^ _221138) ^ [_272063, _272065, _272067, _272069] : [class_Orderings_Oorder(_272063), _272065 = _272067, c_Orderings_Oord__class_Oless(_272063, _272069, _272067), -(c_Orderings_Oord__class_Oless(_272063, _272069, _272065))], (6053 ^ _221138) ^ [_427562, _427564] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _427562, _427564), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _427564, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _427562)))], (11547 ^ _221138) ^ [_625055, _625057] : [class_Lattices_Oboolean__algebra(_625055), -(class_Lattices_Oboolean__algebra(tc_fun(_625057, _625055)))], (6091 ^ _221138) ^ [_428900] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _428900, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9590 ^ _221138) ^ [_551241, _551243] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _551241), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _551243), -(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), _551243), _551241)))], (3710 ^ _221138) ^ [_344817, _344819, _344821, _344823, _344825] : [class_Rings_Oordered__semiring(_344817), c_Orderings_Oord__class_Oless__eq(_344817, _344819, _344821), c_Orderings_Oord__class_Oless__eq(_344817, _344823, _344825), c_Orderings_Oord__class_Oless__eq(_344817, c_Groups_Ozero__class_Ozero(_344817), _344821), c_Orderings_Oord__class_Oless__eq(_344817, c_Groups_Ozero__class_Ozero(_344817), _344823), -(c_Orderings_Oord__class_Oless__eq(_344817, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_344817), _344819), _344823), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_344817), _344821), _344825)))], (5629 ^ _221138) ^ [_413573, _413575] : [class_Groups_Olinordered__ab__group__add(_413573), 5632 ^ _221138 : [(5639 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_413573, _413575, c_Groups_Ozero__class_Ozero(_413573)), -(c_Orderings_Oord__class_Oless__eq(_413573, _413575, c_Groups_Ouminus__class_Ouminus(_413573, _413575)))], (5633 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_413573, _413575, c_Groups_Ouminus__class_Ouminus(_413573, _413575)), -(c_Orderings_Oord__class_Oless__eq(_413573, _413575, c_Groups_Ozero__class_Ozero(_413573)))]]], (8875 ^ _221138) ^ [_525843, _525845, _525847] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _525843, _525845), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _525847), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _525847), _525843), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _525847), _525845)))], (10740 ^ _221138) ^ [_594394, _594396, _594398, _594400] : [class_Rings_Ocomm__ring__1(_594394), c_Rings_Odvd__class_Odvd(_594394, _594396, _594398), c_Rings_Odvd__class_Odvd(_594394, _594396, _594400), -(c_Rings_Odvd__class_Odvd(_594394, _594396, c_Groups_Ominus__class_Ominus(_594394, _594398, _594400)))], (9438 ^ _221138) ^ [_545890, _545892] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _545890, _545892), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _545890, c_Nat_OSuc(_545892)))], (8377 ^ _221138) ^ [_509139, _509141, _509143, _509145] : [class_Rings_Olinordered__semidom(_509139), c_Orderings_Oord__class_Oless(_509139, c_Groups_Oone__class_Oone(_509139), _509141), c_Orderings_Oord__class_Oless(_509139, hAPP(hAPP(c_Power_Opower__class_Opower(_509139), _509141), _509143), hAPP(hAPP(c_Power_Opower__class_Opower(_509139), _509141), _509145)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _509143, _509145))], (11873 ^ _221138) ^ [] : [-(class_Groups_Omonoid__mult(tc_RealDef_Oreal))], (1156 ^ _221138) ^ [_258643, _258645] : [class_RealVector_Oreal__normed__vector(_258643), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_258643, _258645)))], (11803 ^ _221138) ^ [] : [-(class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal))], (11929 ^ _221138) ^ [] : [-(class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex))], (5057 ^ _221138) ^ [_393413, _393415, _393417] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _393413, _393415), _393417), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _393413, _393417))], (12333 ^ _221138) ^ [_647955] : [class_Rings_Oidom(_647955), -(class_Rings_Oidom(tc_Polynomial_Opoly(_647955)))], (9013 ^ _221138) ^ [_531102, _531104] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _531102, _531104), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_531102), c_Nat_OSuc(_531104)))], (7219 ^ _221138) ^ [_468950, _468952] : [class_Rings_Ocomm__semiring__1(_468950), -(c_Rings_Odvd__class_Odvd(_468950, c_Groups_Oone__class_Oone(_468950), _468952))], (974 ^ _221138) ^ [_252060, _252062] : [_252062 = _252060, -(c_RComplete_Onatfloor(_252062) = c_RComplete_Onatfloor(_252060))], (11687 ^ _221138) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (11917 ^ _221138) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex))], (8305 ^ _221138) ^ [_506543, _506545, _506547] : [class_Rings_Olinordered__semidom(_506543), c_Orderings_Oord__class_Oless(_506543, c_Groups_Oone__class_Oone(_506543), _506545), -(c_Orderings_Oord__class_Oless(_506543, c_Groups_Oone__class_Oone(_506543), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_506543), _506545), hAPP(hAPP(c_Power_Opower__class_Opower(_506543), _506545), _506547))))], (20 ^ _221138) ^ [_221914, _221916, _221918, _221920] : [-(c_SEQ_Odecseq(_221918, _221914)), c_SEQ_Odecseq(_221920, _221916), _221920 = _221918, _221916 = _221914], (1203 ^ _221138) ^ [_260231] : [class_Groups_Ozero(_260231), -(c_Polynomial_OpCons(_260231, c_Groups_Ozero__class_Ozero(_260231), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_260231))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_260231)))], (10101 ^ _221138) ^ [_569128, _569130] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _569128), c_RealDef_Oreal(tc_Nat_Onat, _569130)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _569128, _569130))], (4416 ^ _221138) ^ [_368115, _368117] : [class_Rings_Ocomm__semiring__0(_368115), -(c_Polynomial_Osynthetic__div(_368115, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_368115)), _368117) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_368115)))], (374 ^ _221138) ^ [_232531, _232533] : [-(class_Groups_Oab__semigroup__mult(_232531)), _232533 = _232531, class_Groups_Oab__semigroup__mult(_232533)], (6273 ^ _221138) ^ [_435310, _435312, _435314] : [6274 ^ _221138 : [(6277 ^ _221138) ^ [] : [_435312 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (6275 ^ _221138) ^ [] : [_435310 = _435314]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _435310), _435312) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _435314), _435312))], (11185 ^ _221138) ^ [_611345, _611347, _611349] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _611345, _611349), _611347), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _611345, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _611347, _611349)))], (986 ^ _221138) ^ [_252552, _252554, _252556, _252558, _252560, _252562] : [-(c_Groups_Oplus__class_Oplus(_252562, _252558, _252554) = c_Groups_Oplus__class_Oplus(_252560, _252556, _252552)), _252562 = _252560, _252558 = _252556, _252554 = _252552], (10842 ^ _221138) ^ [_598239, _598241, _598243, _598245] : [class_RealVector_Oreal__normed__algebra(_598239), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_598239), _598241), c_Groups_Ominus__class_Ominus(_598239, _598243, _598245)) = c_Groups_Ominus__class_Ominus(_598239, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_598239), _598241), _598243), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_598239), _598241), _598245)))], (11729 ^ _221138) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (11593 ^ _221138) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (8061 ^ _221138) ^ [_497575, _497577, _497579] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _497575), c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _497575), _497577), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _497575), _497579)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _497577, _497579))], (11655 ^ _221138) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (404 ^ _221138) ^ [_233416, _233418] : [-(class_Rings_Oordered__semiring(_233416)), _233418 = _233416, class_Rings_Oordered__semiring(_233418)], (12345 ^ _221138) ^ [_648335] : [class_Rings_Ocomm__semiring__1(_648335), -(class_Rings_Odvd(tc_Polynomial_Opoly(_648335)))], (1473 ^ _221138) ^ [_268870, _268872, _268874, _268876] : [class_Orderings_Oord(_268870), 1476 ^ _221138 : [(1483 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_268870, hAPP(_268874, 1484 ^ [_268870, _268872, _268874, _268876]), hAPP(_268876, 1484 ^ [_268870, _268872, _268874, _268876])), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_268872, _268870), _268874, _268876))], (1477 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_268872, _268870), _268874, _268876), 1480 ^ _221138 : [(1481 ^ _221138) ^ [_269129] : [-(c_Orderings_Oord__class_Oless__eq(_268870, hAPP(_268874, _269129), hAPP(_268876, _269129)))]]]]], (2324 ^ _221138) ^ [_296306, _296308] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _296306), _296308) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _296308), _296306))], (7000 ^ _221138) ^ [_461446, _461448] : [class_RealVector_Oreal__normed__algebra(_461446), 7004 ^ _221138 : [(7007 ^ _221138) ^ [_461745] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_461446, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_461446), _461745), _461448)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_461446, _461745)), 7003 ^ [_461446, _461448])))], (7005 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 7003 ^ [_461446, _461448]))]]], (9750 ^ _221138) ^ [_556562] : [-(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _556562)) = _556562)], (11885 ^ _221138) ^ [] : [-(class_Rings_Ocomm__ring(tc_RealDef_Oreal))], (9264 ^ _221138) ^ [_540065] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _540065, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_540065 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8963 ^ _221138) ^ [_529309] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _529309) = _529309)], (11135 ^ _221138) ^ [_609495, _609497] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _609497, _609495), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _609495, _609497)))], (11173 ^ _221138) ^ [_610878, _610880] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _610878, _610880), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_610880), _610878) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _610880, _610878)))], (5041 ^ _221138) ^ [_392808, _392810, _392812, _392814] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _392808, _392810), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _392812, _392814), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _392808), _392812), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _392810), _392814)))], (6219 ^ _221138) ^ [_433350, _433352, _433354] : [6220 ^ _221138 : [(6223 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _433352, _433354)], (6221 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _433350))]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _433350), _433352), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _433350), _433354)))], (11783 ^ _221138) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (8109 ^ _221138) ^ [_499496, _499498, _499500, _499502] : [class_Rings_Ocomm__semiring__1(_499496), c_Rings_Odvd__class_Odvd(_499496, _499498, _499500), -(c_Rings_Odvd__class_Odvd(_499496, hAPP(hAPP(c_Power_Opower__class_Opower(_499496), _499498), _499502), hAPP(hAPP(c_Power_Opower__class_Opower(_499496), _499500), _499502)))], (2598 ^ _221138) ^ [_306991, _306993] : [class_Groups_Oordered__ab__group__add__abs(_306991), 2601 ^ _221138 : [(2608 ^ _221138) ^ [] : [_306993 = c_Groups_Ozero__class_Ozero(_306991), -(c_Groups_Oabs__class_Oabs(_306991, _306993) = c_Groups_Ozero__class_Ozero(_306991))], (2602 ^ _221138) ^ [] : [c_Groups_Oabs__class_Oabs(_306991, _306993) = c_Groups_Ozero__class_Ozero(_306991), -(_306993 = c_Groups_Ozero__class_Ozero(_306991))]]], (9914 ^ _221138) ^ [_562363, _562365, _562367] : [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), _562363), _562365), _562367), 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), _562367), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _562363), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _562365, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (2586 ^ _221138) ^ [_306567, _306569] : [class_Rings_Olinordered__semidom(_306567), -(c_Orderings_Oord__class_Oless(_306567, _306569, c_Groups_Oplus__class_Oplus(_306567, _306569, c_Groups_Oone__class_Oone(_306567))))], (1760 ^ _221138) ^ [_277958, _277960] : [class_Orderings_Opreorder(_277958), c_Orderings_Oord__class_Oless(_277958, _277960, _277960)], (184 ^ _221138) ^ [_226926, _226928] : [-(class_Rings_Olinordered__comm__semiring__strict(_226926)), _226928 = _226926, class_Rings_Olinordered__comm__semiring__strict(_226928)], (4468 ^ _221138) ^ [_369903, _369905, _369907] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _369903, 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, _369905), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _369903), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _369907))), -(_369905 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (9276 ^ _221138) ^ [_540446] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _540446), -(_540446 = c_Nat_OSuc(9279 ^ [_540446]))], (11991 ^ _221138) ^ [_637125] : [class_Rings_Oidom(_637125), -(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(_637125)))], (12153 ^ _221138) ^ [_642255] : [class_Groups_Ocomm__monoid__add(_642255), -(class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(_642255)))], (2032 ^ _221138) ^ [_286507, _286509, _286511] : [class_Orderings_Olinorder(_286507), -(c_Orderings_Oord__class_Oless(_286507, _286509, _286511)), -(c_Orderings_Oord__class_Oless__eq(_286507, _286511, _286509))], (7157 ^ _221138) ^ [_466979, _466981, _466983, _466985] : [class_Rings_Ocomm__semiring__1(_466979), c_Rings_Odvd__class_Odvd(_466979, _466981, _466983), c_Rings_Odvd__class_Odvd(_466979, _466983, _466985), -(c_Rings_Odvd__class_Odvd(_466979, _466981, _466985))], (11903 ^ _221138) ^ [] : [-(class_Groups_Ominus(tc_RealDef_Oreal))], (5199 ^ _221138) ^ [_398600, _398602] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _398600, _398602), _398600)], (9978 ^ _221138) ^ [_564393] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _564393), -(c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _564393, c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatfloor(_564393), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (6911 ^ _221138) ^ [_458433, _458435] : [class_Groups_Osgn__if(_458433), 6914 ^ _221138 : [(6921 ^ _221138) ^ [] : [-(_458435 = c_Groups_Ozero__class_Ozero(_458433)), 6924 ^ _221138 : [(6931 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(_458433, c_Groups_Ozero__class_Ozero(_458433), _458435)), -(c_Groups_Osgn__class_Osgn(_458433, _458435) = c_Groups_Ouminus__class_Ouminus(_458433, c_Groups_Oone__class_Oone(_458433)))], (6925 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_458433, c_Groups_Ozero__class_Ozero(_458433), _458435), -(c_Groups_Osgn__class_Osgn(_458433, _458435) = c_Groups_Oone__class_Oone(_458433))]]], (6915 ^ _221138) ^ [] : [_458435 = c_Groups_Ozero__class_Ozero(_458433), -(c_Groups_Osgn__class_Osgn(_458433, _458435) = c_Groups_Ozero__class_Ozero(_458433))]]], (2528 ^ _221138) ^ [_304433, _304435] : [class_Groups_Omonoid__mult(_304433), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_304433), _304435), c_Groups_Oone__class_Oone(_304433)) = _304435)], (11381 ^ _221138) ^ [_618636, _618638, _618640] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _618636, _618638), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _618636, _618640), _618638))], (6953 ^ _221138) ^ [_459719, _459721, _459723] : [class_RealVector_Oreal__normed__vector(_459719), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _459721), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_459719, hAPP(_459723, 6962 ^ [_459719, _459721, _459723])), _459721), -(c_SEQ_OBseq(_459719, _459723))], (724 ^ _221138) ^ [_242856, _242858] : [-(class_Rings_Oidom(_242856)), _242858 = _242856, class_Rings_Oidom(_242858)], (6083 ^ _221138) ^ [_428541] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _428541, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), -(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _428541) = _428541)], (3000 ^ _221138) ^ [_321285] : [class_Rings_Olinordered__semidom(_321285), -(c_Orderings_Oord__class_Oless(_321285, c_Groups_Ozero__class_Ozero(_321285), c_Groups_Oplus__class_Oplus(_321285, c_Groups_Oone__class_Oone(_321285), c_Groups_Oone__class_Oone(_321285))))], (6001 ^ _221138) ^ [_425609, _425611] : [class_Groups_Oordered__ab__group__add__abs(_425609), c_Orderings_Oord__class_Oless(_425609, _425611, c_Groups_Ozero__class_Ozero(_425609)), -(c_Groups_Oabs__class_Oabs(_425609, _425611) = c_Groups_Ouminus__class_Ouminus(_425609, _425611))], (1836 ^ _221138) ^ [_280470, _280472, _280474, _280476] : [class_Orderings_Oorder(_280470), c_Orderings_Oord__class_Oless__eq(_280470, _280472, _280474), c_Orderings_Oord__class_Oless(_280470, _280476, _280472), -(c_Orderings_Oord__class_Oless(_280470, _280476, _280474))], (11757 ^ _221138) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (5937 ^ _221138) ^ [_423503, _423505] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _423503), _423505)), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _423505), _423503), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _423503, _423505)], (11089 ^ _221138) ^ [_607611, _607613, _607615] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _607611, _607613), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _607615, _607613), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _607615, _607611)))], (6041 ^ _221138) ^ [_427123, _427125] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _427123, _427125)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _427123), _427125))], (12141 ^ _221138) ^ [_641875] : [class_Rings_Olinordered__idom(_641875), -(class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(_641875)))], (864 ^ _221138) ^ [_248119, _248121, _248123, _248125, _248127, _248129] : [-(c_Polynomial_Opcompose(_248129, _248125, _248121) = c_Polynomial_Opcompose(_248127, _248123, _248119)), _248129 = _248127, _248125 = _248123, _248121 = _248119], (1628 ^ _221138) ^ [_273917, _273919, _273921] : [class_Orderings_Oorder(_273917), c_Orderings_Oord__class_Oless(_273917, _273919, _273921), _273919 = _273921], (10093 ^ _221138) ^ [_568792, _568794] : [_568792 = _568794, -(c_RealDef_Oreal(tc_Nat_Onat, _568792) = c_RealDef_Oreal(tc_Nat_Onat, _568794))], (454 ^ _221138) ^ [_234891, _234893] : [-(class_Rings_Ozero__neq__one(_234891)), _234893 = _234891, class_Rings_Ozero__neq__one(_234893)], (11077 ^ _221138) ^ [_607119, _607121] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _607119, _607121), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _607121, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _607121, _607119)) = _607119)], (7967 ^ _221138) ^ [_494371, _494373] : [7974 ^ _221138 : [(7977 ^ _221138) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _494373, _494371)], (7975 ^ _221138) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _494371, _494373))]], c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _494371, _494373), -(_494371 = _494373)], (11107 ^ _221138) ^ [_608542, _608544, _608546] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _608542, _608544), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _608542, _608546), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _608542, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _608544, _608546)))], (4708 ^ _221138) ^ [_380004, _380006] : [class_Rings_Ocomm__semiring__1(_380004), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_380004), _380006), c_Groups_Ozero__class_Ozero(_380004)) = c_Groups_Ozero__class_Ozero(_380004))], (11955 ^ _221138) ^ [] : [-(class_Groups_Omonoid__mult(tc_Complex_Ocomplex))], (11927 ^ _221138) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex))], (12051 ^ _221138) ^ [_639025] : [class_Groups_Ocancel__comm__monoid__add(_639025), -(class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(_639025)))], (4026 ^ _221138) ^ [_355158, _355160, _355162, _355164] : [class_Rings_Olinordered__ring__strict(_355158), c_Orderings_Oord__class_Oless(_355158, _355160, _355162), c_Orderings_Oord__class_Oless(_355158, _355164, c_Groups_Ozero__class_Ozero(_355158)), -(c_Orderings_Oord__class_Oless(_355158, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_355158), _355162), _355164), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_355158), _355160), _355164)))], (11857 ^ _221138) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal))], (3618 ^ _221138) ^ [_341661, _341663, _341665, _341667] : [class_Rings_Oordered__semiring(_341661), c_Orderings_Oord__class_Oless__eq(_341661, _341663, _341665), c_Orderings_Oord__class_Oless__eq(_341661, c_Groups_Ozero__class_Ozero(_341661), _341667), -(c_Orderings_Oord__class_Oless__eq(_341661, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_341661), _341663), _341667), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_341661), _341665), _341667)))], (8653 ^ _221138) ^ [_518608, _518610, _518612] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _518608), _518610), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _518608), _518612)), -(_518608 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _518610, _518612))], (5301 ^ _221138) ^ [_402182, _402184] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _402182, _402184)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _402184, _402182))], (11005 ^ _221138) ^ [_604867, _604869, _604871] : [class_Rings_Olinordered__idom(_604867), 11008 ^ _221138 : [(11009 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(_604867), _604869, _604871), -(_604869 = _604871), -(c_Polynomial_Opos__poly(_604867, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_604867), _604871, _604869)))], (11019 ^ _221138) ^ [] : [11020 ^ _221138 : [(11023 ^ _221138) ^ [] : [c_Polynomial_Opos__poly(_604867, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_604867), _604871, _604869))], (11021 ^ _221138) ^ [] : [_604869 = _604871]], -(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(_604867), _604869, _604871))]]], (4346 ^ _221138) ^ [_365774, _365776, _365778, _365780] : [class_Rings_Olinordered__semiring__strict(_365774), c_Orderings_Oord__class_Oless__eq(_365774, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_365774), _365776), _365778), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_365774), _365780), _365778)), c_Orderings_Oord__class_Oless(_365774, c_Groups_Ozero__class_Ozero(_365774), _365778), -(c_Orderings_Oord__class_Oless__eq(_365774, _365776, _365780))], (4965 ^ _221138) ^ [_389882, _389884] : [4966 ^ _221138 : [(4969 ^ _221138) ^ [] : [_389882 = _389884], (4967 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _389882, _389884)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _389882, _389884))], (11621 ^ _221138) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (8967 ^ _221138) ^ [_529468] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_529468)], (10940 ^ _221138) ^ [_602147, _602149] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _602147, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _602149, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _602147, _602149))], (7483 ^ _221138) ^ [] : [-(c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11981 ^ _221138) ^ [] : [-(class_Groups_Ozero(tc_Complex_Ocomplex))], (1618 ^ _221138) ^ [_273593, _273595, _273597] : [class_Orderings_Oorder(_273593), c_Orderings_Oord__class_Oless(_273593, _273595, _273597), _273597 = _273595], (1598 ^ _221138) ^ [_272941, _272943, _272945] : [class_Orderings_Oorder(_272941), c_Orderings_Oord__class_Oless(_272941, _272943, _272945), c_Orderings_Oord__class_Oless(_272941, _272945, _272943)], (10776 ^ _221138) ^ [_595628, _595630, _595632, _595634, _595636] : [class_Groups_Ominus(_595628), -(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_595630, _595628), _595632, _595634), _595636) = c_Groups_Ominus__class_Ominus(_595628, hAPP(_595632, _595636), hAPP(_595634, _595636)))], (10680 ^ _221138) ^ [_591969, _591971, _591973] : [class_Groups_Oordered__ab__group__add__abs(_591969), -(c_Orderings_Oord__class_Oless__eq(_591969, c_Groups_Ominus__class_Ominus(_591969, c_Groups_Oabs__class_Oabs(_591969, _591971), c_Groups_Oabs__class_Oabs(_591969, _591973)), c_Groups_Oabs__class_Oabs(_591969, c_Groups_Ominus__class_Ominus(_591969, _591971, _591973))))], (11151 ^ _221138) ^ [_610017, _610019] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _610017, _610019), c_Nat_OSuc(_610017)))], (3358 ^ _221138) ^ [_333339, _333341, _333343] : [class_Groups_Oordered__comm__monoid__add(_333339), c_Orderings_Oord__class_Oless__eq(_333339, _333341, c_Groups_Ozero__class_Ozero(_333339)), c_Orderings_Oord__class_Oless__eq(_333339, _333343, c_Groups_Ozero__class_Ozero(_333339)), -(c_Orderings_Oord__class_Oless__eq(_333339, c_Groups_Oplus__class_Oplus(_333339, _333341, _333343), c_Groups_Ozero__class_Ozero(_333339)))], (1317 ^ _221138) ^ [_263936, _263938, _263940, _263942] : [class_Orderings_Opreorder(_263936), c_Orderings_Oord__class_Oless__eq(_263936, _263938, _263940), c_Orderings_Oord__class_Oless__eq(_263936, _263940, _263942), -(c_Orderings_Oord__class_Oless__eq(_263936, _263938, _263942))], (6071 ^ _221138) ^ [_428148] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _428148, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), -(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _428148) = _428148)], (7535 ^ _221138) ^ [_480818] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _480818, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_RComplete_Onatceiling(_480818) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8989 ^ _221138) ^ [_530345, _530347] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _530345, c_Nat_OSuc(_530347)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _530345, _530347)), -(_530345 = _530347)], (4991 ^ _221138) ^ [_390869, _390871, _390873] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _390869, _390871), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _390869, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _390871, _390873)))], (5201 ^ _221138) ^ [_398684] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _398684, _398684)], (11797 ^ _221138) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal))], (544 ^ _221138) ^ [_237546, _237548] : [-(class_Rings_Omult__zero(_237546)), _237548 = _237546, class_Rings_Omult__zero(_237548)], (9315 ^ _221138) ^ [_541715, _541717] : [-(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _541715, _541717)), 9316 ^ _221138 : [(9323 ^ _221138) ^ [] : [_541715 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _541717 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9317 ^ _221138) ^ [] : [_541715 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _541717 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (8627 ^ _221138) ^ [_517709, _517711, _517713, _517715, _517717] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _517709, _517711), 8630 ^ _221138 : [(8637 ^ _221138) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _517709, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _517713, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _517717), _517711)), _517715)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _517709, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _517713, _517715)))], (8631 ^ _221138) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _517709, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _517713, _517715)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _517709, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _517713, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _517717), _517711)), _517715)))]]], (2 ^ _221138) ^ [_221262] : [-(_221262 = _221262)], (3330 ^ _221138) ^ [_332433, _332435, _332437, _332439] : [class_Groups_Oordered__comm__monoid__add(_332433), c_Orderings_Oord__class_Oless__eq(_332433, c_Groups_Ozero__class_Ozero(_332433), _332435), c_Orderings_Oord__class_Oless__eq(_332433, _332437, _332439), -(c_Orderings_Oord__class_Oless__eq(_332433, _332437, c_Groups_Oplus__class_Oplus(_332433, _332435, _332439)))], (5491 ^ _221138) ^ [_408277, _408279, _408281] : [class_RealVector_Oreal__normed__algebra(_408277), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_408277), _408279), c_Groups_Ouminus__class_Ouminus(_408277, _408281)) = c_Groups_Ouminus__class_Ouminus(_408277, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_408277), _408279), _408281)))], (1046 ^ _221138) ^ [_254682, _254684] : [_254684 = _254682, -(c_Groups_Ozero__class_Ozero(_254684) = c_Groups_Ozero__class_Ozero(_254682))], (7429 ^ _221138) ^ [_476573] : [_476573 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _476573, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (10353 ^ _221138) ^ [_578354, _578356] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _578354), _578356), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _578356, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _578354), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_RComplete_Onatfloor(_578356) = _578354)], (12129 ^ _221138) ^ [_641495] : [class_Groups_Ocomm__monoid__add(_641495), -(class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(_641495)))], (6450 ^ _221138) ^ [_441871, _441873] : [class_RealVector_Oreal__normed__algebra(_441871), 6454 ^ _221138 : [(6457 ^ _221138) ^ [_442170] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_441871, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_441871), _441873), _442170)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_441871, _442170)), 6453 ^ [_441871, _441873])))], (6455 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 6453 ^ [_441871, _441873]))]]], (12195 ^ _221138) ^ [_643585] : [class_Rings_Ocomm__semiring__1(_643585), -(class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(_643585)))], (964 ^ _221138) ^ [_251729, _251731, _251733, _251735] : [-(c_RealDef_Oreal(_251735, _251731) = c_RealDef_Oreal(_251733, _251729)), _251735 = _251733, _251731 = _251729], (5209 ^ _221138) ^ [_399074, _399076, _399078] : [class_Groups_Oab__group__add(_399074), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_399074), c_Polynomial_OpCons(_399074, _399076, _399078)) = c_Polynomial_OpCons(_399074, c_Groups_Ouminus__class_Ouminus(_399074, _399076), c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_399074), _399078)))], (9331 ^ _221138) ^ [_542216, _542218] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _542216, _542218) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 9336 ^ _221138 : [(9339 ^ _221138) ^ [] : [-(_542218 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9337 ^ _221138) ^ [] : [-(_542216 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 9340 ^ _221138 : [(9343 ^ _221138) ^ [] : [-(_542218 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (9341 ^ _221138) ^ [] : [-(_542216 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (2672 ^ _221138) ^ [_309664, _309666] : [class_Groups_Ocomm__monoid__add(_309664), -(c_Groups_Oplus__class_Oplus(_309664, c_Groups_Ozero__class_Ozero(_309664), _309666) = _309666)], (11909 ^ _221138) ^ [] : [-(class_Rings_Oring(tc_RealDef_Oreal))], (9101 ^ _221138) ^ [_534007, _534009] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_534009), _534007), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _534007, _534009)], (12015 ^ _221138) ^ [_637885] : [class_Rings_Olinordered__idom(_637885), -(class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(_637885)))], (11659 ^ _221138) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (4754 ^ _221138) ^ [_381768, _381770, _381772, _381774, _381776] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_381768), 4757 ^ _221138 : [(4758 ^ _221138) ^ [] : [c_Groups_Oplus__class_Oplus(_381768, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_381768), _381770), _381774), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_381768), _381772), _381776)) = c_Groups_Oplus__class_Oplus(_381768, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_381768), _381770), _381776), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_381768), _381772), _381774)), -(_381770 = _381772), -(_381774 = _381776)], (4768 ^ _221138) ^ [] : [-(c_Groups_Oplus__class_Oplus(_381768, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_381768), _381770), _381774), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_381768), _381772), _381776)) = c_Groups_Oplus__class_Oplus(_381768, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_381768), _381770), _381776), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_381768), _381772), _381774))), 4771 ^ _221138 : [(4774 ^ _221138) ^ [] : [_381774 = _381776], (4772 ^ _221138) ^ [] : [_381770 = _381772]]]]], (11661 ^ _221138) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (3460 ^ _221138) ^ [_336615, _336617, _336619, _336621, _336623] : [class_Groups_Oordered__cancel__ab__semigroup__add(_336615), c_Orderings_Oord__class_Oless__eq(_336615, _336617, _336619), c_Orderings_Oord__class_Oless(_336615, _336621, _336623), -(c_Orderings_Oord__class_Oless(_336615, c_Groups_Oplus__class_Oplus(_336615, _336617, _336621), c_Groups_Oplus__class_Oplus(_336615, _336619, _336623)))], (2402 ^ _221138) ^ [_299582, _299584, _299586, _299588] : [class_Groups_Ocancel__semigroup__add(_299582), c_Groups_Oplus__class_Oplus(_299582, _299584, _299586) = c_Groups_Oplus__class_Oplus(_299582, _299588, _299586), -(_299584 = _299588)], (1816 ^ _221138) ^ [_279857, _279859, _279861] : [class_Int_Oring__char__0(_279857), class_Rings_Oidom(_279857), 1823 ^ _221138 : [(1830 ^ _221138) ^ [] : [_279859 = _279861, -(c_Polynomial_Opoly(_279857, _279859) = c_Polynomial_Opoly(_279857, _279861))], (1824 ^ _221138) ^ [] : [c_Polynomial_Opoly(_279857, _279859) = c_Polynomial_Opoly(_279857, _279861), -(_279859 = _279861)]]], (7667 ^ _221138) ^ [_485106, _485108] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _485106, _485108), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _485108, _485106)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _485108, _485106), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _485106, _485108))], (12303 ^ _221138) ^ [_647005] : [class_Rings_Ocomm__ring__1(_647005), -(class_Rings_Oring__1(tc_Polynomial_Opoly(_647005)))], (7387 ^ _221138) ^ [_475001, _475003, _475005] : [class_Rings_Oidom(_475001), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_475001), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_475001)), c_Polynomial_OpCons(_475001, c_Groups_Ouminus__class_Ouminus(_475001, _475003), c_Polynomial_OpCons(_475001, c_Groups_Oone__class_Oone(_475001), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_475001))))), c_Polynomial_Oorder(_475001, _475003, _475005)), _475005))], (8709 ^ _221138) ^ [_520355, _520357] : [-(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, _520355)), _520357)))], (8131 ^ _221138) ^ [_500429, _500431] : [class_Groups_Omonoid__mult(_500429), -(hAPP(hAPP(c_Power_Opower__class_Opower(_500429), _500431), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _500431)], (9087 ^ _221138) ^ [_533503, _533505] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_533503), c_Nat_OSuc(_533505)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _533503, _533505))], (8025 ^ _221138) ^ [_496380, _496382] : [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, _496380)), _496382)), _496380 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_496382 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7359 ^ _221138) ^ [_473953, _473955, _473957] : [class_Rings_Odvd(_473953), class_Rings_Osemiring__0(_473953), 7366 ^ _221138 : [(7376 ^ _221138) ^ [] : [-(hBOOL(hAPP(_473955, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_473953), _473957), 7383 ^ [_473953, _473955, _473957])))), 7377 ^ _221138 : [(7378 ^ _221138) ^ [_474602] : [c_Rings_Odvd__class_Odvd(_473953, _473957, c_Groups_Oplus__class_Oplus(_473953, _474602, c_Groups_Ozero__class_Ozero(_473953))), hBOOL(hAPP(_473955, _474602))]]], (7367 ^ _221138) ^ [] : [7368 ^ _221138 : [(7369 ^ _221138) ^ [_474262] : [hBOOL(hAPP(_473955, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_473953), _473957), _474262)))]], 7371 ^ _221138 : [(7374 ^ _221138) ^ [] : [-(hBOOL(hAPP(_473955, 7370 ^ [_473953, _473955, _473957])))], (7372 ^ _221138) ^ [] : [-(c_Rings_Odvd__class_Odvd(_473953, _473957, c_Groups_Oplus__class_Oplus(_473953, 7370 ^ [_473953, _473955, _473957], c_Groups_Ozero__class_Ozero(_473953))))]]]]], (2738 ^ _221138) ^ [_311930, _311932, _311934, _311936] : [class_Groups_Oordered__ab__semigroup__add(_311930), c_Orderings_Oord__class_Oless__eq(_311930, _311932, _311934), -(c_Orderings_Oord__class_Oless__eq(_311930, c_Groups_Oplus__class_Oplus(_311930, _311932, _311936), c_Groups_Oplus__class_Oplus(_311930, _311934, _311936)))], (8587 ^ _221138) ^ [_516276, _516278, _516280] : [-(_516276 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 8590 ^ _221138 : [(8597 ^ _221138) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _516276), _516278), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _516276), _516280)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _516278, _516280))], (8591 ^ _221138) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _516278, _516280), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _516276), _516278), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _516276), _516280)))]]], (11809 ^ _221138) ^ [] : [-(class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal))], (294 ^ _221138) ^ [_230171, _230173] : [-(class_Rings_Oring__no__zero__divisors(_230171)), _230173 = _230171, class_Rings_Oring__no__zero__divisors(_230173)], (11057 ^ _221138) ^ [_606522, _606524, _606526] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _606522, _606524), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _606522, _606526), 11064 ^ _221138 : [(11071 ^ _221138) ^ [] : [_606524 = _606526, -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _606524, _606522) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _606526, _606522))], (11065 ^ _221138) ^ [] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _606524, _606522) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _606526, _606522), -(_606524 = _606526)]]], (3114 ^ _221138) ^ [_325294, _325296, _325298, _325300] : [class_Rings_Ocomm__semiring__0(_325294), -(hAPP(c_Polynomial_Opoly(_325294, c_Polynomial_OpCons(_325294, _325296, _325298)), _325300) = c_Groups_Oplus__class_Oplus(_325294, _325296, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_325294), _325300), hAPP(c_Polynomial_Opoly(_325294, _325298), _325300))))], (114 ^ _221138) ^ [_224861, _224863] : [-(class_RealVector_Oreal__normed__div__algebra(_224861)), _224863 = _224861, class_RealVector_Oreal__normed__div__algebra(_224863)], (1134 ^ _221138) ^ [_257950, _257952] : [class_RealVector_Oreal__normed__vector(_257950), 1137 ^ _221138 : [(1144 ^ _221138) ^ [] : [_257952 = c_Groups_Ozero__class_Ozero(_257950), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_257950, _257952), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (1138 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_257950, _257952), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(_257952 = c_Groups_Ozero__class_Ozero(_257950))]]], (4120 ^ _221138) ^ [_358260, _358262, _358264, _358266] : [class_Groups_Oordered__comm__monoid__add(_358260), c_Orderings_Oord__class_Oless__eq(_358260, c_Groups_Ozero__class_Ozero(_358260), _358262), c_Orderings_Oord__class_Oless(_358260, _358264, _358266), -(c_Orderings_Oord__class_Oless(_358260, _358264, c_Groups_Oplus__class_Oplus(_358260, _358262, _358266)))], (9984 ^ _221138) ^ [] : [-(c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (11753 ^ _221138) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (1988 ^ _221138) ^ [_285169, _285171, _285173] : [class_Orderings_Oorder(_285169), -(_285171 = _285173), c_Orderings_Oord__class_Oless__eq(_285169, _285171, _285173), -(c_Orderings_Oord__class_Oless(_285169, _285171, _285173))], (10083 ^ _221138) ^ [_568378, _568380] : [-(c_RealDef_Oreal(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _568378), _568380)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _568378)), _568380))], (9496 ^ _221138) ^ [_548040, _548042, _548044] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _548042, _548044), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_548040)), _548042), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_548040)), _548044)))], (7805 ^ _221138) ^ [_489271, _489273] : [_489271 = _489273, c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _489271, _489273), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _489273, _489271))], (10788 ^ _221138) ^ [_596178, _596180, _596182, _596184] : [class_Rings_Ocomm__ring(_596178), -(hAPP(c_Polynomial_Opoly(_596178, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_596178), _596180, _596182)), _596184) = c_Groups_Ominus__class_Ominus(_596178, hAPP(c_Polynomial_Opoly(_596178, _596180), _596184), hAPP(c_Polynomial_Opoly(_596178, _596182), _596184)))], (11899 ^ _221138) ^ [] : [-(class_Groups_Oabs__if(tc_RealDef_Oreal))], (2510 ^ _221138) ^ [_303701, _303703, _303705, _303707] : [class_Groups_Oab__semigroup__add(_303701), -(c_Groups_Oplus__class_Oplus(_303701, c_Groups_Oplus__class_Oplus(_303701, _303703, _303705), _303707) = c_Groups_Oplus__class_Oplus(_303701, _303703, c_Groups_Oplus__class_Oplus(_303701, _303705, _303707)))], (2694 ^ _221138) ^ [_310366, _310368] : [class_Groups_Omonoid__add(_310366), -(c_Groups_Oplus__class_Oplus(_310366, _310368, c_Groups_Ozero__class_Ozero(_310366)) = _310368)], (5555 ^ _221138) ^ [_410890, _410892, _410894] : [class_Groups_Ogroup__add(_410890), -(c_Groups_Oplus__class_Oplus(_410890, c_Groups_Ouminus__class_Ouminus(_410890, _410892), c_Groups_Oplus__class_Oplus(_410890, _410892, _410894)) = _410894)], (12261 ^ _221138) ^ [_645675] : [class_Rings_Olinordered__idom(_645675), -(class_Orderings_Oorder(tc_Polynomial_Opoly(_645675)))], (9852 ^ _221138) ^ [_560258, _560260, _560262, _560264, _560266] : [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), _560258), _560260), _560262), c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _560258), _560264), _560266)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _560266, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _560258, _560266), c_Orderings_Oord__class_Oless(tc_Int_Oint, _560258, _560262), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _560264, _560260))], (5857 ^ _221138) ^ [_420813, _420815, _420817] : [class_Groups_Oordered__ab__group__add__abs(_420813), c_Orderings_Oord__class_Oless__eq(_420813, _420815, _420817), c_Orderings_Oord__class_Oless__eq(_420813, c_Groups_Ouminus__class_Ouminus(_420813, _420815), _420817), -(c_Orderings_Oord__class_Oless__eq(_420813, c_Groups_Oabs__class_Oabs(_420813, _420815), _420817))], (474 ^ _221138) ^ [_235481, _235483] : [-(class_Orderings_Opreorder(_235481)), _235483 = _235481, class_Orderings_Opreorder(_235483)], (2666 ^ _221138) ^ [_309444, _309446] : [class_Groups_Omonoid__add(_309444), -(c_Groups_Oplus__class_Oplus(_309444, c_Groups_Ozero__class_Ozero(_309444), _309446) = _309446)], (1103 ^ _221138) ^ [_256913] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _256913), 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____), _256913)), v_m____))], (2314 ^ _221138) ^ [_295863] : [-(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, _295863) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _295863))], (3514 ^ _221138) ^ [_338358, _338360, _338362] : [class_Rings_Olinordered__ring__strict(_338358), 3517 ^ _221138 : [(3532 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_338358, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_338358), _338360), _338362), c_Groups_Ozero__class_Ozero(_338358))), 3533 ^ _221138 : [(3540 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_338358, _338360, c_Groups_Ozero__class_Ozero(_338358)), c_Orderings_Oord__class_Oless__eq(_338358, c_Groups_Ozero__class_Ozero(_338358), _338362)], (3534 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_338358, c_Groups_Ozero__class_Ozero(_338358), _338360), c_Orderings_Oord__class_Oless__eq(_338358, _338362, c_Groups_Ozero__class_Ozero(_338358))]]], (3518 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_338358, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_338358), _338360), _338362), c_Groups_Ozero__class_Ozero(_338358)), 3523 ^ _221138 : [(3526 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_338358, _338362, c_Groups_Ozero__class_Ozero(_338358)))], (3524 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_338358, c_Groups_Ozero__class_Ozero(_338358), _338360))]], 3527 ^ _221138 : [(3530 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_338358, c_Groups_Ozero__class_Ozero(_338358), _338362))], (3528 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_338358, _338360, c_Groups_Ozero__class_Ozero(_338358)))]]]]], (9163 ^ _221138) ^ [_536183, _536185] : [c_Nat_OSuc(_536183) = c_Nat_OSuc(_536185), -(_536183 = _536185)], (10384 ^ _221138) ^ [_579540, _579542] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _579540), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _579542), 10392 ^ _221138 : [(10397 ^ _221138) ^ [_580044] : [-(_580044 = 10391 ^ [_579540, _579542]), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _580044), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _580044), _579540) = _579542], (10395 ^ _221138) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), 10391 ^ [_579540, _579542]), _579540) = _579542)], (10393 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 10391 ^ [_579540, _579542]))]]], (5871 ^ _221138) ^ [_421245, _421247, _421249] : [class_Groups_Oordered__ab__group__add__abs(_421245), c_Orderings_Oord__class_Oless__eq(_421245, c_Groups_Oabs__class_Oabs(_421245, _421247), _421249), -(c_Orderings_Oord__class_Oless__eq(_421245, c_Groups_Ouminus__class_Ouminus(_421245, _421247), _421249))], (3236 ^ _221138) ^ [_329542, _329544, _329546] : [-(_329542 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 3239 ^ _221138 : [(3246 ^ _221138) ^ [] : [_329544 = _329546, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _329542), _329544) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _329542), _329546))], (3240 ^ _221138) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _329542), _329544) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _329542), _329546), -(_329544 = _329546)]]], (11161 ^ _221138) ^ [_610436, _610438] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _610436, _610438), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _610436, _610438) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6769 ^ _221138) ^ [_453658, _453660] : [class_Rings_Olinordered__idom(_453658), 6772 ^ _221138 : [(6779 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_453658, _453660, c_Groups_Ozero__class_Ozero(_453658)), -(c_Orderings_Oord__class_Oless(_453658, c_Groups_Osgn__class_Osgn(_453658, _453660), c_Groups_Ozero__class_Ozero(_453658)))], (6773 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_453658, c_Groups_Osgn__class_Osgn(_453658, _453660), c_Groups_Ozero__class_Ozero(_453658)), -(c_Orderings_Oord__class_Oless(_453658, _453660, c_Groups_Ozero__class_Ozero(_453658)))]]], (5363 ^ _221138) ^ [_404109, _404111] : [class_Groups_Olinordered__ab__group__add(_404109), 5366 ^ _221138 : [(5373 ^ _221138) ^ [] : [_404111 = c_Groups_Ozero__class_Ozero(_404109), -(c_Groups_Ouminus__class_Ouminus(_404109, _404111) = _404111)], (5367 ^ _221138) ^ [] : [c_Groups_Ouminus__class_Ouminus(_404109, _404111) = _404111, -(_404111 = c_Groups_Ozero__class_Ozero(_404109))]]], (11863 ^ _221138) ^ [] : [-(class_Groups_Oab__group__add(tc_RealDef_Oreal))], (2422 ^ _221138) ^ [_300304, _300306, _300308, _300310] : [class_Groups_Ocancel__semigroup__add(_300304), c_Groups_Oplus__class_Oplus(_300304, _300306, _300308) = c_Groups_Oplus__class_Oplus(_300304, _300306, _300310), -(_300308 = _300310)], (12201 ^ _221138) ^ [_643775] : [class_Rings_Olinordered__idom(_643775), -(class_Rings_Oordered__ring(tc_Polynomial_Opoly(_643775)))], (9295 ^ _221138) ^ [_541068] : [_541068 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _541068, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (6153 ^ _221138) ^ [_430994] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _430994), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3446 ^ _221138) ^ [_336123, _336125, _336127, _336129, _336131] : [class_Groups_Oordered__cancel__ab__semigroup__add(_336123), c_Orderings_Oord__class_Oless(_336123, _336125, _336127), c_Orderings_Oord__class_Oless__eq(_336123, _336129, _336131), -(c_Orderings_Oord__class_Oless(_336123, c_Groups_Oplus__class_Oplus(_336123, _336125, _336129), c_Groups_Oplus__class_Oplus(_336123, _336127, _336131)))], (9826 ^ _221138) ^ [_559385, _559387, _559389, _559391, _559393, _559395] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _559385), _559387), _559389) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _559391), _559393), _559395), 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), _559391), _559393), _559395), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _559389, _559385), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _559395), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _559391), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _559391, _559385), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _559393, _559387))], (7015 ^ _221138) ^ [_462095] : [_462095 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, _462095) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (4318 ^ _221138) ^ [_364806, _364808, _364810, _364812] : [class_Rings_Olinordered__semiring(_364806), c_Orderings_Oord__class_Oless(_364806, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_364806), _364808), _364810), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_364806), _364808), _364812)), c_Orderings_Oord__class_Oless__eq(_364806, c_Groups_Ozero__class_Ozero(_364806), _364808), -(c_Orderings_Oord__class_Oless(_364806, _364810, _364812))], (3194 ^ _221138) ^ [_328206, _328208] : [class_Groups_Oordered__ab__group__add__abs(_328206), 3197 ^ _221138 : [(3204 ^ _221138) ^ [] : [-(_328208 = c_Groups_Ozero__class_Ozero(_328206)), -(c_Orderings_Oord__class_Oless(_328206, c_Groups_Ozero__class_Ozero(_328206), c_Groups_Oabs__class_Oabs(_328206, _328208)))], (3198 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_328206, c_Groups_Ozero__class_Ozero(_328206), c_Groups_Oabs__class_Oabs(_328206, _328208)), _328208 = c_Groups_Ozero__class_Ozero(_328206)]]], (1072 ^ _221138) ^ [_255646, _255648, _255650, _255652] : [-(c_Polynomial_Opoly(_255652, _255648) = c_Polynomial_Opoly(_255650, _255646)), _255652 = _255650, _255648 = _255646], (4911 ^ _221138) ^ [_388035, _388037] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _388035, _388037), -(_388037 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _388035, 4914 ^ [_388035, _388037]))], (11987 ^ _221138) ^ [] : [-(class_Groups_Oone(tc_Complex_Ocomplex))], (6089 ^ _221138) ^ [_428771, _428773, _428775, _428777] : [-(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, _428771, _428773), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _428775), c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _428777)))), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _428771, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _428775))), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _428773, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _428777))))))], (11775 ^ _221138) ^ [] : [-(class_Rings_Odvd(tc_Nat_Onat))], (9490 ^ _221138) ^ [_547836, _547838, _547840] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_547836)), _547838), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_547836)), _547840)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _547838, _547840))], (6467 ^ _221138) ^ [_442703, _442705, _442707] : [_442703 = _442707, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _442703, _442705) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _442707, _442705))], (5105 ^ _221138) ^ [_395215, _395217, _395219, _395221] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _395215, _395217), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _395219, _395217) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _395215, _395221), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _395219, _395221))], (11625 ^ _221138) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (2912 ^ _221138) ^ [_318074, _318076, _318078] : [class_Rings_Ono__zero__divisors(_318074), -(_318076 = c_Groups_Ozero__class_Ozero(_318074)), -(_318078 = c_Groups_Ozero__class_Ozero(_318074)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_318074), _318076), _318078) = c_Groups_Ozero__class_Ozero(_318074)], (344 ^ _221138) ^ [_231646, _231648] : [-(class_Groups_Ocancel__semigroup__add(_231646)), _231648 = _231646, class_Groups_Ocancel__semigroup__add(_231648)], (5331 ^ _221138) ^ [_403157, _403159] : [class_Groups_Olinordered__ab__group__add(_403157), 5334 ^ _221138 : [(5341 ^ _221138) ^ [] : [_403159 = c_Groups_Ozero__class_Ozero(_403157), -(_403159 = c_Groups_Ouminus__class_Ouminus(_403157, _403159))], (5335 ^ _221138) ^ [] : [_403159 = c_Groups_Ouminus__class_Ouminus(_403157, _403159), -(_403159 = c_Groups_Ozero__class_Ozero(_403157))]]], (5203 ^ _221138) ^ [_398806, _398808, _398810] : [class_Rings_Ocomm__ring(_398806), -(hAPP(c_Polynomial_Opoly(_398806, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_398806), _398808)), _398810) = c_Groups_Ouminus__class_Ouminus(_398806, hAPP(c_Polynomial_Opoly(_398806, _398808), _398810)))], (9107 ^ _221138) ^ [_534257, _534259] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _534257, c_Nat_OSuc(_534259)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _534257, _534259)), -(_534257 = c_Nat_OSuc(_534259))], (4380 ^ _221138) ^ [_366925, _366927, _366929] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _366925), 4383 ^ _221138 : [(4390 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _366927, _366929), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _366927), _366925), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _366929), _366925)))], (4384 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _366927), _366925), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _366929), _366925)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _366927, _366929))]]], (12075 ^ _221138) ^ [_639785] : [class_Rings_Oidom(_639785), -(class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(_639785)))], (8615 ^ _221138) ^ [_517233, _517235, _517237] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _517233, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _517235, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _517233), _517237))), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _517233, _517235))], (284 ^ _221138) ^ [_229876, _229878] : [-(class_Rings_Olinordered__ring__strict(_229876)), _229878 = _229876, class_Rings_Olinordered__ring__strict(_229878)], (12063 ^ _221138) ^ [_639405] : [class_Rings_Olinordered__idom(_639405), -(class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(_639405)))], (12171 ^ _221138) ^ [_642825] : [class_Rings_Ocomm__semiring__1(_642825), -(class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(_642825)))], (8565 ^ _221138) ^ [_515588] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(_515588)))], (10866 ^ _221138) ^ [_599501, _599503, _599505, _599507, _599509] : [class_Groups_Oordered__ab__group__add(_599501), c_Groups_Ominus__class_Ominus(_599501, _599503, _599505) = c_Groups_Ominus__class_Ominus(_599501, _599507, _599509), 10873 ^ _221138 : [(10880 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_599501, _599507, _599509), -(c_Orderings_Oord__class_Oless(_599501, _599503, _599505))], (10874 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_599501, _599503, _599505), -(c_Orderings_Oord__class_Oless(_599501, _599507, _599509))]]], (11781 ^ _221138) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (6527 ^ _221138) ^ [_445217, _445219] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _445217), _445219)), _445217 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _445219 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (11851 ^ _221138) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal))], (9942 ^ _221138) ^ [_563237, _563239] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _563237), -(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), _563237), _563239)))], (11907 ^ _221138) ^ [] : [-(class_Groups_Ozero(tc_RealDef_Oreal))], (10191 ^ _221138) ^ [_572280, _572282] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _572280), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), c_RealDef_Oreal(tc_Nat_Onat, _572282)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _572280, _572282))], (7177 ^ _221138) ^ [_467623, _467625, _467627] : [class_Rings_Olinordered__idom(_467623), c_Groups_Oabs__class_Oabs(_467623, _467625) = c_Groups_Oabs__class_Oabs(_467623, _467627), -(c_Rings_Odvd__class_Odvd(_467623, _467625, _467627))], (8775 ^ _221138) ^ [_522553, _522555] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _522553, _522555), 8778 ^ _221138 : [(8781 ^ _221138) ^ [] : [_522553 = _522555], (8779 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _522553, _522555))]]], (6643 ^ _221138) ^ [_449417, _449419, _449421] : [class_Lattices_Oboolean__algebra(_449417), c_Orderings_Oord__class_Oless__eq(_449417, _449419, _449421), -(c_Orderings_Oord__class_Oless__eq(_449417, c_Groups_Ouminus__class_Ouminus(_449417, _449421), c_Groups_Ouminus__class_Ouminus(_449417, _449419)))], (11437 ^ _221138) ^ [_620915] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _620915), -(c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _620915, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = _620915)], (10520 ^ _221138) ^ [_585231, _585233, _585235, _585237] : [class_Rings_Ocomm__ring(_585231), class_Rings_Odvd(_585231), c_Rings_Odvd__class_Odvd(_585231, _585233, _585235), 10531 ^ _221138 : [(10538 ^ _221138) ^ [_585872, _585874] : [c_Rings_Odvd__class_Odvd(_585231, _585233, c_Groups_Oplus__class_Oplus(_585231, c_Groups_Ominus__class_Ominus(_585231, _585874, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_585231), _585872), _585235)), _585237)), -(c_Rings_Odvd__class_Odvd(_585231, _585233, c_Groups_Oplus__class_Oplus(_585231, _585874, _585237)))], (10532 ^ _221138) ^ [_585634, _585636] : [c_Rings_Odvd__class_Odvd(_585231, _585233, c_Groups_Oplus__class_Oplus(_585231, _585636, _585237)), -(c_Rings_Odvd__class_Odvd(_585231, _585233, c_Groups_Oplus__class_Oplus(_585231, c_Groups_Ominus__class_Ominus(_585231, _585636, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_585231), _585634), _585235)), _585237)))]]], (7171 ^ _221138) ^ [_467399, _467401] : [class_Rings_Ocomm__semiring__1(_467399), -(c_Rings_Odvd__class_Odvd(_467399, _467401, _467401))], (1490 ^ _221138) ^ [_269511, _269513, _269515] : [class_Orderings_Olinorder(_269511), -(c_Orderings_Oord__class_Oless(_269511, _269513, _269515)), -(_269513 = _269515), -(c_Orderings_Oord__class_Oless(_269511, _269515, _269513))], (4868 ^ _221138) ^ [_386212, _386214] : [class_Rings_Olinordered__idom(_386212), 4871 ^ _221138 : [(4878 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_386212, _386214, c_Groups_Ozero__class_Ozero(_386212)), -(c_Orderings_Oord__class_Oless(_386212, c_Groups_Oplus__class_Oplus(_386212, _386214, _386214), c_Groups_Ozero__class_Ozero(_386212)))], (4872 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_386212, c_Groups_Oplus__class_Oplus(_386212, _386214, _386214), c_Groups_Ozero__class_Ozero(_386212)), -(c_Orderings_Oord__class_Oless(_386212, _386214, c_Groups_Ozero__class_Ozero(_386212)))]]], (11607 ^ _221138) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (5411 ^ _221138) ^ [_405620, _405622, _405624] : [class_Groups_Oordered__ab__group__add(_405620), 5414 ^ _221138 : [(5421 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_405620, _405624, _405622), -(c_Orderings_Oord__class_Oless__eq(_405620, c_Groups_Ouminus__class_Ouminus(_405620, _405622), c_Groups_Ouminus__class_Ouminus(_405620, _405624)))], (5415 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_405620, c_Groups_Ouminus__class_Ouminus(_405620, _405622), c_Groups_Ouminus__class_Ouminus(_405620, _405624)), -(c_Orderings_Oord__class_Oless__eq(_405620, _405624, _405622))]]], (2282 ^ _221138) ^ [_294927, _294929, _294931] : [class_Rings_Olinordered__idom(_294927), -(_294929 = _294931), -(c_Orderings_Oord__class_Oless(_294927, _294929, _294931)), -(c_Orderings_Oord__class_Oless(_294927, _294931, _294929))], (4454 ^ _221138) ^ [_369443, _369445, _369447, _369449] : [class_RealVector_Oreal__normed__vector(_369443), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _369445, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_369443, _369447), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _369445), c_RealVector_Onorm__class_Onorm(_369443, _369449))), -(_369447 = c_Groups_Ozero__class_Ozero(_369443))], (8567 ^ _221138) ^ [_515669] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _515669))], (10018 ^ _221138) ^ [_565927, _565929] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _565927), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _565929), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_RComplete_Onatfloor(_565927)), c_RComplete_Onatfloor(_565929)), c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _565927), _565929))))], (8491 ^ _221138) ^ [_512923, _512925, _512927, _512929] : [class_Rings_Olinordered__semidom(_512923), c_Orderings_Oord__class_Oless(_512923, c_Groups_Oone__class_Oone(_512923), _512925), c_Orderings_Oord__class_Oless__eq(_512923, hAPP(hAPP(c_Power_Opower__class_Opower(_512923), _512925), _512927), hAPP(hAPP(c_Power_Opower__class_Opower(_512923), _512925), _512929)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _512927, _512929))], (12321 ^ _221138) ^ [_647575] : [class_Groups_Ozero(_647575), -(class_Groups_Ozero(tc_Polynomial_Opoly(_647575)))], (7501 ^ _221138) ^ [_479579, _479581, _479583, _479585] : [class_Rings_Ocomm__semiring__1(_479579), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_479579), hAPP(hAPP(c_Power_Opower__class_Opower(_479579), _479581), _479583)), hAPP(hAPP(c_Power_Opower__class_Opower(_479579), _479581), _479585)) = hAPP(hAPP(c_Power_Opower__class_Opower(_479579), _479581), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _479583, _479585)))], (11397 ^ _221138) ^ [_619150] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _619150, _619150) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5591 ^ _221138) ^ [_412338] : [class_Groups_Oab__group__add(_412338), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_412338), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_412338))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_412338)))], (11361 ^ _221138) ^ [_617812, _617814, _617816] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_617812), _617814), c_Nat_OSuc(_617816)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _617812, _617814), _617816))], (11241 ^ _221138) ^ [_613222, _613224, _613226] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _613222, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _613224, _613226)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _613222, _613224), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _613226, _613224), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _613222, _613226))], (8817 ^ _221138) ^ [_523952, _523954] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _523952, c_Groups_Oone__class_Oone(tc_Int_Oint)), _523954), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _523952, _523954))], (11859 ^ _221138) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal))], (8181 ^ _221138) ^ [_502198, _502200, _502202] : [class_Power_Opower(_502198), class_Rings_Omult__zero(_502198), class_Rings_Ono__zero__divisors(_502198), class_Rings_Ozero__neq__one(_502198), 8196 ^ _221138 : [(8205 ^ _221138) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_502198), _502200), _502202) = c_Groups_Ozero__class_Ozero(_502198)), _502200 = c_Groups_Ozero__class_Ozero(_502198), -(_502202 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8197 ^ _221138) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_502198), _502200), _502202) = c_Groups_Ozero__class_Ozero(_502198), 8200 ^ _221138 : [(8203 ^ _221138) ^ [] : [_502202 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (8201 ^ _221138) ^ [] : [-(_502200 = c_Groups_Ozero__class_Ozero(_502198))]]]]], (774 ^ _221138) ^ [_244387, _244389, _244391, _244393, _244395, _244397] : [-(c_Orderings_Oord__class_Oless(_244395, _244391, _244387)), c_Orderings_Oord__class_Oless(_244397, _244393, _244389), _244397 = _244395, _244393 = _244391, _244389 = _244387], (324 ^ _221138) ^ [_231056, _231058] : [-(class_Groups_Oordered__ab__group__add(_231056)), _231058 = _231056, class_Groups_Oordered__ab__group__add(_231058)], (8569 ^ _221138) ^ [_515777, _515779] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _515777), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _515779), c_Rings_Odvd__class_Odvd(tc_Int_Oint, _515777, _515779), c_Rings_Odvd__class_Odvd(tc_Int_Oint, _515779, _515777), -(_515777 = _515779)], (9896 ^ _221138) ^ [_561768, _561770, _561772, _561774, _561776] : [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), _561768), _561770), _561772), c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _561768), _561774), _561776)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _561772), c_Orderings_Oord__class_Oless(tc_Int_Oint, _561772, _561768), c_Orderings_Oord__class_Oless(tc_Int_Oint, _561776, _561768), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _561770, _561774))], (11101 ^ _221138) ^ [_608149, _608151, _608153] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _608149, _608151), _608153) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _608149, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _608151, _608153)))], (8171 ^ _221138) ^ [_501849, _501851, _501853] : [class_Rings_Olinordered__semidom(_501849), c_Orderings_Oord__class_Oless__eq(_501849, c_Groups_Oone__class_Oone(_501849), _501851), -(c_Orderings_Oord__class_Oless__eq(_501849, c_Groups_Oone__class_Oone(_501849), hAPP(hAPP(c_Power_Opower__class_Opower(_501849), _501851), _501853)))], (9125 ^ _221138) ^ [_534848, _534850] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_534848), c_Nat_OSuc(_534850)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _534848, _534850))], (10117 ^ _221138) ^ [_569683] : [c_RealDef_Oreal(tc_Nat_Onat, _569683) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_569683 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8693 ^ _221138) ^ [_519877, _519879] : [-(_519877 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 8696 ^ _221138 : [(8703 ^ _221138) ^ [] : [c_Groups_Oabs__class_Oabs(tc_Int_Oint, _519879) = 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), _519877), _519879), _519877))], (8697 ^ _221138) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _519877), _519879), _519877), -(c_Groups_Oabs__class_Oabs(tc_Int_Oint, _519879) = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (7605 ^ _221138) ^ [_483096, _483098] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _483096), 7608 ^ _221138 : [(7615 ^ _221138) ^ [] : [_483098 = 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), _483098), _483096), _483096))], (7609 ^ _221138) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _483098), _483096), _483096), -(_483098 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (6389 ^ _221138) ^ [_439222, _439224] : [class_RealVector_Oreal__normed__vector(_439222), 6392 ^ _221138 : [(6403 ^ _221138) ^ [] : [-(c_SEQ_OBseq(_439222, _439224)), 6404 ^ _221138 : [(6405 ^ _221138) ^ [_439848] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _439848), 6409 ^ _221138 : [(6410 ^ _221138) ^ [_440057] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_439222, c_Groups_Oplus__class_Oplus(_439222, hAPP(_439224, 6408 ^ [_439222, _439224, _439848, _440057]), c_Groups_Ouminus__class_Ouminus(_439222, _440057))), _439848)]]]]], (6393 ^ _221138) ^ [] : [c_SEQ_OBseq(_439222, _439224), 6397 ^ _221138 : [(6401 ^ _221138) ^ [_439702] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_439222, c_Groups_Oplus__class_Oplus(_439222, hAPP(_439224, _439702), c_Groups_Ouminus__class_Ouminus(_439222, 6399 ^ [_439222, _439224]))), 6396 ^ [_439222, _439224]))], (6398 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 6396 ^ [_439222, _439224]))]]]]], (11835 ^ _221138) ^ [] : [-(class_Rings_Olinordered__semiring(tc_RealDef_Oreal))], (3970 ^ _221138) ^ [_353244, _353246, _353248] : [class_Rings_Olinordered__ring__strict(_353244), c_Orderings_Oord__class_Oless(_353244, _353246, c_Groups_Ozero__class_Ozero(_353244)), c_Orderings_Oord__class_Oless(_353244, _353248, c_Groups_Ozero__class_Ozero(_353244)), -(c_Orderings_Oord__class_Oless(_353244, c_Groups_Ozero__class_Ozero(_353244), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_353244), _353246), _353248)))], (10644 ^ _221138) ^ [_590459, _590461] : [class_Groups_Ogroup__add(_590459), -(c_Groups_Ominus__class_Ominus(_590459, c_Groups_Ozero__class_Ozero(_590459), _590461) = c_Groups_Ouminus__class_Ouminus(_590459, _590461))], (8023 ^ _221138) ^ [_496212, _496214, _496216] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _496212), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _496214, _496216)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _496212), _496214)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _496212), _496216)))], (6491 ^ _221138) ^ [_443823, _443825] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _443823), _443825) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 6494 ^ _221138 : [(6497 ^ _221138) ^ [] : [-(_443825 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (6495 ^ _221138) ^ [] : [-(_443823 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (8011 ^ _221138) ^ [_495774, _495776] : [-(_495774 = _495776), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _495774, _495776), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _495776, _495774)], (3646 ^ _221138) ^ [_342629, _342631, _342633, _342635] : [class_Rings_Oordered__comm__semiring(_342629), c_Orderings_Oord__class_Oless__eq(_342629, _342631, _342633), c_Orderings_Oord__class_Oless__eq(_342629, c_Groups_Ozero__class_Ozero(_342629), _342635), -(c_Orderings_Oord__class_Oless__eq(_342629, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_342629), _342635), _342631), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_342629), _342635), _342633)))], (2022 ^ _221138) ^ [_286179, _286181, _286183] : [class_Orderings_Olinorder(_286179), -(c_Orderings_Oord__class_Oless__eq(_286179, _286181, _286183)), -(c_Orderings_Oord__class_Oless(_286179, _286183, _286181))], (1036 ^ _221138) ^ [_254351, _254353, _254355, _254357] : [-(c_fequal(_254357, _254353) = c_fequal(_254355, _254351)), _254357 = _254355, _254353 = _254351], (11083 ^ _221138) ^ [_607361, _607363, _607365] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _607361, _607363), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _607361, _607365), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _607363, _607365)))], (958 ^ _221138) ^ [_251483, _251485] : [_251485 = _251483, -(c_RComplete_Onatceiling(_251485) = c_RComplete_Onatceiling(_251483))], (1062 ^ _221138) ^ [_255287, _255289, _255291, _255293] : [-(hAPP(_255293, _255289) = hAPP(_255291, _255287)), _255293 = _255291, _255289 = _255287], (8977 ^ _221138) ^ [_529922, _529924] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _529922, _529924)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _529924, c_Nat_OSuc(_529922)))], (1504 ^ _221138) ^ [_269935, _269937, _269939] : [class_Orderings_Opreorder(_269935), c_Orderings_Oord__class_Oless(_269935, _269937, _269939), c_Orderings_Oord__class_Oless(_269935, _269939, _269937)], (214 ^ _221138) ^ [_227811, _227813] : [-(class_Groups_Oordered__ab__semigroup__add(_227811)), _227813 = _227811, class_Groups_Oordered__ab__semigroup__add(_227813)], (11407 ^ _221138) ^ [_619697, _619699] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _619697, _619699), -(c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _619699, _619697)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _619699), c_RealDef_Oreal(tc_Nat_Onat, _619697)))], (8975 ^ _221138) ^ [_529784] : [c_Nat_OSuc(_529784) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (6155 ^ _221138) ^ [_431136, _431138] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _431136), _431138) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_431136 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_431138 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8767 ^ _221138) ^ [_522232] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _522232), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _522232))], (8927 ^ _221138) ^ [_528009, _528011, _528013] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _528009), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _528011, _528013)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _528009), _528011), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _528009), _528013)))], (9466 ^ _221138) ^ [_546797, _546799] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_546797), _546799), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _546797, _546799))], (2002 ^ _221138) ^ [_285590, _285592, _285594] : [class_Orderings_Olinorder(_285590), -(c_Orderings_Oord__class_Oless(_285590, _285592, _285594)), 2009 ^ _221138 : [(2016 ^ _221138) ^ [] : [_285592 = _285594, -(c_Orderings_Oord__class_Oless__eq(_285590, _285592, _285594))], (2010 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_285590, _285592, _285594), -(_285592 = _285594)]]], (3984 ^ _221138) ^ [_353706, _353708, _353710, _353712] : [class_Rings_Olinordered__semiring__strict(_353706), c_Orderings_Oord__class_Oless(_353706, _353708, _353710), c_Orderings_Oord__class_Oless(_353706, c_Groups_Ozero__class_Ozero(_353706), _353712), -(c_Orderings_Oord__class_Oless(_353706, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_353706), _353708), _353712), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_353706), _353710), _353712)))], (6831 ^ _221138) ^ [_455824, _455826] : [class_Lattices_Oboolean__algebra(_455824), -(c_Groups_Ouminus__class_Ouminus(_455824, c_Groups_Ouminus__class_Ouminus(_455824, _455826)) = _455826)], (9061 ^ _221138) ^ [_532656, _532658, _532660] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _532656, _532658), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _532658, _532660), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_532656), _532660))], (11153 ^ _221138) ^ [_610118, _610120] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _610118, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _610118, _610120)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10085 ^ _221138) ^ [_568476] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _568476, c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatceiling(_568476))))], (9782 ^ _221138) ^ [_557702, _557704, _557706] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _557702, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _557704, _557706)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _557704, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _557702, _557706)))], (3188 ^ _221138) ^ [_327985, _327987] : [class_Groups_Oordered__ab__group__add__abs(_327985), c_Orderings_Oord__class_Oless(_327985, c_Groups_Oabs__class_Oabs(_327985, _327987), c_Groups_Ozero__class_Ozero(_327985))], (204 ^ _221138) ^ [_227516, _227518] : [-(class_Rings_Olinordered__semiring__strict(_227516)), _227518 = _227516, class_Rings_Olinordered__semiring__strict(_227518)], (9994 ^ _221138) ^ [] : [-(c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4484 ^ _221138) ^ [_370529, _370531, _370533] : [class_Rings_Olinordered__ring__strict(_370529), 4487 ^ _221138 : [(4488 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_370529, c_Groups_Ozero__class_Ozero(_370529), c_Groups_Oplus__class_Oplus(_370529, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_370529), _370531), _370531), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_370529), _370533), _370533))), _370531 = c_Groups_Ozero__class_Ozero(_370529), _370533 = c_Groups_Ozero__class_Ozero(_370529)], (4498 ^ _221138) ^ [] : [4499 ^ _221138 : [(4502 ^ _221138) ^ [] : [-(_370533 = c_Groups_Ozero__class_Ozero(_370529))], (4500 ^ _221138) ^ [] : [-(_370531 = c_Groups_Ozero__class_Ozero(_370529))]], -(c_Orderings_Oord__class_Oless(_370529, c_Groups_Ozero__class_Ozero(_370529), c_Groups_Oplus__class_Oplus(_370529, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_370529), _370531), _370531), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_370529), _370533), _370533))))]]], (11585 ^ _221138) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (2772 ^ _221138) ^ [_313152, _313154, _313156, _313158] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_313152), c_Orderings_Oord__class_Oless__eq(_313152, c_Groups_Oplus__class_Oplus(_313152, _313154, _313156), c_Groups_Oplus__class_Oplus(_313152, _313158, _313156)), -(c_Orderings_Oord__class_Oless__eq(_313152, _313154, _313158))], (7315 ^ _221138) ^ [_472471, _472473, _472475, _472477] : [class_Rings_Oidom(_472471), 7318 ^ _221138 : [(7319 ^ _221138) ^ [] : [c_Rings_Odvd__class_Odvd(_472471, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_472471), _472473), _472475), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_472471), _472473), _472477)), -(_472473 = c_Groups_Ozero__class_Ozero(_472471)), -(c_Rings_Odvd__class_Odvd(_472471, _472475, _472477))], (7329 ^ _221138) ^ [] : [7330 ^ _221138 : [(7333 ^ _221138) ^ [] : [c_Rings_Odvd__class_Odvd(_472471, _472475, _472477)], (7331 ^ _221138) ^ [] : [_472473 = c_Groups_Ozero__class_Ozero(_472471)]], -(c_Rings_Odvd__class_Odvd(_472471, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_472471), _472473), _472475), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_472471), _472473), _472477)))]]], (9506 ^ _221138) ^ [_548490, _548492, _548494, _548496] : [class_Rings_Olinordered__semidom(_548490), c_Orderings_Oord__class_Oless__eq(_548490, hAPP(hAPP(c_Power_Opower__class_Opower(_548490), _548492), c_Nat_OSuc(_548494)), hAPP(hAPP(c_Power_Opower__class_Opower(_548490), _548496), c_Nat_OSuc(_548494))), c_Orderings_Oord__class_Oless__eq(_548490, c_Groups_Ozero__class_Ozero(_548490), _548496), -(c_Orderings_Oord__class_Oless__eq(_548490, _548492, _548496))], (10958 ^ _221138) ^ [_602895, _602897, _602899] : [class_Rings_Ocomm__ring__1(_602895), -(c_Groups_Ominus__class_Ominus(_602895, hAPP(hAPP(c_Power_Opower__class_Opower(_602895), _602897), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(hAPP(c_Power_Opower__class_Opower(_602895), _602899), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_602895), c_Groups_Ominus__class_Ominus(_602895, _602897, _602899)), c_Groups_Oplus__class_Oplus(_602895, _602897, _602899)))], (10914 ^ _221138) ^ [_601090, _601092, _601094] : [class_Groups_Ogroup__add(_601090), 10917 ^ _221138 : [(10924 ^ _221138) ^ [] : [_601092 = _601094, -(c_Groups_Ominus__class_Ominus(_601090, _601092, _601094) = c_Groups_Ozero__class_Ozero(_601090))], (10918 ^ _221138) ^ [] : [c_Groups_Ominus__class_Ominus(_601090, _601092, _601094) = c_Groups_Ozero__class_Ozero(_601090), -(_601092 = _601094)]]], (11725 ^ _221138) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (5503 ^ _221138) ^ [_408821, _408823, _408825] : [class_RealVector_Oreal__normed__algebra(_408821), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_408821), c_Groups_Ouminus__class_Ouminus(_408821, _408823)), _408825) = c_Groups_Ouminus__class_Ouminus(_408821, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_408821), _408823), _408825)))], (11921 ^ _221138) ^ [] : [-(class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex))], (7507 ^ _221138) ^ [_479871, _479873] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _479871), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _479871, _479873), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _479873, _479871)], (6895 ^ _221138) ^ [_457942, _457944] : [class_Rings_Olinordered__idom(_457942), 6898 ^ _221138 : [(6905 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_457942, _457944, c_Groups_Ozero__class_Ozero(_457942)), -(c_Groups_Osgn__class_Osgn(_457942, _457944) = c_Groups_Ouminus__class_Ouminus(_457942, c_Groups_Oone__class_Oone(_457942)))], (6899 ^ _221138) ^ [] : [c_Groups_Osgn__class_Osgn(_457942, _457944) = c_Groups_Ouminus__class_Ouminus(_457942, c_Groups_Oone__class_Oone(_457942)), -(c_Orderings_Oord__class_Oless(_457942, _457944, c_Groups_Ozero__class_Ozero(_457942)))]]], (5485 ^ _221138) ^ [_408005, _408007, _408009] : [class_RealVector_Oreal__normed__algebra(_408005), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_408005), _408007), c_Groups_Ouminus__class_Ouminus(_408005, _408009)) = c_Groups_Ouminus__class_Ouminus(_408005, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_408005), _408007), _408009)))], (11771 ^ _221138) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (12285 ^ _221138) ^ [_646435] : [class_Groups_Oab__group__add(_646435), -(class_Groups_Ouminus(tc_Polynomial_Opoly(_646435)))], (9762 ^ _221138) ^ [_556992, _556994, _556996] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _556992, _556994), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _556994, _556996), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _556992, _556996))], (11747 ^ _221138) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (11745 ^ _221138) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (354 ^ _221138) ^ [_231941, _231943] : [-(class_Rings_Olinordered__semiring(_231941)), _231943 = _231941, class_Rings_Olinordered__semiring(_231943)], (2064 ^ _221138) ^ [_287493, _287495, _287497] : [class_Orderings_Opreorder(_287493), 2067 ^ _221138 : [(2076 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(_287493, _287495, _287497)), c_Orderings_Oord__class_Oless__eq(_287493, _287495, _287497), -(c_Orderings_Oord__class_Oless__eq(_287493, _287497, _287495))], (2068 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_287493, _287495, _287497), 2071 ^ _221138 : [(2074 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_287493, _287497, _287495)], (2072 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_287493, _287495, _287497))]]]]], (8071 ^ _221138) ^ [_497928, _497930, _497932] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _497928), _497930), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _497928), _497932)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _497928), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _497930, _497932))], (5963 ^ _221138) ^ [_424342, _424344] : [class_Rings_Ocomm__semiring__0(_424342), -(c_Polynomial_Opcompose(_424342, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_424342)), _424344) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_424342)))], (11901 ^ _221138) ^ [] : [-(class_Rings_Oring__1(tc_RealDef_Oreal))], (4918 ^ _221138) ^ [_388268, _388270] : [4919 ^ _221138 : [(4920 ^ _221138) ^ [_388343] : [_388270 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _388268, _388343)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _388268, _388270))], (9520 ^ _221138) ^ [_548982, _548984, _548986, _548988] : [class_Rings_Olinordered__semidom(_548982), hAPP(hAPP(c_Power_Opower__class_Opower(_548982), _548984), c_Nat_OSuc(_548986)) = hAPP(hAPP(c_Power_Opower__class_Opower(_548982), _548988), c_Nat_OSuc(_548986)), c_Orderings_Oord__class_Oless__eq(_548982, c_Groups_Ozero__class_Ozero(_548982), _548984), c_Orderings_Oord__class_Oless__eq(_548982, c_Groups_Ozero__class_Ozero(_548982), _548988), -(_548984 = _548988)], (11697 ^ _221138) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (7423 ^ _221138) ^ [_476415] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _476415, c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_476415 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (11047 ^ _221138) ^ [_606163, _606165, _606167] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _606163, _606165), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _606163, _606167), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _606165, _606163), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _606167, _606163)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _606165, _606167))], (7767 ^ _221138) ^ [_488153, _488155] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _488153, _488155), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _488155, _488153)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _488155, _488153), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _488153, _488155))], (7109 ^ _221138) ^ [_465424, _465426] : [class_Rings_Ocomm__semiring__1(_465424), -(c_Rings_Odvd__class_Odvd(_465424, _465426, c_Groups_Ozero__class_Ozero(_465424)))], (9301 ^ _221138) ^ [_541305, _541307] : [c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _541305, _541307), 9306 ^ _221138 : [(9309 ^ _221138) ^ [] : [-(_541307 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9307 ^ _221138) ^ [] : [-(_541305 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 9310 ^ _221138 : [(9313 ^ _221138) ^ [] : [-(_541307 