%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWW236+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n005.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 12:25:48 EDT 2023

% Result   : Theorem 148.80s 144.21s
% Output   : Proof 148.80s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SWW236+1 : TPTP v8.1.2. Released v5.2.0.
% 0.04/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n005.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Thu May 18 22:29:53 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 148.80/144.21  
% 148.80/144.21  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 148.80/144.21  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 148.80/144.21  %-----------------------------------------------------
% 148.80/144.21  ncf(matrix, plain, [(11547 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v_da____), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_aa____)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_z____), v_c____)))], (2 ^ _292445) ^ [_292558, _292560] : [hAPP(_292558, 3 ^ [_292558, _292560]) = hAPP(_292560, 3 ^ [_292558, _292560]), -(_292558 = _292560)], (9 ^ _292445) ^ [] : [v_c____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)], (11 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v_da____), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_aa____)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_z____)))], (13 ^ _292445) ^ [] : [v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))], (15 ^ _292445) ^ [_293021, _293023, _293025] : [class_RealVector_Oreal__normed__vector(_293021), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_293021, c_Groups_Oplus__class_Oplus(_293021, _293023, _293025)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_293021, _293023), c_RealVector_Onorm__class_Onorm(_293021, _293025))))], (21 ^ _292445) ^ [_293285, _293287, _293289] : [class_RealVector_Oreal__normed__algebra(_293285), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_293285, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_293285), _293287), _293289)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_293285, _293287)), c_RealVector_Onorm__class_Onorm(_293285, _293289))))], (27 ^ _292445) ^ [_293561, _293563, _293565] : [class_Groups_Oordered__ab__group__add__abs(_293561), -(c_Orderings_Oord__class_Oless__eq(_293561, c_Groups_Oabs__class_Oabs(_293561, c_Groups_Oplus__class_Oplus(_293561, _293563, _293565)), c_Groups_Oplus__class_Oplus(_293561, c_Groups_Oabs__class_Oabs(_293561, _293563), c_Groups_Oabs__class_Oabs(_293561, _293565))))], (33 ^ _292445) ^ [_293811, _293813] : [class_Orderings_Opreorder(_293811), -(c_Orderings_Oord__class_Oless__eq(_293811, _293813, _293813))], (39 ^ _292445) ^ [_294021, _294023] : [class_RealVector_Oreal__normed__vector(_294021), -(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_294021, _294023)) = c_RealVector_Onorm__class_Onorm(_294021, _294023))], (45 ^ _292445) ^ [_294261, _294263, _294265] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _294261, _294263), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _294265, _294261), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _294265, _294263)))], (51 ^ _292445) ^ [_294511, _294513, _294515] : [class_Groups_Oordered__ab__group__add__abs(_294511), -(c_Groups_Oabs__class_Oabs(_294511, c_Groups_Oplus__class_Oplus(_294511, c_Groups_Oabs__class_Oabs(_294511, _294513), c_Groups_Oabs__class_Oabs(_294511, _294515))) = c_Groups_Oplus__class_Oplus(_294511, c_Groups_Oabs__class_Oabs(_294511, _294513), c_Groups_Oabs__class_Oabs(_294511, _294515)))], (57 ^ _292445) ^ [_294785, _294787, _294789] : [class_Rings_Olinordered__idom(_294785), -(c_Groups_Oabs__class_Oabs(_294785, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_294785), _294787), _294789)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_294785), c_Groups_Oabs__class_Oabs(_294785, _294787)), c_Groups_Oabs__class_Oabs(_294785, _294789)))], (63 ^ _292445) ^ [_295049, _295051] : [class_Rings_Olinordered__idom(_295049), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_295049), c_Groups_Oabs__class_Oabs(_295049, _295051)), c_Groups_Oabs__class_Oabs(_295049, _295051)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_295049), _295051), _295051))], (69 ^ _292445) ^ [_295315, _295317, _295319] : [class_RealVector_Oreal__normed__div__algebra(_295315), -(c_RealVector_Onorm__class_Onorm(_295315, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_295315), _295317), _295319)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_295315, _295317)), c_RealVector_Onorm__class_Onorm(_295315, _295319)))], (75 ^ _292445) ^ [_295575, _295577] : [class_Groups_Oordered__ab__group__add__abs(_295575), -(c_Orderings_Oord__class_Oless__eq(_295575, _295577, c_Groups_Oabs__class_Oabs(_295575, _295577)))], (81 ^ _292445) ^ [] : [-(v_cs____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))], (83 ^ _292445) ^ [_295830] : [class_RealVector_Oreal__normed__vector(_295830), -(c_RealVector_Onorm__class_Onorm(_295830, c_Groups_Ozero__class_Ozero(_295830)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (89 ^ _292445) ^ [_296056, _296058, _296060] : [-(c_RealVector_Onorm__class_Onorm(_296056, c_Rings_Oinverse__class_Odivide(_296056, _296058, _296060)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_296056, _296058), c_RealVector_Onorm__class_Onorm(_296056, _296060))), class_Fields_Ofield__inverse__zero(_296056), class_RealVector_Oreal__normed__field(_296056)], (99 ^ _292445) ^ [_296395, _296397] : [class_Rings_Odivision__ring(_296395), -(c_Rings_Oinverse__class_Odivide(_296395, c_Groups_Ozero__class_Ozero(_296395), _296397) = c_Groups_Ozero__class_Ozero(_296395))], (105 ^ _292445) ^ [_296619, _296621] : [class_RealVector_Oreal__normed__field(_296619), -(c_Rings_Oinverse__class_Odivide(_296619, c_Groups_Ozero__class_Ozero(_296619), _296621) = c_Groups_Ozero__class_Ozero(_296619))], (111 ^ _292445) ^ [_296843, _296845] : [class_Groups_Ozero(_296843), 114 ^ _292445 : [(115 ^ _292445) ^ [] : [c_Groups_Ozero__class_Ozero(_296843) = _296845, -(_296845 = c_Groups_Ozero__class_Ozero(_296843))], (121 ^ _292445) ^ [] : [_296845 = c_Groups_Ozero__class_Ozero(_296843), -(c_Groups_Ozero__class_Ozero(_296843) = _296845)]]], (127 ^ _292445) ^ [_297313, _297315] : [class_Rings_Odivision__ring__inverse__zero(_297313), -(c_Rings_Oinverse__class_Odivide(_297313, _297315, c_Groups_Ozero__class_Ozero(_297313)) = c_Groups_Ozero__class_Ozero(_297313))], (133 ^ _292445) ^ [_297522, _297524] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _297522), _297524) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _297524), _297522))], (135 ^ _292445) ^ [_297643, _297645] : [class_RealVector_Oreal__normed__vector(_297643), 138 ^ _292445 : [(139 ^ _292445) ^ [] : [c_RealVector_Onorm__class_Onorm(_297643, _297645) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_297645 = c_Groups_Ozero__class_Ozero(_297643))], (145 ^ _292445) ^ [] : [_297645 = c_Groups_Ozero__class_Ozero(_297643), -(c_RealVector_Onorm__class_Onorm(_297643, _297645) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))]]], (151 ^ _292445) ^ [_298115, _298117, _298119] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _298115), _298117)), _298119) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _298115), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _298117), _298119)))], (153 ^ _292445) ^ [_298264, _298266, _298268] : [class_RealVector_Oreal__normed__field(_298264), -(_298266 = c_Groups_Ozero__class_Ozero(_298264)), -(c_RealVector_Onorm__class_Onorm(_298264, c_Rings_Oinverse__class_Odivide(_298264, _298268, _298266)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_298264, _298268), c_RealVector_Onorm__class_Onorm(_298264, _298266)))], (163 ^ _292445) ^ [_298640, _298642, _298644, _298646] : [class_Rings_Odivision__ring(_298640), -(_298642 = c_Groups_Ozero__class_Ozero(_298640)), 170 ^ _292445 : [(171 ^ _292445) ^ [] : [_298644 = c_Rings_Oinverse__class_Odivide(_298640, _298646, _298642), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_298640), _298644), _298642) = _298646)], (177 ^ _292445) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_298640), _298644), _298642) = _298646, -(_298644 = c_Rings_Oinverse__class_Odivide(_298640, _298646, _298642))]]], (183 ^ _292445) ^ [_299298, _299300, _299302, _299304] : [class_Rings_Odivision__ring(_299298), -(_299300 = c_Groups_Ozero__class_Ozero(_299298)), 190 ^ _292445 : [(191 ^ _292445) ^ [] : [c_Rings_Oinverse__class_Odivide(_299298, _299302, _299300) = _299304, -(_299302 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_299298), _299304), _299300))], (197 ^ _292445) ^ [] : [_299302 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_299298), _299304), _299300), -(c_Rings_Oinverse__class_Odivide(_299298, _299302, _299300) = _299304)]]], (203 ^ _292445) ^ [_299956, _299958, _299960, _299962] : [class_Rings_Odivision__ring(_299956), -(_299958 = c_Groups_Ozero__class_Ozero(_299956)), _299960 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_299956), _299962), _299958), -(c_Rings_Oinverse__class_Odivide(_299956, _299960, _299958) = _299962)], (217 ^ _292445) ^ [_300429, _300431, _300433, _300435] : [class_Rings_Odivision__ring(_300429), -(_300431 = c_Groups_Ozero__class_Ozero(_300429)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_300429), _300433), _300431) = _300435, -(_300433 = c_Rings_Oinverse__class_Odivide(_300429, _300435, _300431))], (231 ^ _292445) ^ [_300902, _300904, _300906, _300908] : [class_Rings_Odivision__ring(_300902), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_300902), _300904), c_Rings_Oinverse__class_Odivide(_300902, _300906, _300908)) = c_Rings_Oinverse__class_Odivide(_300902, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_300902), _300904), _300906), _300908))], (237 ^ _292445) ^ [_301198, _301200, _301202, _301204] : [class_RealVector_Oreal__normed__field(_301198), -(c_Rings_Oinverse__class_Odivide(_301198, c_Groups_Oplus__class_Oplus(_301198, _301200, _301202), _301204) = c_Groups_Oplus__class_Oplus(_301198, c_Rings_Oinverse__class_Odivide(_301198, _301200, _301204), c_Rings_Oinverse__class_Odivide(_301198, _301202, _301204)))], (243 ^ _292445) ^ [_301486, _301488, _301490, _301492] : [class_Rings_Odivision__ring(_301486), -(c_Rings_Oinverse__class_Odivide(_301486, c_Groups_Oplus__class_Oplus(_301486, _301488, _301490), _301492) = c_Groups_Oplus__class_Oplus(_301486, c_Rings_Oinverse__class_Odivide(_301486, _301488, _301492), c_Rings_Oinverse__class_Odivide(_301486, _301490, _301492)))], (249 ^ _292445) ^ [_301760, _301762, _301764] : [class_Rings_Ono__zero__divisors(_301760), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_301760), _301762), _301764) = c_Groups_Ozero__class_Ozero(_301760), -(_301762 = c_Groups_Ozero__class_Ozero(_301760)), -(_301764 = c_Groups_Ozero__class_Ozero(_301760))], (263 ^ _292445) ^ [_302203, _302205, _302207] : [class_Rings_Ono__zero__divisors(_302203), -(_302205 = c_Groups_Ozero__class_Ozero(_302203)), -(_302207 = c_Groups_Ozero__class_Ozero(_302203)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_302203), _302205), _302207) = c_Groups_Ozero__class_Ozero(_302203)], (277 ^ _292445) ^ [_302652, _302654, _302656] : [class_Rings_Oring__no__zero__divisors(_302652), 280 ^ _292445 : [(291 ^ _292445) ^ [] : [292 ^ _292445 : [(293 ^ _292445) ^ [] : [_302654 = c_Groups_Ozero__class_Ozero(_302652)], (295 ^ _292445) ^ [] : [_302656 = c_Groups_Ozero__class_Ozero(_302652)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_302652), _302654), _302656) = c_Groups_Ozero__class_Ozero(_302652))], (281 ^ _292445) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_302652), _302654), _302656) = c_Groups_Ozero__class_Ozero(_302652), -(_302654 = c_Groups_Ozero__class_Ozero(_302652)), -(_302656 = c_Groups_Ozero__class_Ozero(_302652))]]], (299 ^ _292445) ^ [_303332, _303334] : [class_RealVector_Oreal__normed__algebra(_303332), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_303332), _303334), c_Groups_Ozero__class_Ozero(_303332)) = c_Groups_Ozero__class_Ozero(_303332))], (305 ^ _292445) ^ [_303564, _303566] : [class_RealVector_Oreal__normed__algebra(_303564), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_303564), _303566), c_Groups_Ozero__class_Ozero(_303564)) = c_Groups_Ozero__class_Ozero(_303564))], (311 ^ _292445) ^ [_303796, _303798] : [class_Rings_Omult__zero(_303796), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_303796), _303798), c_Groups_Ozero__class_Ozero(_303796)) = c_Groups_Ozero__class_Ozero(_303796))], (317 ^ _292445) ^ [_304028, _304030] : [class_RealVector_Oreal__normed__algebra(_304028), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_304028), c_Groups_Ozero__class_Ozero(_304028)), _304030) = c_Groups_Ozero__class_Ozero(_304028))], (323 ^ _292445) ^ [_304260, _304262] : [class_RealVector_Oreal__normed__algebra(_304260), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_304260), c_Groups_Ozero__class_Ozero(_304260)), _304262) = c_Groups_Ozero__class_Ozero(_304260))], (329 ^ _292445) ^ [_304492, _304494] : [class_Rings_Omult__zero(_304492), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_304492), c_Groups_Ozero__class_Ozero(_304492)), _304494) = c_Groups_Ozero__class_Ozero(_304492))], (335 ^ _292445) ^ [_304724, _304726] : [class_Groups_Ocomm__monoid__add(_304724), -(c_Groups_Oplus__class_Oplus(_304724, _304726, c_Groups_Ozero__class_Ozero(_304724)) = _304726)], (341 ^ _292445) ^ [_304944, _304946] : [class_Groups_Omonoid__add(_304944), -(c_Groups_Oplus__class_Oplus(_304944, _304946, c_Groups_Ozero__class_Ozero(_304944)) = _304946)], (347 ^ _292445) ^ [_305164, _305166] : [class_Groups_Olinordered__ab__group__add(_305164), 350 ^ _292445 : [(351 ^ _292445) ^ [] : [c_Groups_Ozero__class_Ozero(_305164) = c_Groups_Oplus__class_Oplus(_305164, _305166, _305166), -(_305166 = c_Groups_Ozero__class_Ozero(_305164))], (357 ^ _292445) ^ [] : [_305166 = c_Groups_Ozero__class_Ozero(_305164), -(c_Groups_Ozero__class_Ozero(_305164) = c_Groups_Oplus__class_Oplus(_305164, _305166, _305166))]]], (363 ^ _292445) ^ [_305646, _305648] : [class_Groups_Ocomm__monoid__add(_305646), -(c_Groups_Oplus__class_Oplus(_305646, c_Groups_Ozero__class_Ozero(_305646), _305648) = _305648)], (369 ^ _292445) ^ [_305866, _305868] : [class_Groups_Omonoid__add(_305866), -(c_Groups_Oplus__class_Oplus(_305866, c_Groups_Ozero__class_Ozero(_305866), _305868) = _305868)], (375 ^ _292445) ^ [_306057] : [-(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, _306057) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _306057))], (377 ^ _292445) ^ [_306169, _306171, _306173] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _306169, _306171)), _306173) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _306169), _306173), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _306171), _306173)))], (379 ^ _292445) ^ [_306306, _306308] : [class_Groups_Oordered__ab__group__add__abs(_306306), 382 ^ _292445 : [(383 ^ _292445) ^ [] : [c_Groups_Oabs__class_Oabs(_306306, _306308) = c_Groups_Ozero__class_Ozero(_306306), -(_306308 = c_Groups_Ozero__class_Ozero(_306306))], (389 ^ _292445) ^ [] : [_306308 = c_Groups_Ozero__class_Ozero(_306306), -(c_Groups_Oabs__class_Oabs(_306306, _306308) = c_Groups_Ozero__class_Ozero(_306306))]]], (395 ^ _292445) ^ [_306771] : [class_Groups_Oordered__ab__group__add__abs(_306771), -(c_Groups_Oabs__class_Oabs(_306771, c_Groups_Ozero__class_Ozero(_306771)) = c_Groups_Ozero__class_Ozero(_306771))], (401 ^ _292445) ^ [_306987, _306989] : [class_RealVector_Oreal__normed__vector(_306987), 404 ^ _292445 : [(405 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_306987, _306989), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(_306989 = c_Groups_Ozero__class_Ozero(_306987))], (411 ^ _292445) ^ [] : [_306989 = c_Groups_Ozero__class_Ozero(_306987), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_306987, _306989), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))]]], (417 ^ _292445) ^ [_307477, _307479, _307481] : [class_Rings_Oordered__cancel__semiring(_307477), -(c_Orderings_Oord__class_Oless__eq(_307477, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_307477), _307479), _307481), c_Groups_Ozero__class_Ozero(_307477))), 422 ^ _292445 : [(423 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_307477, c_Groups_Ozero__class_Ozero(_307477), _307479), c_Orderings_Oord__class_Oless__eq(_307477, _307481, c_Groups_Ozero__class_Ozero(_307477))], (429 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_307477, _307479, c_Groups_Ozero__class_Ozero(_307477)), c_Orderings_Oord__class_Oless__eq(_307477, c_Groups_Ozero__class_Ozero(_307477), _307481)]]], (437 ^ _292445) ^ [_308106, _308108, _308110] : [class_Rings_Oordered__ring(_308106), -(c_Orderings_Oord__class_Oless__eq(_308106, c_Groups_Ozero__class_Ozero(_308106), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_308106), _308108), _308110))), 442 ^ _292445 : [(443 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_308106, c_Groups_Ozero__class_Ozero(_308106), _308108), c_Orderings_Oord__class_Oless__eq(_308106, c_Groups_Ozero__class_Ozero(_308106), _308110)], (449 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_308106, _308108, c_Groups_Ozero__class_Ozero(_308106)), c_Orderings_Oord__class_Oless__eq(_308106, _308110, c_Groups_Ozero__class_Ozero(_308106))]]], (457 ^ _292445) ^ [_308763, _308765, _308767, _308769, _308771] : [class_Rings_Oordered__semiring(_308763), c_Orderings_Oord__class_Oless__eq(_308763, _308765, _308767), c_Orderings_Oord__class_Oless__eq(_308763, _308769, _308771), c_Orderings_Oord__class_Oless__eq(_308763, c_Groups_Ozero__class_Ozero(_308763), _308767), c_Orderings_Oord__class_Oless__eq(_308763, c_Groups_Ozero__class_Ozero(_308763), _308769), -(c_Orderings_Oord__class_Oless__eq(_308763, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_308763), _308765), _308769), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_308763), _308767), _308771)))], (479 ^ _292445) ^ [_309485, _309487, _309489, _309491, _309493] : [class_Rings_Oordered__semiring(_309485), c_Orderings_Oord__class_Oless__eq(_309485, _309487, _309489), c_Orderings_Oord__class_Oless__eq(_309485, _309491, _309493), c_Orderings_Oord__class_Oless__eq(_309485, c_Groups_Ozero__class_Ozero(_309485), _309487), c_Orderings_Oord__class_Oless__eq(_309485, c_Groups_Ozero__class_Ozero(_309485), _309491), -(c_Orderings_Oord__class_Oless__eq(_309485, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_309485), _309487), _309491), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_309485), _309489), _309493)))], (501 ^ _292445) ^ [_310193, _310195, _310197, _310199] : [class_Rings_Oordered__ring(_310193), c_Orderings_Oord__class_Oless__eq(_310193, _310195, _310197), c_Orderings_Oord__class_Oless__eq(_310193, _310199, c_Groups_Ozero__class_Ozero(_310193)), -(c_Orderings_Oord__class_Oless__eq(_310193, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_310193), _310199), _310197), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_310193), _310199), _310195)))], (515 ^ _292445) ^ [_310677, _310679, _310681, _310683] : [class_Rings_Oordered__ring(_310677), c_Orderings_Oord__class_Oless__eq(_310677, _310679, _310681), c_Orderings_Oord__class_Oless__eq(_310677, _310683, c_Groups_Ozero__class_Ozero(_310677)), -(c_Orderings_Oord__class_Oless__eq(_310677, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_310677), _310681), _310683), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_310677), _310679), _310683)))], (529 ^ _292445) ^ [_311161, _311163, _311165, _311167] : [class_Rings_Oordered__comm__semiring(_311161), c_Orderings_Oord__class_Oless__eq(_311161, _311163, _311165), c_Orderings_Oord__class_Oless__eq(_311161, c_Groups_Ozero__class_Ozero(_311161), _311167), -(c_Orderings_Oord__class_Oless__eq(_311161, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_311161), _311167), _311163), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_311161), _311167), _311165)))], (543 ^ _292445) ^ [_311645, _311647, _311649, _311651] : [class_Rings_Oordered__semiring(_311645), c_Orderings_Oord__class_Oless__eq(_311645, _311647, _311649), c_Orderings_Oord__class_Oless__eq(_311645, c_Groups_Ozero__class_Ozero(_311645), _311651), -(c_Orderings_Oord__class_Oless__eq(_311645, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_311645), _311651), _311647), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_311645), _311651), _311649)))], (557 ^ _292445) ^ [_312129, _312131, _312133, _312135] : [class_Rings_Oordered__semiring(_312129), c_Orderings_Oord__class_Oless__eq(_312129, _312131, _312133), c_Orderings_Oord__class_Oless__eq(_312129, c_Groups_Ozero__class_Ozero(_312129), _312135), -(c_Orderings_Oord__class_Oless__eq(_312129, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_312129), _312131), _312135), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_312129), _312133), _312135)))], (571 ^ _292445) ^ [_312599, _312601, _312603] : [class_Rings_Oordered__ring(_312599), c_Orderings_Oord__class_Oless__eq(_312599, _312601, c_Groups_Ozero__class_Ozero(_312599)), c_Orderings_Oord__class_Oless__eq(_312599, _312603, c_Groups_Ozero__class_Ozero(_312599)), -(c_Orderings_Oord__class_Oless__eq(_312599, c_Groups_Ozero__class_Ozero(_312599), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_312599), _312601), _312603)))], (585 ^ _292445) ^ [_313047, _313049, _313051] : [class_Rings_Oordered__cancel__semiring(_313047), c_Orderings_Oord__class_Oless__eq(_313047, _313049, c_Groups_Ozero__class_Ozero(_313047)), c_Orderings_Oord__class_Oless__eq(_313047, c_Groups_Ozero__class_Ozero(_313047), _313051), -(c_Orderings_Oord__class_Oless__eq(_313047, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_313047), _313049), _313051), c_Groups_Ozero__class_Ozero(_313047)))], (599 ^ _292445) ^ [_313495, _313497, _313499] : [class_Rings_Oordered__cancel__semiring(_313495), c_Orderings_Oord__class_Oless__eq(_313495, c_Groups_Ozero__class_Ozero(_313495), _313497), c_Orderings_Oord__class_Oless__eq(_313495, _313499, c_Groups_Ozero__class_Ozero(_313495)), -(c_Orderings_Oord__class_Oless__eq(_313495, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_313495), _313499), _313497), c_Groups_Ozero__class_Ozero(_313495)))], (613 ^ _292445) ^ [_313943, _313945, _313947] : [class_Rings_Oordered__cancel__semiring(_313943), c_Orderings_Oord__class_Oless__eq(_313943, c_Groups_Ozero__class_Ozero(_313943), _313945), c_Orderings_Oord__class_Oless__eq(_313943, _313947, c_Groups_Ozero__class_Ozero(_313943)), -(c_Orderings_Oord__class_Oless__eq(_313943, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_313943), _313945), _313947), c_Groups_Ozero__class_Ozero(_313943)))], (627 ^ _292445) ^ [_314391, _314393, _314395] : [class_Rings_Oordered__cancel__semiring(_314391), c_Orderings_Oord__class_Oless__eq(_314391, c_Groups_Ozero__class_Ozero(_314391), _314393), c_Orderings_Oord__class_Oless__eq(_314391, c_Groups_Ozero__class_Ozero(_314391), _314395), -(c_Orderings_Oord__class_Oless__eq(_314391, c_Groups_Ozero__class_Ozero(_314391), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_314391), _314393), _314395)))], (641 ^ _292445) ^ [_314839, _314841, _314843] : [class_Rings_Olinordered__ring__strict(_314839), 644 ^ _292445 : [(645 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_314839, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_314839), _314841), _314843), c_Groups_Ozero__class_Ozero(_314839)), 650 ^ _292445 : [(651 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_314839, c_Groups_Ozero__class_Ozero(_314839), _314841))], (653 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_314839, _314843, c_Groups_Ozero__class_Ozero(_314839)))]], 654 ^ _292445 : [(655 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_314839, _314841, c_Groups_Ozero__class_Ozero(_314839)))], (657 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_314839, c_Groups_Ozero__class_Ozero(_314839), _314843))]]], (659 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_314839, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_314839), _314841), _314843), c_Groups_Ozero__class_Ozero(_314839))), 660 ^ _292445 : [(661 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_314839, c_Groups_Ozero__class_Ozero(_314839), _314841), c_Orderings_Oord__class_Oless__eq(_314839, _314843, c_Groups_Ozero__class_Ozero(_314839))], (667 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_314839, _314841, c_Groups_Ozero__class_Ozero(_314839)), c_Orderings_Oord__class_Oless__eq(_314839, c_Groups_Ozero__class_Ozero(_314839), _314843)]]]]], (675 ^ _292445) ^ [_315888, _315890, _315892] : [class_Rings_Olinordered__ring__strict(_315888), 678 ^ _292445 : [(679 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_315888, c_Groups_Ozero__class_Ozero(_315888), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_315888), _315890), _315892)), 684 ^ _292445 : [(685 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_315888, c_Groups_Ozero__class_Ozero(_315888), _315890))], (687 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_315888, c_Groups_Ozero__class_Ozero(_315888), _315892))]], 688 ^ _292445 : [(689 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_315888, _315890, c_Groups_Ozero__class_Ozero(_315888)))], (691 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_315888, _315892, c_Groups_Ozero__class_Ozero(_315888)))]]], (693 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_315888, c_Groups_Ozero__class_Ozero(_315888), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_315888), _315890), _315892))), 694 ^ _292445 : [(695 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_315888, c_Groups_Ozero__class_Ozero(_315888), _315890), c_Orderings_Oord__class_Oless__eq(_315888, c_Groups_Ozero__class_Ozero(_315888), _315892)], (701 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_315888, _315890, c_Groups_Ozero__class_Ozero(_315888)), c_Orderings_Oord__class_Oless__eq(_315888, _315892, c_Groups_Ozero__class_Ozero(_315888))]]]]], (709 ^ _292445) ^ [_316923, _316925] : [class_Rings_Olinordered__ring(_316923), -(c_Orderings_Oord__class_Oless__eq(_316923, c_Groups_Ozero__class_Ozero(_316923), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_316923), _316925), _316925)))], (715 ^ _292445) ^ [_317167, _317169, _317171] : [class_Groups_Oordered__comm__monoid__add(_317167), c_Orderings_Oord__class_Oless__eq(_317167, _317169, c_Groups_Ozero__class_Ozero(_317167)), c_Orderings_Oord__class_Oless__eq(_317167, _317171, c_Groups_Ozero__class_Ozero(_317167)), -(c_Orderings_Oord__class_Oless__eq(_317167, c_Groups_Oplus__class_Oplus(_317167, _317169, _317171), c_Groups_Ozero__class_Ozero(_317167)))], (729 ^ _292445) ^ [_317621, _317623, _317625, _317627] : [class_Groups_Oordered__comm__monoid__add(_317621), c_Orderings_Oord__class_Oless__eq(_317621, c_Groups_Ozero__class_Ozero(_317621), _317623), c_Orderings_Oord__class_Oless__eq(_317621, _317625, _317627), -(c_Orderings_Oord__class_Oless__eq(_317621, _317625, c_Groups_Oplus__class_Oplus(_317621, _317627, _317623)))], (743 ^ _292445) ^ [_318081, _318083, _318085, _318087] : [class_Groups_Oordered__comm__monoid__add(_318081), c_Orderings_Oord__class_Oless__eq(_318081, c_Groups_Ozero__class_Ozero(_318081), _318083), c_Orderings_Oord__class_Oless__eq(_318081, _318085, _318087), -(c_Orderings_Oord__class_Oless__eq(_318081, _318085, c_Groups_Oplus__class_Oplus(_318081, _318083, _318087)))], (757 ^ _292445) ^ [_318527, _318529, _318531] : [class_Groups_Oordered__comm__monoid__add(_318527), c_Orderings_Oord__class_Oless__eq(_318527, c_Groups_Ozero__class_Ozero(_318527), _318529), c_Orderings_Oord__class_Oless__eq(_318527, c_Groups_Ozero__class_Ozero(_318527), _318531), 768 ^ _292445 : [(769 ^ _292445) ^ [] : [c_Groups_Oplus__class_Oplus(_318527, _318529, _318531) = c_Groups_Ozero__class_Ozero(_318527), 772 ^ _292445 : [(773 ^ _292445) ^ [] : [-(_318529 = c_Groups_Ozero__class_Ozero(_318527))], (775 ^ _292445) ^ [] : [-(_318531 = c_Groups_Ozero__class_Ozero(_318527))]]], (777 ^ _292445) ^ [] : [-(c_Groups_Oplus__class_Oplus(_318527, _318529, _318531) = c_Groups_Ozero__class_Ozero(_318527)), _318529 = c_Groups_Ozero__class_Ozero(_318527), _318531 = c_Groups_Ozero__class_Ozero(_318527)]]], (787 ^ _292445) ^ [_319407, _319409, _319411] : [class_Groups_Oordered__comm__monoid__add(_319407), c_Orderings_Oord__class_Oless__eq(_319407, c_Groups_Ozero__class_Ozero(_319407), _319409), c_Orderings_Oord__class_Oless__eq(_319407, c_Groups_Ozero__class_Ozero(_319407), _319411), -(c_Orderings_Oord__class_Oless__eq(_319407, c_Groups_Ozero__class_Ozero(_319407), c_Groups_Oplus__class_Oplus(_319407, _319409, _319411)))], (801 ^ _292445) ^ [_319833, _319835] : [class_Groups_Olinordered__ab__group__add(_319833), 804 ^ _292445 : [(805 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_319833, c_Groups_Oplus__class_Oplus(_319833, _319835, _319835), c_Groups_Ozero__class_Ozero(_319833)), -(c_Orderings_Oord__class_Oless__eq(_319833, _319835, c_Groups_Ozero__class_Ozero(_319833)))], (811 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_319833, _319835, c_Groups_Ozero__class_Ozero(_319833)), -(c_Orderings_Oord__class_Oless__eq(_319833, c_Groups_Oplus__class_Oplus(_319833, _319835, _319835), c_Groups_Ozero__class_Ozero(_319833)))]]], (817 ^ _292445) ^ [_320321, _320323] : [class_Groups_Olinordered__ab__group__add(_320321), 820 ^ _292445 : [(821 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_320321, c_Groups_Ozero__class_Ozero(_320321), c_Groups_Oplus__class_Oplus(_320321, _320323, _320323)), -(c_Orderings_Oord__class_Oless__eq(_320321, c_Groups_Ozero__class_Ozero(_320321), _320323))], (827 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_320321, c_Groups_Ozero__class_Ozero(_320321), _320323), -(c_Orderings_Oord__class_Oless__eq(_320321, c_Groups_Ozero__class_Ozero(_320321), c_Groups_Oplus__class_Oplus(_320321, _320323, _320323)))]]], (833 ^ _292445) ^ [_320809, _320811] : [class_Groups_Oordered__ab__group__add__abs(_320809), c_Orderings_Oord__class_Oless__eq(_320809, c_Groups_Ozero__class_Ozero(_320809), _320811), -(c_Groups_Oabs__class_Oabs(_320809, _320811) = _320811)], (843 ^ _292445) ^ [_321118, _321120] : [class_Groups_Oordered__ab__group__add__abs(_321118), 846 ^ _292445 : [(847 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_321118, c_Groups_Oabs__class_Oabs(_321118, _321120), c_Groups_Ozero__class_Ozero(_321118)), -(_321120 = c_Groups_Ozero__class_Ozero(_321118))], (853 ^ _292445) ^ [] : [_321120 = c_Groups_Ozero__class_Ozero(_321118), -(c_Orderings_Oord__class_Oless__eq(_321118, c_Groups_Oabs__class_Oabs(_321118, _321120), c_Groups_Ozero__class_Ozero(_321118)))]]], (859 ^ _292445) ^ [_321600, _321602] : [class_Groups_Oordered__ab__group__add__abs(_321600), -(c_Orderings_Oord__class_Oless__eq(_321600, c_Groups_Ozero__class_Ozero(_321600), c_Groups_Oabs__class_Oabs(_321600, _321602)))], (865 ^ _292445) ^ [_321834, _321836, _321838] : [class_Rings_Oordered__ring__abs(_321834), -(c_Groups_Oabs__class_Oabs(_321834, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_321834), _321836), _321838)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_321834), c_Groups_Oabs__class_Oabs(_321834, _321836)), c_Groups_Oabs__class_Oabs(_321834, _321838))), 872 ^ _292445 : [(873 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_321834, c_Groups_Ozero__class_Ozero(_321834), _321836)], (875 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_321834, _321836, c_Groups_Ozero__class_Ozero(_321834))]], 876 ^ _292445 : [(877 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_321834, c_Groups_Ozero__class_Ozero(_321834), _321838)], (879 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_321834, _321838, c_Groups_Ozero__class_Ozero(_321834))]]], (883 ^ _292445) ^ [_322474, _322476, _322478] : [class_Rings_Olinordered__idom(_322474), c_Orderings_Oord__class_Oless__eq(_322474, c_Groups_Ozero__class_Ozero(_322474), _322476), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_322474), c_Groups_Oabs__class_Oabs(_322474, _322478)), _322476) = c_Groups_Oabs__class_Oabs(_322474, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_322474), _322478), _322476)))], (893 ^ _292445) ^ [_322845, _322847, _322849] : [class_Orderings_Olinorder(_322845), -(c_Orderings_Oord__class_Oless__eq(_322845, _322847, _322849)), -(c_Orderings_Oord__class_Oless__eq(_322845, _322849, _322847))], (903 ^ _292445) ^ [_323201, _323203, _323205, _323207, _323209] : [class_Orderings_Oord(_323201), c_Orderings_Oord__class_Oless__eq(tc_fun(_323203, _323201), _323205, _323207), -(c_Orderings_Oord__class_Oless__eq(_323201, hAPP(_323205, _323209), hAPP(_323207, _323209)))], (913 ^ _292445) ^ [_323578, _323580, _323582, _323584] : [class_Orderings_Oorder(_323578), c_Orderings_Oord__class_Oless__eq(_323578, _323580, _323582), c_Orderings_Oord__class_Oless__eq(_323578, _323584, _323580), -(c_Orderings_Oord__class_Oless__eq(_323578, _323584, _323582))], (927 ^ _292445) ^ [_324012, _324014, _324016] : [class_Orderings_Oorder(_324012), c_Orderings_Oord__class_Oless__eq(_324012, _324014, _324016), c_Orderings_Oord__class_Oless__eq(_324012, _324016, _324014), -(_324016 = _324014)], (941 ^ _292445) ^ [_324444, _324446, _324448, _324450] : [class_Orderings_Opreorder(_324444), c_Orderings_Oord__class_Oless__eq(_324444, _324446, _324448), c_Orderings_Oord__class_Oless__eq(_324444, _324448, _324450), -(c_Orderings_Oord__class_Oless__eq(_324444, _324446, _324450))], (955 ^ _292445) ^ [_324878, _324880, _324882] : [class_Orderings_Oorder(_324878), c_Orderings_Oord__class_Oless__eq(_324878, _324880, _324882), c_Orderings_Oord__class_Oless__eq(_324878, _324882, _324880), -(_324880 = _324882)], (969 ^ _292445) ^ [_325310, _325312, _325314, _325316] : [class_Orderings_Oorder(_325310), c_Orderings_Oord__class_Oless__eq(_325310, _325312, _325314), _325312 = _325316, -(c_Orderings_Oord__class_Oless__eq(_325310, _325316, _325314))], (983 ^ _292445) ^ [_325756, _325758, _325760, _325762] : [class_Orderings_Oord(_325756), c_Orderings_Oord__class_Oless__eq(_325756, _325758, _325760), _325760 = _325762, -(c_Orderings_Oord__class_Oless__eq(_325756, _325758, _325762))], (997 ^ _292445) ^ [_326202, _326204, _326206, _326208] : [class_Orderings_Oorder(_326202), _326204 = _326206, c_Orderings_Oord__class_Oless__eq(_326202, _326208, _326206), -(c_Orderings_Oord__class_Oless__eq(_326202, _326208, _326204))], (1011 ^ _292445) ^ [_326648, _326650, _326652, _326654] : [class_Orderings_Oord(_326648), _326650 = _326652, c_Orderings_Oord__class_Oless__eq(_326648, _326652, _326654), -(c_Orderings_Oord__class_Oless__eq(_326648, _326650, _326654))], (1025 ^ _292445) ^ [_327080, _327082, _327084] : [class_Orderings_Oorder(_327080), c_Orderings_Oord__class_Oless__eq(_327080, _327082, _327084), 1032 ^ _292445 : [(1033 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_327080, _327084, _327082), -(_327084 = _327082)], (1039 ^ _292445) ^ [] : [_327084 = _327082, -(c_Orderings_Oord__class_Oless__eq(_327080, _327084, _327082))]]], (1045 ^ _292445) ^ [_327694, _327696, _327698, _327700, _327702] : [class_Orderings_Oord(_327694), c_Orderings_Oord__class_Oless__eq(tc_fun(_327696, _327694), _327698, _327700), -(c_Orderings_Oord__class_Oless__eq(_327694, hAPP(_327698, _327702), hAPP(_327700, _327702)))], (1055 ^ _292445) ^ [_328057, _328059, _328061] : [class_Orderings_Opreorder(_328057), _328059 = _328061, -(c_Orderings_Oord__class_Oless__eq(_328057, _328059, _328061))], (1065 ^ _292445) ^ [_328380, _328382, _328384] : [class_Orderings_Oorder(_328380), 1068 ^ _292445 : [(1069 ^ _292445) ^ [] : [_328382 = _328384, 1072 ^ _292445 : [(1073 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_328380, _328382, _328384))], (1075 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_328380, _328384, _328382))]]], (1077 ^ _292445) ^ [] : [-(_328382 = _328384), c_Orderings_Oord__class_Oless__eq(_328380, _328382, _328384), c_Orderings_Oord__class_Oless__eq(_328380, _328384, _328382)]]], (1087 ^ _292445) ^ [_329038, _329040, _329042] : [class_Orderings_Olinorder(_329038), -(c_Orderings_Oord__class_Oless__eq(_329038, _329040, _329042)), -(c_Orderings_Oord__class_Oless__eq(_329038, _329042, _329040))], (1097 ^ _292445) ^ [_329378, _329380, _329382, _329384] : [class_Orderings_Oord(_329378), 1100 ^ _292445 : [(1101 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_329380, _329378), _329382, _329384), 1104 ^ _292445 : [(1105 ^ _292445) ^ [_329637] : [-(c_Orderings_Oord__class_Oless__eq(_329378, hAPP(_329382, _329637), hAPP(_329384, _329637)))]]], (1107 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_329378, hAPP(_329382, 1108 ^ [_329378, _329380, _329382, _329384]), hAPP(_329384, 1108 ^ [_329378, _329380, _329382, _329384])), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_329380, _329378), _329382, _329384))]]], (1114 ^ _292445) ^ [_329990, _329992] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _329990), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, _329990, _329992)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _329992))))], (1116 ^ _292445) ^ [_330145, _330147, _330149, _330151] : [class_Groups_Oab__semigroup__mult(_330145), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_330145), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_330145), _330147), _330149)), _330151) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_330145), _330147), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_330145), _330149), _330151)))], (1122 ^ _292445) ^ [_330457, _330459, _330461, _330463] : [class_Groups_Ocancel__semigroup__add(_330457), c_Groups_Oplus__class_Oplus(_330457, _330459, _330461) = c_Groups_Oplus__class_Oplus(_330457, _330463, _330461), -(_330459 = _330463)], (1132 ^ _292445) ^ [_330818, _330820, _330822, _330824] : [class_Groups_Ocancel__ab__semigroup__add(_330818), c_Groups_Oplus__class_Oplus(_330818, _330820, _330822) = c_Groups_Oplus__class_Oplus(_330818, _330820, _330824), -(_330822 = _330824)], (1142 ^ _292445) ^ [_331179, _331181, _331183, _331185] : [class_Groups_Ocancel__semigroup__add(_331179), c_Groups_Oplus__class_Oplus(_331179, _331181, _331183) = c_Groups_Oplus__class_Oplus(_331179, _331181, _331185), -(_331183 = _331185)], (1152 ^ _292445) ^ [_331540, _331542, _331544, _331546] : [class_Groups_Ocancel__semigroup__add(_331540), 1155 ^ _292445 : [(1156 ^ _292445) ^ [] : [c_Groups_Oplus__class_Oplus(_331540, _331542, _331544) = c_Groups_Oplus__class_Oplus(_331540, _331546, _331544), -(_331542 = _331546)], (1162 ^ _292445) ^ [] : [_331542 = _331546, -(c_Groups_Oplus__class_Oplus(_331540, _331542, _331544) = c_Groups_Oplus__class_Oplus(_331540, _331546, _331544))]]], (1168 ^ _292445) ^ [_332082, _332084, _332086, _332088] : [class_Groups_Ocancel__semigroup__add(_332082), 1171 ^ _292445 : [(1172 ^ _292445) ^ [] : [c_Groups_Oplus__class_Oplus(_332082, _332084, _332086) = c_Groups_Oplus__class_Oplus(_332082, _332084, _332088), -(_332086 = _332088)], (1178 ^ _292445) ^ [] : [_332086 = _332088, -(c_Groups_Oplus__class_Oplus(_332082, _332084, _332086) = c_Groups_Oplus__class_Oplus(_332082, _332084, _332088))]]], (1184 ^ _292445) ^ [_332624, _332626, _332628, _332630] : [class_Groups_Oab__semigroup__add(_332624), -(c_Groups_Oplus__class_Oplus(_332624, c_Groups_Oplus__class_Oplus(_332624, _332626, _332628), _332630) = c_Groups_Oplus__class_Oplus(_332624, _332626, c_Groups_Oplus__class_Oplus(_332624, _332628, _332630)))], (1190 ^ _292445) ^ [_332876, _332878] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _332876, _332878), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _332878, _332876), -(_332876 = _332878)], (1200 ^ _292445) ^ [_333193, _333195, _333197] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _333193, _333195), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _333195, _333197), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _333193, _333197))], (1210 ^ _292445) ^ [_333508, _333510] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _333508, _333510)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _333510, _333508))], (1216 ^ _292445) ^ [_333694] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _333694, _333694))], (1218 ^ _292445) ^ [_333802, _333804] : [class_Groups_Oordered__ab__group__add__abs(_333802), -(c_Groups_Oabs__class_Oabs(_333802, c_Groups_Oabs__class_Oabs(_333802, _333804)) = c_Groups_Oabs__class_Oabs(_333802, _333804))], (1224 ^ _292445) ^ [_334056, _334058, _334060, _334062] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_334056), c_Orderings_Oord__class_Oless__eq(_334056, c_Groups_Oplus__class_Oplus(_334056, _334058, _334060), c_Groups_Oplus__class_Oplus(_334056, _334058, _334062)), -(c_Orderings_Oord__class_Oless__eq(_334056, _334060, _334062))], (1234 ^ _292445) ^ [_334421, _334423, _334425, _334427] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_334421), c_Orderings_Oord__class_Oless__eq(_334421, c_Groups_Oplus__class_Oplus(_334421, _334423, _334425), c_Groups_Oplus__class_Oplus(_334421, _334427, _334425)), -(c_Orderings_Oord__class_Oless__eq(_334421, _334423, _334427))], (1244 ^ _292445) ^ [_334800, _334802, _334804, _334806, _334808] : [class_Groups_Oordered__ab__semigroup__add(_334800), c_Orderings_Oord__class_Oless__eq(_334800, _334802, _334804), c_Orderings_Oord__class_Oless__eq(_334800, _334806, _334808), -(c_Orderings_Oord__class_Oless__eq(_334800, c_Groups_Oplus__class_Oplus(_334800, _334802, _334806), c_Groups_Oplus__class_Oplus(_334800, _334804, _334808)))], (1258 ^ _292445) ^ [_335278, _335280, _335282, _335284] : [class_Groups_Oordered__ab__semigroup__add(_335278), c_Orderings_Oord__class_Oless__eq(_335278, _335280, _335282), -(c_Orderings_Oord__class_Oless__eq(_335278, c_Groups_Oplus__class_Oplus(_335278, _335284, _335280), c_Groups_Oplus__class_Oplus(_335278, _335284, _335282)))], (1268 ^ _292445) ^ [_335643, _335645, _335647, _335649] : [class_Groups_Oordered__ab__semigroup__add(_335643), c_Orderings_Oord__class_Oless__eq(_335643, _335645, _335647), -(c_Orderings_Oord__class_Oless__eq(_335643, c_Groups_Oplus__class_Oplus(_335643, _335645, _335649), c_Groups_Oplus__class_Oplus(_335643, _335647, _335649)))], (1278 ^ _292445) ^ [_336008, _336010, _336012, _336014] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_336008), 1281 ^ _292445 : [(1282 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_336008, c_Groups_Oplus__class_Oplus(_336008, _336010, _336012), c_Groups_Oplus__class_Oplus(_336008, _336010, _336014)), -(c_Orderings_Oord__class_Oless__eq(_336008, _336012, _336014))], (1288 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_336008, _336012, _336014), -(c_Orderings_Oord__class_Oless__eq(_336008, c_Groups_Oplus__class_Oplus(_336008, _336010, _336012), c_Groups_Oplus__class_Oplus(_336008, _336010, _336014)))]]], (1294 ^ _292445) ^ [_336556, _336558, _336560, _336562] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_336556), 1297 ^ _292445 : [(1298 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_336556, c_Groups_Oplus__class_Oplus(_336556, _336558, _336560), c_Groups_Oplus__class_Oplus(_336556, _336562, _336560)), -(c_Orderings_Oord__class_Oless__eq(_336556, _336558, _336562))], (1304 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_336556, _336558, _336562), -(c_Orderings_Oord__class_Oless__eq(_336556, c_Groups_Oplus__class_Oplus(_336556, _336558, _336560), c_Groups_Oplus__class_Oplus(_336556, _336562, _336560)))]]], (1310 ^ _292445) ^ [_337118, _337120, _337122, _337124, _337126] : [class_Rings_Osemiring(_337118), -(c_Groups_Oplus__class_Oplus(_337118, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_337118), _337120), _337122), c_Groups_Oplus__class_Oplus(_337118, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_337118), _337124), _337122), _337126)) = c_Groups_Oplus__class_Oplus(_337118, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_337118), c_Groups_Oplus__class_Oplus(_337118, _337120, _337124)), _337122), _337126))], (1316 ^ _292445) ^ [_337452, _337454, _337456, _337458] : [class_RealVector_Oreal__normed__algebra(_337452), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_337452), c_Groups_Oplus__class_Oplus(_337452, _337454, _337456)), _337458) = c_Groups_Oplus__class_Oplus(_337452, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_337452), _337454), _337458), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_337452), _337456), _337458)))], (1322 ^ _292445) ^ [_337764, _337766, _337768, _337770] : [class_RealVector_Oreal__normed__algebra(_337764), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_337764), c_Groups_Oplus__class_Oplus(_337764, _337766, _337768)), _337770) = c_Groups_Oplus__class_Oplus(_337764, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_337764), _337766), _337770), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_337764), _337768), _337770)))], (1328 ^ _292445) ^ [_338076, _338078, _338080, _338082] : [class_Rings_Ocomm__semiring(_338076), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_338076), c_Groups_Oplus__class_Oplus(_338076, _338078, _338080)), _338082) = c_Groups_Oplus__class_Oplus(_338076, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_338076), _338078), _338082), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_338076), _338080), _338082)))], (1334 ^ _292445) ^ [_338388, _338390, _338392, _338394] : [class_RealVector_Oreal__normed__algebra(_338388), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_338388), _338390), c_Groups_Oplus__class_Oplus(_338388, _338392, _338394)) = c_Groups_Oplus__class_Oplus(_338388, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_338388), _338390), _338392), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_338388), _338390), _338394)))], (1340 ^ _292445) ^ [_338700, _338702, _338704, _338706] : [class_RealVector_Oreal__normed__algebra(_338700), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_338700), _338702), c_Groups_Oplus__class_Oplus(_338700, _338704, _338706)) = c_Groups_Oplus__class_Oplus(_338700, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_338700), _338702), _338704), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_338700), _338702), _338706)))], (1346 ^ _292445) ^ [_338998, _339000, _339002] : [class_Groups_Oordered__ab__group__add__abs(_338998), c_Orderings_Oord__class_Oless__eq(_338998, c_Groups_Oabs__class_Oabs(_338998, _339000), _339002), -(c_Orderings_Oord__class_Oless__eq(_338998, _339000, _339002))], (1356 ^ _292445) ^ [] : [-(v_cs____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))], (1358 ^ _292445) ^ [_339396, _339398, _339400, _339402] : [class_RealVector_Oreal__normed__vector(_339396), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _339398, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_339396, _339400), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _339398), c_RealVector_Onorm__class_Onorm(_339396, _339402))), -(_339400 = c_Groups_Ozero__class_Ozero(_339396))], (1372 ^ _292445) ^ [_339884, _339886, _339888, _339890, _339892] : [class_Fields_Ofield(_339884), -(_339886 = c_Groups_Ozero__class_Ozero(_339884)), -(_339888 = c_Groups_Ozero__class_Ozero(_339884)), -(c_Groups_Oplus__class_Oplus(_339884, c_Rings_Oinverse__class_Odivide(_339884, _339890, _339886), c_Rings_Oinverse__class_Odivide(_339884, _339892, _339888)) = c_Rings_Oinverse__class_Odivide(_339884, c_Groups_Oplus__class_Oplus(_339884, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_339884), _339890), _339888), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_339884), _339892), _339886)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_339884), _339886), _339888)))], (1386 ^ _292445) ^ [_340442, _340444, _340446, _340448] : [class_Fields_Ofield(_340442), -(_340444 = c_Groups_Ozero__class_Ozero(_340442)), -(c_Groups_Oplus__class_Oplus(_340442, c_Rings_Oinverse__class_Odivide(_340442, _340446, _340444), _340448) = c_Rings_Oinverse__class_Odivide(_340442, c_Groups_Oplus__class_Oplus(_340442, _340446, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_340442), _340444), _340448)), _340444))], (1396 ^ _292445) ^ [_340842, _340844, _340846, _340848] : [class_Fields_Ofield__inverse__zero(_340842), -(_340844 = c_Groups_Ozero__class_Ozero(_340842)), -(c_Groups_Oplus__class_Oplus(_340842, c_Rings_Oinverse__class_Odivide(_340842, _340846, _340844), _340848) = c_Rings_Oinverse__class_Odivide(_340842, c_Groups_Oplus__class_Oplus(_340842, _340846, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_340842), _340848), _340844)), _340844))], (1406 ^ _292445) ^ [_341242, _341244, _341246, _341248] : [class_Fields_Ofield(_341242), -(_341244 = c_Groups_Ozero__class_Ozero(_341242)), -(c_Groups_Oplus__class_Oplus(_341242, _341246, c_Rings_Oinverse__class_Odivide(_341242, _341248, _341244)) = c_Rings_Oinverse__class_Odivide(_341242, c_Groups_Oplus__class_Oplus(_341242, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_341242), _341244), _341246), _341248), _341244))], (1416 ^ _292445) ^ [_341642, _341644, _341646, _341648] : [class_Fields_Ofield__inverse__zero(_341642), -(_341644 = c_Groups_Ozero__class_Ozero(_341642)), -(c_Groups_Oplus__class_Oplus(_341642, _341646, c_Rings_Oinverse__class_Odivide(_341642, _341648, _341644)) = c_Rings_Oinverse__class_Odivide(_341642, c_Groups_Oplus__class_Oplus(_341642, _341648, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_341642), _341646), _341644)), _341644))], (1426 ^ _292445) ^ [_342028, _342030, _342032] : [class_Rings_Olinordered__ring__strict(_342028), 1429 ^ _292445 : [(1430 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_342028, c_Groups_Oplus__class_Oplus(_342028, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_342028), _342030), _342030), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_342028), _342032), _342032)), c_Groups_Ozero__class_Ozero(_342028)), 1433 ^ _292445 : [(1434 ^ _292445) ^ [] : [-(_342030 = c_Groups_Ozero__class_Ozero(_342028))], (1436 ^ _292445) ^ [] : [-(_342032 = c_Groups_Ozero__class_Ozero(_342028))]]], (1438 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_342028, c_Groups_Oplus__class_Oplus(_342028, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_342028), _342030), _342030), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_342028), _342032), _342032)), c_Groups_Ozero__class_Ozero(_342028))), _342030 = c_Groups_Ozero__class_Ozero(_342028), _342032 = c_Groups_Ozero__class_Ozero(_342028)]]], (1448 ^ _292445) ^ [_342761, _342763, _342765] : [class_Rings_Olinordered__ring(_342761), -(c_Orderings_Oord__class_Oless__eq(_342761, c_Groups_Ozero__class_Ozero(_342761), c_Groups_Oplus__class_Oplus(_342761, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_342761), _342763), _342763), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_342761), _342765), _342765))))], (1454 ^ _292445) ^ [_343035, _343037, _343039] : [class_Fields_Olinordered__field(_343035), -(_343037 = c_Groups_Ozero__class_Ozero(_343035)), -(c_Groups_Oabs__class_Oabs(_343035, c_Rings_Oinverse__class_Odivide(_343035, _343039, _343037)) = c_Rings_Oinverse__class_Odivide(_343035, c_Groups_Oabs__class_Oabs(_343035, _343039), c_Groups_Oabs__class_Oabs(_343035, _343037)))], (1464 ^ _292445) ^ [_343411, _343413, _343415, _343417] : [class_Fields_Ofield__inverse__zero(_343411), 1467 ^ _292445 : [(1484 ^ _292445) ^ [] : [-(_343413 = c_Rings_Oinverse__class_Odivide(_343411, _343415, _343417)), 1487 ^ _292445 : [(1488 ^ _292445) ^ [] : [_343417 = c_Groups_Ozero__class_Ozero(_343411)], (1490 ^ _292445) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_343411), _343413), _343417) = _343415]], 1491 ^ _292445 : [(1492 ^ _292445) ^ [] : [-(_343417 = c_Groups_Ozero__class_Ozero(_343411))], (1494 ^ _292445) ^ [] : [_343413 = c_Groups_Ozero__class_Ozero(_343411)]]], (1468 ^ _292445) ^ [] : [_343413 = c_Rings_Oinverse__class_Odivide(_343411, _343415, _343417), 1471 ^ _292445 : [(1472 ^ _292445) ^ [] : [-(_343417 = c_Groups_Ozero__class_Ozero(_343411)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_343411), _343413), _343417) = _343415)], (1478 ^ _292445) ^ [] : [_343417 = c_Groups_Ozero__class_Ozero(_343411), -(_343413 = c_Groups_Ozero__class_Ozero(_343411))]]]]], (1498 ^ _292445) ^ [_344495, _344497, _344499, _344501] : [class_Fields_Ofield__inverse__zero(_344495), 1501 ^ _292445 : [(1518 ^ _292445) ^ [] : [-(c_Rings_Oinverse__class_Odivide(_344495, _344497, _344499) = _344501), 1521 ^ _292445 : [(1522 ^ _292445) ^ [] : [_344499 = c_Groups_Ozero__class_Ozero(_344495)], (1524 ^ _292445) ^ [] : [_344497 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_344495), _344501), _344499)]], 1525 ^ _292445 : [(1526 ^ _292445) ^ [] : [-(_344499 = c_Groups_Ozero__class_Ozero(_344495))], (1528 ^ _292445) ^ [] : [_344501 = c_Groups_Ozero__class_Ozero(_344495)]]], (1502 ^ _292445) ^ [] : [c_Rings_Oinverse__class_Odivide(_344495, _344497, _344499) = _344501, 1505 ^ _292445 : [(1506 ^ _292445) ^ [] : [-(_344499 = c_Groups_Ozero__class_Ozero(_344495)), -(_344497 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_344495), _344501), _344499))], (1512 ^ _292445) ^ [] : [_344499 = c_Groups_Ozero__class_Ozero(_344495), -(_344501 = c_Groups_Ozero__class_Ozero(_344495))]]]]], (1532 ^ _292445) ^ [] : [c_Polynomial_OpCons(tc_Complex_Ocomplex, v_c____, v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))], (1534 ^ _292445) ^ [_345617, _345619, _345621] : [-(_345617 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 1537 ^ _292445 : [(1538 ^ _292445) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _345617), _345619) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _345617), _345621), -(_345619 = _345621)], (1544 ^ _292445) ^ [] : [_345619 = _345621, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _345617), _345619) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _345617), _345621))]]], (1550 ^ _292445) ^ [_346146, _346148, _346150] : [-(_346146 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 1553 ^ _292445 : [(1554 ^ _292445) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _346148), _346146) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _346150), _346146), -(_346148 = _346150)], (1560 ^ _292445) ^ [] : [_346148 = _346150, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _346148), _346146) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _346150), _346146))]]], (1566 ^ _292445) ^ [_346675, _346677, _346679] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _346675, 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, _346677), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _346675), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _346679))), -(_346677 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (1576 ^ _292445) ^ [_347012, _347014] : [class_RealVector_Oreal__normed__vector(_347012), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_347012, _347014)))], (1598 ^ _292445) ^ [_347692, _347694] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, _347692, _347694))), 1601 ^ _292445 : [(1602 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _347692, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (1604 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _347694)]], 1605 ^ _292445 : [(1606 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _347692)], (1608 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _347694, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))]]], (1582 ^ _292445) ^ [_347257, _347259] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, _347257, _347259)), 1585 ^ _292445 : [(1586 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _347257, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _347259))], (1592 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _347257)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _347259, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))]]], (1612 ^ _292445) ^ [_348188, _348190] : [c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _348188), _348188), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _348190), _348190)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 1615 ^ _292445 : [(1616 ^ _292445) ^ [] : [-(_348188 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (1618 ^ _292445) ^ [] : [-(_348190 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))]]], (1620 ^ _292445) ^ [_348457, _348459] : [-(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _348457), _348457), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _348459), _348459)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _348457 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _348459 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)], (1630 ^ _292445) ^ [_348832, _348834, _348836, _348838, _348840] : [class_Fields_Ofield__inverse__zero(_348832), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_348832), c_Rings_Oinverse__class_Odivide(_348832, _348834, _348836)), c_Rings_Oinverse__class_Odivide(_348832, _348838, _348840)) = c_Rings_Oinverse__class_Odivide(_348832, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_348832), _348834), _348838), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_348832), _348836), _348840)))], (1636 ^ _292445) ^ [_349144, _349146, _349148] : [class_Fields_Olinordered__field__inverse__zero(_349144), -(c_Groups_Oabs__class_Oabs(_349144, c_Rings_Oinverse__class_Odivide(_349144, _349146, _349148)) = c_Rings_Oinverse__class_Odivide(_349144, c_Groups_Oabs__class_Oabs(_349144, _349146), c_Groups_Oabs__class_Oabs(_349144, _349148)))], (1642 ^ _292445) ^ [_349406, _349408, _349410] : [class_Rings_Olinordered__ring__strict(_349406), 1645 ^ _292445 : [(1646 ^ _292445) ^ [] : [c_Groups_Oplus__class_Oplus(_349406, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_349406), _349408), _349408), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_349406), _349410), _349410)) = c_Groups_Ozero__class_Ozero(_349406), 1649 ^ _292445 : [(1650 ^ _292445) ^ [] : [-(_349408 = c_Groups_Ozero__class_Ozero(_349406))], (1652 ^ _292445) ^ [] : [-(_349410 = c_Groups_Ozero__class_Ozero(_349406))]]], (1654 ^ _292445) ^ [] : [-(c_Groups_Oplus__class_Oplus(_349406, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_349406), _349408), _349408), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_349406), _349410), _349410)) = c_Groups_Ozero__class_Ozero(_349406)), _349408 = c_Groups_Ozero__class_Ozero(_349406), _349410 = c_Groups_Ozero__class_Ozero(_349406)]]], (1664 ^ _292445) ^ [_350150, _350152, _350154, _350156] : [class_Fields_Olinordered__field__inverse__zero(_350150), c_Orderings_Oord__class_Oless__eq(_350150, _350152, _350154), c_Orderings_Oord__class_Oless__eq(_350150, _350156, c_Groups_Ozero__class_Ozero(_350150)), -(c_Orderings_Oord__class_Oless__eq(_350150, c_Rings_Oinverse__class_Odivide(_350150, _350154, _350156), c_Rings_Oinverse__class_Odivide(_350150, _350152, _350156)))], (1678 ^ _292445) ^ [_350618, _350620, _350622, _350624] : [class_Fields_Olinordered__field__inverse__zero(_350618), c_Orderings_Oord__class_Oless__eq(_350618, _350620, _350622), c_Orderings_Oord__class_Oless__eq(_350618, c_Groups_Ozero__class_Ozero(_350618), _350624), -(c_Orderings_Oord__class_Oless__eq(_350618, c_Rings_Oinverse__class_Odivide(_350618, _350620, _350624), c_Rings_Oinverse__class_Odivide(_350618, _350622, _350624)))], (1692 ^ _292445) ^ [_351072, _351074, _351076] : [class_Fields_Olinordered__field__inverse__zero(_351072), 1695 ^ _292445 : [(1696 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_351072, c_Rings_Oinverse__class_Odivide(_351072, _351074, _351076), c_Groups_Ozero__class_Ozero(_351072)), 1701 ^ _292445 : [(1702 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_351072, c_Groups_Ozero__class_Ozero(_351072), _351074))], (1704 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_351072, _351076, c_Groups_Ozero__class_Ozero(_351072)))]], 1705 ^ _292445 : [(1706 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_351072, _351074, c_Groups_Ozero__class_Ozero(_351072)))], (1708 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_351072, c_Groups_Ozero__class_Ozero(_351072), _351076))]]], (1710 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_351072, c_Rings_Oinverse__class_Odivide(_351072, _351074, _351076), c_Groups_Ozero__class_Ozero(_351072))), 1711 ^ _292445 : [(1712 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_351072, c_Groups_Ozero__class_Ozero(_351072), _351074), c_Orderings_Oord__class_Oless__eq(_351072, _351076, c_Groups_Ozero__class_Ozero(_351072))], (1718 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_351072, _351074, c_Groups_Ozero__class_Ozero(_351072)), c_Orderings_Oord__class_Oless__eq(_351072, c_Groups_Ozero__class_Ozero(_351072), _351076)]]]]], (1726 ^ _292445) ^ [_352109, _352111, _352113] : [class_Fields_Olinordered__field__inverse__zero(_352109), 1729 ^ _292445 : [(1730 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_352109, c_Groups_Ozero__class_Ozero(_352109), c_Rings_Oinverse__class_Odivide(_352109, _352111, _352113)), 1735 ^ _292445 : [(1736 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_352109, c_Groups_Ozero__class_Ozero(_352109), _352111))], (1738 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_352109, c_Groups_Ozero__class_Ozero(_352109), _352113))]], 1739 ^ _292445 : [(1740 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_352109, _352111, c_Groups_Ozero__class_Ozero(_352109)))], (1742 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_352109, _352113, c_Groups_Ozero__class_Ozero(_352109)))]]], (1744 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_352109, c_Groups_Ozero__class_Ozero(_352109), c_Rings_Oinverse__class_Odivide(_352109, _352111, _352113))), 1745 ^ _292445 : [(1746 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_352109, c_Groups_Ozero__class_Ozero(_352109), _352111), c_Orderings_Oord__class_Oless__eq(_352109, c_Groups_Ozero__class_Ozero(_352109), _352113)], (1752 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_352109, _352111, c_Groups_Ozero__class_Ozero(_352109)), c_Orderings_Oord__class_Oless__eq(_352109, _352113, c_Groups_Ozero__class_Ozero(_352109))]]]]], (1760 ^ _292445) ^ [_353174, _353176, _353178, _353180, _353182] : [class_Fields_Ofield(_353174), -(_353176 = c_Groups_Ozero__class_Ozero(_353174)), -(_353178 = c_Groups_Ozero__class_Ozero(_353174)), 1771 ^ _292445 : [(1772 ^ _292445) ^ [] : [c_Rings_Oinverse__class_Odivide(_353174, _353180, _353176) = c_Rings_Oinverse__class_Odivide(_353174, _353182, _353178), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_353174), _353180), _353178) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_353174), _353182), _353176))], (1778 ^ _292445) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_353174), _353180), _353178) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_353174), _353182), _353176), -(c_Rings_Oinverse__class_Odivide(_353174, _353180, _353176) = c_Rings_Oinverse__class_Odivide(_353174, _353182, _353178))]]], (1784 ^ _292445) ^ [_353996, _353998, _354000, _354002] : [class_Fields_Ofield__inverse__zero(_353996), -(_353998 = c_Groups_Ozero__class_Ozero(_353996)), -(c_Rings_Oinverse__class_Odivide(_353996, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_353996), _353998), _354000), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_353996), _353998), _354002)) = c_Rings_Oinverse__class_Odivide(_353996, _354000, _354002))], (1794 ^ _292445) ^ [_354396, _354398, _354400, _354402] : [class_Fields_Ofield__inverse__zero(_354396), -(_354398 = c_Groups_Ozero__class_Ozero(_354396)), -(c_Rings_Oinverse__class_Odivide(_354396, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_354396), _354400), _354398), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_354396), _354402), _354398)) = c_Rings_Oinverse__class_Odivide(_354396, _354400, _354402))], (1804 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____)))], (1806 ^ _292445) ^ [_354877, _354879, _354881, _354883, _354885, _354887] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_354877), -(_354879 = c_Groups_Ozero__class_Ozero(_354877)), c_Groups_Oplus__class_Oplus(_354877, _354881, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_354877), _354879), _354885)) = c_Groups_Oplus__class_Oplus(_354877, _354883, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_354877), _354879), _354887)), _354881 = _354883, -(_354885 = _354887)], (1824 ^ _292445) ^ [_355468, _355470] : [-(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _355468), _355470), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _355468), _355468)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, _355470, _355468))], (1826 ^ _292445) ^ [_355625, _355627, _355629, _355631] : [class_Rings_Ocomm__semiring__1(_355625), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_355625), _355627), c_Groups_Oplus__class_Oplus(_355625, _355629, _355631)) = c_Groups_Oplus__class_Oplus(_355625, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_355625), _355627), _355629), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_355625), _355627), _355631)))], (1832 ^ _292445) ^ [_355951, _355953, _355955, _355957, _355959] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_355951), 1835 ^ _292445 : [(1846 ^ _292445) ^ [] : [-(c_Groups_Oplus__class_Oplus(_355951, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_355951), _355953), _355957), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_355951), _355955), _355959)) = c_Groups_Oplus__class_Oplus(_355951, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_355951), _355953), _355959), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_355951), _355955), _355957))), 1849 ^ _292445 : [(1850 ^ _292445) ^ [] : [_355953 = _355955], (1852 ^ _292445) ^ [] : [_355957 = _355959]]], (1836 ^ _292445) ^ [] : [c_Groups_Oplus__class_Oplus(_355951, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_355951), _355953), _355957), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_355951), _355955), _355959)) = c_Groups_Oplus__class_Oplus(_355951, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_355951), _355953), _355959), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_355951), _355955), _355957)), -(_355953 = _355955), -(_355957 = _355959)]]], (1854 ^ _292445) ^ [_356787, _356789, _356791, _356793] : [class_Rings_Ocomm__semiring__1(_356787), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_356787), c_Groups_Oplus__class_Oplus(_356787, _356789, _356791)), _356793) = c_Groups_Oplus__class_Oplus(_356787, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_356787), _356789), _356793), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_356787), _356791), _356793)))], (1860 ^ _292445) ^ [_357099, _357101, _357103, _357105] : [class_Rings_Ocomm__semiring__1(_357099), -(c_Groups_Oplus__class_Oplus(_357099, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_357099), _357101), _357103), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_357099), _357105), _357103)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_357099), c_Groups_Oplus__class_Oplus(_357099, _357101, _357105)), _357103))], (1866 ^ _292445) ^ [_357425, _357427, _357429, _357431, _357433] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_357425), 1869 ^ _292445 : [(1880 ^ _292445) ^ [] : [1881 ^ _292445 : [(1882 ^ _292445) ^ [] : [_357427 = _357431], (1884 ^ _292445) ^ [] : [_357429 = _357433]], -(c_Groups_Oplus__class_Oplus(_357425, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_357425), _357427), _357429), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_357425), _357431), _357433)) = c_Groups_Oplus__class_Oplus(_357425, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_357425), _357427), _357433), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_357425), _357431), _357429)))], (1870 ^ _292445) ^ [] : [c_Groups_Oplus__class_Oplus(_357425, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_357425), _357427), _357429), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_357425), _357431), _357433)) = c_Groups_Oplus__class_Oplus(_357425, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_357425), _357427), _357433), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_357425), _357431), _357429)), -(_357427 = _357431), -(_357429 = _357433)]]], (1888 ^ _292445) ^ [_358227, _358229] : [class_Rings_Ocomm__semiring__1(_358227), -(c_Groups_Oplus__class_Oplus(_358227, c_Groups_Ozero__class_Ozero(_358227), _358229) = _358229)], (1894 ^ _292445) ^ [_358461, _358463, _358465] : [class_Orderings_Olinorder(_358461), -(c_Orderings_Oord__class_Oless(_358461, _358463, _358465)), -(_358463 = _358465), -(c_Orderings_Oord__class_Oless(_358461, _358465, _358463))], (1908 ^ _292445) ^ [_358885, _358887, _358889] : [class_Orderings_Opreorder(_358885), c_Orderings_Oord__class_Oless(_358885, _358887, _358889), c_Orderings_Oord__class_Oless(_358885, _358889, _358887)], (1918 ^ _292445) ^ [_359225, _359227, _359229, _359231] : [class_Orderings_Oorder(_359225), c_Orderings_Oord__class_Oless(_359225, _359227, _359229), c_Orderings_Oord__class_Oless(_359225, _359231, _359227), -(c_Orderings_Oord__class_Oless(_359225, _359231, _359229))], (1932 ^ _292445) ^ [_359673, _359675, _359677, _359679] : [class_Orderings_Opreorder(_359673), c_Orderings_Oord__class_Oless(_359673, _359675, _359677), c_Orderings_Oord__class_Oless(_359673, _359677, _359679), -(c_Orderings_Oord__class_Oless(_359673, _359675, _359679))], (1946 ^ _292445) ^ [_360121, _360123, _360125, _360127] : [class_Orderings_Oorder(_360121), c_Orderings_Oord__class_Oless(_360121, _360123, _360125), _360123 = _360127, -(c_Orderings_Oord__class_Oless(_360121, _360127, _360125))], (1960 ^ _292445) ^ [_360567, _360569, _360571, _360573] : [class_Orderings_Oord(_360567), c_Orderings_Oord__class_Oless(_360567, _360569, _360571), _360571 = _360573, -(c_Orderings_Oord__class_Oless(_360567, _360569, _360573))], (1974 ^ _292445) ^ [_361013, _361015, _361017, _361019] : [class_Orderings_Oorder(_361013), _361015 = _361017, c_Orderings_Oord__class_Oless(_361013, _361019, _361017), -(c_Orderings_Oord__class_Oless(_361013, _361019, _361015))], (1988 ^ _292445) ^ [_361459, _361461, _361463, _361465] : [class_Orderings_Oord(_361459), _361461 = _361463, c_Orderings_Oord__class_Oless(_361459, _361463, _361465), -(c_Orderings_Oord__class_Oless(_361459, _361461, _361465))], (2002 ^ _292445) ^ [_361891, _361893, _361895] : [class_Orderings_Oorder(_361891), c_Orderings_Oord__class_Oless(_361891, _361893, _361895), c_Orderings_Oord__class_Oless(_361891, _361895, _361893)], (2012 ^ _292445) ^ [_362217, _362219, _362221] : [class_Orderings_Opreorder(_362217), c_Orderings_Oord__class_Oless(_362217, _362219, _362221), c_Orderings_Oord__class_Oless(_362217, _362221, _362219)], (2022 ^ _292445) ^ [_362543, _362545, _362547] : [class_Orderings_Oorder(_362543), c_Orderings_Oord__class_Oless(_362543, _362545, _362547), _362547 = _362545], (2032 ^ _292445) ^ [_362867, _362869, _362871] : [class_Orderings_Oorder(_362867), c_Orderings_Oord__class_Oless(_362867, _362869, _362871), _362869 = _362871], (2042 ^ _292445) ^ [_363191, _363193, _363195] : [class_Orderings_Opreorder(_363191), c_Orderings_Oord__class_Oless(_363191, _363193, _363195), c_Orderings_Oord__class_Oless(_363191, _363195, _363193)], (2052 ^ _292445) ^ [_363517, _363519, _363521] : [class_Orderings_Opreorder(_363517), c_Orderings_Oord__class_Oless(_363517, _363519, _363521), c_Orderings_Oord__class_Oless(_363517, _363521, _363519)], (2062 ^ _292445) ^ [_363843, _363845, _363847] : [class_Orderings_Oorder(_363843), c_Orderings_Oord__class_Oless(_363843, _363845, _363847), _363845 = _363847], (2072 ^ _292445) ^ [_364167, _364169, _364171] : [class_Rings_Olinordered__idom(_364167), -(_364169 = _364171), -(c_Orderings_Oord__class_Oless(_364167, _364169, _364171)), -(c_Orderings_Oord__class_Oless(_364167, _364171, _364169))], (2086 ^ _292445) ^ [_364591, _364593, _364595] : [class_Orderings_Olinorder(_364591), -(_364593 = _364595), -(c_Orderings_Oord__class_Oless(_364591, _364593, _364595)), -(c_Orderings_Oord__class_Oless(_364591, _364595, _364593))], (2100 ^ _292445) ^ [_365015, _365017, _365019] : [class_Orderings_Olinorder(_365015), -(c_Orderings_Oord__class_Oless(_365015, _365017, _365019)), 2107 ^ _292445 : [(2108 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_365015, _365019, _365017)), -(_365019 = _365017)], (2114 ^ _292445) ^ [] : [_365019 = _365017, c_Orderings_Oord__class_Oless(_365015, _365019, _365017)]]], (2120 ^ _292445) ^ [_365606, _365608, _365610] : [class_Orderings_Olinorder(_365606), -(c_Orderings_Oord__class_Oless(_365606, _365608, _365610)), -(_365608 = _365610), -(c_Orderings_Oord__class_Oless(_365606, _365610, _365608))], (2134 ^ _292445) ^ [_366026, _366028, _366030] : [class_Orderings_Olinorder(_366026), 2137 ^ _292445 : [(2148 ^ _292445) ^ [] : [2149 ^ _292445 : [(2150 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_366026, _366030, _366028)], (2152 ^ _292445) ^ [] : [_366028 = _366030]], c_Orderings_Oord__class_Oless(_366026, _366028, _366030)], (2138 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_366026, _366028, _366030)), -(c_Orderings_Oord__class_Oless(_366026, _366030, _366028)), -(_366028 = _366030)]]], (2156 ^ _292445) ^ [_366686, _366688, _366690] : [class_Orderings_Olinorder(_366686), 2159 ^ _292445 : [(2170 ^ _292445) ^ [] : [2171 ^ _292445 : [(2172 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_366686, _366688, _366690)], (2174 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_366686, _366690, _366688)]], _366688 = _366690], (2160 ^ _292445) ^ [] : [-(_366688 = _366690), -(c_Orderings_Oord__class_Oless(_366686, _366688, _366690)), -(c_Orderings_Oord__class_Oless(_366686, _366690, _366688))]]], (2178 ^ _292445) ^ [_367332, _367334] : [class_Orderings_Opreorder(_367332), c_Orderings_Oord__class_Oless(_367332, _367334, _367334)], (2184 ^ _292445) ^ [_367571, _367573, _367575, _367577] : [class_Orderings_Oorder(_367571), c_Orderings_Oord__class_Oless__eq(_367571, _367573, _367575), c_Orderings_Oord__class_Oless(_367571, _367577, _367573), -(c_Orderings_Oord__class_Oless(_367571, _367577, _367575))], (2198 ^ _292445) ^ [_368019, _368021, _368023, _368025] : [class_Orderings_Opreorder(_368019), c_Orderings_Oord__class_Oless__eq(_368019, _368021, _368023), c_Orderings_Oord__class_Oless(_368019, _368023, _368025), -(c_Orderings_Oord__class_Oless(_368019, _368021, _368025))], (2212 ^ _292445) ^ [_368467, _368469, _368471, _368473] : [class_Orderings_Oorder(_368467), c_Orderings_Oord__class_Oless(_368467, _368469, _368471), c_Orderings_Oord__class_Oless__eq(_368467, _368473, _368469), -(c_Orderings_Oord__class_Oless(_368467, _368473, _368471))], (2226 ^ _292445) ^ [_368915, _368917, _368919, _368921] : [class_Orderings_Opreorder(_368915), c_Orderings_Oord__class_Oless(_368915, _368917, _368919), c_Orderings_Oord__class_Oless__eq(_368915, _368919, _368921), -(c_Orderings_Oord__class_Oless(_368915, _368917, _368921))], (2240 ^ _292445) ^ [_369349, _369351, _369353] : [class_Orderings_Oorder(_369349), c_Orderings_Oord__class_Oless__eq(_369349, _369351, _369353), -(_369353 = _369351), -(c_Orderings_Oord__class_Oless(_369349, _369351, _369353))], (2254 ^ _292445) ^ [_369770, _369772, _369774] : [class_Orderings_Oorder(_369770), c_Orderings_Oord__class_Oless__eq(_369770, _369772, _369774), -(_369772 = _369774), -(c_Orderings_Oord__class_Oless(_369770, _369772, _369774))], (2268 ^ _292445) ^ [_370191, _370193, _370195] : [class_Orderings_Oorder(_370191), c_Orderings_Oord__class_Oless__eq(_370191, _370193, _370195), -(c_Orderings_Oord__class_Oless(_370191, _370193, _370195)), -(_370193 = _370195)], (2282 ^ _292445) ^ [_370610, _370612, _370614] : [class_Orderings_Olinorder(_370610), c_Orderings_Oord__class_Oless__eq(_370610, _370612, _370614), 2289 ^ _292445 : [(2290 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_370610, _370612, _370614)), -(_370612 = _370614)], (2296 ^ _292445) ^ [] : [_370612 = _370614, c_Orderings_Oord__class_Oless(_370610, _370612, _370614)]]], (2302 ^ _292445) ^ [_371198, _371200, _371202] : [class_Orderings_Opreorder(_371198), c_Orderings_Oord__class_Oless(_371198, _371200, _371202), -(c_Orderings_Oord__class_Oless__eq(_371198, _371200, _371202))], (2312 ^ _292445) ^ [_371523, _371525, _371527] : [class_Orderings_Olinorder(_371523), c_Orderings_Oord__class_Oless__eq(_371523, _371525, _371527), c_Orderings_Oord__class_Oless(_371523, _371527, _371525)], (2322 ^ _292445) ^ [_371849, _371851, _371853] : [class_Orderings_Oorder(_371849), -(_371851 = _371853), c_Orderings_Oord__class_Oless__eq(_371849, _371853, _371851), -(c_Orderings_Oord__class_Oless(_371849, _371853, _371851))], (2336 ^ _292445) ^ [_372270, _372272, _372274] : [class_Orderings_Oorder(_372270), -(_372272 = _372274), c_Orderings_Oord__class_Oless__eq(_372270, _372272, _372274), -(c_Orderings_Oord__class_Oless(_372270, _372272, _372274))], (2350 ^ _292445) ^ [_372691, _372693, _372695] : [class_Orderings_Olinorder(_372691), -(c_Orderings_Oord__class_Oless(_372691, _372693, _372695)), 2357 ^ _292445 : [(2358 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_372691, _372693, _372695), -(_372693 = _372695)], (2364 ^ _292445) ^ [] : [_372693 = _372695, -(c_Orderings_Oord__class_Oless__eq(_372691, _372693, _372695))]]], (2370 ^ _292445) ^ [_373280, _373282, _373284] : [class_Orderings_Olinorder(_373280), -(c_Orderings_Oord__class_Oless__eq(_373280, _373282, _373284)), -(c_Orderings_Oord__class_Oless(_373280, _373284, _373282))], (2380 ^ _292445) ^ [_373608, _373610, _373612] : [class_Orderings_Olinorder(_373608), -(c_Orderings_Oord__class_Oless(_373608, _373610, _373612)), -(c_Orderings_Oord__class_Oless__eq(_373608, _373612, _373610))], (2390 ^ _292445) ^ [_373936, _373938, _373940] : [class_Orderings_Oorder(_373936), 2393 ^ _292445 : [(2404 ^ _292445) ^ [] : [2405 ^ _292445 : [(2406 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_373936, _373938, _373940)], (2408 ^ _292445) ^ [] : [_373938 = _373940]], -(c_Orderings_Oord__class_Oless__eq(_373936, _373938, _373940))], (2394 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_373936, _373938, _373940), -(c_Orderings_Oord__class_Oless(_373936, _373938, _373940)), -(_373938 = _373940)]]], (2412 ^ _292445) ^ [_374594, _374596, _374598] : [class_Orderings_Opreorder(_374594), 2415 ^ _292445 : [(2416 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_374594, _374596, _374598), 2419 ^ _292445 : [(2420 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_374594, _374596, _374598))], (2422 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_374594, _374598, _374596)]]], (2424 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_374594, _374596, _374598)), c_Orderings_Oord__class_Oless__eq(_374594, _374596, _374598), -(c_Orderings_Oord__class_Oless__eq(_374594, _374598, _374596))]]], (2434 ^ _292445) ^ [_375257, _375259, _375261] : [class_Orderings_Oorder(_375257), 2437 ^ _292445 : [(2438 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_375257, _375259, _375261), 2441 ^ _292445 : [(2442 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_375257, _375259, _375261))], (2444 ^ _292445) ^ [] : [_375259 = _375261]]], (2446 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_375257, _375259, _375261)), c_Orderings_Oord__class_Oless__eq(_375257, _375259, _375261), -(_375259 = _375261)]]], (2456 ^ _292445) ^ [_375917, _375919, _375921] : [class_Orderings_Olinorder(_375917), -(c_Orderings_Oord__class_Oless__eq(_375917, _375919, _375921)), -(c_Orderings_Oord__class_Oless(_375917, _375921, _375919))], (2466 ^ _292445) ^ [_376243, _376245, _376247] : [class_Orderings_Olinorder(_376243), 2469 ^ _292445 : [(2470 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_376243, _376245, _376247)), -(c_Orderings_Oord__class_Oless(_376243, _376247, _376245))], (2476 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_376243, _376247, _376245), c_Orderings_Oord__class_Oless__eq(_376243, _376245, _376247)]]], (2482 ^ _292445) ^ [_376739, _376741, _376743] : [class_Orderings_Olinorder(_376739), 2485 ^ _292445 : [(2486 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_376739, _376741, _376743)), -(c_Orderings_Oord__class_Oless__eq(_376739, _376743, _376741))], (2492 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_376739, _376743, _376741), c_Orderings_Oord__class_Oless(_376739, _376741, _376743)]]], (2498 ^ _292445) ^ [_377249, _377251, _377253, _377255] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_377249), c_Orderings_Oord__class_Oless(_377249, c_Groups_Oplus__class_Oplus(_377249, _377251, _377253), c_Groups_Oplus__class_Oplus(_377249, _377251, _377255)), -(c_Orderings_Oord__class_Oless(_377249, _377253, _377255))], (2508 ^ _292445) ^ [_377614, _377616, _377618, _377620] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_377614), c_Orderings_Oord__class_Oless(_377614, c_Groups_Oplus__class_Oplus(_377614, _377616, _377618), c_Groups_Oplus__class_Oplus(_377614, _377620, _377618)), -(c_Orderings_Oord__class_Oless(_377614, _377616, _377620))], (2518 ^ _292445) ^ [_377993, _377995, _377997, _377999, _378001] : [class_Groups_Oordered__cancel__ab__semigroup__add(_377993), c_Orderings_Oord__class_Oless(_377993, _377995, _377997), c_Orderings_Oord__class_Oless(_377993, _377999, _378001), -(c_Orderings_Oord__class_Oless(_377993, c_Groups_Oplus__class_Oplus(_377993, _377995, _377999), c_Groups_Oplus__class_Oplus(_377993, _377997, _378001)))], (2532 ^ _292445) ^ [_378471, _378473, _378475, _378477] : [class_Groups_Oordered__cancel__ab__semigroup__add(_378471), c_Orderings_Oord__class_Oless(_378471, _378473, _378475), -(c_Orderings_Oord__class_Oless(_378471, c_Groups_Oplus__class_Oplus(_378471, _378477, _378473), c_Groups_Oplus__class_Oplus(_378471, _378477, _378475)))], (2542 ^ _292445) ^ [_378836, _378838, _378840, _378842] : [class_Groups_Oordered__cancel__ab__semigroup__add(_378836), c_Orderings_Oord__class_Oless(_378836, _378838, _378840), -(c_Orderings_Oord__class_Oless(_378836, c_Groups_Oplus__class_Oplus(_378836, _378838, _378842), c_Groups_Oplus__class_Oplus(_378836, _378840, _378842)))], (2552 ^ _292445) ^ [_379201, _379203, _379205, _379207] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_379201), 2555 ^ _292445 : [(2556 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_379201, c_Groups_Oplus__class_Oplus(_379201, _379203, _379205), c_Groups_Oplus__class_Oplus(_379201, _379203, _379207)), -(c_Orderings_Oord__class_Oless(_379201, _379205, _379207))], (2562 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_379201, _379205, _379207), -(c_Orderings_Oord__class_Oless(_379201, c_Groups_Oplus__class_Oplus(_379201, _379203, _379205), c_Groups_Oplus__class_Oplus(_379201, _379203, _379207)))]]], (2568 ^ _292445) ^ [_379749, _379751, _379753, _379755] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_379749), 2571 ^ _292445 : [(2572 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_379749, c_Groups_Oplus__class_Oplus(_379749, _379751, _379753), c_Groups_Oplus__class_Oplus(_379749, _379755, _379753)), -(c_Orderings_Oord__class_Oless(_379749, _379751, _379755))], (2578 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_379749, _379751, _379755), -(c_Orderings_Oord__class_Oless(_379749, c_Groups_Oplus__class_Oplus(_379749, _379751, _379753), c_Groups_Oplus__class_Oplus(_379749, _379755, _379753)))]]], (2594 ^ _292445) ^ [_380554, _380556] : [2595 ^ _292445 : [(2596 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _380554, _380556)], (2598 ^ _292445) ^ [] : [_380554 = _380556]], -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _380554, _380556))], (2584 ^ _292445) ^ [_380298, _380300] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _380298, _380300), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _380298, _380300)), -(_380298 = _380300)], (2602 ^ _292445) ^ [_380873, _380875] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _380873, _380875), 2605 ^ _292445 : [(2606 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _380873, _380875))], (2608 ^ _292445) ^ [] : [_380873 = _380875]]], (2610 ^ _292445) ^ [_381115, _381117] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _381115, _381117)), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _381115, _381117), -(_381115 = _381117)], (2620 ^ _292445) ^ [_381438] : [-(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), _381438), _381438))), -(_381438 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (2626 ^ _292445) ^ [_381611] : [_381611 = 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), _381611), _381611))], (2632 ^ _292445) ^ [_381832, _381834] : [class_Rings_Olinordered__ring(_381832), c_Orderings_Oord__class_Oless(_381832, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_381832), _381834), _381834), c_Groups_Ozero__class_Ozero(_381832))], (2638 ^ _292445) ^ [_382091, _382093, _382095, _382097] : [class_Rings_Olinordered__ring__strict(_382091), 2641 ^ _292445 : [(2642 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_382091, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_382091), _382093), _382095), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_382091), _382097), _382095)), 2647 ^ _292445 : [(2648 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_382091, c_Groups_Ozero__class_Ozero(_382091), _382095))], (2650 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_382091, _382093, _382097))]], 2651 ^ _292445 : [(2652 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_382091, _382095, c_Groups_Ozero__class_Ozero(_382091)))], (2654 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_382091, _382097, _382093))]]], (2656 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_382091, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_382091), _382093), _382095), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_382091), _382097), _382095))), 2657 ^ _292445 : [(2658 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_382091, c_Groups_Ozero__class_Ozero(_382091), _382095), c_Orderings_Oord__class_Oless(_382091, _382093, _382097)], (2664 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_382091, _382095, c_Groups_Ozero__class_Ozero(_382091)), c_Orderings_Oord__class_Oless(_382091, _382097, _382093)]]]]], (2672 ^ _292445) ^ [_383194, _383196, _383198, _383200] : [class_Rings_Olinordered__ring__strict(_383194), 2675 ^ _292445 : [(2676 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_383194, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_383194), _383196), _383198), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_383194), _383196), _383200)), 2681 ^ _292445 : [(2682 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_383194, c_Groups_Ozero__class_Ozero(_383194), _383196))], (2684 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_383194, _383198, _383200))]], 2685 ^ _292445 : [(2686 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_383194, _383196, c_Groups_Ozero__class_Ozero(_383194)))], (2688 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_383194, _383200, _383198))]]], (2690 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_383194, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_383194), _383196), _383198), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_383194), _383196), _383200))), 2691 ^ _292445 : [(2692 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_383194, c_Groups_Ozero__class_Ozero(_383194), _383196), c_Orderings_Oord__class_Oless(_383194, _383198, _383200)], (2698 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_383194, _383196, c_Groups_Ozero__class_Ozero(_383194)), c_Orderings_Oord__class_Oless(_383194, _383200, _383198)]]]]], (2706 ^ _292445) ^ [_384297, _384299, _384301, _384303] : [class_Rings_Olinordered__ring__strict(_384297), c_Orderings_Oord__class_Oless(_384297, c_Groups_Ozero__class_Ozero(_384297), _384299), 2713 ^ _292445 : [(2714 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_384297, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_384297), _384299), _384301), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_384297), _384299), _384303)), -(c_Orderings_Oord__class_Oless(_384297, _384301, _384303))], (2720 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_384297, _384301, _384303), -(c_Orderings_Oord__class_Oless(_384297, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_384297), _384299), _384301), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_384297), _384299), _384303)))]]], (2726 ^ _292445) ^ [_384958, _384960, _384962] : [class_Rings_Olinordered__semiring__strict(_384958), c_Orderings_Oord__class_Oless(_384958, c_Groups_Ozero__class_Ozero(_384958), _384960), c_Orderings_Oord__class_Oless(_384958, c_Groups_Ozero__class_Ozero(_384958), _384962), -(c_Orderings_Oord__class_Oless(_384958, c_Groups_Ozero__class_Ozero(_384958), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_384958), _384960), _384962)))], (2740 ^ _292445) ^ [_385406, _385408, _385410] : [class_Rings_Olinordered__semiring__strict(_385406), c_Orderings_Oord__class_Oless(_385406, c_Groups_Ozero__class_Ozero(_385406), _385408), c_Orderings_Oord__class_Oless(_385406, _385410, c_Groups_Ozero__class_Ozero(_385406)), -(c_Orderings_Oord__class_Oless(_385406, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_385406), _385408), _385410), c_Groups_Ozero__class_Ozero(_385406)))], (2754 ^ _292445) ^ [_385854, _385856, _385858] : [class_Rings_Olinordered__semiring__strict(_385854), c_Orderings_Oord__class_Oless(_385854, c_Groups_Ozero__class_Ozero(_385854), _385856), c_Orderings_Oord__class_Oless(_385854, _385858, c_Groups_Ozero__class_Ozero(_385854)), -(c_Orderings_Oord__class_Oless(_385854, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_385854), _385858), _385856), c_Groups_Ozero__class_Ozero(_385854)))], (2768 ^ _292445) ^ [_386302, _386304, _386306] : [class_Rings_Olinordered__semiring__strict(_386302), c_Orderings_Oord__class_Oless(_386302, c_Groups_Ozero__class_Ozero(_386302), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_386302), _386304), _386306)), c_Orderings_Oord__class_Oless(_386302, c_Groups_Ozero__class_Ozero(_386302), _386304), -(c_Orderings_Oord__class_Oless(_386302, c_Groups_Ozero__class_Ozero(_386302), _386306))], (2782 ^ _292445) ^ [_386750, _386752, _386754] : [class_Rings_Olinordered__semiring__strict(_386750), c_Orderings_Oord__class_Oless(_386750, c_Groups_Ozero__class_Ozero(_386750), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_386750), _386752), _386754)), c_Orderings_Oord__class_Oless(_386750, c_Groups_Ozero__class_Ozero(_386750), _386754), -(c_Orderings_Oord__class_Oless(_386750, c_Groups_Ozero__class_Ozero(_386750), _386752))], (2796 ^ _292445) ^ [_387212, _387214, _387216, _387218] : [class_Rings_Olinordered__ring__strict(_387212), c_Orderings_Oord__class_Oless(_387212, _387214, c_Groups_Ozero__class_Ozero(_387212)), 2803 ^ _292445 : [(2804 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_387212, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_387212), _387214), _387216), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_387212), _387214), _387218)), -(c_Orderings_Oord__class_Oless(_387212, _387218, _387216))], (2810 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_387212, _387218, _387216), -(c_Orderings_Oord__class_Oless(_387212, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_387212), _387214), _387216), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_387212), _387214), _387218)))]]], (2816 ^ _292445) ^ [_387873, _387875, _387877] : [class_Rings_Olinordered__semiring__strict(_387873), c_Orderings_Oord__class_Oless(_387873, _387875, c_Groups_Ozero__class_Ozero(_387873)), c_Orderings_Oord__class_Oless(_387873, c_Groups_Ozero__class_Ozero(_387873), _387877), -(c_Orderings_Oord__class_Oless(_387873, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_387873), _387875), _387877), c_Groups_Ozero__class_Ozero(_387873)))], (2830 ^ _292445) ^ [_388321, _388323, _388325] : [class_Rings_Olinordered__ring__strict(_388321), c_Orderings_Oord__class_Oless(_388321, _388323, c_Groups_Ozero__class_Ozero(_388321)), c_Orderings_Oord__class_Oless(_388321, _388325, c_Groups_Ozero__class_Ozero(_388321)), -(c_Orderings_Oord__class_Oless(_388321, c_Groups_Ozero__class_Ozero(_388321), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_388321), _388323), _388325)))], (2844 ^ _292445) ^ [_388783, _388785, _388787, _388789] : [class_Rings_Olinordered__semiring__strict(_388783), c_Orderings_Oord__class_Oless(_388783, _388785, _388787), c_Orderings_Oord__class_Oless(_388783, c_Groups_Ozero__class_Ozero(_388783), _388789), -(c_Orderings_Oord__class_Oless(_388783, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_388783), _388785), _388789), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_388783), _388787), _388789)))], (2858 ^ _292445) ^ [_389267, _389269, _389271, _389273] : [class_Rings_Olinordered__semiring__strict(_389267), c_Orderings_Oord__class_Oless(_389267, _389269, _389271), c_Orderings_Oord__class_Oless(_389267, c_Groups_Ozero__class_Ozero(_389267), _389273), -(c_Orderings_Oord__class_Oless(_389267, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_389267), _389273), _389269), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_389267), _389273), _389271)))], (2872 ^ _292445) ^ [_389751, _389753, _389755, _389757] : [class_Rings_Olinordered__comm__semiring__strict(_389751), c_Orderings_Oord__class_Oless(_389751, _389753, _389755), c_Orderings_Oord__class_Oless(_389751, c_Groups_Ozero__class_Ozero(_389751), _389757), -(c_Orderings_Oord__class_Oless(_389751, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_389751), _389757), _389753), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_389751), _389757), _389755)))], (2886 ^ _292445) ^ [_390235, _390237, _390239, _390241] : [class_Rings_Olinordered__ring__strict(_390235), c_Orderings_Oord__class_Oless(_390235, _390237, _390239), c_Orderings_Oord__class_Oless(_390235, _390241, c_Groups_Ozero__class_Ozero(_390235)), -(c_Orderings_Oord__class_Oless(_390235, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_390235), _390239), _390241), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_390235), _390237), _390241)))], (2900 ^ _292445) ^ [_390719, _390721, _390723, _390725] : [class_Rings_Olinordered__ring__strict(_390719), c_Orderings_Oord__class_Oless(_390719, _390721, _390723), c_Orderings_Oord__class_Oless(_390719, _390725, c_Groups_Ozero__class_Ozero(_390719)), -(c_Orderings_Oord__class_Oless(_390719, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_390719), _390725), _390723), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_390719), _390725), _390721)))], (2914 ^ _292445) ^ [_391175, _391177] : [class_Groups_Olinordered__ab__group__add(_391175), 2917 ^ _292445 : [(2918 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_391175, c_Groups_Ozero__class_Ozero(_391175), c_Groups_Oplus__class_Oplus(_391175, _391177, _391177)), -(c_Orderings_Oord__class_Oless(_391175, c_Groups_Ozero__class_Ozero(_391175), _391177))], (2924 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_391175, c_Groups_Ozero__class_Ozero(_391175), _391177), -(c_Orderings_Oord__class_Oless(_391175, c_Groups_Ozero__class_Ozero(_391175), c_Groups_Oplus__class_Oplus(_391175, _391177, _391177)))]]], (2930 ^ _292445) ^ [_391663, _391665] : [class_Groups_Olinordered__ab__group__add(_391663), 2933 ^ _292445 : [(2934 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_391663, c_Groups_Oplus__class_Oplus(_391663, _391665, _391665), c_Groups_Ozero__class_Ozero(_391663)), -(c_Orderings_Oord__class_Oless(_391663, _391665, c_Groups_Ozero__class_Ozero(_391663)))], (2940 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_391663, _391665, c_Groups_Ozero__class_Ozero(_391663)), -(c_Orderings_Oord__class_Oless(_391663, c_Groups_Oplus__class_Oplus(_391663, _391665, _391665), c_Groups_Ozero__class_Ozero(_391663)))]]], (2946 ^ _292445) ^ [_392165, _392167, _392169] : [class_Groups_Oordered__comm__monoid__add(_392165), c_Orderings_Oord__class_Oless(_392165, c_Groups_Ozero__class_Ozero(_392165), _392167), c_Orderings_Oord__class_Oless(_392165, c_Groups_Ozero__class_Ozero(_392165), _392169), -(c_Orderings_Oord__class_Oless(_392165, c_Groups_Ozero__class_Ozero(_392165), c_Groups_Oplus__class_Oplus(_392165, _392167, _392169)))], (2960 ^ _292445) ^ [_392619, _392621, _392623, _392625] : [class_Rings_Olinordered__semidom(_392619), c_Orderings_Oord__class_Oless(_392619, c_Groups_Ozero__class_Ozero(_392619), _392621), c_Orderings_Oord__class_Oless(_392619, _392623, _392625), -(c_Orderings_Oord__class_Oless(_392619, _392623, c_Groups_Oplus__class_Oplus(_392619, _392621, _392625)))], (2974 ^ _292445) ^ [_393065, _393067, _393069] : [class_Groups_Oordered__comm__monoid__add(_393065), c_Orderings_Oord__class_Oless(_393065, _393067, c_Groups_Ozero__class_Ozero(_393065)), c_Orderings_Oord__class_Oless(_393065, _393069, c_Groups_Ozero__class_Ozero(_393065)), -(c_Orderings_Oord__class_Oless(_393065, c_Groups_Oplus__class_Oplus(_393065, _393067, _393069), c_Groups_Ozero__class_Ozero(_393065)))], (2988 ^ _292445) ^ [_393533, _393535, _393537, _393539, _393541] : [class_Groups_Oordered__cancel__ab__semigroup__add(_393533), c_Orderings_Oord__class_Oless__eq(_393533, _393535, _393537), c_Orderings_Oord__class_Oless(_393533, _393539, _393541), -(c_Orderings_Oord__class_Oless(_393533, c_Groups_Oplus__class_Oplus(_393533, _393535, _393539), c_Groups_Oplus__class_Oplus(_393533, _393537, _393541)))], (3002 ^ _292445) ^ [_394025, _394027, _394029, _394031, _394033] : [class_Groups_Oordered__cancel__ab__semigroup__add(_394025), c_Orderings_Oord__class_Oless(_394025, _394027, _394029), c_Orderings_Oord__class_Oless__eq(_394025, _394031, _394033), -(c_Orderings_Oord__class_Oless(_394025, c_Groups_Oplus__class_Oplus(_394025, _394027, _394031), c_Groups_Oplus__class_Oplus(_394025, _394029, _394033)))], (3016 ^ _292445) ^ [_394489, _394491, _394493] : [class_Fields_Olinordered__field__inverse__zero(_394489), 3019 ^ _292445 : [(3020 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_394489, c_Groups_Ozero__class_Ozero(_394489), c_Rings_Oinverse__class_Odivide(_394489, _394491, _394493)), 3025 ^ _292445 : [(3026 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_394489, c_Groups_Ozero__class_Ozero(_394489), _394491))], (3028 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_394489, c_Groups_Ozero__class_Ozero(_394489), _394493))]], 3029 ^ _292445 : [(3030 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_394489, _394491, c_Groups_Ozero__class_Ozero(_394489)))], (3032 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_394489, _394493, c_Groups_Ozero__class_Ozero(_394489)))]]], (3034 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_394489, c_Groups_Ozero__class_Ozero(_394489), c_Rings_Oinverse__class_Odivide(_394489, _394491, _394493))), 3035 ^ _292445 : [(3036 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_394489, c_Groups_Ozero__class_Ozero(_394489), _394491), c_Orderings_Oord__class_Oless(_394489, c_Groups_Ozero__class_Ozero(_394489), _394493)], (3042 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_394489, _394491, c_Groups_Ozero__class_Ozero(_394489)), c_Orderings_Oord__class_Oless(_394489, _394493, c_Groups_Ozero__class_Ozero(_394489))]]]]], (3050 ^ _292445) ^ [_395526, _395528, _395530] : [class_Fields_Olinordered__field__inverse__zero(_395526), 3053 ^ _292445 : [(3054 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_395526, c_Rings_Oinverse__class_Odivide(_395526, _395528, _395530), c_Groups_Ozero__class_Ozero(_395526)), 3059 ^ _292445 : [(3060 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_395526, c_Groups_Ozero__class_Ozero(_395526), _395528))], (3062 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_395526, _395530, c_Groups_Ozero__class_Ozero(_395526)))]], 3063 ^ _292445 : [(3064 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_395526, _395528, c_Groups_Ozero__class_Ozero(_395526)))], (3066 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_395526, c_Groups_Ozero__class_Ozero(_395526), _395530))]]], (3068 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_395526, c_Rings_Oinverse__class_Odivide(_395526, _395528, _395530), c_Groups_Ozero__class_Ozero(_395526))), 3069 ^ _292445 : [(3070 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_395526, c_Groups_Ozero__class_Ozero(_395526), _395528), c_Orderings_Oord__class_Oless(_395526, _395530, c_Groups_Ozero__class_Ozero(_395526))], (3076 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_395526, _395528, c_Groups_Ozero__class_Ozero(_395526)), c_Orderings_Oord__class_Oless(_395526, c_Groups_Ozero__class_Ozero(_395526), _395530)]]]]], (3084 ^ _292445) ^ [_396563, _396565, _396567] : [class_Fields_Olinordered__field(_396563), c_Orderings_Oord__class_Oless(_396563, c_Groups_Ozero__class_Ozero(_396563), _396565), c_Orderings_Oord__class_Oless(_396563, c_Groups_Ozero__class_Ozero(_396563), _396567), -(c_Orderings_Oord__class_Oless(_396563, c_Groups_Ozero__class_Ozero(_396563), c_Rings_Oinverse__class_Odivide(_396563, _396565, _396567)))], (3098 ^ _292445) ^ [_397003, _397005, _397007] : [class_Fields_Olinordered__field(_397003), c_Orderings_Oord__class_Oless(_397003, c_Groups_Ozero__class_Ozero(_397003), _397005), c_Orderings_Oord__class_Oless(_397003, _397007, c_Groups_Ozero__class_Ozero(_397003)), -(c_Orderings_Oord__class_Oless(_397003, c_Rings_Oinverse__class_Odivide(_397003, _397005, _397007), c_Groups_Ozero__class_Ozero(_397003)))], (3112 ^ _292445) ^ [_397443, _397445, _397447] : [class_Fields_Olinordered__field(_397443), c_Orderings_Oord__class_Oless(_397443, _397445, c_Groups_Ozero__class_Ozero(_397443)), c_Orderings_Oord__class_Oless(_397443, c_Groups_Ozero__class_Ozero(_397443), _397447), -(c_Orderings_Oord__class_Oless(_397443, c_Rings_Oinverse__class_Odivide(_397443, _397445, _397447), c_Groups_Ozero__class_Ozero(_397443)))], (3126 ^ _292445) ^ [_397883, _397885, _397887] : [class_Fields_Olinordered__field(_397883), c_Orderings_Oord__class_Oless(_397883, _397885, c_Groups_Ozero__class_Ozero(_397883)), c_Orderings_Oord__class_Oless(_397883, _397887, c_Groups_Ozero__class_Ozero(_397883)), -(c_Orderings_Oord__class_Oless(_397883, c_Groups_Ozero__class_Ozero(_397883), c_Rings_Oinverse__class_Odivide(_397883, _397885, _397887)))], (3140 ^ _292445) ^ [_398337, _398339, _398341, _398343] : [class_Fields_Olinordered__field(_398337), c_Orderings_Oord__class_Oless(_398337, _398339, _398341), c_Orderings_Oord__class_Oless(_398337, c_Groups_Ozero__class_Ozero(_398337), _398343), -(c_Orderings_Oord__class_Oless(_398337, c_Rings_Oinverse__class_Odivide(_398337, _398339, _398343), c_Rings_Oinverse__class_Odivide(_398337, _398341, _398343)))], (3154 ^ _292445) ^ [_398805, _398807, _398809, _398811] : [class_Fields_Olinordered__field(_398805), c_Orderings_Oord__class_Oless(_398805, _398807, _398809), c_Orderings_Oord__class_Oless(_398805, _398811, c_Groups_Ozero__class_Ozero(_398805)), -(c_Orderings_Oord__class_Oless(_398805, c_Rings_Oinverse__class_Odivide(_398805, _398809, _398811), c_Rings_Oinverse__class_Odivide(_398805, _398807, _398811)))], (3168 ^ _292445) ^ [_399245, _399247] : [class_Groups_Oordered__ab__group__add__abs(_399245), c_Orderings_Oord__class_Oless(_399245, c_Groups_Oabs__class_Oabs(_399245, _399247), c_Groups_Ozero__class_Ozero(_399245))], (3174 ^ _292445) ^ [_399466, _399468] : [class_Groups_Oordered__ab__group__add__abs(_399466), 3177 ^ _292445 : [(3178 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_399466, c_Groups_Ozero__class_Ozero(_399466), c_Groups_Oabs__class_Oabs(_399466, _399468)), _399468 = c_Groups_Ozero__class_Ozero(_399466)], (3184 ^ _292445) ^ [] : [-(_399468 = c_Groups_Ozero__class_Ozero(_399466)), -(c_Orderings_Oord__class_Oless(_399466, c_Groups_Ozero__class_Ozero(_399466), c_Groups_Oabs__class_Oabs(_399466, _399468)))]]], (3190 ^ _292445) ^ [_399950, _399952] : [class_Groups_Oordered__ab__group__add__abs(_399950), c_Orderings_Oord__class_Oless(_399950, c_Groups_Ozero__class_Ozero(_399950), _399952), -(c_Groups_Oabs__class_Oabs(_399950, _399952) = _399952)], (3200 ^ _292445) ^ [_400301, _400303, _400305, _400307, _400309] : [class_Rings_Olinordered__idom(_400301), c_Orderings_Oord__class_Oless(_400301, c_Groups_Oabs__class_Oabs(_400301, _400303), _400305), c_Orderings_Oord__class_Oless(_400301, c_Groups_Oabs__class_Oabs(_400301, _400307), _400309), -(c_Orderings_Oord__class_Oless(_400301, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_400301), c_Groups_Oabs__class_Oabs(_400301, _400303)), c_Groups_Oabs__class_Oabs(_400301, _400307)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_400301), _400305), _400309)))], (3214 ^ _292445) ^ [_400805, _400807, _400809] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _400805), 3217 ^ _292445 : [(3218 