nanoCoP---2.0.THM-Prf.s

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%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWW204+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n008.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 12:25:45 EDT 2023

% Result   : Theorem 0.52s 1.40s
% Output   : Proof 0.52s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SWW204+1 : TPTP v8.1.2. Released v5.2.0.
% 0.11/0.13  % Command  : nanocop.sh %s %d
% 0.13/0.34  % Computer : n008.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Thu May 18 22:08:09 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.52/1.40  
% 0.52/1.40  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 0.52/1.40  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.52/1.40  %-----------------------------------------------------
% 0.52/1.40  ncf(matrix, plain, [(11702 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), v_r))], (756 ^ _393467) ^ [_416504, _416506, _416508, _416510] : [-(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_416510, _416506) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_416508, _416504)), _416510 = _416508, _416506 = _416504], (766 ^ _393467) ^ [_416947, _416949, _416951, _416953, _416955, _416957, _416959, _416961, _416963, _416965] : [-(c_Fun_Ocomp(_416965, _416961, _416957, _416953, _416949) = c_Fun_Ocomp(_416963, _416959, _416955, _416951, _416947)), _416965 = _416963, _416961 = _416959, _416957 = _416955, _416953 = _416951, _416949 = _416947], (788 ^ _393467) ^ [_417769, _417771, _417773, _417775, _417777, _417779] : [-(c_Power_Opower_Opower(_417779, _417775, _417771) = c_Power_Opower_Opower(_417777, _417773, _417769)), _417779 = _417777, _417775 = _417773, _417771 = _417769], (802 ^ _393467) ^ [_418229, _418231] : [_418231 = _418229, -(c_Transcendental_Oln(_418231) = c_Transcendental_Oln(_418229))], (808 ^ _393467) ^ [_418447, _418449] : [_418449 = _418447, -(c_Complex_Oexpi(_418449) = c_Complex_Oexpi(_418447))], (814 ^ _393467) ^ [_418665, _418667] : [_418667 = _418665, -(c_RComplete_Onatceiling(_418667) = c_RComplete_Onatceiling(_418665))], (820 ^ _393467) ^ [_418911, _418913, _418915, _418917] : [-(c_Complex_Orcis(_418917, _418913) = c_Complex_Orcis(_418915, _418911)), _418917 = _418915, _418913 = _418911], (830 ^ _393467) ^ [_419270, _419272, _419274, _419276] : [-(c_NthRoot_Oroot(_419276, _419272) = c_NthRoot_Oroot(_419274, _419270)), _419276 = _419274, _419272 = _419270], (840 ^ _393467) ^ [_419601, _419603] : [_419603 = _419601, -(c_Nat_OSuc(_419603) = c_Nat_OSuc(_419601))], (846 ^ _393467) ^ [_419847, _419849, _419851, _419853] : [-(c_Nat__Transfer_Otsub(_419853, _419849) = c_Nat__Transfer_Otsub(_419851, _419847)), _419853 = _419851, _419849 = _419847], (856 ^ _393467) ^ [_420178, _420180] : [_420180 = _420178, -(c_Complex_Ocis(_420180) = c_Complex_Ocis(_420178))], (862 ^ _393467) ^ [_420396, _420398] : [_420398 = _420396, -(c_Transcendental_Osin(_420398) = c_Transcendental_Osin(_420396))], (868 ^ _393467) ^ [_420614, _420616] : [_420616 = _420614, -(c_Groups_Oplus__class_Oplus(_420616) = c_Groups_Oplus__class_Oplus(_420614))], (874 ^ _393467) ^ [_420860, _420862, _420864, _420866] : [-(c_Groups_Oabs__class_Oabs(_420866, _420862) = c_Groups_Oabs__class_Oabs(_420864, _420860)), _420866 = _420864, _420862 = _420860], (884 ^ _393467) ^ [_421247, _421249, _421251, _421253, _421255, _421257] : [-(c_Groups_Ominus__class_Ominus(_421257, _421253, _421249) = c_Groups_Ominus__class_Ominus(_421255, _421251, _421247)), _421257 = _421255, _421253 = _421251, _421249 = _421247], (898 ^ _393467) ^ [_421707, _421709] : [_421709 = _421707, -(c_Complex_Ocomplex_Ocomplex__size(_421709) = c_Complex_Ocomplex_Ocomplex__size(_421707))], (904 ^ _393467) ^ [_421925, _421927] : [_421927 = _421925, -(c_Transcendental_Ocos(_421927) = c_Transcendental_Ocos(_421925))], (910 ^ _393467) ^ [_422143, _422145] : [_422145 = _422143, -(c_Complex_Oarg(_422145) = c_Complex_Oarg(_422143))], (916 ^ _393467) ^ [_422389, _422391, _422393, _422395] : [-(c_Nat_Osize__class_Osize(_422395, _422391) = c_Nat_Osize__class_Osize(_422393, _422389)), _422395 = _422393, _422391 = _422389], (926 ^ _393467) ^ [_422776, _422778, _422780, _422782, _422784, _422786] : [-(c_Complex_Ocomplex_Ocomplex__case(_422786, _422782, _422778) = c_Complex_Ocomplex_Ocomplex__case(_422784, _422780, _422776)), _422786 = _422784, _422782 = _422780, _422778 = _422776], (940 ^ _393467) ^ [_423292, _423294, _423296, _423298, _423300, _423302] : [-(c_Complex_Ocomplex_Ocomplex__rec(_423302, _423298, _423294) = c_Complex_Ocomplex_Ocomplex__rec(_423300, _423296, _423292)), _423302 = _423300, _423298 = _423296, _423294 = _423292], (954 ^ _393467) ^ [_423780, _423782, _423784, _423786] : [-(c_Complex_Ocomplex_OComplex(_423786, _423782) = c_Complex_Ocomplex_OComplex(_423784, _423780)), _423786 = _423784, _423782 = _423780], (964 ^ _393467) ^ [_424111, _424113] : [_424113 = _424111, -(c_Groups_Oone__class_Oone(_424113) = c_Groups_Oone__class_Oone(_424111))], (970 ^ _393467) ^ [_424357, _424359, _424361, _424363] : [-(c_Orderings_Oord__class_Oless(_424363, _424359) = c_Orderings_Oord__class_Oless(_424361, _424357)), _424363 = _424361, _424359 = _424357], (980 ^ _393467) ^ [_424716, _424718, _424720, _424722] : [-(c_RealDef_Oreal(_424722, _424718) = c_RealDef_Oreal(_424720, _424716)), _424722 = _424720, _424718 = _424716], (990 ^ _393467) ^ [_425103, _425105, _425107, _425109, _425111, _425113] : [-(c_Divides_Odiv__class_Odiv(_425113, _425109, _425105) = c_Divides_Odiv__class_Odiv(_425111, _425107, _425103)), _425113 = _425111, _425109 = _425107, _425105 = _425103], (1004 ^ _393467) ^ [_425563, _425565] : [_425565 = _425563, -(c_RComplete_Onatfloor(_425565) = c_RComplete_Onatfloor(_425563))], (1010 ^ _393467) ^ [_425781, _425783] : [_425783 = _425781, -(c_Groups_Otimes__class_Otimes(_425783) = c_Groups_Otimes__class_Otimes(_425781))], (1016 ^ _393467) ^ [_425999, _426001] : [_426001 = _425999, -(c_Power_Opower__class_Opower(_426001) = c_Power_Opower__class_Opower(_425999))], (1022 ^ _393467) ^ [_426273, _426275, _426277, _426279, _426281, _426283] : [-(c_Rings_Oinverse__class_Odivide(_426283, _426279, _426275) = c_Rings_Oinverse__class_Odivide(_426281, _426277, _426273)), _426283 = _426281, _426279 = _426277, _426275 = _426273], (1036 ^ _393467) ^ [_426761, _426763, _426765, _426767] : [-(c_RealVector_Onorm__class_Onorm(_426767, _426763) = c_RealVector_Onorm__class_Onorm(_426765, _426761)), _426767 = _426765, _426763 = _426761], (1046 ^ _393467) ^ [_427120, _427122, _427124, _427126] : [-(tc_fun(_427126, _427122) = tc_fun(_427124, _427120)), _427126 = _427124, _427122 = _427120], (1056 ^ _393467) ^ [_427451, _427453] : [_427453 = _427451, -(tc_Polynomial_Opoly(_427453) = tc_Polynomial_Opoly(_427451))], (1062 ^ _393467) ^ [_427725, _427727, _427729, _427731, _427733, _427735] : [-(c_COMBK(_427735, _427731, _427727) = c_COMBK(_427733, _427729, _427725)), _427735 = _427733, _427731 = _427729, _427727 = _427725], (1076 ^ _393467) ^ [_428297, _428299, _428301, _428303, _428305, _428307, _428309, _428311, _428313, _428315] : [-(c_COMBB(_428315, _428311, _428307, _428303, _428299) = c_COMBB(_428313, _428309, _428305, _428301, _428297)), _428315 = _428313, _428311 = _428309, _428307 = _428305, _428303 = _428301, _428299 = _428297], (1098 ^ _393467) ^ [_429175, _429177, _429179, _429181, _429183, _429185, _429187, _429189, _429191, _429193] : [-(c_COMBC(_429193, _429189, _429185, _429181, _429177) = c_COMBC(_429191, _429187, _429183, _429179, _429175)), _429193 = _429191, _429189 = _429187, _429185 = _429183, _429181 = _429179, _429177 = _429175], (1120 ^ _393467) ^ [_429969, _429971, _429973, _429975] : [-(hAPP(_429975, _429971) = hAPP(_429973, _429969)), _429975 = _429973, _429971 = _429969], (1140 ^ _393467) ^ [_430639, _430641] : [_430641 = _430639, -(c_Groups_Ozero__class_Ozero(_430641) = c_Groups_Ozero__class_Ozero(_430639))], (1130 ^ _393467) ^ [_430328, _430330, _430332, _430334] : [-(c_Orderings_Oord__class_Oless__eq(_430334, _430330) = c_Orderings_Oord__class_Oless__eq(_430332, _430328)), _430334 = _430332, _430330 = _430328], (2 ^ _393467) ^ [_393611] : [-(_393611 = _393611)], (4 ^ _393467) ^ [_393718, _393720] : [_393720 = _393718, -(_393718 = _393720)], (10 ^ _393467) ^ [_393922, _393924, _393926] : [-(_393926 = _393922), _393926 = _393924, _393924 = _393922], (20 ^ _393467) ^ [_394263, _394265, _394267, _394269] : [-(c_SEQ_Odecseq(_394267, _394263)), c_SEQ_Odecseq(_394269, _394265), _394269 = _394267, _394265 = _394263], (34 ^ _393467) ^ [_394707, _394709, _394711, _394713] : [-(c_SEQ_Oincseq(_394711, _394707)), c_SEQ_Oincseq(_394713, _394709), _394713 = _394711, _394709 = _394707], (48 ^ _393467) ^ [_395123, _395125] : [-(class_Lattices_Oab__semigroup__idem__mult(_395123)), _395125 = _395123, class_Lattices_Oab__semigroup__idem__mult(_395125)], (58 ^ _393467) ^ [_395418, _395420] : [-(c_SEQ_Osubseq(_395418)), _395420 = _395418, c_SEQ_Osubseq(_395420)], (68 ^ _393467) ^ [_395741, _395743, _395745, _395747] : [-(c_SEQ_Omonoseq(_395745, _395741)), c_SEQ_Omonoseq(_395747, _395743), _395747 = _395745, _395743 = _395741], (82 ^ _393467) ^ [_396185, _396187, _396189, _396191] : [-(c_SEQ_OBseq(_396189, _396185)), c_SEQ_OBseq(_396191, _396187), _396191 = _396189, _396187 = _396185], (96 ^ _393467) ^ [_396601, _396603] : [-(class_RealVector_Oreal__normed__div__algebra(_396601)), _396603 = _396601, class_RealVector_Oreal__normed__div__algebra(_396603)], (106 ^ _393467) ^ [_396896, _396898] : [-(class_RealVector_Oreal__normed__algebra__1(_396896)), _396898 = _396896, class_RealVector_Oreal__normed__algebra__1(_396898)], (116 ^ _393467) ^ [_397191, _397193] : [-(class_RealVector_Oreal__normed__algebra(_397191)), _397193 = _397191, class_RealVector_Oreal__normed__algebra(_397193)], (126 ^ _393467) ^ [_397486, _397488] : [-(class_RealVector_Oreal__normed__vector(_397486)), _397488 = _397486, class_RealVector_Oreal__normed__vector(_397488)], (136 ^ _393467) ^ [_397781, _397783] : [-(class_RealVector_Oreal__normed__field(_397781)), _397783 = _397781, class_RealVector_Oreal__normed__field(_397783)], (146 ^ _393467) ^ [_398076, _398078] : [-(class_Fields_Ofield__inverse__zero(_398076)), _398078 = _398076, class_Fields_Ofield__inverse__zero(_398078)], (156 ^ _393467) ^ [_398371, _398373] : [-(class_Rings_Odivision__ring(_398371)), _398373 = _398371, class_Rings_Odivision__ring(_398373)], (166 ^ _393467) ^ [_398666, _398668] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_398666)), _398668 = _398666, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_398668)], (176 ^ _393467) ^ [_398961, _398963] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_398961)), _398963 = _398961, class_Groups_Oordered__cancel__ab__semigroup__add(_398963)], (186 ^ _393467) ^ [_399256, _399258] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_399256)), _399258 = _399256, class_Groups_Oordered__ab__semigroup__add__imp__le(_399258)], (196 ^ _393467) ^ [_399551, _399553] : [-(class_Rings_Olinordered__comm__semiring__strict(_399551)), _399553 = _399551, class_Rings_Olinordered__comm__semiring__strict(_399553)], (206 ^ _393467) ^ [_399846, _399848] : [-(class_Rings_Olinordered__semiring__1__strict(_399846)), _399848 = _399846, class_Rings_Olinordered__semiring__1__strict(_399848)], (216 ^ _393467) ^ [_400141, _400143] : [-(class_Rings_Olinordered__semiring__strict(_400141)), _400143 = _400141, class_Rings_Olinordered__semiring__strict(_400143)], (226 ^ _393467) ^ [_400436, _400438] : [-(class_Groups_Oordered__ab__semigroup__add(_400436)), _400438 = _400436, class_Groups_Oordered__ab__semigroup__add(_400438)], (236 ^ _393467) ^ [_400731, _400733] : [-(class_Groups_Oordered__ab__group__add__abs(_400731)), _400733 = _400731, class_Groups_Oordered__ab__group__add__abs(_400733)], (246 ^ _393467) ^ [_401026, _401028] : [-(class_Groups_Oordered__comm__monoid__add(_401026)), _401028 = _401026, class_Groups_Oordered__comm__monoid__add(_401028)], (256 ^ _393467) ^ [_401321, _401323] : [-(class_Groups_Olinordered__ab__group__add(_401321)), _401323 = _401321, class_Groups_Olinordered__ab__group__add(_401323)], (266 ^ _393467) ^ [_401616, _401618] : [-(class_Groups_Ocancel__ab__semigroup__add(_401616)), _401618 = _401616, class_Groups_Ocancel__ab__semigroup__add(_401618)], (276 ^ _393467) ^ [_401911, _401913] : [-(class_Rings_Oring__1__no__zero__divisors(_401911)), _401913 = _401911, class_Rings_Oring__1__no__zero__divisors(_401913)], (286 ^ _393467) ^ [_402206, _402208] : [-(class_Rings_Oordered__cancel__semiring(_402206)), _402208 = _402206, class_Rings_Oordered__cancel__semiring(_402208)], (296 ^ _393467) ^ [_402501, _402503] : [-(class_Rings_Olinordered__ring__strict(_402501)), _402503 = _402501, class_Rings_Olinordered__ring__strict(_402503)], (306 ^ _393467) ^ [_402796, _402798] : [-(class_Rings_Oring__no__zero__divisors(_402796)), _402798 = _402796, class_Rings_Oring__no__zero__divisors(_402798)], (316 ^ _393467) ^ [_403091, _403093] : [-(class_Rings_Oordered__comm__semiring(_403091)), _403093 = _403091, class_Rings_Oordered__comm__semiring(_403093)], (326 ^ _393467) ^ [_403386, _403388] : [-(class_Rings_Olinordered__semiring__1(_403386)), _403388 = _403386, class_Rings_Olinordered__semiring__1(_403388)], (336 ^ _393467) ^ [_403681, _403683] : [-(class_Groups_Oordered__ab__group__add(_403681)), _403683 = _403681, class_Groups_Oordered__ab__group__add(_403683)], (346 ^ _393467) ^ [_403976, _403978] : [-(class_Groups_Ocancel__comm__monoid__add(_403976)), _403978 = _403976, class_Groups_Ocancel__comm__monoid__add(_403978)], (356 ^ _393467) ^ [_404271, _404273] : [-(class_Groups_Ocancel__semigroup__add(_404271)), _404273 = _404271, class_Groups_Ocancel__semigroup__add(_404273)], (366 ^ _393467) ^ [_404566, _404568] : [-(class_Rings_Olinordered__semiring(_404566)), _404568 = _404566, class_Rings_Olinordered__semiring(_404568)], (376 ^ _393467) ^ [_404861, _404863] : [-(class_Rings_Olinordered__semidom(_404861)), _404863 = _404861, class_Rings_Olinordered__semidom(_404863)], (386 ^ _393467) ^ [_405156, _405158] : [-(class_Groups_Oab__semigroup__mult(_405156)), _405158 = _405156, class_Groups_Oab__semigroup__mult(_405158)], (396 ^ _393467) ^ [_405451, _405453] : [-(class_Groups_Ocomm__monoid__mult(_405451)), _405453 = _405451, class_Groups_Ocomm__monoid__mult(_405453)], (406 ^ _393467) ^ [_405746, _405748] : [-(class_Groups_Oab__semigroup__add(_405746)), _405748 = _405746, class_Groups_Oab__semigroup__add(_405748)], (416 ^ _393467) ^ [_406041, _406043] : [-(class_Rings_Oordered__semiring(_406041)), _406043 = _406041, class_Rings_Oordered__semiring(_406043)], (426 ^ _393467) ^ [_406336, _406338] : [-(class_Rings_Oordered__ring__abs(_406336)), _406338 = _406336, class_Rings_Oordered__ring__abs(_406338)], (436 ^ _393467) ^ [_406631, _406633] : [-(class_Rings_Oidom(_406631)), _406633 = _406631, class_Rings_Oidom(_406633)], (446 ^ _393467) ^ [_406926, _406928] : [-(class_Rings_Ono__zero__divisors(_406926)), _406928 = _406926, class_Rings_Ono__zero__divisors(_406928)], (456 ^ _393467) ^ [_407221, _407223] : [-(class_Rings_Olinordered__ring(_407221)), _407223 = _407221, class_Rings_Olinordered__ring(_407223)], (466 ^ _393467) ^ [_407516, _407518] : [-(class_Fields_Ofield(_407516)), _407518 = _407516, class_Fields_Ofield(_407518)], (476 ^ _393467) ^ [_407811, _407813] : [-(class_Divides_Osemiring__div(_407811)), _407813 = _407811, class_Divides_Osemiring__div(_407813)], (486 ^ _393467) ^ [_408106, _408108] : [-(class_Rings_Ocomm__semiring(_408106)), _408108 = _408106, class_Rings_Ocomm__semiring(_408108)], (496 ^ _393467) ^ [_408401, _408403] : [-(class_Rings_Ozero__neq__one(_408401)), _408403 = _408401, class_Rings_Ozero__neq__one(_408403)], (506 ^ _393467) ^ [_408696, _408698] : [-(class_Rings_Oordered__ring(_408696)), _408698 = _408696, class_Rings_Oordered__ring(_408698)], (516 ^ _393467) ^ [_408991, _408993] : [-(class_Orderings_Opreorder(_408991)), _408993 = _408991, class_Orderings_Opreorder(_408993)], (526 ^ _393467) ^ [_409286, _409288] : [-(class_Orderings_Olinorder(_409286)), _409288 = _409286, class_Orderings_Olinorder(_409288)], (536 ^ _393467) ^ [_409581, _409583] : [-(class_Groups_Omonoid__mult(_409581)), _409583 = _409581, class_Groups_Omonoid__mult(_409583)], (546 ^ _393467) ^ [_409876, _409878] : [-(class_Groups_Ocomm__monoid__add(_409876)), _409878 = _409876, class_Groups_Ocomm__monoid__add(_409878)], (556 ^ _393467) ^ [_410171, _410173] : [-(class_Groups_Omonoid__add(_410171)), _410173 = _410171, class_Groups_Omonoid__add(_410173)], (566 ^ _393467) ^ [_410466, _410468] : [-(class_Rings_Osemiring__0(_410466)), _410468 = _410466, class_Rings_Osemiring__0(_410468)], (576 ^ _393467) ^ [_410761, _410763] : [-(class_Groups_Ogroup__add(_410761)), _410763 = _410761, class_Groups_Ogroup__add(_410763)], (586 ^ _393467) ^ [_411056, _411058] : [-(class_Rings_Omult__zero(_411056)), _411058 = _411056, class_Rings_Omult__zero(_411058)], (596 ^ _393467) ^ [_411351, _411353] : [-(class_Orderings_Oorder(_411351)), _411353 = _411351, class_Orderings_Oorder(_411353)], (606 ^ _393467) ^ [_411646, _411648] : [-(class_Rings_Ocomm__semiring__0(_411646)), _411648 = _411646, class_Rings_Ocomm__semiring__0(_411648)], (616 ^ _393467) ^ [_411941, _411943] : [-(class_Rings_Osemiring(_411941)), _411943 = _411941, class_Rings_Osemiring(_411943)], (626 ^ _393467) ^ [_412236, _412238] : [-(class_Rings_Olinordered__idom(_412236)), _412238 = _412236, class_Rings_Olinordered__idom(_412238)], (636 ^ _393467) ^ [_412531, _412533] : [-(class_Orderings_Oord(_412531)), _412533 = _412531, class_Orderings_Oord(_412533)], (646 ^ _393467) ^ [_412826, _412828] : [-(class_Rings_Ocomm__ring__1(_412826)), _412828 = _412826, class_Rings_Ocomm__ring__1(_412828)], (656 ^ _393467) ^ [_413121, _413123] : [-(class_Rings_Oring__1(_413121)), _413123 = _413121, class_Rings_Oring__1(_413123)], (666 ^ _393467) ^ [_413416, _413418] : [-(class_Groups_Oab__group__add(_413416)), _413418 = _413416, class_Groups_Oab__group__add(_413418)], (676 ^ _393467) ^ [_413711, _413713] : [-(class_Groups_Ominus(_413711)), _413713 = _413711, class_Groups_Ominus(_413713)], (686 ^ _393467) ^ [_414006, _414008] : [-(class_Power_Opower(_414006)), _414008 = _414006, class_Power_Opower(_414008)], (696 ^ _393467) ^ [_414301, _414303] : [-(class_Groups_Ozero(_414301)), _414303 = _414301, class_Groups_Ozero(_414303)], (706 ^ _393467) ^ [_414596, _414598] : [-(class_Rings_Ocomm__ring(_414596)), _414598 = _414596, class_Rings_Ocomm__ring(_414598)], (716 ^ _393467) ^ [_414891, _414893] : [-(class_Rings_Oring(_414891)), _414893 = _414891, class_Rings_Oring(_414893)], (726 ^ _393467) ^ [_415186, _415188] : [-(class_Rings_Ocomm__semiring__1(_415186)), _415188 = _415186, class_Rings_Ocomm__semiring__1(_415188)], (736 ^ _393467) ^ [_415481, _415483] : [-(class_Groups_Oone(_415481)), _415483 = _415481, class_Groups_Oone(_415483)], (746 ^ _393467) ^ [_415756, _415758] : [-(hBOOL(_415756)), _415758 = _415756, hBOOL(_415758)], (1146 ^ _393467) ^ [_431123, _431125] : [hAPP(_431123, 1147 ^ [_431123, _431125]) = hAPP(_431125, 1147 ^ [_431123, _431125]), -(_431123 = _431125)], (1153 ^ _393467) ^ [] : [-(c_SEQ_Osubseq(v_ga____))], (1155 ^ _393467) ^ [_431468, _431470] : [class_Orderings_Opreorder(_431468), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_431468, _431470), _431470)))], (1161 ^ _393467) ^ [_431657] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(v_s, _431657))), v_r)))], (1163 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(v_s, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), v_r)))], (1165 ^ _393467) ^ [] : [-(c_SEQ_Osubseq(v_f____))], (1167 ^ _393467) ^ [_431852] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _431852), _431852)))], (1169 ^ _393467) ^ [_431964, _431966] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _431964), _431966))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _431966), _431964)))], (1175 ^ _393467) ^ [_432209, _432211, _432213] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _432209), _432211)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _432211), _432213)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _432209), _432213)))], (1185 ^ _393467) ^ [_432548, _432550] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _432548), _432550)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _432550), _432548)), -(_432548 = _432550)], (1195 ^ _393467) ^ [_432895, _432897, _432899, _432901] : [class_Orderings_Oord(_432895), 1198 ^ _393467 : [(1199 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_432897, _432895), _432899), _432901)), 1202 ^ _393467 : [(1203 ^ _393467) ^ [_433166] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_432895, hAPP(_432899, _433166)), hAPP(_432901, _433166))))]]], (1205 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_432895, hAPP(_432899, 1206 ^ [_432895, _432897, _432899, _432901])), hAPP(_432901, 1206 ^ [_432895, _432897, _432899, _432901]))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_432897, _432895), _432899), _432901)))]]], (1212 ^ _393467) ^ [_433564, _433566, _433568] : [class_Orderings_Olinorder(_433564), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_433564, _433566), _433568))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_433564, _433568), _433566)))], (1222 ^ _393467) ^ [_433906, _433908, _433910] : [class_Orderings_Oorder(_433906), 1225 ^ _393467 : [(1226 ^ _393467) ^ [] : [_433908 = _433910, 1229 ^ _393467 : [(1230 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_433906, _433908), _433910)))], (1232 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_433906, _433910), _433908)))]]], (1234 ^ _393467) ^ [] : [-(_433908 = _433910), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_433906, _433908), _433910)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_433906, _433910), _433908))]]], (1244 ^ _393467) ^ [_434588, _434590, _434592] : [class_Orderings_Opreorder(_434588), _434590 = _434592, -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_434588, _434590), _434592)))], (1254 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(v_s, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))], (1256 ^ _393467) ^ [_434972, _434974, _434976] : [class_Orderings_Olinorder(_434972), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_434972, _434974), _434976))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_434972, _434976), _434974)))], (1266 ^ _393467) ^ [_435344, _435346, _435348, _435350, _435352] : [class_Orderings_Oord(_435344), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_435346, _435344), _435348), _435350)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_435344, hAPP(_435348, _435352)), hAPP(_435350, _435352))))], (1276 ^ _393467) ^ [_435737, _435739, _435741, _435743] : [class_Orderings_Oorder(_435737), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_435737, _435739), _435741)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_435737, _435743), _435739)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_435737, _435743), _435741)))], (1290 ^ _393467) ^ [_436195, _436197, _436199] : [class_Orderings_Oorder(_436195), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_436195, _436197), _436199)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_436195, _436199), _436197)), -(_436199 = _436197)], (1304 ^ _393467) ^ [_436643, _436645, _436647, _436649] : [class_Orderings_Opreorder(_436643), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_436643, _436645), _436647)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_436643, _436647), _436649)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_436643, _436645), _436649)))], (1318 ^ _393467) ^ [_437101, _437103, _437105] : [class_Orderings_Oorder(_437101), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_437101, _437103), _437105)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_437101, _437105), _437103)), -(_437103 = _437105)], (1332 ^ _393467) ^ [_437549, _437551, _437553, _437555] : [class_Orderings_Oorder(_437549), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_437549, _437551), _437553)), _437551 = _437555, -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_437549, _437555), _437553)))], (1346 ^ _393467) ^ [_438011, _438013, _438015, _438017] : [class_Orderings_Oord(_438011), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_438011, _438013), _438015)), _438015 = _438017, -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_438011, _438013), _438017)))], (1360 ^ _393467) ^ [_438473, _438475, _438477, _438479] : [class_Orderings_Oorder(_438473), _438475 = _438477, hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_438473, _438479), _438477)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_438473, _438479), _438475)))], (1374 ^ _393467) ^ [_438935, _438937, _438939, _438941] : [class_Orderings_Oord(_438935), _438937 = _438939, hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_438935, _438939), _438941)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_438935, _438937), _438941)))], (1388 ^ _393467) ^ [_439383, _439385, _439387] : [class_Orderings_Oorder(_439383), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_439383, _439385), _439387)), 1395 ^ _393467 : [(1396 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_439383, _439387), _439385)), -(_439387 = _439385)], (1402 ^ _393467) ^ [] : [_439387 = _439385, -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_439383, _439387), _439385)))]]], (1408 ^ _393467) ^ [_440017, _440019, _440021, _440023, _440025] : [class_Orderings_Oord(_440017), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_440019, _440017), _440021), _440023)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_440017, hAPP(_440021, _440025)), hAPP(_440023, _440025))))], (1418 ^ _393467) ^ [_440382, _440384] : [class_RealVector_Oreal__normed__vector(_440382), 1421 ^ _393467 : [(1422 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_440382, _440384)), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), -(_440384 = c_Groups_Ozero__class_Ozero(_440382))], (1428 ^ _393467) ^ [] : [_440384 = c_Groups_Ozero__class_Ozero(_440382), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_440382, _440384)), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))]]], (1434 ^ _393467) ^ [_440870, _440872] : [class_RealVector_Oreal__normed__vector(_440870), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_RealVector_Onorm__class_Onorm(_440870, _440872))))], (1440 ^ _393467) ^ [_441088, _441090] : [class_RealVector_Oreal__normed__vector(_441088), 1443 ^ _393467 : [(1444 ^ _393467) ^ [] : [c_RealVector_Onorm__class_Onorm(_441088, _441090) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_441090 = c_Groups_Ozero__class_Ozero(_441088))], (1450 ^ _393467) ^ [] : [_441090 = c_Groups_Ozero__class_Ozero(_441088), -(c_RealVector_Onorm__class_Onorm(_441088, _441090) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))]]], (1456 ^ _393467) ^ [_441547] : [class_RealVector_Oreal__normed__vector(_441547), -(c_RealVector_Onorm__class_Onorm(_441547, c_Groups_Ozero__class_Ozero(_441547)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (1462 ^ _393467) ^ [_441730] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _441730)))], (1464 ^ _393467) ^ [_441839, _441841] : [c_SEQ_Osubseq(_441839), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _441841), hAPP(_441839, _441841))))], (1470 ^ _393467) ^ [_442034] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _442034)))], (1472 ^ _393467) ^ [_442158] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _442158), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_442158 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1478 ^ _393467) ^ [_442324] : [_442324 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _442324), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (1484 ^ _393467) ^ [_442540, _442542] : [class_Groups_Ozero(_442540), 1487 ^ _393467 : [(1488 ^ _393467) ^ [] : [c_Groups_Ozero__class_Ozero(_442540) = _442542, -(_442542 = c_Groups_Ozero__class_Ozero(_442540))], (1494 ^ _393467) ^ [] : [_442542 = c_Groups_Ozero__class_Ozero(_442540), -(c_Groups_Ozero__class_Ozero(_442540) = _442542)]]], (1500 ^ _393467) ^ [_443025] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _443025)), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), -(_443025 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1506 ^ _393467) ^ [_443197] : [_443197 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _443197)), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))], (1512 ^ _393467) ^ [_443447, _443449, _443451, _443453] : [class_RealVector_Oreal__normed__vector(_443447), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _443449), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_443447, _443451)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _443449), c_RealVector_Onorm__class_Onorm(_443447, _443453)))), -(_443451 = c_Groups_Ozero__class_Ozero(_443447))], (1526 ^ _393467) ^ [_443880] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_RealDef_Oreal(tc_Nat_Onat, _443880))))], (1528 ^ _393467) ^ [_443963] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _443963), _443963)))], (1530 ^ _393467) ^ [_444089, _444091, _444093] : [class_RealVector_Oreal__normed__div__algebra(_444089), -(c_RealVector_Onorm__class_Onorm(_444089, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_444089), _444091), _444093)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_444089, _444091)), c_RealVector_Onorm__class_Onorm(_444089, _444093)))], (1536 ^ _393467) ^ [_444334, _444336] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _444334), _444336) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _444336), _444334))], (1538 ^ _393467) ^ [_444455, _444457] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _444455), _444457))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _444457), _444455)))], (1544 ^ _393467) ^ [_444715, _444717] : [c_RealDef_Oreal(tc_Nat_Onat, _444715) = c_RealDef_Oreal(tc_Nat_Onat, _444717), -(_444715 = _444717)], (1550 ^ _393467) ^ [_444889, _444891] : [_444889 = _444891, -(c_RealDef_Oreal(tc_Nat_Onat, _444889) = c_RealDef_Oreal(tc_Nat_Onat, _444891))], (1556 ^ _393467) ^ [_445112, _445114, _445116] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _445112), _445114)), _445116) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _445112), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _445114), _445116)))], (1558 ^ _393467) ^ [_445247, _445249] : [_445247 = _445249, -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _445247), _445249)))], (1564 ^ _393467) ^ [_445481, _445483, _445485] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _445481), _445483)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _445483), _445485)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _445481), _445485)))], (1574 ^ _393467) ^ [_445820, _445822] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _445820), _445822)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _445822), _445820)), -(_445820 = _445822)], (1584 ^ _393467) ^ [_446167, _446169, _446171, _446173] : [class_Groups_Oab__semigroup__mult(_446167), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_446167), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_446167), _446169), _446171)), _446173) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_446167), _446169), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_446167), _446171), _446173)))], (1590 ^ _393467) ^ [_446451, _446453] : [class_RealVector_Oreal__normed__algebra(_446451), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_446451), c_Groups_Ozero__class_Ozero(_446451)), _446453) = c_Groups_Ozero__class_Ozero(_446451))], (1596 ^ _393467) ^ [_446683, _446685] : [class_RealVector_Oreal__normed__algebra(_446683), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_446683), c_Groups_Ozero__class_Ozero(_446683)), _446685) = c_Groups_Ozero__class_Ozero(_446683))], (1602 ^ _393467) ^ [_446915, _446917] : [class_RealVector_Oreal__normed__algebra(_446915), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_446915), _446917), c_Groups_Ozero__class_Ozero(_446915)) = c_Groups_Ozero__class_Ozero(_446915))], (1608 ^ _393467) ^ [_447147, _447149] : [class_RealVector_Oreal__normed__algebra(_447147), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_447147), _447149), c_Groups_Ozero__class_Ozero(_447147)) = c_Groups_Ozero__class_Ozero(_447147))], (1614 ^ _393467) ^ [_447393, _447395, _447397] : [class_RealVector_Oreal__normed__algebra(_447393), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_447393, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_447393), _447395), _447397))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_447393, _447395)), c_RealVector_Onorm__class_Onorm(_447393, _447397)))))], (1620 ^ _393467) ^ [_447692, _447694] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _447692)), c_RealDef_Oreal(tc_Nat_Onat, _447694))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _447692), _447694)))], (1626 ^ _393467) ^ [_447886, _447888] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _447886), _447888)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _447886)), c_RealDef_Oreal(tc_Nat_Onat, _447888))))], (1632 ^ _393467) ^ [_448144, _448146, _448148] : [-(_448144 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 1635 ^ _393467 : [(1636 ^ _393467) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _448146), _448144) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _448148), _448144), -(_448146 = _448148)], (1642 ^ _393467) ^ [] : [_448146 = _448148, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _448146), _448144) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _448148), _448144))]]], (1648 ^ _393467) ^ [_448673, _448675, _448677] : [-(_448673 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 1651 ^ _393467 : [(1652 ^ _393467) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _448673), _448675) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _448673), _448677), -(_448675 = _448677)], (1658 ^ _393467) ^ [] : [_448675 = _448677, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _448673), _448675) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _448673), _448677))]]], (1664 ^ _393467) ^ [_449203] : [c_RealDef_Oreal(tc_Nat_Onat, _449203) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_449203 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1670 ^ _393467) ^ [_449365] : [_449365 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_RealDef_Oreal(tc_Nat_Onat, _449365) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (1676 ^ _393467) ^ [] : [-(c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (1678 ^ _393467) ^ [_449630, _449632] : [class_Rings_Olinordered__ring(_449630), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_449630, c_Groups_Ozero__class_Ozero(_449630)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_449630), _449632), _449632))))], (1684 ^ _393467) ^ [_449882, _449884, _449886] : [class_Rings_Olinordered__ring__strict(_449882), 1687 ^ _393467 : [(1688 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_449882, c_Groups_Ozero__class_Ozero(_449882)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_449882), _449884), _449886))), 1693 ^ _393467 : [(1694 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_449882, c_Groups_Ozero__class_Ozero(_449882)), _449884)))], (1696 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_449882, c_Groups_Ozero__class_Ozero(_449882)), _449886)))]], 1697 ^ _393467 : [(1698 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_449882, _449884), c_Groups_Ozero__class_Ozero(_449882))))], (1700 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_449882, _449886), c_Groups_Ozero__class_Ozero(_449882))))]]], (1702 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_449882, c_Groups_Ozero__class_Ozero(_449882)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_449882), _449884), _449886)))), 1703 ^ _393467 : [(1704 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_449882, c_Groups_Ozero__class_Ozero(_449882)), _449884)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_449882, c_Groups_Ozero__class_Ozero(_449882)), _449886))], (1710 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_449882, _449884), c_Groups_Ozero__class_Ozero(_449882))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_449882, _449886), c_Groups_Ozero__class_Ozero(_449882)))]]]]], (1718 ^ _393467) ^ [_450991, _450993, _450995] : [class_Rings_Olinordered__ring__strict(_450991), 1721 ^ _393467 : [(1722 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_450991, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_450991), _450993), _450995)), c_Groups_Ozero__class_Ozero(_450991))), 1727 ^ _393467 : [(1728 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_450991, c_Groups_Ozero__class_Ozero(_450991)), _450993)))], (1730 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_450991, _450995), c_Groups_Ozero__class_Ozero(_450991))))]], 1731 ^ _393467 : [(1732 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_450991, _450993), c_Groups_Ozero__class_Ozero(_450991))))], (1734 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_450991, c_Groups_Ozero__class_Ozero(_450991)), _450995)))]]], (1736 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_450991, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_450991), _450993), _450995)), c_Groups_Ozero__class_Ozero(_450991)))), 1737 ^ _393467 : [(1738 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_450991, c_Groups_Ozero__class_Ozero(_450991)), _450993)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_450991, _450995), c_Groups_Ozero__class_Ozero(_450991)))], (1744 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_450991, _450993), c_Groups_Ozero__class_Ozero(_450991))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_450991, c_Groups_Ozero__class_Ozero(_450991)), _450995))]]]]], (1752 ^ _393467) ^ [_452100, _452102, _452104] : [class_Rings_Oordered__cancel__semiring(_452100), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_452100, c_Groups_Ozero__class_Ozero(_452100)), _452102)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_452100, c_Groups_Ozero__class_Ozero(_452100)), _452104)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_452100, c_Groups_Ozero__class_Ozero(_452100)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_452100), _452102), _452104))))], (1766 ^ _393467) ^ [_452572, _452574, _452576] : [class_Rings_Oordered__cancel__semiring(_452572), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_452572, c_Groups_Ozero__class_Ozero(_452572)), _452574)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_452572, _452576), c_Groups_Ozero__class_Ozero(_452572))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_452572, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_452572), _452574), _452576)), c_Groups_Ozero__class_Ozero(_452572))))], (1780 ^ _393467) ^ [_453044, _453046, _453048] : [class_Rings_Oordered__cancel__semiring(_453044), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_453044, c_Groups_Ozero__class_Ozero(_453044)), _453046)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_453044, _453048), c_Groups_Ozero__class_Ozero(_453044))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_453044, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_453044), _453048), _453046)), c_Groups_Ozero__class_Ozero(_453044))))], (1794 ^ _393467) ^ [_453516, _453518, _453520] : [class_Rings_Oordered__cancel__semiring(_453516), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_453516, _453518), c_Groups_Ozero__class_Ozero(_453516))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_453516, c_Groups_Ozero__class_Ozero(_453516)), _453520)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_453516, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_453516), _453518), _453520)), c_Groups_Ozero__class_Ozero(_453516))))], (1808 ^ _393467) ^ [_453988, _453990, _453992] : [class_Rings_Oordered__ring(_453988), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_453988, _453990), c_Groups_Ozero__class_Ozero(_453988))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_453988, _453992), c_Groups_Ozero__class_Ozero(_453988))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_453988, c_Groups_Ozero__class_Ozero(_453988)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_453988), _453990), _453992))))], (1822 ^ _393467) ^ [_454474, _454476, _454478, _454480] : [class_Rings_Oordered__semiring(_454474), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_454474, _454476), _454478)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_454474, c_Groups_Ozero__class_Ozero(_454474)), _454480)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_454474, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_454474), _454476), _454480)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_454474), _454478), _454480))))], (1836 ^ _393467) ^ [_454982, _454984, _454986, _454988] : [class_Rings_Oordered__semiring(_454982), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_454982, _454984), _454986)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_454982, c_Groups_Ozero__class_Ozero(_454982)), _454988)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_454982, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_454982), _454988), _454984)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_454982), _454988), _454986))))], (1850 ^ _393467) ^ [_455490, _455492, _455494, _455496] : [class_Rings_Oordered__comm__semiring(_455490), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_455490, _455492), _455494)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_455490, c_Groups_Ozero__class_Ozero(_455490)), _455496)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_455490, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_455490), _455496), _455492)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_455490), _455496), _455494))))], (1864 ^ _393467) ^ [_455941] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _455941) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1866 ^ _393467) ^ [_456022] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _456022), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1878 ^ _393467) ^ [_456428, _456430] : [1879 ^ _393467 : [(1880 ^ _393467) ^ [] : [_456428 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (1882 ^ _393467) ^ [] : [_456430 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _456428), _456430) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1868 ^ _393467) ^ [_456164, _456166] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _456164), _456166) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_456164 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_456166 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1896 ^ _393467) ^ [_457055, _457057, _457059] : [1897 ^ _393467 : [(1898 ^ _393467) ^ [] : [_457057 = _457059], (1900 ^ _393467) ^ [] : [_457055 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _457055), _457057) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _457055), _457059))], (1886 ^ _393467) ^ [_456769, _456771, _456773] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _456769), _456771) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _456769), _456773), -(_456771 = _456773), -(_456769 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1914 ^ _393467) ^ [_457702, _457704, _457706] : [1915 ^ _393467 : [(1916 ^ _393467) ^ [] : [_457702 = _457706], (1918 ^ _393467) ^ [] : [_457704 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _457702), _457704) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _457706), _457704))], (1904 ^ _393467) ^ [_457416, _457418, _457420] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _457416), _457418) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _457420), _457418), -(_457416 = _457420), -(_457418 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1922 ^ _393467) ^ [_458048, _458050, _458052, _458054] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _458048), _458050)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _458052), _458054)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _458048), _458052)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _458050), _458054))))], (1932 ^ _393467) ^ [_458435, _458437, _458439] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _458435), _458437)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _458439), _458435)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _458439), _458437))))], (1938 ^ _393467) ^ [_458709, _458711, _458713] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _458709), _458711)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _458709), _458713)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _458711), _458713))))], (1944 ^ _393467) ^ [_458940] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _458940), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _458940), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _458940), _458940)))))], (1946 ^ _393467) ^ [_459035] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _459035), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _459035), _459035))))], (1948 ^ _393467) ^ [_459138, _459140] : [-(c_RealDef_Oreal(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _459138), _459140)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _459138)), c_RealDef_Oreal(tc_Nat_Onat, _459140)))], (1950 ^ _393467) ^ [_459282, _459284, _459286] : [class_Rings_Ono__zero__divisors(_459282), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_459282), _459284), _459286) = c_Groups_Ozero__class_Ozero(_459282), -(_459284 = c_Groups_Ozero__class_Ozero(_459282)), -(_459286 = c_Groups_Ozero__class_Ozero(_459282))], (1964 ^ _393467) ^ [_459725, _459727, _459729] : [class_Rings_Ono__zero__divisors(_459725), -(_459727 = c_Groups_Ozero__class_Ozero(_459725)), -(_459729 = c_Groups_Ozero__class_Ozero(_459725)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_459725), _459727), _459729) = c_Groups_Ozero__class_Ozero(_459725)], (1978 ^ _393467) ^ [_460174, _460176, _460178] : [class_Rings_Oring__no__zero__divisors(_460174), 1981 ^ _393467 : [(1992 ^ _393467) ^ [] : [1993 ^ _393467 : [(1994 ^ _393467) ^ [] : [_460176 = c_Groups_Ozero__class_Ozero(_460174)], (1996 ^ _393467) ^ [] : [_460178 = c_Groups_Ozero__class_Ozero(_460174)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_460174), _460176), _460178) = c_Groups_Ozero__class_Ozero(_460174))], (1982 ^ _393467) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_460174), _460176), _460178) = c_Groups_Ozero__class_Ozero(_460174), -(_460176 = c_Groups_Ozero__class_Ozero(_460174)), -(_460178 = c_Groups_Ozero__class_Ozero(_460174))]]], (2000 ^ _393467) ^ [_460854, _460856] : [class_Rings_Omult__zero(_460854), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_460854), _460856), c_Groups_Ozero__class_Ozero(_460854)) = c_Groups_Ozero__class_Ozero(_460854))], (2006 ^ _393467) ^ [_461086, _461088] : [class_Rings_Omult__zero(_461086), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_461086), c_Groups_Ozero__class_Ozero(_461086)), _461088) = c_Groups_Ozero__class_Ozero(_461086))], (2012 ^ _393467) ^ [_461332, _461334, _461336] : [class_Rings_Oordered__cancel__semiring(_461332), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_461332, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_461332), _461334), _461336)), c_Groups_Ozero__class_Ozero(_461332)))), 2017 ^ _393467 : [(2018 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_461332, c_Groups_Ozero__class_Ozero(_461332)), _461334)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_461332, _461336), c_Groups_Ozero__class_Ozero(_461332)))], (2024 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_461332, _461334), c_Groups_Ozero__class_Ozero(_461332))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_461332, c_Groups_Ozero__class_Ozero(_461332)), _461336))]]], (2032 ^ _393467) ^ [_462001, _462003, _462005] : [class_Rings_Oordered__ring(_462001), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_462001, c_Groups_Ozero__class_Ozero(_462001)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_462001), _462003), _462005)))), 2037 ^ _393467 : [(2038 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_462001, c_Groups_Ozero__class_Ozero(_462001)), _462003)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_462001, c_Groups_Ozero__class_Ozero(_462001)), _462005))], (2044 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_462001, _462003), c_Groups_Ozero__class_Ozero(_462001))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_462001, _462005), c_Groups_Ozero__class_Ozero(_462001)))]]], (2052 ^ _393467) ^ [_462698, _462700, _462702, _462704, _462706] : [class_Rings_Oordered__semiring(_462698), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_462698, _462700), _462702)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_462698, _462704), _462706)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_462698, c_Groups_Ozero__class_Ozero(_462698)), _462702)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_462698, c_Groups_Ozero__class_Ozero(_462698)), _462704)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_462698, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_462698), _462700), _462704)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_462698), _462702), _462706))))], (2074 ^ _393467) ^ [_463460, _463462, _463464, _463466, _463468] : [class_Rings_Oordered__semiring(_463460), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_463460, _463462), _463464)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_463460, _463466), _463468)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_463460, c_Groups_Ozero__class_Ozero(_463460)), _463462)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_463460, c_Groups_Ozero__class_Ozero(_463460)), _463466)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_463460, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_463460), _463462), _463466)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_463460), _463464), _463468))))], (2096 ^ _393467) ^ [_464208, _464210, _464212, _464214] : [class_Rings_Oordered__ring(_464208), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_464208, _464210), _464212)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_464208, _464214), c_Groups_Ozero__class_Ozero(_464208))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_464208, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_464208), _464214), _464212)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_464208), _464214), _464210))))], (2110 ^ _393467) ^ [_464716, _464718, _464720, _464722] : [class_Rings_Oordered__ring(_464716), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_464716, _464718), _464720)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_464716, _464722), c_Groups_Ozero__class_Ozero(_464716))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_464716, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_464716), _464720), _464722)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_464716), _464718), _464722))))], (2124 ^ _393467) ^ [_465196, _465198] : [class_Orderings_Oorder(_465196), 2127 ^ _393467 : [(2138 ^ _393467) ^ [] : [2141 ^ _393467 : [(2142 