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (9311 ^ _221138) ^ [] : [-(_541305 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (6439 ^ _221138) ^ [_441286] : [-(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, _441286)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _441286)))], (4570 ^ _221138) ^ [_373808, _373810] : [class_Groups_Ocomm__monoid__add(_373808), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_373808), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_373808)), _373810) = _373810)], (11363 ^ _221138) ^ [_617928, _617930] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_617928), c_Nat_OSuc(_617930)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _617928, _617930))], (11413 ^ _221138) ^ [_619943, _619945] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _619943), _619945), -(c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _619945, c_RealDef_Oreal(tc_Nat_Onat, _619943))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_RComplete_Onatceiling(_619945), _619943))], (4736 ^ _221138) ^ [_380974, _380976] : [class_Rings_Ocomm__semiring__1(_380974), -(c_Groups_Oplus__class_Oplus(_380974, _380976, c_Groups_Ozero__class_Ozero(_380974)) = _380976)], (11129 ^ _221138) ^ [_609321, _609323] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _609321, _609323)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _609323, _609321))], (6313 ^ _221138) ^ [_436711, _436713] : [6314 ^ _221138 : [(6317 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _436713)], (6315 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _436711)]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _436711, _436713)))], (8961 ^ _221138) ^ [_529225] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _529225), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _529225)], (11967 ^ _221138) ^ [] : [-(class_Rings_Ocomm__ring(tc_Complex_Ocomplex))], (11295 ^ _221138) ^ [_615190, _615192, _615194] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _615190, _615192), 11298 ^ _221138 : [(11305 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _615194, _615190), _615192), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _615194, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _615192, _615190)))], (11299 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _615194, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _615192, _615190)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _615194, _615190), _615192))]]], (11869 ^ _221138) ^ [] : [-(class_Orderings_Opreorder(tc_RealDef_Oreal))], (3474 ^ _221138) ^ [_337065, _337067] : [class_Rings_Olinordered__ring(_337065), -(c_Orderings_Oord__class_Oless__eq(_337065, c_Groups_Ozero__class_Ozero(_337065), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_337065), _337067), _337067)))], (9187 ^ _221138) ^ [_537047] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _537047, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Groups_Oabs__class_Oabs(tc_Int_Oint, _537047) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _537047))], (11511 ^ _221138) ^ [_623741, _623743, _623745] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _623741, _623743), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _623745, c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _623743, _623741))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _623745, _623741), c_Nat_OSuc(_623743)))], (4690 ^ _221138) ^ [_379156, _379158, _379160, _379162] : [class_Rings_Ocomm__semiring__1(_379156), -(c_Groups_Oplus__class_Oplus(_379156, c_Groups_Oplus__class_Oplus(_379156, _379158, _379160), _379162) = c_Groups_Oplus__class_Oplus(_379156, _379158, c_Groups_Oplus__class_Oplus(_379156, _379160, _379162)))], (234 ^ _221138) ^ [_228401, _228403] : [-(class_Groups_Oordered__comm__monoid__add(_228401)), _228403 = _228401, class_Groups_Oordered__comm__monoid__add(_228403)], (9398 ^ _221138) ^ [_544416, _544418] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _544416, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _544418, _544416))))], (7471 ^ _221138) ^ [_478364, _478366, _478368, _478370] : [class_Rings_Ocomm__semiring__1(_478364), -(hAPP(c_Polynomial_Opoly(_478364, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_478364)), _478366), _478368)), _478370) = hAPP(hAPP(c_Power_Opower__class_Opower(_478364), hAPP(c_Polynomial_Opoly(_478364, _478366), _478370)), _478368))], (11583 ^ _221138) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (7293 ^ _221138) ^ [_471614, _471616, _471618, _471620] : [class_Rings_Ocomm__semiring__1(_471614), c_Rings_Odvd__class_Odvd(_471614, _471616, _471618), -(c_Rings_Odvd__class_Odvd(_471614, _471616, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_471614), _471618), _471620)))], (8919 ^ _221138) ^ [_527527, _527529, _527531] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _527527, _527529)), _527531) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _527527), _527531), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _527529), _527531)))], (4162 ^ _221138) ^ [_359600, _359602, _359604, _359606] : [class_Rings_Olinordered__ring__strict(_359600), c_Orderings_Oord__class_Oless(_359600, c_Groups_Ozero__class_Ozero(_359600), _359602), 4169 ^ _221138 : [(4176 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_359600, _359604, _359606), -(c_Orderings_Oord__class_Oless__eq(_359600, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_359600), _359602), _359604), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_359600), _359602), _359606)))], (4170 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_359600, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_359600), _359602), _359604), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_359600), _359602), _359606)), -(c_Orderings_Oord__class_Oless__eq(_359600, _359604, _359606))]]], (11957 ^ _221138) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex))], (5157 ^ _221138) ^ [_397161, _397163] : [-(_397161 = _397163), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _397161, _397163)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _397163, _397161))], (11961 ^ _221138) ^ [] : [-(class_Rings_Osemiring__0(tc_Complex_Ocomplex))], (6473 ^ _221138) ^ [_442980, _442982, _442984] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _442980, _442982) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _442980, _442984), -(_442982 = _442984)], (5167 ^ _221138) ^ [_397513, _397515, _397517] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _397513, _397515), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _397513, _397517)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _397515, _397517))], (11911 ^ _221138) ^ [] : [-(class_Rings_Oidom(tc_RealDef_Oreal))], (9992 ^ _221138) ^ [_564869] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_RComplete_Onatfloor(_564869)))], (2322 ^ _221138) ^ [_296211] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _296211) = _296211)], (3156 ^ _221138) ^ [_326974, _326976] : [class_Groups_Oordered__ab__group__add__abs(_326974), -(c_Orderings_Oord__class_Oless__eq(_326974, c_Groups_Ozero__class_Ozero(_326974), c_Groups_Oabs__class_Oabs(_326974, _326976)))], (11401 ^ _221138) ^ [_619314] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _619314) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10123 ^ _221138) ^ [_569845] : [_569845 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_RealDef_Oreal(tc_Nat_Onat, _569845) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (11979 ^ _221138) ^ [] : [-(class_Power_Opower(tc_Complex_Ocomplex))], (6981 ^ _221138) ^ [_460697, _460699] : [-(hBOOL(hAPP(_460697, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_460697, _460699)), 6989 ^ _221138 : [(6992 ^ _221138) ^ [_461133] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _461133, 6988 ^ [_460697, _460699]), hBOOL(hAPP(_460697, _461133))], (6998 ^ _221138) ^ [] : [-(hBOOL(hAPP(_460697, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, 6988 ^ [_460697, _460699], c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (6990 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, 6988 ^ [_460697, _460699], _460699))]]], (9117 ^ _221138) ^ [_534521, _534523] : [9118 ^ _221138 : [(9121 ^ _221138) ^ [] : [_534521 = c_Nat_OSuc(_534523)], (9119 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _534521, _534523)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _534521, c_Nat_OSuc(_534523)))], (6173 ^ _221138) ^ [_431741, _431743, _431745] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _431741), _431743), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _431741), _431745)), 6176 ^ _221138 : [(6179 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _431743, _431745))], (6177 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _431741))]]], (3772 ^ _221138) ^ [_346755, _346757] : [class_Rings_Olinordered__ring(_346755), c_Orderings_Oord__class_Oless(_346755, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_346755), _346757), _346757), c_Groups_Ozero__class_Ozero(_346755))], (7131 ^ _221138) ^ [_466155, _466157, _466159] : [class_Rings_Ocomm__ring__1(_466155), 7134 ^ _221138 : [(7141 ^ _221138) ^ [] : [c_Rings_Odvd__class_Odvd(_466155, _466157, _466159), -(c_Rings_Odvd__class_Odvd(_466155, _466157, c_Groups_Ouminus__class_Ouminus(_466155, _466159)))], (7135 ^ _221138) ^ [] : [c_Rings_Odvd__class_Odvd(_466155, _466157, c_Groups_Ouminus__class_Ouminus(_466155, _466159)), -(c_Rings_Odvd__class_Odvd(_466155, _466157, _466159))]]], (11665 ^ _221138) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (11689 ^ _221138) ^ [] : [-(class_Groups_Ominus(tc_Int_Oint))], (10458 ^ _221138) ^ [_582607, _582609, _582611, _582613, _582615, _582617] : [class_Rings_Oordered__ring(_582607), 10461 ^ _221138 : [(10468 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_582607, _582613, c_Groups_Oplus__class_Oplus(_582607, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_582607), c_Groups_Ominus__class_Ominus(_582607, _582615, _582609)), _582611), _582617)), -(c_Orderings_Oord__class_Oless(_582607, c_Groups_Oplus__class_Oplus(_582607, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_582607), _582609), _582611), _582613), c_Groups_Oplus__class_Oplus(_582607, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_582607), _582615), _582611), _582617)))], (10462 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_582607, c_Groups_Oplus__class_Oplus(_582607, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_582607), _582609), _582611), _582613), c_Groups_Oplus__class_Oplus(_582607, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_582607), _582615), _582611), _582617)), -(c_Orderings_Oord__class_Oless(_582607, _582613, c_Groups_Oplus__class_Oplus(_582607, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_582607), c_Groups_Ominus__class_Ominus(_582607, _582615, _582609)), _582611), _582617)))]]], (11003 ^ _221138) ^ [_604733, _604735] : [-(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, _604733, _604735) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, _604733, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, _604735)))], (6513 ^ _221138) ^ [_444632, _444634] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _444632), _444634) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _444634), _444632))], (674 ^ _221138) ^ [_241381, _241383] : [-(class_Groups_Ominus(_241381)), _241383 = _241381, class_Groups_Ominus(_241383)], (8835 ^ _221138) ^ [_524541] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _524541, 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), _524541), _524541), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (11683 ^ _221138) ^ [] : [-(class_Groups_Osgn__if(tc_Int_Oint))], (6099 ^ _221138) ^ [_429184] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _429184), _429184 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (2982 ^ _221138) ^ [_320673, _320675, _320677] : [class_Rings_Oordered__ring__abs(_320673), -(c_Groups_Oabs__class_Oabs(_320673, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_320673), _320675), _320677)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_320673), c_Groups_Oabs__class_Oabs(_320673, _320675)), c_Groups_Oabs__class_Oabs(_320673, _320677))), 2989 ^ _221138 : [(2992 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_320673, _320675, c_Groups_Ozero__class_Ozero(_320673))], (2990 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_320673, c_Groups_Ozero__class_Ozero(_320673), _320675)]], 2993 ^ _221138 : [(2996 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_320673, _320677, c_Groups_Ozero__class_Ozero(_320673))], (2994 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_320673, c_Groups_Ozero__class_Ozero(_320673), _320677)]]], (9816 ^ _221138) ^ [_559037] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _559037, c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_559037 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_559037 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (9720 ^ _221138) ^ [_555610, _555612, _555614] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _555610), _555610 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _555612, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _555610), _555614)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _555612), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _555614, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (2482 ^ _221138) ^ [_302535, _302537, _302539, _302541] : [class_Groups_Ocancel__semigroup__add(_302535), 2485 ^ _221138 : [(2492 ^ _221138) ^ [] : [_302539 = _302541, -(c_Groups_Oplus__class_Oplus(_302535, _302537, _302539) = c_Groups_Oplus__class_Oplus(_302535, _302537, _302541))], (2486 ^ _221138) ^ [] : [c_Groups_Oplus__class_Oplus(_302535, _302537, _302539) = c_Groups_Oplus__class_Oplus(_302535, _302537, _302541), -(_302539 = _302541)]]], (7417 ^ _221138) ^ [_476170] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _476170), -(c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _476170, c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatceiling(_476170), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (4646 ^ _221138) ^ [_376836, _376838, _376840, _376842] : [class_Rings_Ocomm__semiring__1(_376836), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_376836), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_376836), _376838), _376840)), _376842) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_376836), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_376836), _376838), _376842)), _376840))], (9143 ^ _221138) ^ [_535464, _535466] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _535464, c_Nat_OSuc(_535466)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _535464, _535466)), -(_535464 = c_Nat_OSuc(_535466))], (9618 ^ _221138) ^ [_552175, _552177, _552179] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _552175), _552177), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _552179), _552177)), -(_552177 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _552175, _552179))], (2504 ^ _221138) ^ [_303389, _303391, _303393, _303395] : [class_Groups_Oab__semigroup__mult(_303389), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_303389), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_303389), _303391), _303393)), _303395) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_303389), _303391), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_303389), _303393), _303395)))], (12231 ^ _221138) ^ [_644725] : [class_Groups_Ocomm__monoid__add(_644725), -(class_Groups_Omonoid__add(tc_Polynomial_Opoly(_644725)))], (624 ^ _221138) ^ [_239906, _239908] : [-(class_Rings_Olinordered__idom(_239906)), _239908 = _239906, class_Rings_Olinordered__idom(_239908)], (3936 ^ _221138) ^ [_352135, _352137, _352139, _352141] : [class_Rings_Olinordered__ring__strict(_352135), c_Orderings_Oord__class_Oless(_352135, _352137, c_Groups_Ozero__class_Ozero(_352135)), 3943 ^ _221138 : [(3950 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_352135, _352141, _352139), -(c_Orderings_Oord__class_Oless(_352135, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_352135), _352137), _352139), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_352135), _352137), _352141)))], (3944 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_352135, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_352135), _352137), _352139), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_352135), _352137), _352141)), -(c_Orderings_Oord__class_Oless(_352135, _352141, _352139))]]], (9960 ^ _221138) ^ [] : [-(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)))], (11935 ^ _221138) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex))], (11905 ^ _221138) ^ [] : [-(class_Power_Opower(tc_RealDef_Oreal))], (980 ^ _221138) ^ [_252278, _252280] : [_252280 = _252278, -(c_Nat_OSuc(_252280) = c_Nat_OSuc(_252278))], (2376 ^ _221138) ^ [_298727, _298729, _298731, _298733, _298735, _298737] : [class_Rings_Olinordered__semiring__1(_298727), c_Orderings_Oord__class_Oless__eq(_298727, _298729, _298731), c_Orderings_Oord__class_Oless__eq(_298727, _298733, _298731), c_Orderings_Oord__class_Oless__eq(_298727, c_Groups_Ozero__class_Ozero(_298727), _298735), c_Orderings_Oord__class_Oless__eq(_298727, c_Groups_Ozero__class_Ozero(_298727), _298737), c_Groups_Oplus__class_Oplus(_298727, _298735, _298737) = c_Groups_Oone__class_Oone(_298727), -(c_Orderings_Oord__class_Oless__eq(_298727, c_Groups_Oplus__class_Oplus(_298727, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_298727), _298735), _298729), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_298727), _298737), _298733)), _298731))], (444 ^ _221138) ^ [_234596, _234598] : [-(class_Rings_Ocomm__semiring(_234596)), _234598 = _234596, class_Rings_Ocomm__semiring(_234598)], (8405 ^ _221138) ^ [_510107, _510109, _510111, _510113] : [class_Rings_Olinordered__semidom(_510107), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _510109, _510111), c_Orderings_Oord__class_Oless__eq(_510107, c_Groups_Oone__class_Oone(_510107), _510113), -(c_Orderings_Oord__class_Oless__eq(_510107, hAPP(hAPP(c_Power_Opower__class_Opower(_510107), _510113), _510109), hAPP(hAPP(c_Power_Opower__class_Opower(_510107), _510113), _510111)))], (4072 ^ _221138) ^ [_356680] : [class_Rings_Olinordered__semidom(_356680), -(c_Orderings_Oord__class_Oless(_356680, c_Groups_Ozero__class_Ozero(_356680), c_Groups_Oone__class_Oone(_356680)))], (11943 ^ _221138) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex))], (12165 ^ _221138) ^ [_642635] : [class_Rings_Olinordered__idom(_642635), -(class_Rings_Olinordered__idom(tc_Polynomial_Opoly(_642635)))], (11861 ^ _221138) ^ [] : [-(class_Rings_Ocomm__semiring(tc_RealDef_Oreal))], (12021 ^ _221138) ^ [_638075] : [class_Rings_Olinordered__idom(_638075), -(class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(_638075)))], (6245 ^ _221138) ^ [_434377, _434379, _434381] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _434377), _434379) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _434377), _434381), -(_434379 = _434381), -(_434377 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11737 ^ _221138) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (5747 ^ _221138) ^ [_417184, _417186, _417188] : [class_Groups_Ogroup__add(_417184), 5750 ^ _221138 : [(5757 ^ _221138) ^ [] : [c_Groups_Oplus__class_Oplus(_417184, _417186, _417188) = c_Groups_Ozero__class_Ozero(_417184), -(_417186 = c_Groups_Ouminus__class_Ouminus(_417184, _417188))], (5751 ^ _221138) ^ [] : [_417186 = c_Groups_Ouminus__class_Ouminus(_417184, _417188), -(c_Groups_Oplus__class_Oplus(_417184, _417186, _417188) = c_Groups_Ozero__class_Ozero(_417184))]]], (11919 ^ _221138) ^ [] : [-(class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex))], (714 ^ _221138) ^ [_242561, _242563] : [-(class_Rings_Oring(_242561)), _242563 = _242561, class_Rings_Oring(_242563)], (7077 ^ _221138) ^ [_464294, _464296, _464298] : [class_Rings_Oidom(_464294), 7080 ^ _221138 : [(7087 ^ _221138) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_464294), c_Polynomial_OpCons(_464294, c_Groups_Ouminus__class_Ouminus(_464294, _464298), c_Polynomial_OpCons(_464294, c_Groups_Oone__class_Oone(_464294), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_464294)))), _464296), -(hAPP(c_Polynomial_Opoly(_464294, _464296), _464298) = c_Groups_Ozero__class_Ozero(_464294))], (7081 ^ _221138) ^ [] : [hAPP(c_Polynomial_Opoly(_464294, _464296), _464298) = c_Groups_Ozero__class_Ozero(_464294), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_464294), c_Polynomial_OpCons(_464294, c_Groups_Ouminus__class_Ouminus(_464294, _464298), c_Polynomial_OpCons(_464294, c_Groups_Oone__class_Oone(_464294), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_464294)))), _464296))]]], (9538 ^ _221138) ^ [_549559, _549561, _549563] : [class_Rings_Olinordered__semidom(_549559), c_Orderings_Oord__class_Oless(_549559, c_Groups_Oone__class_Oone(_549559), _549561), -(c_Orderings_Oord__class_Oless(_549559, c_Groups_Oone__class_Oone(_549559), hAPP(hAPP(c_Power_Opower__class_Opower(_549559), _549561), c_Nat_OSuc(_549563))))], (9474 ^ _221138) ^ [_547111, _547113, _547115] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_547111)), _547113), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_547111)), _547115)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _547113, _547115))], (9928 ^ _221138) ^ [_562807, _562809, _562811] : [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), _562807), _562809), _562811)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _562811, _562807), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _562807), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _562809))], (10662 ^ _221138) ^ [_591199, _591201, _591203] : [class_Groups_Oab__group__add(_591199), -(c_Groups_Ominus__class_Ominus(_591199, _591201, _591203) = c_Groups_Oplus__class_Oplus(_591199, _591201, c_Groups_Ouminus__class_Ouminus(_591199, _591203)))], (684 ^ _221138) ^ [_241676, _241678] : [-(class_Power_Opower(_241676)), _241678 = _241676, class_Power_Opower(_241678)], (5197 ^ _221138) ^ [_398502, _398504] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _398502, _398504), _398504)], (2592 ^ _221138) ^ [_306775] : [class_Groups_Oordered__ab__group__add__abs(_306775), -(c_Groups_Oabs__class_Oabs(_306775, c_Groups_Ozero__class_Ozero(_306775)) = c_Groups_Ozero__class_Ozero(_306775))], (9972 ^ _221138) ^ [_564185] : [class_Power_Opower(_564185), -(c_Power_Opower__class_Opower(_564185) = c_Power_Opower_Opower(_564185, c_Groups_Oone__class_Oone(_564185), c_Groups_Otimes__class_Otimes(_564185)))], (10578 ^ _221138) ^ [_587527, _587529, _587531] : [class_RealVector_Oreal__normed__vector(_587527), -(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(_587527, _587529), c_RealVector_Onorm__class_Onorm(_587527, _587531))), c_RealVector_Onorm__class_Onorm(_587527, c_Groups_Ominus__class_Ominus(_587527, _587529, _587531))))], (2878 ^ _221138) ^ [_316902, _316904] : [class_Rings_Omult__zero(_316902), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_316902), c_Groups_Ozero__class_Ozero(_316902)), _316904) = c_Groups_Ozero__class_Ozero(_316902))], (9007 ^ _221138) ^ [_530928, _530930] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_530928), c_Nat_OSuc(_530930)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _530928, _530930))], (4588 ^ _221138) ^ [_374508, _374510] : [class_Rings_Ocomm__semiring__0(_374508), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_374508)), _374510), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_374508))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_374508)))], (5881 ^ _221138) ^ [_421582, _421584, _421586] : [class_Rings_Olinordered__idom(_421582), 5884 ^ _221138 : [(5893 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(_421582, c_Groups_Oabs__class_Oabs(_421582, _421584), _421586)), c_Orderings_Oord__class_Oless(_421582, _421584, _421586), c_Orderings_Oord__class_Oless(_421582, c_Groups_Ouminus__class_Ouminus(_421582, _421584), _421586)], (5885 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_421582, c_Groups_Oabs__class_Oabs(_421582, _421584), _421586), 5888 ^ _221138 : [(5891 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(_421582, c_Groups_Ouminus__class_Ouminus(_421582, _421584), _421586))], (5889 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(_421582, _421584, _421586))]]]]], (5215 ^ _221138) ^ [_399344, _399346, _399348] : [class_Groups_Oab__group__add(_399344), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_399344), c_Polynomial_OpCons(_399344, _399346, _399348)) = c_Polynomial_OpCons(_399344, c_Groups_Ouminus__class_Ouminus(_399344, _399346), c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_399344), _399348)))], (9093 ^ _221138) ^ [_533695] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_533695), _533695)], (9131 ^ _221138) ^ [_535022, _535024] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _535022, _535024), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_535022), c_Nat_OSuc(_535024)))], (7187 ^ _221138) ^ [_467958, _467960, _467962] : [class_Rings_Olinordered__idom(_467958), 7190 ^ _221138 : [(7197 ^ _221138) ^ [] : [c_Rings_Odvd__class_Odvd(_467958, _467960, _467962), -(c_Rings_Odvd__class_Odvd(_467958, c_Groups_Oabs__class_Oabs(_467958, _467960), _467962))], (7191 ^ _221138) ^ [] : [c_Rings_Odvd__class_Odvd(_467958, c_Groups_Oabs__class_Oabs(_467958, _467960), _467962), -(c_Rings_Odvd__class_Odvd(_467958, _467960, _467962))]]], (12159 ^ _221138) ^ [_642445] : [class_Rings_Olinordered__idom(_642445), -(class_Rings_Olinordered__ring(tc_Polynomial_Opoly(_642445)))], (694 ^ _221138) ^ [_241971, _241973] : [-(class_Groups_Ozero(_241971)), _241973 = _241971, class_Groups_Ozero(_241973)], (2940 ^ _221138) ^ [_318938] : [class_Rings_Ozero__neq__one(_318938), c_Groups_Oone__class_Oone(_318938) = c_Groups_Ozero__class_Ozero(_318938)], (6859 ^ _221138) ^ [_456828, _456830] : [class_Rings_Olinordered__idom(_456828), c_Orderings_Oord__class_Oless(_456828, c_Groups_Ozero__class_Ozero(_456828), _456830), -(c_Groups_Osgn__class_Osgn(_456828, _456830) = c_Groups_Oone__class_Oone(_456828))], (4884 ^ _221138) ^ [_386670] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _386670, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4066 ^ _221138) ^ [_356481] : [class_Rings_Olinordered__semidom(_356481), c_Orderings_Oord__class_Oless(_356481, c_Groups_Oone__class_Oone(_356481), c_Groups_Ozero__class_Ozero(_356481))], (2958 ^ _221138) ^ [_319678, _319680, _319682, _319684] : [class_Rings_Ocomm__semiring__0(_319678), -(hAPP(c_Polynomial_Opoly(_319678, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_319678)), _319680), _319682)), _319684) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_319678), hAPP(c_Polynomial_Opoly(_319678, _319680), _319684)), hAPP(c_Polynomial_Opoly(_319678, _319682), _319684)))], (11681 ^ _221138) ^ [] : [-(class_Groups_Ouminus(tc_Int_Oint))], (6607 ^ _221138) ^ [_448032, _448034, _448036] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _448032, _448034), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _448032, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _448034, _448036)))], (8097 ^ _221138) ^ [_498936, _498938, _498940, _498942] : [class_Groups_Ocomm__monoid__mult(_498936), -(hAPP(hAPP(c_Power_Opower__class_Opower(_498936), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_498936), _498938), _498940)), _498942) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_498936), hAPP(hAPP(c_Power_Opower__class_Opower(_498936), _498938), _498942)), hAPP(hAPP(c_Power_Opower__class_Opower(_498936), _498940), _498942)))], (11635 ^ _221138) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (5645 ^ _221138) ^ [_414052, _414054] : [class_Groups_Oordered__ab__group__add(_414052), 5648 ^ _221138 : [(5655 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_414052, c_Groups_Ozero__class_Ozero(_414052), _414054), -(c_Orderings_Oord__class_Oless__eq(_414052, c_Groups_Ouminus__class_Ouminus(_414052, _414054), c_Groups_Ozero__class_Ozero(_414052)))], (5649 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_414052, c_Groups_Ouminus__class_Ouminus(_414052, _414054), c_Groups_Ozero__class_Ozero(_414052)), -(c_Orderings_Oord__class_Oless__eq(_414052, c_Groups_Ozero__class_Ozero(_414052), _414054))]]], (7747 ^ _221138) ^ [_487539, _487541] : [_487541 = _487539, c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _487539, _487541), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _487541, _487539))], (10209 ^ _221138) ^ [_572967, _572969] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _572967), 10212 ^ _221138 : [(10219 