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _400807), _400805), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _400809), _400805)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _400807, _400809))], (3224 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _400807, _400809), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _400807), _400805), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _400809), _400805)))]]], (3230 ^ _292445) ^ [_401325, _401327] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _401325), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _401327), -(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), _401325), _401327)))], (3240 ^ _292445) ^ [_401656, _401658, _401660] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _401656), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _401658, _401660), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _401656), _401658), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _401656), _401660)))], (3250 ^ _292445) ^ [_401995, _401997] : [class_RealVector_Oreal__normed__vector(_401995), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_401995, _401997), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (3256 ^ _292445) ^ [_402240, _402242, _402244, _402246] : [class_Rings_Olinordered__semiring__strict(_402240), c_Orderings_Oord__class_Oless__eq(_402240, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_402240), _402242), _402244), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_402240), _402242), _402246)), c_Orderings_Oord__class_Oless(_402240, c_Groups_Ozero__class_Ozero(_402240), _402242), -(c_Orderings_Oord__class_Oless__eq(_402240, _402244, _402246))], (3270 ^ _292445) ^ [_402724, _402726, _402728, _402730] : [class_Rings_Olinordered__semiring__strict(_402724), c_Orderings_Oord__class_Oless__eq(_402724, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_402724), _402726), _402728), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_402724), _402730), _402728)), c_Orderings_Oord__class_Oless(_402724, c_Groups_Ozero__class_Ozero(_402724), _402728), -(c_Orderings_Oord__class_Oless__eq(_402724, _402726, _402730))], (3284 ^ _292445) ^ [_403208, _403210, _403212, _403214] : [class_Rings_Olinordered__semiring__strict(_403208), c_Orderings_Oord__class_Oless(_403208, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_403208), _403210), _403212), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_403208), _403210), _403214)), c_Orderings_Oord__class_Oless__eq(_403208, c_Groups_Ozero__class_Ozero(_403208), _403210), -(c_Orderings_Oord__class_Oless(_403208, _403212, _403214))], (3298 ^ _292445) ^ [_403692, _403694, _403696, _403698] : [class_Rings_Olinordered__semiring(_403692), c_Orderings_Oord__class_Oless(_403692, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_403692), _403694), _403696), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_403692), _403694), _403698)), c_Orderings_Oord__class_Oless__eq(_403692, c_Groups_Ozero__class_Ozero(_403692), _403694), -(c_Orderings_Oord__class_Oless(_403692, _403696, _403698))], (3312 ^ _292445) ^ [_404176, _404178, _404180, _404182] : [class_Rings_Olinordered__semiring__strict(_404176), c_Orderings_Oord__class_Oless(_404176, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_404176), _404178), _404180), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_404176), _404182), _404180)), c_Orderings_Oord__class_Oless__eq(_404176, c_Groups_Ozero__class_Ozero(_404176), _404180), -(c_Orderings_Oord__class_Oless(_404176, _404178, _404182))], (3326 ^ _292445) ^ [_404660, _404662, _404664, _404666] : [class_Rings_Olinordered__semiring(_404660), c_Orderings_Oord__class_Oless(_404660, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_404660), _404662), _404664), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_404660), _404666), _404664)), c_Orderings_Oord__class_Oless__eq(_404660, c_Groups_Ozero__class_Ozero(_404660), _404664), -(c_Orderings_Oord__class_Oless(_404660, _404662, _404666))], (3340 ^ _292445) ^ [_405158, _405160, _405162, _405164, _405166] : [class_Rings_Olinordered__semiring__strict(_405158), c_Orderings_Oord__class_Oless__eq(_405158, _405160, _405162), c_Orderings_Oord__class_Oless(_405158, _405164, _405166), c_Orderings_Oord__class_Oless(_405158, c_Groups_Ozero__class_Ozero(_405158), _405160), c_Orderings_Oord__class_Oless__eq(_405158, c_Groups_Ozero__class_Ozero(_405158), _405164), -(c_Orderings_Oord__class_Oless(_405158, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_405158), _405160), _405164), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_405158), _405162), _405166)))], (3362 ^ _292445) ^ [_405880, _405882, _405884, _405886, _405888] : [class_Rings_Olinordered__semiring__strict(_405880), c_Orderings_Oord__class_Oless(_405880, _405882, _405884), c_Orderings_Oord__class_Oless__eq(_405880, _405886, _405888), c_Orderings_Oord__class_Oless__eq(_405880, c_Groups_Ozero__class_Ozero(_405880), _405882), c_Orderings_Oord__class_Oless(_405880, c_Groups_Ozero__class_Ozero(_405880), _405886), -(c_Orderings_Oord__class_Oless(_405880, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_405880), _405882), _405886), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_405880), _405884), _405888)))], (3384 ^ _292445) ^ [_406602, _406604, _406606, _406608, _406610] : [class_Rings_Olinordered__semiring__strict(_406602), c_Orderings_Oord__class_Oless(_406602, _406604, _406606), c_Orderings_Oord__class_Oless(_406602, _406608, _406610), c_Orderings_Oord__class_Oless__eq(_406602, c_Groups_Ozero__class_Ozero(_406602), _406604), c_Orderings_Oord__class_Oless__eq(_406602, c_Groups_Ozero__class_Ozero(_406602), _406608), -(c_Orderings_Oord__class_Oless(_406602, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_406602), _406604), _406608), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_406602), _406606), _406610)))], (3406 ^ _292445) ^ [_407324, _407326, _407328, _407330, _407332] : [class_Rings_Olinordered__semiring__strict(_407324), c_Orderings_Oord__class_Oless(_407324, _407326, _407328), c_Orderings_Oord__class_Oless(_407324, _407330, _407332), c_Orderings_Oord__class_Oless(_407324, c_Groups_Ozero__class_Ozero(_407324), _407328), c_Orderings_Oord__class_Oless__eq(_407324, c_Groups_Ozero__class_Ozero(_407324), _407330), -(c_Orderings_Oord__class_Oless(_407324, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_407324), _407326), _407330), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_407324), _407328), _407332)))], (3428 ^ _292445) ^ [_408032, _408034, _408036, _408038] : [class_Rings_Olinordered__ring__strict(_408032), c_Orderings_Oord__class_Oless(_408032, _408034, c_Groups_Ozero__class_Ozero(_408032)), 3435 ^ _292445 : [(3436 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_408032, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_408032), _408034), _408036), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_408032), _408034), _408038)), -(c_Orderings_Oord__class_Oless__eq(_408032, _408038, _408036))], (3442 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_408032, _408038, _408036), -(c_Orderings_Oord__class_Oless__eq(_408032, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_408032), _408034), _408036), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_408032), _408034), _408038)))]]], (3448 ^ _292445) ^ [_408707, _408709, _408711, _408713] : [class_Rings_Olinordered__ring__strict(_408707), c_Orderings_Oord__class_Oless(_408707, c_Groups_Ozero__class_Ozero(_408707), _408709), 3455 ^ _292445 : [(3456 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_408707, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_408707), _408709), _408711), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_408707), _408709), _408713)), -(c_Orderings_Oord__class_Oless__eq(_408707, _408711, _408713))], (3462 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_408707, _408711, _408713), -(c_Orderings_Oord__class_Oless__eq(_408707, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_408707), _408709), _408711), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_408707), _408709), _408713)))]]], (3468 ^ _292445) ^ [_409368, _409370, _409372] : [class_Groups_Oordered__comm__monoid__add(_409368), c_Orderings_Oord__class_Oless__eq(_409368, _409370, c_Groups_Ozero__class_Ozero(_409368)), c_Orderings_Oord__class_Oless(_409368, _409372, c_Groups_Ozero__class_Ozero(_409368)), -(c_Orderings_Oord__class_Oless(_409368, c_Groups_Oplus__class_Oplus(_409368, _409370, _409372), c_Groups_Ozero__class_Ozero(_409368)))], (3482 ^ _292445) ^ [_409808, _409810, _409812] : [class_Groups_Oordered__comm__monoid__add(_409808), c_Orderings_Oord__class_Oless(_409808, _409810, c_Groups_Ozero__class_Ozero(_409808)), c_Orderings_Oord__class_Oless__eq(_409808, _409812, c_Groups_Ozero__class_Ozero(_409808)), -(c_Orderings_Oord__class_Oless(_409808, c_Groups_Oplus__class_Oplus(_409808, _409810, _409812), c_Groups_Ozero__class_Ozero(_409808)))], (3496 ^ _292445) ^ [_410262, _410264, _410266, _410268] : [class_Groups_Oordered__comm__monoid__add(_410262), c_Orderings_Oord__class_Oless__eq(_410262, c_Groups_Ozero__class_Ozero(_410262), _410264), c_Orderings_Oord__class_Oless(_410262, _410266, _410268), -(c_Orderings_Oord__class_Oless(_410262, _410266, c_Groups_Oplus__class_Oplus(_410262, _410264, _410268)))], (3510 ^ _292445) ^ [_410722, _410724, _410726, _410728] : [class_Groups_Oordered__comm__monoid__add(_410722), c_Orderings_Oord__class_Oless(_410722, c_Groups_Ozero__class_Ozero(_410722), _410724), c_Orderings_Oord__class_Oless__eq(_410722, _410726, _410728), -(c_Orderings_Oord__class_Oless(_410722, _410726, c_Groups_Oplus__class_Oplus(_410722, _410724, _410728)))], (3524 ^ _292445) ^ [_411168, _411170, _411172] : [class_Groups_Oordered__comm__monoid__add(_411168), c_Orderings_Oord__class_Oless__eq(_411168, c_Groups_Ozero__class_Ozero(_411168), _411170), c_Orderings_Oord__class_Oless(_411168, c_Groups_Ozero__class_Ozero(_411168), _411172), -(c_Orderings_Oord__class_Oless(_411168, c_Groups_Ozero__class_Ozero(_411168), c_Groups_Oplus__class_Oplus(_411168, _411170, _411172)))], (3538 ^ _292445) ^ [_411608, _411610, _411612] : [class_Groups_Oordered__comm__monoid__add(_411608), c_Orderings_Oord__class_Oless(_411608, c_Groups_Ozero__class_Ozero(_411608), _411610), c_Orderings_Oord__class_Oless__eq(_411608, c_Groups_Ozero__class_Ozero(_411608), _411612), -(c_Orderings_Oord__class_Oless(_411608, c_Groups_Ozero__class_Ozero(_411608), c_Groups_Oplus__class_Oplus(_411608, _411610, _411612)))], (3552 ^ _292445) ^ [_412048, _412050, _412052] : [class_Rings_Olinordered__ring__strict(_412048), 3555 ^ _292445 : [(3566 ^ _292445) ^ [] : [3567 ^ _292445 : [(3568 ^ _292445) ^ [] : [-(_412050 = c_Groups_Ozero__class_Ozero(_412048))], (3570 ^ _292445) ^ [] : [-(_412052 = c_Groups_Ozero__class_Ozero(_412048))]], -(c_Orderings_Oord__class_Oless(_412048, c_Groups_Ozero__class_Ozero(_412048), c_Groups_Oplus__class_Oplus(_412048, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_412048), _412050), _412050), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_412048), _412052), _412052))))], (3556 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_412048, c_Groups_Ozero__class_Ozero(_412048), c_Groups_Oplus__class_Oplus(_412048, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_412048), _412050), _412050), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_412048), _412052), _412052))), _412050 = c_Groups_Ozero__class_Ozero(_412048), _412052 = c_Groups_Ozero__class_Ozero(_412048)]]], (3574 ^ _292445) ^ [_412785, _412787, _412789] : [class_Rings_Olinordered__ring(_412785), c_Orderings_Oord__class_Oless(_412785, c_Groups_Oplus__class_Oplus(_412785, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_412785), _412787), _412787), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_412785), _412789), _412789)), c_Groups_Ozero__class_Ozero(_412785))], (3580 ^ _292445) ^ [_413060, _413062, _413064] : [class_Fields_Olinordered__field(_413060), c_Orderings_Oord__class_Oless__eq(_413060, c_Groups_Ozero__class_Ozero(_413060), _413062), c_Orderings_Oord__class_Oless(_413060, c_Groups_Ozero__class_Ozero(_413060), _413064), -(c_Orderings_Oord__class_Oless__eq(_413060, c_Groups_Ozero__class_Ozero(_413060), c_Rings_Oinverse__class_Odivide(_413060, _413062, _413064)))], (3594 ^ _292445) ^ [_413500, _413502, _413504] : [class_Fields_Olinordered__field(_413500), c_Orderings_Oord__class_Oless__eq(_413500, c_Groups_Ozero__class_Ozero(_413500), _413502), c_Orderings_Oord__class_Oless(_413500, _413504, c_Groups_Ozero__class_Ozero(_413500)), -(c_Orderings_Oord__class_Oless__eq(_413500, c_Rings_Oinverse__class_Odivide(_413500, _413502, _413504), c_Groups_Ozero__class_Ozero(_413500)))], (3608 ^ _292445) ^ [_413968, _413970, _413972, _413974, _413976] : [class_Fields_Olinordered__field(_413968), c_Orderings_Oord__class_Oless(_413968, c_Groups_Ozero__class_Ozero(_413968), _413970), c_Orderings_Oord__class_Oless__eq(_413968, _413970, _413972), c_Orderings_Oord__class_Oless(_413968, c_Groups_Ozero__class_Ozero(_413968), _413974), c_Orderings_Oord__class_Oless(_413968, _413974, _413976), -(c_Orderings_Oord__class_Oless(_413968, c_Rings_Oinverse__class_Odivide(_413968, _413970, _413976), c_Rings_Oinverse__class_Odivide(_413968, _413972, _413974)))], (3630 ^ _292445) ^ [_414674, _414676, _414678, _414680, _414682] : [class_Fields_Olinordered__field(_414674), c_Orderings_Oord__class_Oless__eq(_414674, c_Groups_Ozero__class_Ozero(_414674), _414676), c_Orderings_Oord__class_Oless(_414674, _414676, _414678), c_Orderings_Oord__class_Oless(_414674, c_Groups_Ozero__class_Ozero(_414674), _414680), c_Orderings_Oord__class_Oless__eq(_414674, _414680, _414682), -(c_Orderings_Oord__class_Oless(_414674, c_Rings_Oinverse__class_Odivide(_414674, _414676, _414682), c_Rings_Oinverse__class_Odivide(_414674, _414678, _414680)))], (3652 ^ _292445) ^ [_415380, _415382, _415384, _415386, _415388] : [class_Fields_Olinordered__field(_415380), c_Orderings_Oord__class_Oless__eq(_415380, c_Groups_Ozero__class_Ozero(_415380), _415382), c_Orderings_Oord__class_Oless__eq(_415380, _415382, _415384), c_Orderings_Oord__class_Oless(_415380, c_Groups_Ozero__class_Ozero(_415380), _415386), c_Orderings_Oord__class_Oless__eq(_415380, _415386, _415388), -(c_Orderings_Oord__class_Oless__eq(_415380, c_Rings_Oinverse__class_Odivide(_415380, _415382, _415388), c_Rings_Oinverse__class_Odivide(_415380, _415384, _415386)))], (3674 ^ _292445) ^ [_416058, _416060, _416062] : [class_Fields_Olinordered__field(_416058), c_Orderings_Oord__class_Oless__eq(_416058, _416060, c_Groups_Ozero__class_Ozero(_416058)), c_Orderings_Oord__class_Oless(_416058, c_Groups_Ozero__class_Ozero(_416058), _416062), -(c_Orderings_Oord__class_Oless__eq(_416058, c_Rings_Oinverse__class_Odivide(_416058, _416060, _416062), c_Groups_Ozero__class_Ozero(_416058)))], (3688 ^ _292445) ^ [_416498, _416500, _416502] : [class_Fields_Olinordered__field(_416498), c_Orderings_Oord__class_Oless__eq(_416498, _416500, c_Groups_Ozero__class_Ozero(_416498)), c_Orderings_Oord__class_Oless(_416498, _416502, c_Groups_Ozero__class_Ozero(_416498)), -(c_Orderings_Oord__class_Oless__eq(_416498, c_Groups_Ozero__class_Ozero(_416498), c_Rings_Oinverse__class_Odivide(_416498, _416500, _416502)))], (3702 ^ _292445) ^ [_416952, _416954, _416956, _416958] : [class_Fields_Olinordered__field__inverse__zero(_416952), 3705 ^ _292445 : [(3732 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_416952, _416954, c_Rings_Oinverse__class_Odivide(_416952, _416956, _416958))), 3735 ^ _292445 : [(3736 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_416952, c_Groups_Ozero__class_Ozero(_416952), _416958))], (3738 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_416952, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_416952), _416954), _416958), _416956)]], 3739 ^ _292445 : [(3740 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_416952, c_Groups_Ozero__class_Ozero(_416952), _416958)], (3742 ^ _292445) ^ [] : [3743 ^ _292445 : [(3744 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_416952, _416958, c_Groups_Ozero__class_Ozero(_416952)))], (3746 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_416952, _416956, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_416952), _416954), _416958))]], 3747 ^ _292445 : [(3748 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_416952, _416958, c_Groups_Ozero__class_Ozero(_416952))], (3750 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_416952, _416954, c_Groups_Ozero__class_Ozero(_416952))]]]]], (3706 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_416952, _416954, c_Rings_Oinverse__class_Odivide(_416952, _416956, _416958)), 3709 ^ _292445 : [(3710 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_416952, c_Groups_Ozero__class_Ozero(_416952), _416958), -(c_Orderings_Oord__class_Oless(_416952, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_416952), _416954), _416958), _416956))], (3716 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_416952, c_Groups_Ozero__class_Ozero(_416952), _416958)), 3719 ^ _292445 : [(3720 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_416952, _416958, c_Groups_Ozero__class_Ozero(_416952)), -(c_Orderings_Oord__class_Oless(_416952, _416956, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_416952), _416954), _416958)))], (3726 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_416952, _416958, c_Groups_Ozero__class_Ozero(_416952))), -(c_Orderings_Oord__class_Oless(_416952, _416954, c_Groups_Ozero__class_Ozero(_416952)))]]]]]]], (3754 ^ _292445) ^ [_418608, _418610, _418612, _418614] : [class_Fields_Olinordered__field__inverse__zero(_418608), 3757 ^ _292445 : [(3784 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_418608, c_Rings_Oinverse__class_Odivide(_418608, _418610, _418612), _418614)), 3787 ^ _292445 : [(3788 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_418608, c_Groups_Ozero__class_Ozero(_418608), _418612))], (3790 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_418608, _418610, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_418608), _418614), _418612))]], 3791 ^ _292445 : [(3792 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_418608, c_Groups_Ozero__class_Ozero(_418608), _418612)], (3794 ^ _292445) ^ [] : [3795 ^ _292445 : [(3796 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_418608, _418612, c_Groups_Ozero__class_Ozero(_418608)))], (3798 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_418608, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_418608), _418614), _418612), _418610)]], 3799 ^ _292445 : [(3800 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_418608, _418612, c_Groups_Ozero__class_Ozero(_418608))], (3802 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_418608, c_Groups_Ozero__class_Ozero(_418608), _418614)]]]]], (3758 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_418608, c_Rings_Oinverse__class_Odivide(_418608, _418610, _418612), _418614), 3761 ^ _292445 : [(3762 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_418608, c_Groups_Ozero__class_Ozero(_418608), _418612), -(c_Orderings_Oord__class_Oless(_418608, _418610, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_418608), _418614), _418612)))], (3768 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_418608, c_Groups_Ozero__class_Ozero(_418608), _418612)), 3771 ^ _292445 : [(3772 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_418608, _418612, c_Groups_Ozero__class_Ozero(_418608)), -(c_Orderings_Oord__class_Oless(_418608, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_418608), _418614), _418612), _418610))], (3778 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_418608, _418612, c_Groups_Ozero__class_Ozero(_418608))), -(c_Orderings_Oord__class_Oless(_418608, c_Groups_Ozero__class_Ozero(_418608), _418614))]]]]]]], (3806 ^ _292445) ^ [_420264, _420266, _420268, _420270] : [class_Fields_Olinordered__field(_420264), c_Orderings_Oord__class_Oless(_420264, c_Groups_Ozero__class_Ozero(_420264), _420266), 3813 ^ _292445 : [(3814 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_420264, _420268, c_Rings_Oinverse__class_Odivide(_420264, _420270, _420266)), -(c_Orderings_Oord__class_Oless(_420264, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_420264), _420268), _420266), _420270))], (3820 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_420264, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_420264), _420268), _420266), _420270), -(c_Orderings_Oord__class_Oless(_420264, _420268, c_Rings_Oinverse__class_Odivide(_420264, _420270, _420266)))]]], (3826 ^ _292445) ^ [_420927, _420929, _420931, _420933] : [class_Fields_Olinordered__field(_420927), c_Orderings_Oord__class_Oless(_420927, c_Groups_Ozero__class_Ozero(_420927), _420929), 3833 ^ _292445 : [(3834 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_420927, c_Rings_Oinverse__class_Odivide(_420927, _420931, _420929), _420933), -(c_Orderings_Oord__class_Oless(_420927, _420931, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_420927), _420933), _420929)))], (3840 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_420927, _420931, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_420927), _420933), _420929)), -(c_Orderings_Oord__class_Oless(_420927, c_Rings_Oinverse__class_Odivide(_420927, _420931, _420929), _420933))]]], (3846 ^ _292445) ^ [_421590, _421592, _421594, _421596] : [class_Fields_Olinordered__field(_421590), c_Orderings_Oord__class_Oless(_421590, c_Groups_Ozero__class_Ozero(_421590), _421592), c_Orderings_Oord__class_Oless(_421590, _421594, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_421590), _421596), _421592)), -(c_Orderings_Oord__class_Oless(_421590, c_Rings_Oinverse__class_Odivide(_421590, _421594, _421592), _421596))], (3860 ^ _292445) ^ [_422066, _422068, _422070, _422072] : [class_Fields_Olinordered__field(_422066), c_Orderings_Oord__class_Oless(_422066, c_Groups_Ozero__class_Ozero(_422066), _422068), c_Orderings_Oord__class_Oless(_422066, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_422066), _422070), _422068), _422072), -(c_Orderings_Oord__class_Oless(_422066, _422070, c_Rings_Oinverse__class_Odivide(_422066, _422072, _422068)))], (3874 ^ _292445) ^ [_422542, _422544, _422546, _422548] : [class_Fields_Olinordered__field(_422542), c_Orderings_Oord__class_Oless(_422542, _422544, c_Groups_Ozero__class_Ozero(_422542)), 3881 ^ _292445 : [(3882 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_422542, _422546, c_Rings_Oinverse__class_Odivide(_422542, _422548, _422544)), -(c_Orderings_Oord__class_Oless(_422542, _422548, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_422542), _422546), _422544)))], (3888 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_422542, _422548, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_422542), _422546), _422544)), -(c_Orderings_Oord__class_Oless(_422542, _422546, c_Rings_Oinverse__class_Odivide(_422542, _422548, _422544)))]]], (3894 ^ _292445) ^ [_423205, _423207, _423209, _423211] : [class_Fields_Olinordered__field(_423205), c_Orderings_Oord__class_Oless(_423205, _423207, c_Groups_Ozero__class_Ozero(_423205)), 3901 ^ _292445 : [(3902 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_423205, c_Rings_Oinverse__class_Odivide(_423205, _423209, _423207), _423211), -(c_Orderings_Oord__class_Oless(_423205, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_423205), _423211), _423207), _423209))], (3908 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_423205, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_423205), _423211), _423207), _423209), -(c_Orderings_Oord__class_Oless(_423205, c_Rings_Oinverse__class_Odivide(_423205, _423209, _423207), _423211))]]], (3914 ^ _292445) ^ [_423868, _423870, _423872, _423874] : [class_Fields_Olinordered__field(_423868), c_Orderings_Oord__class_Oless(_423868, _423870, _423872), c_Orderings_Oord__class_Oless(_423868, c_Groups_Ozero__class_Ozero(_423868), _423874), c_Orderings_Oord__class_Oless(_423868, c_Groups_Ozero__class_Ozero(_423868), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_423868), _423872), _423870)), -(c_Orderings_Oord__class_Oless(_423868, c_Rings_Oinverse__class_Odivide(_423868, _423874, _423872), c_Rings_Oinverse__class_Odivide(_423868, _423874, _423870)))], (3932 ^ _292445) ^ [_424455, _424457, _424459, _424461] : [class_Fields_Olinordered__field(_424455), c_Orderings_Oord__class_Oless(_424455, _424457, _424459), c_Orderings_Oord__class_Oless(_424455, _424461, c_Groups_Ozero__class_Ozero(_424455)), c_Orderings_Oord__class_Oless(_424455, c_Groups_Ozero__class_Ozero(_424455), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_424455), _424457), _424459)), -(c_Orderings_Oord__class_Oless(_424455, c_Rings_Oinverse__class_Odivide(_424455, _424461, _424457), c_Rings_Oinverse__class_Odivide(_424455, _424461, _424459)))], (3950 ^ _292445) ^ [_425028, _425030, _425032] : [class_Fields_Olinordered__field__inverse__zero(_425028), c_Orderings_Oord__class_Oless(_425028, c_Groups_Ozero__class_Ozero(_425028), _425030), -(c_Rings_Oinverse__class_Odivide(_425028, c_Groups_Oabs__class_Oabs(_425028, _425032), _425030) = c_Groups_Oabs__class_Oabs(_425028, c_Rings_Oinverse__class_Odivide(_425028, _425032, _425030)))], (3960 ^ _292445) ^ [_425369, _425371] : [class_RealVector_Oreal__normed__vector(_425369), 3963 ^ _292445 : [(3964 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_425369, _425371)), _425371 = c_Groups_Ozero__class_Ozero(_425369)], (3970 ^ _292445) ^ [] : [-(_425371 = c_Groups_Ozero__class_Ozero(_425369)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_425369, _425371)))]]], (3976 ^ _292445) ^ [_425889, _425891, _425893, _425895, _425897] : [class_RealVector_Oreal__normed__algebra(_425889), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_425889, _425891), _425893), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_425889, _425895), _425897), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_425889, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_425889), _425891), _425895)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _425893), _425897)))], (3990 ^ _292445) ^ [_426383, _426385, _426387] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _426383), 3993 ^ _292445 : [(3994 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _426385), _426383), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _426387), _426383)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _426385, _426387))], (4000 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _426385, _426387), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _426385), _426383), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _426387), _426383)))]]], (4006 ^ _292445) ^ [_426917, _426919, _426921] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _426917), 4009 ^ _292445 : [(4010 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _426917), _426919), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _426917), _426921)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _426919, _426921))], (4016 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _426919, _426921), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _426917), _426919), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _426917), _426921)))]]], (4022 ^ _292445) ^ [_427479, _427481, _427483, _427485, _427487] : [class_RealVector_Oreal__normed__vector(_427479), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_427479, _427481), _427483), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_427479, _427485), _427487), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_427479, c_Groups_Oplus__class_Oplus(_427479, _427481, _427485)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _427483, _427487)))], (4036 ^ _292445) ^ [_427989, _427991, _427993, _427995, _427997] : [class_Rings_Ocomm__semiring__1(_427989), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_427989), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_427989), _427991), _427993)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_427989), _427995), _427997)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_427989), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_427989), _427991), _427995)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_427989), _427993), _427997)))], (4042 ^ _292445) ^ [_428353, _428355, _428357, _428359, _428361] : [class_Rings_Ocomm__semiring__1(_428353), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_428353), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_428353), _428355), _428357)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_428353), _428359), _428361)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_428353), _428359), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_428353), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_428353), _428355), _428357)), _428361)))], (4048 ^ _292445) ^ [_428717, _428719, _428721, _428723, _428725] : [class_Rings_Ocomm__semiring__1(_428717), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_428717), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_428717), _428719), _428721)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_428717), _428723), _428725)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_428717), _428719), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_428717), _428721), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_428717), _428723), _428725))))], (4054 ^ _292445) ^ [_429067, _429069, _429071, _429073] : [class_Rings_Ocomm__semiring__1(_429067), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_429067), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_429067), _429069), _429071)), _429073) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_429067), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_429067), _429069), _429073)), _429071))], (4060 ^ _292445) ^ [_429379, _429381, _429383, _429385] : [class_Rings_Ocomm__semiring__1(_429379), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_429379), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_429379), _429381), _429383)), _429385) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_429379), _429381), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_429379), _429383), _429385)))], (4066 ^ _292445) ^ [_429691, _429693, _429695, _429697] : [class_Rings_Ocomm__semiring__1(_429691), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_429691), _429693), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_429691), _429695), _429697)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_429691), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_429691), _429693), _429695)), _429697))], (4072 ^ _292445) ^ [_430003, _430005, _430007, _430009] : [class_Rings_Ocomm__semiring__1(_430003), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_430003), _430005), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_430003), _430007), _430009)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_430003), _430007), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_430003), _430005), _430009)))], (4078 ^ _292445) ^ [_430301, _430303, _430305] : [class_Rings_Ocomm__semiring__1(_430301), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_430301), _430303), _430305) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_430301), _430305), _430303))], (4084 ^ _292445) ^ [_430589, _430591, _430593, _430595, _430597] : [class_Rings_Ocomm__semiring__1(_430589), -(c_Groups_Oplus__class_Oplus(_430589, c_Groups_Oplus__class_Oplus(_430589, _430591, _430593), c_Groups_Oplus__class_Oplus(_430589, _430595, _430597)) = c_Groups_Oplus__class_Oplus(_430589, c_Groups_Oplus__class_Oplus(_430589, _430591, _430595), c_Groups_Oplus__class_Oplus(_430589, _430593, _430597)))], (4090 ^ _292445) ^ [_430891, _430893, _430895, _430897] : [class_Rings_Ocomm__semiring__1(_430891), -(c_Groups_Oplus__class_Oplus(_430891, c_Groups_Oplus__class_Oplus(_430891, _430893, _430895), _430897) = c_Groups_Oplus__class_Oplus(_430891, c_Groups_Oplus__class_Oplus(_430891, _430893, _430897), _430895))], (4096 ^ _292445) ^ [_431171, _431173, _431175, _431177] : [class_Rings_Ocomm__semiring__1(_431171), -(c_Groups_Oplus__class_Oplus(_431171, c_Groups_Oplus__class_Oplus(_431171, _431173, _431175), _431177) = c_Groups_Oplus__class_Oplus(_431171, _431173, c_Groups_Oplus__class_Oplus(_431171, _431175, _431177)))], (4102 ^ _292445) ^ [_431451, _431453, _431455, _431457] : [class_Rings_Ocomm__semiring__1(_431451), -(c_Groups_Oplus__class_Oplus(_431451, _431453, c_Groups_Oplus__class_Oplus(_431451, _431455, _431457)) = c_Groups_Oplus__class_Oplus(_431451, c_Groups_Oplus__class_Oplus(_431451, _431453, _431455), _431457))], (4108 ^ _292445) ^ [_431731, _431733, _431735, _431737] : [class_Rings_Ocomm__semiring__1(_431731), -(c_Groups_Oplus__class_Oplus(_431731, _431733, c_Groups_Oplus__class_Oplus(_431731, _431735, _431737)) = c_Groups_Oplus__class_Oplus(_431731, _431735, c_Groups_Oplus__class_Oplus(_431731, _431733, _431737)))], (4114 ^ _292445) ^ [_431997, _431999, _432001] : [class_Rings_Ocomm__semiring__1(_431997), -(c_Groups_Oplus__class_Oplus(_431997, _431999, _432001) = c_Groups_Oplus__class_Oplus(_431997, _432001, _431999))], (4120 ^ _292445) ^ [_432255, _432257, _432259, _432261] : [class_Fields_Olinordered__field__inverse__zero(_432255), c_Orderings_Oord__class_Oless__eq(_432255, _432257, _432259), c_Orderings_Oord__class_Oless__eq(_432255, _432261, c_Groups_Ozero__class_Ozero(_432255)), c_Orderings_Oord__class_Oless(_432255, c_Groups_Ozero__class_Ozero(_432255), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_432255), _432257), _432259)), -(c_Orderings_Oord__class_Oless__eq(_432255, c_Rings_Oinverse__class_Odivide(_432255, _432261, _432257), c_Rings_Oinverse__class_Odivide(_432255, _432261, _432259)))], (4138 ^ _292445) ^ [_432842, _432844, _432846, _432848] : [class_Fields_Olinordered__field(_432842), c_Orderings_Oord__class_Oless__eq(_432842, _432844, _432846), c_Orderings_Oord__class_Oless__eq(_432842, c_Groups_Ozero__class_Ozero(_432842), _432848), c_Orderings_Oord__class_Oless(_432842, c_Groups_Ozero__class_Ozero(_432842), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_432842), _432846), _432844)), -(c_Orderings_Oord__class_Oless__eq(_432842, c_Rings_Oinverse__class_Odivide(_432842, _432848, _432846), c_Rings_Oinverse__class_Odivide(_432842, _432848, _432844)))], (4156 ^ _292445) ^ [_433429, _433431, _433433, _433435] : [class_Fields_Olinordered__field(_433429), c_Orderings_Oord__class_Oless(_433429, _433431, c_Groups_Ozero__class_Ozero(_433429)), 4163 ^ _292445 : [(4164 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_433429, c_Rings_Oinverse__class_Odivide(_433429, _433433, _433431), _433435), -(c_Orderings_Oord__class_Oless__eq(_433429, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_433429), _433435), _433431), _433433))], (4170 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_433429, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_433429), _433435), _433431), _433433), -(c_Orderings_Oord__class_Oless__eq(_433429, c_Rings_Oinverse__class_Odivide(_433429, _433433, _433431), _433435))]]], (4176 ^ _292445) ^ [_434092, _434094, _434096, _434098] : [class_Fields_Olinordered__field(_434092), c_Orderings_Oord__class_Oless(_434092, _434094, c_Groups_Ozero__class_Ozero(_434092)), 4183 ^ _292445 : [(4184 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_434092, _434096, c_Rings_Oinverse__class_Odivide(_434092, _434098, _434094)), -(c_Orderings_Oord__class_Oless__eq(_434092, _434098, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_434092), _434096), _434094)))], (4190 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_434092, _434098, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_434092), _434096), _434094)), -(c_Orderings_Oord__class_Oless__eq(_434092, _434096, c_Rings_Oinverse__class_Odivide(_434092, _434098, _434094)))]]], (4196 ^ _292445) ^ [_434755, _434757, _434759, _434761] : [class_Fields_Olinordered__field(_434755), c_Orderings_Oord__class_Oless(_434755, c_Groups_Ozero__class_Ozero(_434755), _434757), c_Orderings_Oord__class_Oless__eq(_434755, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_434755), _434759), _434757), _434761), -(c_Orderings_Oord__class_Oless__eq(_434755, _434759, c_Rings_Oinverse__class_Odivide(_434755, _434761, _434757)))], (4210 ^ _292445) ^ [_435231, _435233, _435235, _435237] : [class_Fields_Olinordered__field(_435231), c_Orderings_Oord__class_Oless(_435231, c_Groups_Ozero__class_Ozero(_435231), _435233), c_Orderings_Oord__class_Oless__eq(_435231, _435235, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_435231), _435237), _435233)), -(c_Orderings_Oord__class_Oless__eq(_435231, c_Rings_Oinverse__class_Odivide(_435231, _435235, _435233), _435237))], (4224 ^ _292445) ^ [_435707, _435709, _435711, _435713] : [class_Fields_Olinordered__field(_435707), c_Orderings_Oord__class_Oless(_435707, c_Groups_Ozero__class_Ozero(_435707), _435709), 4231 ^ _292445 : [(4232 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_435707, c_Rings_Oinverse__class_Odivide(_435707, _435711, _435709), _435713), -(c_Orderings_Oord__class_Oless__eq(_435707, _435711, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_435707), _435713), _435709)))], (4238 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_435707, _435711, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_435707), _435713), _435709)), -(c_Orderings_Oord__class_Oless__eq(_435707, c_Rings_Oinverse__class_Odivide(_435707, _435711, _435709), _435713))]]], (4244 ^ _292445) ^ [_436370, _436372, _436374, _436376] : [class_Fields_Olinordered__field(_436370), c_Orderings_Oord__class_Oless(_436370, c_Groups_Ozero__class_Ozero(_436370), _436372), 4251 ^ _292445 : [(4252 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_436370, _436374, c_Rings_Oinverse__class_Odivide(_436370, _436376, _436372)), -(c_Orderings_Oord__class_Oless__eq(_436370, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_436370), _436374), _436372), _436376))], (4258 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_436370, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_436370), _436374), _436372), _436376), -(c_Orderings_Oord__class_Oless__eq(_436370, _436374, c_Rings_Oinverse__class_Odivide(_436370, _436376, _436372)))]]], (4264 ^ _292445) ^ [_437033, _437035, _437037, _437039] : [class_Fields_Olinordered__field__inverse__zero(_437033), 4267 ^ _292445 : [(4294 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_437033, c_Rings_Oinverse__class_Odivide(_437033, _437035, _437037), _437039)), 4297 ^ _292445 : [(4298 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_437033, c_Groups_Ozero__class_Ozero(_437033), _437037))], (4300 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_437033, _437035, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_437033), _437039), _437037))]], 4301 ^ _292445 : [(4302 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_437033, c_Groups_Ozero__class_Ozero(_437033), _437037)], (4304 ^ _292445) ^ [] : [4305 ^ _292445 : [(4306 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_437033, _437037, c_Groups_Ozero__class_Ozero(_437033)))], (4308 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_437033, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_437033), _437039), _437037), _437035)]], 4309 ^ _292445 : [(4310 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_437033, _437037, c_Groups_Ozero__class_Ozero(_437033))], (4312 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_437033, c_Groups_Ozero__class_Ozero(_437033), _437039)]]]]], (4268 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_437033, c_Rings_Oinverse__class_Odivide(_437033, _437035, _437037), _437039), 4271 ^ _292445 : [(4272 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_437033, c_Groups_Ozero__class_Ozero(_437033), _437037), -(c_Orderings_Oord__class_Oless__eq(_437033, _437035, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_437033), _437039), _437037)))], (4278 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_437033, c_Groups_Ozero__class_Ozero(_437033), _437037)), 4281 ^ _292445 : [(4282 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_437033, _437037, c_Groups_Ozero__class_Ozero(_437033)), -(c_Orderings_Oord__class_Oless__eq(_437033, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_437033), _437039), _437037), _437035))], (4288 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_437033, _437037, c_Groups_Ozero__class_Ozero(_437033))), -(c_Orderings_Oord__class_Oless__eq(_437033, c_Groups_Ozero__class_Ozero(_437033), _437039))]]]]]]], (4316 ^ _292445) ^ [_438689, _438691, _438693, _438695] : [class_Fields_Olinordered__field__inverse__zero(_438689), 4319 ^ _292445 : [(4346 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_438689, _438691, c_Rings_Oinverse__class_Odivide(_438689, _438693, _438695))), 4349 ^ _292445 : [(4350 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_438689, c_Groups_Ozero__class_Ozero(_438689), _438695))], (4352 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_438689, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_438689), _438691), _438695), _438693)]], 4353 ^ _292445 : [(4354 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_438689, c_Groups_Ozero__class_Ozero(_438689), _438695)], (4356 ^ _292445) ^ [] : [4357 ^ _292445 : [(4358 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_438689, _438695, c_Groups_Ozero__class_Ozero(_438689)))], (4360 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_438689, _438693, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_438689), _438691), _438695))]], 4361 ^ _292445 : [(4362 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_438689, _438695, c_Groups_Ozero__class_Ozero(_438689))], (4364 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_438689, _438691, c_Groups_Ozero__class_Ozero(_438689))]]]]], (4320 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_438689, _438691, c_Rings_Oinverse__class_Odivide(_438689, _438693, _438695)), 4323 ^ _292445 : [(4324 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_438689, c_Groups_Ozero__class_Ozero(_438689), _438695), -(c_Orderings_Oord__class_Oless__eq(_438689, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_438689), _438691), _438695), _438693))], (4330 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_438689, c_Groups_Ozero__class_Ozero(_438689), _438695)), 4333 ^ _292445 : [(4334 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_438689, _438695, c_Groups_Ozero__class_Ozero(_438689)), -(c_Orderings_Oord__class_Oless__eq(_438689, _438693, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_438689), _438691), _438695)))], (4340 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_438689, _438695, c_Groups_Ozero__class_Ozero(_438689))), -(c_Orderings_Oord__class_Oless__eq(_438689, _438691, c_Groups_Ozero__class_Ozero(_438689)))]]]]]]], (4368 ^ _292445) ^ [_440317, _440319] : [class_Rings_Ocomm__semiring__1(_440317), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_440317), _440319), c_Groups_Ozero__class_Ozero(_440317)) = c_Groups_Ozero__class_Ozero(_440317))], (4374 ^ _292445) ^ [_440549, _440551] : [class_Rings_Ocomm__semiring__1(_440549), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_440549), c_Groups_Ozero__class_Ozero(_440549)), _440551) = c_Groups_Ozero__class_Ozero(_440549))], (4380 ^ _292445) ^ [_440795, _440797, _440799] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_440795), 4383 ^ _292445 : [(4384 ^ _292445) ^ [] : [_440797 = c_Groups_Oplus__class_Oplus(_440795, _440797, _440799), -(_440799 = c_Groups_Ozero__class_Ozero(_440795))], (4390 ^ _292445) ^ [] : [_440799 = c_Groups_Ozero__class_Ozero(_440795), -(_440797 = c_Groups_Oplus__class_Oplus(_440795, _440797, _440799))]]], (4396 ^ _292445) ^ [_441287, _441289] : [class_Rings_Ocomm__semiring__1(_441287), -(c_Groups_Oplus__class_Oplus(_441287, _441289, c_Groups_Ozero__class_Ozero(_441287)) = _441289)], (4402 ^ _292445) ^ [] : [-(v_cs____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), 4406 ^ _292445 : [(4407 ^ _292445) ^ [_441615] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, 4405 ^ [], c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _441615)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, v_aa____, c_Polynomial_OpCons(tc_Complex_Ocomplex, v_c____, v_cs____))), _441615))))]]], (4413 ^ _292445) ^ [_441832] : [class_Groups_Ozero(_441832), -(c_Polynomial_OpCons(_441832, c_Groups_Ozero__class_Ozero(_441832), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_441832))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_441832)))], (4419 ^ _292445) ^ [_442076, _442078, _442080] : [class_Groups_Ozero(_442076), 4422 ^ _292445 : [(4423 ^ _292445) ^ [] : [c_Polynomial_OpCons(_442076, _442078, _442080) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_442076)), 4426 ^ _292445 : [(4427 ^ _292445) ^ [] : [-(_442078 = c_Groups_Ozero__class_Ozero(_442076))], (4429 ^ _292445) ^ [] : [-(_442080 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_442076)))]]], (4431 ^ _292445) ^ [] : [-(c_Polynomial_OpCons(_442076, _442078, _442080) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_442076))), _442078 = c_Groups_Ozero__class_Ozero(_442076), _442080 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_442076))]]], (4441 ^ _292445) ^ [_442756, _442758] : [class_Rings_Olinordered__idom(_442756), 4444 ^ _292445 : [(4445 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_442756, c_Groups_Oplus__class_Oplus(_442756, _442758, _442758), c_Groups_Ozero__class_Ozero(_442756)), -(c_Orderings_Oord__class_Oless(_442756, _442758, c_Groups_Ozero__class_Ozero(_442756)))], (4451 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_442756, _442758, c_Groups_Ozero__class_Ozero(_442756)), -(c_Orderings_Oord__class_Oless(_442756, c_Groups_Oplus__class_Oplus(_442756, _442758, _442758), c_Groups_Ozero__class_Ozero(_442756)))]]], (4457 ^ _292445) ^ [_443244, _443246] : [class_RealVector_Oreal__normed__field(_443244), 4461 ^ _292445 : [(4462 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 4460 ^ [_443244, _443246]))], (4464 ^ _292445) ^ [_443535] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_443244, c_Rings_Oinverse__class_Odivide(_443244, _443535, _443246)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_443244, _443535)), 4460 ^ [_443244, _443246])))]]], (4466 ^ _292445) ^ [_443677, _443679] : [class_RealVector_Oreal__normed__algebra(_443677), 4470 ^ _292445 : [(4471 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 4469 ^ [_443677, _443679]))], (4473 ^ _292445) ^ [_443976] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_443677, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_443677), _443976), _443679)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_443677, _443976)), 4469 ^ [_443677, _443679])))]]], (4475 ^ _292445) ^ [_444122, _444124] : [class_RealVector_Oreal__normed__algebra(_444122), 4479 ^ _292445 : [(4480 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 4478 ^ [_444122, _444124]))], (4482 ^ _292445) ^ [_444421] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_444122, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_444122), _444124), _444421)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_444122, _444421)), 4478 ^ [_444122, _444124])))]]], (4484 ^ _292445) ^ [_444553] : [class_RealVector_Oreal__normed__algebra(_444553), 4488 ^ _292445 : [(4489 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 4487 ^ [_444553]))], (4491 ^ _292445) ^ [_444882, _444884] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_444553, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_444553), _444884), _444882)), 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(_444553, _444884)), c_RealVector_Onorm__class_Onorm(_444553, _444882))), 4487 ^ [_444553])))]]], (4493 ^ _292445) ^ [_445063, _445065, _445067, _445069] : [class_Rings_Ocomm__semiring__0(_445063), -(hAPP(c_Polynomial_Opoly(_445063, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_445063)), _445065), _445067)), _445069) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_445063), hAPP(c_Polynomial_Opoly(_445063, _445065), _445069)), hAPP(c_Polynomial_Opoly(_445063, _445067), _445069)))], (4499 ^ _292445) ^ [_445383, _445385, _445387, _445389] : [class_Rings_Ocomm__semiring__0(_445383), -(hAPP(c_Polynomial_Opoly(_445383, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_445383), _445385, _445387)), _445389) = c_Groups_Oplus__class_Oplus(_445383, hAPP(c_Polynomial_Opoly(_445383, _445385), _445389), hAPP(c_Polynomial_Opoly(_445383, _445387), _445389)))], (4505 ^ _292445) ^ [_445673, _445675, _445677] : [class_Int_Oring__char__0(_445673), class_Rings_Oidom(_445673), 4512 ^ _292445 : [(4513 ^ _292445) ^ [] : [c_Polynomial_Opoly(_445673, _445675) = c_Polynomial_Opoly(_445673, _445677), -(_445675 = _445677)], (4519 ^ _292445) ^ [] : [_445675 = _445677, -(c_Polynomial_Opoly(_445673, _445675) = c_Polynomial_Opoly(_445673, _445677))]]], (4525 ^ _292445) ^ [_446258, _446260] : [class_Int_Oring__char__0(_446258), class_Rings_Oidom(_446258), 4532 ^ _292445 : [(4533 ^ _292445) ^ [] : [c_Polynomial_Opoly(_446258, _446260) = c_Polynomial_Opoly(_446258, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_446258))), -(_446260 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_446258)))], (4539 ^ _292445) ^ [] : [_446260 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_446258)), -(c_Polynomial_Opoly(_446258, _446260) = c_Polynomial_Opoly(_446258, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_446258))))]]], (4545 ^ _292445) ^ [_446875, _446877, _446879, _446881] : [class_Orderings_Oord(_446875), 4548 ^ _292445 : [(4549 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_fun(_446877, _446875), _446879, _446881), 4552 ^ _292445 : [(4553 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_fun(_446877, _446875), _446879, _446881))], (4555 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_446877, _446875), _446881, _446879)]]], (4557 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_fun(_446877, _446875), _446879, _446881)), c_Orderings_Oord__class_Oless__eq(tc_fun(_446877, _446875), _446879, _446881), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_446877, _446875), _446881, _446879))]]], (4567 ^ _292445) ^ [_447573, _447575] : [class_Rings_Ocomm__semiring__0(_447573), -(hAPP(c_Polynomial_Opoly(_447573, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_447573))), _447575) = c_Groups_Ozero__class_Ozero(_447573))], (4573 ^ _292445) ^ [_447833, _447835, _447837, _447839] : [class_Rings_Ocomm__semiring__0(_447833), -(hAPP(c_Polynomial_Opoly(_447833, c_Polynomial_OpCons(_447833, _447835, _447837)), _447839) = c_Groups_Oplus__class_Oplus(_447833, _447835, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_447833), _447839), hAPP(c_Polynomial_Opoly(_447833, _447837), _447839))))], (4579 ^ _292445) ^ [_448109, _448111] : [class_Groups_Ocomm__monoid__add(_448109), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_448109), _448111, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_448109))) = _448111)], (4585 ^ _292445) ^ [_448337, _448339] : [class_Rings_Ocomm__semiring__0(_448337), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_448337)), _448339), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_448337))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_448337)))], (4591 ^ _292445) ^ [_448581, _448583] : [class_Groups_Ocomm__monoid__add(_448581), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_448581), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_448581)), _448583) = _448583)], (4597 ^ _292445) ^ [_448809, _448811] : [class_Rings_Ocomm__semiring__0(_448809), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_448809)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_448809))), _448811) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_448809)))], (4603 ^ _292445) ^ [_449095, _449097, _449099, _449101, _449103] : [class_Groups_Ozero(_449095), 4606 ^ _292445 : [(4607 ^ _292445) ^ [] : [c_Polynomial_OpCons(_449095, _449097, _449099) = c_Polynomial_OpCons(_449095, _449101, _449103), 4610 ^ _292445 : [(4611 ^ _292445) ^ [] : [-(_449097 = _449101)], (4613 ^ _292445) ^ [] : [-(_449099 = _449103)]]], (4615 ^ _292445) ^ [] : [-(c_Polynomial_OpCons(_449095, _449097, _449099) = c_Polynomial_OpCons(_449095, _449101, _449103)), _449097 = _449101, _449099 = _449103]]], (4625 ^ _292445) ^ [_449801, _449803] : [class_Groups_Olinordered__ab__group__add(_449801), 4628 ^ _292445 : [(4629 ^ _292445) ^ [] : [c_Groups_Oplus__class_Oplus(_449801, _449803, _449803) = c_Groups_Ozero__class_Ozero(_449801), -(_449803 = c_Groups_Ozero__class_Ozero(_449801))], (4635 ^ _292445) ^ [] : [_449803 = c_Groups_Ozero__class_Ozero(_449801), -(c_Groups_Oplus__class_Oplus(_449801, _449803, _449803) = c_Groups_Ozero__class_Ozero(_449801))]]], (4641 ^ _292445) ^ [_450325, _450327, _450329, _450331, _450333] : [class_Groups_Ocomm__monoid__add(_450325), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_450325), c_Polynomial_OpCons(_450325, _450327, _450329), c_Polynomial_OpCons(_450325, _450331, _450333)) = c_Polynomial_OpCons(_450325, c_Groups_Oplus__class_Oplus(_450325, _450327, _450331), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_450325), _450329, _450333)))], (4647 ^ _292445) ^ [_450607, _450609] : [-(v_cs____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), 4651 ^ _292445 : [(4652 ^ _292445) ^ [_450836] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, 4650 ^ [_450607, _450609], c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _450836)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _450607, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, _450609, v_cs____)), _450836))))]]], (4658 ^ _292445) ^ [_451125, _451127, _451129] : [class_Rings_Olinordered__idom(_451125), 4661 ^ _292445 : [(4662 ^ _292445) ^ [] : [c_Polynomial_Opos__poly(_451125, c_Polynomial_OpCons(_451125, _451127, _451129)), -(c_Polynomial_Opos__poly(_451125, _451129)), 4669 ^ _292445 : [(4670 ^ _292445) ^ [] : [-(_451129 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_451125)))], (4672 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_451125, c_Groups_Ozero__class_Ozero(_451125), _451127))]]], (4674 ^ _292445) ^ [] : [-(c_Polynomial_Opos__poly(_451125, c_Polynomial_OpCons(_451125, _451127, _451129))), 4675 ^ _292445 : [(4676 ^ _292445) ^ [] : [c_Polynomial_Opos__poly(_451125, _451129)], (4678 ^ _292445) ^ [] : [_451129 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_451125)), c_Orderings_Oord__class_Oless(_451125, c_Groups_Ozero__class_Ozero(_451125), _451127)]]]]], (4687 ^ _292445) ^ [_452038, _452040] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 4685 ^ [_452038, _452040]))], (4689 ^ _292445) ^ [_452121, _452123, _452125] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _452121), _452123), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, _452125), _452121)), 4685 ^ [_452123, _452125]))], (4695 ^ _292445) ^ [_452395, _452397, _452399] : [class_Rings_Oidom(_452395), 4698 ^ _292445 : [(4709 ^ _292445) ^ [] : [4710 ^ _292445 : [(4711 ^ _292445) ^ [] : [_452397 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_452395))], (4713 ^ _292445) ^ [] : [-(c_Polynomial_Oorder(_452395, _452399, _452397) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], -(hAPP(c_Polynomial_Opoly(_452395, _452397), _452399) = c_Groups_Ozero__class_Ozero(_452395))], (4699 ^ _292445) ^ [] : [hAPP(c_Polynomial_Opoly(_452395, _452397), _452399) = c_Groups_Ozero__class_Ozero(_452395), -(_452397 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_452395))), c_Polynomial_Oorder(_452395, _452399, _452397) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (4717 ^ _292445) ^ [_453139, _453141, _453143, _453145, _453147, _453149] : [class_Groups_Ozero(_453139), hAPP(hAPP(hAPP(_453141, c_Groups_Ozero__class_Ozero(_453139)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_453139))), _453143) = _453143, -(c_Polynomial_Opoly__rec(_453145, _453139, _453143, _453141, c_Polynomial_OpCons(_453139, _453147, _453149)) = hAPP(hAPP(hAPP(_453141, _453147), _453149), c_Polynomial_Opoly__rec(_453145, _453139, _453143, _453141, _453149)))], (4727 ^ _292445) ^ [_453556, _453558] : [class_RealVector_Oreal__normed__field(_453556), 4731 ^ _292445 : [(4732 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 4730 ^ [_453556, _453558]))], (4734 ^ _292445) ^ [_453847] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_453556, c_Rings_Oinverse__class_Odivide(_453556, _453847, _453558)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_453556, _453847)), 4730 ^ [_453556, _453558])))]]], (4736 ^ _292445) ^ [_454003, _454005, _454007] : [class_Rings_Olinordered__idom(_454003), c_Polynomial_Opos__poly(_454003, _454005), c_Polynomial_Opos__poly(_454003, _454007), -(c_Polynomial_Opos__poly(_454003, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_454003)), _454005), _454007)))], (4750 ^ _292445) ^ [_454437, _454439, _454441] : [class_Rings_Olinordered__idom(_454437), c_Polynomial_Opos__poly(_454437, _454439), c_Polynomial_Opos__poly(_454437, _454441), -(c_Polynomial_Opos__poly(_454437, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_454437), _454439, _454441)))], (4764 ^ _292445) ^ [_454877, _454879, _454881, _454883] : [class_Rings_Ocomm__semiring__0(_454877), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_454877)), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_454877), _454879, _454881)), _454883) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_454877), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_454877)), _454879), _454883), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_454877)), _454881), _454883)))], (4770 ^ _292445) ^ [_455167] : [class_Rings_Olinordered__idom(_455167), c_Polynomial_Opos__poly(_455167, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_455167)))], (4776 ^ _292445) ^ [_455406, _455408, _455410, _455412] : [class_Groups_Ozero(_455406), hAPP(hAPP(hAPP(_455408, c_Groups_Ozero__class_Ozero(_455406)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_455406))), _455410) = _455410, -(c_Polynomial_Opoly__rec(_455412, _455406, _455410, _455408, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_455406))) = _455410)], (4786 ^ _292445) ^ [_455829, _455831, _455833, _455835, _455837, _455839] : [class_Groups_Ozero(_455829), -(c_Polynomial_Opoly__rec(_455831, _455829, _455833, _455835, c_Polynomial_OpCons(_455829, _455837, _455839)) = hAPP(hAPP(hAPP(_455835, _455837), _455839), c_If(_455831, c_fequal(_455839, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_455829))), _455833, c_Polynomial_Opoly__rec(_455831, _455829, _455833, _455835, _455839))))], (4792 ^ _292445) ^ [_456163, _456165, _456167, _456169] : [class_Rings_Ocomm__semiring__0(_456163), -(c_Polynomial_Opcompose(_456163, c_Polynomial_OpCons(_456163, _456165, _456167), _456169) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_456163), c_Polynomial_OpCons(_456163, _456165, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_456163))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_456163)), _456169), c_Polynomial_Opcompose(_456163, _456167, _456169))))], (4798 ^ _292445) ^ [_456455, _456457] : [class_Groups_Ozero(_456455), 4801 ^ _292445 : [(4802 ^ _292445) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_456455, _456457) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_456457 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_456455)))], (4808 ^ _292445) ^ [] : [_456457 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_456455)), -(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_456455, _456457) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (4814 ^ _292445) ^ [_456904] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _456904, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4816 ^ _292445) ^ [_456983] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _456983))], (4818 ^ _292445) ^ [_457091, _457093] : [class_RealVector_Oreal__normed__algebra(_457091), 4822 ^ _292445 : [(4823 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 4821 ^ [_457091, _457093]))], (4825 ^ _292445) ^ [_457390] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_457091, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_457091), _457390), _457093)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_457091, _457390)), 4821 ^ [_457091, _457093])))]]], (4827 ^ _292445) ^ [_457520, _457522] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _457520, _457522), _457520)], (4829 ^ _292445) ^ [_457618, _457620] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _457618, _457620), _457620)], (4831 ^ _292445) ^ [_457761, _457763] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _457761, _457763), 4834 ^ _292445 : [(4835 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _457761, _457763))], (4837 ^ _292445) ^ [] : [_457761 = _457763]]], (4839 ^ _292445) ^ [_458003, _458005] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _458003, _458005)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _458003, _458005), -(_458003 = _458005)], (4859 ^ _292445) ^ [_458596, _458598] : [4860 ^ _292445 : [(4861 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _458596, _458598)], (4863 ^ _292445) ^ [] : [_458596 = _458598]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _458596, _458598))], (4849 ^ _292445) ^ [_458340, _458342] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _458340, _458342), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _458340, _458342)), -(_458340 = _458342)], (4867 ^ _292445) ^ [_458929, _458931, _458933] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _458929, _458931), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _458929, _458933)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _458931, _458933))], (4873 ^ _292445) ^ [_459117, _459119, _459121] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _459119, _459121), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _459117, _459119), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _459117, _459121)))], (4879 ^ _292445) ^ [_459355, _459357] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _459355, _459357), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _459355, _459357))], (4885 ^ _292445) ^ [_459583, _459585, _459587] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _459583, _459585), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _459583, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _459585, _459587)))], (4891 ^ _292445) ^ [_459825, _459827, _459829] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _459825, _459827), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _459825, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _459829, _459827)))], (4897 ^ _292445) ^ [_460067, _460069, _460071] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _460067, _460069), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _460067, _460071), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _460069, _460071)))], (4903 ^ _292445) ^ [_460303, _460305] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _460303, _460305), -(_460303 = _460305), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _460303, _460305))], (4913 ^ _292445) ^ [_460637, _460639, _460641, _460643] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _460637, _460639), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _460641, _460643), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _460637, _460641), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _460639, _460643)))], (4923 ^ _292445) ^ [_461006, _461008, _461010, _461012] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _461006, _461008), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _461010, _461008) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _461006, _461012), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _461010, _461012))], (4933 ^ _292445) ^ [_461359, _461361, _461363] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _461359, _461361), _461363), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _461359, _461363))], (4939 ^ _292445) ^ [_461587, _461589] : [4940 ^ _292445 : [(4941 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _461587, _461589)], (4943 ^ _292445) ^ [] : [_461587 = _461589]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _461587, _461589))], (4947 ^ _292445) ^ [_461845] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _461845, _461845)], (4959 ^ _292445) ^ [_462241, _462243] : [4960 ^ _292445 : [(4961 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _462241, _462243)], (4963 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _462243, _462241)]], _462241 = _462243], (4949 ^ _292445) ^ [_461982, _461984] : [-(_461982 = _461984), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _461982, _461984)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _461984, _461982))], (4967 ^ _292445) ^ [_462532, _462534] : [-(_462532 = _462534), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _462532, _462534)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _462534, _462532))], (4977 ^ _292445) ^ [_462811] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _462811, _462811)], (4979 ^ _292445) ^ [_462919, _462921] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _462919, _462921), _462921 = _462919], (4985 ^ _292445) ^ [_463132, _463134] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _463132, _463134), _463132 = _463134], (4991 ^ _292445) ^ [_463359, _463361, _463363] : [4992 ^ _292445 : [(4993 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _463359, _463361))], (4995 ^ _292445) ^ [] : [hBOOL(hAPP(hAPP(_463363, _463361), _463359))]], 4998 ^ _292445 : [(4999 ^ _292445) ^ [] : [-(_463359 = _463361)], (5001 ^ _292445) ^ [] : [hBOOL(hAPP(hAPP(_463363, _463361), _463359))]], 5004 ^ _292445 : [(5005 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _463361, _463359))], (5007 ^ _292445) ^ [] : [hBOOL(hAPP(hAPP(_463363, _463361), _463359))]], -(hBOOL(hAPP(hAPP(_463363, _463361), _463359)))], (5011 ^ _292445) ^ [_464007] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _464007, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _464007), _464007)))], (5013 ^ _292445) ^ [_464106, _464108] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _464106, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _464108, _464106)))], (5015 ^ _292445) ^ [_464205, _464207] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _464205, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _464205, _464207)))], (5017 ^ _292445) ^ [_464290] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _464290, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _464290), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _464290), _464290))))], (5019 ^ _292445) ^ [_464439, _464441] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _464439, _464441), -(_464441 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _464439, 5022 ^ [_464439, _464441]))], (5026 ^ _292445) ^ [_464672, _464674] : [5027 ^ _292445 : [(5028 ^ _292445) ^ [_464747] : [_464674 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _464672, _464747)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _464672, _464674))], (5032 ^ _292445) ^ [_464945, _464947] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _464945, _464947), -(_464947 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _464945, 5035 ^ [_464945, _464947]))], (5039 ^ _292445) ^ [_465178, _465180] : [5040 ^ _292445 : [(5041 ^ _292445) ^ [_465253] : [_465180 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _465178, _465253)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _465178, _465180))], (5045 ^ _292445) ^ [_465465, _465467, _465469] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _465465, _465467), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _465465, _465469)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _465467, _465469))], (5051 ^ _292445) ^ [_465653, _465655, _465657] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _465655, _465657), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _465653, _465655), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _465653, _465657)))], (5057 ^ _292445) ^ [_465905, _465907, _465909] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _465905, _465907), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _465905, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _465907, _465909)))], (5063 ^ _292445) ^ [_466147, _466149, _466151] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _466147, _466149), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _466147, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _466151, _466149)))], (5069 ^ _292445) ^ [_466389, _466391, _466393] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _466389, _466391), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _466389, _466393), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _466391, _466393)))], (5075 ^ _292445) ^ [_466639, _466641, _466643] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _466639, _466641), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _466639), _466643), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _466641), _466643)))], (5081 ^ _292445) ^ [_466897, _466899, _466901] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _466897, _466899), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _466901), _466897), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _466901), _466899)))], (5087 ^ _292445) ^ [_467169, _467171, _467173, _467175] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _467169, _467171), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _467173, _467175), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _467169, _467173), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _467171, _467175)))], (5097 ^ _292445) ^ [_467538, _467540, _467542, _467544] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _467538, _467540), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _467542, _467544), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _467538), _467542), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _467540), _467544)))], (5107 ^ _292445) ^ [_467901, _467903, _467905] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _467901, _467903), _467905), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _467903, _467905))], (5113 ^ _292445) ^ [_468143, _468145, _468147] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _468143, _468145), _468147), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _468143, _468147))], (5119 ^ _292445) ^ [_468385, _468387, _468389] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _468385, _468387), _468389), 5122 ^ _292445 : [(5123 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _468385, _468389))], (5125 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _468387, _468389))]]], (5127 ^ _292445) ^ [_468696, _468698] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _468696, _468698), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _468698, _468696), -(_468696 = _468698)], (5137 ^ _292445) ^ [_469013, _469015, _469017] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _469013, _469015), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _469015, _469017), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _469013, _469017))], (5147 ^ _292445) ^ [_469328, _469330] : [_469328 = _469330, -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _469328, _469330))], (5153 ^ _292445) ^ [_469540, _469542] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _469540, _469542)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _469542, _469540))], (5159 ^ _292445) ^ [_469726] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _469726, _469726))], (5161 ^ _292445) ^ [_469834, _469836] : [class_Rings_Ocomm__semiring__0(_469834), -(c_Polynomial_Opcompose(_469834, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_469834)), _469836) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_469834)))], (5167 ^ _292445) ^ [_470094, _470096, _470098, _470100] : [class_Rings_Ocomm__semiring__0(_470094), -(hAPP(c_Polynomial_Opoly(_470094, c_Polynomial_Opcompose(_470094, _470096, _470098)), _470100) = hAPP(c_Polynomial_Opoly(_470094, _470096), hAPP(c_Polynomial_Opoly(_470094, _470098), _470100)))], (5173 ^ _292445) ^ [_470329] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _470329) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5175 ^ _292445) ^ [_470410] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _470410))], (5177 ^ _292445) ^ [_470489] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _470489) = _470489)], (5179 ^ _292445) ^ [_470571] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _470571), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5181 ^ _292445) ^ [_470655] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _470655, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _470655)], (5183 ^ _292445) ^ [_470781] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _470781, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_470781 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5189 ^ _292445) ^ [_470939] : [_470939 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _470939, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (5195 ^ _292445) ^ [_471176, _471178] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _471176, _471178) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 5198 ^ _292445 : [(5199 ^ _292445) ^ [] : [-(_471176 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5201 ^ _292445) ^ [] : [-(_471178 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (5203 ^ _292445) ^ [_471421, _471423] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _471421, _471423) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _471421 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _471423 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5223 ^ _292445) ^ [_472023, _472025] : [5224 ^ _292445 : [(5225 ^ _292445) ^ [] : [_472023 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5227 ^ _292445) ^ [] : [_472025 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _472023), _472025) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5213 ^ _292445) ^ [_471759, _471761] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _471759), _471761) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_471759 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_471761 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5241 ^ _292445) ^ [_472650, _472652, _472654] : [5242 ^ _292445 : [(5243 ^ _292445) ^ [] : [_472652 = _472654], (5245 ^ _292445) ^ [] : [_472650 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _472650), _472652) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _472650), _472654))], (5231 ^ _292445) ^ [_472364, _472366, _472368] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _472364), _472366) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _472364), _472368), -(_472366 = _472368), -(_472364 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5259 ^ _292445) ^ [_473297, _473299, _473301] : [5260 ^ _292445 : [(5261 ^ _292445) ^ [] : [_473297 = _473301], (5263 ^ _292445) ^ [] : [_473299 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _473297), _473299) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _473301), _473299))], (5249 ^ _292445) ^ [_473011, _473013, _473015] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _473011), _473013) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _473015), _473013), -(_473011 = _473015), -(_473013 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5267 ^ _292445) ^ [_473615, _473617] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _473615, _473617) = _473615, -(_473617 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5273 ^ _292445) ^ [_473819] : [-(_473819 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _473819))], (5279 ^ _292445) ^ [_474042, _474044, _474046] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _474042, _474044), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _474046), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _474046), _474042), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _474046), _474044)))], (5289 ^ _292445) ^ [_474395, _474397, _474399] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _474395, _474397), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _474399), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _474395), _474399), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _474397), _474399)))], (5299 ^ _292445) ^ [_474734, _474736] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _474734, _474736), _474736 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5315 ^ _292445) ^ [_475281, _475283, _475285] : [5316 ^ _292445 : [(5317 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _475283))], (5319 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _475281, _475285)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _475281), _475283), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _475285), _475283)))], (5305 ^ _292445) ^ [_474990, _474992, _474994] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _474990), _474992), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _474994), _474992)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _474992), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _474990, _474994))], (5333 ^ _292445) ^ [_475940, _475942, _475944] : [5334 ^ _292445 : [(5335 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _475940))], (5337 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _475942, _475944)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _475940), _475942), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _475940), _475944)))], (5323 ^ _292445) ^ [_475649, _475651, _475653] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _475649), _475651), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _475649), _475653)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _475649), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _475651, _475653))], (5341 ^ _292445) ^ [_476308, _476310, _476312] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _476308), _476310), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _476312), _476310)), 5344 ^ _292445 : [(5345 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _476310))], (5347 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _476308, _476312))]]], (5349 ^ _292445) ^ [_476583, _476585, _476587] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _476583), _476585), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _476587), _476585))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _476585), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _476583, _476587)], (5359 ^ _292445) ^ [_476967, _476969, _476971] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _476967), _476969), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _476967), _476971)), 5362 ^ _292445 : [(5363 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _476967))], (5365 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _476969, _476971))]]], (5367 ^ _292445) ^ [_477242, _477244, _477246] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _477242), _477244), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _477242), _477246))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _477242), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _477244, _477246)], (5377 ^ _292445) ^ [_477553] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _477553, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5379 ^ _292445) ^ [_477690, _477692] : [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), _477690), _477692)), 5382 ^ _292445 : [(5383 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _477690))], (5385 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _477692))]]], (5387 ^ _292445) ^ [_477945, _477947] : [-(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), _477945), _477947))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _477945), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _477947)], (5407 ^ _292445) ^ [_478559, _478561] : [5408 ^ _292445 : [(5409 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _478559)], (5411 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _478561)]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _478559, _478561)))], (5397 ^ _292445) ^ [_478293, _478295] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _478293, _478295)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _478293)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _478295))], (5415 ^ _292445) ^ [_478874] : [-(_478874 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _478874))], (5421 ^ _292445) ^ [_479035] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _479035), _479035 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5427 ^ _292445) ^ [_479214] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _479214, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5429 ^ _292445) ^ [_479336, _479338, _479340] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _479336), 5432 ^ _292445 : [(5433 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _479336), _479338), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _479336), _479340)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _479338, _479340))], (5439 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _479338, _479340), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _479336), _479338), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _479336), _479340)))]]], (5445 ^ _292445) ^ [_479856, _479858] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _479856, _479858), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _479856, _479858))], (5451 ^ _292445) ^ [_480084, _480086, _480088] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _480084), 5454 ^ _292445 : [(5455 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _480084), _480086), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _480084), _480088)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _480086, _480088))], (5461 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _480086, _480088), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _480084), _480086), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _480084), _480088)))]]], (5467 ^ _292445) ^ [_480618, _480620, _480622] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _480618), 5470 ^ _292445 : [(5471 ^ _292445) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _480618), _480620) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _480618), _480622), -(_480620 = _480622)], (5477 ^ _292445) ^ [] : [_480620 = _480622, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _480618), _480620) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _480618), _480622))]]], (5483 ^ _292445) ^ [_481118] : [class_RealVector_Oreal__normed__algebra(_481118), 5487 ^ _292445 : [(5488 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 5486 ^ [_481118]))], (5490 ^ _292445) ^ [_481447, _481449] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_481118, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_481118), _481449), _481447)), 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(_481118, _481449)), c_RealVector_Onorm__class_Onorm(_481118, _481447))), 5486 ^ [_481118])))]]], (5492 ^ _292445) ^ [_481585, _481587] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _481585, _481587) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _481587, _481585))], (5494 ^ _292445) ^ [_481701, _481703, _481705] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _481701, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _481703, _481705)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _481703, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _481701, _481705)))], (5496 ^ _292445) ^ [_481827, _481829, _481831] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _481827), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _481829, _481831)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _481827), _481829), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _481827), _481831)))], (5498 ^ _292445) ^ [_481963, _481965, _481967] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _481963, _481965), _481967) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _481963, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _481965, _481967)))], (5500 ^ _292445) ^ [_482089, _482091, _482093] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _482089, _482091)), _482093) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _482089), _482093), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _482091), _482093)))], (5502 ^ _292445) ^ [_482269, _482271, _482273] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _482269, _482271) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _482269, _482273), -(_482271 = _482273)], (5508 ^ _292445) ^ [_482453, _482455, _482457] : [_482455 = _482457, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _482453, _482455) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _482453, _482457))], (5514 ^ _292445) ^ [_482730, _482732, _482734] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _482730, _482732) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _482734, _482732), -(_482730 = _482734)], (5520 ^ _292445) ^ [_482914, _482916, _482918] : [_482914 = _482918, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _482914, _482916) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _482918, _482916))], (5526 ^ _292445) ^ [_483147, _483149, _483151] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _483147), _483149)), _483151) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _483147), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _483149), _483151)))], (5528 ^ _292445) ^ [_483267, _483269] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _483267), _483269) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _483269), _483267))], (5530 ^ _292445) ^ [_483401, _483403, _483405, _483407] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _483401), _483403), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _483405), _483403), _483407)) = 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, _483401, _483405)), _483403), _483407))], (5542 ^ _292445) ^ [_483877, _483879, _483881] : [5543 ^ _292445 : [(5544 ^ _292445) ^ [] : [_483877 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5546 ^ _292445) ^ [] : [_483879 = _483881]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _483877), _483879) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _483877), _483881))], (5532 ^ _292445) ^ [_483591, _483593, _483595] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _483591), _483593) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _483591), _483595), -(_483591 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_483593 = _483595)], (5550 ^ _292445) ^ [_484209, _484211, _484213] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _484209, _484211), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _484209, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _484213, _484211)))], (5556 ^ _292445) ^ [_484451, _484453, _484455] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _484451, _484453), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _484451, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _484453, _484455)))], (5562 ^ _292445) ^ [_484693, _484695, _484697] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _484693, _484695), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _484693, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _484697, _484695)))], (5568 ^ _292445) ^ [_484935, _484937, _484939] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _484935, _484937), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _484935, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _484937, _484939)))], (5574 ^ _292445) ^ [_485163, _485165] : [class_RealVector_Oreal__normed__algebra(_485163), 5578 ^ _292445 : [(5579 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 5577 ^ [_485163, _485165]))], (5581 ^ _292445) ^ [_485462] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_485163, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_485163), _485165), _485462)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_485163, _485462)), 5577 ^ [_485163, _485165])))]]], (5583 ^ _292445) ^ [_485608, _485610] : [class_RealVector_Oreal__normed__field(_485608), 5587 ^ _292445 : [(5588 ^ _292445) ^ [_485811] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_485608, c_Rings_Oinverse__class_Odivide(_485608, _485811, _485610)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_485608, _485811)), 5586 ^ [_485608, _485610])))]]], (5590 ^ _292445) ^ [_485951, _485953] : [class_RealVector_Oreal__normed__algebra(_485951), 5594 ^ _292445 : [(5595 ^ _292445) ^ [_486162] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_485951, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_485951), _486162), _485953)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_485951, _486162)), 5593 ^ [_485951, _485953])))]]], (5597 ^ _292445) ^ [_486306, _486308] : [class_RealVector_Oreal__normed__algebra(_486306), 5601 ^ _292445 : [(5602 ^ _292445) ^ [_486517] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_486306, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_486306), _486308), _486517)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_486306, _486517)), 5600 ^ [_486306, _486308])))]]], (5604 ^ _292445) ^ [_486647] : [class_RealVector_Oreal__normed__algebra(_486647), 5608 ^ _292445 : [(5609 ^ _292445) ^ [_486892, _486894] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_486647, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_486647), _486894), _486892)), 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(_486647, _486894)), c_RealVector_Onorm__class_Onorm(_486647, _486892))), 5607 ^ [_486647])))]]], (5611 ^ _292445) ^ [_487099, _487101, _487103, _487105, _487107, _487109] : [class_Rings_Olinordered__semiring__1__strict(_487099), c_Orderings_Oord__class_Oless(_487099, _487101, _487103), c_Orderings_Oord__class_Oless(_487099, _487105, _487103), c_Orderings_Oord__class_Oless__eq(_487099, c_Groups_Ozero__class_Ozero(_487099), _487107), c_Orderings_Oord__class_Oless__eq(_487099, c_Groups_Ozero__class_Ozero(_487099), _487109), c_Groups_Oplus__class_Oplus(_487099, _487107, _487109) = c_Groups_Oone__class_Oone(_487099), -(c_Orderings_Oord__class_Oless(_487099, c_Groups_Oplus__class_Oplus(_487099, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_487099), _487107), _487101), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_487099), _487109), _487105)), _487103))], (5637 ^ _292445) ^ [_487940, _487942, _487944] : [class_Fields_Olinordered__field(_487940), 5643 ^ _292445 : [(5644 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_487940, c_Groups_Ozero__class_Ozero(_487940), 5642 ^ [_487940, _487942, _487944]))], (5646 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_487940, _487942, c_Groups_Oplus__class_Oplus(_487940, _487944, 5642 ^ [_487940, _487942, _487944]))]], -(c_Orderings_Oord__class_Oless__eq(_487940, _487942, _487944))], (5650 ^ _292445) ^ [_488442, _488444, _488446] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _488442), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _488444), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _488446), -(c_NthRoot_Oroot(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _488442), _488444), _488446) = c_NthRoot_Oroot(_488442, c_NthRoot_Oroot(_488444, _488446)))], (5664 ^ _292445) ^ [_488866] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _488866), -(c_NthRoot_Oroot(_488866, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (5670 ^ _292445) ^ [_489078, _489080] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _489078), 5673 ^ _292445 : [(5674 ^ _292445) ^ [] : [c_NthRoot_Oroot(_489078, _489080) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal), -(_489080 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (5680 ^ _292445) ^ [] : [_489080 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal), -(c_NthRoot_Oroot(_489078, _489080) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))]]], (5686 ^ _292445) ^ [_489535] : [class_RealVector_Oreal__normed__algebra__1(_489535), -(c_RealVector_Onorm__class_Onorm(_489535, c_Groups_Oone__class_Oone(_489535)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (5692 ^ _292445) ^ [_489747, _489749] : [class_Groups_Oone(_489747), 5695 ^ _292445 : [(5696 ^ _292445) ^ [] : [c_Groups_Oone__class_Oone(_489747) = _489749, -(_489749 = c_Groups_Oone__class_Oone(_489747))], (5702 ^ _292445) ^ [] : [_489749 = c_Groups_Oone__class_Oone(_489747), -(c_Groups_Oone__class_Oone(_489747) = _489749)]]], (5708 ^ _292445) ^ [_490203] : [class_Rings_Ocomm__semiring__1(_490203), -(c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_490203)) = c_Polynomial_OpCons(_490203, c_Groups_Oone__class_Oone(_490203), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_490203))))], (5714 ^ _292445) ^ [_490404] : [-(c_NthRoot_Oroot(_490404, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (5716 ^ _292445) ^ [_490514, _490516] : [class_Rings_Ocomm__semiring__1(_490514), -(hAPP(c_Polynomial_Opoly(_490514, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_490514))), _490516) = c_Groups_Oone__class_Oone(_490514))], (5722 ^ _292445) ^ [_490717] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _490717) = _490717)], (5724 ^ _292445) ^ [] : [c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)], (5726 ^ _292445) ^ [_490865] : [class_Rings_Olinordered__idom(_490865), -(c_Groups_Oabs__class_Oabs(_490865, c_Groups_Oone__class_Oone(_490865)) = c_Groups_Oone__class_Oone(_490865))], (5732 ^ _292445) ^ [_491081, _491083] : [class_Rings_Odivision__ring(_491081), -(c_Rings_Oinverse__class_Odivide(_491081, _491083, c_Groups_Oone__class_Oone(_491081)) = _491083)], (5738 ^ _292445) ^ [_491301, _491303] : [class_Groups_Omonoid__mult(_491301), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_491301), c_Groups_Oone__class_Oone(_491301)), _491303) = _491303)], (5744 ^ _292445) ^ [_491529, _491531] : [class_Groups_Ocomm__monoid__mult(_491529), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_491529), c_Groups_Oone__class_Oone(_491529)), _491531) = _491531)], (5750 ^ _292445) ^ [_491757, _491759] : [class_Groups_Omonoid__mult(_491757), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_491757), _491759), c_Groups_Oone__class_Oone(_491757)) = _491759)], (5756 ^ _292445) ^ [_491985, _491987] : [class_Groups_Ocomm__monoid__mult(_491985), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_491985), _491987), c_Groups_Oone__class_Oone(_491985)) = _491987)], (5762 ^ _292445) ^ [_492213, _492215] : [class_Rings_Ocomm__semiring__1(_492213), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_492213), _492215), c_Groups_Oone__class_Oone(_492213)) = _492215)], (5768 ^ _292445) ^ [_492441, _492443] : [class_Rings_Ocomm__semiring__1(_492441), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_492441), c_Groups_Oone__class_Oone(_492441)), _492443) = _492443)], (5774 ^ _292445) ^ [_492655] : [class_Rings_Ozero__neq__one(_492655), c_Groups_Ozero__class_Ozero(_492655) = c_Groups_Oone__class_Oone(_492655)], (5780 ^ _292445) ^ [_492852] : [class_Rings_Ozero__neq__one(_492852), c_Groups_Oone__class_Oone(_492852) = c_Groups_Ozero__class_Ozero(_492852)], (5786 ^ _292445) ^ [_493034] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _493034) = _493034)], (5788 ^ _292445) ^ [_493173, _493175] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _493173), _493175), 5791 ^ _292445 : [(5792 ^ _292445) ^ [] : [-(_493173 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (5794 ^ _292445) ^ [] : [-(_493175 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (5796 ^ _292445) ^ [_493422, _493424] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _493422), _493424)), _493422 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _493424 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (5806 ^ _292445) ^ [_493706] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _493706), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _493706)], (5808 ^ _292445) ^ [_493848, _493850] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _493848), _493850) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 5811 ^ _292445 : [(5812 ^ _292445) ^ [] : [-(_493848 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (5814 ^ _292445) ^ [] : [-(_493850 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (5816 ^ _292445) ^ [_494097, _494099] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _494097), _494099) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _494097 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _494099 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (5826 ^ _292445) ^ [_494424, _494426, _494428] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _494424), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _494424, _494426), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _494428), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_NthRoot_Oroot(_494426, _494428), c_NthRoot_Oroot(_494424, _494428)))], (5840 ^ _292445) ^ [_494846, _494848] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _494846), 5843 ^ _292445 : [(5844 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_NthRoot_Oroot(_494846, _494848), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _494848, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (5850 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _494848, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_NthRoot_Oroot(_494846, _494848), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))]]], (5856 ^ _292445) ^ [_495323, _495325] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _495323), 5859 ^ _292445 : [(5860 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), c_NthRoot_Oroot(_495323, _495325)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _495325))], (5866 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _495325), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), c_NthRoot_Oroot(_495323, _495325)))]]], (5872 ^ _292445) ^ [_495814, _495816, _495818] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _495814), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _495814, _495816), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _495818), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_NthRoot_Oroot(_495816, _495818), c_NthRoot_Oroot(_495814, _495818)))], (5886 ^ _292445) ^ [_496236, _496238] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _496236), 5889 ^ _292445 : [(5890 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_NthRoot_Oroot(_496236, _496238), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _496238, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (5896 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _496238, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_NthRoot_Oroot(_496236, _496238), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))]]], (5902 ^ _292445) ^ [_496713, _496715] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _496713), 5905 ^ _292445 : [(5906 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), c_NthRoot_Oroot(_496713, _496715)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _496715))], (5912 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _496715), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), c_NthRoot_Oroot(_496713, _496715)))]]], (5918 ^ _292445) ^ [_497204, _497206, _497208] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _497204), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _497204, _497206), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _497208), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _497208, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_NthRoot_Oroot(_497204, _497208), c_NthRoot_Oroot(_497206, _497208)))], (5936 ^ _292445) ^ [_497735, _497737, _497739] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _497735), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _497735, _497737), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _497739), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _497739, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_NthRoot_Oroot(_497735, _497739), c_NthRoot_Oroot(_497737, _497739)))], (5954 ^ _292445) ^ [_498266, _498268, _498270] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _498266), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _498268), -(c_NthRoot_Oroot(_498266, c_NthRoot_Oroot(_498268, _498270)) = c_NthRoot_Oroot(_498268, c_NthRoot_Oroot(_498266, _498270)))], (5964 ^ _292445) ^ [_498617, _498619, _498621] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _498617), 5967 ^ _292445 : [(5968 ^ _292445) ^ [] : [c_NthRoot_Oroot(_498617, _498619) = c_NthRoot_Oroot(_498617, _498621), -(_498619 = _498621)], (5974 ^ _292445) ^ [] : [_498619 = _498621, -(c_NthRoot_Oroot(_498617, _498619) = c_NthRoot_Oroot(_498617, _498621))]]], (5980 ^ _292445) ^ [_499099] : [class_Rings_Olinordered__semidom(_499099), c_Orderings_Oord__class_Oless__eq(_499099, c_Groups_Oone__class_Oone(_499099), c_Groups_Ozero__class_Ozero(_499099))], (5986 ^ _292445) ^ [_499298] : [class_Rings_Olinordered__semidom(_499298), -(c_Orderings_Oord__class_Oless__eq(_499298, c_Groups_Ozero__class_Ozero(_499298), c_Groups_Oone__class_Oone(_499298)))], (5992 ^ _292445) ^ [_499496] : [class_Rings_Olinordered__semidom(_499496), -(c_Orderings_Oord__class_Oless(_499496, c_Groups_Ozero__class_Ozero(_499496), c_Groups_Oone__class_Oone(_499496)))], (5998 ^ _292445) ^ [_499694] : [class_Rings_Olinordered__semidom(_499694), c_Orderings_Oord__class_Oless(_499694, c_Groups_Oone__class_Oone(_499694), c_Groups_Ozero__class_Ozero(_499694))], (6004 ^ _292445) ^ [_499921, _499923, _499925] : [class_Rings_Olinordered__semidom(_499921), c_Orderings_Oord__class_Oless(_499921, c_Groups_Oone__class_Oone(_499921), _499923), c_Orderings_Oord__class_Oless(_499921, c_Groups_Oone__class_Oone(_499921), _499925), -(c_Orderings_Oord__class_Oless(_499921, c_Groups_Oone__class_Oone(_499921), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_499921), _499923), _499925)))], (6018 ^ _292445) ^ [_500355, _500357] : [class_Rings_Olinordered__semidom(_500355), -(c_Orderings_Oord__class_Oless(_500355, _500357, c_Groups_Oplus__class_Oplus(_500355, _500357, c_Groups_Oone__class_Oone(_500355))))], (6024 ^ _292445) ^ [_500591, _500593, _500595] : [class_Rings_Ocomm__semiring__1(_500591), -(c_Groups_Oplus__class_Oplus(_500591, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_500591), _500593), _500595), _500595) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_500591), c_Groups_Oplus__class_Oplus(_500591, _500593, c_Groups_Oone__class_Oone(_500591))), _500595))], (6030 ^ _292445) ^ [_500871, _500873, _500875] : [class_Rings_Ocomm__semiring__1(_500871), -(c_Groups_Oplus__class_Oplus(_500871, _500873, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_500871), _500875), _500873)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_500871), c_Groups_Oplus__class_Oplus(_500871, _500875, c_Groups_Oone__class_Oone(_500871))), _500873))], (6036 ^ _292445) ^ [_501137, _501139] : [class_Rings_Ocomm__semiring__1(_501137), -(c_Groups_Oplus__class_Oplus(_501137, _501139, _501139) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_501137), c_Groups_Oplus__class_Oplus(_501137, c_Groups_Oone__class_Oone(_501137), c_Groups_Oone__class_Oone(_501137))), _501139))], (6042 ^ _292445) ^ [_501385, _501387] : [class_Rings_Odivision__ring__inverse__zero(_501385), 6045 ^ _292445 : [(6046 ^ _292445) ^ [] : [_501387 = c_Groups_Ozero__class_Ozero(_501385), -(c_Rings_Oinverse__class_Odivide(_501385, _501387, _501387) = c_Groups_Ozero__class_Ozero(_501385))], (6052 ^ _292445) ^ [] : [-(_501387 = c_Groups_Ozero__class_Ozero(_501385)), -(c_Rings_Oinverse__class_Odivide(_501385, _501387, _501387) = c_Groups_Oone__class_Oone(_501385))]]], (6058 ^ _292445) ^ [_501881, _501883] : [class_Rings_Odivision__ring(_501881), -(_501883 = c_Groups_Ozero__class_Ozero(_501881)), -(c_Rings_Oinverse__class_Odivide(_501881, _501883, _501883) = c_Groups_Oone__class_Oone(_501881))], (6068 ^ _292445) ^ [_502211, _502213, _502215] : [class_Rings_Odivision__ring(_502211), -(_502213 = c_Groups_Ozero__class_Ozero(_502211)), 6075 ^ _292445 : [(6076 ^ _292445) ^ [] : [c_Rings_Oinverse__class_Odivide(_502211, _502215, _502213) = c_Groups_Oone__class_Oone(_502211), -(_502215 = _502213)], (6082 ^ _292445) ^ [] : [_502215 = _502213, -(c_Rings_Oinverse__class_Odivide(_502211, _502215, _502213) = c_Groups_Oone__class_Oone(_502211))]]], (6088 ^ _292445) ^ [_502803, _502805] : [_502803 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _502803), _502805), -(_502805 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_502803 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6098 ^ _292445) ^ [_503129, _503131, _503133] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _503129), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _503131, _503133), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_NthRoot_Oroot(_503129, _503131), c_NthRoot_Oroot(_503129, _503133)))], (6108 ^ _292445) ^ [_503470, _503472, _503474] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _503470), 6111 ^ _292445 : [(6112 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_NthRoot_Oroot(_503470, _503472), c_NthRoot_Oroot(_503470, _503474)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _503472, _503474))], (6118 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _503472, _503474), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_NthRoot_Oroot(_503470, _503472), c_NthRoot_Oroot(_503470, _503474)))]]], (6124 ^ _292445) ^ [_503972, _503974] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _503972), 6127 ^ _292445 : [(6128 ^ _292445) ^ [] : [c_NthRoot_Oroot(_503972, _503974) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_503974 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (6134 ^ _292445) ^ [] : [_503974 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(c_NthRoot_Oroot(_503972, _503974) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))]]], (6140 ^ _292445) ^ [_504457, _504459, _504461] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _504457), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _504459, _504461), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_NthRoot_Oroot(_504457, _504459), c_NthRoot_Oroot(_504457, _504461)))], (6150 ^ _292445) ^ [_504798, _504800, _504802] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _504798), 6153 ^ _292445 : [(6154 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_NthRoot_Oroot(_504798, _504800), c_NthRoot_Oroot(_504798, _504802)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _504800, _504802))], (6160 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _504800, _504802), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_NthRoot_Oroot(_504798, _504800), c_NthRoot_Oroot(_504798, _504802)))]]], (6166 ^ _292445) ^ [_505314, _505316, _505318] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _505314), -(c_NthRoot_Oroot(_505314, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _505316), _505318)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_NthRoot_Oroot(_505314, _505316)), c_NthRoot_Oroot(_505314, _505318)))], (6172 ^ _292445) ^ [_505588, _505590, _505592] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _505588), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _505590), -(c_NthRoot_Oroot(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _505588), _505590), _505592) = c_NthRoot_Oroot(_505588, c_NthRoot_Oroot(_505590, _505592)))], (6182 ^ _292445) ^ [_505945, _505947, _505949] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _505945), -(c_NthRoot_Oroot(_505945, c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, _505947, _505949)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, c_NthRoot_Oroot(_505945, _505947), c_NthRoot_Oroot(_505945, _505949)))], (6188 ^ _292445) ^ [_506197, _506199] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _506197), -(c_NthRoot_Oroot(_506197, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _506199)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_NthRoot_Oroot(_506197, _506199)))], (6194 ^ _292445) ^ [_506447, _506449, _506451] : [class_Rings_Olinordered__idom(_506447), c_Orderings_Oord__class_Oless__eq(_506447, c_Groups_Ozero__class_Ozero(_506447), _506449), c_Orderings_Oord__class_Oless__eq(_506447, c_Groups_Ozero__class_Ozero(_506447), _506451), c_Orderings_Oord__class_Oless__eq(_506447, _506451, c_Groups_Oone__class_Oone(_506447)), -(c_Orderings_Oord__class_Oless__eq(_506447, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_506447), _506451), _506449), _506449))], (6212 ^ _292445) ^ [_506990, _506992, _506994] : [class_Rings_Olinordered__idom(_506990), c_Orderings_Oord__class_Oless__eq(_506990, c_Groups_Ozero__class_Ozero(_506990), _506992), c_Orderings_Oord__class_Oless__eq(_506990, c_Groups_Ozero__class_Ozero(_506990), _506994), c_Orderings_Oord__class_Oless__eq(_506990, _506994, c_Groups_Oone__class_Oone(_506990)), -(c_Orderings_Oord__class_Oless__eq(_506990, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_506990), _506992), _506994), _506992))], (6230 ^ _292445) ^ [_507505] : [class_Rings_Olinordered__semidom(_507505), -(c_Orderings_Oord__class_Oless(_507505, c_Groups_Ozero__class_Ozero(_507505), c_Groups_Oplus__class_Oplus(_507505, c_Groups_Oone__class_Oone(_507505), c_Groups_Oone__class_Oone(_507505))))], (6236 ^ _292445) ^ [_507743, _507745, _507747] : [class_Fields_Olinordered__field(_507743), c_Orderings_Oord__class_Oless(_507743, _507745, _507747), -(c_Orderings_Oord__class_Oless(_507743, _507745, c_Rings_Oinverse__class_Odivide(_507743, c_Groups_Oplus__class_Oplus(_507743, _507745, _507747), c_Groups_Oplus__class_Oplus(_507743, c_Groups_Oone__class_Oone(_507743), c_Groups_Oone__class_Oone(_507743)))))], (6246 ^ _292445) ^ [_508100, _508102, _508104] : [class_Fields_Olinordered__field(_508100), c_Orderings_Oord__class_Oless(_508100, _508102, _508104), -(c_Orderings_Oord__class_Oless(_508100, c_Rings_Oinverse__class_Odivide(_508100, c_Groups_Oplus__class_Oplus(_508100, _508102, _508104), c_Groups_Oplus__class_Oplus(_508100, c_Groups_Oone__class_Oone(_508100), c_Groups_Oone__class_Oone(_508100))), _508104))], (6256 ^ _292445) ^ [_508413] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _508413), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _508413)], (6258 ^ _292445) ^ [_508528, _508530] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _508528), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _508530), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_NthRoot_Oroot(_508528, _508530)))], (6268 ^ _292445) ^ [_508839, _508841] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _508839), 6271 ^ _292445 : [(6272 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_NthRoot_Oroot(_508839, _508841), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _508841, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (6278 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _508841, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_NthRoot_Oroot(_508839, _508841), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))]]], (6284 ^ _292445) ^ [_509316, _509318] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _509316), 6287 ^ _292445 : [(6288 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_NthRoot_Oroot(_509316, _509318)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _509318))], (6294 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _509318), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_NthRoot_Oroot(_509316, _509318)))]]], (6300 ^ _292445) ^ [_509793, _509795] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _509793), 6303 ^ _292445 : [(6304 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_NthRoot_Oroot(_509793, _509795)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _509795))], (6310 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _509795), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_NthRoot_Oroot(_509793, _509795)))]]], (6316 ^ _292445) ^ [_510270, _510272] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _510270), 6319 ^ _292445 : [(6320 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_NthRoot_Oroot(_510270, _510272), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _510272, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (6326 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _510272, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_NthRoot_Oroot(_510270, _510272), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))]]], (6332 ^ _292445) ^ [_510747, _510749] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _510747), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _510749), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_NthRoot_Oroot(_510747, _510749)))], (6342 ^ _292445) ^ [_511114, _511116, _511118, _511120, _511122, _511124] : [class_Rings_Olinordered__semiring__1(_511114), c_Orderings_Oord__class_Oless__eq(_511114, _511116, _511118), c_Orderings_Oord__class_Oless__eq(_511114, _511120, _511118), c_Orderings_Oord__class_Oless__eq(_511114, c_Groups_Ozero__class_Ozero(_511114), _511122), c_Orderings_Oord__class_Oless__eq(_511114, c_Groups_Ozero__class_Ozero(_511114), _511124), c_Groups_Oplus__class_Oplus(_511114, _511122, _511124) = c_Groups_Oone__class_Oone(_511114), -(c_Orderings_Oord__class_Oless__eq(_511114, c_Groups_Oplus__class_Oplus(_511114, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_511114), _511122), _511116), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_511114), _511124), _511120)), _511118))], (6368 ^ _292445) ^ [_511912] : [-(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, _511912))))], (6370 ^ _292445) ^ [_512027, _512029] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _512027), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _512029), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_NthRoot_Oroot(_512027, _512029)))], (6380 ^ _292445) ^ [_512352, _512354, _512356] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _512352), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _512354), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _512354, _512356), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_NthRoot_Oroot(_512352, _512354), c_NthRoot_Oroot(_512352, _512356)))], (6394 ^ _292445) ^ [_512788, _512790, _512792] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _512788), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _512790), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _512792), -(c_NthRoot_Oroot(_512788, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _512790), _512792)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_NthRoot_Oroot(_512788, _512790)), c_NthRoot_Oroot(_512788, _512792)))], (6408 ^ _292445) ^ [_513252, _513254, _513256] : [class_Fields_Olinordered__field__inverse__zero(_513252), 6414 ^ _292445 : [(6415 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_513252, c_Groups_Ozero__class_Ozero(_513252), 6413 ^ [_513252, _513254, _513256]))], (6417 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_513252, 6413 ^ [_513252, _513254, _513256], c_Groups_Oone__class_Oone(_513252)))], (6419 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_513252, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_513252), 6413 ^ [_513252, _513254, _513256]), _513254), _513256)]], -(c_Orderings_Oord__class_Oless__eq(_513252, _513254, _513256))], (6423 ^ _292445) ^ [_513852, _513854] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _513852), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _513854), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_NthRoot_Oroot(_513852, _513854)), _513852) = _513854)], (6433 ^ _292445) ^ [_514173, _514175] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _514173), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _514175), -(c_NthRoot_Oroot(_514173, hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _514175), _514173)) = _514175)], (6443 ^ _292445) ^ [_514494, _514496] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _514494), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _514496), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_NthRoot_Oroot(_514494, _514496)), _514494) = _514496)], (6453 ^ _292445) ^ [_514815, _514817] : [class_Rings_Ocomm__semiring__1(_514815), -(hAPP(hAPP(c_Power_Opower__class_Opower(_514815), _514817), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _514817)], (6459 ^ _292445) ^ [_515067, _515069, _515071, _515073] : [class_Rings_Ocomm__semiring__1(_515067), -(hAPP(hAPP(c_Power_Opower__class_Opower(_515067), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_515067), _515069), _515071)), _515073) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_515067), hAPP(hAPP(c_Power_Opower__class_Opower(_515067), _515069), _515073)), hAPP(hAPP(c_Power_Opower__class_Opower(_515067), _515071), _515073)))], (6465 ^ _292445) ^ [_515395, _515397, _515399, _515401] : [class_Rings_Ocomm__semiring__1(_515395), -(hAPP(hAPP(c_Power_Opower__class_Opower(_515395), hAPP(hAPP(c_Power_Opower__class_Opower(_515395), _515397), _515399)), _515401) = hAPP(hAPP(c_Power_Opower__class_Opower(_515395), _515397), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _515399), _515401)))], (6471 ^ _292445) ^ [_515703, _515705, _515707, _515709] : [class_Rings_Ocomm__semiring__1(_515703), -(hAPP(c_Polynomial_Opoly(_515703, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_515703)), _515705), _515707)), _515709) = hAPP(hAPP(c_Power_Opower__class_Opower(_515703), hAPP(c_Polynomial_Opoly(_515703, _515705), _515709)), _515707))], (6477 ^ _292445) ^ [_515997, _515999, _516001] : [class_RealVector_Oreal__normed__div__algebra(_515997), -(c_RealVector_Onorm__class_Onorm(_515997, hAPP(hAPP(c_Power_Opower__class_Opower(_515997), _515999), _516001)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_515997, _515999)), _516001))], (6483 ^ _292445) ^ [_516265, _516267, _516269] : [class_RealVector_Oreal__normed__algebra__1(_516265), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_516265, hAPP(hAPP(c_Power_Opower__class_Opower(_516265), _516267), _516269)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_516265, _516267)), _516269)))], (6489 ^ _292445) ^ [_516521, _516523] : [class_Rings_Ocomm__semiring__1(_516521), -(hAPP(hAPP(c_Power_Opower__class_Opower(_516521), _516523), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_516521))], (6495 ^ _292445) ^ [_516777, _516779, _516781, _516783] : [class_Rings_Ocomm__semiring__1(_516777), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_516777), hAPP(hAPP(c_Power_Opower__class_Opower(_516777), _516779), _516781)), hAPP(hAPP(c_Power_Opower__class_Opower(_516777), _516779), _516783)) = hAPP(hAPP(c_Power_Opower__class_Opower(_516777), _516779), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _516781, _516783)))], (6501 ^ _292445) ^ [_517083, _517085, _517087] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _517083), -(c_NthRoot_Oroot(_517083, hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _517085), _517087)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_NthRoot_Oroot(_517083, _517085)), _517087))], (6507 ^ _292445) ^ [_517351, _517353, _517355] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _517351), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _517353), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _517353), _517351) = _517355, -(c_NthRoot_Oroot(_517351, _517355) = _517353)], (6521 ^ _292445) ^ [_517803, _517805, _517807, _517809] : [class_Rings_Olinordered__semidom(_517803), c_Orderings_Oord__class_Oless(_517803, _517805, _517807), c_Orderings_Oord__class_Oless__eq(_517803, c_Groups_Ozero__class_Ozero(_517803), _517805), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _517809), -(c_Orderings_Oord__class_Oless(_517803, hAPP(hAPP(c_Power_Opower__class_Opower(_517803), _517805), _517809), hAPP(hAPP(c_Power_Opower__class_Opower(_517803), _517807), _517809)))], (6539 ^ _292445) ^ [_518372, _518374, _518376] : [class_Rings_Olinordered__semidom(_518372), c_Orderings_Oord__class_Oless(_518372, c_Groups_Oone__class_Oone(_518372), _518374), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _518376), -(c_Orderings_Oord__class_Oless(_518372, c_Groups_Oone__class_Oone(_518372), hAPP(hAPP(c_Power_Opower__class_Opower(_518372), _518374), _518376)))], (6553 ^ _292445) ^ [_518830, _518832, _518834, _518836] : [class_Rings_Olinordered__semidom(_518830), c_Orderings_Oord__class_Oless(_518830, c_Groups_Oone__class_Oone(_518830), _518832), c_Orderings_Oord__class_Oless__eq(_518830, hAPP(hAPP(c_Power_Opower__class_Opower(_518830), _518832), _518834), hAPP(hAPP(c_Power_Opower__class_Opower(_518830), _518832), _518836)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _518834, _518836))], (6567 ^ _292445) ^ [_519314, _519316, _519318, _519320] : [class_Rings_Olinordered__semidom(_519314), c_Orderings_Oord__class_Oless(_519314, c_Groups_Oone__class_Oone(_519314), _519316), 6574 ^ _292445 : [(6575 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_519314, hAPP(hAPP(c_Power_Opower__class_Opower(_519314), _519316), _519318), hAPP(hAPP(c_Power_Opower__class_Opower(_519314), _519316), _519320)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _519318, _519320))], (6581 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _519318, _519320), -(c_Orderings_Oord__class_Oless__eq(_519314, hAPP(hAPP(c_Power_Opower__class_Opower(_519314), _519316), _519318), hAPP(hAPP(c_Power_Opower__class_Opower(_519314), _519316), _519320)))]]], (6587 ^ _292445) ^ [_519960, _519962, _519964] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _519960), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _519962, _519964)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _519960), _519962)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _519960), _519964)))], (6589 ^ _292445) ^ [_520098, _520100, _520102] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _520098), _520100)), _520102) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _520098), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _520100), _520102)))], (6601 ^ _292445) ^ [_520535, _520537] : [6602 ^ _292445 : [(6603 ^ _292445) ^ [] : [-(_520535 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (6605 ^ _292445) ^ [] : [_520537 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), c_Groups_Oabs__class_Oabs(tc_Int_Oint, _520535)), _520537)))], (6591 ^ _292445) ^ [_520262, _520264] : [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, _520262)), _520264)), _520262 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_520264 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6609 ^ _292445) ^ [_520858, _520860, _520862] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _520858), c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _520858), _520860), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _520858), _520862)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _520860, _520862))], (6629 ^ _292445) ^ [_521494, _521496] : [6630 ^ _292445 : [(6631 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _521494)], (6633 ^ _292445) ^ [] : [_521496 = 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), _521494), _521496)))], (6619 ^ _292445) ^ [_521226, _521228] : [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), _521226), _521228)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _521226)), -(_521228 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6637 ^ _292445) ^ [_521810, _521812, _521814] : [class_Rings_Oring__1__no__zero__divisors(_521810), -(_521812 = c_Groups_Ozero__class_Ozero(_521810)), hAPP(hAPP(c_Power_Opower__class_Opower(_521810), _521812), _521814) = c_Groups_Ozero__class_Ozero(_521810)], (6647 ^ _292445) ^ [_522159, _522161, _522163] : [class_Groups_Omonoid__mult(_522159), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_522159), hAPP(hAPP(c_Power_Opower__class_Opower(_522159), _522161), _522163)), _522161) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_522159), _522161), hAPP(hAPP(c_Power_Opower__class_Opower(_522159), _522161), _522163)))], (6653 ^ _292445) ^ [_522465, _522467, _522469, _522471] : [class_Groups_Ocomm__monoid__mult(_522465), -(hAPP(hAPP(c_Power_Opower__class_Opower(_522465), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_522465), _522467), _522469)), _522471) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_522465), hAPP(hAPP(c_Power_Opower__class_Opower(_522465), _522467), _522471)), hAPP(hAPP(c_Power_Opower__class_Opower(_522465), _522469), _522471)))], (6659 ^ _292445) ^ [_522765, _522767] : [class_Groups_Omonoid__mult(_522765), -(hAPP(hAPP(c_Power_Opower__class_Opower(_522765), c_Groups_Oone__class_Oone(_522765)), _522767) = c_Groups_Oone__class_Oone(_522765))], (6665 ^ _292445) ^ [_523025, _523027, _523029, _523031] : [class_Fields_Ofield__inverse__zero(_523025), -(hAPP(hAPP(c_Power_Opower__class_Opower(_523025), c_Rings_Oinverse__class_Odivide(_523025, _523027, _523029)), _523031) = c_Rings_Oinverse__class_Odivide(_523025, hAPP(hAPP(c_Power_Opower__class_Opower(_523025), _523027), _523031), hAPP(hAPP(c_Power_Opower__class_Opower(_523025), _523029), _523031)))], (6671 ^ _292445) ^ [_523323, _523325, _523327] : [class_Rings_Olinordered__idom(_523323), -(c_Groups_Oabs__class_Oabs(_523323, hAPP(hAPP(c_Power_Opower__class_Opower(_523323), _523325), _523327)) = hAPP(hAPP(c_Power_Opower__class_Opower(_523323), c_Groups_Oabs__class_Oabs(_523323, _523325)), _523327))], (6677 ^ _292445) ^ [_523609, _523611, _523613, _523615] : [class_Groups_Omonoid__mult(_523609), -(hAPP(hAPP(c_Power_Opower__class_Opower(_523609), _523611), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _523613), _523615)) = hAPP(hAPP(c_Power_Opower__class_Opower(_523609), hAPP(hAPP(c_Power_Opower__class_Opower(_523609), _523611), _523613)), _523615))], (6683 ^ _292445) ^ [_523889, _523891] : [class_Groups_Omonoid__mult(_523889), -(hAPP(hAPP(c_Power_Opower__class_Opower(_523889), _523891), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _523891)], (6689 ^ _292445) ^ [_524141, _524143, _524145, _524147] : [class_Rings_Olinordered__semidom(_524141), c_Orderings_Oord__class_Oless__eq(_524141, _524143, _524145), c_Orderings_Oord__class_Oless__eq(_524141, c_Groups_Ozero__class_Ozero(_524141), _524143), -(c_Orderings_Oord__class_Oless__eq(_524141, hAPP(hAPP(c_Power_Opower__class_Opower(_524141), _524143), _524147), hAPP(hAPP(c_Power_Opower__class_Opower(_524141), _524145), _524147)))], (6703 ^ _292445) ^ [_524611, _524613, _524615] : [class_Rings_Olinordered__semidom(_524611), c_Orderings_Oord__class_Oless__eq(_524611, c_Groups_Ozero__class_Ozero(_524611), _524613), -(c_Orderings_Oord__class_Oless__eq(_524611, c_Groups_Ozero__class_Ozero(_524611), hAPP(hAPP(c_Power_Opower__class_Opower(_524611), _524613), _524615)))], (6713 ^ _292445) ^ [_524960, _524962, _524964] : [class_Rings_Olinordered__semidom(_524960), c_Orderings_Oord__class_Oless(_524960, c_Groups_Ozero__class_Ozero(_524960), _524962), -(c_Orderings_Oord__class_Oless(_524960, c_Groups_Ozero__class_Ozero(_524960), hAPP(hAPP(c_Power_Opower__class_Opower(_524960), _524962), _524964)))], (6723 ^ _292445) ^ [_525309, _525311, _525313] : [class_Rings_Olinordered__semidom(_525309), c_Orderings_Oord__class_Oless__eq(_525309, c_Groups_Oone__class_Oone(_525309), _525311), -(c_Orderings_Oord__class_Oless__eq(_525309, c_Groups_Oone__class_Oone(_525309), hAPP(hAPP(c_Power_Opower__class_Opower(_525309), _525311), _525313)))], (6733 ^ _292445) ^ [_525658, _525660, _525662] : [class_Power_Opower(_525658), class_Rings_Omult__zero(_525658), class_Rings_Ono__zero__divisors(_525658), class_Rings_Ozero__neq__one(_525658), 6748 ^ _292445 : [(6749 ^ _292445) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_525658), _525660), _525662) = c_Groups_Ozero__class_Ozero(_525658), 6752 ^ _292445 : [(6753 ^ _292445) ^ [] : [-(_525660 = c_Groups_Ozero__class_Ozero(_525658))], (6755 ^ _292445) ^ [] : [_525662 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (6757 ^ _292445) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_525658), _525660), _525662) = c_Groups_Ozero__class_Ozero(_525658)), _525660 = c_Groups_Ozero__class_Ozero(_525658), -(_525662 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (6767 ^ _292445) ^ [_526641, _526643, _526645, _526647] : [class_Rings_Olinordered__semidom(_526641), c_Orderings_Oord__class_Oless(_526641, c_Groups_Oone__class_Oone(_526641), _526643), 6774 ^ _292445 : [(6775 ^ _292445) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_526641), _526643), _526645) = hAPP(hAPP(c_Power_Opower__class_Opower(_526641), _526643), _526647), -(_526645 = _526647)], (6781 ^ _292445) ^ [] : [_526645 = _526647, -(hAPP(hAPP(c_Power_Opower__class_Opower(_526641), _526643), _526645) = hAPP(hAPP(c_Power_Opower__class_Opower(_526641), _526643), _526647))]]], (6787 ^ _292445) ^ [_527310, _527312, _527314, _527316] : [class_Fields_Ofield(_527310), -(_527312 = c_Groups_Ozero__class_Ozero(_527310)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_527310), c_Rings_Oinverse__class_Odivide(_527310, _527314, _527312)), _527316) = c_Rings_Oinverse__class_Odivide(_527310, hAPP(hAPP(c_Power_Opower__class_Opower(_527310), _527314), _527316), hAPP(hAPP(c_Power_Opower__class_Opower(_527310), _527312), _527316)))], (6797 ^ _292445) ^ [_527698, _527700] : [class_Power_Opower(_527698), -(hAPP(hAPP(c_Power_Opower__class_Opower(_527698), _527700), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_527698))], (6803 ^ _292445) ^ [_527954, _527956, _527958, _527960] : [class_Groups_Omonoid__mult(_527954), -(hAPP(hAPP(c_Power_Opower__class_Opower(_527954), _527956), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _527958, _527960)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_527954), hAPP(hAPP(c_Power_Opower__class_Opower(_527954), _527956), _527958)), hAPP(hAPP(c_Power_Opower__class_Opower(_527954), _527956), _527960)))], (6809 ^ _292445) ^ [_528260, _528262, _528264] : [class_Fields_Ofield__inverse__zero(_528260), -(c_Rings_Oinverse__class_Odivide(_528260, c_Groups_Oone__class_Oone(_528260), hAPP(hAPP(c_Power_Opower__class_Opower(_528260), _528262), _528264)) = hAPP(hAPP(c_Power_Opower__class_Opower(_528260), c_Rings_Oinverse__class_Odivide(_528260, c_Groups_Oone__class_Oone(_528260), _528262)), _528264))], (6815 ^ _292445) ^ [_528558, _528560, _528562, _528564] : [class_Rings_Olinordered__semidom(_528558), c_Orderings_Oord__class_Oless(_528558, hAPP(hAPP(c_Power_Opower__class_Opower(_528558), _528560), _528562), hAPP(hAPP(c_Power_Opower__class_Opower(_528558), _528564), _528562)), c_Orderings_Oord__class_Oless__eq(_528558, c_Groups_Ozero__class_Ozero(_528558), _528564), -(c_Orderings_Oord__class_Oless(_528558, _528560, _528564))], (6829 ^ _292445) ^ [_529028, _529030, _529032] : [class_Rings_Olinordered__semidom(_529028), c_Orderings_Oord__class_Oless(_529028, c_Groups_Oone__class_Oone(_529028), _529030), -(c_Orderings_Oord__class_Oless(_529028, c_Groups_Oone__class_Oone(_529028), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_529028), _529030), hAPP(hAPP(c_Power_Opower__class_Opower(_529028), _529030), _529032))))], (6839 ^ _292445) ^ [_529393, _529395, _529397] : [class_Rings_Olinordered__semidom(_529393), c_Orderings_Oord__class_Oless(_529393, c_Groups_Oone__class_Oone(_529393), _529395), -(c_Orderings_Oord__class_Oless(_529393, hAPP(hAPP(c_Power_Opower__class_Opower(_529393), _529395), _529397), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_529393), _529395), hAPP(hAPP(c_Power_Opower__class_Opower(_529393), _529395), _529397))))], (6849 ^ _292445) ^ [_529756, _529758] : [class_Power_Opower(_529756), class_Rings_Osemiring__0(_529756), 6856 ^ _292445 : [(6857 ^ _292445) ^ [] : [_529758 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_529756), c_Groups_Ozero__class_Ozero(_529756)), _529758) = c_Groups_Oone__class_Oone(_529756))], (6863 ^ _292445) ^ [] : [-(_529758 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_529756), c_Groups_Ozero__class_Ozero(_529756)), _529758) = c_Groups_Ozero__class_Ozero(_529756))]]], (6869 ^ _292445) ^ [_530371, _530373, _530375] : [class_Rings_Olinordered__idom(_530371), -(c_Orderings_Oord__class_Oless__eq(_530371, c_Groups_Ozero__class_Ozero(_530371), hAPP(hAPP(c_Power_Opower__class_Opower(_530371), c_Groups_Oabs__class_Oabs(_530371, _530373)), _530375)))], (6875 ^ _292445) ^ [_530641, _530643, _530645, _530647] : [class_Rings_Olinordered__semidom(_530641), c_Orderings_Oord__class_Oless(_530641, c_Groups_Oone__class_Oone(_530641), _530643), 6882 ^ _292445 : [(6883 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_530641, hAPP(hAPP(c_Power_Opower__class_Opower(_530641), _530643), _530645), hAPP(hAPP(c_Power_Opower__class_Opower(_530641), _530643), _530647)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _530645, _530647))], (6889 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _530645, _530647), -(c_Orderings_Oord__class_Oless(_530641, hAPP(hAPP(c_Power_Opower__class_Opower(_530641), _530643), _530645), hAPP(hAPP(c_Power_Opower__class_Opower(_530641), _530643), _530647)))]]], (6895 ^ _292445) ^ [_531316, _531318, _531320, _531322] : [class_Rings_Olinordered__semidom(_531316), c_Orderings_Oord__class_Oless(_531316, c_Groups_Oone__class_Oone(_531316), _531318), c_Orderings_Oord__class_Oless(_531316, hAPP(hAPP(c_Power_Opower__class_Opower(_531316), _531318), _531320), hAPP(hAPP(c_Power_Opower__class_Opower(_531316), _531318), _531322)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _531320, _531322))], (6909 ^ _292445) ^ [_531800, _531802, _531804, _531806] : [class_Rings_Olinordered__semidom(_531800), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _531802, _531804), c_Orderings_Oord__class_Oless(_531800, c_Groups_Oone__class_Oone(_531800), _531806), -(c_Orderings_Oord__class_Oless(_531800, hAPP(hAPP(c_Power_Opower__class_Opower(_531800), _531806), _531802), hAPP(hAPP(c_Power_Opower__class_Opower(_531800), _531806), _531804)))], (6923 ^ _292445) ^ [_532284, _532286, _532288, _532290] : [class_Rings_Olinordered__semidom(_532284), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _532286, _532288), c_Orderings_Oord__class_Oless__eq(_532284, c_Groups_Oone__class_Oone(_532284), _532290), -(c_Orderings_Oord__class_Oless__eq(_532284, hAPP(hAPP(c_Power_Opower__class_Opower(_532284), _532290), _532286), hAPP(hAPP(c_Power_Opower__class_Opower(_532284), _532290), _532288)))], (6937 ^ _292445) ^ [_532754, _532756, _532758] : [class_Rings_Olinordered__semidom(_532754), c_Orderings_Oord__class_Oless(_532754, c_Groups_Ozero__class_Ozero(_532754), _532756), c_Orderings_Oord__class_Oless(_532754, _532756, c_Groups_Oone__class_Oone(_532754)), -(c_Orderings_Oord__class_Oless(_532754, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_532754), _532756), hAPP(hAPP(c_Power_Opower__class_Opower(_532754), _532756), _532758)), hAPP(hAPP(c_Power_Opower__class_Opower(_532754), _532756), _532758)))], (6951 ^ _292445) ^ [_533244, _533246, _533248, _533250] : [class_Rings_Olinordered__semidom(_533244), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _533246, _533248), c_Orderings_Oord__class_Oless(_533244, c_Groups_Ozero__class_Ozero(_533244), _533250), c_Orderings_Oord__class_Oless(_533244, _533250, c_Groups_Oone__class_Oone(_533244)), -(c_Orderings_Oord__class_Oless(_533244, hAPP(hAPP(c_Power_Opower__class_Opower(_533244), _533250), _533248), hAPP(hAPP(c_Power_Opower__class_Opower(_533244), _533250), _533246)))], (6969 ^ _292445) ^ [_533831, _533833, _533835, _533837] : [class_Rings_Olinordered__semidom(_533831), hAPP(hAPP(c_Power_Opower__class_Opower(_533831), _533833), _533835) = hAPP(hAPP(c_Power_Opower__class_Opower(_533831), _533837), _533835), c_Orderings_Oord__class_Oless__eq(_533831, c_Groups_Ozero__class_Ozero(_533831), _533833), c_Orderings_Oord__class_Oless__eq(_533831, c_Groups_Ozero__class_Ozero(_533831), _533837), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _533835), -(_533833 = _533837)], (6991 ^ _292445) ^ [_534513, _534515, _534517, _534519] : [class_Rings_Olinordered__semidom(_534513), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _534515, _534517), c_Orderings_Oord__class_Oless__eq(_534513, c_Groups_Ozero__class_Ozero(_534513), _534519), c_Orderings_Oord__class_Oless__eq(_534513, _534519, c_Groups_Oone__class_Oone(_534513)), -(c_Orderings_Oord__class_Oless__eq(_534513, hAPP(hAPP(c_Power_Opower__class_Opower(_534513), _534519), _534517), hAPP(hAPP(c_Power_Opower__class_Opower(_534513), _534519), _534515)))], (7009 ^ _292445) ^ [_535072, _535074] : [-(_535072 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), -(_535074 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), _535072), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), 7016 ^ [_535072, _535074]), _535074)))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (7020 ^ _292445) ^ [_535480] : [class_Power_Opower(_535480), -(c_Power_Opower__class_Opower(_535480) = c_Power_Opower_Opower(_535480, c_Groups_Oone__class_Oone(_535480), c_Groups_Otimes__class_Otimes(_535480)))], (7036 ^ _292445) ^ [_535999, _536001] : [7037 ^ _292445 : [(7038 ^ _292445) ^ [] : [_536001 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (7040 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _535999)]], -(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), _535999), _536001)))], (7026 ^ _292445) ^ [_535731, _535733] : [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), _535731), _535733)), -(_535733 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _535731))], (7044 ^ _292445) ^ [_536286, _536288] : [-(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, _536286)), _536288)))], (7046 ^ _292445) ^ [_536419, _536421, _536423] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _536419, _536421), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _536419, _536423), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _536421, _536423)))], (7052 ^ _292445) ^ [_536669, _536671, _536673] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _536669, _536671), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _536673), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _536673), _536669), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _536673), _536671)))], (7062 ^ _292445) ^ [_537036, _537038, _537040, _537042] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _537036, _537038), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _537040, _537042), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _537036, _537040), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _537038, _537042)))], (7072 ^ _292445) ^ [_537348] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _537348) = _537348)], (7074 ^ _292445) ^ [_537430] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _537430, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _537430)], (7076 ^ _292445) ^ [_537540, _537542, _537544] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _537540), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _537542, _537544)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _537540), _537542), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _537540), _537544)))], (7078 ^ _292445) ^ [_537676, _537678, _537680] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _537676, _537678)), _537680) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _537676), _537680), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _537678), _537680)))], (7080 ^ _292445) ^ [_537812, _537814, _537816] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _537812), _537814)), _537816) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _537812), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _537814), _537816)))], (7082 ^ _292445) ^ [_537932, _537934] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _537932), _537934) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _537934), _537932))], (7084 ^ _292445) ^ [_538053, _538055] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _538053, _538055)), -(_538053 = _538055), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _538055, _538053))], (7094 ^ _292445) ^ [_538387, _538389] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _538387, _538389), 7097 ^ _292445 : [(7098 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _538387, _538389))], (7100 ^ _292445) ^ [] : [_538387 = _538389]]], (7102 ^ _292445) ^ [_538629, _538631] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _538629, _538631)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _538629, _538631), -(_538629 = _538631)], (7112 ^ _292445) ^ [_538966, _538968] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _538966, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _538968, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _538966, _538968))], (7118 ^ _292445) ^ [_539140, _539142] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _539140, _539142), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _539140, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _539142, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (7134 ^ _292445) ^ [_539657, _539659] : [7135 ^ _292445 : [(7136 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _539657, _539659)], (7138 ^ _292445) ^ [] : [_539657 = _539659]], -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _539657, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _539659, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (7124 ^ _292445) ^ [_539393, _539395] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _539393, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _539395, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _539393, _539395)), -(_539393 = _539395)], (7142 ^ _292445) ^ [_539984, _539986] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _539984, c_Groups_Oone__class_Oone(tc_Int_Oint)), _539986), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _539984, _539986))], (7148 ^ _292445) ^ [_540158, _540160] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _540158, _540160), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _540158, c_Groups_Oone__class_Oone(tc_Int_Oint)), _540160))], (7154 ^ _292445) ^ [_540397] : [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), _540397), _540397), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _540397, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (7160 ^ _292445) ^ [_540573] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _540573, 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), _540573), _540573), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (7166 ^ _292445) ^ [_540785] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _540785), -(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), _540785)))], (7172 ^ _292445) ^ [_541001, _541003] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _541001), 7175 ^ _292445 : [(7176 ^ _292445) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _541001), _541003) = c_Groups_Oone__class_Oone(tc_Int_Oint), 7179 ^ _292445 : [(7180 ^ _292445) ^ [] : [-(_541001 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (7182 ^ _292445) ^ [] : [-(_541003 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (7184 ^ _292445) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _541001), _541003) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _541001 = c_Groups_Oone__class_Oone(tc_Int_Oint), _541003 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (7194 ^ _292445) ^ [_541639, _541641] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _541639, _541641), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _541639, c_Groups_Oone__class_Oone(tc_Int_Oint)), _541641))], (7200 ^ _292445) ^ [_541831] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _541831), _541831) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (7202 ^ _292445) ^ [_541946, _541948] : [c_Groups_Oabs__class_Oabs(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _541946), _541948)) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(c_Groups_Oabs__class_Oabs(tc_Int_Oint, _541946) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (7208 ^ _292445) ^ [_542151] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _542151), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _542151)], (7210 ^ _292445) ^ [_542235] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _542235) = _542235)], (7212 ^ _292445) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (7214 ^ _292445) ^ [_542412] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oabs__class_Oabs(tc_Int_Oint, _542412), c_Groups_Oone__class_Oone(tc_Int_Oint)), -(_542412 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (7220 ^ _292445) ^ [_542576] : [_542576 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oabs__class_Oabs(tc_Int_Oint, _542576), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (7226 ^ _292445) ^ [_542805] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _542805), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _542805))], (7232 ^ _292445) ^ [_542965] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _542965), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _542965))], (7238 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (7240 ^ _292445) ^ [_543241, _543243, _543245, _543247] : [-(hAPP(hAPP(c_Power_Opower_Opower(_543241, _543243, _543245), _543247), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _543243)], (7242 ^ _292445) ^ [_543378, _543380, _543382] : [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), _543378), _543380), _543382)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _543382, _543378), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _543378), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _543380))], (7256 ^ _292445) ^ [_543822, _543824, _543826] : [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), _543822), _543824), _543826), 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), _543826), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _543822), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _543824, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (7270 ^ _292445) ^ [_544294, _544296, _544298, _544300, _544302] : [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), _544294), _544296), _544298), c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _544294), _544300), _544302)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _544298), c_Orderings_Oord__class_Oless(tc_Int_Oint, _544298, _544294), c_Orderings_Oord__class_Oless(tc_Int_Oint, _544302, _544294), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _544296, _544300))], (7288 ^ _292445) ^ [_544846] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _544846, _544846))], (7290 ^ _292445) ^ [_544954, _544956] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _544954, _544956)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _544956, _544954))], (7296 ^ _292445) ^ [_545183, _545185, _545187] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _545183, _545185), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _545185, _545187), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _545183, _545187))], (7306 ^ _292445) ^ [_545498, _545500] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _545498, _545500), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _545500, _545498), -(_545498 = _545500)], (7316 ^ _292445) ^ [_545800, _545802, _545804] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _545800, _545802), _545804) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _545800, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _545802, _545804)))], (7318 ^ _292445) ^ [_545926, _545928, _545930] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _545926, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _545928, _545930)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _545928, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _545926, _545930)))], (7320 ^ _292445) ^ [_546038, _546040] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _546038, _546040) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _546040, _546038))], (7322 ^ _292445) ^ [_546169, _546171, _546173] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _546169, _546171), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _546173, _546169), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _546173, _546171)))], (7328 ^ _292445) ^ [_546419, _546421, _546423] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _546419), _546419 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _546421, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _546419), _546423)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _546421, _546419), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _546423))], (7342 ^ _292445) ^ [_546861, _546863, _546865] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _546861), _546861 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _546863, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _546861), _546865)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _546863), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _546865, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (7356 ^ _292445) ^ [_547345, _547347, _547349, _547351, _547353, _547355] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _547345), _547347), _547349) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _547351), _547353), _547355), 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), _547351), _547353), _547355), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _547349, _547345), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _547355), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _547351), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _547351, _547345), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _547353, _547347))], (7382 ^ _292445) ^ [_548218, _548220, _548222, _548224, _548226] : [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), _548218), _548220), _548222), c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _548218), _548224), _548226)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _548226, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _548218, _548226), c_Orderings_Oord__class_Oless(tc_Int_Oint, _548218, _548222), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _548224, _548220))], (7400 ^ _292445) ^ [_548855, _548857, _548859, _548861, _548863, _548865] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _548855), _548857), _548859) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _548861), _548863), _548865), 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), _548861), _548863), _548865)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _548865, _548861), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _548859), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _548861), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _548861, _548855), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _548857, _548863))], (7426 ^ _292445) ^ [_549686, _549688] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _549686), -(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), _549686), _549688)))], (7432 ^ _292445) ^ [_549912, _549914] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _549912), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _549914), -(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), _549912), _549914)))], (7442 ^ _292445) ^ [_550229, _550231] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _550229), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _550231), -(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, _550229, _550231)))], (7452 ^ _292445) ^ [] : [-(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)))], (7454 ^ _292445) ^ [] : [-(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)))], (7456 ^ _292445) ^ [_550648, _550650] : [-(hBOOL(hAPP(_550648, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_550648, _550650)), 7464 ^ _292445 : [(7465 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, 7463 ^ [_550648, _550650], _550650))], (7473 ^ _292445) ^ [] : [-(hBOOL(hAPP(_550648, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, 7463 ^ [_550648, _550650], c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (7467 ^ _292445) ^ [_551084] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _551084, 7463 ^ [_550648, _550650]), hBOOL(hAPP(_550648, _551084))]]], (7475 ^ _292445) ^ [_551397, _551399] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _551397), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _551399), 7483 ^ _292445 : [(7484 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 7482 ^ [_551397, _551399]))], (7486 ^ _292445) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), 7482 ^ [_551397, _551399]), _551397) = _551399)]]], (7488 ^ _292445) ^ [_551866, _551868] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _551866), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _551868), 7496 ^ _292445 : [(7497 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 7495 ^ [_551866, _551868]))], (7499 ^ _292445) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), 7495 ^ [_551866, _551868]), _551866) = _551868)], (7501 ^ _292445) ^ [_552370] : [-(_552370 = 7495 ^ [_551866, _551868]), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _552370), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _552370), _551866) = _551868]]], (7511 ^ _292445) ^ [_552710] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _552710), -(c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _552710, c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatceiling(_552710), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (7517 ^ _292445) ^ [_552926] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _552926), -(c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _552926, c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatfloor(_552926), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (7523 ^ _292445) ^ [_553170, _553172, _553174] : [class_Groups_Omonoid__mult(_553170), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _553172), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_553170), hAPP(hAPP(c_Power_Opower__class_Opower(_553170), _553174), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _553172, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _553174) = hAPP(hAPP(c_Power_Opower__class_Opower(_553170), _553174), _553172))], (7533 ^ _292445) ^ [_553549, _553551, _553553] : [class_Groups_Oordered__ab__group__add(_553549), 7536 ^ _292445 : [(7537 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_553549, _553551, _553553), -(c_Orderings_Oord__class_Oless__eq(_553549, c_Groups_Ominus__class_Ominus(_553549, _553551, _553553), c_Groups_Ozero__class_Ozero(_553549)))], (7543 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_553549, c_Groups_Ominus__class_Ominus(_553549, _553551, _553553), c_Groups_Ozero__class_Ozero(_553549)), -(c_Orderings_Oord__class_Oless__eq(_553549, _553551, _553553))]]], (7549 ^ _292445) ^ [_554061, _554063, _554065] : [class_Groups_Oordered__ab__group__add(_554061), 7552 ^ _292445 : [(7553 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_554061, _554063, _554065), -(c_Orderings_Oord__class_Oless(_554061, c_Groups_Ominus__class_Ominus(_554061, _554063, _554065), c_Groups_Ozero__class_Ozero(_554061)))], (7559 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_554061, c_Groups_Ominus__class_Ominus(_554061, _554063, _554065), c_Groups_Ozero__class_Ozero(_554061)), -(c_Orderings_Oord__class_Oless(_554061, _554063, _554065))]]], (7565 ^ _292445) ^ [_554530] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_RComplete_Onatfloor(_554530)))], (7567 ^ _292445) ^ [_554654, _554656, _554658] : [class_RealVector_Oreal__normed__vector(_554654), -(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(_554654, _554656), c_RealVector_Onorm__class_Onorm(_554654, _554658))), c_RealVector_Onorm__class_Onorm(_554654, c_Groups_Ominus__class_Ominus(_554654, _554656, _554658))))], (7573 ^ _292445) ^ [] : [-(c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (7575 ^ _292445) ^ [_554934] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_RComplete_Onatceiling(_554934)))], (7577 ^ _292445) ^ [_555044, _555046] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _555044, _555046), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_555044), c_RComplete_Onatceiling(_555046)))], (7583 ^ _292445) ^ [] : [-(c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (7585 ^ _292445) ^ [_555319, _555321] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _555319, _555321), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatfloor(_555319), c_RComplete_Onatfloor(_555321)))], (7591 ^ _292445) ^ [_555583, _555585, _555587, _555589, _555591] : [class_Groups_Oordered__ab__group__add(_555583), c_Groups_Ominus__class_Ominus(_555583, _555585, _555587) = c_Groups_Ominus__class_Ominus(_555583, _555589, _555591), 7598 ^ _292445 : [(7599 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_555583, _555585, _555587), -(c_Orderings_Oord__class_Oless__eq(_555583, _555589, _555591))], (7605 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_555583, _555589, _555591), -(c_Orderings_Oord__class_Oless__eq(_555583, _555585, _555587))]]], (7611 ^ _292445) ^ [_556226, _556228, _556230] : [class_RealVector_Oreal__normed__vector(_556226), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_556226, _556228), c_RealVector_Onorm__class_Onorm(_556226, _556230)), c_RealVector_Onorm__class_Onorm(_556226, c_Groups_Ominus__class_Ominus(_556226, _556228, _556230))))], (7617 ^ _292445) ^ [_556490, _556492, _556494] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _556490, _556492), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _556490, _556494), 7624 ^ _292445 : [(7625 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _556492, _556490), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _556494, _556490)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _556492, _556494))], (7631 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _556492, _556494), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _556492, _556490), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _556494, _556490)))]]], (7637 ^ _292445) ^ [_557107, _557109, _557111] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _557107, _557109), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _557107, _557111), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _557109, _557107), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _557111, _557107)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _557109, _557111))], (7647 ^ _292445) ^ [_557466, _557468, _557470] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _557466, _557468), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _557466, _557470), 7654 ^ _292445 : [(7655 ^ _292445) ^ [] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _557468, _557466) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _557470, _557466), -(_557468 = _557470)], (7661 ^ _292445) ^ [] : [_557468 = _557470, -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _557468, _557466) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _557470, _557466))]]], (7667 ^ _292445) ^ [_558063, _558065] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _558063, _558065), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _558065, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _558065, _558063)) = _558063)], (7673 ^ _292445) ^ [_558305, _558307, _558309] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _558305, _558307), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _558305, _558309), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _558307, _558309)))], (7679 ^ _292445) ^ [_558555, _558557, _558559] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _558555, _558557), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _558559, _558557), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _558559, _558555)))], (7685 ^ _292445) ^ [_558776, _558778] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _558776, _558778), _558776))], (7687 ^ _292445) ^ [_558904, _558906, _558908] : [class_Groups_Ogroup__add(_558904), -(c_Groups_Ominus__class_Ominus(_558904, c_Groups_Oplus__class_Oplus(_558904, _558906, _558908), _558908) = _558906)], (7693 ^ _292445) ^ [_559148, _559150, _559152] : [class_Groups_Ogroup__add(_559148), -(c_Groups_Oplus__class_Oplus(_559148, c_Groups_Ominus__class_Ominus(_559148, _559150, _559152), _559152) = _559150)], (7699 ^ _292445) ^ [_559377, _559379, _559381] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _559377, _559379), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _559381, _559379)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _559377, _559381))], (7701 ^ _292445) ^ [_559503, _559505, _559507] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _559503, _559505), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _559503, _559507)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _559505, _559507))], (7703 ^ _292445) ^ [_559629, _559631, _559633] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _559629, _559631), _559633) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _559629, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _559631, _559633)))], (7705 ^ _292445) ^ [_559741, _559743] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _559741, _559743), _559741) = _559743)], (7707 ^ _292445) ^ [_559843, _559845] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _559843, _559845), _559845) = _559843)], (7709 ^ _292445) ^ [_559988, _559990, _559992, _559994] : [class_Rings_Odivision__ring(_559988), -(c_Rings_Oinverse__class_Odivide(_559988, c_Groups_Ominus__class_Ominus(_559988, _559990, _559992), _559994) = c_Groups_Ominus__class_Ominus(_559988, c_Rings_Oinverse__class_Odivide(_559988, _559990, _559994), c_Rings_Oinverse__class_Odivide(_559988, _559992, _559994)))], (7715 ^ _292445) ^ [_560276, _560278, _560280, _560282] : [class_RealVector_Oreal__normed__field(_560276), -(c_Rings_Oinverse__class_Odivide(_560276, c_Groups_Ominus__class_Ominus(_560276, _560278, _560280), _560282) = c_Groups_Ominus__class_Ominus(_560276, c_Rings_Oinverse__class_Odivide(_560276, _560278, _560282), c_Rings_Oinverse__class_Odivide(_560276, _560280, _560282)))], (7721 ^ _292445) ^ [_560550, _560552, _560554] : [class_RealVector_Oreal__normed__vector(_560550), -(c_RealVector_Onorm__class_Onorm(_560550, c_Groups_Ominus__class_Ominus(_560550, _560552, _560554)) = c_RealVector_Onorm__class_Onorm(_560550, c_Groups_Ominus__class_Ominus(_560550, _560554, _560552)))], (7727 ^ _292445) ^ [_560820, _560822, _560824, _560826] : [class_Rings_Ocomm__ring(_560820), -(hAPP(c_Polynomial_Opoly(_560820, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_560820), _560822, _560824)), _560826) = c_Groups_Ominus__class_Ominus(_560820, hAPP(c_Polynomial_Opoly(_560820, _560822), _560826), hAPP(c_Polynomial_Opoly(_560820, _560824), _560826)))], (7733 ^ _292445) ^ [_561138, _561140, _561142, _561144, _561146] : [class_Groups_Oab__group__add(_561138), c_Groups_Ominus__class_Ominus(_561138, _561140, _561142) = c_Groups_Ominus__class_Ominus(_561138, _561144, _561146), 7740 ^ _292445 : [(7741 ^ _292445) ^ [] : [_561140 = _561142, -(_561144 = _561146)], (7747 ^ _292445) ^ [] : [_561144 = _561146, -(_561140 = _561142)]]], (7753 ^ _292445) ^ [_561803, _561805, _561807, _561809, _561811] : [class_Groups_Oab__group__add(_561803), -(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_561803), c_Polynomial_OpCons(_561803, _561805, _561807), c_Polynomial_OpCons(_561803, _561809, _561811)) = c_Polynomial_OpCons(_561803, c_Groups_Ominus__class_Ominus(_561803, _561805, _561809), c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_561803), _561807, _561811)))], (7759 ^ _292445) ^ [_562084, _562086, _562088] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _562084, _562086), _562088) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _562084, _562088), _562086))], (7761 ^ _292445) ^ [] : [-(c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7763 ^ _292445) ^ [] : [-(c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7765 ^ _292445) ^ [_562359, _562361, _562363, _562365, _562367] : [class_Groups_Oordered__ab__group__add(_562359), c_Groups_Ominus__class_Ominus(_562359, _562361, _562363) = c_Groups_Ominus__class_Ominus(_562359, _562365, _562367), 7772 ^ _292445 : [(7773 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_562359, _562361, _562363), -(c_Orderings_Oord__class_Oless(_562359, _562365, _562367))], (7779 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_562359, _562365, _562367), -(c_Orderings_Oord__class_Oless(_562359, _562361, _562363))]]], (7785 ^ _292445) ^ [_563002, _563004, _563006] : [class_Groups_Ogroup__add(_563002), 7788 ^ _292445 : [(7789 ^ _292445) ^ [] : [c_Groups_Ominus__class_Ominus(_563002, _563004, _563006) = c_Groups_Ozero__class_Ozero(_563002), -(_563004 = _563006)], (7795 ^ _292445) ^ [] : [_563004 = _563006, -(c_Groups_Ominus__class_Ominus(_563002, _563004, _563006) = c_Groups_Ozero__class_Ozero(_563002))]]], (7801 ^ _292445) ^ [_563508, _563510, _563512] : [class_Groups_Oab__group__add(_563508), 7804 ^ _292445 : [(7805 ^ _292445) ^ [] : [_563510 = _563512, -(c_Groups_Ominus__class_Ominus(_563508, _563510, _563512) = c_Groups_Ozero__class_Ozero(_563508))], (7811 ^ _292445) ^ [] : [c_Groups_Ominus__class_Ominus(_563508, _563510, _563512) = c_Groups_Ozero__class_Ozero(_563508), -(_563510 = _563512)]]], (7817 ^ _292445) ^ [_564000, _564002] : [class_Groups_Ogroup__add(_564000), -(c_Groups_Ominus__class_Ominus(_564000, _564002, _564002) = c_Groups_Ozero__class_Ozero(_564000))], (7823 ^ _292445) ^ [_564220, _564222] : [class_Groups_Ogroup__add(_564220), -(c_Groups_Ominus__class_Ominus(_564220, _564222, c_Groups_Ozero__class_Ozero(_564220)) = _564222)], (7829 ^ _292445) ^ [_564454, _564456, _564458] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _564454, _564456), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _564454, _564458), _564456))], (7835 ^ _292445) ^ [_564696, _564698, _564700] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _564696, _564698), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _564696, _564700), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _564700, _564698), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _564700, _564696)))], (7845 ^ _292445) ^ [_565041, _565043, _565045] : [class_Groups_Oordered__ab__group__add__abs(_565041), -(c_Groups_Oabs__class_Oabs(_565041, c_Groups_Ominus__class_Ominus(_565041, _565043, _565045)) = c_Groups_Oabs__class_Oabs(_565041, c_Groups_Ominus__class_Ominus(_565041, _565045, _565043)))], (7851 ^ _292445) ^ [_565283, _565285] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _565283, _565285) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _565285, _565283) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_565283 = _565285)], (7861 ^ _292445) ^ [_565569] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _565569, _565569) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7863 ^ _292445) ^ [_565651] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _565651, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _565651)], (7865 ^ _292445) ^ [_565733] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _565733) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7867 ^ _292445) ^ [_565872, _565874, _565876, _565878] : [class_RealVector_Oreal__normed__algebra(_565872), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_565872), c_Groups_Ominus__class_Ominus(_565872, _565874, _565876)), _565878) = c_Groups_Ominus__class_Ominus(_565872, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_565872), _565874), _565878), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_565872), _565876), _565878)))], (7873 ^ _292445) ^ [_566184, _566186, _566188, _566190] : [class_RealVector_Oreal__normed__algebra(_566184), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_566184), c_Groups_Ominus__class_Ominus(_566184, _566186, _566188)), _566190) = c_Groups_Ominus__class_Ominus(_566184, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_566184), _566186), _566190), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_566184), _566188), _566190)))], (7879 ^ _292445) ^ [_566496, _566498, _566500, _566502] : [class_RealVector_Oreal__normed__algebra(_566496), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_566496), _566498), c_Groups_Ominus__class_Ominus(_566496, _566500, _566502)) = c_Groups_Ominus__class_Ominus(_566496, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_566496), _566498), _566500), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_566496), _566498), _566502)))], (7885 ^ _292445) ^ [_566808, _566810, _566812, _566814] : [class_RealVector_Oreal__normed__algebra(_566808), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_566808), _566810), c_Groups_Ominus__class_Ominus(_566808, _566812, _566814)) = c_Groups_Ominus__class_Ominus(_566808, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_566808), _566810), _566812), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_566808), _566810), _566814)))], (7891 ^ _292445) ^ [_567091, _567093, _567095] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _567091), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _567093, _567095)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _567091), _567093), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _567091), _567095)))], (7893 ^ _292445) ^ [_567227, _567229, _567231] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _567227, _567229)), _567231) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _567227), _567231), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _567229), _567231)))], (7895 ^ _292445) ^ [_567406, _567408, _567410, _567412, _567414] : [class_Rings_Oring(_567406), -(c_Groups_Ominus__class_Ominus(_567406, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_567406), _567408), _567410), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_567406), _567412), _567414)) = c_Groups_Oplus__class_Oplus(_567406, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_567406), _567408), c_Groups_Ominus__class_Ominus(_567406, _567410, _567414)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_567406), c_Groups_Ominus__class_Ominus(_567406, _567408, _567412)), _567414)))], (7901 ^ _292445) ^ [_567770, _567772, _567774, _567776, _567778] : [class_RealVector_Oreal__normed__algebra(_567770), -(c_Groups_Ominus__class_Ominus(_567770, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_567770), _567772), _567774), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_567770), _567776), _567778)) = c_Groups_Oplus__class_Oplus(_567770, c_Groups_Oplus__class_Oplus(_567770, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_567770), c_Groups_Ominus__class_Ominus(_567770, _567772, _567776)), c_Groups_Ominus__class_Ominus(_567770, _567774, _567778)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_567770), c_Groups_Ominus__class_Ominus(_567770, _567772, _567776)), _567778)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_567770), _567776), c_Groups_Ominus__class_Ominus(_567770, _567774, _567778))))], (7907 ^ _292445) ^ [_568188, _568190, _568192, _568194, _568196, _568198] : [class_Rings_Oring(_568188), 7910 ^ _292445 : [(7911 ^ _292445) ^ [] : [c_Groups_Oplus__class_Oplus(_568188, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_568188), _568190), _568192), _568194) = c_Groups_Oplus__class_Oplus(_568188, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_568188), _568196), _568192), _568198), -(_568194 = c_Groups_Oplus__class_Oplus(_568188, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_568188), c_Groups_Ominus__class_Ominus(_568188, _568196, _568190)), _568192), _568198))], (7917 ^ _292445) ^ [] : [_568194 = c_Groups_Oplus__class_Oplus(_568188, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_568188), c_Groups_Ominus__class_Ominus(_568188, _568196, _568190)), _568192), _568198), -(c_Groups_Oplus__class_Oplus(_568188, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_568188), _568190), _568192), _568194) = c_Groups_Oplus__class_Oplus(_568188, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_568188), _568196), _568192), _568198))]]], (7923 ^ _292445) ^ [_568886, _568888, _568890, _568892, _568894, _568896] : [class_Rings_Oring(_568886), 7926 ^ _292445 : [(7927 ^ _292445) ^ [] : [c_Groups_Oplus__class_Oplus(_568886, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_568886), _568888), _568890), _568892) = c_Groups_Oplus__class_Oplus(_568886, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_568886), _568894), _568890), _568896), -(c_Groups_Oplus__class_Oplus(_568886, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_568886), c_Groups_Ominus__class_Ominus(_568886, _568888, _568894)), _568890), _568892) = _568896)], (7933 ^ _292445) ^ [] : [c_Groups_Oplus__class_Oplus(_568886, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_568886), c_Groups_Ominus__class_Ominus(_568886, _568888, _568894)), _568890), _568892) = _568896, -(c_Groups_Oplus__class_Oplus(_568886, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_568886), _568888), _568890), _568892) = c_Groups_Oplus__class_Oplus(_568886, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_568886), _568894), _568890), _568896))]]], (7939 ^ _292445) ^ [_569556, _569558, _569560, _569562] : [class_Rings_Olinordered__idom(_569556), 7942 ^ _292445 : [(7943 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_569556, c_Groups_Oabs__class_Oabs(_569556, c_Groups_Ominus__class_Ominus(_569556, _569558, _569560)), _569562), 7946 ^ _292445 : [(7947 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_569556, c_Groups_Ominus__class_Ominus(_569556, _569560, _569562), _569558))], (7949 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_569556, _569558, c_Groups_Oplus__class_Oplus(_569556, _569560, _569562)))]]], (7951 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(_569556, c_Groups_Oabs__class_Oabs(_569556, c_Groups_Ominus__class_Ominus(_569556, _569558, _569560)), _569562)), c_Orderings_Oord__class_Oless(_569556, c_Groups_Ominus__class_Ominus(_569556, _569560, _569562), _569558), c_Orderings_Oord__class_Oless(_569556, _569558, c_Groups_Oplus__class_Oplus(_569556, _569560, _569562))]]], (7961 ^ _292445) ^ [_570284, _570286, _570288] : [class_Groups_Oordered__ab__group__add__abs(_570284), -(c_Orderings_Oord__class_Oless__eq(_570284, c_Groups_Oabs__class_Oabs(_570284, c_Groups_Ominus__class_Ominus(_570284, c_Groups_Oabs__class_Oabs(_570284, _570286), c_Groups_Oabs__class_Oabs(_570284, _570288))), c_Groups_Oabs__class_Oabs(_570284, c_Groups_Ominus__class_Ominus(_570284, _570286, _570288))))], (7967 ^ _292445) ^ [_570554, _570556, _570558] : [class_Groups_Oordered__ab__group__add__abs(_570554), -(c_Orderings_Oord__class_Oless__eq(_570554, c_Groups_Ominus__class_Ominus(_570554, c_Groups_Oabs__class_Oabs(_570554, _570556), c_Groups_Oabs__class_Oabs(_570554, _570558)), c_Groups_Oabs__class_Oabs(_570554, c_Groups_Ominus__class_Ominus(_570554, _570556, _570558))))], (7973 ^ _292445) ^ [_570818, _570820, _570822] : [class_Groups_Oordered__ab__group__add__abs(_570818), -(c_Orderings_Oord__class_Oless__eq(_570818, c_Groups_Ominus__class_Ominus(_570818, c_Groups_Oabs__class_Oabs(_570818, _570820), c_Groups_Oabs__class_Oabs(_570818, _570822)), c_Groups_Oabs__class_Oabs(_570818, c_Groups_Ominus__class_Ominus(_570818, _570822, _570820))))], (7979 ^ _292445) ^ [_571097, _571099] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _571097, _571099)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _571099, _571097))], (7985 ^ _292445) ^ [_571271, _571273] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _571273, _571271), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _571271, _571273)))], (7991 ^ _292445) ^ [_571495, _571497] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _571495), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _571497), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _571497, _571495), _571497))], (8001 ^ _292445) ^ [_571793, _571795] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _571793, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _571793, _571795)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8003 ^ _292445) ^ [_571910, _571912] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _571910, _571912), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _571910, _571912) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8009 ^ _292445) ^ [_572159, _572161] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _572159, _572161) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _572159, _572161))], (8015 ^ _292445) ^ [_572331, _572333] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _572331, _572333), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _572331, _572333) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8021 ^ _292445) ^ [_572596, _572598, _572600] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _572596, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _572598, _572600)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _572596, _572600), _572598))], (8027 ^ _292445) ^ [_572784, _572786, _572788] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _572784, _572788), _572786), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _572784, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _572786, _572788)))], (8033 ^ _292445) ^ [_573022, _573024] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _573022, _573024)), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _573024, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _573022, _573024)) = _573022)], (8039 ^ _292445) ^ [_573267, _573269, _573271] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _573267, _573269), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _573271, _573267), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _573267, _573271), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _573269, _573271)))], (8049 ^ _292445) ^ [_573612, _573614, _573616] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _573612, _573614), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _573612, _573616), 8056 ^ _292445 : [(8057 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _573614, _573612), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _573616, _573612)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _573614, _573616))], (8063 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _573614, _573616), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _573614, _573612), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _573616, _573612)))]]], (8069 ^ _292445) ^ [_574229, _574231, _574233] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _574229, _574231), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _574233, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _574231, _574229)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _574233, _574229), _574231))], (8075 ^ _292445) ^ [_574522, _574524, _574526] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _574522, _574524), _574526), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _574522, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _574526, _574524)))], (8081 ^ _292445) ^ [_574710, _574712, _574714] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _574710, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _574714, _574712)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _574710, _574712), _574714))], (8087 ^ _292445) ^ [_574962, _574964, _574966] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _574962, _574964), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _574966, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _574964, _574966), _574962)))], (8093 ^ _292445) ^ [_575198, _575200] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _575198, _575200), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _575198, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _575200, _575198)) = _575200)], (8099 ^ _292445) ^ [_575440, _575442, _575444] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _575440, _575442), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _575444, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _575442, _575440)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _575444, _575442), _575440))], (8105 ^ _292445) ^ [_575704, _575706, _575708] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _575704, _575706), 8108 ^ _292445 : [(8109 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _575708, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _575706, _575704)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _575708, _575704), _575706))], (8115 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _575708, _575704), _575706), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _575708, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _575706, _575704)))]]], (8121 ^ _292445) ^ [_576212, _576214] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _576212, _576214), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _576214, _576212), _576212) = _576214)], (8127 ^ _292445) ^ [_576454, _576456, _576458] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _576454, _576456), 8130 ^ _292445 : [(8131 ^ _292445) ^ [] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _576456, _576454) = _576458, -(_576456 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _576458, _576454))], (8137 ^ _292445) ^ [] : [_576456 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _576458, _576454), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _576456, _576454) = _576458)]]], (8143 ^ _292445) ^ [_576970, _576972, _576974] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _576970, _576972), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _576974, _576972), _576970) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _576974, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _576972, _576970)))], (8149 ^ _292445) ^ [_577234, _577236, _577238] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _577234, _577236), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _577236, _577234), _577238) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _577236, _577238), _577234))], (8155 ^ _292445) ^ [_577498, _577500, _577502] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _577498, _577500), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _577500, _577502), _577498) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _577500, _577498), _577502))], (8161 ^ _292445) ^ [_577734] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _577734, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_RComplete_Onatfloor(_577734) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8167 ^ _292445) ^ [_577930] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _577930, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_RComplete_Onatceiling(_577930) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8173 ^ _292445) ^ [_578196, _578198, _578200, _578202, _578204, _578206] : [class_Rings_Oordered__ring(_578196), 8176 ^ _292445 : [(8177 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_578196, c_Groups_Oplus__class_Oplus(_578196, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_578196), _578198), _578200), _578202), c_Groups_Oplus__class_Oplus(_578196, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_578196), _578204), _578200), _578206)), -(c_Orderings_Oord__class_Oless__eq(_578196, _578202, c_Groups_Oplus__class_Oplus(_578196, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_578196), c_Groups_Ominus__class_Ominus(_578196, _578204, _578198)), _578200), _578206)))], (8183 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_578196, _578202, c_Groups_Oplus__class_Oplus(_578196, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_578196), c_Groups_Ominus__class_Ominus(_578196, _578204, _578198)), _578200), _578206)), -(c_Orderings_Oord__class_Oless__eq(_578196, c_Groups_Oplus__class_Oplus(_578196, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_578196), _578198), _578200), _578202), c_Groups_Oplus__class_Oplus(_578196, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_578196), _578204), _578200), _578206)))]]], (8189 ^ _292445) ^ [_578900, _578902, _578904, _578906, _578908, _578910] : [class_Rings_Oordered__ring(_578900), 8192 ^ _292445 : [(8193 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_578900, c_Groups_Oplus__class_Oplus(_578900, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_578900), _578902), _578904), _578906), c_Groups_Oplus__class_Oplus(_578900, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_578900), _578908), _578904), _578910)), -(c_Orderings_Oord__class_Oless__eq(_578900, c_Groups_Oplus__class_Oplus(_578900, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_578900), c_Groups_Ominus__class_Ominus(_578900, _578902, _578908)), _578904), _578906), _578910))], (8199 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_578900, c_Groups_Oplus__class_Oplus(_578900, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_578900), c_Groups_Ominus__class_Ominus(_578900, _578902, _578908)), _578904), _578906), _578910), -(c_Orderings_Oord__class_Oless__eq(_578900, c_Groups_Oplus__class_Oplus(_578900, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_578900), _578902), _578904), _578906), c_Groups_Oplus__class_Oplus(_578900, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_578900), _578908), _578904), _578910)))]]], (8205 ^ _292445) ^ [_579604, _579606, _579608, _579610, _579612, _579614] : [class_Rings_Oordered__ring(_579604), 8208 ^ _292445 : [(8209 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_579604, c_Groups_Oplus__class_Oplus(_579604, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_579604), _579606), _579608), _579610), c_Groups_Oplus__class_Oplus(_579604, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_579604), _579612), _579608), _579614)), -(c_Orderings_Oord__class_Oless(_579604, _579610, c_Groups_Oplus__class_Oplus(_579604, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_579604), c_Groups_Ominus__class_Ominus(_579604, _579612, _579606)), _579608), _579614)))], (8215 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_579604, _579610, c_Groups_Oplus__class_Oplus(_579604, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_579604), c_Groups_Ominus__class_Ominus(_579604, _579612, _579606)), _579608), _579614)), -(c_Orderings_Oord__class_Oless(_579604, c_Groups_Oplus__class_Oplus(_579604, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_579604), _579606), _579608), _579610), c_Groups_Oplus__class_Oplus(_579604, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_579604), _579612), _579608), _579614)))]]], (8221 ^ _292445) ^ [_580308, _580310, _580312, _580314, _580316, _580318] : [class_Rings_Oordered__ring(_580308), 8224 ^ _292445 : [(8225 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_580308, c_Groups_Oplus__class_Oplus(_580308, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_580308), _580310), _580312), _580314), c_Groups_Oplus__class_Oplus(_580308, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_580308), _580316), _580312), _580318)), -(c_Orderings_Oord__class_Oless(_580308, c_Groups_Oplus__class_Oplus(_580308, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_580308), c_Groups_Ominus__class_Ominus(_580308, _580310, _580316)), _580312), _580314), _580318))], (8231 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(_580308, c_Groups_Oplus__class_Oplus(_580308, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_580308), c_Groups_Ominus__class_Ominus(_580308, _580310, _580316)), _580312), _580314), _580318), -(c_Orderings_Oord__class_Oless(_580308, c_Groups_Oplus__class_Oplus(_580308, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_580308), _580310), _580312), _580314), c_Groups_Oplus__class_Oplus(_580308, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_580308), _580316), _580312), _580318)))]]], (8237 ^ _292445) ^ [_580956, _580958] : [class_Rings_Oring__1(_580956), -(c_Groups_Ominus__class_Ominus(_580956, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_580956), _580958), _580958), c_Groups_Oone__class_Oone(_580956)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_580956), c_Groups_Oplus__class_Oplus(_580956, _580958, c_Groups_Oone__class_Oone(_580956))), c_Groups_Ominus__class_Ominus(_580956, _580958, c_Groups_Oone__class_Oone(_580956))))], (8243 ^ _292445) ^ [_581274, _581276, _581278, _581280, _581282] : [class_Fields_Ofield(_581274), -(_581276 = c_Groups_Ozero__class_Ozero(_581274)), -(_581278 = c_Groups_Ozero__class_Ozero(_581274)), -(c_Groups_Ominus__class_Ominus(_581274, c_Rings_Oinverse__class_Odivide(_581274, _581280, _581276), c_Rings_Oinverse__class_Odivide(_581274, _581282, _581278)) = c_Rings_Oinverse__class_Odivide(_581274, c_Groups_Ominus__class_Ominus(_581274, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_581274), _581280), _581278), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_581274), _581282), _581276)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_581274), _581276), _581278)))], (8257 ^ _292445) ^ [_581832, _581834, _581836, _581838] : [class_Fields_Ofield(_581832), -(_581834 = c_Groups_Ozero__class_Ozero(_581832)), -(c_Groups_Ominus__class_Ominus(_581832, c_Rings_Oinverse__class_Odivide(_581832, _581836, _581834), _581838) = c_Rings_Oinverse__class_Odivide(_581832, c_Groups_Ominus__class_Ominus(_581832, _581836, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_581832), _581834), _581838)), _581834))], (8267 ^ _292445) ^ [_582232, _582234, _582236, _582238] : [class_Fields_Ofield(_582232), -(_582234 = c_Groups_Ozero__class_Ozero(_582232)), -(c_Groups_Ominus__class_Ominus(_582232, _582236, c_Rings_Oinverse__class_Odivide(_582232, _582238, _582234)) = c_Rings_Oinverse__class_Odivide(_582232, c_Groups_Ominus__class_Ominus(_582232, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_582232), _582234), _582236), _582238), _582234))], (8277 ^ _292445) ^ [_582618, _582620, _582622] : [class_Groups_Oordered__ab__group__add__abs(_582618), -(c_Orderings_Oord__class_Oless__eq(_582618, c_Groups_Oabs__class_Oabs(_582618, c_Groups_Ominus__class_Ominus(_582618, _582620, _582622)), c_Groups_Oplus__class_Oplus(_582618, c_Groups_Oabs__class_Oabs(_582618, _582620), c_Groups_Oabs__class_Oabs(_582618, _582622))))], (8283 ^ _292445) ^ [_582910, _582912, _582914, _582916, _582918] : [class_Groups_Oordered__ab__group__add__abs(_582910), -(c_Orderings_Oord__class_Oless__eq(_582910, c_Groups_Oabs__class_Oabs(_582910, c_Groups_Ominus__class_Ominus(_582910, c_Groups_Oplus__class_Oplus(_582910, _582912, _582914), c_Groups_Oplus__class_Oplus(_582910, _582916, _582918))), c_Groups_Oplus__class_Oplus(_582910, c_Groups_Oabs__class_Oabs(_582910, c_Groups_Ominus__class_Ominus(_582910, _582912, _582916)), c_Groups_Oabs__class_Oabs(_582910, c_Groups_Ominus__class_Ominus(_582910, _582914, _582918)))))], (8289 ^ _292445) ^ [_583218, _583220, _583222] : [class_RealVector_Oreal__normed__vector(_583218), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_583218, c_Groups_Ominus__class_Ominus(_583218, _583220, _583222)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_583218, _583220), c_RealVector_Onorm__class_Onorm(_583218, _583222))))], (8311 ^ _292445) ^ [_584050, _584052, _584054] : [-(hBOOL(hAPP(_584050, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _584052, _584054)))), 8314 ^ _292445 : [(8315 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _584052, _584054))], (8317 ^ _292445) ^ [] : [hBOOL(hAPP(_584050, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 8319 ^ _292445 : [(8320 ^ _292445) ^ [] : [-(_584052 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _584054, 8318 ^ [_584050, _584052, _584054]))], (8322 ^ _292445) ^ [] : [hBOOL(hAPP(_584050, 8318 ^ [_584050, _584052, _584054]))]]], (8295 ^ _292445) ^ [_583511, _583513, _583515] : [hBOOL(hAPP(_583511, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _583513, _583515))), 8298 ^ _292445 : [(8299 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _583513, _583515), -(hBOOL(hAPP(_583511, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (8305 ^ _292445) ^ [_583849] : [_583513 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _583515, _583849), -(hBOOL(hAPP(_583511, _583849)))]]], (8342 ^ _292445) ^ [_585211, _585213, _585215] : [-(hBOOL(hAPP(_585211, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _585213, _585215)))), 8345 ^ _292445 : [(8346 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _585213, _585215))], (8348 ^ _292445) ^ [] : [hBOOL(hAPP(_585211, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 8350 ^ _292445 : [(8351 ^ _292445) ^ [] : [-(_585213 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _585215, 8349 ^ [_585211, _585213, _585215]))], (8353 ^ _292445) ^ [] : [hBOOL(hAPP(_585211, 8349 ^ [_585211, _585213, _585215]))]]], (8326 ^ _292445) ^ [_584680, _584682, _584684] : [hBOOL(hAPP(_584680, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _584682, _584684))), 8329 ^ _292445 : [(8330 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _584682, _584684), -(hBOOL(hAPP(_584680, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (8336 ^ _292445) ^ [_585012] : [_584682 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _584684, _585012), -(hBOOL(hAPP(_584680, _585012)))]]], (8357 ^ _292445) ^ [_585832, _585834, _585836, _585838, _585840] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _585832, _585834), 8360 ^ _292445 : [(8361 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _585834), _585836), _585838), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _585832), _585836), _585840)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _585834, _585832)), _585836), _585838), _585840))], (8367 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _585834, _585832)), _585836), _585838), _585840), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _585834), _585836), _585838), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _585832), _585836), _585840)))]]], (8373 ^ _292445) ^ [_586492, _586494, _586496, _586498, _586500] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _586492, _586494), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _586494), _586496), _586498), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _586492), _586496), _586500)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _586494, _586492)), _586496), _586498), _586500))], (8379 ^ _292445) ^ [_586848, _586850, _586852, _586854, _586856] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _586848, _586850), 8382 ^ _292445 : [(8383 ^ _292445) ^ [] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _586850), _586852), _586854) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _586848), _586852), _586856), -(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, _586850, _586848)), _586852), _586854) = _586856)], (8389 ^ _292445) ^ [] : [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, _586850, _586848)), _586852), _586854) = _586856, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _586850), _586852), _586854) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _586848), _586852), _586856))]]], (8395 ^ _292445) ^ [_587502, _587504, _587506, _587508, _587510] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _587502, _587504), 8398 ^ _292445 : [(8399 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _587502), _587506), _587508), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _587504), _587506), _587510)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _587508, 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, _587504, _587502)), _587506), _587510)))], (8405 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _587508, 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, _587504, _587502)), _587506), _587510)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _587502), _587506), _587508), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _587504), _587506), _587510)))]]], (8411 ^ _292445) ^ [_588162, _588164, _588166, _588168, _588170] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _588162, _588164), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _588162), _588166), _588168), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _588164), _588166), _588170)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _588168, 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, _588164, _588162)), _588166), _588170)))], (8417 ^ _292445) ^ [_588518, _588520, _588522, _588524, _588526] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _588518, _588520), 8420 ^ _292445 : [(8421 ^ _292445) ^ [] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _588518), _588522), _588524) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _588520), _588522), _588526), -(_588524 = 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, _588520, _588518)), _588522), _588526))], (8427 ^ _292445) ^ [] : [_588524 = 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, _588520, _588518)), _588522), _588526), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _588518), _588522), _588524) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _588520), _588522), _588526))]]], (8433 ^ _292445) ^ [_589145] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), c_RComplete_Onatfloor(_589145)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _589145))], (8439 ^ _292445) ^ [_589309] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _589309), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), c_RComplete_Onatfloor(_589309)))], (8445 ^ _292445) ^ [_589538] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_589538), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _589538, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (8451 ^ _292445) ^ [_589702] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _589702, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_589702), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (8457 ^ _292445) ^ [_589958, _589960, _589962, _589964, _589966] : [class_RealVector_Oreal__normed__vector(_589958), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_589958, c_Groups_Ominus__class_Ominus(_589958, c_Groups_Oplus__class_Oplus(_589958, _589960, _589962), c_Groups_Oplus__class_Oplus(_589958, _589964, _589966))), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_589958, c_Groups_Ominus__class_Ominus(_589958, _589960, _589964)), c_RealVector_Onorm__class_Onorm(_589958, c_Groups_Ominus__class_Ominus(_589958, _589962, _589966)))))], (8463 ^ _292445) ^ [_590280, _590282, _590284, _590286] : [class_Fields_Ofield(_590280), -(_590282 = c_Groups_Ozero__class_Ozero(_590280)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _590284, _590286), -(hAPP(hAPP(c_Power_Opower__class_Opower(_590280), _590282), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _590286, _590284)) = c_Rings_Oinverse__class_Odivide(_590280, hAPP(hAPP(c_Power_Opower__class_Opower(_590280), _590282), _590286), hAPP(hAPP(c_Power_Opower__class_Opower(_590280), _590282), _590284)))], (8477 ^ _292445) ^ [_590809, _590811, _590813, _590815, _590817] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _590809, _590811), 8480 ^ _292445 : [(8481 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _590809), _590813), _590815), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _590811), _590813), _590817)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _590815, 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, _590811, _590809)), _590813), _590817)))], (8487 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _590815, 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, _590811, _590809)), _590813), _590817)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _590809), _590813), _590815), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _590811), _590813), _590817)))]]], (8493 ^ _292445) ^ [_591469, _591471, _591473, _591475, _591477] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _591469, _591471), 8496 ^ _292445 : [(8497 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _591471), _591473), _591475), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _591469), _591473), _591477)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _591471, _591469)), _591473), _591475), _591477))], (8503 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _591471, _591469)), _591473), _591475), _591477), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _591471), _591473), _591475), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _591469), _591473), _591477)))]]], (8509 ^ _292445) ^ [_592107, _592109] : [_592107 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _592107), _592109) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8515 ^ _292445) ^ [_592281, _592283] : [-(_592281 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _592281), _592283) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _592283, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _592281, c_Groups_Oone__class_Oone(tc_Nat_Onat))), _592283)))], (8521 ^ _292445) ^ [_592536, _592538] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _592536), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _592538), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_RComplete_Onatfloor(_592536)), c_RComplete_Onatfloor(_592538)), c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _592536), _592538))))], (8531 ^ _292445) ^ [_592897, _592899] : [_592897 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _592899), _592897) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (8537 ^ _292445) ^ [_593071, _593073] : [-(_593071 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _593073), _593071) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _593073), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _593073), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _593071, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (8543 ^ _292445) ^ [_593344, _593346, _593348] : [class_Power_Opower(_593344), 8546 ^ _292445 : [(8547 ^ _292445) ^ [] : [_593346 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_593344), _593348), _593346) = c_Groups_Oone__class_Oone(_593344))], (8553 ^ _292445) ^ [] : [-(_593346 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_593344), _593348), _593346) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_593344), _593348), hAPP(hAPP(c_Power_Opower__class_Opower(_593344), _593348), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _593346, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (8559 ^ _292445) ^ [_593956, _593958, _593960, _593962, _593964, _593966] : [class_RealVector_Oreal__field(_593956), -(c_Rings_Oinverse__class_Odivide(_593956, c_Groups_Ominus__class_Ominus(_593956, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_593956), _593958), _593960), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_593956), _593962), _593964)), _593966) = c_Groups_Oplus__class_Oplus(_593956, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_593956), _593958), c_Rings_Oinverse__class_Odivide(_593956, c_Groups_Ominus__class_Ominus(_593956, _593960, _593964), _593966)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_593956), c_Rings_Oinverse__class_Odivide(_593956, c_Groups_Ominus__class_Ominus(_593956, _593958, _593962), _593966)), _593964)))], (8565 ^ _292445) ^ [_594308, _594310] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _594308), _594310), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _594310, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _594308), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_RComplete_Onatceiling(_594310) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _594308, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (8575 ^ _292445) ^ [_594614] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _594614)))], (8577 ^ _292445) ^ [_594696] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _594696, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatfloor(_594696))))], (8579 ^ _292445) ^ [_594827, _594829, _594831] : [class_Rings_Olinordered__idom(_594827), 8582 ^ _292445 : [(8593 ^ _292445) ^ [] : [8594 ^ _292445 : [(8595 ^ _292445) ^ [] : [_594829 = _594831], (8597 ^ _292445) ^ [] : [c_Polynomial_Opos__poly(_594827, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_594827), _594831, _594829))]], -(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(_594827), _594829, _594831))], (8583 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(_594827), _594829, _594831), -(_594829 = _594831), -(c_Polynomial_Opos__poly(_594827, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_594827), _594831, _594829)))]]], (8601 ^ _292445) ^ [_595492, _595494] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _595492), _595494), -(c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _595494, c_RealDef_Oreal(tc_Nat_Onat, _595492))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_RComplete_Onatceiling(_595494), _595492))], (8607 ^ _292445) ^ [_595740, _595742] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _595740), _595742), -(c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _595742, c_RealDef_Oreal(tc_Nat_Onat, _595740))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_RComplete_Onatfloor(_595742), _595740))], (8613 ^ _292445) ^ [_595988, _595990] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _595988, _595990), -(c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _595990, _595988)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _595990), c_RealDef_Oreal(tc_Nat_Onat, _595988)))], (8619 ^ _292445) ^ [_596205] : [-(c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat, _596205)) = _596205)], (8621 ^ _292445) ^ [_596288] : [-(c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat, _596288)) = _596288)], (8623 ^ _292445) ^ [_596414, _596416, _596418] : [class_Rings_Olinordered__idom(_596414), 8626 ^ _292445 : [(8627 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_596414), _596416, _596418), -(c_Polynomial_Opos__poly(_596414, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_596414), _596418, _596416)))], (8633 ^ _292445) ^ [] : [c_Polynomial_Opos__poly(_596414, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_596414), _596418, _596416)), -(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_596414), _596416, _596418))]]], (8639 ^ _292445) ^ [_596915, _596917] : [class_Groups_Oab__group__add(_596915), -(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_596915), _596917, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_596915))) = _596917)], (8645 ^ _292445) ^ [_597142, _597144, _597146] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _597142), c_Groups_Ominus__class_Ominus(tc_Int_Oint, _597144, _597146)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _597142), _597144), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _597142), _597146)))], (8647 ^ _292445) ^ [_597278, _597280, _597282] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Ominus__class_Ominus(tc_Int_Oint, _597278, _597280)), _597282) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _597278), _597282), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _597280), _597282)))], (8649 ^ _292445) ^ [_597414, _597416, _597418] : [-(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, hAPP(_597414, _597416), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, hAPP(_597414, _597418), hAPP(_597414, _597416)), c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _597418, _597416))), _597416)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, hAPP(_597414, _597418), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, hAPP(_597414, _597418), hAPP(_597414, _597416)), c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _597418, _597416))), _597418)))], (8651 ^ _292445) ^ [_597558] : [-(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _597558)) = c_RealDef_Oreal(tc_Nat_Onat, _597558))], (8653 ^ _292445) ^ [_597703, _597705] : [c_RealDef_Oreal(tc_Nat_Onat, _597703) = c_RealDef_Oreal(tc_Nat_Onat, _597705), -(_597703 = _597705)], (8659 ^ _292445) ^ [_597877, _597879] : [_597877 = _597879, -(c_RealDef_Oreal(tc_Nat_Onat, _597877) = c_RealDef_Oreal(tc_Nat_Onat, _597879))], (8665 ^ _292445) ^ [_598116] : [c_RealDef_Oreal(tc_Nat_Onat, _598116) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_598116 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8671 ^ _292445) ^ [_598278] : [_598278 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_RealDef_Oreal(tc_Nat_Onat, _598278) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (8677 ^ _292445) ^ [] : [-(c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (8679 ^ _292445) ^ [_598513] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _598513), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (8681 ^ _292445) ^ [_598653, _598655] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _598653), c_RealDef_Oreal(tc_Nat_Onat, _598655)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _598653, _598655))], (8687 ^ _292445) ^ [_598831, _598833] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _598831, _598833), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _598831), c_RealDef_Oreal(tc_Nat_Onat, _598833)))], (8693 ^ _292445) ^ [_599088, _599090] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _599088), c_RealDef_Oreal(tc_Nat_Onat, _599090)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _599088, _599090))], (8699 ^ _292445) ^ [_599266, _599268] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _599266, _599268), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _599266), c_RealDef_Oreal(tc_Nat_Onat, _599268)))], (8705 ^ _292445) ^ [_599479, _599481] : [-(c_RealDef_Oreal(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _599479), _599481)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _599479)), c_RealDef_Oreal(tc_Nat_Onat, _599481)))], (8707 ^ _292445) ^ [_599594, _599596] : [-(c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _599594, _599596)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _599594), c_RealDef_Oreal(tc_Nat_Onat, _599596)))], (8709 ^ _292445) ^ [_599749, _599751] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _599749, _599751), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _599749, _599751), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (8715 ^ _292445) ^ [_599923, _599925] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _599923, _599925), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _599923, _599925))], (8721 ^ _292445) ^ [] : [-(c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (8723 ^ _292445) ^ [_600229, _600231] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _600229, _600231), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _600229, _600231), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (8729 ^ _292445) ^ [_600403, _600405] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _600403, _600405), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _600403, _600405))], (8735 ^ _292445) ^ [_600612, _600614] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _600612)), _600614) = c_RealDef_Oreal(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _600612), _600614)))], (8737 ^ _292445) ^ [_600724, _600726] : [-(c_RealDef_Oreal(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _600724), _600726)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _600724)), _600726))], (8739 ^ _292445) ^ [_600822] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _600822, c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatceiling(_600822))))], (8741 ^ _292445) ^ [_600950] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _600950), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(_600950 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8747 ^ _292445) ^ [_601114] : [_601114 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _601114), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (8753 ^ _292445) ^ [_601342, _601344, _601346] : [class_RealVector_Oreal__normed__vector(_601342), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_601342, _601344), c_RealVector_Onorm__class_Onorm(_601342, _601346)), c_RealVector_Onorm__class_Onorm(_601342, c_Groups_Oplus__class_Oplus(_601342, _601344, _601346))))], (8759 ^ _292445) ^ [_601578] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _601578), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatfloor(_601578)), _601578))], (8765 ^ _292445) ^ [_601825, _601827] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _601825, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _601827, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _601825, _601827))], (8771 ^ _292445) ^ [_601999, _602001] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _601999, _602001), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _601999, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _602001, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (8777 ^ _292445) ^ [_602223, _602225] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _602223), _602225), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _602223, c_RComplete_Onatfloor(_602225)))], (8783 ^ _292445) ^ [_602447, _602449] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _602447, c_RealDef_Oreal(tc_Nat_Onat, _602449)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_602447), _602449))], (8789 ^ _292445) ^ [_602671, _602673] : [_602671 = c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatfloor(_602671)), -(c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _602671), _602673)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_RComplete_Onatfloor(_602671)), _602673))], (8795 ^ _292445) ^ [_602938] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _602938)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _602938))], (8801 ^ _292445) ^ [_603104] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _603104), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _603104)))], (8807 ^ _292445) ^ [_603349, _603351] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _603349, _603351), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _603349), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), c_RealDef_Oreal(tc_Nat_Onat, _603351)))], (8813 ^ _292445) ^ [_603535, _603537] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _603535), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), c_RealDef_Oreal(tc_Nat_Onat, _603537)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _603535, _603537))], (8819 ^ _292445) ^ [_603800, _603802] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _603800, _603802), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _603800), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _603802), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))], (8825 ^ _292445) ^ [_603986, _603988] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _603986), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _603988), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _603986, _603988))], (8831 ^ _292445) ^ [_604222, _604224] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _604222), 8834 ^ _292445 : [(8835 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _604224, c_RComplete_Onatfloor(_604222)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _604224), _604222))], (8841 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _604224), _604222), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _604224, c_RComplete_Onatfloor(_604222)))]]], (8847 ^ _292445) ^ [_604705, _604707] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _604705), 8850 ^ _292445 : [(8851 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_604705), _604707), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _604705, c_RealDef_Oreal(tc_Nat_Onat, _604707)))], (8857 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _604705, c_RealDef_Oreal(tc_Nat_Onat, _604707)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_604705), _604707))]]], (8863 ^ _292445) ^ [_605159] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _605159, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatfloor(_605159)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))], (8865 ^ _292445) ^ [_605276, _605278] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _605276), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _605276, c_RealDef_Oreal(tc_Nat_Onat, _605278)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_RComplete_Onatfloor(_605276), _605278))], (8875 ^ _292445) ^ [_605591, _605593] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _605591), -(c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _605591, c_RealDef_Oreal(tc_Nat_Onat, _605593))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatfloor(_605591), _605593))], (8881 ^ _292445) ^ [_605833, _605835] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatfloor(_605833), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _605835), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _605833, c_RealDef_Oreal(tc_Nat_Onat, _605835)))], (8887 ^ _292445) ^ [_606065, _606067] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _606065), _606067), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _606067, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _606065), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_RComplete_Onatfloor(_606067) = _606065)], (8897 ^ _292445) ^ [_606392, _606394] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _606392), -(c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _606392, c_RealDef_Oreal(tc_Nat_Onat, _606394))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatceiling(_606392), _606394))], (8903 ^ _292445) ^ [_606676, _606678, _606680, _606682, _606684] : [class_Groups_Oab__group__add(_606676), -(c_Groups_Ominus__class_Ominus(_606676, c_Groups_Oplus__class_Oplus(_606676, _606678, _606680), c_Groups_Oplus__class_Oplus(_606676, _606682, _606684)) = c_Groups_Oplus__class_Oplus(_606676, c_Groups_Ominus__class_Ominus(_606676, _606678, _606682), c_Groups_Ominus__class_Ominus(_606676, _606680, _606684)))], (8909 ^ _292445) ^ [_606950, _606952] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _606950), -(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, _606952)), _606950), 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, _606950, c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), _606952)))], (8915 ^ _292445) ^ [_607224, _607226, _607228] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _607224), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _607226, 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, _607226, _607228)), c_Groups_Oone__class_Oone(tc_Int_Oint))), _607224)), _607228))], (8921 ^ _292445) ^ [_607500, _607502, _607504] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _607500), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _607502, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _607504, 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, _607504, _607502)), c_Groups_Oone__class_Oone(tc_Int_Oint))), _607500))))], (8927 ^ _292445) ^ [_607747, _607749] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, _607747, _607749)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _607747)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _607749)))], (8929 ^ _292445) ^ [_607874, _607876] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _607874), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _607876), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), -(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Transcendental_Oarctan(_607874), c_Transcendental_Oarctan(_607876)) = c_Transcendental_Oarctan(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _607874, _607876), c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _607874), _607876)))))], (8939 ^ _292445) ^ [_608245, _608247] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _608245, _608247), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Transcendental_Oarctan(_608245), c_Transcendental_Oarctan(_608247)))], (8945 ^ _292445) ^ [_608467, _608469] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _608467, _608469), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Transcendental_Oarctan(_608467), c_Transcendental_Oarctan(_608469)))], (8951 ^ _292445) ^ [] : [-(c_Transcendental_Oarctan(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (8953 ^ _292445) ^ [_608728] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _608728), 8957 ^ _292445 : [(8958 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, 8956 ^ [_608728], c_Groups_Oone__class_Oone(tc_Nat_Onat))), _608728))], (8960 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _608728, c_RealDef_Oreal(tc_Nat_Onat, 8956 ^ [_608728])))]]], (8962 ^ _292445) ^ [_609091] : [c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _609091) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, _609091, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, _609091, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, _609091, c_Complex_Oii)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, _609091, c_Complex_Oii)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (8980 ^ _292445) ^ [] : [c_Complex_Oii = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)], (8982 ^ _292445) ^ [] : [c_Complex_Oii = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)], (8984 ^ _292445) ^ [_609755, _609757, _609759, _609761] : [class_RealVector_Oreal__normed__vector(_609755), class_Orderings_Oord(_609757), 8994 ^ _292445 : [(8995 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_609757, _609759, 8993 ^ [_609755, _609757, _609759, _609761]))], (8997 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_609755, c_Groups_Ominus__class_Ominus(_609755, hAPP(_609761, _609759), hAPP(_609761, 8993 ^ [_609755, _609757, _609759, _609761]))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))]], 8998 ^ _292445 : [(8999 ^ _292445) ^ [_610313] : [c_Orderings_Oord__class_Oless__eq(_609757, _609759, _610313), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_609755, hAPP(_609761, _610313)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_609755, hAPP(_609761, _609759)))))]]], (9005 ^ _292445) ^ [_610611, _610613, _610615] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _610611), 9009 ^ _292445 : [(9010 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 9008 ^ [_610611, _610613, _610615]))], (9012 ^ _292445) ^ [_610995] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, _610615), _610995), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, _610615), _610613))), _610611)), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, _610995, _610613))), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, _610995, _610613)), 9008 ^ [_610611, _610613, _610615])]]], (9022 ^ _292445) ^ [_611437, _611439] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _611437, _611439), -(c_Nat__Transfer_Otsub(_611439, _611437) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, _611439, _611437))], (9028 ^ _292445) ^ [_611615, _611617] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _611615, _611617)), -(c_Nat__Transfer_Otsub(_611617, _611615) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (9034 ^ _292445) ^ [_611838, _611840] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _611838), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _611840), -(c_RComplete_Onatfloor(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, _611838, c_RealDef_Oreal(tc_Nat_Onat, _611840))) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, c_RComplete_Onatfloor(_611838), _611840))], (9044 ^ _292445) ^ [_612205, _612207, _612209] : [_612205 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _612205), _612207), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _612205), _612209)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9050 ^ _292445) ^ [_612405, _612407, _612409] : [-(_612405 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _612405), _612407), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _612405), _612409)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _612407, _612409))], (9056 ^ _292445) ^ [_612694, _612696, _612698, _612700] : [class_Divides_Osemiring__div(_612694), 9059 ^ _292445 : [(9060 ^ _292445) ^ [] : [_612696 = c_Groups_Ozero__class_Ozero(_612694), -(c_Divides_Odiv__class_Odiv(_612694, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_612694), _612696), _612698), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_612694), _612696), _612700)) = c_Groups_Ozero__class_Ozero(_612694))], (9066 ^ _292445) ^ [] : [-(_612696 = c_Groups_Ozero__class_Ozero(_612694)), -(c_Divides_Odiv__class_Odiv(_612694, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_612694), _612696), _612698), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_612694), _612696), _612700)) = c_Divides_Odiv__class_Odiv(_612694, _612698, _612700))]]], (9072 ^ _292445) ^ [_613304, _613306, _613308] : [class_Divides_Osemiring__div(_613304), -(_613306 = c_Groups_Ozero__class_Ozero(_613304)), -(c_Divides_Odiv__class_Odiv(_613304, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_613304), _613308), _613306), _613306) = _613308)], (9082 ^ _292445) ^ [_613656, _613658, _613660] : [class_Divides_Osemiring__div(_613656), -(_613658 = c_Groups_Ozero__class_Ozero(_613656)), -(c_Divides_Odiv__class_Odiv(_613656, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_613656), _613658), _613660), _613658) = _613660)], (9092 ^ _292445) ^ [_614022, _614024, _614026, _614028] : [class_Divides_Osemiring__div(_614022), -(_614024 = c_Groups_Ozero__class_Ozero(_614022)), -(c_Divides_Odiv__class_Odiv(_614022, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_614022), _614026), _614024), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_614022), _614028), _614024)) = c_Divides_Odiv__class_Odiv(_614022, _614026, _614028))], (9102 ^ _292445) ^ [_614422, _614424, _614426, _614428] : [class_Divides_Osemiring__div(_614422), -(_614424 = c_Groups_Ozero__class_Ozero(_614422)), -(c_Divides_Odiv__class_Odiv(_614422, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_614422), _614424), _614426), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_614422), _614424), _614428)) = c_Divides_Odiv__class_Odiv(_614422, _614426, _614428))], (9112 ^ _292445) ^ [_614794, _614796] : [class_Divides_Osemiring__div(_614794), -(_614796 = c_Groups_Ozero__class_Ozero(_614794)), -(c_Divides_Odiv__class_Odiv(_614794, _614796, _614796) = c_Groups_Oone__class_Oone(_614794))], (9122 ^ _292445) ^ [_615109, _615111, _615113] : [-(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _615109, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _615111), _615113)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _615109, _615111), _615113))], (9124 ^ _292445) ^ [_615238, _615240] : [class_Divides_Osemiring__div(_615238), -(c_Divides_Odiv__class_Odiv(_615238, c_Groups_Ozero__class_Ozero(_615238), _615240) = c_Groups_Ozero__class_Ozero(_615238))], (9130 ^ _292445) ^ [_615462, _615464] : [class_Divides_Osemiring__div(_615462), -(c_Divides_Odiv__class_Odiv(_615462, _615464, c_Groups_Ozero__class_Ozero(_615462)) = c_Groups_Ozero__class_Ozero(_615462))], (9136 ^ _292445) ^ [_615686, _615688] : [class_Divides_Osemiring__div(_615686), -(c_Divides_Odiv__class_Odiv(_615686, _615688, c_Groups_Oone__class_Oone(_615686)) = _615688)], (9142 ^ _292445) ^ [_615891, _615893] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _615891, _615893), _615891))], (9144 ^ _292445) ^ [_616019, _616021, _616023] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _616019, _616021), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _616019, _616023), c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _616021, _616023)))], (9150 ^ _292445) ^ [_616255, _616257] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _616255, _616257), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _616255, _616257) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9156 ^ _292445) ^ [_616489, _616491, _616493] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _616489), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _616489, _616491), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _616493, _616491), c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _616493, _616489)))], (9166 ^ _292445) ^ [_616834, _616836, _616838] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _616834), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _616834), _616836), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _616834), _616838)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _616836, _616838))], (9172 ^ _292445) ^ [_617092, _617094] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _617092), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _617094), _617092), _617092) = _617094)], (9178 ^ _292445) ^ [_617324, _617326] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _617324), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _617324), _617326), _617324) = _617326)], (9184 ^ _292445) ^ [_617556, _617558] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _617556), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _617558), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _617558, _617556), _617558))], (9194 ^ _292445) ^ [_617854, _617856] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _617854, _617856)), c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _617854), c_RealDef_Oreal(tc_Nat_Onat, _617856))))], (9196 ^ _292445) ^ [_618009, _618011, _618013, _618015] : [class_Divides_Osemiring__div(_618009), -(_618011 = c_Groups_Ozero__class_Ozero(_618009)), -(c_Divides_Odiv__class_Odiv(_618009, c_Groups_Oplus__class_Oplus(_618009, _618013, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_618009), _618011), _618015)), _618011) = c_Groups_Oplus__class_Oplus(_618009, _618015, c_Divides_Odiv__class_Odiv(_618009, _618013, _618011)))], (9206 ^ _292445) ^ [_618409, _618411, _618413, _618415] : [class_Divides_Osemiring__div(_618409), -(_618411 = c_Groups_Ozero__class_Ozero(_618409)), -(c_Divides_Odiv__class_Odiv(_618409, c_Groups_Oplus__class_Oplus(_618409, _618413, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_618409), _618415), _618411)), _618411) = c_Groups_Oplus__class_Oplus(_618409, _618415, c_Divides_Odiv__class_Odiv(_618409, _618413, _618411)))], (9216 ^ _292445) ^ [_618795, _618797, _618799] : [class_Divides_Osemiring__div(_618795), -(_618797 = c_Groups_Ozero__class_Ozero(_618795)), -(c_Divides_Odiv__class_Odiv(_618795, c_Groups_Oplus__class_Oplus(_618795, _618799, _618797), _618797) = c_Groups_Oplus__class_Oplus(_618795, c_Divides_Odiv__class_Odiv(_618795, _618799, _618797), c_Groups_Oone__class_Oone(_618795)))], (9226 ^ _292445) ^ [_619159, _619161, _619163] : [class_Divides_Osemiring__div(_619159), -(_619161 = c_Groups_Ozero__class_Ozero(_619159)), -(c_Divides_Odiv__class_Odiv(_619159, c_Groups_Oplus__class_Oplus(_619159, _619161, _619163), _619161) = c_Groups_Oplus__class_Oplus(_619159, c_Divides_Odiv__class_Odiv(_619159, _619163, _619161), c_Groups_Oone__class_Oone(_619159)))], (9260 ^ _292445) ^ [_620331, _620333, _620335] : [-(hBOOL(hAPP(_620331, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _620333, _620335)))), 9263 ^ _292445 : [(9264 ^ _292445) ^ [] : [-(_620335 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9266 ^ _292445) ^ [] : [hBOOL(hAPP(_620331, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 9267 ^ _292445 : [(9268 ^ _292445) ^ [] : [_620335 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (9272 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, 9270 ^ [_620331, _620333, _620335], _620335))], (9274 ^ _292445) ^ [] : [-(_620333 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _620335), 9269 ^ [_620331, _620333, _620335]), 9270 ^ [_620331, _620333, _620335]))], (9276 ^ _292445) ^ [] : [hBOOL(hAPP(_620331, 9269 ^ [_620331, _620333, _620335]))]]], (9236 ^ _292445) ^ [_619552, _619554, _619556] : [hBOOL(hAPP(_619552, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _619554, _619556))), 9239 ^ _292445 : [(9240 ^ _292445) ^ [] : [_619556 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_619552, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (9246 ^ _292445) ^ [] : [-(_619556 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 9249 ^ _292445 : [(9250 ^ _292445) ^ [_620006, _620008] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _620006, _619556), _619554 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _619556), _620008), _620006), -(hBOOL(hAPP(_619552, _620008)))]]]]], (9280 ^ _292445) ^ [_621208, _621210] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _621208), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _621210), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Nat__Transfer_Otsub(_621208, _621210)))], (9290 ^ _292445) ^ [_621504, _621506] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _621504), c_RealDef_Oreal(tc_Nat_Onat, _621506)), c_RealDef_Oreal(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _621504, _621506)))))], (9292 ^ _292445) ^ [_621620, _621622] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _621620), c_RealDef_Oreal(tc_Nat_Onat, _621622)), c_RealDef_Oreal(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _621620, _621622))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (9294 ^ _292445) ^ [_621751, _621753] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _621751, _621753), -(c_Nat__Transfer_Otsub(_621753, _621751) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, _621753, _621751))], (9300 ^ _292445) ^ [_621977, _621979] : [class_Orderings_Oorder(_621977), 9303 ^ _292445 : [(9314 ^ _292445) ^ [] : [9317 ^ _292445 : [(9318 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, 9315 ^ [_621977, _621979], 9316 ^ [_621977, _621979]))], (9320 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(_621977, hAPP(_621979, 9316 ^ [_621977, _621979]), hAPP(_621979, 9315 ^ [_621977, _621979]))]], -(c_SEQ_Odecseq(_621977, _621979))], (9304 ^ _292445) ^ [] : [c_SEQ_Odecseq(_621977, _621979), 9307 ^ _292445 : [(9308 ^ _292445) ^ [_622253, _622255] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _622255, _622253), -(c_Orderings_Oord__class_Oless__eq(_621977, hAPP(_621979, _622253), hAPP(_621979, _622255)))]]]]], (9324 ^ _292445) ^ [_622877, _622879, _622881] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Complex_Orcis(_622877, _622879)), _622881) = c_Complex_Orcis(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _622877), _622881), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _622881)), _622879)))], (9326 ^ _292445) ^ [_623001] : [-(_623001 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _623001, _623001) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (9332 ^ _292445) ^ [_623187] : [-(c_Divides_Odiv__class_Odiv(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _623187) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (9334 ^ _292445) ^ [_623326, _623328, _623330, _623332] : [class_Fields_Ofield(_623326), -(c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_623326), _623328, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_623326)), _623330), _623332)) = c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_623326), c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_623326), _623328, _623330), _623332))], (9340 ^ _292445) ^ [_623602, _623604] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _623602), 9343 ^ _292445 : [(9344 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _623604, _623602), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _623604, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (9350 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _623604, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _623604, _623602), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (9356 ^ _292445) ^ [_624082, _624084] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _624082, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 9359 ^ _292445 : [(9360 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _624084, _624082), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _624084))], (9366 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _624084), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _624084, _624082), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (9372 ^ _292445) ^ [_624562, _624564] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _624562, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _624564), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _624562, _624564), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (9382 ^ _292445) ^ [_624875, _624877] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _624875), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _624877), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _624875, _624877)))], (9392 ^ _292445) ^ [_625202, _625204, _625206] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _625202, _625204), c_Orderings_Oord__class_Oless(tc_Int_Oint, _625206, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _625204, _625206), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _625202, _625206)))], (9402 ^ _292445) ^ [_625547, _625549, _625551] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _625547, _625549), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _625551), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _625547, _625551), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _625549, _625551)))], (9412 ^ _292445) ^ [_625878, _625880] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _625878, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _625880, _625878), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _625878, _625880) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (9422 ^ _292445) ^ [_626203, _626205, _626207] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _626203, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _626205), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _626205, _626207), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _626203, _626205), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _626203, _626207)))], (9436 ^ _292445) ^ [_626629, _626631] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _626629, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _626631), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _626629, _626631), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (9446 ^ _292445) ^ [_626942, _626944] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _626942, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 9449 ^ _292445 : [(9450 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _626944, _626942)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _626944, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (9456 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _626944, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _626944, _626942)))]]], (9462 ^ _292445) ^ [_627422, _627424] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _627422), c_Orderings_Oord__class_Oless(tc_Int_Oint, _627422, _627424), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _627422, _627424) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (9472 ^ _292445) ^ [_627733, _627735] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _627733), c_Orderings_Oord__class_Oless(tc_Int_Oint, _627735, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _627733, _627735), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (9482 ^ _292445) ^ [_628060, _628062, _628064] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _628060), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _628062), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _628062, _628064), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _628060, _628064), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _628060, _628062)))], (9496 ^ _292445) ^ [_628486, _628488] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _628486), 9499 ^ _292445 : [(9500 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _628486, _628488)), 9503 ^ _292445 : [(9504 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _628488, _628486))], (9506 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _628488))]]], (9508 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _628486, _628488))), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _628488, _628486), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _628488)]]], (9518 ^ _292445) ^ [_629127, _629129] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _629127), 9521 ^ _292445 : [(9522 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _629129, _629127)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _629127, _629129))], (9528 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _629127, _629129), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _629129, _629127)))]]], (9534 ^ _292445) ^ [_629607, _629609] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _629607), 9537 ^ _292445 : [(9538 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _629609, _629607)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _629609))], (9544 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _629609), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _629609, _629607)))]]], (9550 ^ _292445) ^ [_630116, _630118] : [c_Divides_Odiv__class_Odiv(tc_Int_Oint, _630116, _630118) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_630118 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 9559 ^ _292445 : [(9560 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _630116))], (9562 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _630116, _630118))]], 9563 ^ _292445 : [(9564 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _630116, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (9566 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _630118, _630116))]]], (9568 ^ _292445) ^ [_630624, _630626] : [-(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _630624, _630626) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 9569 ^ _292445 : [(9570 ^ _292445) ^ [] : [_630626 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (9572 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _630624), c_Orderings_Oord__class_Oless(tc_Int_Oint, _630624, _630626)], (9578 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _630624, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _630626, _630624)]]], (9586 ^ _292445) ^ [_631177, _631179] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _631177), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _631179), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _631177, _631179), _631177))], (9596 ^ _292445) ^ [_631504, _631506, _631508] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _631504), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _631506, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _631508), _631504)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _631506, _631508), _631504))], (9602 ^ _292445) ^ [_631771, _631773, _631775, _631777] : [-(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex, c_Complex_Orcis(_631771, _631773), c_Complex_Orcis(_631775, _631777)) = c_Complex_Orcis(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, _631771, _631775), c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _631773, _631777)))], (9604 ^ _292445) ^ [_631890, _631892] : [-(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Complex_Orcis(_631890, _631892)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _631890))], (9606 ^ _292445) ^ [_631979] : [-(c_Complex_Orcis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _631979) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))], (9608 ^ _292445) ^ [_632117, _632119, _632121, _632123] : [_632117 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _632119), _632121), _632123), -(_632119 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _632117, _632119) = _632121), 9615 ^ _292445 : [(9616 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _632119))], (9618 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _632123), c_Orderings_Oord__class_Oless(tc_Int_Oint, _632123, _632119)]], 9623 ^ _292445 : [(9624 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _632119)], (9626 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _632119, _632123), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _632123, c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (9684 ^ _292445) ^ [_634691, _634693, _634695] : [-(hBOOL(hAPP(_634691, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _634693, _634695)))), 9687 ^ _292445 : [(9688 ^ _292445) ^ [] : [-(_634695 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (9690 ^ _292445) ^ [] : [hBOOL(hAPP(_634691, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], 9693 ^ _292445 : [(9694 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _634695))], (9698 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), 9696 ^ [_634691, _634693, _634695]))], (9700 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, 9696 ^ [_634691, _634693, _634695], _634695))], (9702 ^ _292445) ^ [] : [-(_634693 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _634695), 9695 ^ [_634691, _634693, _634695]), 9696 ^ [_634691, _634693, _634695]))], (9704 ^ _292445) ^ [] : [hBOOL(hAPP(_634691, 9695 ^ [_634691, _634693, _634695]))]], 9705 ^ _292445 : [(9706 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _634695, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (9710 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _634695, 9708 ^ [_634691, _634693, _634695]))], (9712 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, 9708 ^ [_634691, _634693, _634695], c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (9714 ^ _292445) ^ [] : [-(_634693 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _634695), 9707 ^ [_634691, _634693, _634695]), 9708 ^ [_634691, _634693, _634695]))], (9716 ^ _292445) ^ [] : [hBOOL(hAPP(_634691, 9707 ^ [_634691, _634693, _634695]))]]], (9638 ^ _292445) ^ [_633071, _633073, _633075] : [hBOOL(hAPP(_633071, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _633073, _633075))), 9641 ^ _292445 : [(9642 ^ _292445) ^ [] : [_633075 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_633071, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (9648 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _633075), 9651 ^ _292445 : [(9652 ^ _292445) ^ [_633592] : [-(hBOOL(hAPP(_633071, _633592))), 9653 ^ _292445 : [(9654 ^ _292445) ^ [_633714] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _633714), c_Orderings_Oord__class_Oless(tc_Int_Oint, _633714, _633075), _633073 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _633075), _633592), _633714)]]]]], (9666 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _633075, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 9669 ^ _292445 : [(9670 ^ _292445) ^ [_634186] : [-(hBOOL(hAPP(_633071, _634186))), 9671 ^ _292445 : [(9672 ^ _292445) ^ [_634308] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _633075, _634308), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _634308, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _633073 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _633075), _634186), _634308)]]]]]]], (9720 ^ _292445) ^ [_636325, _636327, _636329, _636331] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Complex_Orcis(_636325, _636327)), c_Complex_Orcis(_636329, _636331)) = c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _636325), _636329), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _636327, _636331)))], (9722 ^ _292445) ^ [_636477, _636479, _636481] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _636477, _636479), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _636479, _636481), 9730 ^ _292445 : [(9731 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 9729 ^ [_636477, _636479, _636481]))], (9733 ^ _292445) ^ [_636900] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _636479, _636900)), 9729 ^ [_636477, _636479, _636481]), 9736 ^ _292445 : [(9737 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _636477, _636900))], (9739 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _636900, _636481))]]]]], (9741 ^ _292445) ^ [_637270, _637272, _637274] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _637270), 9747 ^ _292445 : [(9748 ^ _292445) ^ [] : [-(hBOOL(hAPP(_637272, 9746 ^ [_637270, _637272, _637274])))], (9750 ^ _292445) ^ [] : [hBOOL(hAPP(_637272, c_Groups_Ominus__class_Ominus(tc_Int_Oint, 9746 ^ [_637270, _637272, _637274], _637270)))]], c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _637274), 9755 ^ _292445 : [(9756 ^ _292445) ^ [_637785] : [hBOOL(hAPP(_637272, _637785)), -(hBOOL(hAPP(_637272, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _637785, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _637274), _637270)))))]]], (9762 ^ _292445) ^ [_638055, _638057] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _638055), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _638057), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _638057), _638055), _638057) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _638057), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _638055, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (9772 ^ _292445) ^ [_638412, _638414, _638416] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _638412), 9778 ^ _292445 : [(9779 ^ _292445) ^ [] : [-(hBOOL(hAPP(_638414, 9777 ^ [_638412, _638414, _638416])))], (9781 ^ _292445) ^ [] : [hBOOL(hAPP(_638414, c_Groups_Oplus__class_Oplus(tc_Int_Oint, 9777 ^ [_638412, _638414, _638416], _638412)))]], c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _638416), 9786 ^ _292445 : [(9787 ^ _292445) ^ [_638927] : [hBOOL(hAPP(_638414, _638927)), -(hBOOL(hAPP(_638414, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _638927, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _638416), _638412)))))]]], (9793 ^ _292445) ^ [_639168] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _639168, c_Nat_OSuc(_639168)))], (9795 ^ _292445) ^ [_639278, _639280] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _639278, _639280), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_639278), c_Nat_OSuc(_639280)))], (9801 ^ _292445) ^ [_639471] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(_639471)))], (9803 ^ _292445) ^ [_639552] : [-(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _639552, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = _639552)], (9805 ^ _292445) ^ [_639691, _639693, _639695, _639697] : [class_Rings_Olinordered__semidom(_639691), hAPP(hAPP(c_Power_Opower__class_Opower(_639691), _639693), c_Nat_OSuc(_639695)) = hAPP(hAPP(c_Power_Opower__class_Opower(_639691), _639697), c_Nat_OSuc(_639695)), c_Orderings_Oord__class_Oless__eq(_639691, c_Groups_Ozero__class_Ozero(_639691), _639693), c_Orderings_Oord__class_Oless__eq(_639691, c_Groups_Ozero__class_Ozero(_639691), _639697), -(_639693 = _639697)], (9823 ^ _292445) ^ [_640282, _640284, _640286, _640288] : [class_Rings_Olinordered__semidom(_640282), c_Orderings_Oord__class_Oless__eq(_640282, hAPP(hAPP(c_Power_Opower__class_Opower(_640282), _640284), c_Nat_OSuc(_640286)), hAPP(hAPP(c_Power_Opower__class_Opower(_640282), _640288), c_Nat_OSuc(_640286))), c_Orderings_Oord__class_Oless__eq(_640282, c_Groups_Ozero__class_Ozero(_640282), _640288), -(c_Orderings_Oord__class_Oless__eq(_640282, _640284, _640288))], (9837 ^ _292445) ^ [_640731, _640733] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _640731, c_Nat_OSuc(_640733)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _640731, c_Groups_Oone__class_Oone(tc_Nat_Onat)), _640733))], (9839 ^ _292445) ^ [_640825] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_640825), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _640825)], (9841 ^ _292445) ^ [_640938, _640940] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _640938, _640940), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_640940), _640938) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _640940, _640938)))], (9847 ^ _292445) ^ [_641159, _641161] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _641159, _641161), c_Nat_OSuc(_641159)))], (9849 ^ _292445) ^ [_641274, _641276, _641278] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_641274), _641276), c_Nat_OSuc(_641278)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _641274, _641276), _641278))], (9851 ^ _292445) ^ [_641390, _641392] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_641390), c_Nat_OSuc(_641392)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _641390, _641392))], (9853 ^ _292445) ^ [_641540, _641542] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _641540, c_Nat_OSuc(_641542)), -(_641540 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 9861 ^ _292445 : [(9862 ^ _292445) ^ [] : [-(_641540 = c_Nat_OSuc(9860 ^ [_641540, _641542]))], (9864 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, 9860 ^ [_641540, _641542], _641542))]]], (9866 ^ _292445) ^ [_641952, _641954] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _641952, c_Nat_OSuc(_641954))), 9867 ^ _292445 : [(9868 ^ _292445) ^ [] : [_641952 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (9870 ^ _292445) ^ [_642121] : [_641952 = c_Nat_OSuc(_642121), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _642121, _641954)]]], (9878 ^ _292445) ^ [_642419] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _642419, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_642419 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9884 ^ _292445) ^ [_642577] : [_642577 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _642577, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (9890 ^ _292445) ^ [_642800] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _642800), -(_642800 = c_Nat_OSuc(9893 ^ [_642800]))], (9897 ^ _292445) ^ [_643015] : [9898 ^ _292445 : [(9899 ^ _292445) ^ [_643086] : [_643015 = c_Nat_OSuc(_643086)]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _643015))], (9903 ^ _292445) ^ [_643235] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _643235, c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_643235 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_643235 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (9913 ^ _292445) ^ [_643556, _643558] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _643556, _643558), -(_643558 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _643556, 9916 ^ [_643556, _643558])))], (9920 ^ _292445) ^ [_643795, _643797] : [9921 ^ _292445 : [(9922 ^ _292445) ^ [_643872] : [_643797 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _643795, _643872))]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _643795, _643797))], (9926 ^ _292445) ^ [_644028, _644030] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _644028, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _644030, _644028))))], (9928 ^ _292445) ^ [_644129, _644131] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _644129, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _644129, _644131))))], (9930 ^ _292445) ^ [_644245, _644247] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_644245), _644247), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _644245, _644247))], (9936 ^ _292445) ^ [_644463, _644465] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _644463, _644465), 9939 ^ _292445 : [(9940 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _644465, c_Nat_OSuc(_644463)), -(_644465 = _644463)], (9946 ^ _292445) ^ [] : [_644465 = _644463, -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _644465, c_Nat_OSuc(_644463)))]]], (9952 ^ _292445) ^ [_644934, _644936] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _644934, _644936), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_644934), _644936))], (9958 ^ _292445) ^ [_645152, _645154] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _645152, _645154), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _645152, c_Nat_OSuc(_645154)))], (9964 ^ _292445) ^ [_645399, _645401] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_645399), _645401), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _645399, _645401))], (9970 ^ _292445) ^ [_645569, _645571] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _645569, _645571), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_645569), _645571))], (9976 ^ _292445) ^ [_645818, _645820] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _645818, c_Nat_OSuc(_645820)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _645818, _645820))], (9982 ^ _292445) ^ [_645988, _645990] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _645988, _645990), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _645988, c_Nat_OSuc(_645990)))], (9988 ^ _292445) ^ [_646237, _646239] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _646237, _646239), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_646237), _646239))], (9994 ^ _292445) ^ [_646407, _646409] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_646407), _646409), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _646407, _646409))], (10000 ^ _292445) ^ [_646670, _646672, _646674] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_646670)), _646672), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_646670)), _646674)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _646672, _646674))], (10006 ^ _292445) ^ [_646874, _646876, _646878] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _646876, _646878), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_646874)), _646876), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_646874)), _646878)))], (10012 ^ _292445) ^ [_647171, _647173, _647175] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_647171)), _647173), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_647171)), _647175)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _647173, _647175))], (10018 ^ _292445) ^ [_647375, _647377, _647379] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _647377, _647379), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_647375)), _647377), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_647375)), _647379)))], (10024 ^ _292445) ^ [_647629, _647631] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_647629), _647631), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _647629, _647631))], (10030 ^ _292445) ^ [_647847, _647849] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _647847, c_Nat_OSuc(_647849)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _647847, _647849)), -(_647847 = c_Nat_OSuc(_647849))], (10040 ^ _292445) ^ [_648161, _648163] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _648161, _648163), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _648161, c_Nat_OSuc(_648163)))], (10046 ^ _292445) ^ [_648408, _648410] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_648408), c_Nat_OSuc(_648410)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _648408, _648410))], (10052 ^ _292445) ^ [_648582, _648584] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _648582, _648584), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_648582), c_Nat_OSuc(_648584)))], (10068 ^ _292445) ^ [_649099, _649101] : [10069 ^ _292445 : [(10070 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _649099, _649101)], (10072 ^ _292445) ^ [] : [_649099 = c_Nat_OSuc(_649101)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _649099, c_Nat_OSuc(_649101)))], (10058 ^ _292445) ^ [_648835, _648837] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _648835, c_Nat_OSuc(_648837)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _648835, _648837)), -(_648835 = c_Nat_OSuc(_648837))], (10076 ^ _292445) ^ [_649426, _649428] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _649426, _649428)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_649428), _649426))], (10082 ^ _292445) ^ [_649599, _649601] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_649601), _649599), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _649599, _649601)], (10088 ^ _292445) ^ [_649790] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_649790), _649790)], (10090 ^ _292445) ^ [_649929, _649931] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _649929, _649931)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _649931, c_Nat_OSuc(_649929)))], (10096 ^ _292445) ^ [_650102, _650104] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _650104, c_Nat_OSuc(_650102)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _650102, _650104)], (10112 ^ _292445) ^ [_650612, _650614] : [10113 ^ _292445 : [(10114 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _650612, _650614)], (10116 ^ _292445) ^ [] : [_650612 = _650614]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _650612, c_Nat_OSuc(_650614)))], (10102 ^ _292445) ^ [_650352, _650354] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _650352, c_Nat_OSuc(_650354)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _650352, _650354)), -(_650352 = _650354)], (10120 ^ _292445) ^ [_650935, _650937] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_650935), c_Nat_OSuc(_650937)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _650935, _650937))], (10126 ^ _292445) ^ [_651109, _651111] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _651109, _651111), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_651109), c_Nat_OSuc(_651111)))], (10132 ^ _292445) ^ [_651333, _651335] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _651333, _651335)), 10135 ^ _292445 : [(10136 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _651333, c_Nat_OSuc(_651335)), -(_651333 = _651335)], (10142 ^ _292445) ^ [] : [_651333 = _651335, -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _651333, c_Nat_OSuc(_651335)))]]], (10148 ^ _292445) ^ [_651807, _651809] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _651807, _651809)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _651807, c_Nat_OSuc(_651809)), -(_651809 = _651807)], (10158 ^ _292445) ^ [_652117, _652119] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _652117, _652119), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _652117, c_Nat_OSuc(_652119)))], (10164 ^ _292445) ^ [_652335, _652337] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _652335, _652337), -(c_Nat_OSuc(_652335) = _652337), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_652335), _652337))], (10174 ^ _292445) ^ [_652663, _652665, _652667] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _652663, _652665), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _652665, _652667), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_652663), _652667))], (10184 ^ _292445) ^ [_652982, _652984] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _652982, c_Nat_OSuc(_652984)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _652982, _652984)), -(_652982 = _652984)], (10194 ^ _292445) ^ [_653292, _653294] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_653292), _653294), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _653292, _653294))], (10200 ^ _292445) ^ [_653510, _653512] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_653510), c_Nat_OSuc(_653512)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _653510, _653512))], (10206 ^ _292445) ^ [_653775, _653777, _653779] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_653775)), _653777) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_653775)), _653779), -(_653777 = _653779)], (10212 ^ _292445) ^ [_653975, _653977, _653979] : [_653977 = _653979, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_653975)), _653977) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_653975)), _653979))], (10218 ^ _292445) ^ [_654195] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_654195)], (10220 ^ _292445) ^ [_654274] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_654274)], (10222 ^ _292445) ^ [_654353] : [c_Nat_OSuc(_654353) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10224 ^ _292445) ^ [_654432] : [c_Nat_OSuc(_654432) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10226 ^ _292445) ^ [_654511] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_654511)], (10228 ^ _292445) ^ [_654590] : [c_Nat_OSuc(_654590) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10230 ^ _292445) ^ [_654699, _654701] : [c_Nat_OSuc(_654699) = c_Nat_OSuc(_654701), -(_654699 = _654701)], (10236 ^ _292445) ^ [_654946, _654948] : [c_Nat_OSuc(_654946) = c_Nat_OSuc(_654948), -(_654946 = _654948)], (10242 ^ _292445) ^ [_655116, _655118] : [_655116 = _655118, -(c_Nat_OSuc(_655116) = c_Nat_OSuc(_655118))], (10248 ^ _292445) ^ [_655306] : [c_Nat_OSuc(_655306) = _655306], (10250 ^ _292445) ^ [_655385] : [_655385 = c_Nat_OSuc(_655385)], (10252 ^ _292445) ^ [_655521, _655523, _655525, _655527, _655529] : [-(hAPP(hAPP(c_Power_Opower_Opower(_655521, _655523, _655525), _655527), c_Nat_OSuc(_655529)) = hAPP(hAPP(_655525, _655527), hAPP(hAPP(c_Power_Opower_Opower(_655521, _655523, _655525), _655527), _655529)))], (10254 ^ _292445) ^ [_655649, _655651] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _655649, c_Nat_OSuc(_655651)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _655649, _655651)))], (10256 ^ _292445) ^ [_655755, _655757] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Nat_OSuc(_655755), _655757) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _655755, _655757)))], (10258 ^ _292445) ^ [_655861, _655863] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Nat_OSuc(_655861), _655863) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _655861, c_Nat_OSuc(_655863)))], (10270 ^ _292445) ^ [_656275, _656277] : [10271 ^ _292445 : [(10272 ^ _292445) ^ [] : [_656277 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10274 ^ _292445) ^ [] : [_656275 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _656275), _656277) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10260 ^ _292445) ^ [_656011, _656013] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _656011), _656013) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_656013 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_656011 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10278 ^ _292445) ^ [_656544] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _656544) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10280 ^ _292445) ^ [_656625] : [-(c_NthRoot_Oroot(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _656625) = _656625)], (10282 ^ _292445) ^ [_656706] : [-(c_Nat_OSuc(_656706) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _656706))], (10284 ^ _292445) ^ [_656790] : [-(c_Nat_OSuc(_656790) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _656790, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (10286 ^ _292445) ^ [_656888, _656890] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_656888)), _656890) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _656890, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _656888), _656890)))], (10288 ^ _292445) ^ [_657000, _657002] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _657000), c_Nat_OSuc(_657002)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _657000, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _657000), _657002)))], (10290 ^ _292445) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10292 ^ _292445) ^ [_657209, _657211] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _657209), _657211) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 10295 ^ _292445 : [(10296 ^ _292445) ^ [] : [-(_657209 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10298 ^ _292445) ^ [] : [-(_657211 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (10300 ^ _292445) ^ [_657458, _657460] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _657458), _657460) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _657458 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _657460 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10310 ^ _292445) ^ [_657800, _657802] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _657800, _657802) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 10315 ^ _292445 : [(10316 ^ _292445) ^ [] : [-(_657800 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10318 ^ _292445) ^ [] : [-(_657802 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 10319 ^ _292445 : [(10320 ^ _292445) ^ [] : [-(_657800 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10322 ^ _292445) ^ [] : [-(_657802 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (10324 ^ _292445) ^ [_658210, _658212] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _658210, _658212) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 10325 ^ _292445 : [(10326 ^ _292445) ^ [] : [_658210 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _658212 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10332 ^ _292445) ^ [] : [_658210 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _658212 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (10340 ^ _292445) ^ [_658711, _658713] : [c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _658711, _658713), 10345 ^ _292445 : [(10346 ^ _292445) ^ [] : [-(_658711 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10348 ^ _292445) ^ [] : [-(_658713 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 10349 ^ _292445 : [(10350 ^ _292445) ^ [] : [-(_658711 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10352 ^ _292445) ^ [] : [-(_658713 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (10354 ^ _292445) ^ [_659121, _659123] : [-(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _659121, _659123)), 10355 ^ _292445 : [(10356 ^ _292445) ^ [] : [_659121 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _659123 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10362 ^ _292445) ^ [] : [_659121 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _659123 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (10370 ^ _292445) ^ [_659607, _659609, _659611] : [class_Rings_Ocomm__semiring__1(_659607), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_659607), hAPP(hAPP(c_Power_Opower__class_Opower(_659607), _659609), _659611)), _659609) = hAPP(hAPP(c_Power_Opower__class_Opower(_659607), _659609), c_Nat_OSuc(_659611)))], (10376 ^ _292445) ^ [_659887, _659889, _659891] : [class_Rings_Ocomm__semiring__1(_659887), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_659887), _659889), hAPP(hAPP(c_Power_Opower__class_Opower(_659887), _659889), _659891)) = hAPP(hAPP(c_Power_Opower__class_Opower(_659887), _659889), c_Nat_OSuc(_659891)))], (10382 ^ _292445) ^ [_660167, _660169, _660171] : [class_Rings_Ocomm__semiring__1(_660167), -(hAPP(hAPP(c_Power_Opower__class_Opower(_660167), _660169), c_Nat_OSuc(_660171)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_660167), _660169), hAPP(hAPP(c_Power_Opower__class_Opower(_660167), _660169), _660171)))], (10388 ^ _292445) ^ [_660447, _660449, _660451] : [class_Groups_Omonoid__mult(_660447), -(hAPP(hAPP(c_Power_Opower__class_Opower(_660447), _660449), c_Nat_OSuc(_660451)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_660447), hAPP(hAPP(c_Power_Opower__class_Opower(_660447), _660449), _660451)), _660449))], (10394 ^ _292445) ^ [_660727, _660729, _660731] : [class_Power_Opower(_660727), -(hAPP(hAPP(c_Power_Opower__class_Opower(_660727), _660729), c_Nat_OSuc(_660731)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_660727), _660729), hAPP(hAPP(c_Power_Opower__class_Opower(_660727), _660729), _660731)))], (10400 ^ _292445) ^ [_660993, _660995] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_660993), c_Groups_Ozero__class_Ozero(_660993)), c_Nat_OSuc(_660995)) = c_Groups_Ozero__class_Ozero(_660993)), class_Power_Opower(_660993), class_Rings_Osemiring__0(_660993)], (10410 ^ _292445) ^ [_661330, _661332, _661334] : [class_Rings_Olinordered__semidom(_661330), c_Orderings_Oord__class_Oless(_661330, c_Groups_Oone__class_Oone(_661330), _661332), -(c_Orderings_Oord__class_Oless(_661330, c_Groups_Oone__class_Oone(_661330), hAPP(hAPP(c_Power_Opower__class_Opower(_661330), _661332), c_Nat_OSuc(_661334))))], (10420 ^ _292445) ^ [_661669, _661671] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _661669), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _661671), -(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), _661671), _661669)))], (10430 ^ _292445) ^ [_661986, _661988] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _661986), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _661988), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _661986, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _661986), _661988)))], (10440 ^ _292445) ^ [_662303, _662305] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _662303), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _662305), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _662303, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _662305), _662303)))], (10450 ^ _292445) ^ [_662620, _662622] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _662620), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _662620, c_Nat_OSuc(_662622)), _662620))], (10456 ^ _292445) ^ [_662832] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _662832), -(c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _662832, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = _662832)], (10462 ^ _292445) ^ [_663079, _663081] : [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), _663079), _663081)), 10465 ^ _292445 : [(10466 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _663079))], (10468 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _663081))]]], (10470 ^ _292445) ^ [_663334, _663336] : [-(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), _663334), _663336))), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _663334), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _663336)], (10480 ^ _292445) ^ [_663624] : [-(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(_663624))))], (10482 ^ _292445) ^ [_663751, _663753, _663755] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _663751, _663753), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _663755, c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _663753, _663751))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _663755, _663751), c_Nat_OSuc(_663753)))], (10488 ^ _292445) ^ [_664023, _664025, _664027] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _664023, _664025), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _664025, _664023)), _664027) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_664025), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _664023, _664027)))], (10494 ^ _292445) ^ [] : [-(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))], (10496 ^ _292445) ^ [_664305] : [-(c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(_664305)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _664305), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (10498 ^ _292445) ^ [_664424, _664426] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _664424), -(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), _664424), _664426)))], (10504 ^ _292445) ^ [_664664, _664666, _664668] : [class_Rings_Olinordered__semidom(_664664), c_Orderings_Oord__class_Oless__eq(_664664, c_Groups_Ozero__class_Ozero(_664664), _664666), c_Orderings_Oord__class_Oless__eq(_664664, _664666, c_Groups_Oone__class_Oone(_664664)), -(c_Orderings_Oord__class_Oless__eq(_664664, hAPP(hAPP(c_Power_Opower__class_Opower(_664664), _664666), c_Nat_OSuc(_664668)), _664666))], (10518 ^ _292445) ^ [_665112, _665114, _665116] : [class_Rings_Olinordered__semidom(_665112), c_Orderings_Oord__class_Oless(_665112, c_Groups_Ozero__class_Ozero(_665112), _665114), c_Orderings_Oord__class_Oless(_665112, _665114, c_Groups_Oone__class_Oone(_665112)), -(c_Orderings_Oord__class_Oless(_665112, hAPP(hAPP(c_Power_Opower__class_Opower(_665112), _665114), c_Nat_OSuc(_665116)), c_Groups_Oone__class_Oone(_665112)))], (10532 ^ _292445) ^ [_665578, _665580, _665582, _665584] : [class_Groups_Omonoid__mult(_665578), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _665580, _665582), -(hAPP(hAPP(c_Power_Opower__class_Opower(_665578), _665584), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_665582), _665580)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_665578), hAPP(hAPP(c_Power_Opower__class_Opower(_665578), _665584), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _665582, _665580))), _665584))], (10542 ^ _292445) ^ [_665951] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _665951), -(_665951 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _665951, c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (10548 ^ _292445) ^ [_666155] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _666155), -(c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _666155, c_Groups_Oone__class_Oone(tc_Nat_Onat))) = _666155)], (10554 ^ _292445) ^ [_666393, _666395] : [_666393 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _666393, _666395) = _666395)], (10560 ^ _292445) ^ [_666563, _666565] : [-(_666563 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _666563, _666565) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _666563, c_Groups_Oone__class_Oone(tc_Nat_Onat)), _666565)))], (10566 ^ _292445) ^ [_666806, _666808] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _666806), 10569 ^ _292445 : [(10570 ^ _292445) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _666808, _666806), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _666808, _666806) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10576 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _666808, _666806)), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _666808, _666806) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _666808, _666806), _666806)))]]], (10582 ^ _292445) ^ [_667314, _667316] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _667314), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _667316, _667314)), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _667316, _667314) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _667316, _667314), _667314)))], (10592 ^ _292445) ^ [_667648, _667650] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _667648), -(c_NthRoot_Oroot(c_Nat_OSuc(_667650), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _667648), c_Nat_OSuc(_667650))) = _667648)], (10598 ^ _292445) ^ [_667900, _667902, _667904] : [class_Rings_Ocomm__ring__1(_667900), -(c_Groups_Ominus__class_Ominus(_667900, hAPP(hAPP(c_Power_Opower__class_Opower(_667900), _667902), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(hAPP(c_Power_Opower__class_Opower(_667900), _667904), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_667900), c_Groups_Ominus__class_Ominus(_667900, _667902, _667904)), c_Groups_Oplus__class_Oplus(_667900, _667902, _667904)))], (10604 ^ _292445) ^ [_668186, _668188] : [class_RealVector_Oreal__normed__vector(_668186), 10607 ^ _292445 : [(10620 ^ _292445) ^ [] : [10622 ^ _292445 : [(10623 ^ _292445) ^ [_668922] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_668186, hAPP(_668188, 10621 ^ [_668186, _668188, _668922])), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(_668922)))]], 10625 ^ _292445 : [(10626 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 10624 ^ [_668186, _668188]))], (10628 ^ _292445) ^ [_669143] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_668186, hAPP(_668188, _669143)), 10624 ^ [_668186, _668188]))]]], (10608 ^ _292445) ^ [] : [10617 ^ _292445 : [(10618 ^ _292445) ^ [_668743] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_668186, hAPP(_668188, _668743)), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(10616 ^ [_668186, _668188]))))]], 10609 ^ _292445 : [(10610 ^ _292445) ^ [_668425] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _668425), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_668186, hAPP(_668188, 10613 ^ [_668186, _668188, _668425])), _668425)]]]]], (10630 ^ _292445) ^ [_669283, _669285] : [class_RealVector_Oreal__normed__vector(_669283), 10633 ^ _292445 : [(10646 ^ _292445) ^ [] : [10648 ^ _292445 : [(10649 ^ _292445) ^ [_670019] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_669283, hAPP(_669285, 10647 ^ [_669283, _669285, _670019])), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(_670019)))]], 10651 ^ _292445 : [(10652 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 10650 ^ [_669283, _669285]))], (10654 ^ _292445) ^ [_670240] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_669283, hAPP(_669285, _670240)), 10650 ^ [_669283, _669285]))]]], (10634 ^ _292445) ^ [] : [10643 ^ _292445 : [(10644 ^ _292445) ^ [_669840] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_669283, hAPP(_669285, _669840)), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(10642 ^ [_669283, _669285]))))]], 10635 ^ _292445 : [(10636 ^ _292445) ^ [_669522] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _669522), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_669283, hAPP(_669285, 10639 ^ [_669283, _669285, _669522])), _669522)]]]]], (10656 ^ _292445) ^ [_670423, _670425, _670427] : [hBOOL(hAPP(_670423, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _670425, _670427))), 10661 ^ _292445 : [(10662 ^ _292445) ^ [] : [-(_670427 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10664 ^ _292445) ^ [] : [-(hBOOL(hAPP(_670423, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]], 10666 ^ _292445 : [(10667 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _670427), 10665 ^ [_670423, _670425, _670427]), _670425))], (10669 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _670425, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _670427), c_Nat_OSuc(10665 ^ [_670423, _670425, _670427]))))], (10671 ^ _292445) ^ [] : [-(hBOOL(hAPP(_670423, 10665 ^ [_670423, _670425, _670427])))]]], (10673 ^ _292445) ^ [_671078, _671080, _671082] : [-(hBOOL(hAPP(_671078, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _671080, _671082)))), 10674 ^ _292445 : [(10675 ^ _292445) ^ [] : [_671082 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hBOOL(hAPP(_671078, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10681 ^ _292445) ^ [_671372] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _671082), _671372), _671080), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _671080, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _671082), c_Nat_OSuc(_671372))), hBOOL(hAPP(_671078, _671372))]]], (10693 ^ _292445) ^ [_671809, _671811, _671813] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _671809), 10696 ^ _292445 : [(10707 ^ _292445) ^ [] : [_671811 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _671813, _671809), 10710 ^ _292445 : [(10711 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _671809), _671811), _671813))], (10713 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _671813, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _671809), c_Nat_OSuc(_671811))))]]], (10697 ^ _292445) ^ [] : [-(_671811 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _671813, _671809)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _671809), _671811), _671813), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _671813, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _671809), c_Nat_OSuc(_671811)))]]], (10715 ^ _292445) ^ [_672511, _672513] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _672511), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _672511, _672513), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _672513, _672511) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _672513, _672511), _672511)))], (10725 ^ _292445) ^ [_672842, _672844] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _672842), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _672844), 10733 ^ _292445 : [(10734 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, 10732 ^ [_672842, _672844])), _672842), _672844))], (10736 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _672844, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(10732 ^ [_672842, _672844]))), _672842)))]]], (10738 ^ _292445) ^ [_673342] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _673342), 10742 ^ _292445 : [(10743 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, 10741 ^ [_673342]), _673342))], (10745 ^ _292445) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _673342, c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(10741 ^ [_673342]))))]]], (10747 ^ _292445) ^ [_673713, _673715] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _673713), -(c_Transcendental_Oln(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _673713), _673715)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _673715)), c_Transcendental_Oln(_673713)))], (10753 ^ _292445) ^ [_673963, _673965] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _673963), -(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _673965), c_RealDef_Oreal(tc_Nat_Onat, _673963)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _673965, _673963)), c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _673965, _673963)), c_RealDef_Oreal(tc_Nat_Onat, _673963))))], (10759 ^ _292445) ^ [_674244, _674246, _674248] : [-(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _674244), _674246), _674248) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _674244), c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _674246, _674248)), c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _674244), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _674246, _674248)), _674248)))], (10761 ^ _292445) ^ [_674392, _674394, _674396] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _674392, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _674394), _674396)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _674394), c_Divides_Odiv__class_Omod(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _674392, _674394), _674396)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _674392, _674394)))], (10763 ^ _292445) ^ [_674521] : [class_Groups_Ocancel__comm__monoid__add(_674521), -(class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(_674521)))], (10769 ^ _292445) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex))], (10771 ^ _292445) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal))], (10773 ^ _292445) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat))], (10775 ^ _292445) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint))], (10777 ^ _292445) ^ [_674937, _674939] : [class_Orderings_Opreorder(_674937), -(class_Orderings_Opreorder(tc_fun(_674939, _674937)))], (10783 ^ _292445) ^ [_675149, _675151] : [class_Orderings_Oorder(_675149), -(class_Orderings_Oorder(tc_fun(_675151, _675149)))], (10789 ^ _292445) ^ [_675361, _675363] : [class_Orderings_Oord(_675361), -(class_Orderings_Oord(tc_fun(_675363, _675361)))], (10795 ^ _292445) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (10797 ^ _292445) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (10799 ^ _292445) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (10801 ^ _292445) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (10803 ^ _292445) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (10805 ^ _292445) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (10807 ^ _292445) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (10809 ^ _292445) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))], (10811 ^ _292445) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (10813 ^ _292445) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (10815 ^ _292445) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (10817 ^ _292445) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (10819 ^ _292445) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (10821 ^ _292445) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (10823 ^ _292445) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (10825 ^ _292445) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (10827 ^ _292445) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (10829 ^ _292445) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (10831 ^ _292445) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (10833 ^ _292445) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (10835 ^ _292445) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (10837 ^ _292445) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (10839 ^ _292445) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (10841 ^ _292445) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (10843 ^ _292445) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (10845 ^ _292445) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_Int_Oint))], (10847 ^ _292445) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (10849 ^ _292445) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (10851 ^ _292445) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (10853 ^ _292445) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (10855 ^ _292445) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (10857 ^ _292445) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Int_Oint))], (10859 ^ _292445) ^ [] : [-(class_Divides_Osemiring__div(tc_Int_Oint))], (10861 ^ _292445) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (10863 ^ _292445) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (10865 ^ _292445) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (10867 ^ _292445) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (10869 ^ _292445) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (10871 ^ _292445) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (10873 ^ _292445) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (10875 ^ _292445) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (10877 ^ _292445) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (10879 ^ _292445) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (10881 ^ _292445) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (10883 ^ _292445) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (10885 ^ _292445) ^ [] : [-(class_Rings_Ocomm__ring(tc_Int_Oint))], (10887 ^ _292445) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (10889 ^ _292445) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (10891 ^ _292445) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (10893 ^ _292445) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (10895 ^ _292445) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (10897 ^ _292445) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (10899 ^ _292445) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (10901 ^ _292445) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (10903 ^ _292445) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (10905 ^ _292445) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (10907 ^ _292445) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (10909 ^ _292445) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (10911 ^ _292445) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (10913 ^ _292445) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (10915 ^ _292445) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (10917 ^ _292445) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (10919 ^ _292445) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (10921 ^ _292445) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (10923 ^ _292445) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (10925 ^ _292445) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (10927 ^ _292445) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (10929 ^ _292445) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (10931 ^ _292445) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (10933 ^ _292445) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (10935 ^ _292445) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (10937 ^ _292445) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (10939 ^ _292445) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (10941 ^ _292445) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (10943 ^ _292445) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (10945 ^ _292445) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (10947 ^ _292445) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Nat_Onat))], (10949 ^ _292445) ^ [] : [-(class_Divides_Osemiring__div(tc_Nat_Onat))], (10951 ^ _292445) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (10953 ^ _292445) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (10955 ^ _292445) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (10957 ^ _292445) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (10959 ^ _292445) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (10961 ^ _292445) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (10963 ^ _292445) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (10965 ^ _292445) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (10967 ^ _292445) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (10969 ^ _292445) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (10971 ^ _292445) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (10973 ^ _292445) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (10975 ^ _292445) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (10977 ^ _292445) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (10979 ^ _292445) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (10981 ^ _292445) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (10983 ^ _292445) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (10985 ^ _292445) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal))], (10987 ^ _292445) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal))], (10989 ^ _292445) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal))], (10991 ^ _292445) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal))], (10993 ^ _292445) ^ [] : [-(class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal))], (10995 ^ _292445) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal))], (10997 ^ _292445) ^ [] : [-(class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal))], (10999 ^ _292445) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal))], (11001 ^ _292445) ^ [] : [-(class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal))], (11003 ^ _292445) ^ [] : [-(class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal))], (11005 ^ _292445) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal))], (11007 ^ _292445) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal))], (11009 ^ _292445) ^ [] : [-(class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal))], (11011 ^ _292445) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal))], (11013 ^ _292445) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal))], (11015 ^ _292445) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal))], (11017 ^ _292445) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal))], (11019 ^ _292445) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal))], (11021 ^ _292445) ^ [] : [-(class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal))], (11023 ^ _292445) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal))], (11025 ^ _292445) ^ [] : [-(class_RealVector_Oreal__normed__field(tc_RealDef_Oreal))], (11027 ^ _292445) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal))], (11029 ^ _292445) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal))], (11031 ^ _292445) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal))], (11033 ^ _292445) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal))], (11035 ^ _292445) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal))], (11037 ^ _292445) ^ [] : [-(class_Rings_Olinordered__semiring(tc_RealDef_Oreal))], (11039 ^ _292445) ^ [] : [-(class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal))], (11041 ^ _292445) ^ [] : [-(class_Rings_Olinordered__semidom(tc_RealDef_Oreal))], (11043 ^ _292445) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal))], (11045 ^ _292445) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal))], (11047 ^ _292445) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_RealDef_Oreal))], (11049 ^ _292445) ^ [] : [-(class_Fields_Olinordered__field(tc_RealDef_Oreal))], (11051 ^ _292445) ^ [] : [-(class_Rings_Oordered__semiring(tc_RealDef_Oreal))], (11053 ^ _292445) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_RealDef_Oreal))], (11055 ^ _292445) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_RealDef_Oreal))], (11057 ^ _292445) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal))], (11059 ^ _292445) ^ [] : [-(class_Rings_Olinordered__ring(tc_RealDef_Oreal))], (11061 ^ _292445) ^ [] : [-(class_Rings_Olinordered__idom(tc_RealDef_Oreal))], (11063 ^ _292445) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal))], (11065 ^ _292445) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal))], (11067 ^ _292445) ^ [] : [-(class_RealVector_Oreal__field(tc_RealDef_Oreal))], (11069 ^ _292445) ^ [] : [-(class_Rings_Odivision__ring(tc_RealDef_Oreal))], (11071 ^ _292445) ^ [] : [-(class_Rings_Ocomm__semiring(tc_RealDef_Oreal))], (11073 ^ _292445) ^ [] : [-(class_Groups_Oab__group__add(tc_RealDef_Oreal))], (11075 ^ _292445) ^ [] : [-(class_Rings_Ozero__neq__one(tc_RealDef_Oreal))], (11077 ^ _292445) ^ [] : [-(class_Rings_Oordered__ring(tc_RealDef_Oreal))], (11079 ^ _292445) ^ [] : [-(class_Orderings_Opreorder(tc_RealDef_Oreal))], (11081 ^ _292445) ^ [] : [-(class_Orderings_Olinorder(tc_RealDef_Oreal))], (11083 ^ _292445) ^ [] : [-(class_Groups_Omonoid__mult(tc_RealDef_Oreal))], (11085 ^ _292445) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_RealDef_Oreal))], (11087 ^ _292445) ^ [] : [-(class_Groups_Omonoid__add(tc_RealDef_Oreal))], (11089 ^ _292445) ^ [] : [-(class_Rings_Osemiring__0(tc_RealDef_Oreal))], (11091 ^ _292445) ^ [] : [-(class_Groups_Ogroup__add(tc_RealDef_Oreal))], (11093 ^ _292445) ^ [] : [-(class_Rings_Omult__zero(tc_RealDef_Oreal))], (11095 ^ _292445) ^ [] : [-(class_Rings_Ocomm__ring(tc_RealDef_Oreal))], (11097 ^ _292445) ^ [] : [-(class_Orderings_Oorder(tc_RealDef_Oreal))], (11099 ^ _292445) ^ [] : [-(class_Int_Oring__char__0(tc_RealDef_Oreal))], (11101 ^ _292445) ^ [] : [-(class_Rings_Osemiring(tc_RealDef_Oreal))], (11103 ^ _292445) ^ [] : [-(class_Orderings_Oord(tc_RealDef_Oreal))], (11105 ^ _292445) ^ [] : [-(class_Rings_Oring__1(tc_RealDef_Oreal))], (11107 ^ _292445) ^ [] : [-(class_Fields_Ofield(tc_RealDef_Oreal))], (11109 ^ _292445) ^ [] : [-(class_Power_Opower(tc_RealDef_Oreal))], (11111 ^ _292445) ^ [] : [-(class_Groups_Ozero(tc_RealDef_Oreal))], (11113 ^ _292445) ^ [] : [-(class_Rings_Oring(tc_RealDef_Oreal))], (11115 ^ _292445) ^ [] : [-(class_Rings_Oidom(tc_RealDef_Oreal))], (11117 ^ _292445) ^ [] : [-(class_Groups_Oone(tc_RealDef_Oreal))], (11119 ^ _292445) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex))], (11121 ^ _292445) ^ [] : [-(class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex))], (11123 ^ _292445) ^ [] : [-(class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex))], (11125 ^ _292445) ^ [] : [-(class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex))], (11127 ^ _292445) ^ [] : [-(class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex))], (11129 ^ _292445) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex))], (11131 ^ _292445) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex))], (11133 ^ _292445) ^ [] : [-(class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex))], (11135 ^ _292445) ^ [] : [-(class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex))], (11137 ^ _292445) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex))], (11139 ^ _292445) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex))], (11141 ^ _292445) ^ [] : [-(class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex))], (11143 ^ _292445) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex))], (11145 ^ _292445) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex))], (11147 ^ _292445) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex))], (11149 ^ _292445) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex))], (11151 ^ _292445) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex))], (11153 ^ _292445) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex))], (11155 ^ _292445) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex))], (11157 ^ _292445) ^ [] : [-(class_RealVector_Oreal__field(tc_Complex_Ocomplex))], (11159 ^ _292445) ^ [] : [-(class_Rings_Odivision__ring(tc_Complex_Ocomplex))], (11161 ^ _292445) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Complex_Ocomplex))], (11163 ^ _292445) ^ [] : [-(class_Groups_Oab__group__add(tc_Complex_Ocomplex))], (11165 ^ _292445) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Complex_Ocomplex))], (11167 ^ _292445) ^ [] : [-(class_Groups_Omonoid__mult(tc_Complex_Ocomplex))], (11169 ^ _292445) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex))], (11171 ^ _292445) ^ [] : [-(class_Groups_Omonoid__add(tc_Complex_Ocomplex))], (11173 ^ _292445) ^ [] : [-(class_Rings_Osemiring__0(tc_Complex_Ocomplex))], (11175 ^ _292445) ^ [] : [-(class_Groups_Ogroup__add(tc_Complex_Ocomplex))], (11177 ^ _292445) ^ [] : [-(class_Rings_Omult__zero(tc_Complex_Ocomplex))], (11179 ^ _292445) ^ [] : [-(class_Rings_Ocomm__ring(tc_Complex_Ocomplex))], (11181 ^ _292445) ^ [] : [-(class_Int_Oring__char__0(tc_Complex_Ocomplex))], (11183 ^ _292445) ^ [] : [-(class_Rings_Osemiring(tc_Complex_Ocomplex))], (11185 ^ _292445) ^ [] : [-(class_Rings_Oring__1(tc_Complex_Ocomplex))], (11187 ^ _292445) ^ [] : [-(class_Fields_Ofield(tc_Complex_Ocomplex))], (11189 ^ _292445) ^ [] : [-(class_Power_Opower(tc_Complex_Ocomplex))], (11191 ^ _292445) ^ [] : [-(class_Groups_Ozero(tc_Complex_Ocomplex))], (11193 ^ _292445) ^ [] : [-(class_Rings_Oring(tc_Complex_Ocomplex))], (11195 ^ _292445) ^ [] : [-(class_Rings_Oidom(tc_Complex_Ocomplex))], (11197 ^ _292445) ^ [] : [-(class_Groups_Oone(tc_Complex_Ocomplex))], (11199 ^ _292445) ^ [_686265] : [class_Rings_Oidom(_686265), -(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(_686265)))], (11205 ^ _292445) ^ [_686455] : [class_Rings_Olinordered__idom(_686455), -(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(_686455)))], (11211 ^ _292445) ^ [_686645] : [class_Rings_Olinordered__idom(_686645), -(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(_686645)))], (11217 ^ _292445) ^ [_686835] : [class_Rings_Olinordered__idom(_686835), -(class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(_686835)))], (11223 ^ _292445) ^ [_687025] : [class_Rings_Olinordered__idom(_687025), -(class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(_687025)))], (11229 ^ _292445) ^ [_687215] : [class_Rings_Olinordered__idom(_687215), -(class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(_687215)))], (11235 ^ _292445) ^ [_687405] : [class_Rings_Olinordered__idom(_687405), -(class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(_687405)))], (11241 ^ _292445) ^ [_687595] : [class_Rings_Olinordered__idom(_687595), -(class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(_687595)))], (11247 ^ _292445) ^ [_687785] : [class_Rings_Olinordered__idom(_687785), -(class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(_687785)))], (11253 ^ _292445) ^ [_687975] : [class_Rings_Olinordered__idom(_687975), -(class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(_687975)))], (11259 ^ _292445) ^ [_688165] : [class_Groups_Ocancel__comm__monoid__add(_688165), -(class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(_688165)))], (11265 ^ _292445) ^ [_688355] : [class_Rings_Oidom(_688355), -(class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(_688355)))], (11271 ^ _292445) ^ [_688545] : [class_Rings_Olinordered__idom(_688545), -(class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(_688545)))], (11277 ^ _292445) ^ [_688735] : [class_Rings_Olinordered__idom(_688735), -(class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(_688735)))], (11283 ^ _292445) ^ [_688925] : [class_Rings_Oidom(_688925), -(class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(_688925)))], (11289 ^ _292445) ^ [_689115] : [class_Rings_Olinordered__idom(_689115), -(class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(_689115)))], (11295 ^ _292445) ^ [_689305] : [class_Rings_Olinordered__idom(_689305), -(class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(_689305)))], (11301 ^ _292445) ^ [_689495] : [class_Rings_Olinordered__idom(_689495), -(class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(_689495)))], (11307 ^ _292445) ^ [_689685] : [class_Groups_Ocancel__comm__monoid__add(_689685), -(class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(_689685)))], (11313 ^ _292445) ^ [_689875] : [class_Rings_Olinordered__idom(_689875), -(class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(_689875)))], (11319 ^ _292445) ^ [_690065] : [class_Rings_Olinordered__idom(_690065), -(class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(_690065)))], (11325 ^ _292445) ^ [_690255] : [class_Rings_Ocomm__semiring__0(_690255), -(class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(_690255)))], (11331 ^ _292445) ^ [_690445] : [class_Rings_Ocomm__semiring__1(_690445), -(class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(_690445)))], (11337 ^ _292445) ^ [_690635] : [class_Groups_Ocomm__monoid__add(_690635), -(class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(_690635)))], (11343 ^ _292445) ^ [_690825] : [class_Rings_Olinordered__idom(_690825), -(class_Rings_Oordered__semiring(tc_Polynomial_Opoly(_690825)))], (11349 ^ _292445) ^ [_691015] : [class_Rings_Olinordered__idom(_691015), -(class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(_691015)))], (11355 ^ _292445) ^ [_691205] : [class_Rings_Oidom(_691205), -(class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(_691205)))], (11361 ^ _292445) ^ [_691395] : [class_Groups_Ocomm__monoid__add(_691395), -(class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(_691395)))], (11367 ^ _292445) ^ [_691585] : [class_Rings_Olinordered__idom(_691585), -(class_Rings_Olinordered__ring(tc_Polynomial_Opoly(_691585)))], (11373 ^ _292445) ^ [_691775] : [class_Rings_Olinordered__idom(_691775), -(class_Rings_Olinordered__idom(tc_Polynomial_Opoly(_691775)))], (11379 ^ _292445) ^ [_691965] : [class_Rings_Ocomm__semiring__1(_691965), -(class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(_691965)))], (11385 ^ _292445) ^ [_692155] : [class_Rings_Ocomm__semiring__0(_692155), -(class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(_692155)))], (11391 ^ _292445) ^ [_692345] : [class_Fields_Ofield(_692345), -(class_Divides_Osemiring__div(tc_Polynomial_Opoly(_692345)))], (11397 ^ _292445) ^ [_692535] : [class_Rings_Ocomm__semiring__0(_692535), -(class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(_692535)))], (11403 ^ _292445) ^ [_692725] : [class_Groups_Oab__group__add(_692725), -(class_Groups_Oab__group__add(tc_Polynomial_Opoly(_692725)))], (11409 ^ _292445) ^ [_692915] : [class_Rings_Ocomm__semiring__1(_692915), -(class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(_692915)))], (11415 ^ _292445) ^ [_693105] : [class_Rings_Olinordered__idom(_693105), -(class_Rings_Oordered__ring(tc_Polynomial_Opoly(_693105)))], (11421 ^ _292445) ^ [_693295] : [class_Rings_Olinordered__idom(_693295), -(class_Orderings_Opreorder(tc_Polynomial_Opoly(_693295)))], (11427 ^ _292445) ^ [_693485] : [class_Rings_Olinordered__idom(_693485), -(class_Orderings_Olinorder(tc_Polynomial_Opoly(_693485)))], (11433 ^ _292445) ^ [_693675] : [class_Rings_Ocomm__semiring__1(_693675), -(class_Groups_Omonoid__mult(tc_Polynomial_Opoly(_693675)))], (11439 ^ _292445) ^ [_693865] : [class_Rings_Ocomm__ring__1(_693865), -(class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(_693865)))], (11445 ^ _292445) ^ [_694055] : [class_Groups_Ocomm__monoid__add(_694055), -(class_Groups_Omonoid__add(tc_Polynomial_Opoly(_694055)))], (11451 ^ _292445) ^ [_694245] : [class_Rings_Ocomm__semiring__0(_694245), -(class_Rings_Osemiring__0(tc_Polynomial_Opoly(_694245)))], (11457 ^ _292445) ^ [_694435] : [class_Groups_Oab__group__add(_694435), -(class_Groups_Ogroup__add(tc_Polynomial_Opoly(_694435)))], (11463 ^ _292445) ^ [_694625] : [class_Rings_Ocomm__semiring__0(_694625), -(class_Rings_Omult__zero(tc_Polynomial_Opoly(_694625)))], (11469 ^ _292445) ^ [_694815] : [class_Rings_Ocomm__ring(_694815), -(class_Rings_Ocomm__ring(tc_Polynomial_Opoly(_694815)))], (11475 ^ _292445) ^ [_695005] : [class_Rings_Olinordered__idom(_695005), -(class_Orderings_Oorder(tc_Polynomial_Opoly(_695005)))], (11481 ^ _292445) ^ [_695195] : [class_Rings_Olinordered__idom(_695195), -(class_Int_Oring__char__0(tc_Polynomial_Opoly(_695195)))], (11487 ^ _292445) ^ [_695385] : [class_Rings_Ocomm__semiring__0(_695385), -(class_Rings_Osemiring(tc_Polynomial_Opoly(_695385)))], (11493 ^ _292445) ^ [_695575] : [class_Rings_Olinordered__idom(_695575), -(class_Orderings_Oord(tc_Polynomial_Opoly(_695575)))], (11499 ^ _292445) ^ [_695765] : [class_Rings_Ocomm__ring__1(_695765), -(class_Rings_Oring__1(tc_Polynomial_Opoly(_695765)))], (11505 ^ _292445) ^ [_695955] : [class_Rings_Ocomm__semiring__1(_695955), -(class_Power_Opower(tc_Polynomial_Opoly(_695955)))], (11511 ^ _292445) ^ [_696145] : [class_Groups_Ozero(_696145), -(class_Groups_Ozero(tc_Polynomial_Opoly(_696145)))], (11517 ^ _292445) ^ [_696335] : [class_Rings_Ocomm__ring(_696335), -(class_Rings_Oring(tc_Polynomial_Opoly(_696335)))], (11523 ^ _292445) ^ [_696525] : [class_Rings_Oidom(_696525), -(class_Rings_Oidom(tc_Polynomial_Opoly(_696525)))], (11529 ^ _292445) ^ [_696715] : [class_Rings_Ocomm__semiring__1(_696715), -(class_Groups_Oone(tc_Polynomial_Opoly(_696715)))], (11535 ^ _292445) ^ [_696919, _696921] : [hBOOL(c_fequal(_696919, _696921)), -(_696919 = _696921)], (11541 ^ _292445) ^ [_697115, _697117] : [_697115 = _697117, -(hBOOL(c_fequal(_697115, _697117)))]], input).
% 148.80/144.21  ncf('1',plain,[c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v_da____), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_aa____)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_z____), v_c____)))],start(11547 ^ 0)).
% 148.80/144.21  ncf('1.1',plain,[-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v_da____), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_aa____)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_z____), v_c____)))), class_Orderings_Oorder(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_z____), v_c____)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_z____)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____)), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v_da____), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_aa____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_z____)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____)))],extension(997 ^ 1,bind([[_326202, _326204, _326206, _326208], [tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_z____), v_c____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_z____)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v_da____), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_aa____))]]))).
% 148.80/144.21  ncf('1.1.1',plain,[-(class_Orderings_Oorder(tc_RealDef_Oreal))],extension(11097 ^ 2)).
% 148.80/144.21  ncf('1.1.2',plain,[-(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_z____), v_c____)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_z____)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____))), class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex)],extension(69 ^ 2,bind([[_295315, _295317, _295319], [tc_Complex_Ocomplex, v_z____, v_c____]]))).
% 148.80/144.21  ncf('1.1.2.1',plain,[-(class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex))],extension(11121 ^ 3)).
% 148.80/144.21  ncf('1.1.3',plain,[-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v_da____), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_aa____)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_z____)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____)))), 4232 : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v_da____), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_aa____)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_z____)), 4232 : class_Fields_Olinordered__field(tc_RealDef_Oreal), 4232 : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____))],extension(4224 ^ 2,bind([[_435707, _435709, _435711, _435713], [tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v_da____), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_aa____)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_z____)]]))).
% 148.80/144.21  ncf('1.1.3.1',plain,[-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v_da____), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_aa____)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_z____)))],extension(11 ^ 5)).
% 148.80/144.21  ncf('1.1.3.2',plain,[-(class_Fields_Olinordered__field(tc_RealDef_Oreal))],extension(11049 ^ 3)).
% 148.80/144.21  ncf('1.1.3.3',plain,[-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____)))],extension(1804 ^ 3)).
% 148.80/144.21  %-----------------------------------------------------
% 148.80/144.21  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------