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, 2139 ^ [_465196, _465198]), 2140 ^ [_465196, _465198])))], (2144 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_465196, hAPP(_465198, 2140 ^ [_465196, _465198])), hAPP(_465198, 2139 ^ [_465196, _465198])))]], -(c_SEQ_Odecseq(_465196, _465198))], (2128 ^ _393467) ^ [] : [c_SEQ_Odecseq(_465196, _465198), 2131 ^ _393467 : [(2132 ^ _393467) ^ [_465480, _465482] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _465482), _465480)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_465196, hAPP(_465198, _465480)), hAPP(_465198, _465482))))]]]]], (2148 ^ _393467) ^ [_466145, _466147] : [class_Rings_Ocomm__semiring__1(_466145), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_466145), _466147), c_Groups_Ozero__class_Ozero(_466145)) = c_Groups_Ozero__class_Ozero(_466145))], (2154 ^ _393467) ^ [_466377, _466379] : [class_Rings_Ocomm__semiring__1(_466377), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_466377), c_Groups_Ozero__class_Ozero(_466377)), _466379) = c_Groups_Ozero__class_Ozero(_466377))], (2160 ^ _393467) ^ [_466595] : [class_RealVector_Oreal__normed__algebra(_466595), 2164 ^ _393467 : [(2165 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 2163 ^ [_466595])))], (2167 ^ _393467) ^ [_466935, _466937] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_466595, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_466595), _466937), _466935))), 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(_466595, _466937)), c_RealVector_Onorm__class_Onorm(_466595, _466935))), 2163 ^ [_466595]))))]]], (2169 ^ _393467) ^ [_467092, _467094] : [class_RealVector_Oreal__normed__algebra(_467092), 2173 ^ _393467 : [(2174 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 2172 ^ [_467092, _467094])))], (2176 ^ _393467) ^ [_467402] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_467092, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_467092), _467094), _467402))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_467092, _467402)), 2172 ^ [_467092, _467094]))))]]], (2178 ^ _393467) ^ [_467552, _467554] : [class_RealVector_Oreal__normed__algebra(_467552), 2182 ^ _393467 : [(2183 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 2181 ^ [_467552, _467554])))], (2185 ^ _393467) ^ [_467862] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_467552, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_467552), _467862), _467554))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_467552, _467862)), 2181 ^ [_467552, _467554]))))]]], (2187 ^ _393467) ^ [_468012, _468014] : [class_Orderings_Oorder(_468012), 2190 ^ _393467 : [(2201 ^ _393467) ^ [] : [2204 ^ _393467 : [(2205 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, 2202 ^ [_468012, _468014]), 2203 ^ [_468012, _468014])))], (2207 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_468012, hAPP(_468014, 2202 ^ [_468012, _468014])), hAPP(_468014, 2203 ^ [_468012, _468014])))]], -(c_SEQ_Oincseq(_468012, _468014))], (2191 ^ _393467) ^ [] : [c_SEQ_Oincseq(_468012, _468014), 2194 ^ _393467 : [(2195 ^ _393467) ^ [_468296, _468298] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _468298), _468296)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_468012, hAPP(_468014, _468298)), hAPP(_468014, _468296))))]]]]], (2211 ^ _393467) ^ [_468947] : [class_RealVector_Oreal__normed__algebra(_468947), 2215 ^ _393467 : [(2216 ^ _393467) ^ [_469200, _469202] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_468947, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_468947), _469202), _469200))), 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(_468947, _469202)), c_RealVector_Onorm__class_Onorm(_468947, _469200))), 2214 ^ [_468947]))))]]], (2218 ^ _393467) ^ [_469355, _469357] : [class_RealVector_Oreal__normed__algebra(_469355), 2222 ^ _393467 : [(2223 ^ _393467) ^ [_469574] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_469355, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_469355), _469357), _469574))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_469355, _469574)), 2221 ^ [_469355, _469357]))))]]], (2225 ^ _393467) ^ [_469722, _469724] : [class_RealVector_Oreal__normed__algebra(_469722), 2229 ^ _393467 : [(2230 ^ _393467) ^ [_469941] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_469722, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_469722), _469941), _469724))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_469722, _469941)), 2228 ^ [_469722, _469724]))))]]], (2232 ^ _393467) ^ [_470088, _470090, _470092] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _470088), _470090)), _470092) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _470088), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _470090), _470092)))], (2234 ^ _393467) ^ [_470208, _470210] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _470208), _470210) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _470210), _470208))], (2236 ^ _393467) ^ [_470371, _470373, _470375, _470377, _470379] : [class_Rings_Ocomm__semiring__1(_470371), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_470371), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_470371), _470373), _470375)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_470371), _470377), _470379)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_470371), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_470371), _470373), _470377)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_470371), _470375), _470379)))], (2242 ^ _393467) ^ [_470735, _470737, _470739, _470741, _470743] : [class_Rings_Ocomm__semiring__1(_470735), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_470735), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_470735), _470737), _470739)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_470735), _470741), _470743)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_470735), _470741), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_470735), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_470735), _470737), _470739)), _470743)))], (2248 ^ _393467) ^ [_471099, _471101, _471103, _471105, _471107] : [class_Rings_Ocomm__semiring__1(_471099), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_471099), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_471099), _471101), _471103)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_471099), _471105), _471107)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_471099), _471101), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_471099), _471103), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_471099), _471105), _471107))))], (2254 ^ _393467) ^ [_471449, _471451, _471453, _471455] : [class_Rings_Ocomm__semiring__1(_471449), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_471449), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_471449), _471451), _471453)), _471455) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_471449), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_471449), _471451), _471455)), _471453))], (2260 ^ _393467) ^ [_471761, _471763, _471765, _471767] : [class_Rings_Ocomm__semiring__1(_471761), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_471761), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_471761), _471763), _471765)), _471767) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_471761), _471763), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_471761), _471765), _471767)))], (2266 ^ _393467) ^ [_472073, _472075, _472077, _472079] : [class_Rings_Ocomm__semiring__1(_472073), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_472073), _472075), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_472073), _472077), _472079)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_472073), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_472073), _472075), _472077)), _472079))], (2272 ^ _393467) ^ [_472385, _472387, _472389, _472391] : [class_Rings_Ocomm__semiring__1(_472385), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_472385), _472387), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_472385), _472389), _472391)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_472385), _472389), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_472385), _472387), _472391)))], (2278 ^ _393467) ^ [_472683, _472685, _472687] : [class_Rings_Ocomm__semiring__1(_472683), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_472683), _472685), _472687) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_472683), _472687), _472685))], (2294 ^ _393467) ^ [_473258, _473260, _473262] : [2295 ^ _393467 : [(2296 ^ _393467) ^ [] : [_473258 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (2298 ^ _393467) ^ [] : [_473260 = _473262]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _473258), _473260) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _473258), _473262))], (2284 ^ _393467) ^ [_472972, _472974, _472976] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _472972), _472974) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _472972), _472976), -(_472972 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_472974 = _472976)], (2302 ^ _393467) ^ [_473576, _473578] : [class_Groups_Ozero(_473576), 2305 ^ _393467 : [(2306 ^ _393467) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_473576, _473578) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_473578 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_473576)))], (2312 ^ _393467) ^ [] : [_473578 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_473576)), -(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_473576, _473578) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (2318 ^ _393467) ^ [_474055, _474057] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _474055)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _474057)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_RComplete_Onatfloor(_474055)), c_RComplete_Onatfloor(_474057))), c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _474055), _474057)))))], (2328 ^ _393467) ^ [_474408, _474410] : [class_Orderings_Oorder(_474408), 2331 ^ _393467 : [(2350 ^ _393467) ^ [] : [2353 ^ _393467 : [(2354 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, 2351 ^ [_474408, _474410]), 2352 ^ [_474408, _474410])))], (2356 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_474408, hAPP(_474410, 2351 ^ [_474408, _474410])), hAPP(_474410, 2352 ^ [_474408, _474410])))], (2360 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, 2357 ^ [_474408, _474410]), 2358 ^ [_474408, _474410])))], (2362 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_474408, hAPP(_474410, 2358 ^ [_474408, _474410])), hAPP(_474410, 2357 ^ [_474408, _474410])))]], -(c_SEQ_Omonoseq(_474408, _474410))], (2332 ^ _393467) ^ [] : [c_SEQ_Omonoseq(_474408, _474410), 2337 ^ _393467 : [(2338 ^ _393467) ^ [_474764, _474766] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _474766), _474764)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_474408, hAPP(_474410, _474766)), hAPP(_474410, _474764))))]], 2343 ^ _393467 : [(2344 ^ _393467) ^ [_475002, _475004] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _475004), _475002)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_474408, hAPP(_474410, _475002)), hAPP(_474410, _475004))))]]]]], (2366 ^ _393467) ^ [_476006, _476008] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _476006)), 2369 ^ _393467 : [(2370 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_476006)), _476008)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _476006), c_RealDef_Oreal(tc_Nat_Onat, _476008))))], (2376 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _476006), c_RealDef_Oreal(tc_Nat_Onat, _476008))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_476006)), _476008)))]]], (2382 ^ _393467) ^ [_476515, _476517] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _476515)), 2385 ^ _393467 : [(2386 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _476517), c_RComplete_Onatfloor(_476515))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _476517)), _476515)))], (2392 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _476517)), _476515)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _476517), c_RComplete_Onatfloor(_476515))))]]], (2398 ^ _393467) ^ [_477024, _477026] : [class_Orderings_Oorder(_477024), c_SEQ_Odecseq(_477024, _477026), -(c_SEQ_Omonoseq(_477024, _477026))], (2408 ^ _393467) ^ [_477335, _477337, _477339] : [class_Lattices_Oab__semigroup__idem__mult(_477335), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_477335), _477337), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_477335), _477337), _477339)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_477335), _477337), _477339))], (2414 ^ _393467) ^ [_477597, _477599] : [class_Lattices_Oab__semigroup__idem__mult(_477597), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_477597), _477599), _477599) = _477599)], (2420 ^ _393467) ^ [_477792] : [-(c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat, _477792)) = _477792)], (2422 ^ _393467) ^ [_477875] : [-(c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat, _477875)) = _477875)], (2424 ^ _393467) ^ [] : [-(c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2426 ^ _393467) ^ [_478011] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_RComplete_Onatfloor(_478011))))], (2428 ^ _393467) ^ [_478122, _478124] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _478122), _478124)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatfloor(_478122)), c_RComplete_Onatfloor(_478124))))], (2434 ^ _393467) ^ [] : [-(c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2436 ^ _393467) ^ [_478384] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_RComplete_Onatceiling(_478384))))], (2438 ^ _393467) ^ [_478495, _478497] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _478495), _478497)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_478495)), c_RComplete_Onatceiling(_478497))))], (2444 ^ _393467) ^ [_478704] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _478704), c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatceiling(_478704)))))], (2446 ^ _393467) ^ [_478807] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _478807), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), -(c_RComplete_Onatfloor(_478807) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2452 ^ _393467) ^ [_479011] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _479011)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatfloor(_479011))), _479011)))], (2458 ^ _393467) ^ [_479239, _479241] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _479239)), _479241)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _479239), c_RComplete_Onatfloor(_479241))))], (2464 ^ _393467) ^ [_479465] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _479465), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), -(c_RComplete_Onatceiling(_479465) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2470 ^ _393467) ^ [_479683, _479685] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _479683), c_RealDef_Oreal(tc_Nat_Onat, _479685))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_479683)), _479685)))], (2476 ^ _393467) ^ [_479923, _479925] : [class_Orderings_Oorder(_479923), c_SEQ_Oincseq(_479923, _479925), -(c_SEQ_Omonoseq(_479923, _479925))], (2486 ^ _393467) ^ [_480220, _480222] : [class_Lattices_Oab__semigroup__idem__mult(_480220), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_480220), _480222), _480222) = _480222)], (2492 ^ _393467) ^ [_480444, _480446] : [class_Orderings_Oorder(_480444), 2499 ^ _393467 : [(2500 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, 2497 ^ [_480444, _480446]), 2498 ^ [_480444, _480446])))], (2502 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_480444, hAPP(_480446, 2497 ^ [_480444, _480446])), hAPP(_480446, 2498 ^ [_480444, _480446])))]], -(c_SEQ_Omonoseq(_480444, _480446))], (2506 ^ _393467) ^ [_481039, _481041] : [class_Orderings_Oorder(_481039), 2513 ^ _393467 : [(2514 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, 2511 ^ [_481039, _481041]), 2512 ^ [_481039, _481041])))], (2516 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_481039, hAPP(_481041, 2512 ^ [_481039, _481041])), hAPP(_481041, 2511 ^ [_481039, _481041])))]], -(c_SEQ_Omonoseq(_481039, _481041))], (2520 ^ _393467) ^ [_481634, _481636] : [class_Rings_Ocomm__semiring__0(_481634), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_481634)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_481634))), _481636) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_481634)))], (2526 ^ _393467) ^ [_481878, _481880] : [class_Rings_Ocomm__semiring__0(_481878), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_481878)), _481880), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_481878))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_481878)))], (2532 ^ _393467) ^ [] : [-(c_SEQ_Omonoseq(tc_RealDef_Oreal, c_COMBB(tc_Complex_Ocomplex, tc_RealDef_Oreal, tc_Nat_Onat, c_Complex_OIm, c_COMBB(tc_Nat_Onat, tc_Complex_Ocomplex, tc_Nat_Onat, v_s, c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____, v_ga____)))))], (2534 ^ _393467) ^ [_482189, _482191, _482193] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _482189)), 2537 ^ _393467 : [(2538 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _482189), _482191)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _482189), _482193))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _482191), _482193)))], (2544 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _482191), _482193)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _482189), _482191)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _482189), _482193))))]]], (2560 ^ _393467) ^ [_483087, _483089, _483091] : [2561 ^ _393467 : [(2562 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _483089)))], (2564 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _483087), _483091))]], -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _483087), _483089)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _483091), _483089))))], (2550 ^ _393467) ^ [_482778, _482780, _482782] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _482778), _482780)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _482782), _482780))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _482780)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _482778), _482782)))], (2578 ^ _393467) ^ [_483782, _483784, _483786] : [2579 ^ _393467 : [(2580 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _483782)))], (2582 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _483784), _483786))]], -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _483782), _483784)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _483782), _483786))))], (2568 ^ _393467) ^ [_483473, _483475, _483477] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _483473), _483475)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _483473), _483477))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _483473)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _483475), _483477)))], (2586 ^ _393467) ^ [_484167, _484169, _484171, _484173, _484175] : [class_RealVector_Oreal__normed__algebra(_484167), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_484167, _484169)), _484171)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_484167, _484173)), _484175)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_484167, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_484167), _484169), _484173))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _484171), _484175))))], (2600 ^ _393467) ^ [_484641] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _484641), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (2602 ^ _393467) ^ [] : [-(c_SEQ_Omonoseq(tc_RealDef_Oreal, c_COMBB(tc_Complex_Ocomplex, tc_RealDef_Oreal, tc_Nat_Onat, c_Complex_ORe, c_COMBB(tc_Nat_Onat, tc_Complex_Ocomplex, tc_Nat_Onat, v_s, v_f____))))], (2604 ^ _393467) ^ [_484820, _484822, _484824] : [class_Rings_Olinordered__idom(_484820), -(_484822 = _484824), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_484820, _484822), _484824))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_484820, _484824), _484822)))], (2618 ^ _393467) ^ [_485246, _485248] : [class_Orderings_Opreorder(_485246), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_485246, _485248), _485248))], (2624 ^ _393467) ^ [_485479, _485481, _485483] : [class_Orderings_Olinorder(_485479), 2627 ^ _393467 : [(2638 ^ _393467) ^ [] : [2639 ^ _393467 : [(2640 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_485479, _485481), _485483))], (2642 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_485479, _485483), _485481))]], _485481 = _485483], (2628 ^ _393467) ^ [] : [-(_485481 = _485483), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_485479, _485481), _485483))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_485479, _485483), _485481)))]]], (2646 ^ _393467) ^ [_486163, _486165, _486167] : [class_Orderings_Olinorder(_486163), 2649 ^ _393467 : [(2660 ^ _393467) ^ [] : [2661 ^ _393467 : [(2662 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_486163, _486167), _486165))], (2664 ^ _393467) ^ [] : [_486165 = _486167]], hBOOL(hAPP(c_Orderings_Oord__class_Oless(_486163, _486165), _486167))], (2650 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_486163, _486165), _486167))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_486163, _486167), _486165))), -(_486165 = _486167)]]], (2668 ^ _393467) ^ [_486847, _486849, _486851] : [class_Orderings_Olinorder(_486847), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_486847, _486849), _486851))), -(_486849 = _486851), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_486847, _486851), _486849)))], (2682 ^ _393467) ^ [_487283, _487285, _487287] : [class_Orderings_Olinorder(_487283), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_487283, _487285), _487287))), 2689 ^ _393467 : [(2690 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_487283, _487287), _487285))), -(_487287 = _487285)], (2696 ^ _393467) ^ [] : [_487287 = _487285, hBOOL(hAPP(c_Orderings_Oord__class_Oless(_487283, _487287), _487285))]]], (2702 ^ _393467) ^ [_487894, _487896, _487898] : [class_Orderings_Olinorder(_487894), -(_487896 = _487898), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_487894, _487896), _487898))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_487894, _487898), _487896)))], (2716 ^ _393467) ^ [_488334, _488336, _488338] : [class_Orderings_Oorder(_488334), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_488334, _488336), _488338)), _488336 = _488338], (2726 ^ _393467) ^ [_488666, _488668, _488670] : [class_Orderings_Opreorder(_488666), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_488666, _488668), _488670)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_488666, _488670), _488668))], (2736 ^ _393467) ^ [_489008, _489010, _489012] : [class_Orderings_Opreorder(_489008), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_489008, _489010), _489012)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_489008, _489012), _489010))], (2746 ^ _393467) ^ [_489350, _489352, _489354] : [class_Orderings_Oorder(_489350), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_489350, _489352), _489354)), _489352 = _489354], (2756 ^ _393467) ^ [_489682, _489684, _489686] : [class_Orderings_Oorder(_489682), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_489682, _489684), _489686)), _489686 = _489684], (2766 ^ _393467) ^ [_490014, _490016, _490018] : [class_Orderings_Opreorder(_490014), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_490014, _490016), _490018)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_490014, _490018), _490016))], (2776 ^ _393467) ^ [_490356, _490358, _490360] : [class_Orderings_Oorder(_490356), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_490356, _490358), _490360)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_490356, _490360), _490358))], (2786 ^ _393467) ^ [_490712, _490714, _490716, _490718] : [class_Orderings_Oord(_490712), _490714 = _490716, hBOOL(hAPP(c_Orderings_Oord__class_Oless(_490712, _490716), _490718)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_490712, _490714), _490718)))], (2800 ^ _393467) ^ [_491174, _491176, _491178, _491180] : [class_Orderings_Oorder(_491174), _491176 = _491178, hBOOL(hAPP(c_Orderings_Oord__class_Oless(_491174, _491180), _491178)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_491174, _491180), _491176)))], (2814 ^ _393467) ^ [_491636, _491638, _491640, _491642] : [class_Orderings_Oord(_491636), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_491636, _491638), _491640)), _491640 = _491642, -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_491636, _491638), _491642)))], (2828 ^ _393467) ^ [_492098, _492100, _492102, _492104] : [class_Orderings_Oorder(_492098), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_492098, _492100), _492102)), _492100 = _492104, -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_492098, _492104), _492102)))], (2842 ^ _393467) ^ [_492560, _492562, _492564, _492566] : [class_Orderings_Opreorder(_492560), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_492560, _492562), _492564)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_492560, _492564), _492566)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_492560, _492562), _492566)))], (2856 ^ _393467) ^ [_493032, _493034, _493036, _493038] : [class_Orderings_Oorder(_493032), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_493032, _493034), _493036)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_493032, _493038), _493034)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_493032, _493038), _493036)))], (2870 ^ _393467) ^ [_493490, _493492, _493494] : [class_Orderings_Opreorder(_493490), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_493490, _493492), _493494)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_493490, _493494), _493492))], (2880 ^ _393467) ^ [_493832, _493834, _493836] : [class_Orderings_Olinorder(_493832), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_493832, _493834), _493836))), -(_493834 = _493836), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_493832, _493836), _493834)))], (2894 ^ _393467) ^ [_494228] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _494228), _494228))], (2906 ^ _393467) ^ [_494644, _494646] : [2907 ^ _393467 : [(2908 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _494644), _494646))], (2910 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _494646), _494644))]], _494644 = _494646], (2896 ^ _393467) ^ [_494369, _494371] : [-(_494369 = _494371), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _494369), _494371))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _494371), _494369)))], (2914 ^ _393467) ^ [_494951, _494953] : [-(_494951 = _494953), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _494951), _494953))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _494953), _494951)))], (2924 ^ _393467) ^ [_495246] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _495246), _495246))], (2926 ^ _393467) ^ [_495358, _495360] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _495358), _495360)), _495360 = _495358], (2932 ^ _393467) ^ [_495579, _495581] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _495579), _495581)), _495579 = _495581], (2938 ^ _393467) ^ [_495814, _495816, _495818] : [2939 ^ _393467 : [(2940 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _495814), _495816)))], (2942 ^ _393467) ^ [] : [hBOOL(hAPP(hAPP(_495818, _495816), _495814))]], 2945 ^ _393467 : [(2946 ^ _393467) ^ [] : [-(_495814 = _495816)], (2948 ^ _393467) ^ [] : [hBOOL(hAPP(hAPP(_495818, _495816), _495814))]], 2951 ^ _393467 : [(2952 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _495816), _495814)))], (2954 ^ _393467) ^ [] : [hBOOL(hAPP(hAPP(_495818, _495816), _495814))]], -(hBOOL(hAPP(hAPP(_495818, _495816), _495814)))], (2958 ^ _393467) ^ [_496536, _496538] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _496536)), c_RealDef_Oreal(tc_Nat_Onat, _496538))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _496536), _496538)))], (2964 ^ _393467) ^ [_496730, _496732] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _496730), _496732)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _496730)), c_RealDef_Oreal(tc_Nat_Onat, _496732))))], (2970 ^ _393467) ^ [_496988, _496990, _496992] : [class_Orderings_Olinorder(_496988), 2973 ^ _393467 : [(2974 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_496988, _496990), _496992))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_496988, _496992), _496990)))], (2980 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_496988, _496992), _496990)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_496988, _496990), _496992))]]], (2986 ^ _393467) ^ [_497508, _497510, _497512] : [class_Orderings_Olinorder(_497508), 2989 ^ _393467 : [(2990 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_497508, _497510), _497512))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_497508, _497512), _497510)))], (2996 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_497508, _497512), _497510)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_497508, _497510), _497512))]]], (3002 ^ _393467) ^ [_498028, _498030, _498032] : [class_Orderings_Olinorder(_498028), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_498028, _498030), _498032))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_498028, _498032), _498030)))], (3012 ^ _393467) ^ [_498370, _498372, _498374] : [class_Orderings_Oorder(_498370), 3015 ^ _393467 : [(3016 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_498370, _498372), _498374)), 3019 ^ _393467 : [(3020 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_498370, _498372), _498374)))], (3022 ^ _393467) ^ [] : [_498372 = _498374]]], (3024 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_498370, _498372), _498374))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_498370, _498372), _498374)), -(_498372 = _498374)]]], (3034 ^ _393467) ^ [_499054, _499056, _499058] : [class_Orderings_Opreorder(_499054), 3037 ^ _393467 : [(3038 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_499054, _499056), _499058)), 3041 ^ _393467 : [(3042 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_499054, _499056), _499058)))], (3044 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_499054, _499058), _499056))]]], (3046 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_499054, _499056), _499058))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_499054, _499056), _499058)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_499054, _499058), _499056)))]]], (3056 ^ _393467) ^ [_499753, _499755, _499757] : [class_Orderings_Oorder(_499753), 3059 ^ _393467 : [(3070 ^ _393467) ^ [] : [3071 ^ _393467 : [(3072 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_499753, _499755), _499757))], (3074 ^ _393467) ^ [] : [_499755 = _499757]], -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_499753, _499755), _499757)))], (3060 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_499753, _499755), _499757)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_499753, _499755), _499757))), -(_499755 = _499757)]]], (3078 ^ _393467) ^ [_500435, _500437, _500439] : [class_Orderings_Olinorder(_500435), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_500435, _500437), _500439))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_500435, _500439), _500437)))], (3088 ^ _393467) ^ [_500779, _500781, _500783] : [class_Orderings_Olinorder(_500779), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_500779, _500781), _500783))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_500779, _500783), _500781)))], (3098 ^ _393467) ^ [_501123, _501125, _501127] : [class_Orderings_Olinorder(_501123), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_501123, _501125), _501127))), 3105 ^ _393467 : [(3106 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_501123, _501125), _501127)), -(_501125 = _501127)], (3112 ^ _393467) ^ [] : [_501125 = _501127, -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_501123, _501125), _501127)))]]], (3118 ^ _393467) ^ [_501732, _501734, _501736] : [class_Orderings_Oorder(_501732), -(_501734 = _501736), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_501732, _501734), _501736)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_501732, _501734), _501736)))], (3132 ^ _393467) ^ [_502169, _502171, _502173] : [class_Orderings_Oorder(_502169), -(_502171 = _502173), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_502169, _502173), _502171)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_502169, _502173), _502171)))], (3146 ^ _393467) ^ [_502606, _502608, _502610] : [class_Orderings_Olinorder(_502606), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_502606, _502608), _502610)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_502606, _502610), _502608))], (3156 ^ _393467) ^ [_502948, _502950, _502952] : [class_Orderings_Opreorder(_502948), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_502948, _502950), _502952)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_502948, _502950), _502952)))], (3166 ^ _393467) ^ [_503289, _503291, _503293] : [class_Orderings_Olinorder(_503289), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_503289, _503291), _503293)), 3173 ^ _393467 : [(3174 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_503289, _503291), _503293))), -(_503291 = _503293)], (3180 ^ _393467) ^ [] : [_503291 = _503293, hBOOL(hAPP(c_Orderings_Oord__class_Oless(_503289, _503291), _503293))]]], (3186 ^ _393467) ^ [_503897, _503899, _503901] : [class_Orderings_Oorder(_503897), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_503897, _503899), _503901)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_503897, _503899), _503901))), -(_503899 = _503901)], (3200 ^ _393467) ^ [_504332, _504334, _504336] : [class_Orderings_Oorder(_504332), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_504332, _504334), _504336)), -(_504334 = _504336), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_504332, _504334), _504336)))], (3214 ^ _393467) ^ [_504769, _504771, _504773] : [class_Orderings_Oorder(_504769), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_504769, _504771), _504773)), -(_504773 = _504771), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_504769, _504771), _504773)))], (3228 ^ _393467) ^ [_505220, _505222, _505224, _505226] : [class_Orderings_Opreorder(_505220), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_505220, _505222), _505224)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_505220, _505224), _505226)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_505220, _505222), _505226)))], (3242 ^ _393467) ^ [_505692, _505694, _505696, _505698] : [class_Orderings_Oorder(_505692), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_505692, _505694), _505696)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_505692, _505698), _505694)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_505692, _505698), _505696)))], (3256 ^ _393467) ^ [_506164, _506166, _506168, _506170] : [class_Orderings_Opreorder(_506164), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_506164, _506166), _506168)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_506164, _506168), _506170)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_506164, _506166), _506170)))], (3270 ^ _393467) ^ [_506636, _506638, _506640, _506642] : [class_Orderings_Oorder(_506636), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_506636, _506638), _506640)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_506636, _506642), _506638)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_506636, _506642), _506640)))], (3284 ^ _393467) ^ [_507066] : [-(_507066 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _507066)))], (3290 ^ _393467) ^ [_507277, _507279] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _507277), _507279)), _507279 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (3296 ^ _393467) ^ [_507468] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _507468), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (3298 ^ _393467) ^ [_507595] : [-(_507595 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _507595)))], (3304 ^ _393467) ^ [_507758] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _507758)), _507758 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (3310 ^ _393467) ^ [_507939] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _507939), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (3312 ^ _393467) ^ [_508080, _508082] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _508080), _508082)), 3315 ^ _393467 : [(3316 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _508080), _508082)))], (3318 ^ _393467) ^ [] : [_508080 = _508082]]], (3320 ^ _393467) ^ [_508338, _508340] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _508338), _508340))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _508338), _508340)), -(_508338 = _508340)], (3340 ^ _393467) ^ [_508963, _508965] : [3341 ^ _393467 : [(3342 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _508963), _508965))], (3344 ^ _393467) ^ [] : [_508963 = _508965]], -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _508963), _508965)))], (3330 ^ _393467) ^ [_508691, _508693] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _508691), _508693)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _508691), _508693))), -(_508691 = _508693)], (3348 ^ _393467) ^ [_509298, _509300] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _509298), _509300)), 3351 ^ _393467 : [(3352 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _509298), _509300)))], (3354 ^ _393467) ^ [] : [_509298 = _509300]]], (3356 ^ _393467) ^ [_509556, _509558] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _509556), _509558))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _509556), _509558)), -(_509556 = _509558)], (3376 ^ _393467) ^ [_510181, _510183] : [3377 ^ _393467 : [(3378 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _510181), _510183))], (3380 ^ _393467) ^ [] : [_510181 = _510183]], -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _510181), _510183)))], (3366 ^ _393467) ^ [_509909, _509911] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _509909), _509911)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _509909), _509911))), -(_509909 = _509911)], (3384 ^ _393467) ^ [_510487, _510489] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _510487), _510489)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _510487), _510489)))], (3390 ^ _393467) ^ [_510717, _510719] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _510717), _510719)), -(_510717 = _510719), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _510717), _510719)))], (3400 ^ _393467) ^ [_511039, _511041] : [3401 ^ _393467 : [(3402 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _511039), _511041))], (3404 ^ _393467) ^ [] : [_511039 = _511041]], -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _511039), _511041)))], (3408 ^ _393467) ^ [_511358] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_RealDef_Oreal(tc_Nat_Onat, _511358))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _511358)))], (3414 ^ _393467) ^ [_511528] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _511528)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_RealDef_Oreal(tc_Nat_Onat, _511528))))], (3430 ^ _393467) ^ [_512136] : [3433 ^ _393467 : [(3434 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, 3431 ^ [_512136]), 3432 ^ [_512136])))], (3436 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(_512136, 3431 ^ [_512136])), hAPP(_512136, 3432 ^ [_512136])))]], -(c_SEQ_Osubseq(_512136))], (3420 ^ _393467) ^ [_511763] : [c_SEQ_Osubseq(_511763), 3423 ^ _393467 : [(3424 ^ _393467) ^ [_511929, _511931] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _511931), _511929)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(_511763, _511931)), hAPP(_511763, _511929))))]]], (3440 ^ _393467) ^ [_512616, _512618] : [class_Rings_Olinordered__ring(_512616), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_512616, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_512616), _512618), _512618)), c_Groups_Ozero__class_Ozero(_512616)))], (3446 ^ _393467) ^ [_512883, _512885, _512887, _512889] : [class_Rings_Olinordered__ring__strict(_512883), 3449 ^ _393467 : [(3450 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_512883, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_512883), _512885), _512887)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_512883), _512889), _512887))), 3455 ^ _393467 : [(3456 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_512883, c_Groups_Ozero__class_Ozero(_512883)), _512887)))], (3458 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_512883, _512885), _512889)))]], 3459 ^ _393467 : [(3460 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_512883, _512887), c_Groups_Ozero__class_Ozero(_512883))))], (3462 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_512883, _512889), _512885)))]]], (3464 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_512883, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_512883), _512885), _512887)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_512883), _512889), _512887)))), 3465 ^ _393467 : [(3466 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_512883, c_Groups_Ozero__class_Ozero(_512883)), _512887)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_512883, _512885), _512889))], (3472 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_512883, _512887), c_Groups_Ozero__class_Ozero(_512883))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_512883, _512889), _512885))]]]]], (3480 ^ _393467) ^ [_514046, _514048, _514050, _514052] : [class_Rings_Olinordered__ring__strict(_514046), 3483 ^ _393467 : [(3484 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_514046, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_514046), _514048), _514050)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_514046), _514048), _514052))), 3489 ^ _393467 : [(3490 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_514046, c_Groups_Ozero__class_Ozero(_514046)), _514048)))], (3492 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_514046, _514050), _514052)))]], 3493 ^ _393467 : [(3494 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_514046, _514048), c_Groups_Ozero__class_Ozero(_514046))))], (3496 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_514046, _514052), _514050)))]]], (3498 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_514046, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_514046), _514048), _514050)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_514046), _514048), _514052)))), 3499 ^ _393467 : [(3500 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_514046, c_Groups_Ozero__class_Ozero(_514046)), _514048)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_514046, _514050), _514052))], (3506 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_514046, _514048), c_Groups_Ozero__class_Ozero(_514046))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_514046, _514052), _514050))]]]]], (3514 ^ _393467) ^ [_515209, _515211, _515213, _515215] : [class_Rings_Olinordered__ring__strict(_515209), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_515209, c_Groups_Ozero__class_Ozero(_515209)), _515211)), 3521 ^ _393467 : [(3522 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_515209, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_515209), _515211), _515213)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_515209), _515211), _515215))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_515209, _515213), _515215)))], (3528 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_515209, _515213), _515215)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_515209, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_515209), _515211), _515213)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_515209), _515211), _515215))))]]], (3534 ^ _393467) ^ [_515902, _515904, _515906] : [class_Rings_Olinordered__semiring__strict(_515902), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_515902, c_Groups_Ozero__class_Ozero(_515902)), _515904)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_515902, c_Groups_Ozero__class_Ozero(_515902)), _515906)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_515902, c_Groups_Ozero__class_Ozero(_515902)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_515902), _515904), _515906))))], (3548 ^ _393467) ^ [_516374, _516376, _516378] : [class_Rings_Olinordered__semiring__strict(_516374), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_516374, c_Groups_Ozero__class_Ozero(_516374)), _516376)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_516374, _516378), c_Groups_Ozero__class_Ozero(_516374))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_516374, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_516374), _516376), _516378)), c_Groups_Ozero__class_Ozero(_516374))))], (3562 ^ _393467) ^ [_516846, _516848, _516850] : [class_Rings_Olinordered__semiring__strict(_516846), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_516846, c_Groups_Ozero__class_Ozero(_516846)), _516848)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_516846, _516850), c_Groups_Ozero__class_Ozero(_516846))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_516846, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_516846), _516850), _516848)), c_Groups_Ozero__class_Ozero(_516846))))], (3576 ^ _393467) ^ [_517318, _517320, _517322] : [class_Rings_Olinordered__semiring__strict(_517318), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_517318, c_Groups_Ozero__class_Ozero(_517318)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_517318), _517320), _517322))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_517318, c_Groups_Ozero__class_Ozero(_517318)), _517320)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_517318, c_Groups_Ozero__class_Ozero(_517318)), _517322)))], (3590 ^ _393467) ^ [_517790, _517792, _517794] : [class_Rings_Olinordered__semiring__strict(_517790), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_517790, c_Groups_Ozero__class_Ozero(_517790)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_517790), _517792), _517794))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_517790, c_Groups_Ozero__class_Ozero(_517790)), _517794)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_517790, c_Groups_Ozero__class_Ozero(_517790)), _517792)))], (3604 ^ _393467) ^ [_518276, _518278, _518280, _518282] : [class_Rings_Olinordered__ring__strict(_518276), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_518276, _518278), c_Groups_Ozero__class_Ozero(_518276))), 3611 ^ _393467 : [(3612 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_518276, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_518276), _518278), _518280)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_518276), _518278), _518282))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_518276, _518282), _518280)))], (3618 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_518276, _518282), _518280)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_518276, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_518276), _518278), _518280)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_518276), _518278), _518282))))]]], (3624 ^ _393467) ^ [_518969, _518971, _518973] : [class_Rings_Olinordered__semiring__strict(_518969), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_518969, _518971), c_Groups_Ozero__class_Ozero(_518969))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_518969, c_Groups_Ozero__class_Ozero(_518969)), _518973)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_518969, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_518969), _518971), _518973)), c_Groups_Ozero__class_Ozero(_518969))))], (3638 ^ _393467) ^ [_519441, _519443, _519445] : [class_Rings_Olinordered__ring__strict(_519441), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_519441, _519443), c_Groups_Ozero__class_Ozero(_519441))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_519441, _519445), c_Groups_Ozero__class_Ozero(_519441))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_519441, c_Groups_Ozero__class_Ozero(_519441)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_519441), _519443), _519445))))], (3652 ^ _393467) ^ [_519927, _519929, _519931, _519933] : [class_Rings_Olinordered__semiring__strict(_519927), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_519927, _519929), _519931)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_519927, c_Groups_Ozero__class_Ozero(_519927)), _519933)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_519927, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_519927), _519929), _519933)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_519927), _519931), _519933))))], (3666 ^ _393467) ^ [_520435, _520437, _520439, _520441] : [class_Rings_Olinordered__semiring__strict(_520435), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_520435, _520437), _520439)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_520435, c_Groups_Ozero__class_Ozero(_520435)), _520441)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_520435, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_520435), _520441), _520437)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_520435), _520441), _520439))))], (3680 ^ _393467) ^ [_520943, _520945, _520947, _520949] : [class_Rings_Olinordered__comm__semiring__strict(_520943), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_520943, _520945), _520947)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_520943, c_Groups_Ozero__class_Ozero(_520943)), _520949)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_520943, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_520943), _520949), _520945)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_520943), _520949), _520947))))], (3694 ^ _393467) ^ [_521451, _521453, _521455, _521457] : [class_Rings_Olinordered__ring__strict(_521451), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_521451, _521453), _521455)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_521451, _521457), c_Groups_Ozero__class_Ozero(_521451))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_521451, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_521451), _521455), _521457)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_521451), _521453), _521457))))], (3708 ^ _393467) ^ [_521959, _521961, _521963, _521965] : [class_Rings_Olinordered__ring__strict(_521959), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_521959, _521961), _521963)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_521959, _521965), c_Groups_Ozero__class_Ozero(_521959))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_521959, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_521959), _521965), _521963)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_521959), _521965), _521961))))], (3722 ^ _393467) ^ [_522439, _522441] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _522439)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _522439), c_RealDef_Oreal(tc_Nat_Onat, _522441))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_RComplete_Onatfloor(_522439)), _522441)))], (3732 ^ _393467) ^ [_522801, _522803] : [hBOOL(hAPP(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), _522801), _522803))), 3735 ^ _393467 : [(3736 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _522801)))], (3738 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _522803)))]]], (3740 ^ _393467) ^ [_523062, _523064] : [-(hBOOL(hAPP(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), _523062), _523064)))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _523062)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _523064))], (3750 ^ _393467) ^ [_523430, _523432, _523434] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _523430), _523432)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _523430), _523434))), 3753 ^ _393467 : [(3754 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _523430)))], (3756 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _523432), _523434)))]]], (3758 ^ _393467) ^ [_523723, _523725, _523727] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _523723), _523725)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _523723), _523727)))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _523723)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _523725), _523727))], (3768 ^ _393467) ^ [_524125, _524127, _524129] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _524125), _524127)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _524129), _524127))), 3771 ^ _393467 : [(3772 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _524127)))], (3774 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _524125), _524129)))]]], (3776 ^ _393467) ^ [_524418, _524420, _524422] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _524418), _524420)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _524422), _524420)))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _524420)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _524418), _524422))], (3786 ^ _393467) ^ [_524791, _524793, _524795] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _524791), _524793)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _524795)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _524791), _524795)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _524793), _524795))))], (3796 ^ _393467) ^ [_525162, _525164, _525166] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _525162), _525164)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _525166)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _525166), _525162)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _525166), _525164))))], (3806 ^ _393467) ^ [_525533, _525535, _525537] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _525533)), 3809 ^ _393467 : [(3810 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _525533), _525535)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _525533), _525537))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _525535), _525537)))], (3816 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _525535), _525537)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _525533), _525535)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _525533), _525537))))]]], (3822 ^ _393467) ^ [_526093, _526095, _526097] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _526093)), 3825 ^ _393467 : [(3826 ^ _393467) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _526093), _526095) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _526093), _526097), -(_526095 = _526097)], (3832 ^ _393467) ^ [] : [_526095 = _526097, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _526093), _526095) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _526093), _526097))]]], (3838 ^ _393467) ^ [_526623, _526625, _526627] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _526623)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _526625), _526627)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _526623), _526625)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _526623), _526627))))], (3848 ^ _393467) ^ [_526980, _526982] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _526980)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _526982)), -(hBOOL(hAPP(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), _526980), _526982))))], (3858 ^ _393467) ^ [_527317, _527319, _527321] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _527317)), 3861 ^ _393467 : [(3862 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _527319), _527317)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _527321), _527317))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _527319), _527321)))], (3868 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _527319), _527321)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _527319), _527317)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _527321), _527317))))]]], (3874 ^ _393467) ^ [_527863, _527865] : [class_RealVector_Oreal__normed__vector(_527863), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_527863, _527865)), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (3880 ^ _393467) ^ [_528058] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _528058)), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (3882 ^ _393467) ^ [_528201, _528203, _528205, _528207] : [class_Rings_Olinordered__ring__strict(_528201), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_528201, c_Groups_Ozero__class_Ozero(_528201)), _528203)), 3889 ^ _393467 : [(3890 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_528201, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_528201), _528203), _528205)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_528201), _528203), _528207))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_528201, _528205), _528207)))], (3896 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_528201, _528205), _528207)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_528201, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_528201), _528203), _528205)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_528201), _528203), _528207))))]]], (3902 ^ _393467) ^ [_528908, _528910, _528912, _528914] : [class_Rings_Olinordered__ring__strict(_528908), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_528908, _528910), c_Groups_Ozero__class_Ozero(_528908))), 3909 ^ _393467 : [(3910 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_528908, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_528908), _528910), _528912)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_528908), _528910), _528914))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_528908, _528914), _528912)))], (3916 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_528908, _528914), _528912)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_528908, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_528908), _528910), _528912)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_528908), _528910), _528914))))]]], (3922 ^ _393467) ^ [_529629, _529631, _529633, _529635, _529637] : [class_Rings_Olinordered__semiring__strict(_529629), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_529629, _529631), _529633)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_529629, _529635), _529637)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_529629, c_Groups_Ozero__class_Ozero(_529629)), _529633)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_529629, c_Groups_Ozero__class_Ozero(_529629)), _529635)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_529629, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_529629), _529631), _529635)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_529629), _529633), _529637))))], (3944 ^ _393467) ^ [_530391, _530393, _530395, _530397, _530399] : [class_Rings_Olinordered__semiring__strict(_530391), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_530391, _530393), _530395)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_530391, _530397), _530399)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_530391, c_Groups_Ozero__class_Ozero(_530391)), _530393)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_530391, c_Groups_Ozero__class_Ozero(_530391)), _530397)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_530391, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_530391), _530393), _530397)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_530391), _530395), _530399))))], (3966 ^ _393467) ^ [_531153, _531155, _531157, _531159, _531161] : [class_Rings_Olinordered__semiring__strict(_531153), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_531153, _531155), _531157)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_531153, _531159), _531161)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_531153, c_Groups_Ozero__class_Ozero(_531153)), _531155)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_531153, c_Groups_Ozero__class_Ozero(_531153)), _531159)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_531153, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_531153), _531155), _531159)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_531153), _531157), _531161))))], (3988 ^ _393467) ^ [_531915, _531917, _531919, _531921, _531923] : [class_Rings_Olinordered__semiring__strict(_531915), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_531915, _531917), _531919)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_531915, _531921), _531923)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_531915, c_Groups_Ozero__class_Ozero(_531915)), _531917)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_531915, c_Groups_Ozero__class_Ozero(_531915)), _531921)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_531915, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_531915), _531917), _531921)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_531915), _531919), _531923))))], (4010 ^ _393467) ^ [_532663, _532665, _532667, _532669] : [class_Rings_Olinordered__semiring(_532663), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_532663, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_532663), _532665), _532667)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_532663), _532669), _532667))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_532663, c_Groups_Ozero__class_Ozero(_532663)), _532667)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_532663, _532665), _532669)))], (4024 ^ _393467) ^ [_533171, _533173, _533175, _533177] : [class_Rings_Olinordered__semiring__strict(_533171), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_533171, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_533171), _533173), _533175)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_533171), _533177), _533175))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_533171, c_Groups_Ozero__class_Ozero(_533171)), _533175)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_533171, _533173), _533177)))], (4038 ^ _393467) ^ [_533679, _533681, _533683, _533685] : [class_Rings_Olinordered__semiring(_533679), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_533679, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_533679), _533681), _533683)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_533679), _533681), _533685))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_533679, c_Groups_Ozero__class_Ozero(_533679)), _533681)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_533679, _533683), _533685)))], (4052 ^ _393467) ^ [_534187, _534189, _534191, _534193] : [class_Rings_Olinordered__semiring__strict(_534187), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_534187, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_534187), _534189), _534191)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_534187), _534189), _534193))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_534187, c_Groups_Ozero__class_Ozero(_534187)), _534189)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_534187, _534191), _534193)))], (4066 ^ _393467) ^ [_534695, _534697, _534699, _534701] : [class_Rings_Olinordered__semiring__strict(_534695), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_534695, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_534695), _534697), _534699)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_534695), _534701), _534699))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_534695, c_Groups_Ozero__class_Ozero(_534695)), _534699)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_534695, _534697), _534701)))], (4080 ^ _393467) ^ [_535203, _535205, _535207, _535209] : [class_Rings_Olinordered__semiring__strict(_535203), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_535203, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_535203), _535205), _535207)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_535203), _535205), _535209))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_535203, c_Groups_Ozero__class_Ozero(_535203)), _535205)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_535203, _535207), _535209)))], (4094 ^ _393467) ^ [_535683, _535685] : [class_RealVector_Oreal__normed__vector(_535683), 4097 ^ _393467 : [(4098 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_RealVector_Onorm__class_Onorm(_535683, _535685))), _535685 = c_Groups_Ozero__class_Ozero(_535683)], (4104 ^ _393467) ^ [] : [-(_535685 = c_Groups_Ozero__class_Ozero(_535683)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_RealVector_Onorm__class_Onorm(_535683, _535685))))]]], (4110 ^ _393467) ^ [_536178, _536180, _536182] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _536178)), 4113 ^ _393467 : [(4114 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _536180), _536178)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _536182), _536178))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _536180), _536182)))], (4120 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _536180), _536182)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _536180), _536178)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _536182), _536178))))]]], (4126 ^ _393467) ^ [_536738, _536740, _536742] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _536738)), 4129 ^ _393467 : [(4130 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _536738), _536740)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _536738), _536742))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _536740), _536742)))], (4136 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _536740), _536742)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _536738), _536740)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _536738), _536742))))]]], (4143 ^ _393467) ^ [] : [-(c_SEQ_Osubseq(4141 ^ []))], (4145 ^ _393467) ^ [] : [-(c_SEQ_Omonoseq(tc_RealDef_Oreal, c_COMBB(tc_Complex_Ocomplex, tc_RealDef_Oreal, tc_Nat_Onat, c_Complex_OIm, c_COMBB(tc_Nat_Onat, tc_Complex_Ocomplex, tc_Nat_Onat, v_s, c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____, 4141 ^ [])))))], (4147 ^ _393467) ^ [_537469] : [-(hBOOL(hAPP(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), _537469), _537469)))), -(_537469 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (4153 ^ _393467) ^ [_537644] : [_537644 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), hBOOL(hAPP(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), _537644), _537644)))], (4159 ^ _393467) ^ [_537867, _537869] : [class_RealVector_Oreal__normed__algebra(_537867), 4163 ^ _393467 : [(4164 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 4162 ^ [_537867, _537869])))], (4166 ^ _393467) ^ [_538177] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_537867, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_537867), _538177), _537869))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_537867, _538177)), 4162 ^ [_537867, _537869]))))]]], (4168 ^ _393467) ^ [_538327, _538329] : [class_RealVector_Oreal__normed__algebra(_538327), 4172 ^ _393467 : [(4173 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 4171 ^ [_538327, _538329])))], (4175 ^ _393467) ^ [_538637] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_538327, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_538327), _538329), _538637))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_538327, _538637)), 4171 ^ [_538327, _538329]))))]]], (4177 ^ _393467) ^ [_538773] : [class_RealVector_Oreal__normed__algebra(_538773), 4181 ^ _393467 : [(4182 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 4180 ^ [_538773])))], (4184 ^ _393467) ^ [_539113, _539115] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_538773, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_538773), _539115), _539113))), 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(_538773, _539115)), c_RealVector_Onorm__class_Onorm(_538773, _539113))), 4180 ^ [_538773]))))]]], (4186 ^ _393467) ^ [] : [-(hAPP(c_Complex_OIm, c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (4188 ^ _393467) ^ [_539323, _539325] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _539323), _539325)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _539323), _539325)))], (4194 ^ _393467) ^ [_539553, _539555] : [class_RealVector_Oreal__normed__vector(_539553), 4197 ^ _393467 : [(4198 ^ _393467) ^ [] : [c_SEQ_OBseq(_539553, _539555), 4202 ^ _393467 : [(4203 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 4201 ^ [_539553, _539555])))], (4205 ^ _393467) ^ [_539949] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_539553, hAPP(_539555, _539949))), 4201 ^ [_539553, _539555])))]]], (4207 ^ _393467) ^ [] : [-(c_SEQ_OBseq(_539553, _539555)), 4208 ^ _393467 : [(4209 ^ _393467) ^ [_540085] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _540085)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_539553, hAPP(_539555, 4212 ^ [_539553, _539555, _540085]))), _540085))]]]]], (4219 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 4217 ^ [])))], (4221 ^ _393467) ^ [_540556] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, hAPP(c_Complex_OIm, _540556))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _540556)), 4217 ^ []))))], (4223 ^ _393467) ^ [_540685, _540687] : [hAPP(c_Complex_ORe, _540685) = hAPP(c_Complex_ORe, _540687), hAPP(c_Complex_OIm, _540685) = hAPP(c_Complex_OIm, _540687), -(_540685 = _540687)], (4233 ^ _393467) ^ [_541037, _541039] : [_541037 = _541039, 4236 ^ _393467 : [(4237 ^ _393467) ^ [] : [-(hAPP(c_Complex_ORe, _541037) = hAPP(c_Complex_ORe, _541039))], (4239 ^ _393467) ^ [] : [-(hAPP(c_Complex_OIm, _541037) = hAPP(c_Complex_OIm, _541039))]]], (4241 ^ _393467) ^ [_541298, _541300] : [-(_541298 = _541300), hAPP(c_Complex_ORe, _541298) = hAPP(c_Complex_ORe, _541300), hAPP(c_Complex_OIm, _541298) = hAPP(c_Complex_OIm, _541300)], (4251 ^ _393467) ^ [] : [-(hAPP(c_Complex_ORe, c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (4253 ^ _393467) ^ [_541704, _541706, _541708, _541710] : [class_Orderings_Oord(_541704), 4256 ^ _393467 : [(4257 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_541706, _541704), _541708), _541710)), 4260 ^ _393467 : [(4261 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_541706, _541704), _541708), _541710)))], (4263 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_541706, _541704), _541710), _541708))]]], (4265 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_541706, _541704), _541708), _541710))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_541706, _541704), _541708), _541710)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_541706, _541704), _541710), _541708)))]]], (4275 ^ _393467) ^ [_542409] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(c_Complex_ORe, _542409)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _542409))))], (4278 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 4276 ^ [])))], (4280 ^ _393467) ^ [_542621] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, hAPP(c_Complex_ORe, _542621))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _542621)), 4276 ^ []))))], (4283 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 4281 ^ [])))], (4285 ^ _393467) ^ [_542844] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, hAPP(c_Complex_OIm, _542844))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _542844)), 4281 ^ []))))], (4288 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 4286 ^ [])))], (4290 ^ _393467) ^ [_543067] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, hAPP(c_Complex_ORe, _543067))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _543067)), 4286 ^ []))))], (4293 ^ _393467) ^ [_543229] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, hAPP(c_Complex_OIm, _543229))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _543229)), 4291 ^ []))))], (4296 ^ _393467) ^ [_543389] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, hAPP(c_Complex_ORe, _543389))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _543389)), 4294 ^ []))))], (4298 ^ _393467) ^ [_543516, _543518] : [class_RealVector_Oreal__normed__vector(_543516), c_SEQ_OBseq(_543516, _543518), 4306 ^ _393467 : [(4307 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 4305 ^ [_543516, _543518])))], (4309 ^ _393467) ^ [_543883] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_543516, hAPP(_543518, _543883))), 4305 ^ [_543516, _543518])))]]], (4311 ^ _393467) ^ [_544037, _544039, _544041] : [class_RealVector_Oreal__normed__vector(_544037), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _544039)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_544037, hAPP(_544041, 4320 ^ [_544037, _544039, _544041]))), _544039)), -(c_SEQ_OBseq(_544037, _544041))], (4326 ^ _393467) ^ [_544565, _544567, _544569, _544571] : [class_RealVector_Oreal__normed__vector(_544565), 4332 ^ _393467 : [(4333 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _544567), 4331 ^ [_544565, _544567, _544569, _544571])))], (4335 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_544565, hAPP(_544569, 4331 ^ [_544565, _544567, _544569, _544571]))), _544571))]], -(c_SEQ_OBseq(_544565, _544569))], (4339 ^ _393467) ^ [_545095, _545097] : [class_RealVector_Oreal__normed__vector(_545095), 4342 ^ _393467 : [(4355 ^ _393467) ^ [] : [4357 ^ _393467 : [(4358 ^ _393467) ^ [_545866] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_545095, hAPP(_545097, 4356 ^ [_545095, _545097, _545866]))), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(_545866))))]], 4360 ^ _393467 : [(4361 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 4359 ^ [_545095, _545097])))], (4363 ^ _393467) ^ [_546097] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_545095, hAPP(_545097, _546097))), 4359 ^ [_545095, _545097])))]]], (4343 ^ _393467) ^ [] : [4352 ^ _393467 : [(4353 ^ _393467) ^ [_545679] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_545095, hAPP(_545097, _545679))), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(4351 ^ [_545095, _545097])))))]], 4344 ^ _393467 : [(4345 ^ _393467) ^ [_545343] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _545343)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_545095, hAPP(_545097, 4348 ^ [_545095, _545097, _545343]))), _545343))]]]]], (4365 ^ _393467) ^ [_546241, _546243] : [class_RealVector_Oreal__normed__vector(_546241), 4368 ^ _393467 : [(4381 ^ _393467) ^ [] : [4383 ^ _393467 : [(4384 ^ _393467) ^ [_547012] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_546241, hAPP(_546243, 4382 ^ [_546241, _546243, _547012]))), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(_547012))))]], 4386 ^ _393467 : [(4387 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 4385 ^ [_546241, _546243])))], (4389 ^ _393467) ^ [_547243] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_546241, hAPP(_546243, _547243))), 4385 ^ [_546241, _546243])))]]], (4369 ^ _393467) ^ [] : [4378 ^ _393467 : [(4379 ^ _393467) ^ [_546825] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_546241, hAPP(_546243, _546825))), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(4377 ^ [_546241, _546243])))))]], 4370 ^ _393467 : [(4371 ^ _393467) ^ [_546489] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _546489)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_546241, hAPP(_546243, 4374 ^ [_546241, _546243, _546489]))), _546489))]]]]], (4391 ^ _393467) ^ [_547373] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _547373)), 4395 ^ _393467 : [(4396 ^ _393467) ^ [_547565] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _547565), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, 4394 ^ [_547373, _547565])), _547373))))]]], (4399 ^ _393467) ^ [] : [-(c_SEQ_Osubseq(4397 ^ []))], (4401 ^ _393467) ^ [] : [-(c_SEQ_Omonoseq(tc_RealDef_Oreal, c_COMBB(tc_Nat_Onat, tc_RealDef_Oreal, tc_Nat_Onat, c_Fun_Ocomp(tc_Complex_Ocomplex, tc_RealDef_Oreal, tc_Nat_Onat, c_Complex_ORe, v_s), 4397 ^ [])))], (4403 ^ _393467) ^ [_547856, _547858] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _547856), _547858)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_547856)), c_Nat_OSuc(_547858))))], (4409 ^ _393467) ^ [_548065] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _548065), c_Nat_OSuc(_548065))))], (4411 ^ _393467) ^ [_548150] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Nat_OSuc(_548150))))], (4413 ^ _393467) ^ [_548261, _548263] : [c_Nat_OSuc(_548261) = c_Nat_OSuc(_548263), -(_548261 = _548263)], (4419 ^ _393467) ^ [_548508, _548510] : [c_Nat_OSuc(_548508) = c_Nat_OSuc(_548510), -(_548508 = _548510)], (4425 ^ _393467) ^ [_548678, _548680] : [_548678 = _548680, -(c_Nat_OSuc(_548678) = c_Nat_OSuc(_548680))], (4431 ^ _393467) ^ [_548868] : [c_Nat_OSuc(_548868) = _548868], (4433 ^ _393467) ^ [_548947] : [_548947 = c_Nat_OSuc(_548947)], (4435 ^ _393467) ^ [_549182, _549184, _549186, _549188, _549190, _549192, _549194, _549196, _549198, _549200, _549202] : [hAPP(_549182, hAPP(_549184, _549186)) = hAPP(_549188, hAPP(_549190, _549192)), -(hAPP(c_Fun_Ocomp(_549194, _549196, _549198, _549182, _549184), _549186) = hAPP(c_Fun_Ocomp(_549200, _549196, _549202, _549188, _549190), _549192))], (4441 ^ _393467) ^ [_549476] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_549476)], (4443 ^ _393467) ^ [_549555] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_549555)], (4445 ^ _393467) ^ [_549634] : [c_Nat_OSuc(_549634) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (4447 ^ _393467) ^ [_549713] : [c_Nat_OSuc(_549713) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (4449 ^ _393467) ^ [_549792] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_549792)], (4451 ^ _393467) ^ [_549871] : [c_Nat_OSuc(_549871) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (4453 ^ _393467) ^ [_549980, _549982] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_549980)), c_Nat_OSuc(_549982))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _549980), _549982)))], (4459 ^ _393467) ^ [_550218, _550220] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_550218)), _550220)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _550218), _550220)))], (4465 ^ _393467) ^ [_550452, _550454] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _550452), c_Nat_OSuc(_550454))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _550452), _550454))), -(_550452 = _550454)], (4475 ^ _393467) ^ [_550792, _550794, _550796] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _550792), _550794)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _550794), _550796)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_550792)), _550796)))], (4485 ^ _393467) ^ [_551135, _551137] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _551135), _551137)), -(c_Nat_OSuc(_551135) = _551137), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_551135)), _551137)))], (4495 ^ _393467) ^ [_551465, _551467] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _551465), _551467)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _551465), c_Nat_OSuc(_551467))))], (4501 ^ _393467) ^ [_551699, _551701] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _551699), _551701))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _551699), c_Nat_OSuc(_551701))), -(_551701 = _551699)], (4511 ^ _393467) ^ [_552025, _552027] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _552025), _552027))), 4514 ^ _393467 : [(4515 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _552025), c_Nat_OSuc(_552027))), -(_552025 = _552027)], (4521 ^ _393467) ^ [] : [_552025 = _552027, -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _552025), c_Nat_OSuc(_552027))))]]], (4527 ^ _393467) ^ [_552548, _552550] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_552548)), c_Nat_OSuc(_552550))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _552548), _552550)))], (4533 ^ _393467) ^ [_552738, _552740] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _552738), _552740)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_552738)), c_Nat_OSuc(_552740))))], (4549 ^ _393467) ^ [_553283, _553285] : [4550 ^ _393467 : [(4551 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _553283), _553285))], (4553 ^ _393467) ^ [] : [_553283 = _553285]], -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _553283), c_Nat_OSuc(_553285))))], (4539 ^ _393467) ^ [_553007, _553009] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _553007), c_Nat_OSuc(_553009))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _553007), _553009))), -(_553007 = _553009)], (4557 ^ _393467) ^ [_553622, _553624] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _553622), _553624))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _553624), c_Nat_OSuc(_553622))))], (4563 ^ _393467) ^ [_553811, _553813] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _553813), c_Nat_OSuc(_553811))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _553811), _553813))], (4569 ^ _393467) ^ [_554048, _554050] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_554048)), _554050)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _554048), _554050)))], (4575 ^ _393467) ^ [_554282, _554284] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _554282), c_Nat_OSuc(_554284))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _554282), _554284))), -(_554282 = c_Nat_OSuc(_554284))], (4585 ^ _393467) ^ [_554612, _554614] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _554612), _554614)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _554612), c_Nat_OSuc(_554614))))], (4591 ^ _393467) ^ [_554875, _554877] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_554875)), c_Nat_OSuc(_554877))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _554875), _554877)))], (4597 ^ _393467) ^ [_555065, _555067] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _555065), _555067)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_555065)), c_Nat_OSuc(_555067))))], (4613 ^ _393467) ^ [_555614, _555616] : [4614 ^ _393467 : [(4615 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _555614), _555616))], (4617 ^ _393467) ^ [] : [_555614 = c_Nat_OSuc(_555616)]], -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _555614), c_Nat_OSuc(_555616))))], (4603 ^ _393467) ^ [_555334, _555336] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _555334), c_Nat_OSuc(_555336))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _555334), _555336))), -(_555334 = c_Nat_OSuc(_555336))], (4621 ^ _393467) ^ [_555957, _555959] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _555957), _555959))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_555959)), _555957)))], (4627 ^ _393467) ^ [_556146, _556148] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_556148)), _556146)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _556146), _556148))], (4633 ^ _393467) ^ [_556353] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_556353)), _556353))], (4635 ^ _393467) ^ [_556510, _556512, _556514] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_556510)), _556512) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_556510)), _556514), -(_556512 = _556514)], (4641 ^ _393467) ^ [_556710, _556712, _556714] : [_556712 = _556714, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_556710)), _556712) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_556710)), _556714))], (4647 ^ _393467) ^ [_556989, _556991] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _556989), c_Nat_OSuc(_556991))), -(_556989 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 4655 ^ _393467 : [(4656 ^ _393467) ^ [] : [-(_556989 = c_Nat_OSuc(4654 ^ [_556989, _556991]))], (4658 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, 4654 ^ [_556989, _556991]), _556991)))]]], (4660 ^ _393467) ^ [_557421, _557423] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _557421), c_Nat_OSuc(_557423)))), 4661 ^ _393467 : [(4662 ^ _393467) ^ [] : [_557421 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (4664 ^ _393467) ^ [_557598] : [_557421 = c_Nat_OSuc(_557598), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _557598), _557423))]]], (4672 ^ _393467) ^ [_557908] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _557908), c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_557908 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4678 ^ _393467) ^ [_558074] : [_558074 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _558074), c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (4684 ^ _393467) ^ [_558305] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _558305)), -(_558305 = c_Nat_OSuc(4687 ^ [_558305]))], (4691 ^ _393467) ^ [_558522] : [4692 ^ _393467 : [(4693 ^ _393467) ^ [_558594] : [_558522 = c_Nat_OSuc(_558594)]], -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _558522)))], (4697 ^ _393467) ^ [_558787, _558789] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _558787), _558789) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 4700 ^ _393467 : [(4701 ^ _393467) ^ [] : [-(_558787 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (4703 ^ _393467) ^ [] : [-(_558789 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (4705 ^ _393467) ^ [_559036, _559038] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _559036), _559038) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _559036 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _559038 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4715 ^ _393467) ^ [_559378, _559380] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _559378), _559380)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_559378)), _559380)))], (4721 ^ _393467) ^ [_559564, _559566] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_559564)), _559566)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _559564), _559566)))], (4727 ^ _393467) ^ [_559829, _559831] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _559829), c_Nat_OSuc(_559831))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _559829), _559831)))], (4733 ^ _393467) ^ [_560015, _560017] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _560015), _560017)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _560015), c_Nat_OSuc(_560017))))], (4739 ^ _393467) ^ [_560280, _560282] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_560280)), _560282)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _560280), _560282)))], (4745 ^ _393467) ^ [_560466, _560468] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _560466), _560468)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_560466)), _560468)))], (4751 ^ _393467) ^ [_560702, _560704] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _560702), _560704)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _560702), c_Nat_OSuc(_560704))))], (4757 ^ _393467) ^ [_560936, _560938] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _560936), _560938)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_560936)), _560938)))], (4763 ^ _393467) ^ [_561170, _561172] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _561170), _561172)), 4766 ^ _393467 : [(4767 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _561172), c_Nat_OSuc(_561170))), -(_561172 = _561170)], (4773 ^ _393467) ^ [] : [_561172 = _561170, -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _561172), c_Nat_OSuc(_561170))))]]], (4779 ^ _393467) ^ [_561661, _561663] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_561661)), _561663)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _561661), _561663)))], (4785 ^ _393467) ^ [_561938, _561940, _561942] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_561938)), _561940)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_561938)), _561942))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _561940), _561942)))], (4791 ^ _393467) ^ [_562158, _562160, _562162] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _562160), _562162)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_562158)), _562160)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_562158)), _562162))))], (4797 ^ _393467) ^ [_562471, _562473, _562475] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_562471)), _562473)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_562471)), _562475))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _562473), _562475)))], (4803 ^ _393467) ^ [_562691, _562693, _562695] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _562693), _562695)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_562691)), _562693)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_562691)), _562695))))], (4809 ^ _393467) ^ [_562961, _562963] : [class_Orderings_Oorder(_562961), 4812 ^ _393467 : [(4823 ^ _393467) ^ [] : [4825 ^ _393467 : [(4826 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_562961, hAPP(_562963, 4824 ^ [_562961, _562963])), hAPP(_562963, c_Nat_OSuc(4824 ^ [_562961, _562963]))))], (4829 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_562961, hAPP(_562963, c_Nat_OSuc(4827 ^ [_562961, _562963]))), hAPP(_562963, 4827 ^ [_562961, _562963])))]], -(c_SEQ_Omonoseq(_562961, _562963))], (4813 ^ _393467) ^ [] : [c_SEQ_Omonoseq(_562961, _562963), 4818 ^ _393467 : [(4819 ^ _393467) ^ [_563260] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_562961, hAPP(_562963, _563260)), hAPP(_562963, c_Nat_OSuc(_563260)))))]], 4820 ^ _393467 : [(4821 ^ _393467) ^ [_563335] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_562961, hAPP(_562963, c_Nat_OSuc(_563335))), hAPP(_562963, _563335))))]]]]], (4833 ^ _393467) ^ [_563858] : [c_SEQ_Osubseq(_563858), 4836 ^ _393467 : [(4837 ^ _393467) ^ [_563981] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(_563858, _563981)), hAPP(_563858, c_Nat_OSuc(_563981)))))]]], (4839 ^ _393467) ^ [_564060] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(_564060, 4840 ^ [_564060])), hAPP(_564060, c_Nat_OSuc(4840 ^ [_564060])))), -(c_SEQ_Osubseq(_564060))], (4846 ^ _393467) ^ [_564330] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _564330) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_564330)))], (4848 ^ _393467) ^ [_564445, _564447] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _564445)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _564447)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _564445), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _564447), _564445))))], (4858 ^ _393467) ^ [_564774, _564776] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _564774)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _564776)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _564774), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _564774), _564776))))], (4868 ^ _393467) ^ [_565103, _565105] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _565103)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _565105)), -(hBOOL(hAPP(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), _565105), _565103))))], (4878 ^ _393467) ^ [_565455, _565457] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _565455), _565457))), 4881 ^ _393467 : [(4882 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _565455)))], (4884 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _565457)))]]], (4886 ^ _393467) ^ [_565716, _565718] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _565716), _565718)))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _565716)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _565718))], (4896 ^ _393467) ^ [_566012] : [-(hBOOL(hAPP(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(_566012)))))], (4898 ^ _393467) ^ [_566126, _566128] : [class_RealVector_Oreal__normed__vector(_566126), 4901 ^ _393467 : [(4902 ^ _393467) ^ [] : [c_SEQ_OBseq(_566126, _566128), 4906 ^ _393467 : [(4907 ^ _393467) ^ [_566441] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_566126, hAPP(_566128, _566441))), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(4905 ^ [_566126, _566128])))))]]], (4909 ^ _393467) ^ [] : [4911 ^ _393467 : [(4912 ^ _393467) ^ [_566627] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_566126, hAPP(_566128, 4910 ^ [_566126, _566128, _566627]))), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(_566627))))]], -(c_SEQ_OBseq(_566126, _566128))]]], (4916 ^ _393467) ^ [_566821, _566823] : [class_RealVector_Oreal__normed__vector(_566821), 4919 ^ _393467 : [(4920 ^ _393467) ^ [] : [c_SEQ_OBseq(_566821, _566823), 4924 ^ _393467 : [(4925 ^ _393467) ^ [_567136] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_566821, hAPP(_566823, _567136))), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(4923 ^ [_566821, _566823])))))]]], (4927 ^ _393467) ^ [] : [4929 ^ _393467 : [(4930 ^ _393467) ^ [_567322] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_566821, hAPP(_566823, 4928 ^ [_566821, _566823, _567322]))), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(_567322))))]], -(c_SEQ_OBseq(_566821, _566823))]]], (4934 ^ _393467) ^ [_567502] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _567502), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))), -(_567502 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_567502 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (4945 ^ _393467) ^ [] : [-(c_SEQ_Osubseq(4943 ^ []))], (4947 ^ _393467) ^ [] : [-(c_SEQ_Omonoseq(tc_RealDef_Oreal, c_COMBB(tc_Nat_Onat, tc_RealDef_Oreal, tc_Nat_Onat, c_Fun_Ocomp(tc_Nat_Onat, tc_RealDef_Oreal, tc_Nat_Onat, c_Fun_Ocomp(tc_Complex_Ocomplex, tc_RealDef_Oreal, tc_Nat_Onat, c_Complex_OIm, v_s), v_f____), 4943 ^ [])))], (4949 ^ _393467) ^ [_567944] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _567944)), 4953 ^ _393467 : [(4954 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, 4952 ^ [_567944])), _567944)))], (4956 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _567944), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(4952 ^ [_567944])))))]]], (4958 ^ _393467) ^ [_568341, _568343] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _568341)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _568343)), 4966 ^ _393467 : [(4967 ^ _393467) ^ [] : [-(hBOOL(hAPP(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, 4965 ^ [_568341, _568343])), _568341)), _568343)))], (4969 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _568343), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(4965 ^ [_568341, _568343]))), _568341))))]]], (4971 ^ _393467) ^ [_568924, _568926, _568928, _568930, _568932, _568934] : [-(hAPP(c_Fun_Ocomp(_568924, _568926, _568928, c_COMBK(_568926, _568924, _568930), _568932), _568934) = _568930)], (4973 ^ _393467) ^ [_569124, _569126, _569128, _569130, _569132, _569134, _569136] : [c_Fun_Ocomp(_569124, _569126, _569128, _569130, _569132) = _569134, -(hAPP(_569130, hAPP(_569132, _569136)) = hAPP(_569134, _569136))], (4979 ^ _393467) ^ [_569435, _569437, _569439, _569441, _569443, _569445] : [-(hAPP(c_Fun_Ocomp(_569435, _569437, _569439, _569441, _569443), _569445) = hAPP(_569441, hAPP(_569443, _569445)))], (4981 ^ _393467) ^ [_569581, _569583, _569585] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _569581)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _569583)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _569585)), -(c_NthRoot_Oroot(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _569581), _569583), _569585) = c_NthRoot_Oroot(_569581, c_NthRoot_Oroot(_569583, _569585)))], (4995 ^ _393467) ^ [_570039, _570041, _570043] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _570039)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _570041)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _570043)), -(c_NthRoot_Oroot(_570039, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _570041), _570043)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_NthRoot_Oroot(_570039, _570041)), c_NthRoot_Oroot(_570039, _570043)))], (5009 ^ _393467) ^ [_570509, _570511, _570513] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _570509)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _570511)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _570511), _570513)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_NthRoot_Oroot(_570509, _570511)), c_NthRoot_Oroot(_570509, _570513))))], (5023 ^ _393467) ^ [_570951, _570953] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _570951)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _570953)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_NthRoot_Oroot(_570951, _570953))))], (5033 ^ _393467) ^ [_571239] : [-(c_NthRoot_Oroot(_571239, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (5035 ^ _393467) ^ [_571320] : [-(c_NthRoot_Oroot(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _571320) = _571320)], (5037 ^ _393467) ^ [_571444, _571446, _571448] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _571444)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _571446)), -(c_NthRoot_Oroot(_571444, c_NthRoot_Oroot(_571446, _571448)) = c_NthRoot_Oroot(_571446, c_NthRoot_Oroot(_571444, _571448)))], (5047 ^ _393467) ^ [_571799, _571801, _571803] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _571799)), 5050 ^ _393467 : [(5051 ^ _393467) ^ [] : [c_NthRoot_Oroot(_571799, _571801) = c_NthRoot_Oroot(_571799, _571803), -(_571801 = _571803)], (5057 ^ _393467) ^ [] : [_571801 = _571803, -(c_NthRoot_Oroot(_571799, _571801) = c_NthRoot_Oroot(_571799, _571803))]]], (5063 ^ _393467) ^ [_572311, _572313, _572315] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _572311)), 5066 ^ _393467 : [(5067 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_NthRoot_Oroot(_572311, _572313)), c_NthRoot_Oroot(_572311, _572315))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _572313), _572315)))], (5073 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _572313), _572315)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_NthRoot_Oroot(_572311, _572313)), c_NthRoot_Oroot(_572311, _572315))))]]], (5079 ^ _393467) ^ [_572853, _572855, _572857] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _572853)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _572855), _572857)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_NthRoot_Oroot(_572853, _572855)), c_NthRoot_Oroot(_572853, _572857))))], (5089 ^ _393467) ^ [_573198, _573200] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _573198)), 5092 ^ _393467 : [(5093 ^ _393467) ^ [] : [c_NthRoot_Oroot(_573198, _573200) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_573200 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (5099 ^ _393467) ^ [] : [_573200 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(c_NthRoot_Oroot(_573198, _573200) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))]]], (5105 ^ _393467) ^ [_573685, _573687, _573689] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _573685)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _573687), _573689)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_NthRoot_Oroot(_573685, _573687)), c_NthRoot_Oroot(_573685, _573689))))], (5115 ^ _393467) ^ [_574044, _574046, _574048] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _574044)), 5118 ^ _393467 : [(5119 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_NthRoot_Oroot(_574044, _574046)), c_NthRoot_Oroot(_574044, _574048))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _574046), _574048)))], (5125 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _574046), _574048)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_NthRoot_Oroot(_574044, _574046)), c_NthRoot_Oroot(_574044, _574048))))]]], (5131 ^ _393467) ^ [_574586, _574588, _574590] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _574586)), -(c_NthRoot_Oroot(_574586, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _574588), _574590)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_NthRoot_Oroot(_574586, _574588)), c_NthRoot_Oroot(_574586, _574590)))], (5137 ^ _393467) ^ [_574862, _574864, _574866] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _574862)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _574864)), -(c_NthRoot_Oroot(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _574862), _574864), _574866) = c_NthRoot_Oroot(_574862, c_NthRoot_Oroot(_574864, _574866)))], (5147 ^ _393467) ^ [_575264, _575266, _575268, _575270, _575272, _575274, _575276] : [-(c_Fun_Ocomp(_575264, _575266, _575268, _575270, c_Fun_Ocomp(_575272, _575264, _575268, _575274, _575276)) = c_Fun_Ocomp(_575272, _575266, _575268, c_Fun_Ocomp(_575264, _575266, _575272, _575270, _575274), _575276))], (5149 ^ _393467) ^ [_575448, _575450, _575452, _575454, _575456, _575458] : [-(hAPP(c_Fun_Ocomp(_575448, _575450, _575452, _575454, _575456), _575458) = hAPP(_575454, hAPP(_575456, _575458)))], (5151 ^ _393467) ^ [_575678, _575680, _575682, _575684, _575686, _575688, _575690, _575692, _575694] : [c_Fun_Ocomp(_575678, _575680, _575682, _575684, _575686) = c_Fun_Ocomp(_575688, _575680, _575682, _575690, _575692), -(hAPP(_575684, hAPP(_575686, _575694)) = hAPP(_575690, hAPP(_575692, _575694)))], (5157 ^ _393467) ^ [_576062, _576064, _576066, _576068, _576070, _576072, _576074, _576076] : [c_Fun_Ocomp(_576062, _576064, _576066, _576068, _576070) = c_Fun_Ocomp(_576072, _576064, _576066, _576074, _576076), 5160 ^ _393467 : [(5161 ^ _393467) ^ [_576238] : [-(hAPP(_576068, hAPP(_576070, _576238)) = hAPP(_576074, hAPP(_576076, _576238)))]]], (5163 ^ _393467) ^ [_576378, _576380] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _576378)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _576380)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_NthRoot_Oroot(_576378, _576380))))], (5173 ^ _393467) ^ [_576695, _576697] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _576695)), 5176 ^ _393467 : [(5177 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_NthRoot_Oroot(_576695, _576697)), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _576697), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))], (5183 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _576697), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_NthRoot_Oroot(_576695, _576697)), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))]]], (5189 ^ _393467) ^ [_577198, _577200] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _577198)), 5192 ^ _393467 : [(5193 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_NthRoot_Oroot(_577198, _577200))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _577200)))], (5199 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _577200)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_NthRoot_Oroot(_577198, _577200))))]]], (5205 ^ _393467) ^ [_577683, _577685] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _577683)), 5208 ^ _393467 : [(5209 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_NthRoot_Oroot(_577683, _577685))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _577685)))], (5215 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _577685)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_NthRoot_Oroot(_577683, _577685))))]]], (5221 ^ _393467) ^ [_578168, _578170] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _578168)), 5224 ^ _393467 : [(5225 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_NthRoot_Oroot(_578168, _578170)), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _578170), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))], (5231 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _578170), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_NthRoot_Oroot(_578168, _578170)), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))]]], (5237 ^ _393467) ^ [_578671, _578673] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _578671)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _578673)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_NthRoot_Oroot(_578671, _578673))))], (5247 ^ _393467) ^ [_579002, _579004, _579006] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _579002)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _579002), _579004)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _579006)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _579006), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_NthRoot_Oroot(_579002, _579006)), c_NthRoot_Oroot(_579004, _579006))))], (5265 ^ _393467) ^ [_579561, _579563, _579565] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _579561)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _579561), _579563)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _579565)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _579565), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_NthRoot_Oroot(_579561, _579565)), c_NthRoot_Oroot(_579563, _579565))))], (5283 ^ _393467) ^ [_580106, _580108] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _580106)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _580108)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_NthRoot_Oroot(_580106, _580108)), _580106) = _580108)], (5293 ^ _393467) ^ [_580431, _580433] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _580431)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _580433)), -(c_NthRoot_Oroot(_580431, hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _580433), _580431)) = _580433)], (5303 ^ _393467) ^ [_580756, _580758] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _580756)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _580758)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_NthRoot_Oroot(_580756, _580758)), _580756) = _580758)], (5313 ^ _393467) ^ [_581095, _581097, _581099] : [class_RealVector_Oreal__normed__div__algebra(_581095), -(c_RealVector_Onorm__class_Onorm(_581095, hAPP(hAPP(c_Power_Opower__class_Opower(_581095), _581097), _581099)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_581095, _581097)), _581099))], (5319 ^ _393467) ^ [_581335] : [class_RealVector_Oreal__normed__algebra__1(_581335), -(c_RealVector_Onorm__class_Onorm(_581335, c_Groups_Oone__class_Oone(_581335)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (5325 ^ _393467) ^ [_581547, _581549] : [class_Rings_Ocomm__semiring__1(_581547), -(hAPP(hAPP(c_Power_Opower__class_Opower(_581547), _581549), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_581547))], (5331 ^ _393467) ^ [_581775, _581777] : [class_Groups_Oone(_581775), 5334 ^ _393467 : [(5335 ^ _393467) ^ [] : [c_Groups_Oone__class_Oone(_581775) = _581777, -(_581777 = c_Groups_Oone__class_Oone(_581775))], (5341 ^ _393467) ^ [] : [_581777 = c_Groups_Oone__class_Oone(_581775), -(c_Groups_Oone__class_Oone(_581775) = _581777)]]], (5347 ^ _393467) ^ [_582259, _582261, _582263] : [class_RealVector_Oreal__normed__algebra__1(_582259), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_582259, hAPP(hAPP(c_Power_Opower__class_Opower(_582259), _582261), _582263))), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_582259, _582261)), _582263))))], (5353 ^ _393467) ^ [_582551, _582553, _582555, _582557] : [class_Rings_Ocomm__semiring__1(_582551), -(hAPP(hAPP(c_Power_Opower__class_Opower(_582551), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_582551), _582553), _582555)), _582557) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_582551), hAPP(hAPP(c_Power_Opower__class_Opower(_582551), _582553), _582557)), hAPP(hAPP(c_Power_Opower__class_Opower(_582551), _582555), _582557)))], (5359 ^ _393467) ^ [_582837] : [class_Rings_Ozero__neq__one(_582837), c_Groups_Oone__class_Oone(_582837) = c_Groups_Ozero__class_Ozero(_582837)], (5365 ^ _393467) ^ [_583034] : [class_Rings_Ozero__neq__one(_583034), c_Groups_Ozero__class_Ozero(_583034) = c_Groups_Oone__class_Oone(_583034)], (5371 ^ _393467) ^ [_583245, _583247] : [class_Rings_Ocomm__semiring__1(_583245), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_583245), _583247), c_Groups_Oone__class_Oone(_583245)) = _583247)], (5377 ^ _393467) ^ [_583473, _583475] : [class_Rings_Ocomm__semiring__1(_583473), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_583473), c_Groups_Oone__class_Oone(_583473)), _583475) = _583475)], (5383 ^ _393467) ^ [_583701, _583703] : [class_Groups_Ocomm__monoid__mult(_583701), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_583701), _583703), c_Groups_Oone__class_Oone(_583701)) = _583703)], (5389 ^ _393467) ^ [_583929, _583931] : [class_Groups_Omonoid__mult(_583929), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_583929), _583931), c_Groups_Oone__class_Oone(_583929)) = _583931)], (5395 ^ _393467) ^ [_584157, _584159] : [class_Groups_Ocomm__monoid__mult(_584157), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_584157), c_Groups_Oone__class_Oone(_584157)), _584159) = _584159)], (5401 ^ _393467) ^ [_584385, _584387] : [class_Groups_Omonoid__mult(_584385), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_584385), c_Groups_Oone__class_Oone(_584385)), _584387) = _584387)], (5407 ^ _393467) ^ [_584641, _584643, _584645, _584647] : [class_Rings_Ocomm__semiring__1(_584641), -(hAPP(hAPP(c_Power_Opower__class_Opower(_584641), hAPP(hAPP(c_Power_Opower__class_Opower(_584641), _584643), _584645)), _584647) = hAPP(hAPP(c_Power_Opower__class_Opower(_584641), _584643), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _584645), _584647)))], (5413 ^ _393467) ^ [_584907] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _584907)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _584907), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_SEQ_OBseq(tc_RealDef_Oreal, hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _584907)))], (5423 ^ _393467) ^ [] : [c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)], (5425 ^ _393467) ^ [_585239] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _585239) = _585239)], (5427 ^ _393467) ^ [_585363, _585365, _585367] : [class_Rings_Olinordered__semidom(_585363), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_585363, c_Groups_Ozero__class_Ozero(_585363)), _585365)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_585363, _585365), c_Groups_Oone__class_Oone(_585363))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_585363, hAPP(hAPP(c_Power_Opower__class_Opower(_585363), _585365), c_Nat_OSuc(_585367))), _585365)))], (5441 ^ _393467) ^ [_585807] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _585807)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _585807), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_SEQ_Omonoseq(tc_RealDef_Oreal, hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _585807)))], (5451 ^ _393467) ^ [_586130, _586132, _586134] : [class_Rings_Ocomm__semiring__1(_586130), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_586130), hAPP(hAPP(c_Power_Opower__class_Opower(_586130), _586132), _586134)), _586132) = hAPP(hAPP(c_Power_Opower__class_Opower(_586130), _586132), c_Nat_OSuc(_586134)))], (5457 ^ _393467) ^ [_586410, _586412, _586414] : [class_Rings_Ocomm__semiring__1(_586410), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_586410), _586412), hAPP(hAPP(c_Power_Opower__class_Opower(_586410), _586412), _586414)) = hAPP(hAPP(c_Power_Opower__class_Opower(_586410), _586412), c_Nat_OSuc(_586414)))], (5463 ^ _393467) ^ [_586690, _586692, _586694] : [class_Rings_Ocomm__semiring__1(_586690), -(hAPP(hAPP(c_Power_Opower__class_Opower(_586690), _586692), c_Nat_OSuc(_586694)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_586690), _586692), hAPP(hAPP(c_Power_Opower__class_Opower(_586690), _586692), _586694)))], (5469 ^ _393467) ^ [_586942] : [class_Rings_Olinordered__semidom(_586942), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_586942, c_Groups_Oone__class_Oone(_586942)), c_Groups_Ozero__class_Ozero(_586942)))], (5475 ^ _393467) ^ [_587149] : [class_Rings_Olinordered__semidom(_587149), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_587149, c_Groups_Ozero__class_Ozero(_587149)), c_Groups_Oone__class_Oone(_587149))))], (5481 ^ _393467) ^ [_587355] : [class_Rings_Olinordered__semidom(_587355), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_587355, c_Groups_Ozero__class_Ozero(_587355)), c_Groups_Oone__class_Oone(_587355))))], (5487 ^ _393467) ^ [_587561] : [class_Rings_Olinordered__semidom(_587561), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_587561, c_Groups_Oone__class_Oone(_587561)), c_Groups_Ozero__class_Ozero(_587561)))], (5493 ^ _393467) ^ [_587796, _587798, _587800] : [class_Rings_Olinordered__semidom(_587796), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_587796, c_Groups_Oone__class_Oone(_587796)), _587798)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_587796, c_Groups_Oone__class_Oone(_587796)), _587800)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_587796, c_Groups_Oone__class_Oone(_587796)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_587796), _587798), _587800))))], (5507 ^ _393467) ^ [_588268, _588270, _588272] : [class_Rings_Olinordered__idom(_588268), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_588268, c_Groups_Ozero__class_Ozero(_588268)), _588270)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_588268, c_Groups_Ozero__class_Ozero(_588268)), _588272)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_588268, _588272), c_Groups_Oone__class_Oone(_588268))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_588268, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_588268), _588270), _588272)), _588270)))], (5525 ^ _393467) ^ [_588843, _588845, _588847] : [class_Rings_Olinordered__idom(_588843), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_588843, c_Groups_Ozero__class_Ozero(_588843)), _588845)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_588843, c_Groups_Ozero__class_Ozero(_588843)), _588847)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_588843, _588847), c_Groups_Oone__class_Oone(_588843))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_588843, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_588843), _588847), _588845)), _588845)))], (5543 ^ _393467) ^ [_589418, _589420, _589422] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _589418)), -(c_NthRoot_Oroot(_589418, hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _589420), _589422)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_NthRoot_Oroot(_589418, _589420)), _589422))], (5549 ^ _393467) ^ [] : [-(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))], (5551 ^ _393467) ^ [_589727, _589729] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _589727)), 5554 ^ _393467 : [(5555 ^ _393467) ^ [] : [c_NthRoot_Oroot(_589727, _589729) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal), -(_589729 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (5561 ^ _393467) ^ [] : [_589729 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal), -(c_NthRoot_Oroot(_589727, _589729) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))]]], (5567 ^ _393467) ^ [_590186] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _590186)), -(c_NthRoot_Oroot(_590186, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (5573 ^ _393467) ^ [_590400, _590402] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _590400)), -(c_NthRoot_Oroot(c_Nat_OSuc(_590402), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _590400), c_Nat_OSuc(_590402))) = _590400)], (5579 ^ _393467) ^ [_590654, _590656, _590658] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _590654)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _590654), _590656)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _590658)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_NthRoot_Oroot(_590656, _590658)), c_NthRoot_Oroot(_590654, _590658))))], (5593 ^ _393467) ^ [_591096, _591098] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _591096)), 5596 ^ _393467 : [(5597 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_NthRoot_Oroot(_591096, _591098)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _591098), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))], (5603 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _591098), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_NthRoot_Oroot(_591096, _591098)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))]]], (5609 ^ _393467) ^ [_591599, _591601] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _591599)), 5612 ^ _393467 : [(5613 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), c_NthRoot_Oroot(_591599, _591601))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _591601)))], (5619 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _591601)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), c_NthRoot_Oroot(_591599, _591601))))]]], (5625 ^ _393467) ^ [_592084, _592086] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _592084)), 5628 ^ _393467 : [(5629 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), c_NthRoot_Oroot(_592084, _592086))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _592086)))], (5635 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _592086)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), c_NthRoot_Oroot(_592084, _592086))))]]], (5641 ^ _393467) ^ [_592569, _592571] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _592569)), 5644 ^ _393467 : [(5645 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_NthRoot_Oroot(_592569, _592571)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _592571), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))], (5651 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _592571), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_NthRoot_Oroot(_592569, _592571)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))]]], (5657 ^ _393467) ^ [_593086, _593088, _593090] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _593086)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _593086), _593088)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _593090)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_NthRoot_Oroot(_593088, _593090)), c_NthRoot_Oroot(_593086, _593090))))], (5671 ^ _393467) ^ [_593542, _593544, _593546] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _593542)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _593544)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _593544), _593542) = _593546, -(c_NthRoot_Oroot(_593542, _593546) = _593544)], (5685 ^ _393467) ^ [_593998, _594000, _594002, _594004] : [class_Rings_Olinordered__semidom(_593998), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_593998, _594000), _594002)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_593998, c_Groups_Ozero__class_Ozero(_593998)), _594000)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _594004)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_593998, hAPP(hAPP(c_Power_Opower__class_Opower(_593998), _594000), _594004)), hAPP(hAPP(c_Power_Opower__class_Opower(_593998), _594002), _594004))))], (5703 ^ _393467) ^ [_594593, _594595, _594597] : [class_Rings_Olinordered__semidom(_594593), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_594593, c_Groups_Oone__class_Oone(_594593)), _594595)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _594597)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_594593, c_Groups_Oone__class_Oone(_594593)), hAPP(hAPP(c_Power_Opower__class_Opower(_594593), _594595), _594597))))], (5717 ^ _393467) ^ [_595069, _595071, _595073, _595075] : [class_Rings_Olinordered__semidom(_595069), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_595069, c_Groups_Oone__class_Oone(_595069)), _595071)), 5724 ^ _393467 : [(5725 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_595069, hAPP(hAPP(c_Power_Opower__class_Opower(_595069), _595071), _595073)), hAPP(hAPP(c_Power_Opower__class_Opower(_595069), _595071), _595075))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _595073), _595075)))], (5731 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _595073), _595075)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_595069, hAPP(hAPP(c_Power_Opower__class_Opower(_595069), _595071), _595073)), hAPP(hAPP(c_Power_Opower__class_Opower(_595069), _595071), _595075))))]]], (5737 ^ _393467) ^ [_595776, _595778, _595780, _595782] : [class_Rings_Olinordered__semidom(_595776), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_595776, c_Groups_Oone__class_Oone(_595776)), _595778)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_595776, hAPP(hAPP(c_Power_Opower__class_Opower(_595776), _595778), _595780)), hAPP(hAPP(c_Power_Opower__class_Opower(_595776), _595778), _595782))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _595780), _595782)))], (5751 ^ _393467) ^ [_596284, _596286, _596288, _596290] : [class_Rings_Olinordered__semidom(_596284), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _596286), _596288)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_596284, c_Groups_Ozero__class_Ozero(_596284)), _596290)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_596284, _596290), c_Groups_Oone__class_Oone(_596284))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_596284, hAPP(hAPP(c_Power_Opower__class_Opower(_596284), _596290), _596288)), hAPP(hAPP(c_Power_Opower__class_Opower(_596284), _596290), _596286))))], (5769 ^ _393467) ^ [_596875, _596877] : [class_Groups_Omonoid__mult(_596875), -(hAPP(hAPP(c_Power_Opower__class_Opower(_596875), _596877), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _596877)], (5775 ^ _393467) ^ [_597099, _597101] : [class_Rings_Ocomm__semiring__1(_597099), -(hAPP(hAPP(c_Power_Opower__class_Opower(_597099), _597101), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _597101)], (5781 ^ _393467) ^ [_597294] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _597294) = _597294)], (5783 ^ _393467) ^ [_597433, _597435] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _597433), _597435), 5786 ^ _393467 : [(5787 ^ _393467) ^ [] : [-(_597433 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (5789 ^ _393467) ^ [] : [-(_597435 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (5791 ^ _393467) ^ [_597682, _597684] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _597682), _597684)), _597682 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _597684 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (5801 ^ _393467) ^ [_597966] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _597966), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _597966)], (5803 ^ _393467) ^ [_598108, _598110] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _598108), _598110) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 5806 ^ _393467 : [(5807 ^ _393467) ^ [] : [-(_598108 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (5809 ^ _393467) ^ [] : [-(_598110 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (5811 ^ _393467) ^ [_598357, _598359] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _598357), _598359) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _598357 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _598359 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (5821 ^ _393467) ^ [_598641] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _598641) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (5833 ^ _393467) ^ [_599044, _599046] : [5834 ^ _393467 : [(5835 ^ _393467) ^ [] : [_599046 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5837 ^ _393467) ^ [] : [_599044 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _599044), _599046) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (5823 ^ _393467) ^ [_598780, _598782] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _598780), _598782) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_598782 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_598780 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (5841 ^ _393467) ^ [_599356, _599358, _599360] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _599356)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _599356), _599358)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _599356), _599360))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _599358), _599360)))], (5861 ^ _393467) ^ [_600014, _600016] : [5862 ^ _393467 : [(5863 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _600014))], (5865 ^ _393467) ^ [] : [_600016 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hBOOL(hAPP(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), _600014), _600016))))], (5851 ^ _393467) ^ [_599742, _599744] : [hBOOL(hAPP(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), _599742), _599744))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _599742))), -(_599744 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5869 ^ _393467) ^ [_600320, _600322] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _600320)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _600320), _600322))))], (5885 ^ _393467) ^ [_600851, _600853] : [5886 ^ _393467 : [(5887 ^ _393467) ^ [] : [_600853 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5889 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _600851))]], -(hBOOL(hAPP(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), _600851), _600853))))], (5875 ^ _393467) ^ [_600579, _600581] : [hBOOL(hAPP(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), _600579), _600581))), -(_600581 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _600579)))], (5893 ^ _393467) ^ [_601142, _601144] : [-(c_RealDef_Oreal(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _601142), _601144)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _601142)), _601144))], (5895 ^ _393467) ^ [_601254, _601256] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _601254)), _601256) = c_RealDef_Oreal(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _601254), _601256)))], (5897 ^ _393467) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (5899 ^ _393467) ^ [_601434, _601436] : [_601434 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _601434), _601436), -(_601436 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_601434 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5909 ^ _393467) ^ [] : [-(hAPP(c_Complex_OIm, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (5911 ^ _393467) ^ [] : [-(hAPP(c_Complex_ORe, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (5913 ^ _393467) ^ [] : [-(c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (5915 ^ _393467) ^ [] : [-(c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (5917 ^ _393467) ^ [] : [-(c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (5919 ^ _393467) ^ [_602011, _602013] : [_602011 = c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatfloor(_602011)), -(c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _602011), _602013)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_RComplete_Onatfloor(_602011)), _602013))], (5925 ^ _393467) ^ [_602278] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat)), c_RComplete_Onatfloor(_602278))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _602278)))], (5931 ^ _393467) ^ [_602446] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _602446)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat)), c_RComplete_Onatfloor(_602446))))], (5937 ^ _393467) ^ [_602679] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_602679)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _602679), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))], (5943 ^ _393467) ^ [_602859] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _602859), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_602859)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (5949 ^ _393467) ^ [_603103, _603105, _603107] : [class_Rings_Oring__1__no__zero__divisors(_603103), -(_603105 = c_Groups_Ozero__class_Ozero(_603103)), hAPP(hAPP(c_Power_Opower__class_Opower(_603103), _603105), _603107) = c_Groups_Ozero__class_Ozero(_603103)], (5959 ^ _393467) ^ [_603452, _603454, _603456] : [class_Groups_Omonoid__mult(_603452), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_603452), hAPP(hAPP(c_Power_Opower__class_Opower(_603452), _603454), _603456)), _603454) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_603452), _603454), hAPP(hAPP(c_Power_Opower__class_Opower(_603452), _603454), _603456)))], (5965 ^ _393467) ^ [_603758, _603760, _603762, _603764] : [class_Groups_Ocomm__monoid__mult(_603758), -(hAPP(hAPP(c_Power_Opower__class_Opower(_603758), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_603758), _603760), _603762)), _603764) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_603758), hAPP(hAPP(c_Power_Opower__class_Opower(_603758), _603760), _603764)), hAPP(hAPP(c_Power_Opower__class_Opower(_603758), _603762), _603764)))], (5971 ^ _393467) ^ [_604058, _604060] : [class_Groups_Omonoid__mult(_604058), -(hAPP(hAPP(c_Power_Opower__class_Opower(_604058), c_Groups_Oone__class_Oone(_604058)), _604060) = c_Groups_Oone__class_Oone(_604058))], (5977 ^ _393467) ^ [_604318, _604320, _604322, _604324] : [class_Groups_Omonoid__mult(_604318), -(hAPP(hAPP(c_Power_Opower__class_Opower(_604318), _604320), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _604322), _604324)) = hAPP(hAPP(c_Power_Opower__class_Opower(_604318), hAPP(hAPP(c_Power_Opower__class_Opower(_604318), _604320), _604322)), _604324))], (5983 ^ _393467) ^ [_604626, _604628, _604630, _604632] : [class_Rings_Olinordered__semidom(_604626), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_604626, _604628), _604630)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_604626, c_Groups_Ozero__class_Ozero(_604626)), _604628)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_604626, hAPP(hAPP(c_Power_Opower__class_Opower(_604626), _604628), _604632)), hAPP(hAPP(c_Power_Opower__class_Opower(_604626), _604630), _604632))))], (5997 ^ _393467) ^ [_605120, _605122, _605124] : [class_Rings_Olinordered__semidom(_605120), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_605120, c_Groups_Ozero__class_Ozero(_605120)), _605122)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_605120, c_Groups_Ozero__class_Ozero(_605120)), hAPP(hAPP(c_Power_Opower__class_Opower(_605120), _605122), _605124))))], (6007 ^ _393467) ^ [_605485, _605487, _605489] : [class_Rings_Olinordered__semidom(_605485), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_605485, c_Groups_Ozero__class_Ozero(_605485)), _605487)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_605485, c_Groups_Ozero__class_Ozero(_605485)), hAPP(hAPP(c_Power_Opower__class_Opower(_605485), _605487), _605489))))], (6017 ^ _393467) ^ [_605850, _605852, _605854] : [class_Rings_Olinordered__semidom(_605850), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_605850, c_Groups_Oone__class_Oone(_605850)), _605852)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_605850, c_Groups_Oone__class_Oone(_605850)), hAPP(hAPP(c_Power_Opower__class_Opower(_605850), _605852), _605854))))], (6027 ^ _393467) ^ [_606215, _606217, _606219] : [class_Power_Opower(_606215), class_Rings_Omult__zero(_606215), class_Rings_Ono__zero__divisors(_606215), class_Rings_Ozero__neq__one(_606215), 6042 ^ _393467 : [(6043 ^ _393467) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_606215), _606217), _606219) = c_Groups_Ozero__class_Ozero(_606215), 6046 ^ _393467 : [(6047 ^ _393467) ^ [] : [-(_606217 = c_Groups_Ozero__class_Ozero(_606215))], (6049 ^ _393467) ^ [] : [_606219 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (6051 ^ _393467) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_606215), _606217), _606219) = c_Groups_Ozero__class_Ozero(_606215)), _606217 = c_Groups_Ozero__class_Ozero(_606215), -(_606219 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (6061 ^ _393467) ^ [_607198, _607200, _607202, _607204] : [class_Rings_Olinordered__semidom(_607198), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_607198, c_Groups_Oone__class_Oone(_607198)), _607200)), 6068 ^ _393467 : [(6069 ^ _393467) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_607198), _607200), _607202) = hAPP(hAPP(c_Power_Opower__class_Opower(_607198), _607200), _607204), -(_607202 = _607204)], (6075 ^ _393467) ^ [] : [_607202 = _607204, -(hAPP(hAPP(c_Power_Opower__class_Opower(_607198), _607200), _607202) = hAPP(hAPP(c_Power_Opower__class_Opower(_607198), _607200), _607204))]]], (6081 ^ _393467) ^ [_607847, _607849] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_607847), c_Groups_Ozero__class_Ozero(_607847)), c_Nat_OSuc(_607849)) = c_Groups_Ozero__class_Ozero(_607847)), class_Power_Opower(_607847), class_Rings_Osemiring__0(_607847)], (6091 ^ _393467) ^ [_608184, _608186, _608188] : [class_Power_Opower(_608184), -(hAPP(hAPP(c_Power_Opower__class_Opower(_608184), _608186), c_Nat_OSuc(_608188)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_608184), _608186), hAPP(hAPP(c_Power_Opower__class_Opower(_608184), _608186), _608188)))], (6097 ^ _393467) ^ [_608464, _608466, _608468] : [class_Groups_Omonoid__mult(_608464), -(hAPP(hAPP(c_Power_Opower__class_Opower(_608464), _608466), c_Nat_OSuc(_608468)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_608464), hAPP(hAPP(c_Power_Opower__class_Opower(_608464), _608466), _608468)), _608466))], (6103 ^ _393467) ^ [_608730, _608732] : [class_Power_Opower(_608730), -(hAPP(hAPP(c_Power_Opower__class_Opower(_608730), _608732), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_608730))], (6109 ^ _393467) ^ [_608986, _608988, _608990, _608992] : [class_Rings_Olinordered__semidom(_608986), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_608986, hAPP(hAPP(c_Power_Opower__class_Opower(_608986), _608988), _608990)), hAPP(hAPP(c_Power_Opower__class_Opower(_608986), _608992), _608990))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_608986, c_Groups_Ozero__class_Ozero(_608986)), _608992)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_608986, _608988), _608992)))], (6123 ^ _393467) ^ [_609494, _609496, _609498, _609500] : [class_Rings_Olinordered__semidom(_609494), hAPP(hAPP(c_Power_Opower__class_Opower(_609494), _609496), c_Nat_OSuc(_609498)) = hAPP(hAPP(c_Power_Opower__class_Opower(_609494), _609500), c_Nat_OSuc(_609498)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_609494, c_Groups_Ozero__class_Ozero(_609494)), _609496)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_609494, c_Groups_Ozero__class_Ozero(_609494)), _609500)), -(_609496 = _609500)], (6141 ^ _393467) ^ [_610101, _610103, _610105, _610107] : [class_Rings_Olinordered__semidom(_610101), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_610101, hAPP(hAPP(c_Power_Opower__class_Opower(_610101), _610103), c_Nat_OSuc(_610105))), hAPP(hAPP(c_Power_Opower__class_Opower(_610101), _610107), c_Nat_OSuc(_610105)))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_610101, c_Groups_Ozero__class_Ozero(_610101)), _610107)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_610101, _610103), _610107)))], (6155 ^ _393467) ^ [_610603, _610605, _610607] : [class_Rings_Olinordered__semidom(_610603), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_610603, c_Groups_Oone__class_Oone(_610603)), _610605)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_610603, hAPP(hAPP(c_Power_Opower__class_Opower(_610603), _610605), _610607)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_610603), _610605), hAPP(hAPP(c_Power_Opower__class_Opower(_610603), _610605), _610607)))))], (6165 ^ _393467) ^ [_610996, _610998, _611000] : [class_Rings_Olinordered__semidom(_610996), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_610996, c_Groups_Oone__class_Oone(_610996)), _610998)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_610996, c_Groups_Oone__class_Oone(_610996)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_610996), _610998), hAPP(hAPP(c_Power_Opower__class_Opower(_610996), _610998), _611000)))))], (6175 ^ _393467) ^ [_611363, _611365] : [class_Power_Opower(_611363), class_Rings_Osemiring__0(_611363), 6182 ^ _393467 : [(6183 ^ _393467) ^ [] : [_611365 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_611363), c_Groups_Ozero__class_Ozero(_611363)), _611365) = c_Groups_Oone__class_Oone(_611363))], (6189 ^ _393467) ^ [] : [-(_611365 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_611363), c_Groups_Ozero__class_Ozero(_611363)), _611365) = c_Groups_Ozero__class_Ozero(_611363))]]], (6195 ^ _393467) ^ [_611978, _611980, _611982] : [class_Rings_Olinordered__semidom(_611978), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_611978, c_Groups_Oone__class_Oone(_611978)), _611980)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_611978, c_Groups_Oone__class_Oone(_611978)), hAPP(hAPP(c_Power_Opower__class_Opower(_611978), _611980), c_Nat_OSuc(_611982)))))], (6205 ^ _393467) ^ [_612361, _612363, _612365, _612367] : [class_Rings_Olinordered__semidom(_612361), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_612361, c_Groups_Oone__class_Oone(_612361)), _612363)), 6212 ^ _393467 : [(6213 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_612361, hAPP(hAPP(c_Power_Opower__class_Opower(_612361), _612363), _612365)), hAPP(hAPP(c_Power_Opower__class_Opower(_612361), _612363), _612367))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _612365), _612367)))], (6219 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _612365), _612367)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_612361, hAPP(hAPP(c_Power_Opower__class_Opower(_612361), _612363), _612365)), hAPP(hAPP(c_Power_Opower__class_Opower(_612361), _612363), _612367))))]]], (6225 ^ _393467) ^ [_613068, _613070, _613072, _613074] : [class_Rings_Olinordered__semidom(_613068), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_613068, c_Groups_Oone__class_Oone(_613068)), _613070)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_613068, hAPP(hAPP(c_Power_Opower__class_Opower(_613068), _613070), _613072)), hAPP(hAPP(c_Power_Opower__class_Opower(_613068), _613070), _613074))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _613072), _613074)))], (6239 ^ _393467) ^ [_613576, _613578, _613580, _613582] : [class_Rings_Olinordered__semidom(_613576), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _613578), _613580)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_613576, c_Groups_Oone__class_Oone(_613576)), _613582)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_613576, hAPP(hAPP(c_Power_Opower__class_Opower(_613576), _613582), _613578)), hAPP(hAPP(c_Power_Opower__class_Opower(_613576), _613582), _613580))))], (6253 ^ _393467) ^ [_614084, _614086, _614088, _614090] : [class_Rings_Olinordered__semidom(_614084), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _614086), _614088)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_614084, c_Groups_Oone__class_Oone(_614084)), _614090)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_614084, hAPP(hAPP(c_Power_Opower__class_Opower(_614084), _614090), _614086)), hAPP(hAPP(c_Power_Opower__class_Opower(_614084), _614090), _614088))))], (6267 ^ _393467) ^ [_614578, _614580, _614582] : [class_Rings_Olinordered__semidom(_614578), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_614578, c_Groups_Ozero__class_Ozero(_614578)), _614580)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_614578, _614580), c_Groups_Oone__class_Oone(_614578))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_614578, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_614578), _614580), hAPP(hAPP(c_Power_Opower__class_Opower(_614578), _614580), _614582))), hAPP(hAPP(c_Power_Opower__class_Opower(_614578), _614580), _614582))))], (6281 ^ _393467) ^ [_615078, _615080, _615082] : [class_Rings_Olinordered__semidom(_615078), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_615078, c_Groups_Ozero__class_Ozero(_615078)), _615080)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_615078, _615080), c_Groups_Oone__class_Oone(_615078))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_615078, hAPP(hAPP(c_Power_Opower__class_Opower(_615078), _615080), c_Nat_OSuc(_615082))), c_Groups_Oone__class_Oone(_615078))))], (6295 ^ _393467) ^ [_615568, _615570, _615572, _615574] : [class_Rings_Olinordered__semidom(_615568), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _615570), _615572)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_615568, c_Groups_Ozero__class_Ozero(_615568)), _615574)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_615568, _615574), c_Groups_Oone__class_Oone(_615568))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_615568, hAPP(hAPP(c_Power_Opower__class_Opower(_615568), _615574), _615572)), hAPP(hAPP(c_Power_Opower__class_Opower(_615568), _615574), _615570))))], (6313 ^ _393467) ^ [_616187, _616189, _616191, _616193] : [class_Rings_Olinordered__semidom(_616187), hAPP(hAPP(c_Power_Opower__class_Opower(_616187), _616189), _616191) = hAPP(hAPP(c_Power_Opower__class_Opower(_616187), _616193), _616191), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_616187, c_Groups_Ozero__class_Ozero(_616187)), _616189)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_616187, c_Groups_Ozero__class_Ozero(_616187)), _616193)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _616191)), -(_616189 = _616193)], (6335 ^ _393467) ^ [_616845] : [class_Power_Opower(_616845), -(c_Power_Opower__class_Opower(_616845) = c_Power_Opower_Opower(_616845, c_Groups_Oone__class_Oone(_616845), c_Groups_Otimes__class_Otimes(_616845)))], (6341 ^ _393467) ^ [_617067, _617069] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _617067)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _617069)), 6349 ^ _393467 : [(6350 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 6348 ^ [_617067, _617069])))], (6352 ^ _393467) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), 6348 ^ [_617067, _617069]), _617067) = _617069)], (6354 ^ _393467) ^ [_617580] : [-(_617580 = 6348 ^ [_617067, _617069]), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _617580)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _617580), _617067) = _617069]]], (6364 ^ _393467) ^ [_617936, _617938] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _617936)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _617938)), 6372 ^ _393467 : [(6373 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 6371 ^ [_617936, _617938])))], (6375 ^ _393467) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), 6371 ^ [_617936, _617938]), _617936) = _617938)]]], (6377 ^ _393467) ^ [_618412, _618414] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _618412)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _618414)), _618412)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), _618412), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), _618414))))], (6383 ^ _393467) ^ [_618690, _618692] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _618690)), -(c_Transcendental_Oln(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _618690), _618692)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _618692)), c_Transcendental_Oln(_618690)))], (6389 ^ _393467) ^ [_618956, _618958, _618960] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _618956), _618958)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), _618960), _618956)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), _618960), _618958))))], (6395 ^ _393467) ^ [_619215, _619217, _619219] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), _619215), _619217)), _619219) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _619215), _619219)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _619217), _619219)))], (6397 ^ _393467) ^ [_619384, _619386, _619388, _619390] : [class_Groups_Oab__semigroup__add(_619384), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_619384), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_619384), _619386), _619388)), _619390) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_619384), _619386), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_619384), _619388), _619390)))], (6403 ^ _393467) ^ [_619696, _619698, _619700, _619702] : [class_Groups_Ocancel__semigroup__add(_619696), 6406 ^ _393467 : [(6407 ^ _393467) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_619696), _619698), _619700) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_619696), _619698), _619702), -(_619700 = _619702)], (6413 ^ _393467) ^ [] : [_619700 = _619702, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_619696), _619698), _619700) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_619696), _619698), _619702))]]], (6419 ^ _393467) ^ [_620262, _620264, _620266, _620268] : [class_Groups_Ocancel__semigroup__add(_620262), 6422 ^ _393467 : [(6423 ^ _393467) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_620262), _620264), _620266) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_620262), _620268), _620266), -(_620264 = _620268)], (6429 ^ _393467) ^ [] : [_620264 = _620268, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_620262), _620264), _620266) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_620262), _620268), _620266))]]], (6435 ^ _393467) ^ [_620828, _620830, _620832, _620834] : [class_Groups_Ocancel__semigroup__add(_620828), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_620828), _620830), _620832) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_620828), _620830), _620834), -(_620832 = _620834)], (6445 ^ _393467) ^ [_621205, _621207, _621209, _621211] : [class_Groups_Ocancel__ab__semigroup__add(_621205), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_621205), _621207), _621209) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_621205), _621207), _621211), -(_621209 = _621211)], (6455 ^ _393467) ^ [_621582, _621584, _621586, _621588] : [class_Groups_Ocancel__semigroup__add(_621582), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_621582), _621584), _621586) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_621582), _621588), _621586), -(_621584 = _621588)], (6465 ^ _393467) ^ [_621945, _621947, _621949] : [class_Rings_Ocomm__semiring__1(_621945), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_621945), _621947), _621949) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_621945), _621949), _621947))], (6471 ^ _393467) ^ [_622219, _622221, _622223, _622225] : [class_Rings_Ocomm__semiring__1(_622219), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_622219), _622221), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_622219), _622223), _622225)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_622219), _622223), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_622219), _622221), _622225)))], (6477 ^ _393467) ^ [_622531, _622533, _622535, _622537] : [class_Rings_Ocomm__semiring__1(_622531), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_622531), _622533), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_622531), _622535), _622537)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_622531), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_622531), _622533), _622535)), _622537))], (6483 ^ _393467) ^ [_622843, _622845, _622847, _622849] : [class_Rings_Ocomm__semiring__1(_622843), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_622843), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_622843), _622845), _622847)), _622849) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_622843), _622845), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_622843), _622847), _622849)))], (6489 ^ _393467) ^ [_623155, _623157, _623159, _623161] : [class_Rings_Ocomm__semiring__1(_623155), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_623155), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_623155), _623157), _623159)), _623161) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_623155), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_623155), _623157), _623161)), _623159))], (6495 ^ _393467) ^ [_623481, _623483, _623485, _623487, _623489] : [class_Rings_Ocomm__semiring__1(_623481), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_623481), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_623481), _623483), _623485)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_623481), _623487), _623489)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_623481), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_623481), _623483), _623487)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_623481), _623485), _623489)))], (6501 ^ _393467) ^ [_623845, _623847, _623849, _623851, _623853] : [class_RealVector_Oreal__normed__vector(_623845), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_623845, _623847)), _623849)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_623845, _623851)), _623853)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_623845, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_623845), _623847), _623851))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), _623849), _623853))))], (6515 ^ _393467) ^ [_624363, _624365, _624367] : [class_RealVector_Oreal__normed__vector(_624363), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_624363, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_624363), _624365), _624367))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_624363, _624365)), c_RealVector_Onorm__class_Onorm(_624363, _624367)))))], (6521 ^ _393467) ^ [_624661, _624663, _624665, _624667] : [class_Rings_Ocomm__semiring(_624661), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_624661), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_624661), _624663), _624665)), _624667) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_624661), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_624661), _624663), _624667)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_624661), _624665), _624667)))], (6527 ^ _393467) ^ [_625003, _625005, _625007, _625009, _625011] : [class_Rings_Osemiring(_625003), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_625003), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_625003), _625005), _625007)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_625003), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_625003), _625009), _625007)), _625011)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_625003), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_625003), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_625003), _625005), _625009)), _625007)), _625011))], (6533 ^ _393467) ^ [_625369, _625371, _625373, _625375] : [class_RealVector_Oreal__normed__algebra(_625369), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_625369), _625371), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_625369), _625373), _625375)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_625369), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_625369), _625371), _625373)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_625369), _625371), _625375)))], (6539 ^ _393467) ^ [_625697, _625699, _625701, _625703] : [class_RealVector_Oreal__normed__algebra(_625697), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_625697), _625699), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_625697), _625701), _625703)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_625697), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_625697), _625699), _625701)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_625697), _625699), _625703)))], (6545 ^ _393467) ^ [_626025, _626027, _626029, _626031] : [class_RealVector_Oreal__normed__algebra(_626025), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_626025), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_626025), _626027), _626029)), _626031) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_626025), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_626025), _626027), _626031)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_626025), _626029), _626031)))], (6551 ^ _393467) ^ [_626353, _626355, _626357, _626359] : [class_RealVector_Oreal__normed__algebra(_626353), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_626353), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_626353), _626355), _626357)), _626359) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_626353), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_626353), _626355), _626359)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_626353), _626357), _626359)))], (6557 ^ _393467) ^ [_626681, _626683, _626685, _626687] : [class_Rings_Ocomm__semiring__1(_626681), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_626681), _626683), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_626681), _626685), _626687)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_626681), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_626681), _626683), _626685)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_626681), _626683), _626687)))], (6563 ^ _393467) ^ [_627023, _627025, _627027, _627029, _627031] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_627023), 6566 ^ _393467 : [(6577 ^ _393467) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_627023), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_627023), _627025), _627029)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_627023), _627027), _627031)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_627023), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_627023), _627025), _627031)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_627023), _627027), _627029))), 6580 ^ _393467 : [(6581 ^ _393467) ^ [] : [_627025 = _627027], (6583 ^ _393467) ^ [] : [_627029 = _627031]]], (6567 ^ _393467) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_627023), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_627023), _627025), _627029)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_627023), _627027), _627031)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_627023), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_627023), _627025), _627031)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_627023), _627027), _627029)), -(_627025 = _627027), -(_627029 = _627031)]]], (6585 ^ _393467) ^ [_627883, _627885, _627887, _627889] : [class_Rings_Ocomm__semiring__1(_627883), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_627883), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_627883), _627885), _627887)), _627889) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_627883), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_627883), _627885), _627889)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_627883), _627887), _627889)))], (6591 ^ _393467) ^ [_628211, _628213, _628215, _628217] : [class_Rings_Ocomm__semiring__1(_628211), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_628211), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_628211), _628213), _628215)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_628211), _628217), _628215)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_628211), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_628211), _628213), _628217)), _628215))], (6597 ^ _393467) ^ [_628553, _628555, _628557, _628559, _628561] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_628553), 6600 ^ _393467 : [(6611 ^ _393467) ^ [] : [6612 ^ _393467 : [(6613 ^ _393467) ^ [] : [_628555 = _628559], (6615 ^ _393467) ^ [] : [_628557 = _628561]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_628553), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_628553), _628555), _628557)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_628553), _628559), _628561)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_628553), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_628553), _628555), _628561)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_628553), _628559), _628557)))], (6601 ^ _393467) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_628553), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_628553), _628555), _628557)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_628553), _628559), _628561)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_628553), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_628553), _628555), _628561)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_628553), _628559), _628557)), -(_628555 = _628559), -(_628557 = _628561)]]], (6619 ^ _393467) ^ [_629407, _629409, _629411, _629413] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_629407), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_629407, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_629407), _629409), _629411)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_629407), _629409), _629413))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_629407, _629411), _629413)))], (6629 ^ _393467) ^ [_629804, _629806, _629808, _629810] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_629804), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_629804, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_629804), _629806), _629808)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_629804), _629810), _629808))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_629804, _629806), _629810)))], (6639 ^ _393467) ^ [_630215, _630217, _630219, _630221, _630223] : [class_Groups_Oordered__cancel__ab__semigroup__add(_630215), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_630215, _630217), _630219)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_630215, _630221), _630223)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_630215, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_630215), _630217), _630221)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_630215), _630219), _630223))))], (6653 ^ _393467) ^ [_630733, _630735, _630737, _630739] : [class_Groups_Oordered__cancel__ab__semigroup__add(_630733), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_630733, _630735), _630737)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_630733, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_630733), _630739), _630735)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_630733), _630739), _630737))))], (6663 ^ _393467) ^ [_631130, _631132, _631134, _631136] : [class_Groups_Oordered__cancel__ab__semigroup__add(_631130), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_631130, _631132), _631134)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_631130, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_631130), _631132), _631136)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_631130), _631134), _631136))))], (6673 ^ _393467) ^ [_631527, _631529, _631531, _631533] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_631527), 6676 ^ _393467 : [(6677 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_631527, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_631527), _631529), _631531)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_631527), _631529), _631533))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_631527, _631531), _631533)))], (6683 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_631527, _631531), _631533)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_631527, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_631527), _631529), _631531)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_631527), _631529), _631533))))]]], (6689 ^ _393467) ^ [_632123, _632125, _632127, _632129] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_632123), 6692 ^ _393467 : [(6693 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_632123, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_632123), _632125), _632127)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_632123), _632129), _632127))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_632123, _632125), _632129)))], (6699 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_632123, _632125), _632129)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_632123, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_632123), _632125), _632127)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_632123), _632129), _632127))))]]], (6705 ^ _393467) ^ [_632719, _632721, _632723, _632725] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_632719), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_632719, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_632719), _632721), _632723)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_632719), _632721), _632725))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_632719, _632723), _632725)))], (6715 ^ _393467) ^ [_633116, _633118, _633120, _633122] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_633116), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_633116, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_633116), _633118), _633120)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_633116), _633122), _633120))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_633116, _633118), _633122)))], (6725 ^ _393467) ^ [_633527, _633529, _633531, _633533, _633535] : [class_Groups_Oordered__ab__semigroup__add(_633527), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_633527, _633529), _633531)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_633527, _633533), _633535)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_633527, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_633527), _633529), _633533)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_633527), _633531), _633535))))], (6739 ^ _393467) ^ [_634045, _634047, _634049, _634051] : [class_Groups_Oordered__ab__semigroup__add(_634045), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_634045, _634047), _634049)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_634045, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_634045), _634051), _634047)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_634045), _634051), _634049))))], (6749 ^ _393467) ^ [_634442, _634444, _634446, _634448] : [class_Groups_Oordered__ab__semigroup__add(_634442), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_634442, _634444), _634446)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_634442, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_634442), _634444), _634448)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_634442), _634446), _634448))))], (6759 ^ _393467) ^ [_634839, _634841, _634843, _634845] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_634839), 6762 ^ _393467 : [(6763 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_634839, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_634839), _634841), _634843)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_634839), _634841), _634845))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_634839, _634843), _634845)))], (6769 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_634839, _634843), _634845)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_634839, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_634839), _634841), _634843)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_634839), _634841), _634845))))]]], (6775 ^ _393467) ^ [_635435, _635437, _635439, _635441] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_635435), 6778 ^ _393467 : [(6779 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_635435, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_635435), _635437), _635439)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_635435), _635441), _635439))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_635435, _635437), _635441)))], (6785 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_635435, _635437), _635441)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_635435, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_635435), _635437), _635439)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_635435), _635441), _635439))))]]], (6791 ^ _393467) ^ [_636003, _636005] : [class_Groups_Ocomm__monoid__add(_636003), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_636003), _636005), c_Groups_Ozero__class_Ozero(_636003)) = _636005)], (6797 ^ _393467) ^ [_636231, _636233] : [class_Groups_Omonoid__add(_636231), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_636231), _636233), c_Groups_Ozero__class_Ozero(_636231)) = _636233)], (6803 ^ _393467) ^ [_636459, _636461] : [class_Groups_Olinordered__ab__group__add(_636459), 6806 ^ _393467 : [(6807 ^ _393467) ^ [] : [c_Groups_Ozero__class_Ozero(_636459) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_636459), _636461), _636461), -(_636461 = c_Groups_Ozero__class_Ozero(_636459))], (6813 ^ _393467) ^ [] : [_636461 = c_Groups_Ozero__class_Ozero(_636459), -(c_Groups_Ozero__class_Ozero(_636459) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_636459), _636461), _636461))]]], (6819 ^ _393467) ^ [_636953, _636955] : [class_Groups_Ocomm__monoid__add(_636953), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_636953), c_Groups_Ozero__class_Ozero(_636953)), _636955) = _636955)], (6825 ^ _393467) ^ [_637181, _637183] : [class_Groups_Omonoid__add(_637181), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_637181), c_Groups_Ozero__class_Ozero(_637181)), _637183) = _637183)], (6831 ^ _393467) ^ [_637423, _637425, _637427] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_637423), 6834 ^ _393467 : [(6835 ^ _393467) ^ [] : [_637425 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_637423), _637425), _637427), -(_637427 = c_Groups_Ozero__class_Ozero(_637423))], (6841 ^ _393467) ^ [] : [_637427 = c_Groups_Ozero__class_Ozero(_637423), -(_637425 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_637423), _637425), _637427))]]], (6847 ^ _393467) ^ [_637927, _637929] : [class_Rings_Ocomm__semiring__1(_637927), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_637927), _637929), c_Groups_Ozero__class_Ozero(_637927)) = _637929)], (6853 ^ _393467) ^ [_638155, _638157] : [class_Rings_Ocomm__semiring__1(_638155), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_638155), c_Groups_Ozero__class_Ozero(_638155)), _638157) = _638157)], (6859 ^ _393467) ^ [_638383, _638385] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _638383)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _638385)), -(c_Transcendental_Oln(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _638383), _638385)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), c_Transcendental_Oln(_638383)), c_Transcendental_Oln(_638385)))], (6869 ^ _393467) ^ [_638712] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _638712)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Transcendental_Oln(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _638712))), _638712)))], (6875 ^ _393467) ^ [_638940, _638942] : [class_Groups_Olinordered__ab__group__add(_638940), 6878 ^ _393467 : [(6879 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_638940, c_Groups_Ozero__class_Ozero(_638940)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_638940), _638942), _638942))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_638940, c_Groups_Ozero__class_Ozero(_638940)), _638942)))], (6885 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_638940, c_Groups_Ozero__class_Ozero(_638940)), _638942)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_638940, c_Groups_Ozero__class_Ozero(_638940)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_638940), _638942), _638942))))]]], (6891 ^ _393467) ^ [_639464, _639466] : [class_Groups_Olinordered__ab__group__add(_639464), 6894 ^ _393467 : [(6895 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_639464, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_639464), _639466), _639466)), c_Groups_Ozero__class_Ozero(_639464))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_639464, _639466), c_Groups_Ozero__class_Ozero(_639464))))], (6901 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_639464, _639466), c_Groups_Ozero__class_Ozero(_639464))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_639464, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_639464), _639466), _639466)), c_Groups_Ozero__class_Ozero(_639464))))]]], (6907 ^ _393467) ^ [_640002, _640004, _640006] : [class_Groups_Oordered__comm__monoid__add(_640002), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_640002, c_Groups_Ozero__class_Ozero(_640002)), _640004)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_640002, c_Groups_Ozero__class_Ozero(_640002)), _640006)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_640002, c_Groups_Ozero__class_Ozero(_640002)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_640002), _640004), _640006))))], (6921 ^ _393467) ^ [_640474, _640476, _640478] : [class_Groups_Oordered__comm__monoid__add(_640474), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_640474, c_Groups_Ozero__class_Ozero(_640474)), _640476)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_640474, c_Groups_Ozero__class_Ozero(_640474)), _640478)), 6932 ^ _393467 : [(6933 ^ _393467) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_640474), _640476), _640478) = c_Groups_Ozero__class_Ozero(_640474), 6936 ^ _393467 : [(6937 ^ _393467) ^ [] : [-(_640476 = c_Groups_Ozero__class_Ozero(_640474))], (6939 ^ _393467) ^ [] : [-(_640478 = c_Groups_Ozero__class_Ozero(_640474))]]], (6941 ^ _393467) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_640474), _640476), _640478) = c_Groups_Ozero__class_Ozero(_640474)), _640476 = c_Groups_Ozero__class_Ozero(_640474), _640478 = c_Groups_Ozero__class_Ozero(_640474)]]], (6951 ^ _393467) ^ [_641396, _641398, _641400, _641402] : [class_Groups_Oordered__comm__monoid__add(_641396), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_641396, c_Groups_Ozero__class_Ozero(_641396)), _641398)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_641396, _641400), _641402)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_641396, _641400), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_641396), _641398), _641402))))], (6965 ^ _393467) ^ [_641888, _641890, _641892, _641894] : [class_Groups_Oordered__comm__monoid__add(_641888), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_641888, c_Groups_Ozero__class_Ozero(_641888)), _641890)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_641888, _641892), _641894)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_641888, _641892), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_641888), _641894), _641890))))], (6979 ^ _393467) ^ [_642366, _642368, _642370] : [class_Groups_Oordered__comm__monoid__add(_642366), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_642366, _642368), c_Groups_Ozero__class_Ozero(_642366))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_642366, _642370), c_Groups_Ozero__class_Ozero(_642366))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_642366, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_642366), _642368), _642370)), c_Groups_Ozero__class_Ozero(_642366))))], (6993 ^ _393467) ^ [_642824, _642826] : [class_Groups_Olinordered__ab__group__add(_642824), 6996 ^ _393467 : [(6997 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_642824, c_Groups_Ozero__class_Ozero(_642824)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_642824), _642826), _642826))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_642824, c_Groups_Ozero__class_Ozero(_642824)), _642826)))], (7003 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_642824, c_Groups_Ozero__class_Ozero(_642824)), _642826)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_642824, c_Groups_Ozero__class_Ozero(_642824)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_642824), _642826), _642826))))]]], (7009 ^ _393467) ^ [_643348, _643350] : [class_Groups_Olinordered__ab__group__add(_643348), 7012 ^ _393467 : [(7013 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_643348, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_643348), _643350), _643350)), c_Groups_Ozero__class_Ozero(_643348))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_643348, _643350), c_Groups_Ozero__class_Ozero(_643348))))], (7019 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_643348, _643350), c_Groups_Ozero__class_Ozero(_643348))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_643348, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_643348), _643350), _643350)), c_Groups_Ozero__class_Ozero(_643348))))]]], (7025 ^ _393467) ^ [_643886, _643888, _643890] : [class_Groups_Oordered__comm__monoid__add(_643886), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_643886, c_Groups_Ozero__class_Ozero(_643886)), _643888)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_643886, c_Groups_Ozero__class_Ozero(_643886)), _643890)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_643886, c_Groups_Ozero__class_Ozero(_643886)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_643886), _643888), _643890))))], (7039 ^ _393467) ^ [_644358, _644360, _644362] : [class_Groups_Oordered__comm__monoid__add(_644358), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_644358, _644360), c_Groups_Ozero__class_Ozero(_644358))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_644358, _644362), c_Groups_Ozero__class_Ozero(_644358))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_644358, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_644358), _644360), _644362)), c_Groups_Ozero__class_Ozero(_644358))))], (7053 ^ _393467) ^ [_644844, _644846, _644848, _644850] : [class_Rings_Olinordered__semidom(_644844), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_644844, c_Groups_Ozero__class_Ozero(_644844)), _644846)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_644844, _644848), _644850)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_644844, _644848), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_644844), _644846), _644850))))], (7067 ^ _393467) ^ [_645350, _645352, _645354, _645356, _645358] : [class_Groups_Oordered__cancel__ab__semigroup__add(_645350), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_645350, _645352), _645354)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_645350, _645356), _645358)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_645350, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_645350), _645352), _645356)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_645350), _645354), _645358))))], (7081 ^ _393467) ^ [_645882, _645884, _645886, _645888, _645890] : [class_Groups_Oordered__cancel__ab__semigroup__add(_645882), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_645882, _645884), _645886)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_645882, _645888), _645890)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_645882, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_645882), _645884), _645888)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_645882), _645886), _645890))))], (7095 ^ _393467) ^ [_646386, _646388, _646390] : [class_Rings_Olinordered__ring__strict(_646386), 7098 ^ _393467 : [(7099 ^ _393467) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_646386), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_646386), _646388), _646388)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_646386), _646390), _646390)) = c_Groups_Ozero__class_Ozero(_646386), 7102 ^ _393467 : [(7103 ^ _393467) ^ [] : [-(_646388 = c_Groups_Ozero__class_Ozero(_646386))], (7105 ^ _393467) ^ [] : [-(_646390 = c_Groups_Ozero__class_Ozero(_646386))]]], (7107 ^ _393467) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_646386), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_646386), _646388), _646388)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_646386), _646390), _646390)) = c_Groups_Ozero__class_Ozero(_646386)), _646388 = c_Groups_Ozero__class_Ozero(_646386), _646390 = c_Groups_Ozero__class_Ozero(_646386)]]], (7117 ^ _393467) ^ [_647170, _647172, _647174, _647176, _647178, _647180] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_647170), -(_647172 = c_Groups_Ozero__class_Ozero(_647170)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_647170), _647174), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_647170), _647172), _647178)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_647170), _647176), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_647170), _647172), _647180)), _647174 = _647176, -(_647178 = _647180)], (7135 ^ _393467) ^ [_647792, _647794] : [class_Rings_Olinordered__semidom(_647792), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_647792, _647794), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_647792), _647794), c_Groups_Oone__class_Oone(_647792)))))], (7141 ^ _393467) ^ [_648044, _648046, _648048] : [class_Rings_Ocomm__semiring__1(_648044), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_648044), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_648044), _648046), _648048)), _648048) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_648044), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_648044), _648046), c_Groups_Oone__class_Oone(_648044))), _648048))], (7147 ^ _393467) ^ [_648340, _648342, _648344] : [class_Rings_Ocomm__semiring__1(_648340), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_648340), _648342), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_648340), _648344), _648342)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_648340), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_648340), _648344), c_Groups_Oone__class_Oone(_648340))), _648342))], (7153 ^ _393467) ^ [_648622, _648624] : [class_Rings_Ocomm__semiring__1(_648622), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_648622), _648624), _648624) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_648622), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_648622), c_Groups_Oone__class_Oone(_648622)), c_Groups_Oone__class_Oone(_648622))), _648624))], (7159 ^ _393467) ^ [_648915, _648917] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _648915), _648915)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _648917), _648917)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 7162 ^ _393467 : [(7163 ^ _393467) ^ [] : [-(_648915 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (7165 ^ _393467) ^ [] : [-(_648917 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))]]], (7167 ^ _393467) ^ [_649188, _649190] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _649188), _649188)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _649190), _649190)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _649188 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _649190 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)], (7177 ^ _393467) ^ [_649511] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _649511)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Transcendental_Oln(_649511)), _649511)))], (7183 ^ _393467) ^ [_649733, _649735] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _649733)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _649735)), 7190 ^ _393467 : [(7191 ^ _393467) ^ [] : [c_Transcendental_Oln(_649733) = c_Transcendental_Oln(_649735), -(_649733 = _649735)], (7197 ^ _393467) ^ [] : [_649733 = _649735, -(c_Transcendental_Oln(_649733) = c_Transcendental_Oln(_649735))]]], (7203 ^ _393467) ^ [_650302, _650304] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _650302)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _650304)), 7210 ^ _393467 : [(7211 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Transcendental_Oln(_650302)), c_Transcendental_Oln(_650304))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _650302), _650304)))], (7217 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _650302), _650304)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Transcendental_Oln(_650302)), c_Transcendental_Oln(_650304))))]]], (7223 ^ _393467) ^ [] : [-(c_Transcendental_Oln(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (7225 ^ _393467) ^ [_650968, _650970, _650972] : [class_Groups_Oordered__comm__monoid__add(_650968), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_650968, c_Groups_Ozero__class_Ozero(_650968)), _650970)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_650968, c_Groups_Ozero__class_Ozero(_650968)), _650972)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_650968, c_Groups_Ozero__class_Ozero(_650968)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_650968), _650970), _650972))))], (7239 ^ _393467) ^ [_651440, _651442, _651444] : [class_Groups_Oordered__comm__monoid__add(_651440), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_651440, c_Groups_Ozero__class_Ozero(_651440)), _651442)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_651440, c_Groups_Ozero__class_Ozero(_651440)), _651444)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_651440, c_Groups_Ozero__class_Ozero(_651440)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_651440), _651442), _651444))))], (7253 ^ _393467) ^ [_651926, _651928, _651930, _651932] : [class_Groups_Oordered__comm__monoid__add(_651926), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_651926, c_Groups_Ozero__class_Ozero(_651926)), _651928)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_651926, _651930), _651932)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_651926, _651930), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_651926), _651928), _651932))))], (7267 ^ _393467) ^ [_652418, _652420, _652422, _652424] : [class_Groups_Oordered__comm__monoid__add(_652418), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_652418, c_Groups_Ozero__class_Ozero(_652418)), _652420)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_652418, _652422), _652424)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_652418, _652422), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_652418), _652420), _652424))))], (7281 ^ _393467) ^ [_652896, _652898, _652900] : [class_Groups_Oordered__comm__monoid__add(_652896), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_652896, _652898), c_Groups_Ozero__class_Ozero(_652896))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_652896, _652900), c_Groups_Ozero__class_Ozero(_652896))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_652896, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_652896), _652898), _652900)), c_Groups_Ozero__class_Ozero(_652896))))], (7295 ^ _393467) ^ [_653368, _653370, _653372] : [class_Groups_Oordered__comm__monoid__add(_653368), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_653368, _653370), c_Groups_Ozero__class_Ozero(_653368))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_653368, _653372), c_Groups_Ozero__class_Ozero(_653368))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_653368, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_653368), _653370), _653372)), c_Groups_Ozero__class_Ozero(_653368))))], (7309 ^ _393467) ^ [_653840, _653842, _653844] : [class_Rings_Olinordered__ring(_653840), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_653840, c_Groups_Ozero__class_Ozero(_653840)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_653840), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_653840), _653842), _653842)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_653840), _653844), _653844)))))], (7315 ^ _393467) ^ [_654130, _654132, _654134] : [class_Rings_Olinordered__ring__strict(_654130), 7318 ^ _393467 : [(7319 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_654130, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_654130), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_654130), _654132), _654132)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_654130), _654134), _654134))), c_Groups_Ozero__class_Ozero(_654130))), 7322 ^ _393467 : [(7323 ^ _393467) ^ [] : [-(_654132 = c_Groups_Ozero__class_Ozero(_654130))], (7325 ^ _393467) ^ [] : [-(_654134 = c_Groups_Ozero__class_Ozero(_654130))]]], (7327 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_654130, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_654130), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_654130), _654132), _654132)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_654130), _654134), _654134))), c_Groups_Ozero__class_Ozero(_654130)))), _654132 = c_Groups_Ozero__class_Ozero(_654130), _654134 = c_Groups_Ozero__class_Ozero(_654130)]]], (7337 ^ _393467) ^ [_654887, _654889, _654891] : [class_Rings_Olinordered__ring(_654887), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_654887, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_654887), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_654887), _654889), _654889)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_654887), _654891), _654891))), c_Groups_Ozero__class_Ozero(_654887)))], (7343 ^ _393467) ^ [_655178, _655180, _655182] : [class_Rings_Olinordered__ring__strict(_655178), 7346 ^ _393467 : [(7357 ^ _393467) ^ [] : [7358 ^ _393467 : [(7359 ^ _393467) ^ [] : [-(_655180 = c_Groups_Ozero__class_Ozero(_655178))], (7361 ^ _393467) ^ [] : [-(_655182 = c_Groups_Ozero__class_Ozero(_655178))]], -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_655178, c_Groups_Ozero__class_Ozero(_655178)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_655178), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_655178), _655180), _655180)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_655178), _655182), _655182)))))], (7347 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_655178, c_Groups_Ozero__class_Ozero(_655178)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_655178), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_655178), _655180), _655180)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_655178), _655182), _655182)))), _655180 = c_Groups_Ozero__class_Ozero(_655178), _655182 = c_Groups_Ozero__class_Ozero(_655178)]]], (7365 ^ _393467) ^ [_655911] : [class_Rings_Olinordered__semidom(_655911), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_655911, c_Groups_Ozero__class_Ozero(_655911)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_655911), c_Groups_Oone__class_Oone(_655911)), c_Groups_Oone__class_Oone(_655911)))))], (7371 ^ _393467) ^ [_656164, _656166, _656168, _656170] : [-(hAPP(hAPP(c_Power_Opower_Opower(_656164, _656166, _656168), _656170), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _656166)], (7373 ^ _393467) ^ [_656314, _656316, _656318, _656320, _656322] : [-(hAPP(hAPP(c_Power_Opower_Opower(_656314, _656316, _656318), _656320), c_Nat_OSuc(_656322)) = hAPP(hAPP(_656318, _656320), hAPP(hAPP(c_Power_Opower_Opower(_656314, _656316, _656318), _656320), _656322)))], (7375 ^ _393467) ^ [_656428] : [-(c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(_656428)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _656428)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (7377 ^ _393467) ^ [_656534, _656536] : [-(hAPP(c_Complex_OIm, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), _656534), _656536)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(c_Complex_ORe, _656534)), hAPP(c_Complex_OIm, _656536))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(c_Complex_OIm, _656534)), hAPP(c_Complex_ORe, _656536))))], (7379 ^ _393467) ^ [_656682, _656684] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _656682)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _656684)), 7386 ^ _393467 : [(7387 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Transcendental_Oln(_656682)), c_Transcendental_Oln(_656684))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _656682), _656684)))], (7393 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _656682), _656684)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Transcendental_Oln(_656682)), c_Transcendental_Oln(_656684))))]]], (7399 ^ _393467) ^ [_657267] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _657267)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_Transcendental_Oln(_657267))))], (7405 ^ _393467) ^ [_657469] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_Transcendental_Oln(_657469))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _657469)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _657469)))], (7415 ^ _393467) ^ [_657760] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _657760)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _657760), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Transcendental_Oln(_657760)), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))], (7425 ^ _393467) ^ [_658063] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _658063)), 7428 ^ _393467 : [(7429 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Transcendental_Oln(_658063)), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _658063), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))], (7435 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _658063), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Transcendental_Oln(_658063)), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))]]], (7441 ^ _393467) ^ [_658533] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _658533)), 7444 ^ _393467 : [(7445 ^ _393467) ^ [] : [c_Transcendental_Oln(_658533) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_658533 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (7451 ^ _393467) ^ [] : [_658533 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal), -(c_Transcendental_Oln(_658533) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))]]], (7457 ^ _393467) ^ [_658973] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _658973)), 7460 ^ _393467 : [(7461 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_Transcendental_Oln(_658973))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _658973)))], (7467 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _658973)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_Transcendental_Oln(_658973))))]]], (7473 ^ _393467) ^ [_659425] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _659425)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_Transcendental_Oln(_659425))))], (7479 ^ _393467) ^ [_659697, _659699, _659701, _659703, _659705, _659707] : [class_Rings_Olinordered__semiring__1(_659697), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_659697, _659699), _659701)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_659697, _659703), _659701)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_659697, c_Groups_Ozero__class_Ozero(_659697)), _659705)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_659697, c_Groups_Ozero__class_Ozero(_659697)), _659707)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_659697), _659705), _659707) = c_Groups_Oone__class_Oone(_659697), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_659697, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_659697), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_659697), _659705), _659699)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_659697), _659707), _659703))), _659701)))], (7505 ^ _393467) ^ [_660609, _660611] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _660609), _660611)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _660609)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), c_RealDef_Oreal(tc_Nat_Onat, _660611))))], (7511 ^ _393467) ^ [_660815, _660817] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _660815)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), c_RealDef_Oreal(tc_Nat_Onat, _660817))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _660815), _660817)))], (7517 ^ _393467) ^ [_661100, _661102] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _661100), _661102)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _661100)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _661102)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))))], (7523 ^ _393467) ^ [_661306, _661308] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _661306)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _661308)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _661306), _661308)))], (7529 ^ _393467) ^ [_661533] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _661533), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatfloor(_661533))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))))], (7531 ^ _393467) ^ [_661642] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _661642)), 7534 ^ _393467 : [(7535 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_Transcendental_Oln(_661642))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _661642)))], (7541 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _661642)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_Transcendental_Oln(_661642))))]]], (7547 ^ _393467) ^ [_662094] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_Transcendental_Oln(_662094))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _662094)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _662094)))], (7557 ^ _393467) ^ [_662455, _662457, _662459, _662461, _662463, _662465] : [class_Rings_Olinordered__semiring__1__strict(_662455), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_662455, _662457), _662459)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_662455, _662461), _662459)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_662455, c_Groups_Ozero__class_Ozero(_662455)), _662463)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_662455, c_Groups_Ozero__class_Ozero(_662455)), _662465)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_662455), _662463), _662465) = c_Groups_Oone__class_Oone(_662455), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_662455, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_662455), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_662455), _662463), _662457)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_662455), _662465), _662461))), _662459)))], (7583 ^ _393467) ^ [_663338, _663340] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _663338)), _663340)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _663340), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _663338)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))), -(c_RComplete_Onatfloor(_663340) = _663338)], (7593 ^ _393467) ^ [_663685, _663687] : [class_Rings_Olinordered__idom(_663685), 7596 ^ _393467 : [(7597 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_663685, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_663685), _663687), _663687)), c_Groups_Ozero__class_Ozero(_663685))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_663685, _663687), c_Groups_Ozero__class_Ozero(_663685))))], (7603 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_663685, _663687), c_Groups_Ozero__class_Ozero(_663685))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_663685, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_663685), _663687), _663687)), c_Groups_Ozero__class_Ozero(_663685))))]]], (7609 ^ _393467) ^ [_664209, _664211] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _664209)), _664211)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _664211), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _664209)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))), -(c_RComplete_Onatceiling(_664211) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _664209), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (7619 ^ _393467) ^ [_664568, _664570] : [class_Groups_Olinordered__ab__group__add(_664568), 7622 ^ _393467 : [(7623 ^ _393467) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_664568), _664570), _664570) = c_Groups_Ozero__class_Ozero(_664568), -(_664570 = c_Groups_Ozero__class_Ozero(_664568))], (7629 ^ _393467) ^ [] : [_664570 = c_Groups_Ozero__class_Ozero(_664568), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_664568), _664570), _664570) = c_Groups_Ozero__class_Ozero(_664568))]]], (7635 ^ _393467) ^ [_665048] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _665048)), -(c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), _665048), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_RComplete_Onatceiling(_665048)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (7641 ^ _393467) ^ [_665287, _665289, _665291] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _665287), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _665289), _665291)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _665287), _665289)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _665287), _665291)))], (7643 ^ _393467) ^ [_665399] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _665399) = _665399)], (7645 ^ _393467) ^ [_665480] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _665480), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _665480)], (7647 ^ _393467) ^ [_665622, _665624] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _665622), _665624) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 7650 ^ _393467 : [(7651 ^ _393467) ^ [] : [-(_665622 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7653 ^ _393467) ^ [] : [-(_665624 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (7655 ^ _393467) ^ [_665871, _665873] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _665871), _665873) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _665871 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _665873 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (7665 ^ _393467) ^ [_666184, _666186] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _666184), _666186) = _666184, -(_666186 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7671 ^ _393467) ^ [_666391, _666393] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Nat_OSuc(_666391)), _666393) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _666391), c_Nat_OSuc(_666393)))], (7673 ^ _393467) ^ [_666501, _666503] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Nat_OSuc(_666501)), _666503) = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _666501), _666503)))], (7675 ^ _393467) ^ [_666611, _666613] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _666611), c_Nat_OSuc(_666613)) = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _666611), _666613)))], (7677 ^ _393467) ^ [_666750, _666752, _666754] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _666750), _666752)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _666750), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _666754), _666752))))], (7683 ^ _393467) ^ [_667012, _667014, _667016] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _667012), _667014)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _667012), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _667014), _667016))))], (7689 ^ _393467) ^ [_667274, _667276, _667278] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _667274), _667276)), _667278)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _667274), _667278)))], (7695 ^ _393467) ^ [_667550, _667552, _667554, _667556] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _667550), _667552)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _667554), _667552) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _667550), _667556), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _667554), _667556)))], (7705 ^ _393467) ^ [_667941, _667943, _667945, _667947] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _667941), _667943)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _667945), _667947)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _667941), _667945)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _667943), _667947))))], (7715 ^ _393467) ^ [_668328, _668330, _668332] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _668328), _668330)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _668328), _668332)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _668330), _668332))))], (7721 ^ _393467) ^ [_668602, _668604, _668606] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _668602), _668604)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _668602), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _668606), _668604))))], (7727 ^ _393467) ^ [_668864, _668866, _668868] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _668864), _668866)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _668864), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _668866), _668868))))], (7733 ^ _393467) ^ [_669155, _669157, _669159] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _669155), _669157)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _669155), _669159))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _669157), _669159)))], (7739 ^ _393467) ^ [_669367, _669369, _669371] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _669369), _669371)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _669367), _669369)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _669367), _669371))))], (7745 ^ _393467) ^ [_669613, _669615] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _669613), _669615)), _669615))], (7747 ^ _393467) ^ [_669717, _669719] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _669717), _669719)), _669717))], (7749 ^ _393467) ^ [_669851, _669853, _669855] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _669851), _669853)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _669851), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _669853), _669855))))], (7755 ^ _393467) ^ [_670113, _670115, _670117] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _670113), _670115)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _670113), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _670117), _670115))))], (7761 ^ _393467) ^ [_670375, _670377, _670379] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _670375), _670377)), _670379)), 7764 ^ _393467 : [(7765 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _670375), _670379)))], (7767 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _670377), _670379)))]]], (7769 ^ _393467) ^ [_670728, _670730, _670732] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _670728), _670730)), _670732)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _670728), _670732)))], (7775 ^ _393467) ^ [_670990, _670992, _670994] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _670990), _670992)), _670994)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _670992), _670994)))], (7781 ^ _393467) ^ [_671266, _671268, _671270, _671272] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _671266), _671268)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _671270), _671272)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _671266), _671270)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _671268), _671272))))], (7791 ^ _393467) ^ [_671653, _671655, _671657] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _671653), _671655)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _671653), _671657)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _671655), _671657))))], (7797 ^ _393467) ^ [_671927, _671929, _671931] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _671927), _671929)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _671927), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _671931), _671929))))], (7803 ^ _393467) ^ [_672189, _672191, _672193] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _672189), _672191)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _672189), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _672191), _672193))))], (7809 ^ _393467) ^ [_672480, _672482, _672484] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _672480), _672482)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _672480), _672484))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _672482), _672484)))], (7815 ^ _393467) ^ [_672692, _672694, _672696] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _672694), _672696)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _672692), _672694)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _672692), _672696))))], (7821 ^ _393467) ^ [_672983, _672985] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _672983), _672985)), -(_672985 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _672983), 7824 ^ [_672983, _672985]))], (7828 ^ _393467) ^ [_673230, _673232] : [7829 ^ _393467 : [(7830 ^ _393467) ^ [_673311] : [_673232 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _673230), _673311)]], -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _673230), _673232)))], (7834 ^ _393467) ^ [_673515, _673517] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _673515), _673517)), -(_673517 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _673515), 7837 ^ [_673515, _673517]))], (7841 ^ _393467) ^ [_673762, _673764] : [7842 ^ _393467 : [(7843 ^ _393467) ^ [_673843] : [_673764 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _673762), _673843)]], -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _673762), _673764)))], (7847 ^ _393467) ^ [_674003, _674005] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _674003), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _674003), _674005))))], (7849 ^ _393467) ^ [_674108, _674110] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _674108), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _674110), _674108))))], (7851 ^ _393467) ^ [_674241, _674243, _674245, _674247] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _674241), _674243)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _674245), _674243)), _674247)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _674241), _674245)), _674243)), _674247))], (7853 ^ _393467) ^ [_674395, _674397, _674399] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _674395), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _674397), _674399)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _674395), _674397)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _674395), _674399)))], (7855 ^ _393467) ^ [_674535, _674537, _674539] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _674535), _674537)), _674539) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _674535), _674539)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _674537), _674539)))], (7857 ^ _393467) ^ [_674676, _674678] : [class_Groups_Ocomm__monoid__add(_674676), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_674676)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_674676))), _674678) = _674678)], (7863 ^ _393467) ^ [_674912, _674914] : [class_Groups_Ocomm__monoid__add(_674912), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_674912)), _674914), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_674912))) = _674914)], (7869 ^ _393467) ^ [_675133, _675135] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _675133), _675135) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _675135), _675133))], (7871 ^ _393467) ^ [_675253, _675255, _675257] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _675253), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _675255), _675257)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _675255), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _675253), _675257)))], (7873 ^ _393467) ^ [_675387, _675389, _675391] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _675387), _675389)), _675391) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _675387), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _675389), _675391)))], (7875 ^ _393467) ^ [_675565, _675567, _675569] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _675565), _675567) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _675565), _675569), -(_675567 = _675569)], (7881 ^ _393467) ^ [_675757, _675759, _675761] : [_675759 = _675761, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _675757), _675759) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _675757), _675761))], (7887 ^ _393467) ^ [_676042, _676044, _676046] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _676042), _676044) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _676046), _676044), -(_676042 = _676046)], (7893 ^ _393467) ^ [_676234, _676236, _676238] : [_676234 = _676238, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _676234), _676236) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _676238), _676236))], (7899 ^ _393467) ^ [_676504, _676506, _676508, _676510] : [class_Rings_Ocomm__semiring__0(_676504), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_676504)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_676504)), _676506), _676508)), _676510) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_676504)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_676504)), _676506), _676510)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_676504)), _676508), _676510)))], (7905 ^ _393467) ^ [_676838, _676840, _676842] : [class_RealVector_Oreal__normed__vector(_676838), c_SEQ_OBseq(_676838, _676840), -(c_SEQ_OBseq(_676838, c_COMBB(tc_Nat_Onat, _676838, tc_Nat_Onat, _676840, c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _676842))))], (7915 ^ _393467) ^ [_677183, _677185, _677187] : [class_RealVector_Oreal__normed__vector(_677183), c_SEQ_OBseq(_677183, c_COMBB(tc_Nat_Onat, _677183, tc_Nat_Onat, _677185, c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _677187))), -(c_SEQ_OBseq(_677183, _677185))], (7925 ^ _393467) ^ [_677542, _677544, _677546, _677548] : [class_Groups_Omonoid__mult(_677542), -(hAPP(hAPP(c_Power_Opower__class_Opower(_677542), _677544), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _677546), _677548)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_677542), hAPP(hAPP(c_Power_Opower__class_Opower(_677542), _677544), _677546)), hAPP(hAPP(c_Power_Opower__class_Opower(_677542), _677544), _677548)))], (7931 ^ _393467) ^ [_677866, _677868, _677870, _677872] : [class_Rings_Ocomm__semiring__1(_677866), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_677866), hAPP(hAPP(c_Power_Opower__class_Opower(_677866), _677868), _677870)), hAPP(hAPP(c_Power_Opower__class_Opower(_677866), _677868), _677872)) = hAPP(hAPP(c_Power_Opower__class_Opower(_677866), _677868), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _677870), _677872)))], (7937 ^ _393467) ^ [_678191, _678193] : [c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _678191), _678193), 7942 ^ _393467 : [(7943 ^ _393467) ^ [] : [-(_678191 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (7945 ^ _393467) ^ [] : [-(_678193 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 7946 ^ _393467 : [(7947 ^ _393467) ^ [] : [-(_678191 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7949 ^ _393467) ^ [] : [-(_678193 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (7951 ^ _393467) ^ [_678605, _678607] : [-(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _678605), _678607)), 7952 ^ _393467 : [(7953 ^ _393467) ^ [] : [_678605 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _678607 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (7959 ^ _393467) ^ [] : [_678605 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _678607 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (7967 ^ _393467) ^ [_679110, _679112] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _679110), _679112) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 7972 ^ _393467 : [(7973 ^ _393467) ^ [] : [-(_679110 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (7975 ^ _393467) ^ [] : [-(_679112 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 7976 ^ _393467 : [(7977 ^ _393467) ^ [] : [-(_679110 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7979 ^ _393467) ^ [] : [-(_679112 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (7981 ^ _393467) ^ [_679524, _679526] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _679524), _679526) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 7982 ^ _393467 : [(7983 ^ _393467) ^ [] : [_679524 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _679526 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (7989 ^ _393467) ^ [] : [_679524 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _679526 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (8007 ^ _393467) ^ [_680305, _680307] : [8008 ^ _393467 : [(8009 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _680305))], (8011 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _680307))]], -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _680305), _680307))))], (7997 ^ _393467) ^ [_680029, _680031] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _680029), _680031))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _680029))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _680031)))], (8015 ^ _393467) ^ [_680600, _680602] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _680600), c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _680600), _680602)))))], (8017 ^ _393467) ^ [_680707, _680709] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _680707), c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _680709), _680707)))))], (8019 ^ _393467) ^ [_680858, _680860] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _680858), _680860)), -(_680860 = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _680858), 8022 ^ [_680858, _680860])))], (8026 ^ _393467) ^ [_681111, _681113] : [8027 ^ _393467 : [(8028 ^ _393467) ^ [_681194] : [_681113 = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _681111), _681194))]], -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _681111), _681113)))], (8032 ^ _393467) ^ [_681356, _681358] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _681356), c_Nat_OSuc(_681358)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _681356), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _681356), _681358)))], (8034 ^ _393467) ^ [_681470, _681472] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_681470)), _681472) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _681472), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _681470), _681472)))], (8036 ^ _393467) ^ [_681570] : [-(c_Nat_OSuc(_681570) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _681570))], (8038 ^ _393467) ^ [_681653] : [-(c_Nat_OSuc(_681653) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _681653), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (8040 ^ _393467) ^ [_681753, _681755] : [-(hAPP(c_Complex_ORe, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex), _681753), _681755)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), hAPP(c_Complex_ORe, _681753)), hAPP(c_Complex_ORe, _681755)))], (8042 ^ _393467) ^ [_681868, _681870] : [-(hAPP(c_Complex_OIm, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex), _681868), _681870)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), hAPP(c_Complex_OIm, _681868)), hAPP(c_Complex_OIm, _681870)))], (8044 ^ _393467) ^ [_681983, _681985] : [-(c_RealDef_Oreal(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _681983), _681985)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _681983)), c_RealDef_Oreal(tc_Nat_Onat, _681985)))], (8046 ^ _393467) ^ [_682098, _682100] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _682098)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex), _682098), _682100))), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _682100)))))], (8048 ^ _393467) ^ [_682232, _682234, _682236] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _682232), _682234)), _682236) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _682232), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _682234), _682236)))], (8050 ^ _393467) ^ [_682367, _682369] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _682367)), -(c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), _682367), c_RealDef_Oreal(tc_Nat_Onat, _682369))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_RComplete_Onatfloor(_682367)), _682369))], (8056 ^ _393467) ^ [_682619, _682621] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_RComplete_Onatfloor(_682619)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _682621)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _682619), c_RealDef_Oreal(tc_Nat_Onat, _682621))))], (8062 ^ _393467) ^ [_682871, _682873] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _682871)), -(c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), _682871), c_RealDef_Oreal(tc_Nat_Onat, _682873))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_RComplete_Onatceiling(_682871)), _682873))], (8068 ^ _393467) ^ [_683109] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _683109)), -(c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), _683109), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_RComplete_Onatfloor(_683109)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (8074 ^ _393467) ^ [_683349, _683351] : [-(_683349 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), -(_683351 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(hAPP(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), _683349), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), 8081 ^ [_683349, _683351]), _683351))))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))], (8085 ^ _393467) ^ [_683780, _683782] : [-(hBOOL(hAPP(_683780, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_683780, _683782)), 8093 ^ _393467 : [(8094 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, 8092 ^ [_683780, _683782]), _683782)))], (8102 ^ _393467) ^ [] : [-(hBOOL(hAPP(_683780, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 8092 ^ [_683780, _683782]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (8096 ^ _393467) ^ [_684240] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _684240), 8092 ^ [_683780, _683782])), hBOOL(hAPP(_683780, _684240))]]], (8104 ^ _393467) ^ [_684548, _684550] : [-(c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(_684548))), _684550)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Complex_Ocis(_684550)), c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _684548)), _684550))))], (8106 ^ _393467) ^ [_684660] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _684660), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _684660)], (8108 ^ _393467) ^ [_684744] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _684744) = _684744)], (8110 ^ _393467) ^ [_684854, _684856] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _684854)), 8113 ^ _393467 : [(8114 ^ _393467) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _684854), _684856) = c_Groups_Oone__class_Oone(tc_Int_Oint), 8117 ^ _393467 : [(8118 ^ _393467) ^ [] : [-(_684854 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (8120 ^ _393467) ^ [] : [-(_684856 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (8122 ^ _393467) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _684854), _684856) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _684854 = c_Groups_Oone__class_Oone(tc_Int_Oint), _684856 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (8132 ^ _393467) ^ [_685493, _685495, _685497] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _685493), _685495)), _685497) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _685493), _685497)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _685495), _685497)))], (8134 ^ _393467) ^ [_685633, _685635, _685637] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _685633), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _685635), _685637)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _685633), _685635)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _685633), _685637)))], (8136 ^ _393467) ^ [_685788, _685790, _685792] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _685788), _685790)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _685792)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _685792), _685788)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _685792), _685790))))], (8146 ^ _393467) ^ [_686130, _686132] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _686130), _686132) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _686132), _686130))], (8148 ^ _393467) ^ [_686250, _686252, _686254] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _686250), _686252)), _686254) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _686250), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _686252), _686254)))], (8150 ^ _393467) ^ [_686370, _686372] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Complex_Ocis(_686370)), _686372) = c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _686372)), _686370)))], (8152 ^ _393467) ^ [_686483, _686485] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Complex_Ocis(_686483)), c_Complex_Ocis(_686485)) = c_Complex_Ocis(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), _686483), _686485)))], (8154 ^ _393467) ^ [] : [-(c_Complex_Ocis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))], (8156 ^ _393467) ^ [_686662, _686664, _686666] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Complex_Orcis(_686662, _686664)), _686666) = c_Complex_Orcis(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _686662), _686666), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _686666)), _686664)))], (8158 ^ _393467) ^ [] : [-(c_Complex_Oexpi(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))], (8160 ^ _393467) ^ [_686838, _686840] : [-(c_Transcendental_Ocos(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _686838)), _686840)) = hAPP(c_Complex_ORe, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Complex_Ocis(_686840)), _686838)))], (8162 ^ _393467) ^ [_686939] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _686939)), _686939) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (8164 ^ _393467) ^ [_687084, _687086] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _687084), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _687086), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _687084), _687086)))], (8170 ^ _393467) ^ [_687278, _687280] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _687278), _687280)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _687278), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _687280), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (8176 ^ _393467) ^ [_687551, _687553] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _687551), c_Groups_Oone__class_Oone(tc_Int_Oint))), _687553)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _687551), _687553)))], (8182 ^ _393467) ^ [_687745, _687747] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _687745), _687747)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _687745), c_Groups_Oone__class_Oone(tc_Int_Oint))), _687747)))], (8188 ^ _393467) ^ [_687989, _687991] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _687989), _687991)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _687989), c_Groups_Oone__class_Oone(tc_Int_Oint))), _687991)))], (8204 ^ _393467) ^ [_688544, _688546] : [8205 ^ _393467 : [(8206 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _688544), _688546))], (8208 ^ _393467) ^ [] : [_688544 = _688546]], -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _688544), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _688546), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (8194 ^ _393467) ^ [_688260, _688262] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _688260), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _688262), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _688260), _688262))), -(_688260 = _688262)], (8212 ^ _393467) ^ [_688848] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _688848)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _688848))))], (8218 ^ _393467) ^ [_689081] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _689081)), _689081)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _689081), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (8224 ^ _393467) ^ [_689275] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _689275), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _689275)), _689275)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (8230 ^ _393467) ^ [_689490] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _689490), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _689490)], (8232 ^ _393467) ^ [_689574] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _689574) = _689574)], (8234 ^ _393467) ^ [_689683, _689685, _689687] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _689683), _689685)), _689687) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _689683), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _689685), _689687)))], (8236 ^ _393467) ^ [_689817, _689819, _689821] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _689817), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _689819), _689821)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _689819), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _689817), _689821)))], (8238 ^ _393467) ^ [_689937, _689939] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _689937), _689939) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _689939), _689937))], (8240 ^ _393467) ^ [_690072, _690074, _690076] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _690072), _690074)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _690076), _690072)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _690076), _690074))))], (8246 ^ _393467) ^ [_690360, _690362, _690364, _690366] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _690360), _690362)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _690364), _690366)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _690360), _690364)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _690362), _690366))))], (8256 ^ _393467) ^ [_690747, _690749, _690751] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _690747), _690749)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _690747), _690751)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _690749), _690751))))], (8262 ^ _393467) ^ [_690992, _690994] : [-(hAPP(c_Complex_ORe, c_Complex_Orcis(_690992, _690994)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _690992), c_Transcendental_Ocos(_690994)))], (8264 ^ _393467) ^ [_691086] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Transcendental_Ocos(_691086)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))], (8266 ^ _393467) ^ [] : [-(c_Transcendental_Ocos(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (8268 ^ _393467) ^ [_691282, _691284] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _691282), _691284)), 8271 ^ _393467 : [(8272 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _691282), _691284)))], (8274 ^ _393467) ^ [] : [_691282 = _691284]]], (8276 ^ _393467) ^ [_691540, _691542] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _691540), _691542))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _691540), _691542)), -(_691540 = _691542)], (8286 ^ _393467) ^ [_691864, _691866] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _691864), _691866))), -(_691864 = _691866), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _691866), _691864)))], (8296 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (8298 ^ _393467) ^ [_692253] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint)), _692253)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _692253)))], (8304 ^ _393467) ^ [_692417] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _692417)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint)), _692417)))], (8310 ^ _393467) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (8312 ^ _393467) ^ [_692654] : [-(hAPP(c_Complex_ORe, c_Complex_Ocis(_692654)) = c_Transcendental_Ocos(_692654))], (8314 ^ _393467) ^ [_692739] : [-(c_Complex_Ocis(_692739) = c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _692739))], (8316 ^ _393467) ^ [_692822] : [-(c_Complex_Orcis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _692822) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))], (8318 ^ _393467) ^ [_692945, _692947, _692949, _692951] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Complex_Orcis(_692945, _692947)), c_Complex_Orcis(_692949, _692951)) = c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _692945), _692949), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), _692947), _692951)))], (8320 ^ _393467) ^ [_693070, _693072] : [-(c_Complex_Oexpi(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex), _693070), _693072)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Complex_Oexpi(_693070)), c_Complex_Oexpi(_693072)))], (8322 ^ _393467) ^ [_693211, _693213, _693215] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _693211)), _693211 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _693213), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _693211), _693215)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _693213)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _693215), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (8336 ^ _393467) ^ [_693669, _693671, _693673] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _693669)), _693669 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _693671), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _693669), _693673)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _693671), _693669)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint)), _693673)))], (8350 ^ _393467) ^ [_694127, _694129, _694131] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _694127), _694129)), _694131))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _694131), _694127)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _694127)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _694129)))], (8364 ^ _393467) ^ [_694546] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _694546), _694546)))], (8366 ^ _393467) ^ [_694658, _694660] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _694658), _694660))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _694660), _694658)))], (8372 ^ _393467) ^ [_694903, _694905, _694907] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _694903), _694905)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _694905), _694907)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _694903), _694907)))], (8382 ^ _393467) ^ [_695242, _695244] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _695242), _695244)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _695244), _695242)), -(_695242 = _695244)], (8392 ^ _393467) ^ [_695617, _695619, _695621, _695623, _695625, _695627] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _695617), _695619)), _695621) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _695623), _695625)), _695627), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _695623), _695625)), _695627)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _695621), _695617)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _695627)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _695623)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _695623), _695617)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _695625), _695619)))], (8418 ^ _393467) ^ [_696538, _696540, _696542, _696544, _696546] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _696538), _696540)), _696542)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _696538), _696544)), _696546))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _696546), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _696538), _696546)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _696538), _696542)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _696544), _696540)))], (8436 ^ _393467) ^ [_697223, _697225, _697227, _697229, _697231, _697233] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _697223), _697225)), _697227) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _697229), _697231)), _697233), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _697229), _697231)), _697233))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _697233), _697229)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _697227)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _697229)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _697229), _697223)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _697225), _697231)))], (8462 ^ _393467) ^ [_698138, _698140, _698142, _698144, _698146] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _698138), _698140)), _698142)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _698138), _698144)), _698146))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _698142)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _698142), _698138)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _698146), _698138)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _698140), _698144)))], (8480 ^ _393467) ^ [_698775, _698777, _698779] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _698775), _698777)), _698779)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _698779)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _698775)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _698777), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (8494 ^ _393467) ^ [_699229, _699231] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _699229)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _699229), _699231))))], (8500 ^ _393467) ^ [_699459, _699461] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _699459)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _699461)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _699459), _699461))))], (8510 ^ _393467) ^ [_699782, _699784] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _699782)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _699784)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _699782), _699784))))], (8520 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (8522 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (8524 ^ _393467) ^ [_700196, _700198] : [-(c_Transcendental_Osin(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _700196)), _700198)) = hAPP(c_Complex_OIm, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), c_Complex_Ocis(_700198)), _700196)))], (8526 ^ _393467) ^ [_700327, _700329] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _700327)), 8530 ^ _393467 : [(8531 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 8529 ^ [_700327, _700329])))], (8533 ^ _393467) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), 8529 ^ [_700327, _700329]), c_Nat_OSuc(_700329)) = _700327)]]], (8535 ^ _393467) ^ [] : [-(c_Transcendental_Osin(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (8537 ^ _393467) ^ [_700740] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Transcendental_Osin(_700740)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))], (8539 ^ _393467) ^ [_700825] : [-(hAPP(c_Complex_OIm, c_Complex_Ocis(_700825)) = c_Transcendental_Osin(_700825))], (8541 ^ _393467) ^ [_700925] : [c_Transcendental_Ocos(_700925) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal), -(c_Transcendental_Osin(_700925) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (8547 ^ _393467) ^ [_701122, _701124] : [-(c_Transcendental_Osin(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), _701122), _701124)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Transcendental_Osin(_701122)), c_Transcendental_Ocos(_701124))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Transcendental_Ocos(_701122)), c_Transcendental_Osin(_701124))))], (8549 ^ _393467) ^ [_701250, _701252] : [-(hAPP(c_Complex_OIm, c_Complex_Orcis(_701250, _701252)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _701250), c_Transcendental_Osin(_701252)))], (8551 ^ _393467) ^ [_701344] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Transcendental_Ocos(_701344)), c_Transcendental_Ocos(_701344))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Transcendental_Osin(_701344)), c_Transcendental_Osin(_701344))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (8553 ^ _393467) ^ [_701491, _701493, _701495] : [class_Groups_Omonoid__mult(_701491), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _701493)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_701491), hAPP(hAPP(c_Power_Opower__class_Opower(_701491), _701495), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _701493, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _701495) = hAPP(hAPP(c_Power_Opower__class_Opower(_701491), _701495), _701493))], (8563 ^ _393467) ^ [_701872, _701874, _701876] : [class_Power_Opower(_701872), 8566 ^ _393467 : [(8567 ^ _393467) ^ [] : [_701874 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_701872), _701876), _701874) = c_Groups_Oone__class_Oone(_701872))], (8573 ^ _393467) ^ [] : [-(_701874 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_701872), _701876), _701874) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_701872), _701876), hAPP(hAPP(c_Power_Opower__class_Opower(_701872), _701876), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _701874, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (8579 ^ _393467) ^ [_702442, _702444, _702446] : [class_Groups_Oordered__ab__group__add(_702442), 8582 ^ _393467 : [(8583 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_702442, _702444), _702446)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_702442, c_Groups_Ominus__class_Ominus(_702442, _702444, _702446)), c_Groups_Ozero__class_Ozero(_702442))))], (8589 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_702442, c_Groups_Ominus__class_Ominus(_702442, _702444, _702446)), c_Groups_Ozero__class_Ozero(_702442))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_702442, _702444), _702446)))]]], (8595 ^ _393467) ^ [_702978, _702980, _702982] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _702978), _702980)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _702978), _702982)), 8602 ^ _393467 : [(8603 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _702980, _702978)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _702982, _702978))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _702980), _702982)))], (8609 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _702980), _702982)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _702980, _702978)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _702982, _702978))))]]], (8615 ^ _393467) ^ [_703635, _703637, _703639] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _703635), _703637)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _703635), _703639)), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _703637, _703635), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _703639, _703635)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _703637, _703639))], (8625 ^ _393467) ^ [_704010, _704012, _704014] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _704010), _704012)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _704010), _704014)), 8632 ^ _393467 : [(8633 ^ _393467) ^ [] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _704012, _704010) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _704014, _704010), -(_704012 = _704014)], (8639 ^ _393467) ^ [] : [_704012 = _704014, -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _704012, _704010) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _704014, _704010))]]], (8645 ^ _393467) ^ [_704623, _704625] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _704623), _704625)), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _704625, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _704625, _704623)) = _704623)], (8651 ^ _393467) ^ [_704873, _704875, _704877] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _704873), _704875)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _704873, _704877)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _704875, _704877))))], (8657 ^ _393467) ^ [_705139, _705141, _705143] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _705139), _705141)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _705143, _705141)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _705143, _705139))))], (8663 ^ _393467) ^ [_705376, _705378] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _705376, _705378)), _705376)))], (8665 ^ _393467) ^ [_705536, _705538, _705540, _705542, _705544] : [class_Groups_Oordered__ab__group__add(_705536), c_Groups_Ominus__class_Ominus(_705536, _705538, _705540) = c_Groups_Ominus__class_Ominus(_705536, _705542, _705544), 8672 ^ _393467 : [(8673 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_705536, _705538), _705540)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_705536, _705542), _705544)))], (8679 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_705536, _705542), _705544)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_705536, _705538), _705540)))]]], (8685 ^ _393467) ^ [_706203, _706205, _706207] : [class_RealVector_Oreal__normed__vector(_706203), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_706203, _706205), c_RealVector_Onorm__class_Onorm(_706203, _706207))), c_RealVector_Onorm__class_Onorm(_706203, c_Groups_Ominus__class_Ominus(_706203, _706205, _706207)))))], (8691 ^ _393467) ^ [_706446, _706448] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _706446, _706448)), c_Nat_OSuc(_706446))))], (8693 ^ _393467) ^ [_706551, _706553] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _706551, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _706551), _706553)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8695 ^ _393467) ^ [_706670, _706672] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _706670), _706672)), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _706670, _706672) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8701 ^ _393467) ^ [_706927, _706929] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _706927, _706929) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _706927), _706929)))], (8707 ^ _393467) ^ [_707107, _707109] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _707107), _707109)), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _707107, _707109) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8713 ^ _393467) ^ [_707337, _707339] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _707337), _707339)), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_707339), _707337) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _707339, _707337)))], (8719 ^ _393467) ^ [_707624, _707626, _707628] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _707624), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _707626, _707628))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _707624), _707628)), _707626)))], (8725 ^ _393467) ^ [_707832, _707834, _707836] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _707832), _707836)), _707834)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _707832), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _707834, _707836))))], (8731 ^ _393467) ^ [_708090, _708092] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _708090), _708092))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _708092), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _708090, _708092)) = _708090)], (8737 ^ _393467) ^ [_708347, _708349, _708351] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _708347), _708349)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _708347), _708351)), 8744 ^ _393467 : [(8745 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _708349, _708347)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _708351, _708347))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _708349), _708351)))], (8751 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _708349), _708351)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _708349, _708347)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _708351, _708347))))]]], (8757 ^ _393467) ^ [_709004, _709006, _709008] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _709004), _709006)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _709008), _709004)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _709004, _709008)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _709006, _709008))))], (8767 ^ _393467) ^ [_709373, _709375, _709377] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _709373), _709375)), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _709377, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _709375, _709373)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _709377), _709373), _709375))], (8773 ^ _393467) ^ [_709678, _709680, _709682] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _709678, _709680)), _709682)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _709678), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _709682), _709680))))], (8779 ^ _393467) ^ [_709886, _709888, _709890] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _709886), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _709890), _709888))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _709886, _709888)), _709890)))], (8785 ^ _393467) ^ [_710158, _710160, _710162] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _710158), _710160)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _710162), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _710160), _710162), _710158))))], (8791 ^ _393467) ^ [_710414, _710416] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _710414), _710416)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _710414), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _710416, _710414)) = _710416)], (8797 ^ _393467) ^ [_710668, _710670, _710672] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _710668), _710670)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _710672), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _710670, _710668)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _710672), _710670), _710668))], (8803 ^ _393467) ^ [_710948, _710950, _710952] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _710948), _710950)), 8806 ^ _393467 : [(8807 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _710952), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _710950, _710948))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _710952), _710948)), _710950)))], (8813 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _710952), _710948)), _710950)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _710952), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _710950, _710948))))]]], (8819 ^ _393467) ^ [_711494, _711496] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _711494), _711496)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _711496, _711494)), _711494) = _711496)], (8825 ^ _393467) ^ [_711748, _711750, _711752] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _711748), _711750)), 8828 ^ _393467 : [(8829 ^ _393467) ^ [] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _711750, _711748) = _711752, -(_711750 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _711752), _711748))], (8835 ^ _393467) ^ [] : [_711750 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _711752), _711748), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _711750, _711748) = _711752)]]], (8841 ^ _393467) ^ [_712278, _712280, _712282] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _712278), _712280)), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _712282), _712280), _712278) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _712282), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _712280, _712278)))], (8847 ^ _393467) ^ [_712558, _712560, _712562] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _712558), _712560)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _712560, _712558)), _712562) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _712560), _712562), _712558))], (8853 ^ _393467) ^ [_712838, _712840, _712842] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _712838), _712840)), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _712840), _712842), _712838) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _712840, _712838)), _712842))], (8859 ^ _393467) ^ [_713075] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_713075), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _713075)], (8861 ^ _393467) ^ [_713173, _713175] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _713173, c_Nat_OSuc(_713175)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _713173, c_Groups_Oone__class_Oone(tc_Nat_Onat)), _713175))], (8863 ^ _393467) ^ [_713324, _713326, _713328, _713330] : [class_RealVector_Oreal__normed__algebra(_713324), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_713324), c_Groups_Ominus__class_Ominus(_713324, _713326, _713328)), _713330) = c_Groups_Ominus__class_Ominus(_713324, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_713324), _713326), _713330), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_713324), _713328), _713330)))], (8869 ^ _393467) ^ [_713636, _713638, _713640, _713642] : [class_RealVector_Oreal__normed__algebra(_713636), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_713636), c_Groups_Ominus__class_Ominus(_713636, _713638, _713640)), _713642) = c_Groups_Ominus__class_Ominus(_713636, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_713636), _713638), _713642), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_713636), _713640), _713642)))], (8875 ^ _393467) ^ [_713948, _713950, _713952, _713954] : [class_RealVector_Oreal__normed__algebra(_713948), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_713948), _713950), c_Groups_Ominus__class_Ominus(_713948, _713952, _713954)) = c_Groups_Ominus__class_Ominus(_713948, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_713948), _713950), _713952), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_713948), _713950), _713954)))], (8881 ^ _393467) ^ [_714260, _714262, _714264, _714266] : [class_RealVector_Oreal__normed__algebra(_714260), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_714260), _714262), c_Groups_Ominus__class_Ominus(_714260, _714264, _714266)) = c_Groups_Ominus__class_Ominus(_714260, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_714260), _714262), _714264), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_714260), _714262), _714266)))], (8887 ^ _393467) ^ [_714543, _714545, _714547] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _714543, _714545)), _714547) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _714543), _714547), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _714545), _714547)))], (8889 ^ _393467) ^ [_714679, _714681, _714683] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _714679), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _714681, _714683)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _714679), _714681), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _714679), _714683)))], (8891 ^ _393467) ^ [_714830, _714832, _714834] : [class_RealVector_Oreal__normed__vector(_714830), -(c_RealVector_Onorm__class_Onorm(_714830, c_Groups_Ominus__class_Ominus(_714830, _714832, _714834)) = c_RealVector_Onorm__class_Onorm(_714830, c_Groups_Ominus__class_Ominus(_714830, _714834, _714832)))], (8897 ^ _393467) ^ [_715057, _715059] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_715057), c_Nat_OSuc(_715059)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _715057, _715059))], (8899 ^ _393467) ^ [_715177, _715179, _715181] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_715177), _715179), c_Nat_OSuc(_715181)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _715177, _715179), _715181))], (8901 ^ _393467) ^ [_715350, _715352, _715354, _715356, _715358] : [class_Groups_Ominus(_715350), -(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_715352, _715350), _715354, _715356), _715358) = c_Groups_Ominus__class_Ominus(_715350, hAPP(_715354, _715358), hAPP(_715356, _715358)))], (8907 ^ _393467) ^ [_715658, _715660, _715662, _715664, _715666] : [class_Groups_Oab__group__add(_715658), c_Groups_Ominus__class_Ominus(_715658, _715660, _715662) = c_Groups_Ominus__class_Ominus(_715658, _715664, _715666), 8914 ^ _393467 : [(8915 ^ _393467) ^ [] : [_715660 = _715662, -(_715664 = _715666)], (8921 ^ _393467) ^ [] : [_715664 = _715666, -(_715660 = _715662)]]], (8927 ^ _393467) ^ [_716280, _716282, _716284] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _716280, _716282), _716284) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _716280, _716284), _716282))], (8929 ^ _393467) ^ [_716449, _716451, _716453, _716455, _716457] : [class_Groups_Ominus(_716449), -(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_716451, _716449), _716453, _716455), _716457) = c_Groups_Ominus__class_Ominus(_716449, hAPP(_716453, _716457), hAPP(_716455, _716457)))], (8935 ^ _393467) ^ [_716744, _716746] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _716744, _716746))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _716746), _716744)))], (8941 ^ _393467) ^ [_716928, _716930] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _716930), _716928)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _716928, _716930))))], (8947 ^ _393467) ^ [_717162, _717164] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _717162)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _717164)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _717164, _717162)), _717164)))], (8957 ^ _393467) ^ [_717501, _717503, _717505] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _717501), _717503)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _717501), _717505)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _717505, _717503)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _717505, _717501))))], (8967 ^ _393467) ^ [_717870, _717872, _717874] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _717870), _717872)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _717870, _717874)), _717872)))], (8973 ^ _393467) ^ [_718156, _718158, _718160, _718162, _718164] : [class_Groups_Oordered__ab__group__add(_718156), c_Groups_Ominus__class_Ominus(_718156, _718158, _718160) = c_Groups_Ominus__class_Ominus(_718156, _718162, _718164), 8980 ^ _393467 : [(8981 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_718156, _718158), _718160)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_718156, _718162), _718164)))], (8987 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_718156, _718162), _718164)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_718156, _718158), _718160)))]]], (8993 ^ _393467) ^ [_718823, _718825, _718827] : [class_Groups_Ogroup__add(_718823), 8996 ^ _393467 : [(8997 ^ _393467) ^ [] : [c_Groups_Ominus__class_Ominus(_718823, _718825, _718827) = c_Groups_Ozero__class_Ozero(_718823), -(_718825 = _718827)], (9003 ^ _393467) ^ [] : [_718825 = _718827, -(c_Groups_Ominus__class_Ominus(_718823, _718825, _718827) = c_Groups_Ozero__class_Ozero(_718823))]]], (9009 ^ _393467) ^ [_719329, _719331, _719333] : [class_Groups_Oab__group__add(_719329), 9012 ^ _393467 : [(9013 ^ _393467) ^ [] : [_719331 = _719333, -(c_Groups_Ominus__class_Ominus(_719329, _719331, _719333) = c_Groups_Ozero__class_Ozero(_719329))], (9019 ^ _393467) ^ [] : [c_Groups_Ominus__class_Ominus(_719329, _719331, _719333) = c_Groups_Ozero__class_Ozero(_719329), -(_719331 = _719333)]]], (9025 ^ _393467) ^ [_719821, _719823] : [class_Groups_Ogroup__add(_719821), -(c_Groups_Ominus__class_Ominus(_719821, _719823, _719823) = c_Groups_Ozero__class_Ozero(_719821))], (9031 ^ _393467) ^ [_720041, _720043] : [class_Groups_Ogroup__add(_720041), -(c_Groups_Ominus__class_Ominus(_720041, _720043, c_Groups_Ozero__class_Ozero(_720041)) = _720043)], (9037 ^ _393467) ^ [_720232] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _720232) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9039 ^ _393467) ^ [_720314] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _720314, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _720314)], (9041 ^ _393467) ^ [_720396] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _720396, _720396) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9043 ^ _393467) ^ [_720507, _720509] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _720507, _720509) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _720509, _720507) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_720507 = _720509)], (9053 ^ _393467) ^ [_720864, _720866, _720868, _720870, _720872] : [class_Rings_Oring(_720864), -(c_Groups_Ominus__class_Ominus(_720864, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_720864), _720866), _720868), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_720864), _720870), _720872)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_720864), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_720864), _720866), c_Groups_Ominus__class_Ominus(_720864, _720868, _720872))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_720864), c_Groups_Ominus__class_Ominus(_720864, _720866, _720870)), _720872)))], (9059 ^ _393467) ^ [_721236, _721238, _721240, _721242, _721244] : [class_RealVector_Oreal__normed__algebra(_721236), -(c_Groups_Ominus__class_Ominus(_721236, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_721236), _721238), _721240), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_721236), _721242), _721244)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_721236), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_721236), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_721236), c_Groups_Ominus__class_Ominus(_721236, _721238, _721242)), c_Groups_Ominus__class_Ominus(_721236, _721240, _721244))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_721236), c_Groups_Ominus__class_Ominus(_721236, _721238, _721242)), _721244))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_721236), _721242), c_Groups_Ominus__class_Ominus(_721236, _721240, _721244))))], (9065 ^ _393467) ^ [_721670, _721672, _721674, _721676, _721678, _721680] : [class_Rings_Oring(_721670), 9068 ^ _393467 : [(9069 ^ _393467) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_721670), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_721670), _721672), _721674)), _721676) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_721670), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_721670), _721678), _721674)), _721680), -(_721676 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_721670), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_721670), c_Groups_Ominus__class_Ominus(_721670, _721678, _721672)), _721674)), _721680))], (9075 ^ _393467) ^ [] : [_721676 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_721670), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_721670), c_Groups_Ominus__class_Ominus(_721670, _721678, _721672)), _721674)), _721680), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_721670), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_721670), _721672), _721674)), _721676) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_721670), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_721670), _721678), _721674)), _721680))]]], (9081 ^ _393467) ^ [_722404, _722406, _722408, _722410, _722412, _722414] : [class_Rings_Oring(_722404), 9084 ^ _393467 : [(9085 ^ _393467) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_722404), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_722404), _722406), _722408)), _722410) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_722404), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_722404), _722412), _722408)), _722414), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_722404), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_722404), c_Groups_Ominus__class_Ominus(_722404, _722406, _722412)), _722408)), _722410) = _722414)], (9091 ^ _393467) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_722404), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_722404), c_Groups_Ominus__class_Ominus(_722404, _722406, _722412)), _722408)), _722410) = _722414, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_722404), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_722404), _722406), _722408)), _722410) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_722404), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_722404), _722412), _722408)), _722414))]]], (9097 ^ _393467) ^ [_723096, _723098, _723100] : [class_Groups_Oordered__ab__group__add(_723096), 9100 ^ _393467 : [(9101 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_723096, _723098), _723100)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_723096, c_Groups_Ominus__class_Ominus(_723096, _723098, _723100)), c_Groups_Ozero__class_Ozero(_723096))))], (9107 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_723096, c_Groups_Ominus__class_Ominus(_723096, _723098, _723100)), c_Groups_Ozero__class_Ozero(_723096))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_723096, _723098), _723100)))]]], (9113 ^ _393467) ^ [_723617, _723619, _723621] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _723617), _723619), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _723621), _723619)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _723617, _723621))], (9115 ^ _393467) ^ [_723747, _723749, _723751] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _723747), _723749), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _723747), _723751)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _723749, _723751))], (9117 ^ _393467) ^ [_723877, _723879, _723881] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _723877, _723879), _723881) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _723877, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _723879), _723881)))], (9119 ^ _393467) ^ [_723991, _723993] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _723991), _723993), _723991) = _723993)], (9121 ^ _393467) ^ [_724095, _724097] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _724095), _724097), _724097) = _724095)], (9123 ^ _393467) ^ [_724228, _724230, _724232] : [class_Groups_Ogroup__add(_724228), -(c_Groups_Ominus__class_Ominus(_724228, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_724228), _724230), _724232), _724232) = _724230)], (9129 ^ _393467) ^ [_724480, _724482, _724484] : [class_Groups_Ogroup__add(_724480), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_724480), c_Groups_Ominus__class_Ominus(_724480, _724482, _724484)), _724484) = _724482)], (9135 ^ _393467) ^ [_724774, _724776, _724778, _724780, _724782, _724784] : [class_Rings_Oordered__ring(_724774), 9138 ^ _393467 : [(9139 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_724774, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_724774), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_724774), _724776), _724778)), _724780)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_724774), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_724774), _724782), _724778)), _724784))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_724774, _724780), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_724774), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_724774), c_Groups_Ominus__class_Ominus(_724774, _724782, _724776)), _724778)), _724784))))], (9145 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_724774, _724780), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_724774), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_724774), c_Groups_Ominus__class_Ominus(_724774, _724782, _724776)), _724778)), _724784))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_724774, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_724774), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_724774), _724776), _724778)), _724780)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_724774), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_724774), _724782), _724778)), _724784))))]]], (9151 ^ _393467) ^ [_725538, _725540, _725542, _725544, _725546, _725548] : [class_Rings_Oordered__ring(_725538), 9154 ^ _393467 : [(9155 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_725538, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_725538), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_725538), _725540), _725542)), _725544)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_725538), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_725538), _725546), _725542)), _725548))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_725538, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_725538), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_725538), c_Groups_Ominus__class_Ominus(_725538, _725540, _725546)), _725542)), _725544)), _725548)))], (9161 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_725538, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_725538), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_725538), c_Groups_Ominus__class_Ominus(_725538, _725540, _725546)), _725542)), _725544)), _725548)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_725538, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_725538), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_725538), _725540), _725542)), _725544)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_725538), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_725538), _725546), _725542)), _725548))))]]], (9167 ^ _393467) ^ [_726302, _726304, _726306, _726308, _726310, _726312] : [class_Rings_Oordered__ring(_726302), 9170 ^ _393467 : [(9171 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_726302, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_726302), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_726302), _726304), _726306)), _726308)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_726302), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_726302), _726310), _726306)), _726312))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_726302, _726308), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_726302), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_726302), c_Groups_Ominus__class_Ominus(_726302, _726310, _726304)), _726306)), _726312))))], (9177 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_726302, _726308), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_726302), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_726302), c_Groups_Ominus__class_Ominus(_726302, _726310, _726304)), _726306)), _726312))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_726302, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_726302), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_726302), _726304), _726306)), _726308)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_726302), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_726302), _726310), _726306)), _726312))))]]], (9183 ^ _393467) ^ [_727066, _727068, _727070, _727072, _727074, _727076] : [class_Rings_Oordered__ring(_727066), 9186 ^ _393467 : [(9187 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_727066, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_727066), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_727066), _727068), _727070)), _727072)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_727066), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_727066), _727074), _727070)), _727076))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_727066, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_727066), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_727066), c_Groups_Ominus__class_Ominus(_727066, _727068, _727074)), _727070)), _727072)), _727076)))], (9193 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_727066, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_727066), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_727066), c_Groups_Ominus__class_Ominus(_727066, _727068, _727074)), _727070)), _727072)), _727076)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_727066, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_727066), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_727066), _727068), _727070)), _727072)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_727066), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_727066), _727074), _727070)), _727076))))]]], (9199 ^ _393467) ^ [_727774, _727776] : [class_Rings_Oring__1(_727774), -(c_Groups_Ominus__class_Ominus(_727774, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_727774), _727776), _727776), c_Groups_Oone__class_Oone(_727774)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_727774), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_727774), _727776), c_Groups_Oone__class_Oone(_727774))), c_Groups_Ominus__class_Ominus(_727774, _727776, c_Groups_Oone__class_Oone(_727774))))], (9205 ^ _393467) ^ [_728072, _728074, _728076] : [class_RealVector_Oreal__normed__vector(_728072), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_728072, c_Groups_Ominus__class_Ominus(_728072, _728074, _728076))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_728072, _728074)), c_RealVector_Onorm__class_Onorm(_728072, _728076)))))], (9211 ^ _393467) ^ [_728334, _728336] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _728334)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _728334, c_Nat_OSuc(_728336))), _728334)))], (9217 ^ _393467) ^ [_728556] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _728556)), -(c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _728556, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = _728556)], (9239 ^ _393467) ^ [_729364, _729366, _729368] : [-(hBOOL(hAPP(_729364, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _729366, _729368)))), 9242 ^ _393467 : [(9243 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _729366), _729368)))], (9245 ^ _393467) ^ [] : [hBOOL(hAPP(_729364, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 9247 ^ _393467 : [(9248 ^ _393467) ^ [] : [-(_729366 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _729368), 9246 ^ [_729364, _729366, _729368]))], (9250 ^ _393467) ^ [] : [hBOOL(hAPP(_729364, 9246 ^ [_729364, _729366, _729368]))]]], (9223 ^ _393467) ^ [_728819, _728821, _728823] : [hBOOL(hAPP(_728819, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _728821, _728823))), 9226 ^ _393467 : [(9227 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _728821), _728823)), -(hBOOL(hAPP(_728819, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (9233 ^ _393467) ^ [_729161] : [_728821 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _728823), _729161), -(hBOOL(hAPP(_728819, _729161)))]]], (9270 ^ _393467) ^ [_730553, _730555, _730557] : [-(hBOOL(hAPP(_730553, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _730555, _730557)))), 9273 ^ _393467 : [(9274 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _730555), _730557)))], (9276 ^ _393467) ^ [] : [hBOOL(hAPP(_730553, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 9278 ^ _393467 : [(9279 ^ _393467) ^ [] : [-(_730555 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _730557), 9277 ^ [_730553, _730555, _730557]))], (9281 ^ _393467) ^ [] : [hBOOL(hAPP(_730553, 9277 ^ [_730553, _730555, _730557]))]]], (9254 ^ _393467) ^ [_730000, _730002, _730004] : [hBOOL(hAPP(_730000, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _730002, _730004))), 9257 ^ _393467 : [(9258 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _730002), _730004)), -(hBOOL(hAPP(_730000, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (9264 ^ _393467) ^ [_730348] : [_730002 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _730004), _730348), -(hBOOL(hAPP(_730000, _730348)))]]], (9285 ^ _393467) ^ [_731168, _731170, _731172] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _731168), _731170)), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _731172, c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _731170, _731168))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _731172), _731168), c_Nat_OSuc(_731170)))], (9291 ^ _393467) ^ [_731452, _731454, _731456] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _731452), _731454)), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _731454, _731452)), _731456) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_731454), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _731452), _731456)))], (9297 ^ _393467) ^ [_731764, _731766, _731768, _731770, _731772] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _731764), _731766)), 9300 ^ _393467 : [(9301 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _731766), _731768)), _731770)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _731764), _731768)), _731772))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(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, _731766, _731764)), _731768)), _731770)), _731772)))], (9307 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(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, _731766, _731764)), _731768)), _731770)), _731772)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _731766), _731768)), _731770)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _731764), _731768)), _731772))))]]], (9313 ^ _393467) ^ [_732474, _732476, _732478, _732480, _732482] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _732474), _732476)), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _732476), _732478)), _732480), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _732474), _732478)), _732482)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(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, _732476, _732474)), _732478)), _732480), _732482))], (9319 ^ _393467) ^ [_732850, _732852, _732854, _732856, _732858] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _732850), _732852)), 9322 ^ _393467 : [(9323 ^ _393467) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _732852), _732854)), _732856) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _732850), _732854)), _732858), -(hAPP(hAPP(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, _732852, _732850)), _732854)), _732856) = _732858)], (9329 ^ _393467) ^ [] : [hAPP(hAPP(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, _732852, _732850)), _732854)), _732856) = _732858, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _732852), _732854)), _732856) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _732850), _732854)), _732858))]]], (9335 ^ _393467) ^ [_733530, _733532, _733534, _733536, _733538] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _733530), _733532)), 9338 ^ _393467 : [(9339 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _733530), _733534)), _733536)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _733532), _733534)), _733538))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _733536), hAPP(hAPP(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, _733532, _733530)), _733534)), _733538))))], (9345 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _733536), hAPP(hAPP(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, _733532, _733530)), _733534)), _733538))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _733530), _733534)), _733536)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _733532), _733534)), _733538))))]]], (9351 ^ _393467) ^ [_734240, _734242, _734244, _734246, _734248] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _734240), _734242)), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _734240), _734244)), _734246), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _734242), _734244)), _734248)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _734246, hAPP(hAPP(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, _734242, _734240)), _734244)), _734248)))], (9357 ^ _393467) ^ [_734616, _734618, _734620, _734622, _734624] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _734616), _734618)), 9360 ^ _393467 : [(9361 ^ _393467) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _734616), _734620)), _734622) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _734618), _734620)), _734624), -(_734622 = hAPP(hAPP(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, _734618, _734616)), _734620)), _734624))], (9367 ^ _393467) ^ [] : [_734622 = hAPP(hAPP(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, _734618, _734616)), _734620)), _734624), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _734616), _734620)), _734622) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _734618), _734620)), _734624))]]], (9373 ^ _393467) ^ [_735296, _735298, _735300, _735302, _735304] : [class_RealVector_Oreal__normed__vector(_735296), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_735296, c_Groups_Ominus__class_Ominus(_735296, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_735296), _735298), _735300), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_735296), _735302), _735304)))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_735296, c_Groups_Ominus__class_Ominus(_735296, _735298, _735302))), c_RealVector_Onorm__class_Onorm(_735296, c_Groups_Ominus__class_Ominus(_735296, _735300, _735304))))))], (9379 ^ _393467) ^ [_735646, _735648, _735650, _735652] : [class_Groups_Omonoid__mult(_735646), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _735648), _735650)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_735646), _735652), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_735650), _735648)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_735646), hAPP(hAPP(c_Power_Opower__class_Opower(_735646), _735652), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _735650, _735648))), _735652))], (9389 ^ _393467) ^ [_736027] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _736027)), -(c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _736027, c_Groups_Oone__class_Oone(tc_Nat_Onat))) = _736027)], (9395 ^ _393467) ^ [_736233] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _736233)), -(_736233 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _736233, c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (9401 ^ _393467) ^ [_736473, _736475] : [_736473 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _736473), _736475) = _736475)], (9407 ^ _393467) ^ [_736647, _736649] : [-(_736647 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _736647), _736649) = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _736647, c_Groups_Oone__class_Oone(tc_Nat_Onat))), _736649)))], (9413 ^ _393467) ^ [_736940, _736942, _736944, _736946, _736948] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _736940), _736942)), 9416 ^ _393467 : [(9417 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _736940), _736944)), _736946)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _736942), _736944)), _736948))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _736946), hAPP(hAPP(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, _736942, _736940)), _736944)), _736948))))], (9423 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _736946), hAPP(hAPP(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, _736942, _736940)), _736944)), _736948))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _736940), _736944)), _736946)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _736942), _736944)), _736948))))]]], (9429 ^ _393467) ^ [_737650, _737652, _737654, _737656, _737658] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _737650), _737652)), 9432 ^ _393467 : [(9433 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _737652), _737654)), _737656)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _737650), _737654)), _737658))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(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, _737652, _737650)), _737654)), _737656)), _737658)))], (9439 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(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, _737652, _737650)), _737654)), _737656)), _737658)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _737652), _737654)), _737656)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _737650), _737654)), _737658))))]]], (9445 ^ _393467) ^ [_738338, _738340] : [_738338 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _738338), _738340) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9451 ^ _393467) ^ [_738512, _738514] : [-(_738512 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _738512), _738514) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _738514), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _738512, c_Groups_Oone__class_Oone(tc_Nat_Onat))), _738514)))], (9457 ^ _393467) ^ [_738791, _738793] : [_738791 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _738793), _738791) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (9463 ^ _393467) ^ [_738965, _738967] : [-(_738965 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _738967), _738965) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _738967), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _738967), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _738965, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (9469 ^ _393467) ^ [_739238, _739240, _739242] : [class_Rings_Ocomm__ring__1(_739238), -(c_Groups_Ominus__class_Ominus(_739238, hAPP(hAPP(c_Power_Opower__class_Opower(_739238), _739240), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(hAPP(c_Power_Opower__class_Opower(_739238), _739242), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_739238), c_Groups_Ominus__class_Ominus(_739238, _739240, _739242)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_739238), _739240), _739242)))], (9475 ^ _393467) ^ [_739518] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _739518)), 9479 ^ _393467 : [(9480 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, 9478 ^ [_739518], c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _739518)))], (9482 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _739518), c_RealDef_Oreal(tc_Nat_Onat, 9478 ^ [_739518]))))]]], (9484 ^ _393467) ^ [_739949, _739951, _739953, _739955] : [class_RealVector_Oreal__normed__vector(_739949), class_Orderings_Oord(_739951), 9494 ^ _393467 : [(9495 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_739951, _739953), 9493 ^ [_739949, _739951, _739953, _739955])))], (9497 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_739949, c_Groups_Ominus__class_Ominus(_739949, hAPP(_739955, _739953), hAPP(_739955, 9493 ^ [_739949, _739951, _739953, _739955])))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))]], 9498 ^ _393467 : [(9499 ^ _393467) ^ [_740538] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_739951, _739953), _740538)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_739949, hAPP(_739955, _740538))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), c_RealVector_Onorm__class_Onorm(_739949, hAPP(_739955, _739953))))))]]], (9505 ^ _393467) ^ [_740865, _740867] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _740865), _740867)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _740865, _740867)), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))], (9511 ^ _393467) ^ [_741055, _741057] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _741055, _741057)), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _741055), _741057)))], (9517 ^ _393467) ^ [_741294, _741296, _741298] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _741294), c_Groups_Ominus__class_Ominus(tc_Int_Oint, _741296, _741298)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _741294), _741296), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _741294), _741298)))], (9519 ^ _393467) ^ [_741430, _741432, _741434] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Ominus__class_Ominus(tc_Int_Oint, _741430, _741432)), _741434) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _741430), _741434), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _741432), _741434)))], (9521 ^ _393467) ^ [_741552, _741554] : [-(hAPP(c_Complex_ORe, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, _741552, _741554)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, hAPP(c_Complex_ORe, _741552), hAPP(c_Complex_ORe, _741554)))], (9523 ^ _393467) ^ [_741663, _741665] : [-(hAPP(c_Complex_OIm, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, _741663, _741665)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, hAPP(c_Complex_OIm, _741663), hAPP(c_Complex_OIm, _741665)))], (9525 ^ _393467) ^ [_741818, _741820] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _741818), _741820)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _741818, _741820)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (9531 ^ _393467) ^ [_742008, _742010] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _742008, _742010)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _742008), _742010)))], (9537 ^ _393467) ^ [_742248, _742250] : [class_Groups_Oab__group__add(_742248), -(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_742248), _742250, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_742248))) = _742250)], (9543 ^ _393467) ^ [_742490, _742492, _742494] : [class_RealVector_Oreal__normed__vector(_742490), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_742490, _742492), c_RealVector_Onorm__class_Onorm(_742490, _742494))), c_RealVector_Onorm__class_Onorm(_742490, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_742490), _742492), _742494)))))], (9549 ^ _393467) ^ [_742785, _742787] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _742785), c_Groups_Ominus__class_Ominus(tc_Int_Oint, _742787, c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _742785), _742787)))], (9555 ^ _393467) ^ [_742975, _742977] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _742975), _742977)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _742975), c_Groups_Ominus__class_Ominus(tc_Int_Oint, _742977, c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (9561 ^ _393467) ^ [_743215, _743217] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _743215), _743217)), -(c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _743217, _743215)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _743217), c_RealDef_Oreal(tc_Nat_Onat, _743215)))], (9567 ^ _393467) ^ [_743454, _743456] : [-(c_Transcendental_Osin(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _743454, _743456)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Transcendental_Osin(_743454)), c_Transcendental_Ocos(_743456)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Transcendental_Ocos(_743454)), c_Transcendental_Osin(_743456))))], (9569 ^ _393467) ^ [_743578, _743580] : [-(c_Transcendental_Osin(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _743578, _743580)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Transcendental_Ocos(_743580)), c_Transcendental_Osin(_743578)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Transcendental_Osin(_743580)), c_Transcendental_Ocos(_743578))))], (9571 ^ _393467) ^ [_743702, _743704] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex), _743702), _743704)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _743702))), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _743704))))], (9573 ^ _393467) ^ [_743820, _743822] : [-(c_Transcendental_Ocos(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), _743820), _743822)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Transcendental_Ocos(_743820)), c_Transcendental_Ocos(_743822)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Transcendental_Osin(_743820)), c_Transcendental_Osin(_743822))))], (9575 ^ _393467) ^ [_743946, _743948] : [-(c_Transcendental_Ocos(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _743946, _743948)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Transcendental_Ocos(_743946)), c_Transcendental_Ocos(_743948))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Transcendental_Osin(_743946)), c_Transcendental_Osin(_743948))))], (9577 ^ _393467) ^ [_744072, _744074] : [-(c_Transcendental_Ocos(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _744072, _744074)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Transcendental_Ocos(_744074)), c_Transcendental_Ocos(_744072))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Transcendental_Osin(_744074)), c_Transcendental_Osin(_744072))))], (9579 ^ _393467) ^ [_744213, _744215] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _744213)), _744215)), -(c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _744215, c_RealDef_Oreal(tc_Nat_Onat, _744213))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_RComplete_Onatfloor(_744215), _744213))], (9585 ^ _393467) ^ [_744440] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _744440, c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatfloor(_744440)))))], (9587 ^ _393467) ^ [_744561, _744563] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _744561)), _744563)), -(c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _744563, c_RealDef_Oreal(tc_Nat_Onat, _744561))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_RComplete_Onatceiling(_744563), _744561))], (9593 ^ _393467) ^ [_744802, _744804] : [-(hAPP(c_Complex_ORe, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), _744802), _744804)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(c_Complex_ORe, _744802)), hAPP(c_Complex_ORe, _744804)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(c_Complex_OIm, _744802)), hAPP(c_Complex_OIm, _744804))))], (9595 ^ _393467) ^ [_744934] : [c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _744934) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex), _744934), c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, _744934, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex), _744934), c_Complex_Oii))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, _744934, c_Complex_Oii))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))], (9613 ^ _393467) ^ [_745506, _745508] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _745506)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _745508)), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _745508), _745506), _745508) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _745508), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _745506, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (9623 ^ _393467) ^ [_745881, _745883, _745885, _745887] : [class_Divides_Osemiring__div(_745881), 9626 ^ _393467 : [(9627 ^ _393467) ^ [] : [_745883 = c_Groups_Ozero__class_Ozero(_745881), -(c_Divides_Odiv__class_Odiv(_745881, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_745881), _745883), _745885), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_745881), _745883), _745887)) = c_Groups_Ozero__class_Ozero(_745881))], (9633 ^ _393467) ^ [] : [-(_745883 = c_Groups_Ozero__class_Ozero(_745881)), -(c_Divides_Odiv__class_Odiv(_745881, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_745881), _745883), _745885), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_745881), _745883), _745887)) = c_Divides_Odiv__class_Odiv(_745881, _745885, _745887))]]], (9639 ^ _393467) ^ [_746491, _746493, _746495] : [class_Divides_Osemiring__div(_746491), -(_746493 = c_Groups_Ozero__class_Ozero(_746491)), -(c_Divides_Odiv__class_Odiv(_746491, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_746491), _746495), _746493), _746493) = _746495)], (9649 ^ _393467) ^ [_746843, _746845, _746847] : [class_Divides_Osemiring__div(_746843), -(_746845 = c_Groups_Ozero__class_Ozero(_746843)), -(c_Divides_Odiv__class_Odiv(_746843, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_746843), _746845), _746847), _746845) = _746847)], (9659 ^ _393467) ^ [_747209, _747211, _747213, _747215] : [class_Divides_Osemiring__div(_747209), -(_747211 = c_Groups_Ozero__class_Ozero(_747209)), -(c_Divides_Odiv__class_Odiv(_747209, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_747209), _747213), _747211), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_747209), _747215), _747211)) = c_Divides_Odiv__class_Odiv(_747209, _747213, _747215))], (9669 ^ _393467) ^ [_747609, _747611, _747613, _747615] : [class_Divides_Osemiring__div(_747609), -(_747611 = c_Groups_Ozero__class_Ozero(_747609)), -(c_Divides_Odiv__class_Odiv(_747609, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_747609), _747611), _747613), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_747609), _747611), _747615)) = c_Divides_Odiv__class_Odiv(_747609, _747613, _747615))], (9679 ^ _393467) ^ [_747967] : [-(_747967 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _747967, _747967) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (9685 ^ _393467) ^ [_748182, _748184] : [class_Divides_Osemiring__div(_748182), -(c_Divides_Odiv__class_Odiv(_748182, _748184, c_Groups_Oone__class_Oone(_748182)) = _748184)], (9691 ^ _393467) ^ [_748402, _748404] : [class_Divides_Osemiring__div(_748402), -(_748404 = c_Groups_Ozero__class_Ozero(_748402)), -(c_Divides_Odiv__class_Odiv(_748402, _748404, _748404) = c_Groups_Oone__class_Oone(_748402))], (9701 ^ _393467) ^ [_748718, _748720] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _748718)), 9704 ^ _393467 : [(9705 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _748720, _748718)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _748720), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (9711 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _748720), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _748720, _748718)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (9717 ^ _393467) ^ [_749224, _749226] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _749224), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 9720 ^ _393467 : [(9721 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _749226, _749224)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _749226)))], (9727 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _749226)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _749226, _749224)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (9733 ^ _393467) ^ [_749727, _749729] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _749727), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _749729)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _749727, _749729)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (9743 ^ _393467) ^ [_750029] : [-(c_Divides_Odiv__class_Odiv(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _750029) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (9745 ^ _393467) ^ [_750140, _750142] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _750140)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _750142)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _750140, _750142))))], (9755 ^ _393467) ^ [_750459, _750461] : [class_Divides_Osemiring__div(_750459), -(c_Divides_Odiv__class_Odiv(_750459, _750461, c_Groups_Ozero__class_Ozero(_750459)) = c_Groups_Ozero__class_Ozero(_750459))], (9761 ^ _393467) ^ [_750683, _750685] : [class_Divides_Osemiring__div(_750683), -(c_Divides_Odiv__class_Odiv(_750683, c_Groups_Ozero__class_Ozero(_750683), _750685) = c_Groups_Ozero__class_Ozero(_750683))], (9767 ^ _393467) ^ [] : [c_Complex_Oii = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)], (9769 ^ _393467) ^ [] : [c_Complex_Oii = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)], (9771 ^ _393467) ^ [] : [-(hAPP(c_Complex_ORe, c_Complex_Oii) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (9773 ^ _393467) ^ [_751078, _751080, _751082] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _751078), _751080)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _751082), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _751080, _751082)), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _751078, _751082))))], (9783 ^ _393467) ^ [_751447, _751449, _751451] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _751447), _751449)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _751451)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _751447, _751451)), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _751449, _751451))))], (9793 ^ _393467) ^ [_751796, _751798] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _751796), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _751798), _751796)), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _751796, _751798) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (9803 ^ _393467) ^ [_752137, _752139, _752141] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _752137), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _752139)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _752139), _752141)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _752137, _752139)), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _752137, _752141))))], (9817 ^ _393467) ^ [_752589, _752591] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _752589), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _752591)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _752589, _752591)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (9827 ^ _393467) ^ [_752920, _752922] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _752920), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 9830 ^ _393467 : [(9831 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _752922, _752920))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _752922), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (9837 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _752922), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _752922, _752920))))]]], (9843 ^ _393467) ^ [_753423, _753425] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _753423)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _753423), _753425)), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _753423, _753425) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (9853 ^ _393467) ^ [_753744, _753746] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _753744)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _753746), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _753744, _753746)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (9863 ^ _393467) ^ [_754089, _754091, _754093] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _754089)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _754091)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _754091), _754093)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _754089, _754093)), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _754089, _754091))))], (9877 ^ _393467) ^ [_754535, _754537] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _754535)), 9880 ^ _393467 : [(9881 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _754535, _754537))), 9884 ^ _393467 : [(9885 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _754537), _754535)))], (9887 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _754537)))]]], (9889 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _754535, _754537)))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _754537), _754535)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _754537))]]], (9899 ^ _393467) ^ [_755196, _755198] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _755196)), 9902 ^ _393467 : [(9903 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _755198, _755196))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _755196), _755198)))], (9909 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _755196), _755198)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _755198, _755196))))]]], (9915 ^ _393467) ^ [_755693, _755695] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _755693)), 9918 ^ _393467 : [(9919 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _755695, _755693))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _755695)))], (9925 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _755695)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _755695, _755693))))]]], (9931 ^ _393467) ^ [_756210, _756212] : [c_Divides_Odiv__class_Odiv(tc_Int_Oint, _756210, _756212) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_756212 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 9940 ^ _393467 : [(9941 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _756210)))], (9943 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _756210), _756212)))]], 9944 ^ _393467 : [(9945 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _756210), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (9947 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _756212), _756210)))]]], (9949 ^ _393467) ^ [_756744, _756746] : [-(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _756744, _756746) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 9950 ^ _393467 : [(9951 ^ _393467) ^ [] : [_756746 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (9953 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _756744)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _756744), _756746))], (9959 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _756744), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _756746), _756744))]]], (9967 ^ _393467) ^ [_757323, _757325] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _757323)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint)), _757325)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _757323, _757325)), _757323)))], (9977 ^ _393467) ^ [_757662, _757664, _757666] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _757662)), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _757664, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _757666), _757662)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _757664, _757666), _757662))], (9983 ^ _393467) ^ [] : [-(hAPP(c_Complex_OIm, c_Complex_Oii) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (9985 ^ _393467) ^ [_757999, _758001, _758003, _758005] : [class_Divides_Osemiring__div(_757999), -(_758001 = c_Groups_Ozero__class_Ozero(_757999)), -(c_Divides_Odiv__class_Odiv(_757999, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_757999), _758003), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_757999), _758001), _758005)), _758001) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_757999), _758005), c_Divides_Odiv__class_Odiv(_757999, _758003, _758001)))], (9995 ^ _393467) ^ [_758415, _758417, _758419, _758421] : [class_Divides_Osemiring__div(_758415), -(_758417 = c_Groups_Ozero__class_Ozero(_758415)), -(c_Divides_Odiv__class_Odiv(_758415, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_758415), _758419), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_758415), _758421), _758417)), _758417) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_758415), _758421), c_Divides_Odiv__class_Odiv(_758415, _758419, _758417)))], (10005 ^ _393467) ^ [_758817, _758819, _758821] : [class_Divides_Osemiring__div(_758817), -(_758819 = c_Groups_Ozero__class_Ozero(_758817)), -(c_Divides_Odiv__class_Odiv(_758817, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_758817), _758821), _758819), _758819) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_758817), c_Divides_Odiv__class_Odiv(_758817, _758821, _758819)), c_Groups_Oone__class_Oone(_758817)))], (10015 ^ _393467) ^ [_759197, _759199, _759201] : [class_Divides_Osemiring__div(_759197), -(_759199 = c_Groups_Ozero__class_Ozero(_759197)), -(c_Divides_Odiv__class_Odiv(_759197, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_759197), _759199), _759201), _759199) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_759197), c_Divides_Odiv__class_Odiv(_759197, _759201, _759199)), c_Groups_Oone__class_Oone(_759197)))], (10025 ^ _393467) ^ [_759591, _759593, _759595, _759597] : [_759591 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _759593), _759595)), _759597), -(_759593 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _759591, _759593) = _759595), 10032 ^ _393467 : [(10033 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _759593)))], (10035 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _759597)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _759597), _759593))]], 10040 ^ _393467 : [(10041 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _759593))], (10043 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _759593), _759597)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _759597), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (10101 ^ _393467) ^ [_762277, _762279, _762281] : [-(hBOOL(hAPP(_762277, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _762279, _762281)))), 10104 ^ _393467 : [(10105 ^ _393467) ^ [] : [-(_762281 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (10107 ^ _393467) ^ [] : [hBOOL(hAPP(_762277, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], 10110 ^ _393467 : [(10111 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _762281)))], (10115 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 10113 ^ [_762277, _762279, _762281])))], (10117 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, 10113 ^ [_762277, _762279, _762281]), _762281)))], (10119 ^ _393467) ^ [] : [-(_762279 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _762281), 10112 ^ [_762277, _762279, _762281])), 10113 ^ [_762277, _762279, _762281]))], (10121 ^ _393467) ^ [] : [hBOOL(hAPP(_762277, 10112 ^ [_762277, _762279, _762281]))]], 10122 ^ _393467 : [(10123 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _762281), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (10127 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _762281), 10125 ^ [_762277, _762279, _762281])))], (10129 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, 10125 ^ [_762277, _762279, _762281]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (10131 ^ _393467) ^ [] : [-(_762279 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _762281), 10124 ^ [_762277, _762279, _762281])), 10125 ^ [_762277, _762279, _762281]))], (10133 ^ _393467) ^ [] : [hBOOL(hAPP(_762277, 10124 ^ [_762277, _762279, _762281]))]]], (10055 ^ _393467) ^ [_760579, _760581, _760583] : [hBOOL(hAPP(_760579, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _760581, _760583))), 10058 ^ _393467 : [(10059 ^ _393467) ^ [] : [_760583 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_760579, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (10065 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _760583)), 10068 ^ _393467 : [(10069 ^ _393467) ^ [_761123] : [-(hBOOL(hAPP(_760579, _761123))), 10070 ^ _393467 : [(10071 ^ _393467) ^ [_761252] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _761252)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _761252), _760583)), _760581 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _760583), _761123)), _761252)]]]]], (10083 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _760583), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 10086 ^ _393467 : [(10087 ^ _393467) ^ [_761742] : [-(hBOOL(hAPP(_760579, _761742))), 10088 ^ _393467 : [(10089 ^ _393467) ^ [_761874] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _760583), _761874)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _761874), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _760581 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _760583), _761742)), _761874)]]]]]]], (10137 ^ _393467) ^ [_763961, _763963] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, _763961, _763963))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, hAPP(c_Complex_ORe, _763961), hAPP(c_Complex_ORe, _763963)))), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, hAPP(c_Complex_OIm, _763961), hAPP(c_Complex_OIm, _763963)))))))], (10139 ^ _393467) ^ [_764134, _764136] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _764134), _764136)), -(c_Nat__Transfer_Otsub(_764136, _764134) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, _764136, _764134))], (10145 ^ _393467) ^ [_764320, _764322] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _764320), _764322))), -(c_Nat__Transfer_Otsub(_764322, _764320) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (10151 ^ _393467) ^ [_764565, _764567, _764569] : [class_Groups_Oordered__ab__group__add__abs(_764565), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_764565, c_Groups_Ominus__class_Ominus(_764565, c_Groups_Oabs__class_Oabs(_764565, _764567), c_Groups_Oabs__class_Oabs(_764565, _764569))), c_Groups_Oabs__class_Oabs(_764565, c_Groups_Ominus__class_Ominus(_764565, _764569, _764567)))))], (10157 ^ _393467) ^ [_764837, _764839, _764841] : [class_Groups_Oordered__ab__group__add__abs(_764837), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_764837, c_Groups_Ominus__class_Ominus(_764837, c_Groups_Oabs__class_Oabs(_764837, _764839), c_Groups_Oabs__class_Oabs(_764837, _764841))), c_Groups_Oabs__class_Oabs(_764837, c_Groups_Ominus__class_Ominus(_764837, _764839, _764841)))))], (10163 ^ _393467) ^ [_765109, _765111, _765113] : [class_Groups_Oordered__ab__group__add__abs(_765109), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_765109, c_Groups_Oabs__class_Oabs(_765109, c_Groups_Ominus__class_Ominus(_765109, c_Groups_Oabs__class_Oabs(_765109, _765111), c_Groups_Oabs__class_Oabs(_765109, _765113)))), c_Groups_Oabs__class_Oabs(_765109, c_Groups_Ominus__class_Ominus(_765109, _765111, _765113)))))], (10169 ^ _393467) ^ [_765387, _765389, _765391] : [class_Groups_Oordered__ab__group__add__abs(_765387), -(c_Groups_Oabs__class_Oabs(_765387, c_Groups_Ominus__class_Ominus(_765387, _765389, _765391)) = c_Groups_Oabs__class_Oabs(_765387, c_Groups_Ominus__class_Ominus(_765387, _765391, _765389)))], (10175 ^ _393467) ^ [_765643, _765645, _765647] : [class_Groups_Oordered__ab__group__add__abs(_765643), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_765643, c_Groups_Oabs__class_Oabs(_765643, c_Groups_Ominus__class_Ominus(_765643, _765645, _765647))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_765643), c_Groups_Oabs__class_Oabs(_765643, _765645)), c_Groups_Oabs__class_Oabs(_765643, _765647)))))], (10181 ^ _393467) ^ [_765951, _765953, _765955, _765957, _765959] : [class_Groups_Oordered__ab__group__add__abs(_765951), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_765951, c_Groups_Oabs__class_Oabs(_765951, c_Groups_Ominus__class_Ominus(_765951, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_765951), _765953), _765955), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_765951), _765957), _765959)))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_765951), c_Groups_Oabs__class_Oabs(_765951, c_Groups_Ominus__class_Ominus(_765951, _765953, _765957))), c_Groups_Oabs__class_Oabs(_765951, c_Groups_Ominus__class_Ominus(_765951, _765955, _765959))))))], (10187 ^ _393467) ^ [_766305, _766307, _766309, _766311] : [class_Rings_Olinordered__idom(_766305), 10190 ^ _393467 : [(10191 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_766305, c_Groups_Oabs__class_Oabs(_766305, c_Groups_Ominus__class_Ominus(_766305, _766307, _766309))), _766311)), 10194 ^ _393467 : [(10195 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_766305, c_Groups_Ominus__class_Ominus(_766305, _766309, _766311)), _766307)))], (10197 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_766305, _766307), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_766305), _766309), _766311))))]]], (10199 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_766305, c_Groups_Oabs__class_Oabs(_766305, c_Groups_Ominus__class_Ominus(_766305, _766307, _766309))), _766311))), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_766305, c_Groups_Ominus__class_Ominus(_766305, _766309, _766311)), _766307)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_766305, _766307), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_766305), _766309), _766311)))]]], (10209 ^ _393467) ^ [_767067, _767069] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _767067), _767069)), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _767067, _767069) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10215 ^ _393467) ^ [_767266] : [-(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _767266, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = _767266)], (10217 ^ _393467) ^ [_767391, _767393, _767395] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _767391), _767393)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _767391, _767395)), c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _767393, _767395))))], (10223 ^ _393467) ^ [_767628, _767630] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _767628, _767630)), _767628)))], (10225 ^ _393467) ^ [_767745, _767747, _767749] : [-(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _767745, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _767747), _767749)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _767745, _767747), _767749))], (10227 ^ _393467) ^ [_767902, _767904, _767906, _767908] : [class_Fields_Ofield(_767902), -(c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_767902), _767904, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_767902)), _767906), _767908)) = c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_767902), c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_767902), _767904, _767906), _767908))], (10233 ^ _393467) ^ [_768212, _768214, _768216] : [_768212 = 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), _768212), _768214), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _768212), _768216)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10239 ^ _393467) ^ [_768412, _768414, _768416] : [-(_768412 = 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), _768412), _768414), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _768412), _768416)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _768414, _768416))], (10245 ^ _393467) ^ [_768687, _768689, _768691] : [class_Groups_Oordered__ab__group__add__abs(_768687), -(c_Groups_Oabs__class_Oabs(_768687, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_768687), c_Groups_Oabs__class_Oabs(_768687, _768689)), c_Groups_Oabs__class_Oabs(_768687, _768691))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_768687), c_Groups_Oabs__class_Oabs(_768687, _768689)), c_Groups_Oabs__class_Oabs(_768687, _768691)))], (10251 ^ _393467) ^ [_768963, _768965] : [class_Groups_Oordered__ab__group__add__abs(_768963), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_768963, c_Groups_Oabs__class_Oabs(_768963, _768965)), c_Groups_Ozero__class_Ozero(_768963)))], (10257 ^ _393467) ^ [_769192, _769194] : [class_Groups_Oordered__ab__group__add__abs(_769192), 10260 ^ _393467 : [(10261 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(_769192, c_Groups_Ozero__class_Ozero(_769192)), c_Groups_Oabs__class_Oabs(_769192, _769194))), _769194 = c_Groups_Ozero__class_Ozero(_769192)], (10267 ^ _393467) ^ [] : [-(_769194 = c_Groups_Ozero__class_Ozero(_769192)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_769192, c_Groups_Ozero__class_Ozero(_769192)), c_Groups_Oabs__class_Oabs(_769192, _769194))))]]], (10273 ^ _393467) ^ [_769688, _769690] : [class_Groups_Oordered__ab__group__add__abs(_769688), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_769688, c_Groups_Ozero__class_Ozero(_769688)), _769690)), -(c_Groups_Oabs__class_Oabs(_769688, _769690) = _769690)], (10283 ^ _393467) ^ [_770047, _770049, _770051, _770053, _770055] : [class_Rings_Olinordered__idom(_770047), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_770047, c_Groups_Oabs__class_Oabs(_770047, _770049)), _770051)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(_770047, c_Groups_Oabs__class_Oabs(_770047, _770053)), _770055)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(_770047, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_770047), c_Groups_Oabs__class_Oabs(_770047, _770049)), c_Groups_Oabs__class_Oabs(_770047, _770053))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_770047), _770051), _770055))))], (10297 ^ _393467) ^ [_770547] : [class_Rings_Olinordered__idom(_770547), -(c_Groups_Oabs__class_Oabs(_770547, c_Groups_Oone__class_Oone(_770547)) = c_Groups_Oone__class_Oone(_770547))], (10303 ^ _393467) ^ [_770749] : [class_Groups_Oordered__ab__group__add__abs(_770749), -(c_Groups_Oabs__class_Oabs(_770749, c_Groups_Ozero__class_Ozero(_770749)) = c_Groups_Ozero__class_Ozero(_770749))], (10309 ^ _393467) ^ [_770965, _770967] : [class_Groups_Oordered__ab__group__add__abs(_770965), 10312 ^ _393467 : [(10313 ^ _393467) ^ [] : [c_Groups_Oabs__class_Oabs(_770965, _770967) = c_Groups_Ozero__class_Ozero(_770965), -(_770967 = c_Groups_Ozero__class_Ozero(_770965))], (10319 ^ _393467) ^ [] : [_770967 = c_Groups_Ozero__class_Ozero(_770965), -(c_Groups_Oabs__class_Oabs(_770965, _770967) = c_Groups_Ozero__class_Ozero(_770965))]]], (10325 ^ _393467) ^ [_771444, _771446] : [class_Groups_Oordered__ab__group__add__abs(_771444), -(c_Groups_Oabs__class_Oabs(_771444, c_Groups_Oabs__class_Oabs(_771444, _771446)) = c_Groups_Oabs__class_Oabs(_771444, _771446))], (10331 ^ _393467) ^ [_771641] : [-(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _771641)) = c_RealDef_Oreal(tc_Nat_Onat, _771641))], (10333 ^ _393467) ^ [_771757, _771759] : [class_RealVector_Oreal__normed__vector(_771757), -(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_771757, _771759)) = c_RealVector_Onorm__class_Onorm(_771757, _771759))], (10339 ^ _393467) ^ [_771954] : [-(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, _771954) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _771954))], (10341 ^ _393467) ^ [_772081, _772083, _772085] : [class_Rings_Olinordered__idom(_772081), -(c_Groups_Oabs__class_Oabs(_772081, hAPP(hAPP(c_Power_Opower__class_Opower(_772081), _772083), _772085)) = hAPP(hAPP(c_Power_Opower__class_Opower(_772081), c_Groups_Oabs__class_Oabs(_772081, _772083)), _772085))], (10347 ^ _393467) ^ [_772353, _772355, _772357] : [class_Rings_Olinordered__idom(_772353), -(c_Groups_Oabs__class_Oabs(_772353, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_772353), _772355), _772357)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_772353), c_Groups_Oabs__class_Oabs(_772353, _772355)), c_Groups_Oabs__class_Oabs(_772353, _772357)))], (10353 ^ _393467) ^ [_772617, _772619] : [class_Rings_Olinordered__idom(_772617), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_772617), c_Groups_Oabs__class_Oabs(_772617, _772619)), c_Groups_Oabs__class_Oabs(_772617, _772619)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_772617), _772619), _772619))], (10359 ^ _393467) ^ [_772869, _772871] : [class_Groups_Oordered__ab__group__add__abs(_772869), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_772869, _772871), c_Groups_Oabs__class_Oabs(_772869, _772871))))], (10365 ^ _393467) ^ [_773107, _773109, _773111] : [class_Groups_Oordered__ab__group__add__abs(_773107), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_773107, c_Groups_Oabs__class_Oabs(_773107, _773109)), _773111)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_773107, _773109), _773111)))], (10375 ^ _393467) ^ [_773454, _773456, _773458] : [class_Groups_Oordered__ab__group__add__abs(_773454), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_773454, c_Groups_Oabs__class_Oabs(_773454, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_773454), _773456), _773458))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_773454), c_Groups_Oabs__class_Oabs(_773454, _773456)), c_Groups_Oabs__class_Oabs(_773454, _773458)))))], (10381 ^ _393467) ^ [_773728, _773730] : [class_Groups_Oordered__ab__group__add__abs(_773728), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_773728, c_Groups_Ozero__class_Ozero(_773728)), _773730)), -(c_Groups_Oabs__class_Oabs(_773728, _773730) = _773730)], (10391 ^ _393467) ^ [_774045, _774047] : [class_Groups_Oordered__ab__group__add__abs(_774045), 10394 ^ _393467 : [(10395 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_774045, c_Groups_Oabs__class_Oabs(_774045, _774047)), c_Groups_Ozero__class_Ozero(_774045))), -(_774047 = c_Groups_Ozero__class_Ozero(_774045))], (10401 ^ _393467) ^ [] : [_774047 = c_Groups_Ozero__class_Ozero(_774045), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_774045, c_Groups_Oabs__class_Oabs(_774045, _774047)), c_Groups_Ozero__class_Ozero(_774045))))]]], (10407 ^ _393467) ^ [_774539, _774541] : [class_Groups_Oordered__ab__group__add__abs(_774539), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_774539, c_Groups_Ozero__class_Ozero(_774539)), c_Groups_Oabs__class_Oabs(_774539, _774541))))], (10413 ^ _393467) ^ [_774781, _774783, _774785] : [class_Rings_Olinordered__idom(_774781), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_774781, c_Groups_Ozero__class_Ozero(_774781)), hAPP(hAPP(c_Power_Opower__class_Opower(_774781), c_Groups_Oabs__class_Oabs(_774781, _774783)), _774785))))], (10419 ^ _393467) ^ [_775045, _775047, _775049] : [class_Rings_Oordered__ring__abs(_775045), -(c_Groups_Oabs__class_Oabs(_775045, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_775045), _775047), _775049)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_775045), c_Groups_Oabs__class_Oabs(_775045, _775047)), c_Groups_Oabs__class_Oabs(_775045, _775049))), 10426 ^ _393467 : [(10427 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_775045, c_Groups_Ozero__class_Ozero(_775045)), _775047))], (10429 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_775045, _775047), c_Groups_Ozero__class_Ozero(_775045)))]], 10430 ^ _393467 : [(10431 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_775045, c_Groups_Ozero__class_Ozero(_775045)), _775049))], (10433 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_775045, _775049), c_Groups_Ozero__class_Ozero(_775045)))]]], (10437 ^ _393467) ^ [_775717, _775719, _775721] : [class_Rings_Olinordered__idom(_775717), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_775717, c_Groups_Ozero__class_Ozero(_775717)), _775719)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_775717), c_Groups_Oabs__class_Oabs(_775717, _775721)), _775719) = c_Groups_Oabs__class_Oabs(_775717, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_775717), _775721), _775719)))], (10447 ^ _393467) ^ [_776067, _776069] : [-(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Complex_Orcis(_776067, _776069)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _776067))], (10449 ^ _393467) ^ [_776199, _776201, _776203] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _776199)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _776199), _776201)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _776203, _776201)), c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _776203, _776199))))], (10459 ^ _393467) ^ [_776548, _776550] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _776548)), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _776550), _776548), _776548) = _776550)], (10465 ^ _393467) ^ [_776782, _776784] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _776782)), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _776782), _776784), _776782) = _776784)], (10471 ^ _393467) ^ [_777030, _777032, _777034] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _777030)), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _777030), _777032), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _777030), _777034)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _777032, _777034))], (10477 ^ _393467) ^ [_777290, _777292] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat)), _777290)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _777292)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _777292, _777290)), _777292)))], (10487 ^ _393467) ^ [_777629, _777631, _777633] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _777629), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _777631)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _777629), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _777633)))), -(_777631 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (10497 ^ _393467) ^ [_777952] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _777952)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), _777952))], (10499 ^ _393467) ^ [_778073, _778075] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _778073)), -(c_NthRoot_Oroot(_778073, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _778075)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_NthRoot_Oroot(_778073, _778075)))], (10505 ^ _393467) ^ [_778282] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Transcendental_Ocos(_778282))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))], (10507 ^ _393467) ^ [_778370] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Transcendental_Osin(_778370))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))], (10509 ^ _393467) ^ [_778458] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, hAPP(c_Complex_ORe, _778458))), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _778458))))], (10511 ^ _393467) ^ [_778550] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, hAPP(c_Complex_OIm, _778550))), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _778550))))], (10513 ^ _393467) ^ [_778671, _778673] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _778671)), 10516 ^ _393467 : [(10517 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _778673), _778671)), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _778673, _778671) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10523 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _778673), _778671))), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _778673, _778671) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _778673, _778671), _778671)))]]], (10529 ^ _393467) ^ [_779197, _779199] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _779197)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _779199), _779197))), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _779199, _779197) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _779199, _779197), _779197)))], (10563 ^ _393467) ^ [_780381, _780383, _780385] : [-(hBOOL(hAPP(_780381, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _780383, _780385)))), 10566 ^ _393467 : [(10567 ^ _393467) ^ [] : [-(_780385 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10569 ^ _393467) ^ [] : [hBOOL(hAPP(_780381, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 10570 ^ _393467 : [(10571 ^ _393467) ^ [] : [_780385 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10575 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, 10573 ^ [_780381, _780383, _780385]), _780385)))], (10577 ^ _393467) ^ [] : [-(_780383 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _780385), 10572 ^ [_780381, _780383, _780385])), 10573 ^ [_780381, _780383, _780385]))], (10579 ^ _393467) ^ [] : [hBOOL(hAPP(_780381, 10572 ^ [_780381, _780383, _780385]))]]], (10539 ^ _393467) ^ [_779584, _779586, _779588] : [hBOOL(hAPP(_779584, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _779586, _779588))), 10542 ^ _393467 : [(10543 ^ _393467) ^ [] : [_779588 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_779584, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (10549 ^ _393467) ^ [] : [-(_779588 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 10552 ^ _393467 : [(10553 ^ _393467) ^ [_780044, _780046] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _780044), _779588)), _779586 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _779588), _780046)), _780044), -(hBOOL(hAPP(_779584, _780046)))]]]]], (10583 ^ _393467) ^ [_781296, _781298, _781300] : [class_RealVector_Oreal__normed__vector(_781296), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_781296, _781298), c_RealVector_Onorm__class_Onorm(_781296, _781300)))), c_RealVector_Onorm__class_Onorm(_781296, c_Groups_Ominus__class_Ominus(_781296, _781298, _781300)))))], (10589 ^ _393467) ^ [_781531] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _781531)))))], (10591 ^ _393467) ^ [_781632] : [c_Transcendental_Osin(_781632) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Transcendental_Ocos(_781632)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (10597 ^ _393467) ^ [_781893, _781895, _781897] : [hBOOL(hAPP(_781893, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _781895, _781897))), 10602 ^ _393467 : [(10603 ^ _393467) ^ [] : [-(_781897 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10605 ^ _393467) ^ [] : [-(hBOOL(hAPP(_781893, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]], 10607 ^ _393467 : [(10608 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _781897), 10606 ^ [_781893, _781895, _781897])), _781895)))], (10610 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _781895), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _781897), c_Nat_OSuc(10606 ^ [_781893, _781895, _781897])))))], (10612 ^ _393467) ^ [] : [-(hBOOL(hAPP(_781893, 10606 ^ [_781893, _781895, _781897])))]]], (10614 ^ _393467) ^ [_782572, _782574, _782576] : [-(hBOOL(hAPP(_782572, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _782574, _782576)))), 10615 ^ _393467 : [(10616 ^ _393467) ^ [] : [_782576 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hBOOL(hAPP(_782572, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10622 ^ _393467) ^ [_782874] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _782576), _782874)), _782574)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _782574), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _782576), c_Nat_OSuc(_782874)))), hBOOL(hAPP(_782572, _782874))]]], (10634 ^ _393467) ^ [_783327, _783329, _783331] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _783327)), 10637 ^ _393467 : [(10648 ^ _393467) ^ [] : [_783329 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _783331, _783327), 10651 ^ _393467 : [(10652 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _783327), _783329)), _783331)))], (10654 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _783331), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _783327), c_Nat_OSuc(_783329)))))]]], (10638 ^ _393467) ^ [] : [-(_783329 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _783331, _783327)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _783327), _783329)), _783331)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _783331), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _783327), c_Nat_OSuc(_783329))))]]], (10656 ^ _393467) ^ [_784055, _784057] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _784055)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _784055), _784057)), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _784057, _784055) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _784057, _784055), _784055)))], (10666 ^ _393467) ^ [_784396, _784398] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _784396)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _784398)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Nat__Transfer_Otsub(_784396, _784398))))], (10676 ^ _393467) ^ [_784713, _784715] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _784713), _784715)), -(c_Nat__Transfer_Otsub(_784715, _784713) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, _784715, _784713))], (10682 ^ _393467) ^ [_784989, _784991, _784993, _784995, _784997] : [class_Groups_Oab__group__add(_784989), -(c_Groups_Ominus__class_Ominus(_784989, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_784989), _784991), _784993), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_784989), _784995), _784997)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_784989), c_Groups_Ominus__class_Ominus(_784989, _784991, _784995)), c_Groups_Ominus__class_Ominus(_784989, _784993, _784997)))], (10688 ^ _393467) ^ [_785272, _785274] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), _785272), _785274) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(c_Complex_ORe, _785272)), hAPP(c_Complex_ORe, _785274)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(c_Complex_OIm, _785272)), hAPP(c_Complex_OIm, _785274))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(c_Complex_ORe, _785272)), hAPP(c_Complex_OIm, _785274))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(c_Complex_OIm, _785272)), hAPP(c_Complex_ORe, _785274)))))], (10690 ^ _393467) ^ [_785448, _785450] : [c_Groups_Oabs__class_Oabs(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _785448), _785450)) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(c_Groups_Oabs__class_Oabs(tc_Int_Oint, _785448) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (10696 ^ _393467) ^ [_785697] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oabs__class_Oabs(tc_Int_Oint, _785697)), c_Groups_Oone__class_Oone(tc_Int_Oint))), -(_785697 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (10702 ^ _393467) ^ [_785869] : [_785869 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oabs__class_Oabs(tc_Int_Oint, _785869)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (10708 ^ _393467) ^ [_786120, _786122] : [c_Complex_Ocomplex_OComplex(_786120, _786122) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), 10711 ^ _393467 : [(10712 ^ _393467) ^ [] : [-(_786120 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (10714 ^ _393467) ^ [] : [-(_786122 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))]]], (10716 ^ _393467) ^ [_786363, _786365] : [-(c_Complex_Ocomplex_OComplex(_786363, _786365) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), _786363 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _786365 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)], (10726 ^ _393467) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (10728 ^ _393467) ^ [_786736, _786738, _786740, _786742] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex), c_Complex_Ocomplex_OComplex(_786736, _786738)), c_Complex_Ocomplex_OComplex(_786740, _786742)) = c_Complex_Ocomplex_OComplex(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), _786736), _786740), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), _786738), _786742)))], (10730 ^ _393467) ^ [_786933, _786935, _786937, _786939] : [c_Complex_Ocomplex_OComplex(_786933, _786935) = c_Complex_Ocomplex_OComplex(_786937, _786939), 10733 ^ _393467 : [(10734 ^ _393467) ^ [] : [-(_786933 = _786937)], (10736 ^ _393467) ^ [] : [-(_786935 = _786939)]]], (10738 ^ _393467) ^ [_787198, _787200, _787202, _787204] : [-(c_Complex_Ocomplex_OComplex(_787198, _787200) = c_Complex_Ocomplex_OComplex(_787202, _787204)), _787198 = _787202, _787200 = _787204], (10748 ^ _393467) ^ [_787516, _787518] : [-(hAPP(c_Complex_OIm, c_Complex_Ocomplex_OComplex(_787516, _787518)) = _787518)], (10750 ^ _393467) ^ [_787616, _787618] : [-(hAPP(c_Complex_ORe, c_Complex_Ocomplex_OComplex(_787616, _787618)) = _787616)], (10752 ^ _393467) ^ [_787702] : [-(c_Complex_Ocomplex_OComplex(hAPP(c_Complex_ORe, _787702), hAPP(c_Complex_OIm, _787702)) = _787702)], (10754 ^ _393467) ^ [_787831, _787833, _787835, _787837] : [-(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex, c_Complex_Ocomplex_OComplex(_787831, _787833), c_Complex_Ocomplex_OComplex(_787835, _787837)) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _787831, _787835), c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _787833, _787837)))], (10756 ^ _393467) ^ [_787950, _787952] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), c_Groups_Oabs__class_Oabs(tc_Int_Oint, _787950)), _787952))))], (10758 ^ _393467) ^ [_788099, _788101] : [c_Complex_Ocomplex_OComplex(_788099, _788101) = c_Complex_Oii, 10761 ^ _393467 : [(10762 ^ _393467) ^ [] : [-(_788099 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (10764 ^ _393467) ^ [] : [-(_788101 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))]]], (10766 ^ _393467) ^ [_788342, _788344] : [-(c_Complex_Ocomplex_OComplex(_788342, _788344) = c_Complex_Oii), _788342 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _788344 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)], (10776 ^ _393467) ^ [] : [-(c_Complex_Oii = c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (10778 ^ _393467) ^ [_788731, _788733] : [c_Complex_Ocomplex_OComplex(_788731, _788733) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), 10781 ^ _393467 : [(10782 ^ _393467) ^ [] : [-(_788731 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (10784 ^ _393467) ^ [] : [-(_788733 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))]]], (10786 ^ _393467) ^ [_788974, _788976] : [-(c_Complex_Ocomplex_OComplex(_788974, _788976) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)), _788974 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _788976 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)], (10796 ^ _393467) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Groups_Oone__class_Oone(tc_RealDef_Oreal), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (10798 ^ _393467) ^ [_789305] : [-(c_Complex_Ocis(_789305) = c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(_789305), c_Transcendental_Osin(_789305)))], (10810 ^ _393467) ^ [_789725, _789727] : [10811 ^ _393467 : [(10812 ^ _393467) ^ [] : [-(_789725 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (10814 ^ _393467) ^ [] : [_789727 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hBOOL(hAPP(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, _789725)), _789727))))], (10800 ^ _393467) ^ [_789450, _789452] : [hBOOL(hAPP(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, _789450)), _789452))), _789450 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_789452 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10818 ^ _393467) ^ [_790007] : [-(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(_790007), c_Transcendental_Osin(_790007))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (10820 ^ _393467) ^ [_790137, _790139, _790141, _790143] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Complex_Ocomplex_OComplex(_790137, _790139)), c_Complex_Ocomplex_OComplex(_790141, _790143)) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _790137), _790141), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _790139), _790143)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _790137), _790143)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _790139), _790141))))], (10822 ^ _393467) ^ [_790284, _790286] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex), _790284), _790286) = c_Complex_Ocomplex_OComplex(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), hAPP(c_Complex_ORe, _790284)), hAPP(c_Complex_ORe, _790286)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal), hAPP(c_Complex_OIm, _790284)), hAPP(c_Complex_OIm, _790286))))], (10824 ^ _393467) ^ [_790440, _790442, _790444] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _790440)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _790442, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oabs__class_Oabs(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _790442, _790444))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _790440))), _790444)))], (10830 ^ _393467) ^ [_790730, _790732, _790734] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _790730)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint, _790732), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _790734), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oabs__class_Oabs(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _790734, _790732))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _790730)))))], (10836 ^ _393467) ^ [_790995, _790997] : [-(c_Complex_Ocomplex_Ocomplex__size(c_Complex_Ocomplex_OComplex(_790995, _790997)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10838 ^ _393467) ^ [_791095] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _791095)), -(c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _791095))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (10844 ^ _393467) ^ [_791303] : [-(_791303 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _791303))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (10850 ^ _393467) ^ [_791510] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _791510), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), -(c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _791510))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (10856 ^ _393467) ^ [_791723, _791725] : [-(c_Nat_Osize__class_Osize(tc_Complex_Ocomplex, c_Complex_Ocomplex_OComplex(_791723, _791725)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10858 ^ _393467) ^ [_791851, _791853, _791855, _791857] : [-(c_Complex_Ocomplex_Ocomplex__case(_791851, _791853, c_Complex_Ocomplex_OComplex(_791855, _791857)) = hAPP(hAPP(_791853, _791855), _791857))], (10860 ^ _393467) ^ [_791990, _791992, _791994, _791996] : [-(c_Complex_Ocomplex_Ocomplex__rec(_791990, _791992, c_Complex_Ocomplex_OComplex(_791994, _791996)) = hAPP(hAPP(_791992, _791994), _791996))], (10862 ^ _393467) ^ [_792116, _792118] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _792116)), hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _792118)), -(c_RComplete_Onatfloor(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, _792116, c_RealDef_Oreal(tc_Nat_Onat, _792118))) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, c_RComplete_Onatfloor(_792116), _792118))], (10888 ^ _393467) ^ [_792939, _792941] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, _792939, _792941)))), 10891 ^ _393467 : [(10892 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _792939), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (10894 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _792941))]], 10895 ^ _393467 : [(10896 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _792939))], (10898 ^ _393467) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _792941), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))]]], (10872 ^ _393467) ^ [_792482, _792484] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, _792482, _792484))), 10875 ^ _393467 : [(10876 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _792482), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _792484)))], (10882 ^ _393467) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _792482))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _792484), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))]]], (10902 ^ _393467) ^ [_793456, _793458, _793460, _793462] : [class_Rings_Odivision__ring(_793456), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_793456), _793458), c_Rings_Oinverse__class_Odivide(_793456, _793460, _793462)) = c_Rings_Oinverse__class_Odivide(_793456, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_793456), _793458), _793460), _793462))], (10908 ^ _393467) ^ [_793709, _793711] : [-(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _793709), _793711), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _793709), _793709)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, _793711, _793709))], (10910 ^ _393467) ^ [_793866, _793868, _793870, _793872] : [class_Fields_Ofield__inverse__zero(_793866), -(hAPP(hAPP(c_Power_Opower__class_Opower(_793866), c_Rings_Oinverse__class_Odivide(_793866, _793868, _793870)), _793872) = c_Rings_Oinverse__class_Odivide(_793866, hAPP(hAPP(c_Power_Opower__class_Opower(_793866), _793868), _793872), hAPP(hAPP(c_Power_Opower__class_Opower(_793866), _793870), _793872)))], (10916 ^ _393467) ^ [_794164, _794166, _794168] : [-(c_RealVector_Onorm__class_Onorm(_794164, c_Rings_Oinverse__class_Odivide(_794164, _794166, _794168)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_794164, _794166), c_RealVector_Onorm__class_Onorm(_794164, _794168))), class_Fields_Ofield__inverse__zero(_794164), class_RealVector_Oreal__normed__field(_794164)], (10926 ^ _393467) ^ [_794489] : [class_Rings_Oidom(_794489), -(class_Rings_Oidom(tc_Polynomial_Opoly(_794489)))], (10932 ^ _393467) ^ [_794679] : [class_Groups_Ocancel__comm__monoid__add(_794679), -(class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(_794679)))], (10938 ^ _393467) ^ [_794869] : [class_Rings_Ocomm__ring(_794869), -(class_Rings_Ocomm__ring(tc_Polynomial_Opoly(_794869)))], (10944 ^ _393467) ^ [] : [-(class_Rings_Oidom(tc_Complex_Ocomplex))], (10946 ^ _393467) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex))], (10948 ^ _393467) ^ [] : [-(class_Rings_Ocomm__ring(tc_Complex_Ocomplex))], (10950 ^ _393467) ^ [] : [-(class_Rings_Oidom(tc_RealDef_Oreal))], (10952 ^ _393467) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal))], (10954 ^ _393467) ^ [] : [-(class_Rings_Ocomm__ring(tc_RealDef_Oreal))], (10956 ^ _393467) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat))], (10958 ^ _393467) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (10960 ^ _393467) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint))], (10962 ^ _393467) ^ [] : [-(class_Rings_Ocomm__ring(tc_Int_Oint))], (10964 ^ _393467) ^ [_795603, _795605] : [class_Orderings_Opreorder(_795603), -(class_Orderings_Opreorder(tc_fun(_795605, _795603)))], (10970 ^ _393467) ^ [_795815, _795817] : [class_Orderings_Oorder(_795815), -(class_Orderings_Oorder(tc_fun(_795817, _795815)))], (10976 ^ _393467) ^ [_796027, _796029] : [class_Orderings_Oord(_796027), -(class_Orderings_Oord(tc_fun(_796029, _796027)))], (10982 ^ _393467) ^ [_796239, _796241] : [class_Groups_Ominus(_796239), -(class_Groups_Ominus(tc_fun(_796241, _796239)))], (10988 ^ _393467) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (10990 ^ _393467) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (10992 ^ _393467) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (10994 ^ _393467) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (10996 ^ _393467) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (10998 ^ _393467) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (11000 ^ _393467) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (11002 ^ _393467) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))], (11004 ^ _393467) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (11006 ^ _393467) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (11008 ^ _393467) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (11010 ^ _393467) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (11012 ^ _393467) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (11014 ^ _393467) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (11016 ^ _393467) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (11018 ^ _393467) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (11020 ^ _393467) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (11022 ^ _393467) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (11024 ^ _393467) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (11026 ^ _393467) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (11028 ^ _393467) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (11030 ^ _393467) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (11032 ^ _393467) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (11034 ^ _393467) ^ [] : 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^ _393467) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (11092 ^ _393467) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (11094 ^ _393467) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (11096 ^ _393467) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (11098 ^ _393467) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (11100 ^ _393467) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (11102 ^ _393467) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (11104 ^ _393467) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (11106 ^ _393467) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (11108 ^ _393467) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (11110 ^ _393467) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (11112 ^ _393467) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], 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[-(class_Rings_Oring__1(tc_RealDef_Oreal))], (11288 ^ _393467) ^ [] : [-(class_Groups_Ominus(tc_RealDef_Oreal))], (11290 ^ _393467) ^ [] : [-(class_Fields_Ofield(tc_RealDef_Oreal))], (11292 ^ _393467) ^ [] : [-(class_Power_Opower(tc_RealDef_Oreal))], (11294 ^ _393467) ^ [] : [-(class_Groups_Ozero(tc_RealDef_Oreal))], (11296 ^ _393467) ^ [] : [-(class_Rings_Oring(tc_RealDef_Oreal))], (11298 ^ _393467) ^ [] : [-(class_Groups_Oone(tc_RealDef_Oreal))], (11300 ^ _393467) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex))], (11302 ^ _393467) ^ [] : [-(class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex))], (11304 ^ _393467) ^ [] : [-(class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex))], (11306 ^ _393467) ^ [] : [-(class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex))], (11308 ^ _393467) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex))], (11310 ^ _393467) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex))], (11312 ^ _393467) ^ [] : [-(class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex))], (11314 ^ _393467) ^ [] : [-(class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex))], (11316 ^ _393467) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex))], (11318 ^ _393467) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex))], (11320 ^ _393467) ^ [] : [-(class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex))], (11322 ^ _393467) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex))], (11324 ^ _393467) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex))], (11326 ^ _393467) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex))], (11328 ^ _393467) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex))], (11330 ^ _393467) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex))], (11332 ^ _393467) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex))], (11334 ^ _393467) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex))], (11336 ^ _393467) ^ [] : [-(class_Rings_Odivision__ring(tc_Complex_Ocomplex))], (11338 ^ _393467) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Complex_Ocomplex))], (11340 ^ _393467) ^ [] : [-(class_Groups_Oab__group__add(tc_Complex_Ocomplex))], (11342 ^ _393467) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Complex_Ocomplex))], (11344 ^ _393467) ^ [] : [-(class_Groups_Omonoid__mult(tc_Complex_Ocomplex))], (11346 ^ _393467) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex))], (11348 ^ _393467) ^ [] : [-(class_Groups_Omonoid__add(tc_Complex_Ocomplex))], (11350 ^ _393467) ^ [] : [-(class_Rings_Osemiring__0(tc_Complex_Ocomplex))], (11352 ^ _393467) ^ [] : [-(class_Groups_Ogroup__add(tc_Complex_Ocomplex))], (11354 ^ _393467) ^ [] : [-(class_Rings_Omult__zero(tc_Complex_Ocomplex))], (11356 ^ _393467) ^ [] : [-(class_Rings_Osemiring(tc_Complex_Ocomplex))], (11358 ^ _393467) ^ [] : [-(class_Rings_Oring__1(tc_Complex_Ocomplex))], (11360 ^ _393467) ^ [] : [-(class_Groups_Ominus(tc_Complex_Ocomplex))], (11362 ^ _393467) ^ [] : [-(class_Fields_Ofield(tc_Complex_Ocomplex))], (11364 ^ _393467) ^ [] : [-(class_Power_Opower(tc_Complex_Ocomplex))], (11366 ^ _393467) ^ [] : [-(class_Groups_Ozero(tc_Complex_Ocomplex))], (11368 ^ _393467) ^ [] : [-(class_Rings_Oring(tc_Complex_Ocomplex))], (11370 ^ _393467) ^ [] : [-(class_Groups_Oone(tc_Complex_Ocomplex))], (11372 ^ _393467) ^ [_806613] : [class_Rings_Oidom(_806613), -(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(_806613)))], (11378 ^ _393467) ^ [_806803] : [class_Rings_Olinordered__idom(_806803), -(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(_806803)))], (11384 ^ _393467) ^ [_806993] : [class_Rings_Olinordered__idom(_806993), -(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(_806993)))], (11390 ^ _393467) ^ [_807183] : [class_Rings_Olinordered__idom(_807183), -(class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(_807183)))], (11396 ^ _393467) ^ [_807373] : [class_Rings_Olinordered__idom(_807373), -(class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(_807373)))], (11402 ^ _393467) ^ [_807563] : [class_Rings_Olinordered__idom(_807563), -(class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(_807563)))], (11408 ^ _393467) ^ [_807753] : [class_Rings_Olinordered__idom(_807753), -(class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(_807753)))], (11414 ^ _393467) ^ [_807943] : [class_Rings_Olinordered__idom(_807943), -(class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(_807943)))], (11420 ^ _393467) ^ [_808133] : [class_Rings_Olinordered__idom(_808133), -(class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(_808133)))], (11426 ^ _393467) ^ [_808323] : [class_Rings_Olinordered__idom(_808323), -(class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(_808323)))], (11432 ^ _393467) ^ [_808513] : [class_Groups_Ocancel__comm__monoid__add(_808513), -(class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(_808513)))], (11438 ^ _393467) ^ [_808703] : [class_Rings_Oidom(_808703), -(class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(_808703)))], (11444 ^ _393467) ^ [_808893] : [class_Rings_Olinordered__idom(_808893), -(class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(_808893)))], (11450 ^ _393467) ^ [_809083] : [class_Rings_Olinordered__idom(_809083), -(class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(_809083)))], (11456 ^ _393467) ^ [_809273] : [class_Rings_Oidom(_809273), -(class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(_809273)))], (11462 ^ _393467) ^ [_809463] : [class_Rings_Olinordered__idom(_809463), -(class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(_809463)))], (11468 ^ _393467) ^ [_809653] : [class_Rings_Olinordered__idom(_809653), -(class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(_809653)))], (11474 ^ _393467) ^ [_809843] : [class_Rings_Olinordered__idom(_809843), -(class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(_809843)))], (11480 ^ _393467) ^ [_810033] : [class_Groups_Ocancel__comm__monoid__add(_810033), -(class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(_810033)))], (11486 ^ _393467) ^ [_810223] : [class_Rings_Olinordered__idom(_810223), -(class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(_810223)))], (11492 ^ _393467) ^ [_810413] : [class_Rings_Olinordered__idom(_810413), -(class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(_810413)))], (11498 ^ _393467) ^ [_810603] : [class_Rings_Ocomm__semiring__0(_810603), -(class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(_810603)))], (11504 ^ _393467) ^ [_810793] : [class_Rings_Ocomm__semiring__1(_810793), -(class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(_810793)))], (11510 ^ _393467) ^ [_810983] : [class_Groups_Ocomm__monoid__add(_810983), -(class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(_810983)))], (11516 ^ _393467) ^ [_811173] : [class_Rings_Olinordered__idom(_811173), -(class_Rings_Oordered__semiring(tc_Polynomial_Opoly(_811173)))], (11522 ^ _393467) ^ [_811363] : [class_Rings_Olinordered__idom(_811363), -(class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(_811363)))], (11528 ^ _393467) ^ [_811553] : [class_Rings_Oidom(_811553), -(class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(_811553)))], (11534 ^ _393467) ^ [_811743] : [class_Groups_Ocomm__monoid__add(_811743), -(class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(_811743)))], (11540 ^ _393467) ^ [_811933] : [class_Rings_Olinordered__idom(_811933), -(class_Rings_Olinordered__ring(tc_Polynomial_Opoly(_811933)))], (11546 ^ _393467) ^ [_812123] : [class_Rings_Olinordered__idom(_812123), -(class_Rings_Olinordered__idom(tc_Polynomial_Opoly(_812123)))], (11552 ^ _393467) ^ [_812313] : [class_Rings_Ocomm__semiring__1(_812313), -(class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(_812313)))], (11558 ^ _393467) ^ [_812503] : [class_Rings_Ocomm__semiring__0(_812503), -(class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(_812503)))], (11564 ^ _393467) ^ [_812693] : [class_Fields_Ofield(_812693), -(class_Divides_Osemiring__div(tc_Polynomial_Opoly(_812693)))], (11570 ^ _393467) ^ [_812883] : [class_Rings_Ocomm__semiring__0(_812883), -(class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(_812883)))], (11576 ^ _393467) ^ [_813073] : [class_Groups_Oab__group__add(_813073), -(class_Groups_Oab__group__add(tc_Polynomial_Opoly(_813073)))], (11582 ^ _393467) ^ [_813263] : [class_Rings_Ocomm__semiring__1(_813263), -(class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(_813263)))], (11588 ^ _393467) ^ [_813453] : [class_Rings_Olinordered__idom(_813453), -(class_Rings_Oordered__ring(tc_Polynomial_Opoly(_813453)))], (11594 ^ _393467) ^ [_813643] : [class_Rings_Olinordered__idom(_813643), -(class_Orderings_Opreorder(tc_Polynomial_Opoly(_813643)))], (11600 ^ _393467) ^ [_813833] : [class_Rings_Olinordered__idom(_813833), -(class_Orderings_Olinorder(tc_Polynomial_Opoly(_813833)))], (11606 ^ _393467) ^ [_814023] : [class_Rings_Ocomm__semiring__1(_814023), -(class_Groups_Omonoid__mult(tc_Polynomial_Opoly(_814023)))], (11612 ^ _393467) ^ [_814213] : [class_Rings_Ocomm__ring__1(_814213), -(class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(_814213)))], (11618 ^ _393467) ^ [_814403] : [class_Groups_Ocomm__monoid__add(_814403), -(class_Groups_Omonoid__add(tc_Polynomial_Opoly(_814403)))], (11624 ^ _393467) ^ [_814593] : [class_Rings_Ocomm__semiring__0(_814593), -(class_Rings_Osemiring__0(tc_Polynomial_Opoly(_814593)))], (11630 ^ _393467) ^ [_814783] : [class_Groups_Oab__group__add(_814783), -(class_Groups_Ogroup__add(tc_Polynomial_Opoly(_814783)))], (11636 ^ _393467) ^ [_814973] : [class_Rings_Ocomm__semiring__0(_814973), -(class_Rings_Omult__zero(tc_Polynomial_Opoly(_814973)))], (11642 ^ _393467) ^ [_815163] : [class_Rings_Olinordered__idom(_815163), -(class_Orderings_Oorder(tc_Polynomial_Opoly(_815163)))], (11648 ^ _393467) ^ [_815353] : [class_Rings_Ocomm__semiring__0(_815353), -(class_Rings_Osemiring(tc_Polynomial_Opoly(_815353)))], (11654 ^ _393467) ^ [_815543] : [class_Rings_Olinordered__idom(_815543), -(class_Orderings_Oord(tc_Polynomial_Opoly(_815543)))], (11660 ^ _393467) ^ [_815733] : [class_Rings_Ocomm__ring__1(_815733), -(class_Rings_Oring__1(tc_Polynomial_Opoly(_815733)))], (11666 ^ _393467) ^ [_815923] : [class_Groups_Oab__group__add(_815923), -(class_Groups_Ominus(tc_Polynomial_Opoly(_815923)))], (11672 ^ _393467) ^ [_816113] : [class_Rings_Ocomm__semiring__1(_816113), -(class_Power_Opower(tc_Polynomial_Opoly(_816113)))], (11678 ^ _393467) ^ [_816303] : [class_Groups_Ozero(_816303), -(class_Groups_Ozero(tc_Polynomial_Opoly(_816303)))], (11684 ^ _393467) ^ [_816493] : [class_Rings_Ocomm__ring(_816493), -(class_Rings_Oring(tc_Polynomial_Opoly(_816493)))], (11696 ^ _393467) ^ [_816900, _816902, _816904, _816906] : [-(hAPP(c_COMBK(_816900, _816902, _816904), _816906) = _816904)], (11698 ^ _393467) ^ [_817061, _817063, _817065, _817067, _817069, _817071] : [-(hAPP(c_COMBB(_817061, _817063, _817065, _817067, _817069), _817071) = hAPP(_817067, hAPP(_817069, _817071)))], (11700 ^ _393467) ^ [_817214, _817216, _817218, _817220, _817222, _817224] : [-(hAPP(c_COMBC(_817214, _817216, _817218, _817220, _817222), _817224) = hAPP(hAPP(_817220, _817224), _817222))], (11690 ^ _393467) ^ [_816683] : [class_Rings_Ocomm__semiring__1(_816683), -(class_Groups_Oone(tc_Polynomial_Opoly(_816683)))]], input).
% 0.52/1.40  ncf('1',plain,[hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), v_r))],start(11702 ^ 0)).
% 0.52/1.40  ncf('1.1',plain,[-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), v_r))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(v_s, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(v_s, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), v_r))],extension(1175 ^ 1,bind([[_432209, _432211, _432213], [c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(v_s, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), v_r]]))).
% 0.52/1.40  ncf('1.1.1',plain,[-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(v_s, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))],extension(1254 ^ 2)).
% 0.52/1.40  ncf('1.1.2',plain,[-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(v_s, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), v_r)))],extension(1163 ^ 2)).
% 0.52/1.40  %-----------------------------------------------------
% 0.52/1.40  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------