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _572969), _572967), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _572969, c_RComplete_Onatfloor(_572967)))], (10213 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _572969, c_RComplete_Onatfloor(_572967)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _572969), _572967))]]], (2706 ^ _221138) ^ [_310834, _310836, _310838, _310840] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_310834), 2709 ^ _221138 : [(2716 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_310834, _310836, _310840), -(c_Orderings_Oord__class_Oless__eq(_310834, c_Groups_Oplus__class_Oplus(_310834, _310836, _310838), c_Groups_Oplus__class_Oplus(_310834, _310840, _310838)))], (2710 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_310834, c_Groups_Oplus__class_Oplus(_310834, _310836, _310838), c_Groups_Oplus__class_Oplus(_310834, _310840, _310838)), -(c_Orderings_Oord__class_Oless__eq(_310834, _310836, _310840))]]], (11651 ^ _221138) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (11761 ^ _221138) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (11881 ^ _221138) ^ [] : [-(class_Groups_Ogroup__add(tc_RealDef_Oreal))], (11657 ^ _221138) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (5911 ^ _221138) ^ [_422562, _422564] : [_422562 = _422564, -(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _422562, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _422564)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (3286 ^ _221138) ^ [_331099, _331101, _331103] : [class_Groups_Oordered__comm__monoid__add(_331099), c_Orderings_Oord__class_Oless__eq(_331099, c_Groups_Ozero__class_Ozero(_331099), _331101), c_Orderings_Oord__class_Oless__eq(_331099, c_Groups_Ozero__class_Ozero(_331099), _331103), -(c_Orderings_Oord__class_Oless__eq(_331099, c_Groups_Ozero__class_Ozero(_331099), c_Groups_Oplus__class_Oplus(_331099, _331101, _331103)))], (11765 ^ _221138) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (1345 ^ _221138) ^ [_264802, _264804, _264806, _264808] : [class_Orderings_Oorder(_264802), c_Orderings_Oord__class_Oless__eq(_264802, _264804, _264806), _264804 = _264808, -(c_Orderings_Oord__class_Oless__eq(_264802, _264808, _264806))], (11545 ^ _221138) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint))], (7435 ^ _221138) ^ [_476810, _476812] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _476810, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _476812, _476810)), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _476810, _476812))], (8729 ^ _221138) ^ [_521036] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _521036) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (11871 ^ _221138) ^ [] : [-(class_Orderings_Olinorder(tc_RealDef_Oreal))], (10277 ^ _221138) ^ [_575254] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _575254, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatfloor(_575254)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))], (10794 ^ _221138) ^ [_596496, _596498, _596500, _596502, _596504] : [class_Groups_Oab__group__add(_596496), -(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_596496), c_Polynomial_OpCons(_596496, _596498, _596500), c_Polynomial_OpCons(_596496, _596502, _596504)) = c_Polynomial_OpCons(_596496, c_Groups_Ominus__class_Ominus(_596496, _596498, _596502), c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_596496), _596500, _596504)))], (9071 ^ _221138) ^ [_532975, _532977] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _532975, c_Nat_OSuc(_532977)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _532975, _532977)), -(_532975 = _532977)], (8525 ^ _221138) ^ [_514054, _514056] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _514054), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _514056, _514054), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _514056))], (6047 ^ _221138) ^ [_427303, _427305] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _427303), _427305), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _427303, _427305)))], (8291 ^ _221138) ^ [_506073, _506075, _506077, _506079] : [class_Rings_Olinordered__semidom(_506073), c_Orderings_Oord__class_Oless(_506073, hAPP(hAPP(c_Power_Opower__class_Opower(_506073), _506075), _506077), hAPP(hAPP(c_Power_Opower__class_Opower(_506073), _506079), _506077)), c_Orderings_Oord__class_Oless__eq(_506073, c_Groups_Ozero__class_Ozero(_506073), _506079), -(c_Orderings_Oord__class_Oless(_506073, _506075, _506079))], (892 ^ _221138) ^ [_249123, _249125, _249127, _249129] : [-(c_Groups_Osgn__class_Osgn(_249129, _249125) = c_Groups_Osgn__class_Osgn(_249127, _249123)), _249129 = _249127, _249125 = _249123], (11419 ^ _221138) ^ [_620191, _620193] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _620191), _620193), -(c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _620193, c_RealDef_Oreal(tc_Nat_Onat, _620191))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_RComplete_Onatfloor(_620193), _620191))], (11613 ^ _221138) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (6539 ^ _221138) ^ [_445654, _445656, _445658] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _445654), _445656) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _445654), _445658), -(_445654 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_445656 = _445658)], (3372 ^ _221138) ^ [_333765, _333767] : [class_Groups_Olinordered__ab__group__add(_333765), 3375 ^ _221138 : [(3382 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_333765, c_Groups_Ozero__class_Ozero(_333765), _333767), -(c_Orderings_Oord__class_Oless(_333765, c_Groups_Ozero__class_Ozero(_333765), c_Groups_Oplus__class_Oplus(_333765, _333767, _333767)))], (3376 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_333765, c_Groups_Ozero__class_Ozero(_333765), c_Groups_Oplus__class_Oplus(_333765, _333767, _333767)), -(c_Orderings_Oord__class_Oless(_333765, c_Groups_Ozero__class_Ozero(_333765), _333767))]]], (2466 ^ _221138) ^ [_301993, _301995, _301997, _301999] : [class_Groups_Ocancel__semigroup__add(_301993), 2469 ^ _221138 : [(2476 ^ _221138) ^ [] : [_301995 = _301999, -(c_Groups_Oplus__class_Oplus(_301993, _301995, _301997) = c_Groups_Oplus__class_Oplus(_301993, _301999, _301997))], (2470 ^ _221138) ^ [] : [c_Groups_Oplus__class_Oplus(_301993, _301995, _301997) = c_Groups_Oplus__class_Oplus(_301993, _301999, _301997), -(_301995 = _301999)]]], (8965 ^ _221138) ^ [_529389] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_529389)], (5949 ^ _221138) ^ [_423936, _423938] : [class_Rings_Olinordered__idom(_423936), -(_423938 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_423936))), -(c_Polynomial_Opos__poly(_423936, _423938)), -(c_Polynomial_Opos__poly(_423936, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_423936), _423938)))], (10006 ^ _221138) ^ [_565549] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), c_RComplete_Onatfloor(_565549)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _565549))], (8925 ^ _221138) ^ [_527889, _527891] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Nat_OSuc(_527889), _527891) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _527889, _527891)))], (12279 ^ _221138) ^ [_646245] : [class_Rings_Olinordered__idom(_646245), -(class_Orderings_Oord(tc_Polynomial_Opoly(_646245)))], (6619 ^ _221138) ^ [_448502, _448504] : [class_Orderings_Oorder(_448502), 6622 ^ _221138 : [(6623 ^ _221138) ^ [] : [c_SEQ_Odecseq(_448502, _448504), 6626 ^ _221138 : [(6627 ^ _221138) ^ [_448778, _448780] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _448780, _448778), -(c_Orderings_Oord__class_Oless__eq(_448502, hAPP(_448504, _448778), hAPP(_448504, _448780)))]]], (6633 ^ _221138) ^ [] : [6636 ^ _221138 : [(6639 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_448502, hAPP(_448504, 6635 ^ [_448502, _448504]), hAPP(_448504, 6634 ^ [_448502, _448504]))], (6637 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, 6634 ^ [_448502, _448504], 6635 ^ [_448502, _448504]))]], -(c_SEQ_Odecseq(_448502, _448504))]]], (7393 ^ _221138) ^ [_475283, _475285] : [class_Orderings_Oorder(_475283), 7396 ^ _221138 : [(7397 ^ _221138) ^ [] : [c_SEQ_Oincseq(_475283, _475285), 7400 ^ _221138 : [(7401 ^ _221138) ^ [_475559, _475561] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _475561, _475559), -(c_Orderings_Oord__class_Oless__eq(_475283, hAPP(_475285, _475561), hAPP(_475285, _475559)))]]], (7407 ^ _221138) ^ [] : [7410 ^ _221138 : [(7413 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_475283, hAPP(_475285, 7408 ^ [_475283, _475285]), hAPP(_475285, 7409 ^ [_475283, _475285]))], (7411 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, 7408 ^ [_475283, _475285], 7409 ^ [_475283, _475285]))]], -(c_SEQ_Oincseq(_475283, _475285))]]], (9810 ^ _221138) ^ [_558829, _558831] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _558829), _558831), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _558829, _558831))], (6011 ^ _221138) ^ [_425952, _425954, _425956, _425958] : [class_Rings_Ocomm__semiring__0(_425952), -(hAPP(c_Polynomial_Opoly(_425952, c_Polynomial_Opcompose(_425952, _425954, _425956)), _425958) = hAPP(c_Polynomial_Opoly(_425952, _425954), hAPP(c_Polynomial_Opoly(_425952, _425956), _425958)))], (3254 ^ _221138) ^ [_330109, _330111] : [class_Groups_Olinordered__ab__group__add(_330109), 3257 ^ _221138 : [(3264 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_330109, c_Groups_Ozero__class_Ozero(_330109), _330111), -(c_Orderings_Oord__class_Oless__eq(_330109, c_Groups_Ozero__class_Ozero(_330109), c_Groups_Oplus__class_Oplus(_330109, _330111, _330111)))], (3258 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_330109, c_Groups_Ozero__class_Ozero(_330109), c_Groups_Oplus__class_Oplus(_330109, _330111, _330111)), -(c_Orderings_Oord__class_Oless__eq(_330109, c_Groups_Ozero__class_Ozero(_330109), _330111))]]], (1934 ^ _221138) ^ [_283509, _283511, _283513] : [class_Orderings_Olinorder(_283509), c_Orderings_Oord__class_Oless__eq(_283509, _283511, _283513), 1941 ^ _221138 : [(1948 ^ _221138) ^ [] : [_283511 = _283513, c_Orderings_Oord__class_Oless(_283509, _283511, _283513)], (1942 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(_283509, _283511, _283513)), -(_283511 = _283513)]]], (11779 ^ _221138) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (11749 ^ _221138) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (6303 ^ _221138) ^ [_436445, _436447] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _436445, _436447)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _436445)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _436447))], (11711 ^ _221138) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (11889 ^ _221138) ^ [] : [-(class_Int_Oring__char__0(tc_RealDef_Oreal))], (4608 ^ _221138) ^ [_375192, _375194, _375196] : [class_Rings_Olinordered__idom(_375192), c_Polynomial_Opos__poly(_375192, _375194), c_Polynomial_Opos__poly(_375192, _375196), -(c_Polynomial_Opos__poly(_375192, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_375192)), _375194), _375196)))], (11759 ^ _221138) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (10496 ^ _221138) ^ [_584263, _584265, _584267, _584269] : [class_Rings_Ocomm__ring(_584263), class_Rings_Odvd(_584263), c_Rings_Odvd__class_Odvd(_584263, _584265, _584267), 10507 ^ _221138 : [(10514 ^ _221138) ^ [_584904, _584906] : [c_Rings_Odvd__class_Odvd(_584263, _584265, c_Groups_Oplus__class_Oplus(_584263, c_Groups_Ominus__class_Ominus(_584263, _584906, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_584263), _584904), _584267)), _584269)), -(c_Rings_Odvd__class_Odvd(_584263, _584265, c_Groups_Oplus__class_Oplus(_584263, _584906, _584269)))], (10508 ^ _221138) ^ [_584666, _584668] : [c_Rings_Odvd__class_Odvd(_584263, _584265, c_Groups_Oplus__class_Oplus(_584263, _584668, _584269)), -(c_Rings_Odvd__class_Odvd(_584263, _584265, c_Groups_Oplus__class_Oplus(_584263, c_Groups_Ominus__class_Ominus(_584263, _584668, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_584263), _584666), _584267)), _584269)))]]], (11841 ^ _221138) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal))], (3138 ^ _221138) ^ [_326266, _326268] : [class_RealVector_Oreal__normed__algebra(_326266), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_326266), _326268), c_Groups_Ozero__class_Ozero(_326266)) = c_Groups_Ozero__class_Ozero(_326266))], (10782 ^ _221138) ^ [_595908, _595910, _595912] : [class_RealVector_Oreal__normed__vector(_595908), -(c_RealVector_Onorm__class_Onorm(_595908, c_Groups_Ominus__class_Ominus(_595908, _595910, _595912)) = c_RealVector_Onorm__class_Onorm(_595908, c_Groups_Ominus__class_Ominus(_595908, _595912, _595910)))], (8885 ^ _221138) ^ [_526210, _526212, _526214, _526216] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _526210, _526212), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _526214, _526216), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _526210, _526214), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _526212, _526216)))], (9233 ^ _221138) ^ [_538891, _538893, _538895] : [class_Power_Opower(_538891), -(hAPP(hAPP(c_Power_Opower__class_Opower(_538891), _538893), c_Nat_OSuc(_538895)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_538891), _538893), hAPP(hAPP(c_Power_Opower__class_Opower(_538891), _538893), _538895)))], (948 ^ _221138) ^ [_251152, _251154, _251156, _251158] : [-(c_Groups_Ouminus__class_Ouminus(_251158, _251154) = c_Groups_Ouminus__class_Ouminus(_251156, _251152)), _251158 = _251156, _251154 = _251152], (1864 ^ _221138) ^ [_281366, _281368, _281370, _281372] : [class_Orderings_Oorder(_281366), c_Orderings_Oord__class_Oless(_281366, _281368, _281370), c_Orderings_Oord__class_Oless__eq(_281366, _281372, _281368), -(c_Orderings_Oord__class_Oless(_281366, _281372, _281370))], (5079 ^ _221138) ^ [_394268, _394270, _394272] : [5080 ^ _221138 : [(5083 ^ _221138) ^ [] : [hBOOL(hAPP(hAPP(_394272, _394270), _394268))], (5081 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _394268, _394270))]], 5086 ^ _221138 : [(5089 ^ _221138) ^ [] : [hBOOL(hAPP(hAPP(_394272, _394270), _394268))], (5087 ^ _221138) ^ [] : [-(_394268 = _394270)]], 5092 ^ _221138 : [(5095 ^ _221138) ^ [] : [hBOOL(hAPP(hAPP(_394272, _394270), _394268))], (5093 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _394270, _394268))]], -(hBOOL(hAPP(hAPP(_394272, _394270), _394268)))], (10720 ^ _221138) ^ [_593737, _593739, _593741, _593743, _593745] : [class_Groups_Oordered__ab__group__add(_593737), c_Groups_Ominus__class_Ominus(_593737, _593739, _593741) = c_Groups_Ominus__class_Ominus(_593737, _593743, _593745), 10727 ^ _221138 : [(10734 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_593737, _593743, _593745), -(c_Orderings_Oord__class_Oless__eq(_593737, _593739, _593741))], (10728 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_593737, _593739, _593741), -(c_Orderings_Oord__class_Oless__eq(_593737, _593743, _593745))]]], (11443 ^ _221138) ^ [_621176, _621178, _621180] : [hBOOL(hAPP(_621176, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _621178, _621180))), 11446 ^ _221138 : [(11453 ^ _221138) ^ [_621508] : [_621178 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _621180, _621508), -(hBOOL(hAPP(_621176, _621508)))], (11447 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _621178, _621180), -(hBOOL(hAPP(_621176, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (11891 ^ _221138) ^ [] : [-(class_Rings_Osemiring(tc_RealDef_Oreal))], (11719 ^ _221138) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (1964 ^ _221138) ^ [_284422, _284424, _284426] : [class_Orderings_Olinorder(_284422), c_Orderings_Oord__class_Oless__eq(_284422, _284424, _284426), c_Orderings_Oord__class_Oless(_284422, _284426, _284424)], (10107 ^ _221138) ^ [_569306, _569308] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _569306, _569308), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _569306), c_RealDef_Oreal(tc_Nat_Onat, _569308)))], (6301 ^ _221138) ^ [_436305] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _436305) = _436305)], (9161 ^ _221138) ^ [_536045] : [c_Nat_OSuc(_536045) = _536045], (9548 ^ _221138) ^ [_549912, _549914, _549916] : [class_Rings_Oidom(_549912), 9551 ^ _221138 : [(9552 ^ _221138) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_549912), _549914), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(_549912), _549916), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_549914 = _549916), -(_549914 = c_Groups_Ouminus__class_Ouminus(_549912, _549916))], (9562 ^ _221138) ^ [] : [9563 ^ _221138 : [(9566 ^ _221138) ^ [] : [_549914 = c_Groups_Ouminus__class_Ouminus(_549912, _549916)], (9564 ^ _221138) ^ [] : [_549914 = _549916]], -(hAPP(hAPP(c_Power_Opower__class_Opower(_549912), _549914), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(_549912), _549916), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))]]], (2312 ^ _221138) ^ [_295777] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _295777), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _295777)], (9580 ^ _221138) ^ [_550924, _550926] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _550924), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _550926), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _550924, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _550924), _550926)))], (10145 ^ _221138) ^ [] : [-(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))], (11311 ^ _221138) ^ [_615712, _615714, _615716] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _615712, _615714), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _615716, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _615714, _615712)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _615716, _615714), _615712))], (11989 ^ _221138) ^ [] : [-(class_Rings_Odvd(tc_Complex_Ocomplex))], (11751 ^ _221138) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (174 ^ _221138) ^ [_226631, _226633] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_226631)), _226633 = _226631, class_Groups_Oordered__ab__semigroup__add__imp__le(_226633)], (1052 ^ _221138) ^ [_254928, _254930, _254932, _254934] : [-(c_RealVector_Onorm__class_Onorm(_254934, _254930) = c_RealVector_Onorm__class_Onorm(_254932, _254928)), _254934 = _254932, _254930 = _254928], (11355 ^ _221138) ^ [_617575, _617577] : [class_Groups_Oab__group__add(_617575), -(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_617575), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_617575)), _617577) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_617575), _617577))], (11883 ^ _221138) ^ [] : [-(class_Rings_Omult__zero(tc_RealDef_Oreal))], (6499 ^ _221138) ^ [_444072, _444074] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _444072), _444074) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _444072 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _444074 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (7283 ^ _221138) ^ [_471249, _471251, _471253, _471255] : [class_Rings_Ocomm__semiring__1(_471249), c_Rings_Odvd__class_Odvd(_471249, _471251, _471253), -(c_Rings_Odvd__class_Odvd(_471249, _471251, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_471249), _471255), _471253)))], (9504 ^ _221138) ^ [_548349] : [-(c_Nat_OSuc(_548349) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _548349, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (7465 ^ _221138) ^ [_478082, _478084, _478086] : [class_RealVector_Oreal__normed__div__algebra(_478082), -(c_RealVector_Onorm__class_Onorm(_478082, hAPP(hAPP(c_Power_Opower__class_Opower(_478082), _478084), _478086)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_478082, _478084)), _478086))], (9700 ^ _221138) ^ [_554889] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _554889))], (2446 ^ _221138) ^ [_301183, _301185, _301187] : [class_Rings_Olinordered__semidom(_301183), c_Orderings_Oord__class_Oless(_301183, c_Groups_Oone__class_Oone(_301183), _301185), c_Orderings_Oord__class_Oless(_301183, c_Groups_Oone__class_Oone(_301183), _301187), -(c_Orderings_Oord__class_Oless(_301183, c_Groups_Oone__class_Oone(_301183), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_301183), _301185), _301187)))], (12009 ^ _221138) ^ [_637695] : [class_Rings_Olinordered__idom(_637695), -(class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(_637695)))], (9962 ^ _221138) ^ [_563886, _563888] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _563886), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _563888), -(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, _563886, _563888)))], (8285 ^ _221138) ^ [_505781, _505783, _505785] : [class_Rings_Olinordered__idom(_505781), -(c_Groups_Oabs__class_Oabs(_505781, hAPP(hAPP(c_Power_Opower__class_Opower(_505781), c_Groups_Ouminus__class_Ouminus(_505781, _505783)), _505785)) = c_Groups_Oabs__class_Oabs(_505781, hAPP(hAPP(c_Power_Opower__class_Opower(_505781), _505783), _505785)))], (11973 ^ _221138) ^ [] : [-(class_Groups_Ouminus(tc_Complex_Ocomplex))], (8147 ^ _221138) ^ [_501030, _501032, _501034, _501036] : [class_Rings_Olinordered__semidom(_501030), c_Orderings_Oord__class_Oless__eq(_501030, _501032, _501034), c_Orderings_Oord__class_Oless__eq(_501030, c_Groups_Ozero__class_Ozero(_501030), _501032), -(c_Orderings_Oord__class_Oless__eq(_501030, hAPP(hAPP(c_Power_Opower__class_Opower(_501030), _501032), _501036), hAPP(hAPP(c_Power_Opower__class_Opower(_501030), _501034), _501036)))], (10860 ^ _221138) ^ [_599175, _599177, _599179, _599181] : [class_RealVector_Oreal__normed__algebra(_599175), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_599175), c_Groups_Ominus__class_Ominus(_599175, _599177, _599179)), _599181) = c_Groups_Ominus__class_Ominus(_599175, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_599175), _599177), _599181), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_599175), _599179), _599181)))], (3178 ^ _221138) ^ [_327676, _327678] : [class_Groups_Oordered__ab__group__add__abs(_327676), c_Orderings_Oord__class_Oless__eq(_327676, c_Groups_Ozero__class_Ozero(_327676), _327678), -(c_Groups_Oabs__class_Oabs(_327676, _327678) = _327678)], (11601 ^ _221138) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (464 ^ _221138) ^ [_235186, _235188] : [-(class_Rings_Oordered__ring(_235186)), _235188 = _235186, class_Rings_Oordered__ring(_235188)], (6837 ^ _221138) ^ [_456072, _456074, _456076, _456078] : [class_Groups_Ouminus(_456072), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_456074, _456072), _456076), _456078) = c_Groups_Ouminus__class_Ouminus(_456072, hAPP(_456076, _456078)))], (2970 ^ _221138) ^ [_320173] : [-(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, _320173))))], (7561 ^ _221138) ^ [_481700, _481702, _481704] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _481700), 7564 ^ _221138 : [(7571 ^ _221138) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _481702, _481704), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _481700), _481702), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _481700), _481704)))], (7565 ^ _221138) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _481700), _481702), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _481700), _481704)), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _481702, _481704))]]], (11577 ^ _221138) ^ [_626115, _626117] : [class_Groups_Ominus(_626115), -(class_Groups_Ominus(tc_fun(_626117, _626115)))], (5549 ^ _221138) ^ [_410618, _410620, _410622] : [class_Rings_Oring(_410618), -(c_Groups_Ouminus__class_Ouminus(_410618, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_410618), _410620), _410622)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_410618), _410620), c_Groups_Ouminus__class_Ouminus(_410618, _410622)))], (1082 ^ _221138) ^ [_256013, _256015, _256017, _256019, _256021, _256023] : [-(c_Polynomial_OpCons(_256023, _256019, _256015) = c_Polynomial_OpCons(_256021, _256017, _256013)), _256023 = _256021, _256019 = _256017, _256015 = _256013], (11717 ^ _221138) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (10854 ^ _221138) ^ [_598863, _598865, _598867, _598869] : [class_RealVector_Oreal__normed__algebra(_598863), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_598863), c_Groups_Ominus__class_Ominus(_598863, _598865, _598867)), _598869) = c_Groups_Ominus__class_Ominus(_598863, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_598863), _598865), _598869), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_598863), _598867), _598869)))], (12111 ^ _221138) ^ [_640925] : [class_Rings_Olinordered__idom(_640925), -(class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(_640925)))], (5929 ^ _221138) ^ [_423248, _423250] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _423248), _423250), 5932 ^ _221138 : [(5935 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _423248, _423250))], (5933 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _423250), _423248))]]], (6237 ^ _221138) ^ [_434009, _434011, _434013] : [6238 ^ _221138 : [(6241 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _434009, _434013)], (6239 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _434011))]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _434009), _434011), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _434013), _434011)))], (11843 ^ _221138) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_RealDef_Oreal))], (4678 ^ _221138) ^ [_378596, _378598, _378600, _378602] : [class_Rings_Ocomm__semiring__1(_378596), -(c_Groups_Oplus__class_Oplus(_378596, _378598, c_Groups_Oplus__class_Oplus(_378596, _378600, _378602)) = c_Groups_Oplus__class_Oplus(_378596, _378600, c_Groups_Oplus__class_Oplus(_378596, _378598, _378602)))], (11289 ^ _221138) ^ [_614948, _614950] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _614948, _614950), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _614950, _614948), _614948) = _614950)], (11627 ^ _221138) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (4290 ^ _221138) ^ [_363838, _363840, _363842, _363844] : [class_Rings_Olinordered__semiring(_363838), c_Orderings_Oord__class_Oless(_363838, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_363838), _363840), _363842), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_363838), _363844), _363842)), c_Orderings_Oord__class_Oless__eq(_363838, c_Groups_Ozero__class_Ozero(_363838), _363842), -(c_Orderings_Oord__class_Oless(_363838, _363840, _363844))], (3998 ^ _221138) ^ [_354190, _354192, _354194, _354196] : [class_Rings_Olinordered__semiring__strict(_354190), c_Orderings_Oord__class_Oless(_354190, _354192, _354194), c_Orderings_Oord__class_Oless(_354190, c_Groups_Ozero__class_Ozero(_354190), _354196), -(c_Orderings_Oord__class_Oless(_354190, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_354190), _354196), _354192), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_354190), _354196), _354194)))], (1000 ^ _221138) ^ [_253012, _253014] : [_253014 = _253012, -(c_Groups_Otimes__class_Otimes(_253014) = c_Groups_Otimes__class_Otimes(_253012))], (6601 ^ _221138) ^ [_447804, _447806] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _447804, _447806), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _447804, _447806))], (10668 ^ _221138) ^ [_591449, _591451, _591453] : [class_Groups_Ogroup__add(_591449), -(c_Groups_Ominus__class_Ominus(_591449, _591451, _591453) = c_Groups_Oplus__class_Oplus(_591449, _591451, c_Groups_Ouminus__class_Ouminus(_591449, _591453)))], (7955 ^ _221138) ^ [_494035, _494037] : [7962 ^ _221138 : [(7965 ^ _221138) ^ [] : [_494035 = _494037], (7963 ^ _221138) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _494035, _494037))]], c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _494035, _494037), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _494037, _494035))], (3074 ^ _221138) ^ [_323784, _323786, _323788, _323790, _323792] : [class_RealVector_Oreal__normed__vector(_323784), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_323784, _323786), _323788), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_323784, _323790), _323792), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_323784, c_Groups_Oplus__class_Oplus(_323784, _323786, _323790)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _323788, _323792)))], (11727 ^ _221138) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (10149 ^ _221138) ^ [_570750] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _570750), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatfloor(_570750)), _570750))], (9051 ^ _221138) ^ [_532328, _532330] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _532328, _532330), -(c_Nat_OSuc(_532328) = _532330), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_532328), _532330))], (2562 ^ _221138) ^ [_305601, _305603, _305605] : [class_Groups_Oordered__ab__group__add__abs(_305601), -(c_Groups_Oabs__class_Oabs(_305601, c_Groups_Oplus__class_Oplus(_305601, c_Groups_Oabs__class_Oabs(_305601, _305603), c_Groups_Oabs__class_Oabs(_305601, _305605))) = c_Groups_Oplus__class_Oplus(_305601, c_Groups_Oabs__class_Oabs(_305601, _305603), c_Groups_Oabs__class_Oabs(_305601, _305605)))], (3732 ^ _221138) ^ [_345511, _345513, _345515] : [class_Rings_Oordered__ring(_345511), -(c_Orderings_Oord__class_Oless__eq(_345511, c_Groups_Ozero__class_Ozero(_345511), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_345511), _345513), _345515))), 3737 ^ _221138 : [(3744 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_345511, _345513, c_Groups_Ozero__class_Ozero(_345511)), c_Orderings_Oord__class_Oless__eq(_345511, _345515, c_Groups_Ozero__class_Ozero(_345511))], (3738 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_345511, c_Groups_Ozero__class_Ozero(_345511), _345513), c_Orderings_Oord__class_Oless__eq(_345511, c_Groups_Ozero__class_Ozero(_345511), _345515)]]], (3270 ^ _221138) ^ [_330597, _330599] : [class_Groups_Olinordered__ab__group__add(_330597), 3273 ^ _221138 : [(3280 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_330597, _330599, c_Groups_Ozero__class_Ozero(_330597)), -(c_Orderings_Oord__class_Oless__eq(_330597, c_Groups_Oplus__class_Oplus(_330597, _330599, _330599), c_Groups_Ozero__class_Ozero(_330597)))], (3274 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_330597, c_Groups_Oplus__class_Oplus(_330597, _330599, _330599), c_Groups_Ozero__class_Ozero(_330597)), -(c_Orderings_Oord__class_Oless__eq(_330597, _330599, c_Groups_Ozero__class_Ozero(_330597)))]]], (7037 ^ _221138) ^ [_462734] : [_462734 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, _462734) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (314 ^ _221138) ^ [_230761, _230763] : [-(class_Rings_Olinordered__semiring__1(_230761)), _230763 = _230761, class_Rings_Olinordered__semiring__1(_230763)], (10686 ^ _221138) ^ [_592233, _592235, _592237] : [class_Groups_Oordered__ab__group__add__abs(_592233), -(c_Orderings_Oord__class_Oless__eq(_592233, c_Groups_Ominus__class_Ominus(_592233, c_Groups_Oabs__class_Oabs(_592233, _592235), c_Groups_Oabs__class_Oabs(_592233, _592237)), c_Groups_Oabs__class_Oabs(_592233, c_Groups_Ominus__class_Ominus(_592233, _592237, _592235))))], (10964 ^ _221138) ^ [_603195, _603197, _603199] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _603195), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _603197, 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, _603197, _603199)), c_Groups_Oone__class_Oone(tc_Int_Oint))), _603195)), _603199))], (11669 ^ _221138) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (2964 ^ _221138) ^ [_319970, _319972] : [class_Rings_Ocomm__semiring__1(_319970), -(hAPP(c_Polynomial_Opoly(_319970, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_319970))), _319972) = c_Groups_Oone__class_Oone(_319970))], (10426 ^ _221138) ^ [_581199, _581201, _581203, _581205, _581207, _581209] : [class_Rings_Oordered__ring(_581199), 10429 ^ _221138 : [(10436 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_581199, c_Groups_Oplus__class_Oplus(_581199, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_581199), c_Groups_Ominus__class_Ominus(_581199, _581201, _581207)), _581203), _581205), _581209), -(c_Orderings_Oord__class_Oless__eq(_581199, c_Groups_Oplus__class_Oplus(_581199, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_581199), _581201), _581203), _581205), c_Groups_Oplus__class_Oplus(_581199, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_581199), _581207), _581203), _581209)))], (10430 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_581199, c_Groups_Oplus__class_Oplus(_581199, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_581199), _581201), _581203), _581205), c_Groups_Oplus__class_Oplus(_581199, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_581199), _581207), _581203), _581209)), -(c_Orderings_Oord__class_Oless__eq(_581199, c_Groups_Oplus__class_Oplus(_581199, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_581199), c_Groups_Ominus__class_Ominus(_581199, _581201, _581207)), _581203), _581205), _581209))]]], (6414 ^ _221138) ^ [_440258, _440260] : [class_RealVector_Oreal__normed__vector(_440258), 6417 ^ _221138 : [(6428 ^ _221138) ^ [] : [-(c_SEQ_OBseq(_440258, _440260)), 6429 ^ _221138 : [(6430 ^ _221138) ^ [_440896] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _440896), 6434 ^ _221138 : [(6435 ^ _221138) ^ [_441111] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_440258, c_Groups_Oplus__class_Oplus(_440258, hAPP(_440260, 6433 ^ [_440258, _440260, _440896, _441111]), c_Groups_Ouminus__class_Ouminus(_440258, hAPP(_440260, _441111)))), _440896)]]]]], (6418 ^ _221138) ^ [] : [c_SEQ_OBseq(_440258, _440260), 6422 ^ _221138 : [(6426 ^ _221138) ^ [_440747] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_440258, c_Groups_Oplus__class_Oplus(_440258, hAPP(_440260, _440747), c_Groups_Ouminus__class_Ouminus(_440258, hAPP(_440260, 6424 ^ [_440258, _440260])))), 6421 ^ [_440258, _440260]))], (6423 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 6421 ^ [_440258, _440260]))]]]]], (3604 ^ _221138) ^ [_341199, _341201, _341203] : [class_Rings_Oordered__ring(_341199), c_Orderings_Oord__class_Oless__eq(_341199, _341201, c_Groups_Ozero__class_Ozero(_341199)), c_Orderings_Oord__class_Oless__eq(_341199, _341203, c_Groups_Ozero__class_Ozero(_341199)), -(c_Orderings_Oord__class_Oless__eq(_341199, c_Groups_Ozero__class_Ozero(_341199), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_341199), _341201), _341203)))], (11123 ^ _221138) ^ [_609068, _609070] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _609068, _609070), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _609068, _609070))], (7577 ^ _221138) ^ [_482235] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_482235), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _482235, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (12213 ^ _221138) ^ [_644155] : [class_Rings_Olinordered__idom(_644155), -(class_Orderings_Olinorder(tc_Polynomial_Opoly(_644155)))], (5071 ^ _221138) ^ [_393966, _393968] : [5072 ^ _221138 : [(5075 ^ _221138) ^ [] : [_393966 = _393968], (5073 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _393966, _393968)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _393966, _393968))], (10898 ^ _221138) ^ [_600584, _600586, _600588] : [class_Groups_Oab__group__add(_600584), 10901 ^ _221138 : [(10908 ^ _221138) ^ [] : [c_Groups_Ominus__class_Ominus(_600584, _600586, _600588) = c_Groups_Ozero__class_Ozero(_600584), -(_600586 = _600588)], (10902 ^ _221138) ^ [] : [_600586 = _600588, -(c_Groups_Ominus__class_Ominus(_600584, _600586, _600588) = c_Groups_Ozero__class_Ozero(_600584))]]], (5427 ^ _221138) ^ [_406132, _406134, _406136] : [class_Groups_Oordered__ab__group__add(_406132), c_Orderings_Oord__class_Oless__eq(_406132, _406134, _406136), -(c_Orderings_Oord__class_Oless__eq(_406132, c_Groups_Ouminus__class_Ouminus(_406132, _406136), c_Groups_Ouminus__class_Ouminus(_406132, _406134)))], (1096 ^ _221138) ^ [_256635, _256637] : [hAPP(_256635, 1097 ^ [_256635, _256637]) = hAPP(_256637, 1097 ^ [_256635, _256637]), -(_256635 = _256637)], (8043 ^ _221138) ^ [_496991, _496993] : [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), _496991), _496993)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _496991)), -(_496993 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10161 ^ _221138) ^ [_571192, _571194] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _571192, c_RealDef_Oreal(tc_Nat_Onat, _571194)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_571192), _571194))], (9420 ^ _221138) ^ [_545251, _545253] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _545251, _545253), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _545251, c_Nat_OSuc(_545253)))], (11117 ^ _221138) ^ [_608894, _608896] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _608894, _608896), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _608894, _608896), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (4406 ^ _221138) ^ [_367776, _367778, _367780] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _367776), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _367778, _367780), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _367776), _367778), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _367776), _367780)))], (2362 ^ _221138) ^ [_297939, _297941, _297943, _297945] : [class_RealVector_Oreal__normed__algebra(_297939), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_297939), c_Groups_Oplus__class_Oplus(_297939, _297941, _297943)), _297945) = c_Groups_Oplus__class_Oplus(_297939, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_297939), _297941), _297945), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_297939), _297943), _297945)))], (1638 ^ _221138) ^ [_274241, _274243, _274245] : [class_Orderings_Opreorder(_274241), c_Orderings_Oord__class_Oless(_274241, _274243, _274245), c_Orderings_Oord__class_Oless(_274241, _274245, _274243)], (9998 ^ _221138) ^ [_565195, _565197, _565199, _565201, _565203] : [-(hAPP(hAPP(c_Power_Opower_Opower(_565195, _565197, _565199), _565201), c_Nat_OSuc(_565203)) = hAPP(hAPP(_565199, _565201), hAPP(hAPP(c_Power_Opower_Opower(_565195, _565197, _565199), _565201), _565203)))], (4478 ^ _221138) ^ [_370254, _370256, _370258] : [class_Rings_Olinordered__ring(_370254), c_Orderings_Oord__class_Oless(_370254, c_Groups_Oplus__class_Oplus(_370254, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_370254), _370256), _370256), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_370254), _370258), _370258)), c_Groups_Ozero__class_Ozero(_370254))], (10754 ^ _221138) ^ [_594836, _594838, _594840] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _594836, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _594838, _594840)), c_Rings_Odvd__class_Odvd(tc_Int_Oint, _594836, _594840), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _594836, _594838))], (10848 ^ _221138) ^ [_598551, _598553, _598555, _598557] : [class_RealVector_Oreal__normed__algebra(_598551), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_598551), _598553), c_Groups_Ominus__class_Ominus(_598551, _598555, _598557)) = c_Groups_Ominus__class_Ominus(_598551, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_598551), _598553), _598555), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_598551), _598553), _598557)))], (9199 ^ _221138) ^ [_537434, _537436] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_537434), c_Groups_Ozero__class_Ozero(_537434)), c_Nat_OSuc(_537436)) = c_Groups_Ozero__class_Ozero(_537434)), class_Power_Opower(_537434), class_Rings_Osemiring__0(_537434)], (3778 ^ _221138) ^ [_347014, _347016, _347018, _347020] : [class_Rings_Olinordered__ring__strict(_347014), 3781 ^ _221138 : [(3796 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(_347014, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_347014), _347016), _347018), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_347014), _347020), _347018))), 3797 ^ _221138 : [(3804 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_347014, _347018, c_Groups_Ozero__class_Ozero(_347014)), c_Orderings_Oord__class_Oless(_347014, _347020, _347016)], (3798 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_347014, c_Groups_Ozero__class_Ozero(_347014), _347018), c_Orderings_Oord__class_Oless(_347014, _347016, _347020)]]], (3782 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_347014, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_347014), _347016), _347018), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_347014), _347020), _347018)), 3787 ^ _221138 : [(3790 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(_347014, _347016, _347020))], (3788 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(_347014, c_Groups_Ozero__class_Ozero(_347014), _347018))]], 3791 ^ _221138 : [(3794 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(_347014, _347020, _347016))], (3792 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(_347014, _347018, c_Groups_Ozero__class_Ozero(_347014)))]]]]], (654 ^ _221138) ^ [_240791, _240793] : [-(class_Rings_Oring__1(_240791)), _240793 = _240791, class_Rings_Oring__1(_240793)], (932 ^ _221138) ^ [_250575, _250577, _250579, _250581] : [-(c_Nat__Transfer_Otsub(_250581, _250577) = c_Nat__Transfer_Otsub(_250579, _250575)), _250581 = _250579, _250577 = _250575], (9392 ^ _221138) ^ [_544183, _544185] : [9393 ^ _221138 : [(9394 ^ _221138) ^ [_544260] : [_544185 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _544183, _544260))]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _544183, _544185))], (2858 ^ _221138) ^ [_316200, _316202, _316204, _316206] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_316200), c_Orderings_Oord__class_Oless(_316200, c_Groups_Oplus__class_Oplus(_316200, _316202, _316204), c_Groups_Oplus__class_Oplus(_316200, _316206, _316204)), -(c_Orderings_Oord__class_Oless(_316200, _316202, _316206))], (10946 ^ _221138) ^ [_602321, _602323] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _602321, _602323), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _602321, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _602323, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (9784 ^ _221138) ^ [_557828, _557830, _557832] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _557828, _557830), _557832) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _557828, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _557830, _557832)))], (11815 ^ _221138) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal))], (9183 ^ _221138) ^ [_536829, _536831] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _536829)), _536831) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _536829), _536831)))], (1387 ^ _221138) ^ [_266140, _266142, _266144, _266146] : [class_Orderings_Oord(_266140), _266142 = _266144, c_Orderings_Oord__class_Oless__eq(_266140, _266144, _266146), -(c_Orderings_Oord__class_Oless__eq(_266140, _266142, _266146))], (4540 ^ _221138) ^ [_372447] : [_372447 = 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), _372447), _372447))], (9169 ^ _221138) ^ [_536353, _536355] : [_536353 = _536355, -(c_Nat_OSuc(_536353) = c_Nat_OSuc(_536355))], (1556 ^ _221138) ^ [_271617, _271619, _271621, _271623] : [class_Orderings_Oord(_271617), c_Orderings_Oord__class_Oless(_271617, _271619, _271621), _271621 = _271623, -(c_Orderings_Oord__class_Oless(_271617, _271619, _271623))], (4332 ^ _221138) ^ [_365290, _365292, _365294, _365296] : [class_Rings_Olinordered__semiring__strict(_365290), c_Orderings_Oord__class_Oless(_365290, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_365290), _365292), _365294), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_365290), _365292), _365296)), c_Orderings_Oord__class_Oless__eq(_365290, c_Groups_Ozero__class_Ozero(_365290), _365292), -(c_Orderings_Oord__class_Oless(_365290, _365294, _365296))], (11721 ^ _221138) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (6357 ^ _221138) ^ [_438206, _438208] : [class_Groups_Olinordered__ab__group__add(_438206), 6360 ^ _221138 : [(6367 ^ _221138) ^ [] : [_438208 = c_Groups_Ozero__class_Ozero(_438206), -(c_Groups_Oplus__class_Oplus(_438206, _438208, _438208) = c_Groups_Ozero__class_Ozero(_438206))], (6361 ^ _221138) ^ [] : [c_Groups_Oplus__class_Oplus(_438206, _438208, _438208) = c_Groups_Ozero__class_Ozero(_438206), -(_438208 = c_Groups_Ozero__class_Ozero(_438206))]]], (6255 ^ _221138) ^ [_434663, _434665, _434667] : [6256 ^ _221138 : [(6259 ^ _221138) ^ [] : [_434663 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (6257 ^ _221138) ^ [] : [_434665 = _434667]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _434663), _434665) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _434663), _434667))], (8923 ^ _221138) ^ [_527783, _527785] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Nat_OSuc(_527783), _527785) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _527783, c_Nat_OSuc(_527785)))], (5709 ^ _221138) ^ [_415980, _415982] : [class_Groups_Oordered__ab__group__add(_415980), 5712 ^ _221138 : [(5719 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_415980, c_Groups_Ozero__class_Ozero(_415980), _415982), -(c_Orderings_Oord__class_Oless(_415980, c_Groups_Ouminus__class_Ouminus(_415980, _415982), c_Groups_Ozero__class_Ozero(_415980)))], (5713 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_415980, c_Groups_Ouminus__class_Ouminus(_415980, _415982), c_Groups_Ozero__class_Ozero(_415980)), -(c_Orderings_Oord__class_Oless(_415980, c_Groups_Ozero__class_Ozero(_415980), _415982))]]], (11097 ^ _221138) ^ [_607931, _607933] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _607931, _607933), _607933) = _607931)], (4202 ^ _221138) ^ [_360964, _360966, _360968, _360970, _360972] : [class_Rings_Olinordered__semiring__strict(_360964), c_Orderings_Oord__class_Oless(_360964, _360966, _360968), c_Orderings_Oord__class_Oless(_360964, _360970, _360972), c_Orderings_Oord__class_Oless(_360964, c_Groups_Ozero__class_Ozero(_360964), _360968), c_Orderings_Oord__class_Oless__eq(_360964, c_Groups_Ozero__class_Ozero(_360964), _360970), -(c_Orderings_Oord__class_Oless(_360964, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_360964), _360966), _360970), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_360964), _360968), _360972)))], (8451 ^ _221138) ^ [_511654, _511656, _511658, _511660] : [class_Rings_Olinordered__semidom(_511654), hAPP(hAPP(c_Power_Opower__class_Opower(_511654), _511656), _511658) = hAPP(hAPP(c_Power_Opower__class_Opower(_511654), _511660), _511658), c_Orderings_Oord__class_Oless__eq(_511654, c_Groups_Ozero__class_Ozero(_511654), _511656), c_Orderings_Oord__class_Oless__eq(_511654, c_Groups_Ozero__class_Ozero(_511654), _511660), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _511658), -(_511656 = _511660)], (11925 ^ _221138) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex))], (1197 ^ _221138) ^ [_260013, _260015] : [class_Rings_Ocomm__semiring__0(_260013), -(hAPP(c_Polynomial_Opoly(_260013, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_260013))), _260015) = c_Groups_Ozero__class_Ozero(_260013))], (254 ^ _221138) ^ [_228991, _228993] : [-(class_Groups_Ocancel__ab__semigroup__add(_228991)), _228993 = _228991, class_Groups_Ocancel__ab__semigroup__add(_228993)], (6023 ^ _221138) ^ [_426425, _426427] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _426425), _426427), -(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, _426425, _426427)))], (11335 ^ _221138) ^ [_616671, _616673, _616675] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _616671, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _616675, _616673)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _616671, _616673), _616675))], (12099 ^ _221138) ^ [_640545] : [class_Groups_Ocancel__comm__monoid__add(_640545), -(class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(_640545)))], (9486 ^ _221138) ^ [_547554, _547556] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _547554), c_Nat_OSuc(_547556)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _547554, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _547554), _547556)))], (11819 ^ _221138) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal))], (11691 ^ _221138) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (1892 ^ _221138) ^ [_282248, _282250, _282252] : [class_Orderings_Oorder(_282248), c_Orderings_Oord__class_Oless__eq(_282248, _282250, _282252), -(_282252 = _282250), -(c_Orderings_Oord__class_Oless(_282248, _282250, _282252))], (7477 ^ _221138) ^ [_478658, _478660, _478662] : [class_RealVector_Oreal__normed__algebra__1(_478658), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_478658, hAPP(hAPP(c_Power_Opower__class_Opower(_478658), _478660), _478662)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_478658, _478660)), _478662)))], (10952 ^ _221138) ^ [_602587, _602589, _602591, _602593, _602595] : [class_RealVector_Oreal__normed__vector(_602587), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_602587, c_Groups_Ominus__class_Ominus(_602587, c_Groups_Oplus__class_Oplus(_602587, _602589, _602591), c_Groups_Oplus__class_Oplus(_602587, _602593, _602595))), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_602587, c_Groups_Ominus__class_Ominus(_602587, _602589, _602593)), c_RealVector_Onorm__class_Onorm(_602587, c_Groups_Ominus__class_Ominus(_602587, _602591, _602595)))))], (1401 ^ _221138) ^ [_266572, _266574, _266576] : [class_Orderings_Oorder(_266572), c_Orderings_Oord__class_Oless__eq(_266572, _266574, _266576), 1408 ^ _221138 : [(1415 ^ _221138) ^ [] : [_266576 = _266574, -(c_Orderings_Oord__class_Oless__eq(_266572, _266576, _266574))], (1409 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_266572, _266576, _266574), -(_266576 = _266574)]]], (7309 ^ _221138) ^ [_472211, _472213, _472215] : [class_Rings_Ocomm__semiring__1(_472211), -(c_Rings_Odvd__class_Odvd(_472211, _472213, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_472211), _472213), _472215)))], (11587 ^ _221138) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (9402 ^ _221138) ^ [_544662, _544664] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _544662, _544664), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_544662), _544664))], (534 ^ _221138) ^ [_237251, _237253] : [-(class_Groups_Ogroup__add(_237251)), _237253 = _237251, class_Groups_Ogroup__add(_237253)], (4840 ^ _221138) ^ [_385176, _385178, _385180] : [class_Rings_Olinordered__ring__strict(_385176), 4843 ^ _221138 : [(4852 ^ _221138) ^ [] : [-(c_Groups_Oplus__class_Oplus(_385176, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_385176), _385178), _385178), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_385176), _385180), _385180)) = c_Groups_Ozero__class_Ozero(_385176)), _385178 = c_Groups_Ozero__class_Ozero(_385176), _385180 = c_Groups_Ozero__class_Ozero(_385176)], (4844 ^ _221138) ^ [] : [c_Groups_Oplus__class_Oplus(_385176, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_385176), _385178), _385178), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_385176), _385180), _385180)) = c_Groups_Ozero__class_Ozero(_385176), 4847 ^ _221138 : [(4850 ^ _221138) ^ [] : [-(_385180 = c_Groups_Ozero__class_Ozero(_385176))], (4848 ^ _221138) ^ [] : [-(_385178 = c_Groups_Ozero__class_Ozero(_385176))]]]]], (3132 ^ _221138) ^ [_326034, _326036] : [class_RealVector_Oreal__normed__algebra(_326034), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_326034), _326036), c_Groups_Ozero__class_Ozero(_326034)) = c_Groups_Ozero__class_Ozero(_326034))], (12243 ^ _221138) ^ [_645105] : [class_Groups_Oab__group__add(_645105), -(class_Groups_Ogroup__add(tc_Polynomial_Opoly(_645105)))], (2946 ^ _221138) ^ [_319135] : [class_Rings_Ozero__neq__one(_319135), c_Groups_Ozero__class_Ozero(_319135) = c_Groups_Oone__class_Oone(_319135)], (9432 ^ _221138) ^ [_545670, _545672] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _545670, _545672), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_545670), _545672))], (6937 ^ _221138) ^ [_459209, _459211] : [class_RealVector_Oreal__normed__vector(_459209), 6940 ^ _221138 : [(6947 ^ _221138) ^ [] : [-(_459211 = c_Groups_Ozero__class_Ozero(_459209)), -(c_RealVector_Onorm__class_Onorm(_459209, c_Groups_Osgn__class_Osgn(_459209, _459211)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (6941 ^ _221138) ^ [] : [_459211 = c_Groups_Ozero__class_Ozero(_459209), -(c_RealVector_Onorm__class_Onorm(_459209, c_Groups_Osgn__class_Osgn(_459209, _459211)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))]]], (1584 ^ _221138) ^ [_272509, _272511, _272513, _272515] : [class_Orderings_Oord(_272509), _272511 = _272513, c_Orderings_Oord__class_Oless(_272509, _272513, _272515), -(c_Orderings_Oord__class_Oless(_272509, _272511, _272515))], (6347 ^ _221138) ^ [_437894, _437896] : [_437894 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _437894), _437896), -(_437896 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_437894 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4594 ^ _221138) ^ [_374766, _374768, _374770] : [class_Rings_Olinordered__idom(_374766), c_Polynomial_Opos__poly(_374766, _374768), c_Polynomial_Opos__poly(_374766, _374770), -(c_Polynomial_Opos__poly(_374766, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_374766), _374768, _374770)))], (2614 ^ _221138) ^ [_307499, _307501] : [c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _307499), _307499), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _307501), _307501)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 2617 ^ _221138 : [(2620 ^ _221138) ^ [] : [-(_307501 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (2618 ^ _221138) ^ [] : [-(_307499 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))]]], (878 ^ _221138) ^ [_248635, _248637, _248639, _248641, _248643, _248645] : [-(c_Polynomial_Oorder(_248645, _248641, _248637) = c_Polynomial_Oorder(_248643, _248639, _248635)), _248645 = _248643, _248641 = _248639, _248637 = _248635], (4909 ^ _221138) ^ [_387886] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _387886, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _387886), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _387886), _387886))))], (12177 ^ _221138) ^ [_643015] : [class_Rings_Ocomm__semiring__0(_643015), -(class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(_643015)))], (11837 ^ _221138) ^ [] : [-(class_Rings_Olinordered__semidom(tc_RealDef_Oreal))], (10442 ^ _221138) ^ [_581903, _581905, _581907, _581909, _581911, _581913] : [class_Rings_Oordered__ring(_581903), 10445 ^ _221138 : [(10452 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_581903, _581909, c_Groups_Oplus__class_Oplus(_581903, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_581903), c_Groups_Ominus__class_Ominus(_581903, _581911, _581905)), _581907), _581913)), -(c_Orderings_Oord__class_Oless__eq(_581903, c_Groups_Oplus__class_Oplus(_581903, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_581903), _581905), _581907), _581909), c_Groups_Oplus__class_Oplus(_581903, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_581903), _581911), _581907), _581913)))], (10446 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_581903, c_Groups_Oplus__class_Oplus(_581903, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_581903), _581905), _581907), _581909), c_Groups_Oplus__class_Oplus(_581903, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_581903), _581911), _581907), _581913)), -(c_Orderings_Oord__class_Oless__eq(_581903, _581909, c_Groups_Oplus__class_Oplus(_581903, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_581903), c_Groups_Ominus__class_Ominus(_581903, _581911, _581905)), _581907), _581913)))]]], (7249 ^ _221138) ^ [_470013, _470015, _470017, _470019] : [class_Rings_Ocomm__semiring__1(_470013), c_Rings_Odvd__class_Odvd(_470013, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_470013), _470015), _470017), _470019), -(c_Rings_Odvd__class_Odvd(_470013, _470015, _470019))], (4748 ^ _221138) ^ [_381442, _381444, _381446, _381448] : [class_Rings_Ocomm__semiring__1(_381442), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_381442), _381444), c_Groups_Oplus__class_Oplus(_381442, _381446, _381448)) = c_Groups_Oplus__class_Oplus(_381442, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_381442), _381444), _381446), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_381442), _381444), _381448)))], (5031 ^ _221138) ^ [_392439, _392441, _392443, _392445] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _392439, _392441), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _392443, _392445), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _392439, _392443), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _392441, _392445)))], (1006 ^ _221138) ^ [_253286, _253288, _253290, _253292, _253294, _253296] : [-(c_Groups_Ominus__class_Ominus(_253296, _253292, _253288) = c_Groups_Ominus__class_Ominus(_253294, _253290, _253286)), _253296 = _253294, _253292 = _253290, _253288 = _253286], (11769 ^ _221138) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (9095 ^ _221138) ^ [_533834, _533836] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _533834, _533836)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_533836), _533834))], (11490 ^ _221138) ^ [_622868, _622870, _622872] : [-(hBOOL(hAPP(_622868, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _622870, _622872)))), 11493 ^ _221138 : [(11496 ^ _221138) ^ [] : [hBOOL(hAPP(_622868, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (11494 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _622870, _622872))]], 11498 ^ _221138 : [(11501 ^ _221138) ^ [] : [hBOOL(hAPP(_622868, 11497 ^ [_622868, _622870, _622872]))], (11499 ^ _221138) ^ [] : [-(_622870 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _622872, 11497 ^ [_622868, _622870, _622872]))]]], (10556 ^ _221138) ^ [_586799, _586801, _586803, _586805] : [class_Rings_Olinordered__idom(_586799), 10559 ^ _221138 : [(10568 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(_586799, c_Groups_Oabs__class_Oabs(_586799, c_Groups_Ominus__class_Ominus(_586799, _586801, _586803)), _586805)), c_Orderings_Oord__class_Oless(_586799, c_Groups_Ominus__class_Ominus(_586799, _586803, _586805), _586801), c_Orderings_Oord__class_Oless(_586799, _586801, c_Groups_Oplus__class_Oplus(_586799, _586803, _586805))], (10560 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_586799, c_Groups_Oabs__class_Oabs(_586799, c_Groups_Ominus__class_Ominus(_586799, _586801, _586803)), _586805), 10563 ^ _221138 : [(10566 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(_586799, _586801, c_Groups_Oplus__class_Oplus(_586799, _586803, _586805)))], (10564 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(_586799, c_Groups_Ominus__class_Ominus(_586799, _586803, _586805), _586801))]]]]], (2556 ^ _221138) ^ [_305359, _305361] : [class_Groups_Omonoid__mult(_305359), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_305359), c_Groups_Oone__class_Oone(_305359)), _305361) = _305361)], (7487 ^ _221138) ^ [_479048, _479050] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _479048, _479050), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_479048), c_RComplete_Onatceiling(_479050)))], (4997 ^ _221138) ^ [_391111, _391113, _391115] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _391111, _391113), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _391111, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _391115, _391113)))], (11789 ^ _221138) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal))], (7203 ^ _221138) ^ [_468461, _468463, _468465] : [class_Rings_Olinordered__idom(_468461), 7206 ^ _221138 : [(7213 ^ _221138) ^ [] : [c_Rings_Odvd__class_Odvd(_468461, _468463, _468465), -(c_Rings_Odvd__class_Odvd(_468461, _468463, c_Groups_Oabs__class_Oabs(_468461, _468465)))], (7207 ^ _221138) ^ [] : [c_Rings_Odvd__class_Odvd(_468461, _468463, c_Groups_Oabs__class_Oabs(_468461, _468465)), -(c_Rings_Odvd__class_Odvd(_468461, _468463, _468465))]]], (11597 ^ _221138) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))], (4931 ^ _221138) ^ [_388774, _388776] : [4932 ^ _221138 : [(4933 ^ _221138) ^ [_388849] : [_388776 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _388774, _388849)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _388774, _388776))], (514 ^ _221138) ^ [_236661, _236663] : [-(class_Groups_Omonoid__add(_236661)), _236663 = _236661, class_Groups_Omonoid__add(_236663)], (4973 ^ _221138) ^ [_390215, _390217, _390219] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _390215, _390217), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _390215, _390219)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _390217, _390219))], (10628 ^ _221138) ^ [_589817, _589819, _589821, _589823, _589825, _589827] : [class_Rings_Oring(_589817), 10631 ^ _221138 : [(10638 ^ _221138) ^ [] : [_589823 = c_Groups_Oplus__class_Oplus(_589817, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_589817), c_Groups_Ominus__class_Ominus(_589817, _589825, _589819)), _589821), _589827), -(c_Groups_Oplus__class_Oplus(_589817, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_589817), _589819), _589821), _589823) = c_Groups_Oplus__class_Oplus(_589817, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_589817), _589825), _589821), _589827))], (10632 ^ _221138) ^ [] : [c_Groups_Oplus__class_Oplus(_589817, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_589817), _589819), _589821), _589823) = c_Groups_Oplus__class_Oplus(_589817, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_589817), _589825), _589821), _589827), -(_589823 = c_Groups_Oplus__class_Oplus(_589817, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_589817), c_Groups_Ominus__class_Ominus(_589817, _589825, _589819)), _589821), _589827))]]], (3480 ^ _221138) ^ [_337309, _337311, _337313] : [class_Rings_Olinordered__ring__strict(_337309), 3483 ^ _221138 : [(3498 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_337309, c_Groups_Ozero__class_Ozero(_337309), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_337309), _337311), _337313))), 3499 ^ _221138 : [(3506 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_337309, _337311, c_Groups_Ozero__class_Ozero(_337309)), c_Orderings_Oord__class_Oless__eq(_337309, _337313, c_Groups_Ozero__class_Ozero(_337309))], (3500 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_337309, c_Groups_Ozero__class_Ozero(_337309), _337311), c_Orderings_Oord__class_Oless__eq(_337309, c_Groups_Ozero__class_Ozero(_337309), _337313)]]], (3484 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_337309, c_Groups_Ozero__class_Ozero(_337309), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_337309), _337311), _337313)), 3489 ^ _221138 : [(3492 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_337309, c_Groups_Ozero__class_Ozero(_337309), _337313))], (3490 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_337309, c_Groups_Ozero__class_Ozero(_337309), _337311))]], 3493 ^ _221138 : [(3496 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_337309, _337313, c_Groups_Ozero__class_Ozero(_337309)))], (3494 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_337309, _337311, c_Groups_Ozero__class_Ozero(_337309)))]]]]], (11267 ^ _221138) ^ [_614182, _614184, _614186] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _614182, _614184), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _614186, _614184), _614182) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _614186, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _614184, _614182)))], (8783 ^ _221138) ^ [_522795, _522797] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _522795, _522797)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _522795, _522797), -(_522795 = _522797)], (6035 ^ _221138) ^ [_426864, _426866] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _426866, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _426864)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _426864, _426866), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (3162 ^ _221138) ^ [_327194, _327196] : [class_Groups_Oordered__ab__group__add__abs(_327194), 3165 ^ _221138 : [(3172 ^ _221138) ^ [] : [_327196 = c_Groups_Ozero__class_Ozero(_327194), -(c_Orderings_Oord__class_Oless__eq(_327194, c_Groups_Oabs__class_Oabs(_327194, _327196), c_Groups_Ozero__class_Ozero(_327194)))], (3166 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_327194, c_Groups_Oabs__class_Oabs(_327194, _327196), c_Groups_Ozero__class_Ozero(_327194)), -(_327196 = c_Groups_Ozero__class_Ozero(_327194))]]], (12147 ^ _221138) ^ [_642065] : [class_Rings_Oidom(_642065), -(class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(_642065)))], (12189 ^ _221138) ^ [_643395] : [class_Groups_Oab__group__add(_643395), -(class_Groups_Oab__group__add(tc_Polynomial_Opoly(_643395)))], (11539 ^ _221138) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex))], (2316 ^ _221138) ^ [_295990, _295992, _295994] : [class_Groups_Oordered__ab__group__add__abs(_295990), -(c_Orderings_Oord__class_Oless__eq(_295990, c_Groups_Oabs__class_Oabs(_295990, c_Groups_Oplus__class_Oplus(_295990, _295992, _295994)), c_Groups_Oplus__class_Oplus(_295990, c_Groups_Oabs__class_Oabs(_295990, _295992), c_Groups_Oabs__class_Oabs(_295990, _295994))))], (3088 ^ _221138) ^ [_324266, _324268, _324270] : [class_RealVector_Oreal__normed__algebra(_324266), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_324266, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_324266), _324268), _324270)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_324266, _324268)), c_RealVector_Onorm__class_Onorm(_324266, _324270))))], (634 ^ _221138) ^ [_240201, _240203] : [-(class_Groups_Oabs__if(_240201)), _240203 = _240201, class_Groups_Oabs__if(_240203)], (3956 ^ _221138) ^ [_352796, _352798, _352800] : [class_Rings_Olinordered__semiring__strict(_352796), c_Orderings_Oord__class_Oless(_352796, _352798, c_Groups_Ozero__class_Ozero(_352796)), c_Orderings_Oord__class_Oless(_352796, c_Groups_Ozero__class_Ozero(_352796), _352800), -(c_Orderings_Oord__class_Oless(_352796, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_352796), _352798), _352800), c_Groups_Ozero__class_Ozero(_352796)))], (6813 ^ _221138) ^ [_455100, _455102] : [class_Lattices_Oab__semigroup__idem__mult(_455100), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_455100), _455102), _455102) = _455102)], (11347 ^ _221138) ^ [_617158, _617160] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _617158, c_Nat_OSuc(_617160)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _617158, c_Groups_Oone__class_Oone(tc_Nat_Onat)), _617160))], (8805 ^ _221138) ^ [_523545] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oabs__class_Oabs(tc_Int_Oint, _523545), c_Groups_Oone__class_Oone(tc_Int_Oint)), -(_523545 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (5307 ^ _221138) ^ [_402368] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _402368, _402368))], (2926 ^ _221138) ^ [_318523, _318525, _318527] : [class_Rings_Ono__zero__divisors(_318523), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_318523), _318525), _318527) = c_Groups_Ozero__class_Ozero(_318523), -(_318525 = c_Groups_Ozero__class_Ozero(_318523)), -(_318527 = c_Groups_Ozero__class_Ozero(_318523))], (4822 ^ _221138) ^ [_384556, _384558, _384560, _384562, _384564, _384566] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_384556), -(_384558 = c_Groups_Ozero__class_Ozero(_384556)), c_Groups_Oplus__class_Oplus(_384556, _384560, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_384556), _384558), _384564)) = c_Groups_Oplus__class_Oplus(_384556, _384562, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_384556), _384558), _384566)), _384560 = _384562, -(_384564 = _384566)], (5801 ^ _221138) ^ [_418991, _418993] : [class_Rings_Oring__1__no__zero__divisors(_418991), 5804 ^ _221138 : [(5805 ^ _221138) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_418991), _418993), _418993) = c_Groups_Oone__class_Oone(_418991), -(_418993 = c_Groups_Oone__class_Oone(_418991)), -(_418993 = c_Groups_Ouminus__class_Ouminus(_418991, c_Groups_Oone__class_Oone(_418991)))], (5815 ^ _221138) ^ [] : [5816 ^ _221138 : [(5819 ^ _221138) ^ [] : [_418993 = c_Groups_Ouminus__class_Ouminus(_418991, c_Groups_Oone__class_Oone(_418991))], (5817 ^ _221138) ^ [] : [_418993 = c_Groups_Oone__class_Oone(_418991)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_418991), _418993), _418993) = c_Groups_Oone__class_Oone(_418991))]]], (12039 ^ _221138) ^ [_638645] : [class_Rings_Olinordered__idom(_638645), -(class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(_638645)))], (5923 ^ _221138) ^ [_422993, _422995] : [_422995 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _422993), -(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _422993, _422995) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (5189 ^ _221138) ^ [_398227, _398229] : [5190 ^ _221138 : [(5193 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _398229, _398227)], (5191 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _398227, _398229)]], _398227 = _398229], (7651 ^ _221138) ^ [_484597, _484599, _484601] : [class_Rings_Olinordered__semidom(_484597), c_Orderings_Oord__class_Oless(_484597, c_Groups_Oone__class_Oone(_484597), _484599), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _484601), -(c_Orderings_Oord__class_Oless(_484597, c_Groups_Oone__class_Oone(_484597), hAPP(hAPP(c_Power_Opower__class_Opower(_484597), _484599), _484601)))], (4905 ^ _221138) ^ [_387702, _387704] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _387702, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _387704, _387702)))], (4714 ^ _221138) ^ [_380236, _380238] : [class_Rings_Ocomm__semiring__1(_380236), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_380236), c_Groups_Ozero__class_Ozero(_380236)), _380238) = c_Groups_Ozero__class_Ozero(_380236))], (4776 ^ _221138) ^ [_382604, _382606, _382608, _382610] : [class_Rings_Ocomm__semiring__1(_382604), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_382604), c_Groups_Oplus__class_Oplus(_382604, _382606, _382608)), _382610) = c_Groups_Oplus__class_Oplus(_382604, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_382604), _382606), _382610), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_382604), _382608), _382610)))], (1110 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 1108 ^ []))], (11887 ^ _221138) ^ [] : [-(class_Orderings_Oorder(tc_RealDef_Oreal))], (8419 ^ _221138) ^ [_510577, _510579, _510581] : [class_Rings_Olinordered__semidom(_510577), c_Orderings_Oord__class_Oless(_510577, c_Groups_Ozero__class_Ozero(_510577), _510579), c_Orderings_Oord__class_Oless(_510577, _510579, c_Groups_Oone__class_Oone(_510577)), -(c_Orderings_Oord__class_Oless(_510577, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_510577), _510579), hAPP(hAPP(c_Power_Opower__class_Opower(_510577), _510579), _510581)), hAPP(hAPP(c_Power_Opower__class_Opower(_510577), _510579), _510581)))], (9996 ^ _221138) ^ [_565045, _565047, _565049, _565051] : [-(hAPP(hAPP(c_Power_Opower_Opower(_565045, _565047, _565049), _565051), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _565047)], (10028 ^ _221138) ^ [_566268, _566270] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _566268), _566270), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _566270, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _566268), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_RComplete_Onatceiling(_566270) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _566268, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (2844 ^ _221138) ^ [_315722, _315724, _315726, _315728, _315730] : [class_Groups_Oordered__cancel__ab__semigroup__add(_315722), c_Orderings_Oord__class_Oless(_315722, _315724, _315726), c_Orderings_Oord__class_Oless(_315722, _315728, _315730), -(c_Orderings_Oord__class_Oless(_315722, c_Groups_Oplus__class_Oplus(_315722, _315724, _315728), c_Groups_Oplus__class_Oplus(_315722, _315726, _315730)))], (5823 ^ _221138) ^ [_419658, _419660] : [class_Rings_Ocomm__ring__1(_419658), -(c_Groups_Ouminus__class_Ouminus(_419658, _419660) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_419658), c_Groups_Ouminus__class_Ouminus(_419658, c_Groups_Oone__class_Oone(_419658))), _419660))], (1030 ^ _221138) ^ [_254105, _254107] : [_254107 = _254105, -(tc_Polynomial_Opoly(_254107) = tc_Polynomial_Opoly(_254105))], (3548 ^ _221138) ^ [_339407, _339409, _339411] : [class_Rings_Oordered__cancel__semiring(_339407), c_Orderings_Oord__class_Oless__eq(_339407, c_Groups_Ozero__class_Ozero(_339407), _339409), c_Orderings_Oord__class_Oless__eq(_339407, c_Groups_Ozero__class_Ozero(_339407), _339411), -(c_Orderings_Oord__class_Oless__eq(_339407, c_Groups_Ozero__class_Ozero(_339407), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_339407), _339409), _339411)))], (12327 ^ _221138) ^ [_647765] : [class_Rings_Ocomm__ring(_647765), -(class_Rings_Oring(tc_Polynomial_Opoly(_647765)))], (7731 ^ _221138) ^ [_487046, _487048, _487050] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _487046, _487048), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _487048, _487046)), _487048 = _487050, 7742 ^ _221138 : [(7745 ^ _221138) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _487050, _487046)], (7743 ^ _221138) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _487046, _487050))]]], (4670 ^ _221138) ^ [_378197, _378199] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _378197), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, _378197, _378199)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _378199))))], (7921 ^ _221138) ^ [_492945, _492947] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _492945, _492947), 7924 ^ _221138 : [(7931 ^ _221138) ^ [] : [_492947 = _492945, -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _492947, _492945))], (7925 ^ _221138) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _492947, _492945), -(_492947 = _492945)]]], (9672 ^ _221138) ^ [_553921] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _553921, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (6517 ^ _221138) ^ [_444826] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _444826), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _444826)], (1441 ^ _221138) ^ [_267872, _267874, _267876] : [class_Orderings_Oorder(_267872), 1444 ^ _221138 : [(1453 ^ _221138) ^ [] : [-(_267874 = _267876), c_Orderings_Oord__class_Oless__eq(_267872, _267874, _267876), c_Orderings_Oord__class_Oless__eq(_267872, _267876, _267874)], (1445 ^ _221138) ^ [] : [_267874 = _267876, 1448 ^ _221138 : [(1451 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_267872, _267876, _267874))], (1449 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_267872, _267874, _267876))]]]]], (10369 ^ _221138) ^ [_578923, _578925] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _578923), -(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, _578925)), _578923), 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, _578923, c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), _578925)))], (11953 ^ _221138) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Complex_Ocomplex))], (916 ^ _221138) ^ [_249970, _249972] : [_249972 = _249970, -(c_Power_Opower__class_Opower(_249972) = c_Power_Opower__class_Opower(_249970))], (1249 ^ _221138) ^ [_261734, _261736] : [class_Int_Oring__char__0(_261734), class_Rings_Oidom(_261734), 1256 ^ _221138 : [(1263 ^ _221138) ^ [] : [_261736 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_261734)), -(c_Polynomial_Opoly(_261734, _261736) = c_Polynomial_Opoly(_261734, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_261734))))], (1257 ^ _221138) ^ [] : [c_Polynomial_Opoly(_261734, _261736) = c_Polynomial_Opoly(_261734, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_261734))), -(_261736 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_261734)))]]], (12357 ^ _221138) ^ [_648735, _648737] : [_648735 = _648737, -(hBOOL(c_fequal(_648735, _648737)))], (124 ^ _221138) ^ [_225156, _225158] : [-(class_RealVector_Oreal__normed__algebra__1(_225156)), _225158 = _225156, class_RealVector_Oreal__normed__algebra__1(_225158)], (11559 ^ _221138) ^ [_625479, _625481] : [class_Orderings_Oorder(_625479), -(class_Orderings_Oorder(tc_fun(_625481, _625479)))], (434 ^ _221138) ^ [_234301, _234303] : [-(class_Rings_Olinordered__ring(_234301)), _234303 = _234301, class_Rings_Olinordered__ring(_234303)], (11839 ^ _221138) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal))], (5009 ^ _221138) ^ [_391603, _391605, _391607] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _391603, _391605), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _391603), _391607), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _391605), _391607)))], (5125 ^ _221138) ^ [_395937, _395939, _395941] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _395937, _395939), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _395937, _395941), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _395939, _395941)))], (5051 ^ _221138) ^ [_393171, _393173, _393175] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _393171, _393173), _393175), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _393173, _393175))], (7897 ^ _221138) ^ [_492179, _492181] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _492179, _492181), -(_492179 = _492181), 7904 ^ _221138 : [(7907 ^ _221138) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _492181, _492179)], (7905 ^ _221138) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _492179, _492181))]]], (3210 ^ _221138) ^ [_328690, _328692] : [class_Groups_Oordered__ab__group__add__abs(_328690), c_Orderings_Oord__class_Oless(_328690, c_Groups_Ozero__class_Ozero(_328690), _328692), -(c_Groups_Oabs__class_Oabs(_328690, _328692) = _328692)], (7441 ^ _221138) ^ [_476984, _476986] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _476984, _476986), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _476984, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _476986, _476984)))], (4552 ^ _221138) ^ [_372962, _372964, _372966] : [class_Rings_Ocomm__semiring__1(_372962), -(c_Groups_Oplus__class_Oplus(_372962, _372964, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_372962), _372966), _372964)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_372962), c_Groups_Oplus__class_Oplus(_372962, _372966, c_Groups_Oone__class_Oone(_372962))), _372964))], (1463 ^ _221138) ^ [_268530, _268532, _268534] : [class_Orderings_Olinorder(_268530), -(c_Orderings_Oord__class_Oless__eq(_268530, _268532, _268534)), -(c_Orderings_Oord__class_Oless__eq(_268530, _268534, _268532))], (8345 ^ _221138) ^ [_507886, _507888, _507890] : [class_Rings_Olinordered__idom(_507886), -(c_Orderings_Oord__class_Oless__eq(_507886, c_Groups_Ozero__class_Ozero(_507886), hAPP(hAPP(c_Power_Opower__class_Opower(_507886), c_Groups_Oabs__class_Oabs(_507886, _507888)), _507890)))], (1954 ^ _221138) ^ [_284097, _284099, _284101] : [class_Orderings_Opreorder(_284097), c_Orderings_Oord__class_Oless(_284097, _284099, _284101), -(c_Orderings_Oord__class_Oless__eq(_284097, _284099, _284101))], (12315 ^ _221138) ^ [_647385] : [class_Rings_Ocomm__semiring__1(_647385), -(class_Power_Opower(tc_Polynomial_Opoly(_647385)))], (6077 ^ _221138) ^ [_428371] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _428371, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _428371) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _428371))], (12027 ^ _221138) ^ [_638265] : [class_Rings_Olinordered__idom(_638265), -(class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(_638265)))], (3894 ^ _221138) ^ [_350777, _350779, _350781] : [class_Rings_Olinordered__semiring__strict(_350777), c_Orderings_Oord__class_Oless(_350777, c_Groups_Ozero__class_Ozero(_350777), _350779), c_Orderings_Oord__class_Oless(_350777, _350781, c_Groups_Ozero__class_Ozero(_350777)), -(c_Orderings_Oord__class_Oless(_350777, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_350777), _350781), _350779), c_Groups_Ozero__class_Ozero(_350777)))], (1118 ^ _221138) ^ [_257472, _257474] : [class_RealVector_Oreal__normed__vector(_257472), 1121 ^ _221138 : [(1128 ^ _221138) ^ [] : [-(_257474 = c_Groups_Ozero__class_Ozero(_257472)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_257472, _257474)))], (1122 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_257472, _257474)), _257474 = c_Groups_Ozero__class_Ozero(_257472)]]], (4224 ^ _221138) ^ [_361686, _361688, _361690, _361692, _361694] : [class_Rings_Olinordered__semiring__strict(_361686), c_Orderings_Oord__class_Oless(_361686, _361688, _361690), c_Orderings_Oord__class_Oless(_361686, _361692, _361694), c_Orderings_Oord__class_Oless__eq(_361686, c_Groups_Ozero__class_Ozero(_361686), _361688), c_Orderings_Oord__class_Oless__eq(_361686, c_Groups_Ozero__class_Ozero(_361686), _361692), -(c_Orderings_Oord__class_Oless(_361686, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_361686), _361688), _361692), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_361686), _361690), _361694)))], (3812 ^ _221138) ^ [_348117, _348119, _348121, _348123] : [class_Rings_Olinordered__ring__strict(_348117), 3815 ^ _221138 : [(3830 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(_348117, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_348117), _348119), _348121), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_348117), _348119), _348123))), 3831 ^ _221138 : [(3838 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_348117, _348119, c_Groups_Ozero__class_Ozero(_348117)), c_Orderings_Oord__class_Oless(_348117, _348123, _348121)], (3832 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_348117, c_Groups_Ozero__class_Ozero(_348117), _348119), c_Orderings_Oord__class_Oless(_348117, _348121, _348123)]]], (3816 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_348117, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_348117), _348119), _348121), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_348117), _348119), _348123)), 3821 ^ _221138 : [(3824 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(_348117, _348121, _348123))], (3822 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(_348117, c_Groups_Ozero__class_Ozero(_348117), _348119))]], 3825 ^ _221138 : [(3828 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(_348117, _348123, _348121))], (3826 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(_348117, _348119, c_Groups_Ozero__class_Ozero(_348117)))]]]]], (12183 ^ _221138) ^ [_643205] : [class_Rings_Ocomm__semiring__0(_643205), -(class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(_643205)))], (2648 ^ _221138) ^ [_308662, _308664, _308666] : [class_RealVector_Oreal__normed__div__algebra(_308662), -(c_RealVector_Onorm__class_Onorm(_308662, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_308662), _308664), _308666)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_308662, _308664)), c_RealVector_Onorm__class_Onorm(_308662, _308666)))], (7909 ^ _221138) ^ [_492563, _492565] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _492563, _492565), 7914 ^ _221138 : [(7917 ^ _221138) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _492565, _492563)], (7915 ^ _221138) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _492563, _492565))]], -(_492563 = _492565)], (12291 ^ _221138) ^ [_646625] : [class_Rings_Olinordered__idom(_646625), -(class_Groups_Osgn__if(tc_Polynomial_Opoly(_646625)))], (10764 ^ _221138) ^ [_595188, _595190] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _595188, _595190), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _595188, _595190), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (4888 ^ _221138) ^ [_386871, _386873, _386875] : [class_Rings_Ocomm__ring__1(_386871), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_386871), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_386871)), c_Polynomial_OpCons(_386871, c_Groups_Ouminus__class_Ouminus(_386871, _386873), c_Polynomial_OpCons(_386871, c_Groups_Oone__class_Oone(_386871), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_386871))))), c_Polynomial_Osynthetic__div(_386871, _386875, _386873)), c_Polynomial_OpCons(_386871, hAPP(c_Polynomial_Opoly(_386871, _386875), _386873), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_386871)))) = _386875)], (1920 ^ _221138) ^ [_283090, _283092, _283094] : [class_Orderings_Oorder(_283090), c_Orderings_Oord__class_Oless__eq(_283090, _283092, _283094), -(c_Orderings_Oord__class_Oless(_283090, _283092, _283094)), -(_283092 = _283094)], (4903 ^ _221138) ^ [_387603] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _387603, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _387603), _387603)))], (5021 ^ _221138) ^ [_392105, _392107] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _392105, _392107), -(_392105 = _392107), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _392105, _392107))], (9786 ^ _221138) ^ [_557969, _557971, _557973] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _557969, _557971), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _557973, _557969), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _557973, _557971)))], (11823 ^ _221138) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal))], (5947 ^ _221138) ^ [_423807, _423809] : [-(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _423807, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _423809))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _423809, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _423807))))], (11743 ^ _221138) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Nat_Onat))], (7991 ^ _221138) ^ [_495120, _495122] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _495120, _495122)), 7992 ^ _221138 : [(7993 ^ _221138) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _495120, _495122), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _495122, _495120))], (7999 ^ _221138) ^ [] : [_495120 = _495122]]], (11799 ^ _221138) ^ [] : [-(class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal))], (10147 ^ _221138) ^ [_570645] : [-(c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(_570645)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _570645), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (9283 ^ _221138) ^ [_540661] : [9284 ^ _221138 : [(9285 ^ _221138) ^ [_540732] : [_540661 = c_Nat_OSuc(_540732)]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _540661))], (6093 ^ _221138) ^ [_429023] : [-(_429023 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _429023))], (11217 ^ _221138) ^ [_612445, _612447, _612449] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _612445, _612447), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _612449, _612445), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _612445, _612449), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _612447, _612449)))], (1702 ^ _221138) ^ [_276232, _276234, _276236] : [class_Orderings_Olinorder(_276232), -(c_Orderings_Oord__class_Oless(_276232, _276234, _276236)), -(_276234 = _276236), -(c_Orderings_Oord__class_Oless(_276232, _276236, _276234))], (11609 ^ _221138) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (11795 ^ _221138) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal))], (12273 ^ _221138) ^ [_646055] : [class_Rings_Ocomm__semiring__0(_646055), -(class_Rings_Osemiring(tc_Polynomial_Opoly(_646055)))], (9153 ^ _221138) ^ [_535778, _535780] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_535778), _535780), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _535778, _535780))], (2258 ^ _221138) ^ [_294033, _294035] : [class_RealVector_Oreal__normed__vector(_294033), 2261 ^ _221138 : [(2271 ^ _221138) ^ [] : [-(c_SEQ_OBseq(_294033, _294035)), 2272 ^ _221138 : [(2273 ^ _221138) ^ [_294550] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _294550), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_294033, hAPP(_294035, 2276 ^ [_294033, _294035, _294550])), _294550)]]], (2262 ^ _221138) ^ [] : [c_SEQ_OBseq(_294033, _294035), 2266 ^ _221138 : [(2269 ^ _221138) ^ [_294418] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_294033, hAPP(_294035, _294418)), 2265 ^ [_294033, _294035]))], (2267 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 2265 ^ [_294033, _294035]))]]]]], (7639 ^ _221138) ^ [_484176, _484178, _484180] : [class_Rings_Ocomm__semiring__1(_484176), 7644 ^ _221138 : [(7647 ^ _221138) ^ [] : [_484180 = c_Groups_Oone__class_Oone(_484176)], (7645 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _484178)]], -(c_Rings_Odvd__class_Odvd(_484176, _484180, hAPP(hAPP(c_Power_Opower__class_Opower(_484176), _484180), _484178)))], (11167 ^ _221138) ^ [_610658, _610660] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _610658, _610660), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _610658, _610660) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9221 ^ _221138) ^ [_538331, _538333, _538335] : [class_Rings_Ocomm__semiring__1(_538331), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_538331), hAPP(hAPP(c_Power_Opower__class_Opower(_538331), _538333), _538335)), _538333) = hAPP(hAPP(c_Power_Opower__class_Opower(_538331), _538333), c_Nat_OSuc(_538335)))], (2326 ^ _221138) ^ [_296455, _296457, _296459, _296461] : [class_Orderings_Oord(_296455), 2329 ^ _221138 : [(2338 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_fun(_296457, _296455), _296459, _296461)), c_Orderings_Oord__class_Oless__eq(tc_fun(_296457, _296455), _296459, _296461), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_296457, _296455), _296461, _296459))], (2330 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(tc_fun(_296457, _296455), _296459, _296461), 2333 ^ _221138 : [(2336 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_296457, _296455), _296461, _296459)], (2334 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_fun(_296457, _296455), _296459, _296461))]]]]], (5015 ^ _221138) ^ [_391861, _391863, _391865] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _391861, _391863), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _391865), _391861), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _391865), _391863)))], (11849 ^ _221138) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_RealDef_Oreal))], (6291 ^ _221138) ^ [_435995, _435997, _435999] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _435995, _435997), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _435999), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _435999), _435995), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _435999), _435997)))], (6143 ^ _221138) ^ [_430704, _430706] : [-(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), _430704), _430706))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _430704), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _430706)], (11095 ^ _221138) ^ [_607832, _607834] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _607832, _607834), _607832))], (850 ^ _221138) ^ [_247603, _247605, _247607, _247609, _247611, _247613] : [-(c_Polynomial_Osynthetic__div(_247613, _247609, _247605) = c_Polynomial_Osynthetic__div(_247611, _247607, _247603)), _247613 = _247611, _247609 = _247607, _247605 = _247603], (4742 ^ _221138) ^ [_381194, _381196] : [class_Rings_Ocomm__semiring__1(_381194), -(c_Groups_Oplus__class_Oplus(_381194, c_Groups_Ozero__class_Ozero(_381194), _381196) = _381196)], (7551 ^ _221138) ^ [_481347, _481349, _481351] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _481347), _481349), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _481347), _481351)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _481347), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _481349, _481351))], (9239 ^ _221138) ^ [_539186, _539188] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _539186, c_Nat_OSuc(_539188)), -(_539186 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 9247 ^ _221138 : [(9250 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, 9246 ^ [_539186, _539188], _539188))], (9248 ^ _221138) ^ [] : [-(_539186 = c_Nat_OSuc(9246 ^ [_539186, _539188]))]]], (6059 ^ _221138) ^ [_427742, _427744] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _427744, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _427742)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _427742, _427744), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (8215 ^ _221138) ^ [_503181, _503183, _503185, _503187] : [class_Rings_Olinordered__semidom(_503181), c_Orderings_Oord__class_Oless(_503181, c_Groups_Oone__class_Oone(_503181), _503183), 8222 ^ _221138 : [(8229 ^ _221138) ^ [] : [_503185 = _503187, -(hAPP(hAPP(c_Power_Opower__class_Opower(_503181), _503183), _503185) = hAPP(hAPP(c_Power_Opower__class_Opower(_503181), _503183), _503187))], (8223 ^ _221138) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_503181), _503183), _503185) = hAPP(hAPP(c_Power_Opower__class_Opower(_503181), _503183), _503187), -(_503185 = _503187)]]], (1794 ^ _221138) ^ [_279137, _279139, _279141, _279143, _279145] : [class_Groups_Ozero(_279137), 1797 ^ _221138 : [(1806 ^ _221138) ^ [] : [-(c_Polynomial_OpCons(_279137, _279139, _279141) = c_Polynomial_OpCons(_279137, _279143, _279145)), _279139 = _279143, _279141 = _279145], (1798 ^ _221138) ^ [] : [c_Polynomial_OpCons(_279137, _279139, _279141) = c_Polynomial_OpCons(_279137, _279143, _279145), 1801 ^ _221138 : [(1804 ^ _221138) ^ [] : [-(_279141 = _279145)], (1802 ^ _221138) ^ [] : [-(_279139 = _279143)]]]]], (4684 ^ _221138) ^ [_378876, _378878, _378880, _378882] : [class_Rings_Ocomm__semiring__1(_378876), -(c_Groups_Oplus__class_Oplus(_378876, _378878, c_Groups_Oplus__class_Oplus(_378876, _378880, _378882)) = c_Groups_Oplus__class_Oplus(_378876, c_Groups_Oplus__class_Oplus(_378876, _378878, _378880), _378882))], (12207 ^ _221138) ^ [_643965] : [class_Rings_Olinordered__idom(_643965), -(class_Orderings_Opreorder(tc_Polynomial_Opoly(_643965)))], (7527 ^ _221138) ^ [_480510, _480512, _480514] : [7528 ^ _221138 : [(7531 ^ _221138) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _480512, _480514)], (7529 ^ _221138) ^ [] : [_480510 = 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), _480510), _480512), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _480510), _480514)))], (3220 ^ _221138) ^ [_329013, _329015, _329017] : [-(_329013 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 3223 ^ _221138 : [(3230 ^ _221138) ^ [] : [_329015 = _329017, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _329015), _329013) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _329017), _329013))], (3224 ^ _221138) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _329015), _329013) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _329017), _329013), -(_329015 = _329017)]]], (11975 ^ _221138) ^ [] : [-(class_Rings_Oring__1(tc_Complex_Ocomplex))], (8847 ^ _221138) ^ [_524969, _524971] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _524969), 8850 ^ _221138 : [(8859 ^ _221138) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _524969), _524971) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _524969 = c_Groups_Oone__class_Oone(tc_Int_Oint), _524971 = c_Groups_Oone__class_Oone(tc_Int_Oint)], (8851 ^ _221138) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _524969), _524971) = c_Groups_Oone__class_Oone(tc_Int_Oint), 8854 ^ _221138 : [(8857 ^ _221138) ^ [] : [-(_524971 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (8855 ^ _221138) ^ [] : [-(_524969 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]]]], (10331 ^ _221138) ^ [_577565, _577567] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _577565), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _577565, c_RealDef_Oreal(tc_Nat_Onat, _577567)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_RComplete_Onatfloor(_577565), _577567))], (11553 ^ _221138) ^ [_625267, _625269] : [class_Orderings_Opreorder(_625267), -(class_Orderings_Opreorder(tc_fun(_625269, _625267)))], (3660 ^ _221138) ^ [_343113, _343115, _343117, _343119] : [class_Rings_Oordered__ring(_343113), c_Orderings_Oord__class_Oless__eq(_343113, _343115, _343117), c_Orderings_Oord__class_Oless__eq(_343113, _343119, c_Groups_Ozero__class_Ozero(_343113)), -(c_Orderings_Oord__class_Oless__eq(_343113, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_343113), _343117), _343119), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_343113), _343115), _343119)))], (6695 ^ _221138) ^ [_451080, _451082] : [class_Rings_Olinordered__idom(_451080), -(c_Groups_Osgn__class_Osgn(_451080, c_Groups_Osgn__class_Osgn(_451080, _451082)) = c_Groups_Osgn__class_Osgn(_451080, _451082))], (11653 ^ _221138) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (2042 ^ _221138) ^ [_286835, _286837, _286839] : [class_Orderings_Oorder(_286835), 2045 ^ _221138 : [(2046 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_286835, _286837, _286839), -(c_Orderings_Oord__class_Oless(_286835, _286837, _286839)), -(_286837 = _286839)], (2056 ^ _221138) ^ [] : [2057 ^ _221138 : [(2060 ^ _221138) ^ [] : [_286837 = _286839], (2058 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_286835, _286837, _286839)]], -(c_Orderings_Oord__class_Oless__eq(_286835, _286837, _286839))]]], (1850 ^ _221138) ^ [_280918, _280920, _280922, _280924] : [class_Orderings_Opreorder(_280918), c_Orderings_Oord__class_Oless__eq(_280918, _280920, _280922), c_Orderings_Oord__class_Oless(_280918, _280922, _280924), -(c_Orderings_Oord__class_Oless(_280918, _280920, _280924))], (4782 ^ _221138) ^ [_382916, _382918, _382920, _382922] : [class_Rings_Ocomm__semiring__1(_382916), -(c_Groups_Oplus__class_Oplus(_382916, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_382916), _382918), _382920), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_382916), _382922), _382920)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_382916), c_Groups_Oplus__class_Oplus(_382916, _382918, _382922)), _382920))], (8663 ^ _221138) ^ [_518948, _518950] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _518948, _518950), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _518950), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _518948, _518950))], (4374 ^ _221138) ^ [_366700] : [class_Rings_Olinordered__idom(_366700), c_Polynomial_Opos__poly(_366700, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_366700)))], (11255 ^ _221138) ^ [_613654, _613656, _613658] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _613654, _613656), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _613656, _613658), _613654) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _613656, _613654), _613658))], (1658 ^ _221138) ^ [_274893, _274895, _274897] : [class_Orderings_Oorder(_274893), c_Orderings_Oord__class_Oless(_274893, _274895, _274897), _274895 = _274897], (3150 ^ _221138) ^ [_326738, _326740, _326742] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _326738, _326740), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _326742, _326738), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _326742, _326740)))], (10714 ^ _221138) ^ [_593465, _593467, _593469] : [class_Groups_Ogroup__add(_593465), -(c_Groups_Oplus__class_Oplus(_593465, c_Groups_Ominus__class_Ominus(_593465, _593467, _593469), _593469) = _593467)], (7847 ^ _221138) ^ [_490604, _490606, _490608] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _490604, _490606), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _490606, _490608), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _490604, _490608))], (4924 ^ _221138) ^ [_388541, _388543] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _388541, _388543), -(_388543 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _388541, 4927 ^ [_388541, _388543]))], (72 ^ _221138) ^ [_223541, _223543, _223545, _223547] : [-(c_Polynomial_Opos__poly(_223545, _223541)), c_Polynomial_Opos__poly(_223547, _223543), _223547 = _223545, _223543 = _223541], (1608 ^ _221138) ^ [_273267, _273269, _273271] : [class_Orderings_Opreorder(_273267), c_Orderings_Oord__class_Oless(_273267, _273269, _273271), c_Orderings_Oord__class_Oless(_273267, _273271, _273269)], (1542 ^ _221138) ^ [_271171, _271173, _271175, _271177] : [class_Orderings_Oorder(_271171), c_Orderings_Oord__class_Oless(_271171, _271173, _271175), _271173 = _271177, -(c_Orderings_Oord__class_Oless(_271171, _271177, _271175))], (7757 ^ _221138) ^ [_487846, _487848] : [_487846 = _487848, c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _487846, _487848), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _487848, _487846))], (3024 ^ _221138) ^ [_322066, _322068, _322070] : [class_Rings_Olinordered__idom(_322066), c_Orderings_Oord__class_Oless__eq(_322066, c_Groups_Ozero__class_Ozero(_322066), _322068), c_Orderings_Oord__class_Oless__eq(_322066, c_Groups_Ozero__class_Ozero(_322066), _322070), c_Orderings_Oord__class_Oless__eq(_322066, _322070, c_Groups_Oone__class_Oone(_322066)), -(c_Orderings_Oord__class_Oless__eq(_322066, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_322066), _322070), _322068), _322068))], (524 ^ _221138) ^ [_236956, _236958] : [-(class_Rings_Osemiring__0(_236956)), _236958 = _236956, class_Rings_Osemiring__0(_236958)], (8907 ^ _221138) ^ [_527078, _527080, _527082] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_527078)), _527080) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_527078)), _527082), -(_527080 = _527082)], (11965 ^ _221138) ^ [] : [-(class_Rings_Omult__zero(tc_Complex_Ocomplex))], (6107 ^ _221138) ^ [_429442] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _429442, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1682 ^ _221138) ^ [_275641, _275643, _275645] : [class_Orderings_Olinorder(_275641), -(c_Orderings_Oord__class_Oless(_275641, _275643, _275645)), 1689 ^ _221138 : [(1696 ^ _221138) ^ [] : [_275645 = _275643, c_Orderings_Oord__class_Oless(_275641, _275645, _275643)], (1690 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(_275641, _275645, _275643)), -(_275645 = _275643)]]], (8235 ^ _221138) ^ [_503822, _503824] : [class_Power_Opower(_503822), -(hAPP(hAPP(c_Power_Opower__class_Opower(_503822), _503824), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_503822))], (1269 ^ _221138) ^ [_262337, _262339, _262341] : [class_Orderings_Olinorder(_262337), -(c_Orderings_Oord__class_Oless__eq(_262337, _262339, _262341)), -(c_Orderings_Oord__class_Oless__eq(_262337, _262341, _262339))], (11777 ^ _221138) ^ [] : [-(class_Lattices_Oboolean__algebra(tc_HOL_Obool))], (10612 ^ _221138) ^ [_589119, _589121, _589123, _589125, _589127, _589129] : [class_Rings_Oring(_589119), 10615 ^ _221138 : [(10622 ^ _221138) ^ [] : [c_Groups_Oplus__class_Oplus(_589119, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_589119), c_Groups_Ominus__class_Ominus(_589119, _589121, _589127)), _589123), _589125) = _589129, -(c_Groups_Oplus__class_Oplus(_589119, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_589119), _589121), _589123), _589125) = c_Groups_Oplus__class_Oplus(_589119, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_589119), _589127), _589123), _589129))], (10616 ^ _221138) ^ [] : [c_Groups_Oplus__class_Oplus(_589119, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_589119), _589121), _589123), _589125) = c_Groups_Oplus__class_Oplus(_589119, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_589119), _589127), _589123), _589129), -(c_Groups_Oplus__class_Oplus(_589119, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_589119), c_Groups_Ominus__class_Ominus(_589119, _589121, _589127)), _589123), _589125) = _589129)]]], (9608 ^ _221138) ^ [_551842, _551844] : [-(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), _551842), _551844))), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _551842), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _551844)], (10 ^ _221138) ^ [_221573, _221575, _221577] : [-(_221577 = _221573), _221577 = _221575, _221575 = _221573], (604 ^ _221138) ^ [_239316, _239318] : [-(class_Groups_Ouminus(_239316)), _239318 = _239316, class_Groups_Ouminus(_239318)], (11813 ^ _221138) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal))], (4582 ^ _221138) ^ [_374264, _374266] : [class_Rings_Ocomm__semiring__0(_374264), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_374264)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_374264))), _374266) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_374264)))], (10836 ^ _221138) ^ [_597969, _597971, _597973] : [class_Groups_Oordered__ab__group__add__abs(_597969), -(c_Groups_Oabs__class_Oabs(_597969, c_Groups_Ominus__class_Ominus(_597969, _597971, _597973)) = c_Groups_Oabs__class_Oabs(_597969, c_Groups_Ominus__class_Ominus(_597969, _597973, _597971)))], (3880 ^ _221138) ^ [_350329, _350331, _350333] : [class_Rings_Olinordered__semiring__strict(_350329), c_Orderings_Oord__class_Oless(_350329, c_Groups_Ozero__class_Ozero(_350329), _350331), c_Orderings_Oord__class_Oless(_350329, _350333, c_Groups_Ozero__class_Ozero(_350329)), -(c_Orderings_Oord__class_Oless(_350329, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_350329), _350331), _350333), c_Groups_Ozero__class_Ozero(_350329)))], (11667 ^ _221138) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (2108 ^ _221138) ^ [_288816, _288818, _288820] : [class_Orderings_Olinorder(_288816), -(c_Orderings_Oord__class_Oless__eq(_288816, _288818, _288820)), -(c_Orderings_Oord__class_Oless(_288816, _288820, _288818))], (2134 ^ _221138) ^ [_289638, _289640, _289642] : [class_Orderings_Olinorder(_289638), 2137 ^ _221138 : [(2144 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless__eq(_289638, _289642, _289640), c_Orderings_Oord__class_Oless(_289638, _289640, _289642)], (2138 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(_289638, _289640, _289642)), -(c_Orderings_Oord__class_Oless__eq(_289638, _289642, _289640))]]], (9658 ^ _221138) ^ [_553512, _553514, _553516] : [class_Rings_Olinordered__semidom(_553512), c_Orderings_Oord__class_Oless(_553512, c_Groups_Ozero__class_Ozero(_553512), _553514), c_Orderings_Oord__class_Oless(_553512, _553514, c_Groups_Oone__class_Oone(_553512)), -(c_Orderings_Oord__class_Oless(_553512, hAPP(hAPP(c_Power_Opower__class_Opower(_553512), _553514), c_Nat_OSuc(_553516)), c_Groups_Oone__class_Oone(_553512)))], (9798 ^ _221138) ^ [_558406, _558408] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _558406, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _558408)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _558406, _558408))], (4894 ^ _221138) ^ [_387187, _387189] : [class_RealVector_Oreal__normed__algebra(_387187), 4898 ^ _221138 : [(4901 ^ _221138) ^ [_387486] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_387187, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_387187), _387486), _387189)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_387187, _387486)), 4897 ^ [_387187, _387189])))], (4899 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 4897 ^ [_387187, _387189]))]]], (11913 ^ _221138) ^ [] : [-(class_Groups_Oone(tc_RealDef_Oreal))], (6725 ^ _221138) ^ [_452282] : [class_Groups_Osgn__if(_452282), -(c_Groups_Osgn__class_Osgn(_452282, c_Groups_Ozero__class_Ozero(_452282)) = c_Groups_Ozero__class_Ozero(_452282))], (11431 ^ _221138) ^ [_620703, _620705] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _620703), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _620703, c_Nat_OSuc(_620705)), _620703))], (2234 ^ _221138) ^ [_292987, _292989, _292991, _292993, _292995, _292997] : [class_Groups_Ozero(_292987), -(c_Polynomial_Opoly__rec(_292989, _292987, _292991, _292993, c_Polynomial_OpCons(_292987, _292995, _292997)) = hAPP(hAPP(hAPP(_292993, _292995), _292997), c_If(_292989, c_fequal(_292997, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_292987))), _292991, c_Polynomial_Opoly__rec(_292989, _292987, _292991, _292993, _292997))))], (594 ^ _221138) ^ [_239021, _239023] : [-(class_Orderings_Oord(_239021)), _239023 = _239021, class_Orderings_Oord(_239023)], (6519 ^ _221138) ^ [_444968, _444970] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _444968), _444970), 6522 ^ _221138 : [(6525 ^ _221138) ^ [] : [-(_444970 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (6523 ^ _221138) ^ [] : [-(_444968 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (3388 ^ _221138) ^ [_334253, _334255] : [class_Groups_Olinordered__ab__group__add(_334253), 3391 ^ _221138 : [(3398 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_334253, _334255, c_Groups_Ozero__class_Ozero(_334253)), -(c_Orderings_Oord__class_Oless(_334253, c_Groups_Oplus__class_Oplus(_334253, _334255, _334255), c_Groups_Ozero__class_Ozero(_334253)))], (3392 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(_334253, c_Groups_Oplus__class_Oplus(_334253, _334255, _334255), c_Groups_Ozero__class_Ozero(_334253)), -(c_Orderings_Oord__class_Oless(_334253, _334255, c_Groups_Ozero__class_Ozero(_334253)))]]], (10970 ^ _221138) ^ [_603485, _603487, _603489, _603491] : [class_RealVector_Oreal__normed__vector(_603485), class_Orderings_Oord(_603487), 10980 ^ _221138 : [(10983 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_603485, c_Groups_Ominus__class_Ominus(_603485, hAPP(_603491, _603489), hAPP(_603491, 10979 ^ [_603485, _603487, _603489, _603491]))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (10981 ^ _221138) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_603487, _603489, 10979 ^ [_603485, _603487, _603489, _603491]))]], 10984 ^ _221138 : [(10985 ^ _221138) ^ [_604043] : [c_Orderings_Oord__class_Oless__eq(_603487, _603489, _604043), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_603485, hAPP(_603491, _604043)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_603485, hAPP(_603491, _603489)))))]]], (10600 ^ _221138) ^ [_588337, _588339, _588341, _588343, _588345] : [class_Rings_Oring(_588337), -(c_Groups_Ominus__class_Ominus(_588337, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_588337), _588339), _588341), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_588337), _588343), _588345)) = c_Groups_Oplus__class_Oplus(_588337, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_588337), _588339), c_Groups_Ominus__class_Ominus(_588337, _588341, _588345)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_588337), c_Groups_Ominus__class_Ominus(_588337, _588339, _588343)), _588345)))], (11959 ^ _221138) ^ [] : [-(class_Groups_Omonoid__add(tc_Complex_Ocomplex))], (10167 ^ _221138) ^ [_571416, _571418] : [_571416 = c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatfloor(_571416)), -(c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _571416), _571418)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_RComplete_Onatfloor(_571416)), _571418))], (10997 ^ _221138) ^ [_604525, _604527] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _604525, _604527)), -(c_Nat__Transfer_Otsub(_604527, _604525) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (942 ^ _221138) ^ [_250906, _250908] : [_250908 = _250906, -(c_Groups_Oone__class_Oone(_250908) = c_Groups_Oone__class_Oone(_250906))], (11629 ^ _221138) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (10000 ^ _221138) ^ [_565324] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _565324, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_RComplete_Onatfloor(_565324) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8609 ^ _221138) ^ [_516976] : [c_Groups_Oabs__class_Oabs(tc_Int_Oint, _516976) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _516976, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (11847 ^ _221138) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_RealDef_Oreal))], (8433 ^ _221138) ^ [_511067, _511069, _511071, _511073] : [class_Rings_Olinordered__semidom(_511067), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _511069, _511071), c_Orderings_Oord__class_Oless(_511067, c_Groups_Ozero__class_Ozero(_511067), _511073), c_Orderings_Oord__class_Oless(_511067, _511073, c_Groups_Oone__class_Oone(_511067)), -(c_Orderings_Oord__class_Oless(_511067, hAPP(hAPP(c_Power_Opower__class_Opower(_511067), _511073), _511071), hAPP(hAPP(c_Power_Opower__class_Opower(_511067), _511073), _511069)))], (11474 ^ _221138) ^ [_622329, _622331, _622333] : [hBOOL(hAPP(_622329, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _622331, _622333))), 11477 ^ _221138 : [(11484 ^ _221138) ^ [_622667] : [_622331 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _622333, _622667), -(hBOOL(hAPP(_622329, _622667)))], (11478 ^ _221138) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _622331, _622333), -(hBOOL(hAPP(_622329, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]]], input).
% 192.54/185.85  ncf('1',plain,[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____)))), 12370 : 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____)), 12366 ^ [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____)))])), 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(12363 ^ 0,bind([[_668277], [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____)))]]))).
% 192.54/185.85  ncf('1.1',plain,[-(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____))))), class_Orderings_Opreorder(tc_RealDef_Oreal), 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____)))), c_Orderings_Oord__class_Oless__eq(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____))), 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____))))],extension(1878 ^ 1,bind([[_281814, _281816, _281818, _281820], [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____))), 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____)))]]))).
% 192.54/185.85  ncf('1.1.1',plain,[-(class_Orderings_Opreorder(tc_RealDef_Oreal))],extension(11869 ^ 2)).
% 192.54/185.85  ncf('1.1.2',plain,[-(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____)))))],extension(2240 ^ 2)).
% 192.54/185.85  ncf('1.1.3',plain,[-(c_Orderings_Oord__class_Oless__eq(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____))), 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____)))))],extension(1792 ^ 2,bind([[_278987], [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____)))]]))).
% 192.54/185.85  ncf('1.2',plain,[-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, v_c____, v_cs____)), 12366 ^ [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____)))])), 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____))))), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, 12366 ^ [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____)))]), v_r)],extension(2168 ^ 3,bind([[_290681], [12366 ^ [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____)))]]]))).
% 192.54/185.85  ncf('1.2.1',plain,[-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, 12366 ^ [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____)))]), v_r))],extension(12368 ^ 4)).
% 192.54/185.85  %-----------------------------------------------------
% 192.54/185.85  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------