%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWW323+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n004.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 12:25:57 EDT 2023

% Result   : Theorem 1.84s 2.49s
% Output   : Proof 1.88s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWW323+1 : TPTP v8.1.2. Released v5.2.0.
% 0.03/0.13  % Command  : nanocop.sh %s %d
% 0.13/0.34  % Computer : n004.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 22:29:39 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 1.84/2.49  
% 1.84/2.49  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 1.84/2.49  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.84/2.49  %-----------------------------------------------------
% 1.84/2.49  ncf(matrix, plain, [(52451 ^ _780086) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(t_b, v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b), hAPP(v_P, v_x)), hAPP(v_c0, v_x)), hAPP(v_Q, v_x))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b), tc_HOL_Obool))))], (2 ^ _780086) ^ [_780116] : [-(_780116 = _780116)], (4 ^ _780086) ^ [_780139, _780141] : [_780141 = _780139, -(_780139 = _780141)], (10 ^ _780086) ^ [_780212, _780214, _780216] : [-(_780216 = _780212), _780216 = _780214, _780214 = _780212], (20 ^ _780086) ^ [_780349, _780351, _780353, _780355, _780357, _780359, _780361, _780363, _780365, _780367, _780369, _780371] : [-(c_Nitpick_Ofold__graph_H(_780369, _780365, _780361, _780357, _780353, _780349)), c_Nitpick_Ofold__graph_H(_780371, _780367, _780363, _780359, _780355, _780351), _780371 = _780369, _780367 = _780365, _780363 = _780361, _780359 = _780357, _780355 = _780353, _780351 = _780349], (50 ^ _780086) ^ [_780894, _780896, _780898, _780900, _780902, _780904] : [-(c_Big__Operators_Osemilattice__big(_780902, _780898, _780894)), c_Big__Operators_Osemilattice__big(_780904, _780900, _780896), _780904 = _780902, _780900 = _780898, _780896 = _780894], (68 ^ _780086) ^ [_781163, _781165, _781167, _781169, _781171, _781173, _781175, _781177, _781179, _781181, _781183, _781185] : [-(c_Finite__Set_Ofolding__image__simple__idem(_781183, _781179, _781175, _781171, _781167, _781163)), c_Finite__Set_Ofolding__image__simple__idem(_781185, _781181, _781177, _781173, _781169, _781165), _781185 = _781183, _781181 = _781179, _781177 = _781175, _781173 = _781171, _781169 = _781167, _781165 = _781163], (98 ^ _780086) ^ [_781708, _781710, _781712, _781714, _781716, _781718] : [-(c_Finite__Set_Ofolding__one__idem(_781716, _781712, _781708)), c_Finite__Set_Ofolding__one__idem(_781718, _781714, _781710), _781718 = _781716, _781714 = _781712, _781710 = _781708], (116 ^ _780086) ^ [_781977, _781979, _781981, _781983, _781985, _781987, _781989, _781991, _781993, _781995] : [-(c_Big__Operators_Ocomm__monoid__big(_781993, _781989, _781985, _781981, _781977)), c_Big__Operators_Ocomm__monoid__big(_781995, _781991, _781987, _781983, _781979), _781995 = _781993, _781991 = _781989, _781987 = _781985, _781983 = _781981, _781979 = _781977], (142 ^ _780086) ^ [_782422, _782424, _782426, _782428, _782430, _782432] : [-(c_Finite__Set_Ofolding__one(_782430, _782426, _782422)), c_Finite__Set_Ofolding__one(_782432, _782428, _782424), _782432 = _782430, _782428 = _782426, _782424 = _782422], (160 ^ _780086) ^ [_782691, _782693] : [-(class_Rings_Odivision__ring__inverse__zero(_782691)), _782693 = _782691, class_Rings_Odivision__ring__inverse__zero(_782693)], (170 ^ _780086) ^ [_782816, _782818] : [-(class_Rings_Odivision__ring(_782816)), _782818 = _782816, class_Rings_Odivision__ring(_782818)], (180 ^ _780086) ^ [_782941, _782943, _782945, _782947, _782949, _782951, _782953, _782955, _782957, _782959, _782961, _782963] : [-(c_Finite__Set_Ofolding__image__simple(_782961, _782957, _782953, _782949, _782945, _782941)), c_Finite__Set_Ofolding__image__simple(_782963, _782959, _782955, _782951, _782947, _782943), _782963 = _782961, _782959 = _782957, _782955 = _782953, _782951 = _782949, _782947 = _782945, _782943 = _782941], (210 ^ _780086) ^ [_783486, _783488] : [-(class_Fields_Ofield(_783486)), _783488 = _783486, class_Fields_Ofield(_783488)], (220 ^ _780086) ^ [_783611, _783613] : [-(c_Nat__Transfer_Ois__nat(_783611)), _783613 = _783611, c_Nat__Transfer_Ois__nat(_783613)], (230 ^ _780086) ^ [_783736, _783738] : [-(class_Fields_Olinordered__field__inverse__zero(_783736)), _783738 = _783736, class_Fields_Olinordered__field__inverse__zero(_783738)], (240 ^ _780086) ^ [_783861, _783863, _783865, _783867] : [-(c_Int_Oiszero(_783865, _783861)), c_Int_Oiszero(_783867, _783863), _783867 = _783865, _783863 = _783861], (254 ^ _780086) ^ [_784054, _784056] : [-(class_Fields_Ofield__inverse__zero(_784054)), _784056 = _784054, class_Fields_Ofield__inverse__zero(_784056)], (264 ^ _780086) ^ [_784179, _784181, _784183, _784185] : [-(c_Nitpick_Orefl_H(_784183, _784179)), c_Nitpick_Orefl_H(_784185, _784181), _784185 = _784183, _784181 = _784179], (278 ^ _780086) ^ [_784372, _784374, _784376, _784378] : [-(c_FunDef_Oreduction__pair(_784376, _784372)), c_FunDef_Oreduction__pair(_784378, _784374), _784378 = _784376, _784374 = _784372], (292 ^ _780086) ^ [_784565, _784567, _784569, _784571] : [-(c_Nitpick_Owf_H(_784569, _784565)), c_Nitpick_Owf_H(_784571, _784567), _784571 = _784569, _784567 = _784565], (306 ^ _780086) ^ [_784758, _784760] : [-(c_Nitpick_Ounknown(_784758)), _784760 = _784758, c_Nitpick_Ounknown(_784760)], (316 ^ _780086) ^ [_784883, _784885, _784887, _784889] : [-(c_Wellfounded_OwfP(_784887, _784883)), c_Wellfounded_OwfP(_784889, _784885), _784889 = _784887, _784885 = _784883], (330 ^ _780086) ^ [_785076, _785078, _785080, _785082, _785084, _785086, _785088, _785090] : [-(c_Finite__Set_Ofolding(_785088, _785084, _785080, _785076)), c_Finite__Set_Ofolding(_785090, _785086, _785082, _785078), _785090 = _785088, _785086 = _785084, _785082 = _785080, _785078 = _785076], (352 ^ _780086) ^ [_785429, _785431, _785433, _785435, _785437, _785439, _785441, _785443] : [-(c_Finite__Set_Ofolding__idem(_785441, _785437, _785433, _785429)), c_Finite__Set_Ofolding__idem(_785443, _785439, _785435, _785431), _785443 = _785441, _785439 = _785437, _785435 = _785433, _785431 = _785429], (374 ^ _780086) ^ [_785782, _785784, _785786, _785788] : [-(c_Relation_Oirrefl(_785786, _785782)), c_Relation_Oirrefl(_785788, _785784), _785788 = _785786, _785784 = _785782], (388 ^ _780086) ^ [_785975, _785977, _785979, _785981, _785983, _785985] : [-(c_Relation_Osingle__valued(_785983, _785979, _785975)), c_Relation_Osingle__valued(_785985, _785981, _785977), _785985 = _785983, _785981 = _785979, _785977 = _785975], (406 ^ _780086) ^ [_786244, _786246, _786248, _786250, _786252, _786254] : [-(c_Relation_Ototal__on(_786252, _786248, _786244)), c_Relation_Ototal__on(_786254, _786250, _786246), _786254 = _786252, _786250 = _786248, _786246 = _786244], (424 ^ _780086) ^ [_786513, _786515] : [-(class_Rings_Oinverse(_786513)), _786515 = _786513, class_Rings_Oinverse(_786515)], (434 ^ _780086) ^ [_786638, _786640, _786642, _786644, _786646, _786648] : [-(c_Nitpick_Oless__frac(_786646, _786642, _786638)), c_Nitpick_Oless__frac(_786648, _786644, _786640), _786648 = _786646, _786644 = _786642, _786640 = _786638], (452 ^ _780086) ^ [_786907, _786909, _786911, _786913, _786915, _786917] : [-(c_Nitpick_Oless__eq__frac(_786915, _786911, _786907)), c_Nitpick_Oless__eq__frac(_786917, _786913, _786909), _786917 = _786915, _786913 = _786911, _786909 = _786907], (470 ^ _780086) ^ [_787176, _787178] : [-(c_Nat__Transfer_Onat__set(_787176)), _787178 = _787176, c_Nat__Transfer_Onat__set(_787178)], (480 ^ _780086) ^ [_787301, _787303, _787305, _787307, _787309, _787311, _787313, _787315] : [-(c_List_Olistrelp(_787313, _787309, _787305, _787301)), c_List_Olistrelp(_787315, _787311, _787307, _787303), _787315 = _787313, _787311 = _787309, _787307 = _787305, _787303 = _787301], (502 ^ _780086) ^ [_787654, _787656] : [-(class_Lattices_Oab__semigroup__idem__mult(_787654)), _787656 = _787654, class_Lattices_Oab__semigroup__idem__mult(_787656)], (512 ^ _780086) ^ [_787779, _787781, _787783, _787785, _787787, _787789] : [-(c_Finite__Set_Ofun__left__comm__idem(_787787, _787783, _787779)), c_Finite__Set_Ofun__left__comm__idem(_787789, _787785, _787781), _787789 = _787787, _787785 = _787783, _787781 = _787779], (530 ^ _780086) ^ [_788048, _788050, _788052, _788054, _788056, _788058, _788060, _788062, _788064, _788066] : [-(c_Typedef_Otype__definition(_788064, _788060, _788056, _788052, _788048)), c_Typedef_Otype__definition(_788066, _788062, _788058, _788054, _788050), _788066 = _788064, _788062 = _788060, _788058 = _788056, _788054 = _788052, _788050 = _788048], (556 ^ _780086) ^ [_788493, _788495, _788497, _788499, _788501, _788503] : [-(c_Finite__Set_Ofun__left__comm(_788501, _788497, _788493)), c_Finite__Set_Ofun__left__comm(_788503, _788499, _788495), _788503 = _788501, _788499 = _788497, _788495 = _788493], (574 ^ _780086) ^ [_788762, _788764] : [-(c_List_Onat__list(_788762)), _788764 = _788762, c_List_Onat__list(_788764)], (584 ^ _780086) ^ [_788887, _788889, _788891, _788893, _788895, _788897, _788899, _788901, _788903, _788905] : [-(c_List_Olist__all2(_788903, _788899, _788895, _788891, _788887)), c_List_Olist__all2(_788905, _788901, _788897, _788893, _788889), _788905 = _788903, _788901 = _788899, _788897 = _788895, _788893 = _788891, _788889 = _788887], (610 ^ _780086) ^ [_789332, _789334, _789336, _789338] : [-(c_List_Olinorder__class_Osorted(_789336, _789332)), c_List_Olinorder__class_Osorted(_789338, _789334), _789338 = _789336, _789334 = _789332], (624 ^ _780086) ^ [_789525, _789527, _789529, _789531] : [-(c_FunDef_Ois__measure(_789529, _789525)), c_FunDef_Ois__measure(_789531, _789527), _789531 = _789529, _789527 = _789525], (638 ^ _780086) ^ [_789718, _789720, _789722, _789724, _789726, _789728, _789730, _789732] : [-(c_Nat__Transfer_Otransfer__morphism(_789730, _789726, _789722, _789718)), c_Nat__Transfer_Otransfer__morphism(_789732, _789728, _789724, _789720), _789732 = _789730, _789728 = _789726, _789724 = _789722, _789720 = _789718], (660 ^ _780086) ^ [_790071, _790073] : [-(class_Fields_Olinordered__field(_790071)), _790073 = _790071, class_Fields_Olinordered__field(_790073)], (670 ^ _780086) ^ [_790196, _790198, _790200, _790202, _790204, _790206] : [-(c_List_Olist__ex1(_790204, _790200, _790196)), c_List_Olist__ex1(_790206, _790202, _790198), _790206 = _790204, _790202 = _790200, _790198 = _790196], (688 ^ _780086) ^ [_790465, _790467, _790469, _790471, _790473, _790475] : [-(c_List_Oall__interval__int(_790473, _790469, _790465)), c_List_Oall__interval__int(_790475, _790471, _790467), _790475 = _790473, _790471 = _790469, _790467 = _790465], (706 ^ _780086) ^ [_790734, _790736, _790738, _790740] : [-(c_Predicate_Oreflp(_790738, _790734)), c_Predicate_Oreflp(_790740, _790736), _790740 = _790738, _790736 = _790734], (720 ^ _780086) ^ [_790927, _790929, _790931, _790933, _790935, _790937, _790939, _790941] : [-(c_Wellfounded_Omax__extp(_790939, _790935, _790931, _790927)), c_Wellfounded_Omax__extp(_790941, _790937, _790933, _790929), _790941 = _790939, _790937 = _790935, _790933 = _790931, _790929 = _790927], (742 ^ _780086) ^ [_791280, _791282, _791284, _791286] : [-(c_Wellfounded_Oacyclic(_791284, _791280)), c_Wellfounded_Oacyclic(_791286, _791282), _791286 = _791284, _791282 = _791280], (756 ^ _780086) ^ [_791473, _791475, _791477, _791479] : [-(c_Relation_Oantisym(_791477, _791473)), c_Relation_Oantisym(_791479, _791475), _791479 = _791477, _791475 = _791473], (770 ^ _780086) ^ [_791666, _791668, _791670, _791672, _791674, _791676] : [-(c_Equiv__Relations_Oequiv(_791674, _791670, _791666)), c_Equiv__Relations_Oequiv(_791676, _791672, _791668), _791676 = _791674, _791672 = _791670, _791668 = _791666], (788 ^ _780086) ^ [_791935, _791937, _791939, _791941] : [-(c_Relation_Otrans(_791939, _791935)), c_Relation_Otrans(_791941, _791937), _791941 = _791939, _791937 = _791935], (802 ^ _780086) ^ [_792128, _792130, _792132, _792134] : [-(c_Relation_Osym(_792132, _792128)), c_Relation_Osym(_792134, _792130), _792134 = _792132, _792130 = _792128], (816 ^ _780086) ^ [_792321, _792323, _792325, _792327] : [-(c_Predicate_Osymp(_792325, _792321)), c_Predicate_Osymp(_792327, _792323), _792327 = _792325, _792323 = _792321], (830 ^ _780086) ^ [_792514, _792516, _792518, _792520] : [-(c_Predicate_Otransp(_792518, _792514)), c_Predicate_Otransp(_792520, _792516), _792520 = _792518, _792516 = _792514], (844 ^ _780086) ^ [_792707, _792709, _792711, _792713] : [-(c_Equiv__Relations_Opart__equivp(_792711, _792707)), c_Equiv__Relations_Opart__equivp(_792713, _792709), _792713 = _792711, _792709 = _792707], (858 ^ _780086) ^ [_792900, _792902, _792904, _792906, _792908, _792910, _792912, _792914] : [-(c_Fun_Oinj__on(_792912, _792908, _792904, _792900)), c_Fun_Oinj__on(_792914, _792910, _792906, _792902), _792914 = _792912, _792910 = _792908, _792906 = _792904, _792902 = _792900], (880 ^ _780086) ^ [_793253, _793255, _793257, _793259, _793261, _793263, _793265, _793267, _793269, _793271] : [-(c_Fun_Obij__betw(_793269, _793265, _793261, _793257, _793253)), c_Fun_Obij__betw(_793271, _793267, _793263, _793259, _793255), _793271 = _793269, _793267 = _793265, _793263 = _793261, _793259 = _793257, _793255 = _793253], (906 ^ _780086) ^ [_793698, _793700, _793702, _793704, _793706, _793708] : [-(c_Relation_Orefl__on(_793706, _793702, _793698)), c_Relation_Orefl__on(_793708, _793704, _793700), _793708 = _793706, _793704 = _793702, _793700 = _793698], (924 ^ _780086) ^ [_793967, _793969, _793971, _793973] : [-(c_Equiv__Relations_Oequivp(_793971, _793967)), c_Equiv__Relations_Oequivp(_793973, _793969), _793973 = _793971, _793969 = _793967], (938 ^ _780086) ^ [_794160, _794162, _794164, _794166] : [-(c_Wellfounded_Owf(_794164, _794160)), c_Wellfounded_Owf(_794166, _794162), _794166 = _794164, _794162 = _794160], (952 ^ _780086) ^ [_794353, _794355, _794357, _794359, _794361, _794363, _794365, _794367, _794369, _794371, _794373, _794375] : [-(c_Equiv__Relations_Ocongruent2(_794373, _794369, _794365, _794361, _794357, _794353)), c_Equiv__Relations_Ocongruent2(_794375, _794371, _794367, _794363, _794359, _794355), _794375 = _794373, _794371 = _794369, _794367 = _794365, _794363 = _794361, _794359 = _794357, _794355 = _794353], (982 ^ _780086) ^ [_794898, _794900, _794902, _794904, _794906, _794908, _794910, _794912] : [-(c_Equiv__Relations_Ocongruent(_794910, _794906, _794902, _794898)), c_Equiv__Relations_Ocongruent(_794912, _794908, _794904, _794900), _794912 = _794910, _794908 = _794906, _794904 = _794902, _794900 = _794898], (1004 ^ _780086) ^ [_795251, _795253, _795255, _795257, _795259, _795261] : [-(c_List_Olist__all(_795259, _795255, _795251)), c_List_Olist__all(_795261, _795257, _795253), _795261 = _795259, _795257 = _795255, _795253 = _795251], (1022 ^ _780086) ^ [_795520, _795522, _795524, _795526, _795528, _795530] : [-(c_List_Olist__ex(_795528, _795524, _795520)), c_List_Olist__ex(_795530, _795526, _795522), _795530 = _795528, _795526 = _795524, _795522 = _795520], (1040 ^ _780086) ^ [_795789, _795791, _795793, _795795, _795797, _795799] : [-(c_List_Oall__interval__nat(_795797, _795793, _795789)), c_List_Oall__interval__nat(_795799, _795795, _795791), _795799 = _795797, _795795 = _795793, _795791 = _795789], (1058 ^ _780086) ^ [_796058, _796060, _796062, _796064, _796066, _796068, _796070, _796072, _796074, _796076] : [-(c_Finite__Set_Ofolding__image(_796074, _796070, _796066, _796062, _796058)), c_Finite__Set_Ofolding__image(_796076, _796072, _796068, _796064, _796060), _796076 = _796074, _796072 = _796070, _796068 = _796066, _796064 = _796062, _796060 = _796058], (1084 ^ _780086) ^ [_796503, _796505] : [-(class_Lattices_Obounded__lattice(_796503)), _796505 = _796503, class_Lattices_Obounded__lattice(_796505)], (1094 ^ _780086) ^ [_796628, _796630] : [-(class_Rings_Olinordered__semiring__1__strict(_796628)), _796630 = _796628, class_Rings_Olinordered__semiring__1__strict(_796630)], (1104 ^ _780086) ^ [_796753, _796755] : [-(class_Groups_Oordered__ab__group__add__abs(_796753)), _796755 = _796753, class_Groups_Oordered__ab__group__add__abs(_796755)], (1114 ^ _780086) ^ [_796878, _796880] : [-(class_Groups_Olinordered__ab__group__add(_796878)), _796880 = _796878, class_Groups_Olinordered__ab__group__add(_796880)], (1124 ^ _780086) ^ [_797003, _797005] : [-(class_Rings_Oring__1__no__zero__divisors(_797003)), _797005 = _797003, class_Rings_Oring__1__no__zero__divisors(_797005)], (1134 ^ _780086) ^ [_797128, _797130] : [-(class_Rings_Olinordered__ring__strict(_797128)), _797130 = _797128, class_Rings_Olinordered__ring__strict(_797130)], (1144 ^ _780086) ^ [_797253, _797255] : [-(class_Rings_Oring__no__zero__divisors(_797253)), _797255 = _797253, class_Rings_Oring__no__zero__divisors(_797255)], (1154 ^ _780086) ^ [_797378, _797380] : [-(class_Rings_Olinordered__semiring__1(_797378)), _797380 = _797378, class_Rings_Olinordered__semiring__1(_797380)], (1164 ^ _780086) ^ [_797503, _797505] : [-(class_Groups_Oordered__ab__group__add(_797503)), _797505 = _797503, class_Groups_Oordered__ab__group__add(_797505)], (1174 ^ _780086) ^ [_797628, _797630] : [-(class_Rings_Oordered__ring__abs(_797628)), _797630 = _797628, class_Rings_Oordered__ring__abs(_797630)], (1184 ^ _780086) ^ [_797753, _797755] : [-(class_Rings_Olinordered__ring(_797753)), _797755 = _797753, class_Rings_Olinordered__ring(_797755)], (1194 ^ _780086) ^ [_797878, _797880] : [-(class_Rings_Olinordered__idom(_797878)), _797880 = _797878, class_Rings_Olinordered__idom(_797880)], (1204 ^ _780086) ^ [_798003, _798005] : [-(class_Groups_Oab__group__add(_798003)), _798005 = _798003, class_Groups_Oab__group__add(_798005)], (1214 ^ _780086) ^ [_798128, _798130] : [-(class_Rings_Oordered__ring(_798128)), _798130 = _798128, class_Rings_Oordered__ring(_798130)], (1224 ^ _780086) ^ [_798253, _798255] : [-(class_Rings_Ocomm__ring__1(_798253)), _798255 = _798253, class_Rings_Ocomm__ring__1(_798255)], (1234 ^ _780086) ^ [_798378, _798380] : [-(class_Groups_Ogroup__add(_798378)), _798380 = _798378, class_Groups_Ogroup__add(_798380)], (1244 ^ _780086) ^ [_798503, _798505] : [-(class_Divides_Oring__div(_798503)), _798505 = _798503, class_Divides_Oring__div(_798505)], (1254 ^ _780086) ^ [_798628, _798630] : [-(class_Rings_Ocomm__ring(_798628)), _798630 = _798628, class_Rings_Ocomm__ring(_798630)], (1264 ^ _780086) ^ [_798753, _798755] : [-(class_Int_Oring__char__0(_798753)), _798755 = _798753, class_Int_Oring__char__0(_798755)], (1274 ^ _780086) ^ [_798878, _798880] : [-(class_Int_Onumber__ring(_798878)), _798880 = _798878, class_Int_Onumber__ring(_798880)], (1284 ^ _780086) ^ [_799003, _799005] : [-(class_Groups_Osgn__if(_799003)), _799005 = _799003, class_Groups_Osgn__if(_799005)], (1294 ^ _780086) ^ [_799128, _799130] : [-(class_Groups_Oabs__if(_799128)), _799130 = _799128, class_Groups_Oabs__if(_799130)], (1304 ^ _780086) ^ [_799253, _799255] : [-(class_Rings_Oring__1(_799253)), _799255 = _799253, class_Rings_Oring__1(_799255)], (1314 ^ _780086) ^ [_799378, _799380] : [-(class_Rings_Oring(_799378)), _799380 = _799378, class_Rings_Oring(_799380)], (1324 ^ _780086) ^ [_799503, _799505] : [-(class_Rings_Oidom(_799503)), _799505 = _799503, class_Rings_Oidom(_799505)], (1334 ^ _780086) ^ [_799628, _799630] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_799628)), _799630 = _799628, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_799630)], (1344 ^ _780086) ^ [_799753, _799755] : [-(class_Orderings_Owellorder(_799753)), _799755 = _799753, class_Orderings_Owellorder(_799755)], (1354 ^ _780086) ^ [_799878, _799880] : [-(class_Complete__Lattice_Ocomplete__lattice(_799878)), _799880 = _799878, class_Complete__Lattice_Ocomplete__lattice(_799880)], (1364 ^ _780086) ^ [_800003, _800005] : [-(class_Lattices_Obounded__lattice__top(_800003)), _800005 = _800003, class_Lattices_Obounded__lattice__top(_800005)], (1374 ^ _780086) ^ [_800128, _800130] : [-(class_Lattices_Obounded__lattice__bot(_800128)), _800130 = _800128, class_Lattices_Obounded__lattice__bot(_800130)], (1384 ^ _780086) ^ [_800253, _800255] : [-(class_Lattices_Osemilattice__sup(_800253)), _800255 = _800253, class_Lattices_Osemilattice__sup(_800255)], (1394 ^ _780086) ^ [_800378, _800380] : [-(class_Lattices_Osemilattice__inf(_800378)), _800380 = _800378, class_Lattices_Osemilattice__inf(_800380)], (1404 ^ _780086) ^ [_800503, _800505] : [-(class_Lattices_Odistrib__lattice(_800503)), _800505 = _800503, class_Lattices_Odistrib__lattice(_800505)], (1414 ^ _780086) ^ [_800628, _800630] : [-(class_Lattices_Oboolean__algebra(_800628)), _800630 = _800628, class_Lattices_Oboolean__algebra(_800630)], (1424 ^ _780086) ^ [_800753, _800755] : [-(class_Lattices_Olattice(_800753)), _800755 = _800753, class_Lattices_Olattice(_800755)], (1434 ^ _780086) ^ [_800878, _800880] : [-(class_Orderings_Otop(_800878)), _800880 = _800878, class_Orderings_Otop(_800880)], (1444 ^ _780086) ^ [_801003, _801005] : [-(class_Orderings_Obot(_801003)), _801005 = _801003, class_Orderings_Obot(_801005)], (1454 ^ _780086) ^ [_801128, _801130] : [-(class_Groups_Ouminus(_801128)), _801130 = _801128, class_Groups_Ouminus(_801130)], (1464 ^ _780086) ^ [_801253, _801255] : [-(class_Lazy__Sequence_Osmall__lazy(_801253)), _801255 = _801253, class_Lazy__Sequence_Osmall__lazy(_801255)], (1474 ^ _780086) ^ [_801378, _801380] : [-(class_Finite__Set_Ofinite(_801378)), _801380 = _801378, class_Finite__Set_Ofinite(_801380)], (1484 ^ _780086) ^ [_801503, _801505] : [-(class_Enum_Oenum(_801503)), _801505 = _801503, class_Enum_Oenum(_801505)], (1494 ^ _780086) ^ [_801628, _801630] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_801628)), _801630 = _801628, class_Groups_Oordered__cancel__ab__semigroup__add(_801630)], (1504 ^ _780086) ^ [_801753, _801755] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_801753)), _801755 = _801753, class_Groups_Oordered__ab__semigroup__add__imp__le(_801755)], (1514 ^ _780086) ^ [_801878, _801880] : [-(class_Rings_Olinordered__comm__semiring__strict(_801878)), _801880 = _801878, class_Rings_Olinordered__comm__semiring__strict(_801880)], (1524 ^ _780086) ^ [_802003, _802005] : [-(class_Groups_Olinordered__ab__semigroup__add(_802003)), _802005 = _802003, class_Groups_Olinordered__ab__semigroup__add(_802005)], (1534 ^ _780086) ^ [_802128, _802130] : [-(class_Rings_Olinordered__semiring__strict(_802128)), _802130 = _802128, class_Rings_Olinordered__semiring__strict(_802130)], (1544 ^ _780086) ^ [_802253, _802255] : [-(class_Groups_Oordered__ab__semigroup__add(_802253)), _802255 = _802253, class_Groups_Oordered__ab__semigroup__add(_802255)], (1554 ^ _780086) ^ [_802378, _802380] : [-(class_Groups_Oordered__comm__monoid__add(_802378)), _802380 = _802378, class_Groups_Oordered__comm__monoid__add(_802380)], (1564 ^ _780086) ^ [_802503, _802505] : [-(class_Groups_Ocancel__ab__semigroup__add(_802503)), _802505 = _802503, class_Groups_Ocancel__ab__semigroup__add(_802505)], (1574 ^ _780086) ^ [_802628, _802630] : [-(class_Rings_Oordered__cancel__semiring(_802628)), _802630 = _802628, class_Rings_Oordered__cancel__semiring(_802630)], (1584 ^ _780086) ^ [_802753, _802755] : [-(class_Rings_Oordered__comm__semiring(_802753)), _802755 = _802753, class_Rings_Oordered__comm__semiring(_802755)], (1594 ^ _780086) ^ [_802878, _802880] : [-(class_Groups_Ocancel__semigroup__add(_802878)), _802880 = _802878, class_Groups_Ocancel__semigroup__add(_802880)], (1604 ^ _780086) ^ [_803003, _803005] : [-(class_Rings_Olinordered__semiring(_803003)), _803005 = _803003, class_Rings_Olinordered__semiring(_803005)], (1614 ^ _780086) ^ [_803128, _803130] : [-(class_Rings_Olinordered__semidom(_803128)), _803130 = _803128, class_Rings_Olinordered__semidom(_803130)], (1624 ^ _780086) ^ [_803253, _803255] : [-(class_Groups_Oab__semigroup__mult(_803253)), _803255 = _803253, class_Groups_Oab__semigroup__mult(_803255)], (1634 ^ _780086) ^ [_803378, _803380] : [-(class_Groups_Ocomm__monoid__mult(_803378)), _803380 = _803378, class_Groups_Ocomm__monoid__mult(_803380)], (1644 ^ _780086) ^ [_803503, _803505] : [-(class_Groups_Oab__semigroup__add(_803503)), _803505 = _803503, class_Groups_Oab__semigroup__add(_803505)], (1654 ^ _780086) ^ [_803628, _803630] : [-(class_Rings_Oordered__semiring(_803628)), _803630 = _803628, class_Rings_Oordered__semiring(_803630)], (1664 ^ _780086) ^ [_803753, _803755] : [-(class_Rings_Ono__zero__divisors(_803753)), _803755 = _803753, class_Rings_Ono__zero__divisors(_803755)], (1674 ^ _780086) ^ [_803878, _803880] : [-(class_Groups_Ocomm__monoid__add(_803878)), _803880 = _803878, class_Groups_Ocomm__monoid__add(_803880)], (1684 ^ _780086) ^ [_804003, _804005] : [-(class_Rings_Ocomm__semiring__1(_804003)), _804005 = _804003, class_Rings_Ocomm__semiring__1(_804005)], (1694 ^ _780086) ^ [_804128, _804130] : [-(class_Groups_Osemigroup__add(_804128)), _804130 = _804128, class_Groups_Osemigroup__add(_804130)], (1704 ^ _780086) ^ [_804253, _804255] : [-(class_Divides_Osemiring__div(_804253)), _804255 = _804253, class_Divides_Osemiring__div(_804255)], (1714 ^ _780086) ^ [_804378, _804380] : [-(class_Rings_Ocomm__semiring(_804378)), _804380 = _804378, class_Rings_Ocomm__semiring(_804380)], (1724 ^ _780086) ^ [_804503, _804505] : [-(class_Nat_Osemiring__char__0(_804503)), _804505 = _804503, class_Nat_Osemiring__char__0(_804505)], (1734 ^ _780086) ^ [_804628, _804630] : [-(class_Rings_Ozero__neq__one(_804628)), _804630 = _804628, class_Rings_Ozero__neq__one(_804630)], (1744 ^ _780086) ^ [_804753, _804755] : [-(class_Orderings_Opreorder(_804753)), _804755 = _804753, class_Orderings_Opreorder(_804755)], (1754 ^ _780086) ^ [_804878, _804880] : [-(class_Orderings_Olinorder(_804878)), _804880 = _804878, class_Orderings_Olinorder(_804880)], (1764 ^ _780086) ^ [_805003, _805005] : [-(class_Groups_Omonoid__mult(_805003)), _805005 = _805003, class_Groups_Omonoid__mult(_805005)], (1774 ^ _780086) ^ [_805128, _805130] : [-(class_Groups_Omonoid__add(_805128)), _805130 = _805128, class_Groups_Omonoid__add(_805130)], (1784 ^ _780086) ^ [_805253, _805255] : [-(class_Rings_Osemiring__1(_805253)), _805255 = _805253, class_Rings_Osemiring__1(_805255)], (1794 ^ _780086) ^ [_805378, _805380] : [-(class_Rings_Osemiring__0(_805378)), _805380 = _805378, class_Rings_Osemiring__0(_805380)], (1804 ^ _780086) ^ [_805503, _805505] : [-(class_Rings_Omult__zero(_805503)), _805505 = _805503, class_Rings_Omult__zero(_805505)], (1814 ^ _780086) ^ [_805628, _805630] : [-(class_Orderings_Oorder(_805628)), _805630 = _805628, class_Orderings_Oorder(_805630)], (1824 ^ _780086) ^ [_805753, _805755] : [-(class_Rings_Osemiring(_805753)), _805755 = _805753, class_Rings_Osemiring(_805755)], (1834 ^ _780086) ^ [_805878, _805880] : [-(class_Orderings_Oord(_805878)), _805880 = _805878, class_Orderings_Oord(_805880)], (1844 ^ _780086) ^ [_806003, _806005] : [-(class_Groups_Ominus(_806003)), _806005 = _806003, class_Groups_Ominus(_806005)], (1854 ^ _780086) ^ [_806128, _806130] : [-(class_Power_Opower(_806128)), _806130 = _806128, class_Power_Opower(_806130)], (1864 ^ _780086) ^ [_806253, _806255] : [-(class_Groups_Ozero(_806253)), _806255 = _806253, class_Groups_Ozero(_806255)], (1874 ^ _780086) ^ [_806378, _806380] : [-(class_Int_Onumber(_806378)), _806380 = _806378, class_Int_Onumber(_806380)], (1884 ^ _780086) ^ [_806503, _806505] : [-(class_Groups_Oone(_806503)), _806505 = _806503, class_Groups_Oone(_806505)], (1894 ^ _780086) ^ [_806628, _806630] : [-(class_Rings_Odvd(_806628)), _806630 = _806628, class_Rings_Odvd(_806630)], (1904 ^ _780086) ^ [_806753, _806755] : [-(class_Nat_Osize(_806753)), _806755 = _806753, class_Nat_Osize(_806755)], (1914 ^ _780086) ^ [_806878, _806880] : [-(hBOOL(_806878)), _806880 = _806878, hBOOL(_806880)], (1924 ^ _780086) ^ [_806999, _807001, _807003, _807005, _807007, _807009] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_807007, _807003, _806999)), c_Hoare__Mirabelle_Ohoare__derivs(_807009, _807005, _807001), _807009 = _807007, _807005 = _807003, _807001 = _806999], (1942 ^ _780086) ^ [_808049, _808051, _808053, _808055, _808057, _808059, _808061, _808063] : [-(c_Hoare__Mirabelle_Otriple_Otriple__case(_808063, _808059, _808055, _808051) = c_Hoare__Mirabelle_Otriple_Otriple__case(_808061, _808057, _808053, _808049)), _808063 = _808061, _808059 = _808057, _808055 = _808053, _808051 = _808049], (1960 ^ _780086) ^ [_808350, _808352, _808354, _808356, _808358, _808360, _808362, _808364] : [-(c_Hoare__Mirabelle_Otriple_Otriple__rec(_808364, _808360, _808356, _808352) = c_Hoare__Mirabelle_Otriple_Otriple__rec(_808362, _808358, _808354, _808350)), _808364 = _808362, _808360 = _808358, _808356 = _808354, _808352 = _808350], (1978 ^ _780086) ^ [_808651, _808653, _808655, _808657, _808659, _808661, _808663, _808665, _808667, _808669] : [-(c_Fun_Ooverride__on(_808669, _808665, _808661, _808657, _808653) = c_Fun_Ooverride__on(_808667, _808663, _808659, _808655, _808651)), _808669 = _808667, _808665 = _808663, _808661 = _808659, _808657 = _808655, _808653 = _808651], (2000 ^ _780086) ^ [_809040, _809042, _809044, _809046, _809048, _809050] : [-(c_Partial__Function_Oflat__lub(_809050, _809046, _809042) = c_Partial__Function_Oflat__lub(_809048, _809044, _809040)), _809050 = _809048, _809046 = _809044, _809042 = _809040], (2014 ^ _780086) ^ [_809261, _809263, _809265, _809267, _809269, _809271, _809273, _809275, _809277, _809279] : [-(c_Finite__Set_Ofold__graph(_809279, _809275, _809271, _809267, _809263) = c_Finite__Set_Ofold__graph(_809277, _809273, _809269, _809265, _809261)), _809279 = _809277, _809275 = _809273, _809271 = _809269, _809267 = _809265, _809263 = _809261], (2036 ^ _780086) ^ [_809650, _809652, _809654, _809656, _809658, _809660] : [-(c_Finite__Set_Ofold1Set(_809660, _809656, _809652) = c_Finite__Set_Ofold1Set(_809658, _809654, _809650)), _809660 = _809658, _809656 = _809654, _809652 = _809650], (2050 ^ _780086) ^ [_809871, _809873, _809875, _809877] : [-(c_Orderings_Oord_Omax(_809877, _809873) = c_Orderings_Oord_Omax(_809875, _809871)), _809877 = _809875, _809873 = _809871], (2060 ^ _780086) ^ [_810020, _810022, _810024, _810026] : [-(c_Orderings_Oord_Omin(_810026, _810022) = c_Orderings_Oord_Omin(_810024, _810020)), _810026 = _810024, _810022 = _810020], (2070 ^ _780086) ^ [_810169, _810171, _810173, _810175, _810177, _810179] : [-(c_SetInterval_Oord_OatMost(_810179, _810175, _810171) = c_SetInterval_Oord_OatMost(_810177, _810173, _810169)), _810179 = _810177, _810175 = _810173, _810171 = _810169], (2084 ^ _780086) ^ [_810390, _810392, _810394, _810396, _810398, _810400] : [-(c_SetInterval_Oord_OatLeast(_810400, _810396, _810392) = c_SetInterval_Oord_OatLeast(_810398, _810394, _810390)), _810400 = _810398, _810396 = _810394, _810392 = _810390], (2098 ^ _780086) ^ [_810611, _810613, _810615, _810617, _810619, _810621] : [-(c_SetInterval_Oord_OlessThan(_810621, _810617, _810613) = c_SetInterval_Oord_OlessThan(_810619, _810615, _810611)), _810621 = _810619, _810617 = _810615, _810613 = _810611], (2112 ^ _780086) ^ [_810832, _810834, _810836, _810838, _810840, _810842] : [-(c_SetInterval_Oord_OgreaterThan(_810842, _810838, _810834) = c_SetInterval_Oord_OgreaterThan(_810840, _810836, _810832)), _810842 = _810840, _810838 = _810836, _810834 = _810832], (2126 ^ _780086) ^ [_811053, _811055, _811057, _811059, _811061, _811063] : [-(c_Power_Opower_Opower(_811063, _811059, _811055) = c_Power_Opower_Opower(_811061, _811057, _811053)), _811063 = _811061, _811059 = _811057, _811055 = _811053], (2140 ^ _780086) ^ [_811274, _811276, _811278, _811280, _811282, _811284] : [-(c_Hoare__Mirabelle_Otriple_Otriple__size(_811284, _811280, _811276) = c_Hoare__Mirabelle_Otriple_Otriple__size(_811282, _811278, _811274)), _811284 = _811282, _811280 = _811278, _811276 = _811274], (2154 ^ _780086) ^ [_811495, _811497, _811499, _811501, _811503, _811505, _811507, _811509] : [-(c_Nat_Osemiring__1__class_Oof__nat__aux(_811509, _811505, _811501, _811497) = c_Nat_Osemiring__1__class_Oof__nat__aux(_811507, _811503, _811499, _811495)), _811509 = _811507, _811505 = _811503, _811501 = _811499, _811497 = _811495], (2172 ^ _780086) ^ [_811796, _811798, _811800, _811802] : [-(c_SMT_Oz3div(_811802, _811798) = c_SMT_Oz3div(_811800, _811796)), _811802 = _811800, _811798 = _811796], (2182 ^ _780086) ^ [_811945, _811947, _811949, _811951, _811953, _811955, _811957, _811959] : [-(c_Sum__Type_OPlus(_811959, _811955, _811951, _811947) = c_Sum__Type_OPlus(_811957, _811953, _811949, _811945)), _811959 = _811957, _811955 = _811953, _811951 = _811949, _811947 = _811945], (2200 ^ _780086) ^ [_812246, _812248, _812250, _812252] : [-(c_Int_Onat__aux(_812252, _812248) = c_Int_Onat__aux(_812250, _812246)), _812252 = _812250, _812248 = _812246], (2210 ^ _780086) ^ [_812395, _812397, _812399, _812401] : [-(c_Nat__Transfer_Otsub(_812401, _812397) = c_Nat__Transfer_Otsub(_812399, _812395)), _812401 = _812399, _812397 = _812395], (2220 ^ _780086) ^ [_812544, _812546] : [_812546 = _812544, -(c_SetInterval_Oord__class_OgreaterThan(_812546) = c_SetInterval_Oord__class_OgreaterThan(_812544))], (2226 ^ _780086) ^ [_812629, _812631] : [_812631 = _812629, -(c_SetInterval_Oord__class_OatLeast(_812631) = c_SetInterval_Oord__class_OatLeast(_812629))], (2232 ^ _780086) ^ [_812714, _812716, _812718, _812720] : [-(c_SMT_Oz3mod(_812720, _812716) = c_SMT_Oz3mod(_812718, _812714)), _812720 = _812718, _812716 = _812714], (2242 ^ _780086) ^ [_812863, _812865, _812867, _812869] : [-(c_Nitpick_Onat__lcm(_812869, _812865) = c_Nitpick_Onat__lcm(_812867, _812863)), _812869 = _812867, _812865 = _812863], (2252 ^ _780086) ^ [_813012, _813014] : [_813014 = _813012, -(c_Com_Ocom_Ocom__size(_813014) = c_Com_Ocom_Ocom__size(_813012))], (2258 ^ _780086) ^ [_813097, _813099, _813101, _813103] : [-(c_Com_Ocom_OSemi(_813103, _813099) = c_Com_Ocom_OSemi(_813101, _813097)), _813103 = _813101, _813099 = _813097], (2268 ^ _780086) ^ [_813246, _813248] : [_813248 = _813246, -(c_Int_Oring__1__class_OInts(_813248) = c_Int_Oring__1__class_OInts(_813246))], (2274 ^ _780086) ^ [_813331, _813333, _813335, _813337, _813339, _813341] : [-(c_Com_Ocom_OLocal(_813341, _813337, _813333) = c_Com_Ocom_OLocal(_813339, _813335, _813331)), _813341 = _813339, _813337 = _813335, _813333 = _813331], (2288 ^ _780086) ^ [_813552, _813554, _813556, _813558, _813560, _813562] : [-(c_Nat_Onat_Onat__rec(_813562, _813558, _813554) = c_Nat_Onat_Onat__rec(_813560, _813556, _813552)), _813562 = _813560, _813558 = _813556, _813554 = _813552], (2302 ^ _780086) ^ [_813773, _813775] : [_813775 = _813773, -(c_Int_Opred(_813775) = c_Int_Opred(_813773))], (2308 ^ _780086) ^ [_813858, _813860] : [_813860 = _813858, -(c_Int_Osucc(_813860) = c_Int_Osucc(_813858))], (2314 ^ _780086) ^ [_813943, _813945, _813947, _813949, _813951, _813953, _813955, _813957] : [-(c_Nitpick_Oprod(_813957, _813953, _813949, _813945) = c_Nitpick_Oprod(_813955, _813951, _813947, _813943)), _813957 = _813955, _813953 = _813951, _813949 = _813947, _813945 = _813943], (2332 ^ _780086) ^ [_814244, _814246] : [_814246 = _814244, -(c_Nat_Osemiring__1__class_ONats(_814246) = c_Nat_Osemiring__1__class_ONats(_814244))], (2338 ^ _780086) ^ [_814329, _814331, _814333, _814335] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_814335, _814331) = c_Code__Numeral_Odiv__mod__code__numeral(_814333, _814329)), _814335 = _814333, _814331 = _814329], (2348 ^ _780086) ^ [_814478, _814480, _814482, _814484] : [-(c_Divides_Odivmod__int__rel(_814484, _814480) = c_Divides_Odivmod__int__rel(_814482, _814478)), _814484 = _814482, _814480 = _814478], (2358 ^ _780086) ^ [_814627, _814629, _814631, _814633] : [-(c_Groups_Osgn__class_Osgn(_814633, _814629) = c_Groups_Osgn__class_Osgn(_814631, _814627)), _814633 = _814631, _814629 = _814627], (2368 ^ _780086) ^ [_814776, _814778, _814780, _814782] : [-(c_Divides_Opdivmod(_814782, _814778) = c_Divides_Opdivmod(_814780, _814776)), _814782 = _814780, _814778 = _814776], (2378 ^ _780086) ^ [_814925, _814927] : [_814927 = _814925, -(c_Divides_Oadjust(_814927) = c_Divides_Oadjust(_814925))], (2384 ^ _780086) ^ [_815010, _815012] : [_815012 = _815010, -(c_Int_OBit0(_815012) = c_Int_OBit0(_815010))], (2390 ^ _780086) ^ [_815095, _815097, _815099, _815101] : [-(c_Nitpick_Onat__gcd(_815101, _815097) = c_Nitpick_Onat__gcd(_815099, _815095)), _815101 = _815099, _815097 = _815095], (2400 ^ _780086) ^ [_815244, _815246] : [_815246 = _815244, -(c_Nat_Onat_Onat__size(_815246) = c_Nat_Onat_Onat__size(_815244))], (2406 ^ _780086) ^ [_815329, _815331, _815333, _815335] : [-(c_Set_Othe__elem(_815335, _815331) = c_Set_Othe__elem(_815333, _815329)), _815335 = _815333, _815331 = _815329], (2416 ^ _780086) ^ [_815478, _815480, _815482, _815484] : [-(c_Divides_Odivmod__int(_815484, _815480) = c_Divides_Odivmod__int(_815482, _815478)), _815484 = _815482, _815480 = _815478], (2426 ^ _780086) ^ [_815627, _815629, _815631, _815633] : [-(c_Divides_OnegDivAlg(_815633, _815629) = c_Divides_OnegDivAlg(_815631, _815627)), _815633 = _815631, _815629 = _815627], (2436 ^ _780086) ^ [_815776, _815778, _815780, _815782] : [-(c_Divides_OposDivAlg(_815782, _815778) = c_Divides_OposDivAlg(_815780, _815776)), _815782 = _815780, _815778 = _815776], (2446 ^ _780086) ^ [_815925, _815927, _815929, _815931, _815933, _815935, _815937, _815939, _815941, _815943] : [-(c_Product__Type_Oprod_Oprod__size(_815943, _815939, _815935, _815931, _815927) = c_Product__Type_Oprod_Oprod__size(_815941, _815937, _815933, _815929, _815925)), _815943 = _815941, _815939 = _815937, _815935 = _815933, _815931 = _815929, _815927 = _815925], (2468 ^ _780086) ^ [_816314, _816316, _816318, _816320] : [-(c_Divides_Odivmod__nat(_816320, _816316) = c_Divides_Odivmod__nat(_816318, _816314)), _816320 = _816318, _816316 = _816314], (2478 ^ _780086) ^ [_816463, _816465, _816467, _816469] : [-(c_Divides_Odivmod__nat__rel(_816469, _816465) = c_Divides_Odivmod__nat__rel(_816467, _816463)), _816469 = _816467, _816465 = _816463], (2488 ^ _780086) ^ [_816612, _816614] : [_816614 = _816612, -(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_816614) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_816612))], (2494 ^ _780086) ^ [_816697, _816699, _816701, _816703, _816705, _816707, _816709, _816711, _816713, _816715] : [-(c_Product__Type_Oprod_Oprod__rec(_816715, _816711, _816707, _816703, _816699) = c_Product__Type_Oprod_Oprod__rec(_816713, _816709, _816705, _816701, _816697)), _816715 = _816713, _816711 = _816709, _816707 = _816705, _816703 = _816701, _816699 = _816697], (2516 ^ _780086) ^ [_817086, _817088, _817090, _817092] : [-(c_FunDef_Orp__inv__image(_817092, _817088) = c_FunDef_Orp__inv__image(_817090, _817086)), _817092 = _817090, _817088 = _817086], (2526 ^ _780086) ^ [_817235, _817237, _817239, _817241, _817243, _817245, _817247, _817249] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_817249, _817245, _817241, _817237) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_817247, _817243, _817239, _817235)), _817249 = _817247, _817245 = _817243, _817241 = _817239, _817237 = _817235], (2544 ^ _780086) ^ [_817536, _817538] : [_817538 = _817536, -(c_Wellfounded_Omeasure(_817538) = c_Wellfounded_Omeasure(_817536))], (2550 ^ _780086) ^ [_817621, _817623, _817625, _817627] : [-(c_Wellfounded_Omin__ext(_817627, _817623) = c_Wellfounded_Omin__ext(_817625, _817621)), _817627 = _817625, _817623 = _817621], (2560 ^ _780086) ^ [_817770, _817772, _817774, _817776, _817778, _817780] : [-(c_Wellfounded_Omlex__prod(_817780, _817776, _817772) = c_Wellfounded_Omlex__prod(_817778, _817774, _817770)), _817780 = _817778, _817776 = _817774, _817772 = _817770], (2574 ^ _780086) ^ [_817991, _817993] : [_817993 = _817991, -(c_Int_Oint__ge__less__than2(_817993) = c_Int_Oint__ge__less__than2(_817991))], (2580 ^ _780086) ^ [_818076, _818078] : [_818078 = _818076, -(c_Int_Oint__ge__less__than(_818078) = c_Int_Oint__ge__less__than(_818076))], (2586 ^ _780086) ^ [_818161, _818163, _818165, _818167, _818169, _818171, _818173, _818175] : [-(c_Recdef_Osame__fst(_818175, _818171, _818167, _818163) = c_Recdef_Osame__fst(_818173, _818169, _818165, _818161)), _818175 = _818173, _818171 = _818169, _818167 = _818165, _818163 = _818161], (2604 ^ _780086) ^ [_818462, _818464] : [_818464 = _818462, -(c_Nitpick_Ozero__frac(_818464) = c_Nitpick_Ozero__frac(_818462))], (2610 ^ _780086) ^ [_818547, _818549] : [_818549 = _818547, -(c_Nitpick_Oone__frac(_818549) = c_Nitpick_Oone__frac(_818547))], (2616 ^ _780086) ^ [_818632, _818634, _818636, _818638] : [-(c_Nitpick_Onumber__of__frac(_818638, _818634) = c_Nitpick_Onumber__of__frac(_818636, _818632)), _818638 = _818636, _818634 = _818632], (2626 ^ _780086) ^ [_818781, _818783, _818785, _818787] : [-(c_Nitpick_Onorm__frac(_818787, _818783) = c_Nitpick_Onorm__frac(_818785, _818781)), _818787 = _818785, _818783 = _818781], (2636 ^ _780086) ^ [_818930, _818932] : [_818932 = _818930, -(c_Equiv__Relations_Oquotient(_818932) = c_Equiv__Relations_Oquotient(_818930))], (2642 ^ _780086) ^ [_819015, _819017, _819019, _819021, _819023, _819025] : [-(c_FunDef_Oin__rel(_819025, _819021, _819017) = c_FunDef_Oin__rel(_819023, _819019, _819015)), _819025 = _819023, _819021 = _819019, _819017 = _819015], (2656 ^ _780086) ^ [_819236, _819238] : [_819238 = _819236, -(c_Set_OBall(_819238) = c_Set_OBall(_819236))], (2662 ^ _780086) ^ [_819321, _819323, _819325, _819327] : [-(c_Predicate_OPowp(_819327, _819323) = c_Predicate_OPowp(_819325, _819321)), _819327 = _819325, _819323 = _819321], (2672 ^ _780086) ^ [_819470, _819472, _819474, _819476, _819478, _819480] : [-(c_Predicate_ODomainP(_819480, _819476, _819472) = c_Predicate_ODomainP(_819478, _819474, _819470)), _819480 = _819478, _819476 = _819474, _819472 = _819470], (2686 ^ _780086) ^ [_819691, _819693, _819695, _819697, _819699, _819701] : [-(c_Predicate_ORangeP(_819701, _819697, _819693) = c_Predicate_ORangeP(_819699, _819695, _819691)), _819701 = _819699, _819697 = _819695, _819693 = _819691], (2700 ^ _780086) ^ [_819912, _819914] : [_819914 = _819912, -(c_HOL_OAll(_819914) = c_HOL_OAll(_819912))], (2706 ^ _780086) ^ [_819997, _819999, _820001, _820003, _820005, _820007, _820009, _820011] : [-(c_Product__Type_Oapsnd(_820011, _820007, _820003, _819999) = c_Product__Type_Oapsnd(_820009, _820005, _820001, _819997)), _820011 = _820009, _820007 = _820005, _820003 = _820001, _819999 = _819997], (2724 ^ _780086) ^ [_820298, _820300, _820302, _820304, _820306, _820308, _820310, _820312] : [-(c_Product__Type_Oapfst(_820312, _820308, _820304, _820300) = c_Product__Type_Oapfst(_820310, _820306, _820302, _820298)), _820312 = _820310, _820308 = _820306, _820304 = _820302, _820300 = _820298], (2742 ^ _780086) ^ [_820599, _820601, _820603, _820605, _820607, _820609] : [-(c_Com_Ocom_OCond(_820609, _820605, _820601) = c_Com_Ocom_OCond(_820607, _820603, _820599)), _820609 = _820607, _820605 = _820603, _820601 = _820599], (2756 ^ _780086) ^ [_820820, _820822, _820824, _820826] : [-(c_Com_Ocom_OWhile(_820826, _820822) = c_Com_Ocom_OWhile(_820824, _820820)), _820826 = _820824, _820822 = _820820], (2766 ^ _780086) ^ [_820969, _820971, _820973, _820975, _820977, _820979] : [-(c_Hoare__Mirabelle_Opeek__and(_820979, _820975, _820971) = c_Hoare__Mirabelle_Opeek__and(_820977, _820973, _820969)), _820979 = _820977, _820975 = _820973, _820971 = _820969], (2780 ^ _780086) ^ [_821190, _821192, _821194, _821196] : [-(c_Wellfounded_Omax__ext(_821196, _821192) = c_Wellfounded_Omax__ext(_821194, _821190)), _821196 = _821194, _821192 = _821190], (2790 ^ _780086) ^ [_821339, _821341, _821343, _821345, _821347, _821349, _821351, _821353] : [-(c_Random_Oiterate(_821353, _821349, _821345, _821341) = c_Random_Oiterate(_821351, _821347, _821343, _821339)), _821353 = _821351, _821349 = _821347, _821345 = _821343, _821341 = _821339], (2808 ^ _780086) ^ [_821640, _821642, _821644, _821646] : [-(c_Random_Olog(_821646, _821642) = c_Random_Olog(_821644, _821640)), _821646 = _821644, _821642 = _821640], (2818 ^ _780086) ^ [_821789, _821791, _821793, _821795, _821797, _821799] : [-(c_Random_Ominus__shift(_821799, _821795, _821791) = c_Random_Ominus__shift(_821797, _821793, _821789)), _821799 = _821797, _821795 = _821793, _821791 = _821789], (2832 ^ _780086) ^ [_822010, _822012, _822014, _822016] : [-(c_Random_Oinc__shift(_822016, _822012) = c_Random_Oinc__shift(_822014, _822010)), _822016 = _822014, _822012 = _822010], (2842 ^ _780086) ^ [_822159, _822161] : [_822161 = _822159, -(c_Relation_OField(_822161) = c_Relation_OField(_822159))], (2848 ^ _780086) ^ [_822244, _822246, _822248, _822250] : [-(c_Relation_ODomain(_822250, _822246) = c_Relation_ODomain(_822248, _822244)), _822250 = _822248, _822246 = _822244], (2858 ^ _780086) ^ [_822393, _822395, _822397, _822399] : [-(c_Relation_ORange(_822399, _822395) = c_Relation_ORange(_822397, _822393)), _822399 = _822397, _822395 = _822393], (2868 ^ _780086) ^ [_822542, _822544] : [_822544 = _822542, -(c_Nat_Ofunpow(_822544) = c_Nat_Ofunpow(_822542))], (2874 ^ _780086) ^ [_822627, _822629, _822631, _822633] : [-(c_Nitpick_Oint__lcm(_822633, _822629) = c_Nitpick_Oint__lcm(_822631, _822627)), _822633 = _822631, _822629 = _822627], (2884 ^ _780086) ^ [_822776, _822778, _822780, _822782, _822784, _822786] : [-(c_Nitpick_Otimes__frac(_822786, _822782, _822778) = c_Nitpick_Otimes__frac(_822784, _822780, _822776)), _822786 = _822784, _822782 = _822780, _822778 = _822776], (2898 ^ _780086) ^ [_822997, _822999, _823001, _823003, _823005, _823007] : [-(c_Nitpick_Oof__frac(_823007, _823003, _822999) = c_Nitpick_Oof__frac(_823005, _823001, _822997)), _823007 = _823005, _823003 = _823001, _822999 = _822997], (2912 ^ _780086) ^ [_823218, _823220] : [_823220 = _823218, -(c_Rings_Oinverse__class_Odivide(_823220) = c_Rings_Oinverse__class_Odivide(_823218))], (2918 ^ _780086) ^ [_823303, _823305] : [_823305 = _823303, -(c_Int_Oring__1__class_Oof__int(_823305) = c_Int_Oring__1__class_Oof__int(_823303))], (2924 ^ _780086) ^ [_823388, _823390, _823392, _823394] : [-(c_Nitpick_Oinverse__frac(_823394, _823390) = c_Nitpick_Oinverse__frac(_823392, _823388)), _823394 = _823392, _823390 = _823388], (2934 ^ _780086) ^ [_823537, _823539] : [_823539 = _823537, -(c_Nitpick_Ofrac(_823539) = c_Nitpick_Ofrac(_823537))], (2940 ^ _780086) ^ [_823622, _823624, _823626, _823628] : [-(c_Nitpick_OAbs__Frac(_823628, _823624) = c_Nitpick_OAbs__Frac(_823626, _823622)), _823628 = _823626, _823624 = _823622], (2950 ^ _780086) ^ [_823771, _823773, _823775, _823777, _823779, _823781] : [-(c_Nitpick_Oplus__frac(_823781, _823777, _823773) = c_Nitpick_Oplus__frac(_823779, _823775, _823771)), _823781 = _823779, _823777 = _823775, _823773 = _823771], (2964 ^ _780086) ^ [_823992, _823994, _823996, _823998] : [-(c_Nitpick_Ouminus__frac(_823998, _823994) = c_Nitpick_Ouminus__frac(_823996, _823992)), _823998 = _823996, _823994 = _823992], (2974 ^ _780086) ^ [_824141, _824143] : [_824143 = _824141, -(c_Nitpick_Onum(_824143) = c_Nitpick_Onum(_824141))], (2980 ^ _780086) ^ [_824226, _824228] : [_824228 = _824226, -(c_Nitpick_Odenom(_824228) = c_Nitpick_Odenom(_824226))], (2986 ^ _780086) ^ [_824311, _824313] : [_824313 = _824311, -(c_Nitpick_ORep__Frac(_824313) = c_Nitpick_ORep__Frac(_824311))], (2992 ^ _780086) ^ [_824396, _824398, _824400, _824402, _824404, _824406] : [-(c_Product__Type_Ointernal__split(_824406, _824402, _824398) = c_Product__Type_Ointernal__split(_824404, _824400, _824396)), _824406 = _824404, _824402 = _824400, _824398 = _824396], (3006 ^ _780086) ^ [_824617, _824619] : [_824619 = _824617, -(c_HOL_Obool_Obool__size(_824619) = c_HOL_Obool_Obool__size(_824617))], (3012 ^ _780086) ^ [_824702, _824704, _824706, _824708] : [-(c_List_Olenlex(_824708, _824704) = c_List_Olenlex(_824706, _824702)), _824708 = _824706, _824704 = _824702], (3022 ^ _780086) ^ [_824851, _824853, _824855, _824857, _824859, _824861, _824863, _824865, _824867, _824869, _824871, _824873] : [-(c_Product__Type_Omap__pair(_824873, _824869, _824865, _824861, _824857, _824853) = c_Product__Type_Omap__pair(_824871, _824867, _824863, _824859, _824855, _824851)), _824873 = _824871, _824869 = _824867, _824865 = _824863, _824861 = _824859, _824857 = _824855, _824853 = _824851], (3048 ^ _780086) ^ [_825336, _825338, _825340, _825342] : [-(c_List_Olexn(_825342, _825338) = c_List_Olexn(_825340, _825336)), _825342 = _825340, _825338 = _825336], (3058 ^ _780086) ^ [_825485, _825487, _825489, _825491] : [-(c_Wellfounded_Oacc(_825491, _825487) = c_Wellfounded_Oacc(_825489, _825485)), _825491 = _825489, _825487 = _825485], (3068 ^ _780086) ^ [_825634, _825636, _825638, _825640] : [-(c_Nitpick_Ocard_H(_825640, _825636) = c_Nitpick_Ocard_H(_825638, _825634)), _825640 = _825638, _825636 = _825634], (3078 ^ _780086) ^ [_825783, _825785, _825787, _825789, _825791, _825793] : [-(c_List_Oset__Cons(_825793, _825789, _825785) = c_List_Oset__Cons(_825791, _825787, _825783)), _825793 = _825791, _825789 = _825787, _825785 = _825783], (3092 ^ _780086) ^ [_826004, _826006, _826008, _826010] : [-(c_List_Olistset(_826010, _826006) = c_List_Olistset(_826008, _826004)), _826010 = _826008, _826006 = _826004], (3102 ^ _780086) ^ [_826153, _826155, _826157, _826159] : [-(c_List_Olistrel1(_826159, _826155) = c_List_Olistrel1(_826157, _826153)), _826159 = _826157, _826155 = _826153], (3112 ^ _780086) ^ [_826302, _826304, _826306, _826308, _826310, _826312, _826314, _826316] : [-(c_Nat_Onat_Onat__case(_826316, _826312, _826308, _826304) = c_Nat_Onat_Onat__case(_826314, _826310, _826306, _826302)), _826316 = _826314, _826312 = _826310, _826308 = _826306, _826304 = _826302], (3130 ^ _780086) ^ [_826603, _826605, _826607, _826609] : [-(c_Nat_Ocompow(_826609, _826605) = c_Nat_Ocompow(_826607, _826603)), _826609 = _826607, _826605 = _826603], (3140 ^ _780086) ^ [_826752, _826754] : [_826754 = _826752, -(c_List_Orotate1(_826754) = c_List_Orotate1(_826752))], (3146 ^ _780086) ^ [_826837, _826839, _826841, _826843] : [-(c_Finite__Set_Ofold1(_826843, _826839) = c_Finite__Set_Ofold1(_826841, _826837)), _826843 = _826841, _826839 = _826837], (3156 ^ _780086) ^ [_826986, _826988, _826990, _826992] : [-(c_Big__Operators_Olattice__class_OSup__fin(_826992, _826988) = c_Big__Operators_Olattice__class_OSup__fin(_826990, _826986)), _826992 = _826990, _826988 = _826986], (3166 ^ _780086) ^ [_827135, _827137, _827139, _827141] : [-(c_Big__Operators_Olattice__class_OInf__fin(_827141, _827137) = c_Big__Operators_Olattice__class_OInf__fin(_827139, _827135)), _827141 = _827139, _827137 = _827135], (3176 ^ _780086) ^ [_827284, _827286, _827288, _827290] : [-(c_Big__Operators_Olinorder__class_OMin(_827290, _827286) = c_Big__Operators_Olinorder__class_OMin(_827288, _827284)), _827290 = _827288, _827286 = _827284], (3186 ^ _780086) ^ [_827433, _827435, _827437, _827439] : [-(c_Big__Operators_Olinorder__class_OMax(_827439, _827435) = c_Big__Operators_Olinorder__class_OMax(_827437, _827433)), _827439 = _827437, _827435 = _827433], (3196 ^ _780086) ^ [_827582, _827584, _827586, _827588, _827590, _827592] : [-(c_Big__Operators_Olattice_OInf__fin(_827592, _827588, _827584) = c_Big__Operators_Olattice_OInf__fin(_827590, _827586, _827582)), _827592 = _827590, _827588 = _827586, _827584 = _827582], (3210 ^ _780086) ^ [_827803, _827805, _827807, _827809, _827811, _827813] : [-(c_Big__Operators_Olattice_OSup__fin(_827813, _827809, _827805) = c_Big__Operators_Olattice_OSup__fin(_827811, _827807, _827803)), _827813 = _827811, _827809 = _827807, _827805 = _827803], (3224 ^ _780086) ^ [_828024, _828026, _828028, _828030, _828032, _828034, _828036, _828038, _828040, _828042] : [-(c_Fun_Ofun__upd(_828042, _828038, _828034, _828030, _828026) = c_Fun_Ofun__upd(_828040, _828036, _828032, _828028, _828024)), _828042 = _828040, _828038 = _828036, _828034 = _828032, _828030 = _828028, _828026 = _828024], (3246 ^ _780086) ^ [_828413, _828415, _828417, _828419, _828421, _828423, _828425, _828427] : [-(c_Nitpick_Osetsum_H(_828427, _828423, _828419, _828415) = c_Nitpick_Osetsum_H(_828425, _828421, _828417, _828413)), _828427 = _828425, _828423 = _828421, _828419 = _828417, _828415 = _828413], (3264 ^ _780086) ^ [_828714, _828716, _828718, _828720, _828722, _828724] : [-(c_List_Olist_Olist__size(_828724, _828720, _828716) = c_List_Olist_Olist__size(_828722, _828718, _828714)), _828724 = _828722, _828720 = _828718, _828716 = _828714], (3278 ^ _780086) ^ [_828935, _828937, _828939, _828941] : [-(c_Random_Oselect(_828941, _828937) = c_Random_Oselect(_828939, _828935)), _828941 = _828939, _828937 = _828935], (3288 ^ _780086) ^ [_829084, _829086] : [_829086 = _829084, -(c_Random_Orange(_829086) = c_Random_Orange(_829084))], (3294 ^ _780086) ^ [_829169, _829171, _829173, _829175] : [-(c_Code__Numeral_Onat__of__aux(_829175, _829171) = c_Code__Numeral_Onat__of__aux(_829173, _829169)), _829175 = _829173, _829171 = _829169], (3304 ^ _780086) ^ [_829318, _829320] : [_829320 = _829318, -(c_Lazy__Sequence_Ohb__not__seq(_829320) = c_Lazy__Sequence_Ohb__not__seq(_829318))], (3310 ^ _780086) ^ [_829403, _829405] : [_829405 = _829403, -(c_Int_OBit1(_829405) = c_Int_OBit1(_829403))], (3316 ^ _780086) ^ [_829488, _829490, _829492, _829494] : [-(c_List_Olistsp(_829494, _829490) = c_List_Olistsp(_829492, _829488)), _829494 = _829492, _829490 = _829488], (3326 ^ _780086) ^ [_829637, _829639, _829641, _829643] : [-(c_List_Olists(_829643, _829639) = c_List_Olists(_829641, _829637)), _829643 = _829641, _829639 = _829637], (3336 ^ _780086) ^ [_829786, _829788, _829790, _829792, _829794, _829796, _829798, _829800] : [-(c_Enum_Oproduct(_829800, _829796, _829792, _829788) = c_Enum_Oproduct(_829798, _829794, _829790, _829786)), _829800 = _829798, _829796 = _829794, _829792 = _829790, _829788 = _829786], (3354 ^ _780086) ^ [_830087, _830089, _830091, _830093] : [-(c_Product__Type_OSigma(_830093, _830089) = c_Product__Type_OSigma(_830091, _830087)), _830093 = _830091, _830089 = _830087], (3364 ^ _780086) ^ [_830236, _830238] : [_830238 = _830236, -(c_Set_OPow(_830238) = c_Set_OPow(_830236))], (3370 ^ _780086) ^ [_830321, _830323, _830325, _830327] : [-(c_HOL_OLet(_830327, _830323) = c_HOL_OLet(_830325, _830321)), _830327 = _830325, _830323 = _830321], (3380 ^ _780086) ^ [_830470, _830472, _830474, _830476] : [-(c_Enum_Osublists(_830476, _830472) = c_Enum_Osublists(_830474, _830470)), _830476 = _830474, _830472 = _830470], (3390 ^ _780086) ^ [_830619, _830621, _830623, _830625] : [-(c_Enum_Oenum__the(_830625, _830621) = c_Enum_Oenum__the(_830623, _830619)), _830625 = _830623, _830621 = _830619], (3400 ^ _780086) ^ [_830768, _830770, _830772, _830774, _830776, _830778] : [-(c_Finite__Set_Ofold(_830778, _830774, _830770) = c_Finite__Set_Ofold(_830776, _830772, _830768)), _830778 = _830776, _830774 = _830772, _830770 = _830768], (3414 ^ _780086) ^ [_830989, _830991, _830993, _830995, _830997, _830999] : [-(c_Enum_On__lists(_830999, _830995, _830991) = c_Enum_On__lists(_830997, _830993, _830989)), _830999 = _830997, _830995 = _830993, _830991 = _830989], (3428 ^ _780086) ^ [_831210, _831212, _831214, _831216] : [-(c_List_OremoveAll(_831216, _831212) = c_List_OremoveAll(_831214, _831210)), _831216 = _831214, _831212 = _831210], (3438 ^ _780086) ^ [_831359, _831361, _831363, _831365, _831367, _831369] : [-(c_List_Opartition(_831369, _831365, _831361) = c_List_Opartition(_831367, _831363, _831359)), _831369 = _831367, _831365 = _831363, _831361 = _831359], (3452 ^ _780086) ^ [_831580, _831582, _831584, _831586, _831588, _831590, _831592, _831594] : [-(c_List_Olist_Olist__case(_831594, _831590, _831586, _831582) = c_List_Olist_Olist__case(_831592, _831588, _831584, _831580)), _831594 = _831592, _831590 = _831588, _831586 = _831584, _831582 = _831580], (3470 ^ _780086) ^ [_831881, _831883, _831885, _831887] : [-(c_Random_Oselect__weight(_831887, _831883) = c_Random_Oselect__weight(_831885, _831881)), _831887 = _831885, _831883 = _831881], (3480 ^ _780086) ^ [_832030, _832032, _832034, _832036] : [-(c_Random_Opick(_832036, _832032) = c_Random_Opick(_832034, _832030)), _832036 = _832034, _832032 = _832030], (3490 ^ _780086) ^ [_832179, _832181] : [_832181 = _832179, -(c_List_Otranspose__rel(_832181) = c_List_Otranspose__rel(_832179))], (3496 ^ _780086) ^ [_832264, _832266, _832268, _832270, _832272, _832274] : [-(c_List_Osublist(_832274, _832270, _832266) = c_List_Osublist(_832272, _832268, _832264)), _832274 = _832272, _832270 = _832268, _832266 = _832264], (3510 ^ _780086) ^ [_832485, _832487] : [_832487 = _832485, -(c_Int_Onumber__class_Onumber__of(_832487) = c_Int_Onumber__class_Onumber__of(_832485))], (3516 ^ _780086) ^ [_832570, _832572] : [_832572 = _832570, -(c_SetInterval_Oord__class_OlessThan(_832572) = c_SetInterval_Oord__class_OlessThan(_832570))], (3522 ^ _780086) ^ [_832655, _832657, _832659, _832661, _832663, _832665] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(_832665, _832661, _832657) = c_SetInterval_Oord__class_OgreaterThanAtMost(_832663, _832659, _832655)), _832665 = _832663, _832661 = _832659, _832657 = _832655], (3536 ^ _780086) ^ [_832876, _832878, _832880, _832882, _832884, _832886] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(_832886, _832882, _832878) = c_SetInterval_Oord__class_OgreaterThanLessThan(_832884, _832880, _832876)), _832886 = _832884, _832882 = _832880, _832878 = _832876], (3550 ^ _780086) ^ [_833097, _833099] : [_833099 = _833097, -(c_SetInterval_Oord__class_OatMost(_833099) = c_SetInterval_Oord__class_OatMost(_833097))], (3556 ^ _780086) ^ [_833182, _833184, _833186, _833188, _833190, _833192, _833194, _833196] : [-(c_List_Olinorder__class_Osort__key(_833196, _833192, _833188, _833184) = c_List_Olinorder__class_Osort__key(_833194, _833190, _833186, _833182)), _833196 = _833194, _833192 = _833190, _833188 = _833186, _833184 = _833182], (3574 ^ _780086) ^ [_833483, _833485, _833487, _833489, _833491, _833493, _833495, _833497, _833499, _833501] : [-(c_List_Olinorder__class_Oinsort__insert__key(_833501, _833497, _833493, _833489, _833485) = c_List_Olinorder__class_Oinsort__insert__key(_833499, _833495, _833491, _833487, _833483)), _833501 = _833499, _833497 = _833495, _833493 = _833491, _833489 = _833487, _833485 = _833483], (3596 ^ _780086) ^ [_833872, _833874, _833876, _833878] : [-(c_List_Olinorder__class_Osorted__list__of__set(_833878, _833874) = c_List_Olinorder__class_Osorted__list__of__set(_833876, _833872)), _833878 = _833876, _833874 = _833872], (3606 ^ _780086) ^ [_834021, _834023, _834025, _834027, _834029, _834031] : [-(c_List_Oremove1(_834031, _834027, _834023) = c_List_Oremove1(_834029, _834025, _834021)), _834031 = _834029, _834027 = _834025, _834023 = _834021], (3620 ^ _780086) ^ [_834242, _834244, _834246, _834248] : [-(c_List_Orotate(_834248, _834244) = c_List_Orotate(_834246, _834242)), _834248 = _834246, _834244 = _834242], (3630 ^ _780086) ^ [_834391, _834393, _834395, _834397] : [-(c_List_Olist__update(_834397, _834393) = c_List_Olist__update(_834395, _834391)), _834397 = _834395, _834393 = _834391], (3640 ^ _780086) ^ [_834540, _834542, _834544, _834546, _834548, _834550, _834552, _834554, _834556, _834558] : [-(c_List_Ofoldr(_834558, _834554, _834550, _834546, _834542) = c_List_Ofoldr(_834556, _834552, _834548, _834544, _834540)), _834558 = _834556, _834554 = _834552, _834550 = _834548, _834546 = _834544, _834542 = _834540], (3662 ^ _780086) ^ [_834929, _834931] : [_834931 = _834929, -(c_Orderings_Oord__class_Omax(_834931) = c_Orderings_Oord__class_Omax(_834929))], (3668 ^ _780086) ^ [_835014, _835016, _835018, _835020] : [-(c_List_Otranspose(_835020, _835016) = c_List_Otranspose(_835018, _835014)), _835020 = _835018, _835016 = _835014], (3678 ^ _780086) ^ [_835163, _835165, _835167, _835169] : [-(c_List_Obutlast(_835169, _835165) = c_List_Obutlast(_835167, _835163)), _835169 = _835167, _835165 = _835163], (3688 ^ _780086) ^ [_835312, _835314] : [_835314 = _835312, -(c_List_Oreturn__list(_835314) = c_List_Oreturn__list(_835312))], (3694 ^ _780086) ^ [_835397, _835399] : [_835399 = _835397, -(c_List_Oembed__list(_835399) = c_List_Oembed__list(_835397))], (3700 ^ _780086) ^ [_835482, _835484] : [_835484 = _835482, -(c_List_Omonoid__add__class_Olistsum(_835484) = c_List_Omonoid__add__class_Olistsum(_835482))], (3706 ^ _780086) ^ [_835567, _835569, _835571, _835573] : [-(c_List_Oremdups(_835573, _835569) = c_List_Oremdups(_835571, _835567)), _835573 = _835571, _835569 = _835567], (3716 ^ _780086) ^ [_835716, _835718, _835720, _835722, _835724, _835726] : [-(c_List_Oinsert(_835726, _835722, _835718) = c_List_Oinsert(_835724, _835720, _835716)), _835726 = _835724, _835722 = _835720, _835718 = _835716], (3730 ^ _780086) ^ [_835937, _835939, _835941, _835943, _835945, _835947, _835949, _835951] : [-(c_List_Omaps(_835951, _835947, _835943, _835939) = c_List_Omaps(_835949, _835945, _835941, _835937)), _835951 = _835949, _835947 = _835945, _835943 = _835941, _835939 = _835937], (3748 ^ _780086) ^ [_836238, _836240, _836242, _836244] : [-(c_List_Olex(_836244, _836240) = c_List_Olex(_836242, _836238)), _836244 = _836242, _836240 = _836238], (3758 ^ _780086) ^ [_836387, _836389, _836391, _836393] : [-(c_List_Omeasures(_836393, _836389) = c_List_Omeasures(_836391, _836387)), _836393 = _836391, _836389 = _836387], (3768 ^ _780086) ^ [_836536, _836538, _836540, _836542, _836544, _836546, _836548, _836550] : [-(c_List_Ofoldl(_836550, _836546, _836542, _836538) = c_List_Ofoldl(_836548, _836544, _836540, _836536)), _836550 = _836548, _836546 = _836544, _836542 = _836540, _836538 = _836536], (3786 ^ _780086) ^ [_836837, _836839] : [_836839 = _836837, -(c_Enum_Oenum__class_Oenum__ex(_836839) = c_Enum_Oenum__class_Oenum__ex(_836837))], (3792 ^ _780086) ^ [_836922, _836924, _836926, _836928, _836930, _836932, _836934, _836936] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_836936, _836932, _836928, _836924) = c_New__Random__Sequence_Opos__not__random__dseq(_836934, _836930, _836926, _836922)), _836936 = _836934, _836932 = _836930, _836928 = _836926, _836924 = _836922], (3810 ^ _780086) ^ [_837223, _837225] : [_837225 = _837223, -(c_New__DSequence_Opos__not__seq(_837225) = c_New__DSequence_Opos__not__seq(_837223))], (3816 ^ _780086) ^ [_837308, _837310, _837312, _837314, _837316, _837318] : [-(c_List_OdropWhile(_837318, _837314, _837310) = c_List_OdropWhile(_837316, _837312, _837308)), _837318 = _837316, _837314 = _837312, _837310 = _837308], (3830 ^ _780086) ^ [_837529, _837531] : [_837531 = _837529, -(c_List_Odistinct(_837531) = c_List_Odistinct(_837529))], (3836 ^ _780086) ^ [_837614, _837616, _837618, _837620, _837622, _837624] : [-(c_List_OtakeWhile(_837624, _837620, _837616) = c_List_OtakeWhile(_837622, _837618, _837614)), _837624 = _837622, _837620 = _837618, _837616 = _837614], (3850 ^ _780086) ^ [_837835, _837837, _837839, _837841, _837843, _837845] : [-(c_List_Olinorder__class_Oinsort__key(_837845, _837841, _837837) = c_List_Olinorder__class_Oinsort__key(_837843, _837839, _837835)), _837845 = _837843, _837841 = _837839, _837837 = _837835], (3864 ^ _780086) ^ [_838056, _838058] : [_838058 = _838056, -(c_Enum_Oenum__class_Oenum__all(_838058) = c_Enum_Oenum__class_Oenum__all(_838056))], (3870 ^ _780086) ^ [_838141, _838143] : [_838143 = _838141, -(c_Groups_Oabs__class_Oabs(_838143) = c_Groups_Oabs__class_Oabs(_838141))], (3876 ^ _780086) ^ [_838226, _838228] : [_838228 = _838226, -(c_Nat_Osemiring__1__class_Oof__nat(_838228) = c_Nat_Osemiring__1__class_Oof__nat(_838226))], (3882 ^ _780086) ^ [_838311, _838313] : [_838313 = _838311, -(c_Lazy__Sequence_Ohit__bound(_838313) = c_Lazy__Sequence_Ohit__bound(_838311))], (3888 ^ _780086) ^ [_838396, _838398, _838400, _838402, _838404, _838406, _838408, _838410, _838412, _838414, _838416, _838418, _838420, _838422] : [-(c_New__Random__Sequence_Oneg__decr__bind(_838422, _838418, _838414, _838410, _838406, _838402, _838398) = c_New__Random__Sequence_Oneg__decr__bind(_838420, _838416, _838412, _838408, _838404, _838400, _838396)), _838422 = _838420, _838418 = _838416, _838414 = _838412, _838410 = _838408, _838406 = _838404, _838402 = _838400, _838398 = _838396], (3918 ^ _780086) ^ [_838985, _838987, _838989, _838991, _838993, _838995, _838997, _838999] : [-(c_New__DSequence_Oneg__decr__bind(_838999, _838995, _838991, _838987) = c_New__DSequence_Oneg__decr__bind(_838997, _838993, _838989, _838985)), _838999 = _838997, _838995 = _838993, _838991 = _838989, _838987 = _838985], (3936 ^ _780086) ^ [_839286, _839288, _839290, _839292, _839294, _839296, _839298, _839300, _839302, _839304, _839306, _839308, _839310, _839312] : [-(c_New__Random__Sequence_Opos__decr__bind(_839312, _839308, _839304, _839300, _839296, _839292, _839288) = c_New__Random__Sequence_Opos__decr__bind(_839310, _839306, _839302, _839298, _839294, _839290, _839286)), _839312 = _839310, _839308 = _839306, _839304 = _839302, _839300 = _839298, _839296 = _839294, _839292 = _839290, _839288 = _839286], (3966 ^ _780086) ^ [_839875, _839877, _839879, _839881, _839883, _839885, _839887, _839889] : [-(c_New__DSequence_Opos__decr__bind(_839889, _839885, _839881, _839877) = c_New__DSequence_Opos__decr__bind(_839887, _839883, _839879, _839875)), _839889 = _839887, _839885 = _839883, _839881 = _839879, _839877 = _839875], (3984 ^ _780086) ^ [_840176, _840178, _840180, _840182, _840184, _840186, _840188, _840190] : [-(c_Lazy__Sequence_Ohb__bind(_840190, _840186, _840182, _840178) = c_Lazy__Sequence_Ohb__bind(_840188, _840184, _840180, _840176)), _840190 = _840188, _840186 = _840184, _840182 = _840180, _840178 = _840176], (4002 ^ _780086) ^ [_840477, _840479, _840481, _840483, _840485, _840487, _840489, _840491] : [-(c_New__Random__Sequence_Opos__empty(_840491, _840487, _840483, _840479) = c_New__Random__Sequence_Opos__empty(_840489, _840485, _840481, _840477)), _840491 = _840489, _840487 = _840485, _840483 = _840481, _840479 = _840477], (4020 ^ _780086) ^ [_840778, _840780] : [_840780 = _840778, -(c_New__DSequence_Opos__empty(_840780) = c_New__DSequence_Opos__empty(_840778))], (4026 ^ _780086) ^ [_840863, _840865, _840867, _840869, _840871, _840873, _840875, _840877] : [-(c_New__DSequence_Oneg__bind(_840877, _840873, _840869, _840865) = c_New__DSequence_Oneg__bind(_840875, _840871, _840867, _840863)), _840877 = _840875, _840873 = _840871, _840869 = _840867, _840865 = _840863], (4044 ^ _780086) ^ [_841164, _841166, _841168, _841170, _841172, _841174, _841176, _841178] : [-(c_New__Random__Sequence_Oneg__map(_841178, _841174, _841170, _841166) = c_New__Random__Sequence_Oneg__map(_841176, _841172, _841168, _841164)), _841178 = _841176, _841174 = _841172, _841170 = _841168, _841166 = _841164], (4062 ^ _780086) ^ [_841465, _841467, _841469, _841471, _841473, _841475, _841477, _841479] : [-(c_New__Random__Sequence_Oneg__bind(_841479, _841475, _841471, _841467) = c_New__Random__Sequence_Oneg__bind(_841477, _841473, _841469, _841465)), _841479 = _841477, _841475 = _841473, _841471 = _841469, _841467 = _841465], (4080 ^ _780086) ^ [_841766, _841768] : [_841768 = _841766, -(c_New__Random__Sequence_Oneg__single(_841768) = c_New__Random__Sequence_Oneg__single(_841766))], (4086 ^ _780086) ^ [_841851, _841853, _841855, _841857, _841859, _841861, _841863, _841865] : [-(c_New__DSequence_Opos__bind(_841865, _841861, _841857, _841853) = c_New__DSequence_Opos__bind(_841863, _841859, _841855, _841851)), _841865 = _841863, _841861 = _841859, _841857 = _841855, _841853 = _841851], (4104 ^ _780086) ^ [_842152, _842154, _842156, _842158] : [-(c_New__DSequence_Oneg__single(_842158, _842154) = c_New__DSequence_Oneg__single(_842156, _842152)), _842158 = _842156, _842154 = _842152], (4114 ^ _780086) ^ [_842301, _842303, _842305, _842307] : [-(c_Lazy__Sequence_Ohb__single(_842307, _842303) = c_Lazy__Sequence_Ohb__single(_842305, _842301)), _842307 = _842305, _842303 = _842301], (4124 ^ _780086) ^ [_842450, _842452, _842454, _842456, _842458, _842460, _842462, _842464] : [-(c_New__Random__Sequence_Opos__map(_842464, _842460, _842456, _842452) = c_New__Random__Sequence_Opos__map(_842462, _842458, _842454, _842450)), _842464 = _842462, _842460 = _842458, _842456 = _842454, _842452 = _842450], (4142 ^ _780086) ^ [_842751, _842753, _842755, _842757, _842759, _842761, _842763, _842765] : [-(c_New__Random__Sequence_Opos__bind(_842765, _842761, _842757, _842753) = c_New__Random__Sequence_Opos__bind(_842763, _842759, _842755, _842751)), _842765 = _842763, _842761 = _842759, _842757 = _842755, _842753 = _842751], (4160 ^ _780086) ^ [_843052, _843054] : [_843054 = _843052, -(c_New__Random__Sequence_Opos__single(_843054) = c_New__Random__Sequence_Opos__single(_843052))], (4166 ^ _780086) ^ [_843137, _843139, _843141, _843143, _843145, _843147] : [-(c_List_Osplice(_843147, _843143, _843139) = c_List_Osplice(_843145, _843141, _843137)), _843147 = _843145, _843143 = _843141, _843139 = _843137], (4180 ^ _780086) ^ [_843358, _843360, _843362, _843364] : [-(c_New__DSequence_Opos__single(_843364, _843360) = c_New__DSequence_Opos__single(_843362, _843358)), _843364 = _843362, _843360 = _843358], (4190 ^ _780086) ^ [_843507, _843509, _843511, _843513, _843515, _843517] : [-(c_Predicate_Oconversep(_843517, _843513, _843509) = c_Predicate_Oconversep(_843515, _843511, _843507)), _843517 = _843515, _843513 = _843511, _843509 = _843507], (4204 ^ _780086) ^ [_843728, _843730] : [_843730 = _843728, -(c_List_Otl(_843730) = c_List_Otl(_843728))], (4210 ^ _780086) ^ [_843813, _843815] : [_843815 = _843813, -(c_List_Orev(_843815) = c_List_Orev(_843813))], (4216 ^ _780086) ^ [_843898, _843900] : [_843900 = _843898, -(c_List_Odrop(_843900) = c_List_Odrop(_843898))], (4222 ^ _780086) ^ [_843983, _843985] : [_843985 = _843983, -(c_List_Ohd(_843985) = c_List_Ohd(_843983))], (4228 ^ _780086) ^ [_844068, _844070] : [_844070 = _844068, -(c_List_Otake(_844070) = c_List_Otake(_844068))], (4234 ^ _780086) ^ [_844153, _844155, _844157, _844159] : [-(c_List_Olast(_844159, _844155) = c_List_Olast(_844157, _844153)), _844159 = _844157, _844155 = _844153], (4244 ^ _780086) ^ [_844302, _844304, _844306, _844308] : [-(c_List_Ozip(_844308, _844304) = c_List_Ozip(_844306, _844302)), _844308 = _844306, _844304 = _844302], (4254 ^ _780086) ^ [_844451, _844453] : [_844453 = _844451, -(c_Orderings_Oord__class_Omin(_844453) = c_Orderings_Oord__class_Omin(_844451))], (4260 ^ _780086) ^ [_844536, _844538] : [_844538 = _844536, -(c_List_Onth(_844538) = c_List_Onth(_844536))], (4266 ^ _780086) ^ [_844621, _844623, _844625, _844627] : [-(c_List_Ofilter(_844627, _844623) = c_List_Ofilter(_844625, _844621)), _844627 = _844625, _844623 = _844621], (4276 ^ _780086) ^ [_844770, _844772, _844774, _844776] : [-(c_List_Oconcat(_844776, _844772) = c_List_Oconcat(_844774, _844770)), _844776 = _844774, _844772 = _844770], (4286 ^ _780086) ^ [_844919, _844921] : [_844921 = _844919, -(c_List_Oappend(_844921) = c_List_Oappend(_844919))], (4292 ^ _780086) ^ [_845004, _845006, _845008, _845010] : [-(c_List_Omap(_845010, _845006) = c_List_Omap(_845008, _845004)), _845010 = _845008, _845006 = _845004], (4302 ^ _780086) ^ [_845153, _845155, _845157, _845159, _845161, _845163] : [-(c_List_Oreplicate(_845163, _845159, _845155) = c_List_Oreplicate(_845161, _845157, _845153)), _845163 = _845161, _845159 = _845157, _845155 = _845153], (4316 ^ _780086) ^ [_845374, _845376] : [_845376 = _845374, -(c_If(_845376) = c_If(_845374))], (4322 ^ _780086) ^ [_845459, _845461, _845463, _845465, _845467, _845469, _845471, _845473, _845475, _845477] : [-(c_Predicate_Opred__comp(_845477, _845473, _845469, _845465, _845461) = c_Predicate_Opred__comp(_845475, _845471, _845467, _845463, _845459)), _845477 = _845475, _845473 = _845471, _845469 = _845467, _845465 = _845463, _845461 = _845459], (4344 ^ _780086) ^ [_845848, _845850, _845852, _845854, _845856, _845858, _845860, _845862] : [-(c_Lazy__Sequence_Oproduct(_845862, _845858, _845854, _845850) = c_Lazy__Sequence_Oproduct(_845860, _845856, _845852, _845848)), _845862 = _845860, _845858 = _845856, _845854 = _845852, _845850 = _845848], (4362 ^ _780086) ^ [_846149, _846151, _846153, _846155, _846157, _846159, _846161, _846163, _846165, _846167, _846169, _846171] : [-(c_New__Random__Sequence_Opos__union(_846171, _846167, _846163, _846159, _846155, _846151) = c_New__Random__Sequence_Opos__union(_846169, _846165, _846161, _846157, _846153, _846149)), _846171 = _846169, _846167 = _846165, _846163 = _846161, _846159 = _846157, _846155 = _846153, _846151 = _846149], (4388 ^ _780086) ^ [_846634, _846636, _846638, _846640, _846642, _846644] : [-(c_New__DSequence_Opos__union(_846644, _846640, _846636) = c_New__DSequence_Opos__union(_846642, _846638, _846634)), _846644 = _846642, _846640 = _846638, _846636 = _846634], (4402 ^ _780086) ^ [_846855, _846857, _846859, _846861] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_846861, _846857) = c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_846859, _846855)), _846861 = _846859, _846857 = _846855], (4412 ^ _780086) ^ [_847004, _847006] : [_847006 = _847004, -(c_Lazy__Sequence_Oempty(_847006) = c_Lazy__Sequence_Oempty(_847004))], (4418 ^ _780086) ^ [_847089, _847091] : [_847091 = _847089, -(c_Lazy__Sequence_Osingle(_847091) = c_Lazy__Sequence_Osingle(_847089))], (4424 ^ _780086) ^ [_847174, _847176, _847178, _847180] : [-(c_Lazy__Sequence_Osmall__lazy_H(_847180, _847176) = c_Lazy__Sequence_Osmall__lazy_H(_847178, _847174)), _847180 = _847178, _847176 = _847174], (4434 ^ _780086) ^ [_847323, _847325, _847327, _847329] : [-(c_Wellfounded_Oaccp(_847329, _847325) = c_Wellfounded_Oaccp(_847327, _847323)), _847329 = _847327, _847325 = _847323], (4444 ^ _780086) ^ [_847472, _847474, _847476, _847478, _847480, _847482, _847484, _847486, _847488, _847490] : [-(c_Option_Ooption_Ooption__case(_847490, _847486, _847482, _847478, _847474) = c_Option_Ooption_Ooption__case(_847488, _847484, _847480, _847476, _847472)), _847490 = _847488, _847486 = _847484, _847482 = _847480, _847478 = _847476, _847474 = _847472], (4466 ^ _780086) ^ [_847861, _847863] : [_847863 = _847861, -(c_Lazy__Sequence_Oyieldn(_847863) = c_Lazy__Sequence_Oyieldn(_847861))], (4472 ^ _780086) ^ [_847946, _847948, _847950, _847952, _847954, _847956] : [-(c_Lazy__Sequence_Oanamorph(_847956, _847952, _847948) = c_Lazy__Sequence_Oanamorph(_847954, _847950, _847946)), _847956 = _847954, _847952 = _847950, _847948 = _847946], (4486 ^ _780086) ^ [_848167, _848169] : [_848169 = _848167, -(c_Lazy__Sequence_Oyield(_848169) = c_Lazy__Sequence_Oyield(_848167))], (4492 ^ _780086) ^ [_848252, _848254] : [_848254 = _848252, -(c_List_Olist_OCons(_848254) = c_List_Olist_OCons(_848252))], (4498 ^ _780086) ^ [_848337, _848339] : [_848339 = _848337, -(c_List_Olist_ONil(_848339) = c_List_Olist_ONil(_848337))], (4504 ^ _780086) ^ [_848422, _848424] : [_848424 = _848422, -(c_List_Omember(_848424) = c_List_Omember(_848422))], (4510 ^ _780086) ^ [_848507, _848509, _848511, _848513, _848515, _848517, _848519, _848521, _848523, _848525] : [-(c_Nitpick_Opair__box_Opair__box__size(_848525, _848521, _848517, _848513, _848509) = c_Nitpick_Opair__box_Opair__box__size(_848523, _848519, _848515, _848511, _848507)), _848525 = _848523, _848521 = _848519, _848517 = _848515, _848513 = _848511, _848509 = _848507], (4532 ^ _780086) ^ [_848896, _848898, _848900, _848902, _848904, _848906, _848908, _848910, _848912, _848914] : [-(c_Nitpick_Opair__box_Opair__box__case(_848914, _848910, _848906, _848902, _848898) = c_Nitpick_Opair__box_Opair__box__case(_848912, _848908, _848904, _848900, _848896)), _848914 = _848912, _848910 = _848908, _848906 = _848904, _848902 = _848900, _848898 = _848896], (4554 ^ _780086) ^ [_849285, _849287, _849289, _849291, _849293, _849295, _849297, _849299, _849301, _849303] : [-(c_Nitpick_Opair__box_Opair__box__rec(_849303, _849299, _849295, _849291, _849287) = c_Nitpick_Opair__box_Opair__box__rec(_849301, _849297, _849293, _849289, _849285)), _849303 = _849301, _849299 = _849297, _849295 = _849293, _849291 = _849289, _849287 = _849285], (4576 ^ _780086) ^ [_849674, _849676, _849678, _849680, _849682, _849684, _849686, _849688] : [-(c_Nitpick_Opair__box_OPairBox(_849688, _849684, _849680, _849676) = c_Nitpick_Opair__box_OPairBox(_849686, _849682, _849678, _849674)), _849688 = _849686, _849684 = _849682, _849680 = _849678, _849676 = _849674], (4594 ^ _780086) ^ [_849975, _849977, _849979, _849981] : [-(c_HOL_OThe(_849981, _849977) = c_HOL_OThe(_849979, _849975)), _849981 = _849979, _849977 = _849975], (4604 ^ _780086) ^ [_850124, _850126, _850128, _850130, _850132, _850134] : [-(c_FunDef_OTHE__default(_850134, _850130, _850126) = c_FunDef_OTHE__default(_850132, _850128, _850124)), _850134 = _850132, _850130 = _850128, _850126 = _850124], (4618 ^ _780086) ^ [_850345, _850347, _850349, _850351] : [-(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_850351, _850347) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_850349, _850345)), _850351 = _850349, _850347 = _850345], (4628 ^ _780086) ^ [_850494, _850496] : [_850496 = _850494, -(c_Nat_Osize__class_Osize(_850496) = c_Nat_Osize__class_Osize(_850494))], (4634 ^ _780086) ^ [_850579, _850581, _850583, _850585, _850587, _850589, _850591, _850593, _850595, _850597] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_850597, _850593, _850589, _850585, _850581) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_850595, _850591, _850587, _850583, _850579)), _850597 = _850595, _850593 = _850591, _850589 = _850587, _850585 = _850583, _850581 = _850579], (4656 ^ _780086) ^ [_850968, _850970, _850972, _850974] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_850974, _850970) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_850972, _850968)), _850974 = _850972, _850970 = _850968], (4666 ^ _780086) ^ [_851117, _851119, _851121, _851123] : [-(c_List_Oupto(_851123, _851119) = c_List_Oupto(_851121, _851117)), _851123 = _851121, _851119 = _851117], (4676 ^ _780086) ^ [_851266, _851268] : [_851268 = _851266, -(c_Code__Numeral_OSuc__code__numeral(_851268) = c_Code__Numeral_OSuc__code__numeral(_851266))], (4682 ^ _780086) ^ [_851351, _851353, _851355, _851357, _851359, _851361, _851363, _851365] : [-(c_Product__Type_Oscomp(_851365, _851361, _851357, _851353) = c_Product__Type_Oscomp(_851363, _851359, _851355, _851351)), _851365 = _851363, _851361 = _851359, _851357 = _851355, _851353 = _851351], (4700 ^ _780086) ^ [_851652, _851654, _851656, _851658, _851660, _851662, _851664, _851666] : [-(c_Random__Sequence_ORandom(_851666, _851662, _851658, _851654) = c_Random__Sequence_ORandom(_851664, _851660, _851656, _851652)), _851666 = _851664, _851662 = _851660, _851658 = _851656, _851654 = _851652], (4718 ^ _780086) ^ [_851953, _851955] : [_851955 = _851953, -(c_DSequence_Ounion(_851955) = c_DSequence_Ounion(_851953))], (4724 ^ _780086) ^ [_852038, _852040, _852042, _852044, _852046, _852048, _852050, _852052] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_852052, _852048, _852044, _852040) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_852050, _852046, _852042, _852038)), _852052 = _852050, _852048 = _852046, _852044 = _852042, _852040 = _852038], (4742 ^ _780086) ^ [_852339, _852341, _852343, _852345, _852347, _852349] : [-(c_Random__Sequence_Oempty(_852349, _852345, _852341) = c_Random__Sequence_Oempty(_852347, _852343, _852339)), _852349 = _852347, _852345 = _852343, _852341 = _852339], (4756 ^ _780086) ^ [_852560, _852562] : [_852562 = _852560, -(c_DSequence_Oempty(_852562) = c_DSequence_Oempty(_852560))], (4762 ^ _780086) ^ [_852645, _852647] : [_852647 = _852645, -(c_DSequence_Osingle(_852647) = c_DSequence_Osingle(_852645))], (4768 ^ _780086) ^ [_852730, _852732, _852734, _852736, _852738, _852740, _852742, _852744] : [-(c_Random__Sequence_Omap(_852744, _852740, _852736, _852732) = c_Random__Sequence_Omap(_852742, _852738, _852734, _852730)), _852744 = _852742, _852740 = _852738, _852736 = _852734, _852732 = _852730], (4786 ^ _780086) ^ [_853031, _853033, _853035, _853037, _853039, _853041, _853043, _853045] : [-(c_Random__Sequence_Obind(_853045, _853041, _853037, _853033) = c_Random__Sequence_Obind(_853043, _853039, _853035, _853031)), _853045 = _853043, _853041 = _853039, _853037 = _853035, _853033 = _853031], (4804 ^ _780086) ^ [_853332, _853334] : [_853334 = _853332, -(c_Random__Sequence_Osingle(_853334) = c_Random__Sequence_Osingle(_853332))], (4810 ^ _780086) ^ [_853417, _853419, _853421, _853423] : [-(c_Product__Type_Osnd(_853423, _853419) = c_Product__Type_Osnd(_853421, _853417)), _853423 = _853421, _853419 = _853417], (4820 ^ _780086) ^ [_853566, _853568, _853570, _853572] : [-(c_Product__Type_Ofst(_853572, _853568) = c_Product__Type_Ofst(_853570, _853566)), _853572 = _853570, _853568 = _853566], (4830 ^ _780086) ^ [_853715, _853717, _853719, _853721, _853723, _853725] : [-(c_Relation_OImage(_853725, _853721, _853717) = c_Relation_OImage(_853723, _853719, _853715)), _853725 = _853723, _853721 = _853719, _853717 = _853715], (4844 ^ _780086) ^ [_853936, _853938, _853940, _853942, _853944, _853946, _853948, _853950] : [-(c_Wellfounded_Olex__prod(_853950, _853946, _853942, _853938) = c_Wellfounded_Olex__prod(_853948, _853944, _853940, _853936)), _853950 = _853948, _853946 = _853944, _853942 = _853940, _853938 = _853936], (4862 ^ _780086) ^ [_854237, _854239] : [_854239 = _854237, -(c_Wellfounded_Ofinite__psubset(_854239) = c_Wellfounded_Ofinite__psubset(_854237))], (4868 ^ _780086) ^ [_854322, _854324, _854326, _854328] : [-(c_List_Olexord(_854328, _854324) = c_List_Olexord(_854326, _854322)), _854328 = _854326, _854324 = _854322], (4878 ^ _780086) ^ [_854471, _854473] : [_854473 = _854471, -(c_Set_OBex(_854473) = c_Set_OBex(_854471))], (4884 ^ _780086) ^ [_854556, _854558] : [_854558 = _854556, -(c_List_Oset(_854558) = c_List_Oset(_854556))], (4890 ^ _780086) ^ [_854641, _854643, _854645, _854647] : [-(c_Complete__Lattice_OSup__class_OSup(_854647, _854643) = c_Complete__Lattice_OSup__class_OSup(_854645, _854641)), _854647 = _854645, _854643 = _854641], (4900 ^ _780086) ^ [_854790, _854792, _854794, _854796] : [-(c_Complete__Lattice_OInf__class_OInf(_854796, _854792) = c_Complete__Lattice_OInf__class_OInf(_854794, _854790)), _854796 = _854794, _854792 = _854790], (4910 ^ _780086) ^ [_854939, _854941, _854943, _854945, _854947, _854949, _854951, _854953, _854955, _854957, _854959, _854961] : [-(c_Partial__Function_Ofun__lub(_854961, _854957, _854953, _854949, _854945, _854941) = c_Partial__Function_Ofun__lub(_854959, _854955, _854951, _854947, _854943, _854939)), _854961 = _854959, _854957 = _854955, _854953 = _854951, _854949 = _854947, _854945 = _854943, _854941 = _854939], (4936 ^ _780086) ^ [_855424, _855426, _855428, _855430, _855432, _855434] : [-(c_Relation_Orel__comp(_855434, _855430, _855426) = c_Relation_Orel__comp(_855432, _855428, _855424)), _855434 = _855432, _855430 = _855428, _855426 = _855424], (4950 ^ _780086) ^ [_855645, _855647] : [_855647 = _855645, -(c_Relation_OId(_855647) = c_Relation_OId(_855645))], (4956 ^ _780086) ^ [_855730, _855732, _855734, _855736] : [-(c_Relation_OId__on(_855736, _855732) = c_Relation_OId__on(_855734, _855730)), _855736 = _855734, _855732 = _855730], (4966 ^ _780086) ^ [_855879, _855881, _855883, _855885] : [-(c_List_Olistrel(_855885, _855881) = c_List_Olistrel(_855883, _855879)), _855885 = _855883, _855881 = _855879], (4976 ^ _780086) ^ [_856028, _856030, _856032, _856034] : [-(c_Relation_Oinv__image(_856034, _856030) = c_Relation_Oinv__image(_856032, _856028)), _856034 = _856032, _856030 = _856028], (4986 ^ _780086) ^ [_856177, _856179, _856181, _856183] : [-(c_Relation_Oconverse(_856183, _856179) = c_Relation_Oconverse(_856181, _856177)), _856183 = _856181, _856179 = _856177], (4996 ^ _780086) ^ [_856326, _856328] : [_856328 = _856326, -(c_HOL_OEx(_856328) = c_HOL_OEx(_856326))], (5002 ^ _780086) ^ [_856411, _856413, _856415, _856417] : [-(c_Hilbert__Choice_OEps(_856417, _856413) = c_Hilbert__Choice_OEps(_856415, _856411)), _856417 = _856415, _856413 = _856411], (5012 ^ _780086) ^ [_856560, _856562, _856564, _856566, _856568, _856570] : [-(c_Finite__Set_Ofold__image(_856570, _856566, _856562) = c_Finite__Set_Ofold__image(_856568, _856564, _856560)), _856570 = _856568, _856566 = _856564, _856562 = _856560], (5026 ^ _780086) ^ [_856781, _856783, _856785, _856787] : [-(c_Quickcheck_Obeyond(_856787, _856783) = c_Quickcheck_Obeyond(_856785, _856781)), _856787 = _856785, _856783 = _856781], (5036 ^ _780086) ^ [_856930, _856932, _856934, _856936, _856938, _856940, _856942, _856944, _856946, _856948] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_856948, _856944, _856940, _856936, _856932) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_856946, _856942, _856938, _856934, _856930)), _856948 = _856946, _856944 = _856942, _856940 = _856938, _856936 = _856934, _856932 = _856930], (5058 ^ _780086) ^ [_857319, _857321] : [_857321 = _857319, -(c_Set_OCollect(_857321) = c_Set_OCollect(_857319))], (5064 ^ _780086) ^ [_857404, _857406, _857408, _857410, _857412, _857414, _857416, _857418] : [-(c_Product__Type_Ocurry(_857418, _857414, _857410, _857406) = c_Product__Type_Ocurry(_857416, _857412, _857408, _857404)), _857418 = _857416, _857414 = _857412, _857410 = _857408, _857406 = _857404], (5082 ^ _780086) ^ [_857705, _857707, _857709, _857711, _857713, _857715] : [-(c_Product__Type_Oprod_Oprod__case(_857715, _857711, _857707) = c_Product__Type_Oprod_Oprod__case(_857713, _857709, _857705)), _857715 = _857713, _857711 = _857709, _857707 = _857705], (5096 ^ _780086) ^ [_857926, _857928, _857930, _857932, _857934, _857936, _857938, _857940] : [-(c_Fun_Othe__inv__into(_857940, _857936, _857932, _857928) = c_Fun_Othe__inv__into(_857938, _857934, _857930, _857926)), _857940 = _857938, _857936 = _857934, _857932 = _857930, _857928 = _857926], (5114 ^ _780086) ^ [_858227, _858229] : [_858229 = _858227, -(c_Fun_Oid(_858229) = c_Fun_Oid(_858227))], (5120 ^ _780086) ^ [_858312, _858314] : [_858314 = _858312, -(c_Lattices_Osemilattice__inf__class_Oinf(_858314) = c_Lattices_Osemilattice__inf__class_Oinf(_858312))], (5126 ^ _780086) ^ [_858397, _858399] : [_858399 = _858397, -(c_Lattices_Osemilattice__sup__class_Osup(_858399) = c_Lattices_Osemilattice__sup__class_Osup(_858397))], (5132 ^ _780086) ^ [_858482, _858484, _858486, _858488, _858490, _858492] : [-(c_Set_Ovimage(_858492, _858488, _858484) = c_Set_Ovimage(_858490, _858486, _858482)), _858492 = _858490, _858488 = _858486, _858484 = _858482], (5146 ^ _780086) ^ [_858703, _858705, _858707, _858709, _858711, _858713, _858715, _858717] : [-(c_Hilbert__Choice_Oinv__into(_858717, _858713, _858709, _858705) = c_Hilbert__Choice_Oinv__into(_858715, _858711, _858707, _858703)), _858717 = _858715, _858713 = _858711, _858709 = _858707, _858705 = _858703], (5164 ^ _780086) ^ [_859004, _859006] : [_859006 = _859004, -(c_Orderings_Otop__class_Otop(_859006) = c_Orderings_Otop__class_Otop(_859004))], (5170 ^ _780086) ^ [_859089, _859091, _859093, _859095, _859097, _859099] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_859099, _859095, _859091) = c_SetInterval_Oord__class_OatLeastAtMost(_859097, _859093, _859089)), _859099 = _859097, _859095 = _859093, _859091 = _859089], (5184 ^ _780086) ^ [_859310, _859312] : [_859312 = _859310, -(c_Finite__Set_Ocard(_859312) = c_Finite__Set_Ocard(_859310))], (5190 ^ _780086) ^ [_859395, _859397, _859399, _859401] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_859401, _859397) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_859399, _859395)), _859401 = _859399, _859397 = _859395], (5200 ^ _780086) ^ [_859544, _859546, _859548, _859550] : [-(c_Quotient_ORespects(_859550, _859546) = c_Quotient_ORespects(_859548, _859544)), _859550 = _859548, _859546 = _859544], (5210 ^ _780086) ^ [_859693, _859695, _859697, _859699, _859701, _859703, _859705, _859707] : [-(c_Quotient_OBabs(_859707, _859703, _859699, _859695) = c_Quotient_OBabs(_859705, _859701, _859697, _859693)), _859707 = _859705, _859703 = _859701, _859699 = _859697, _859695 = _859693], (5228 ^ _780086) ^ [_859994, _859996, _859998, _860000] : [-(c_Transitive__Closure_Otrancl(_860000, _859996) = c_Transitive__Closure_Otrancl(_859998, _859994)), _860000 = _859998, _859996 = _859994], (5238 ^ _780086) ^ [_860143, _860145, _860147, _860149] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_860149, _860145) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_860147, _860143)), _860149 = _860147, _860145 = _860143], (5248 ^ _780086) ^ [_860292, _860294, _860296, _860298] : [-(c_Transitive__Closure_Ortrancl(_860298, _860294) = c_Transitive__Closure_Ortrancl(_860296, _860292)), _860298 = _860296, _860294 = _860292], (5258 ^ _780086) ^ [_860441, _860443, _860445, _860447] : [-(c_Product__Type_OPair(_860447, _860443) = c_Product__Type_OPair(_860445, _860441)), _860447 = _860445, _860443 = _860441], (5268 ^ _780086) ^ [_860590, _860592, _860594, _860596, _860598, _860600] : [-(c_Lazy__Sequence_Oappend(_860600, _860596, _860592) = c_Lazy__Sequence_Oappend(_860598, _860594, _860590)), _860600 = _860598, _860596 = _860594, _860592 = _860590], (5282 ^ _780086) ^ [_860811, _860813, _860815, _860817] : [-(c_SetInterval_Oord__class_OatLeastLessThan(_860817, _860813) = c_SetInterval_Oord__class_OatLeastLessThan(_860815, _860811)), _860817 = _860815, _860813 = _860811], (5292 ^ _780086) ^ [_860960, _860962, _860964, _860966] : [-(c_List_Oupt(_860966, _860962) = c_List_Oupt(_860964, _860960)), _860966 = _860964, _860962 = _860960], (5302 ^ _780086) ^ [_861109, _861111, _861113, _861115, _861117, _861119, _861121, _861123] : [-(c_Fun_Ocomp(_861123, _861119, _861115, _861111) = c_Fun_Ocomp(_861121, _861117, _861113, _861109)), _861123 = _861121, _861119 = _861117, _861115 = _861113, _861111 = _861109], (5320 ^ _780086) ^ [_861410, _861412, _861414, _861416, _861418, _861420] : [-(c_Lazy__Sequence_Obind(_861420, _861416, _861412) = c_Lazy__Sequence_Obind(_861418, _861414, _861410)), _861420 = _861418, _861416 = _861414, _861412 = _861410], (5334 ^ _780086) ^ [_861631, _861633, _861635, _861637] : [-(c_Lazy__Sequence_Oflat(_861637, _861633) = c_Lazy__Sequence_Oflat(_861635, _861631)), _861637 = _861635, _861633 = _861631], (5344 ^ _780086) ^ [_861780, _861782, _861784, _861786, _861788, _861790] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_861790, _861786, _861782) = c_Lazy__Sequence_Olazy__sequence_OInsert(_861788, _861784, _861780)), _861790 = _861788, _861786 = _861784, _861782 = _861780], (5358 ^ _780086) ^ [_862001, _862003] : [_862003 = _862001, -(c_Lazy__Sequence_Olazy__sequence_OEmpty(_862003) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_862001))], (5364 ^ _780086) ^ [_862086, _862088, _862090, _862092, _862094, _862096, _862098, _862100, _862102, _862104] : [-(c_New__DSequence_Opos__map(_862104, _862100, _862096, _862092, _862088) = c_New__DSequence_Opos__map(_862102, _862098, _862094, _862090, _862086)), _862104 = _862102, _862100 = _862098, _862096 = _862094, _862092 = _862090, _862088 = _862086], (5386 ^ _780086) ^ [_862475, _862477, _862479, _862481, _862483, _862485, _862487, _862489] : [-(c_Lazy__Sequence_Omap(_862489, _862485, _862481, _862477) = c_Lazy__Sequence_Omap(_862487, _862483, _862479, _862475)), _862489 = _862487, _862485 = _862483, _862481 = _862479, _862477 = _862475], (5404 ^ _780086) ^ [_862776, _862778] : [_862778 = _862776, -(c_Power_Opower__class_Opower(_862778) = c_Power_Opower__class_Opower(_862776))], (5410 ^ _780086) ^ [_862861, _862863] : [_862863 = _862861, -(c_Groups_Oone__class_Oone(_862863) = c_Groups_Oone__class_Oone(_862861))], (5416 ^ _780086) ^ [_862946, _862948] : [_862948 = _862946, -(c_Orderings_Oord__class_Oless(_862948) = c_Orderings_Oord__class_Oless(_862946))], (5422 ^ _780086) ^ [_863031, _863033] : [_863033 = _863031, -(c_Orderings_Oord__class_Oless__eq(_863033) = c_Orderings_Oord__class_Oless__eq(_863031))], (5428 ^ _780086) ^ [_863116, _863118, _863120, _863122] : [-(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_863122, _863118) = c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_863120, _863116)), _863122 = _863120, _863118 = _863116], (5438 ^ _780086) ^ [_863265, _863267] : [_863267 = _863265, -(c_Groups_Ominus__class_Ominus(_863267) = c_Groups_Ominus__class_Ominus(_863265))], (5444 ^ _780086) ^ [_863350, _863352] : [_863352 = _863350, -(c_Groups_Otimes__class_Otimes(_863352) = c_Groups_Otimes__class_Otimes(_863350))], (5450 ^ _780086) ^ [_863435, _863437] : [_863437 = _863435, -(c_Groups_Oplus__class_Oplus(_863437) = c_Groups_Oplus__class_Oplus(_863435))], (5456 ^ _780086) ^ [_863520, _863522, _863524, _863526, _863528, _863530, _863532, _863534] : [-(c_SetInterval_Oord_OgreaterThanLessThan(_863534, _863530, _863526, _863522) = c_SetInterval_Oord_OgreaterThanLessThan(_863532, _863528, _863524, _863520)), _863534 = _863532, _863530 = _863528, _863526 = _863524, _863522 = _863520], (5474 ^ _780086) ^ [_863821, _863823, _863825, _863827, _863829, _863831, _863833, _863835, _863837, _863839] : [-(c_SetInterval_Oord_OatLeastLessThan(_863839, _863835, _863831, _863827, _863823) = c_SetInterval_Oord_OatLeastLessThan(_863837, _863833, _863829, _863825, _863821)), _863839 = _863837, _863835 = _863833, _863831 = _863829, _863827 = _863825, _863823 = _863821], (5496 ^ _780086) ^ [_864210, _864212, _864214, _864216, _864218, _864220, _864222, _864224, _864226, _864228] : [-(c_SetInterval_Oord_OgreaterThanAtMost(_864228, _864224, _864220, _864216, _864212) = c_SetInterval_Oord_OgreaterThanAtMost(_864226, _864222, _864218, _864214, _864210)), _864228 = _864226, _864224 = _864222, _864220 = _864218, _864216 = _864214, _864212 = _864210], (5518 ^ _780086) ^ [_864599, _864601, _864603, _864605, _864607, _864609, _864611, _864613] : [-(c_SetInterval_Oord_OatLeastAtMost(_864613, _864609, _864605, _864601) = c_SetInterval_Oord_OatLeastAtMost(_864611, _864607, _864603, _864599)), _864613 = _864611, _864609 = _864607, _864605 = _864603, _864601 = _864599], (5536 ^ _780086) ^ [_864900, _864902] : [_864902 = _864900, -(c_Groups_Ouminus__class_Ouminus(_864902) = c_Groups_Ouminus__class_Ouminus(_864900))], (5542 ^ _780086) ^ [_864985, _864987] : [_864987 = _864985, -(c_Divides_Odiv__class_Odiv(_864987) = c_Divides_Odiv__class_Odiv(_864985))], (5548 ^ _780086) ^ [_865070, _865072] : [_865072 = _865070, -(c_Groups_Ozero__class_Ozero(_865072) = c_Groups_Ozero__class_Ozero(_865070))], (5554 ^ _780086) ^ [_865155, _865157, _865159, _865161, _865163, _865165] : [-(c_Divides_Odiv__class_Omod(_865165, _865161, _865157) = c_Divides_Odiv__class_Omod(_865163, _865159, _865155)), _865165 = _865163, _865161 = _865159, _865157 = _865155], (5568 ^ _780086) ^ [_865376, _865378] : [_865378 = _865376, -(c_Rings_Odvd__class_Odvd(_865378) = c_Rings_Odvd__class_Odvd(_865376))], (5574 ^ _780086) ^ [_865461, _865463] : [_865463 = _865461, -(tc_List_Olist(_865463) = tc_List_Olist(_865461))], (5580 ^ _780086) ^ [_865546, _865548, _865550, _865552] : [-(tc_sum(_865552, _865548) = tc_sum(_865550, _865546)), _865552 = _865550, _865548 = _865546], (5590 ^ _780086) ^ [_865695, _865697] : [_865697 = _865695, -(tc_Option_Ooption(_865697) = tc_Option_Ooption(_865695))], (5596 ^ _780086) ^ [_865780, _865782, _865784, _865786] : [-(tc_Nitpick_Opair__box(_865786, _865782) = tc_Nitpick_Opair__box(_865784, _865780)), _865786 = _865784, _865782 = _865780], (5606 ^ _780086) ^ [_865929, _865931, _865933, _865935] : [-(tc_prod(_865935, _865931) = tc_prod(_865933, _865929)), _865935 = _865933, _865931 = _865929], (5616 ^ _780086) ^ [_866078, _866080] : [_866080 = _866078, -(tc_Lazy__Sequence_Olazy__sequence(_866080) = tc_Lazy__Sequence_Olazy__sequence(_866078))], (5622 ^ _780086) ^ [_866163, _866165] : [_866165 = _866163, -(c_COMBI(_866165) = c_COMBI(_866163))], (5628 ^ _780086) ^ [_866248, _866250, _866252, _866254] : [-(c_COMBK(_866254, _866250) = c_COMBK(_866252, _866248)), _866254 = _866252, _866250 = _866248], (5638 ^ _780086) ^ [_866397, _866399, _866401, _866403, _866405, _866407] : [-(c_COMBC(_866407, _866403, _866399) = c_COMBC(_866405, _866401, _866397)), _866407 = _866405, _866403 = _866401, _866399 = _866397], (5652 ^ _780086) ^ [_866618, _866620] : [_866620 = _866618, -(c_Finite__Set_Ofinite(_866620) = c_Finite__Set_Ofinite(_866618))], (5658 ^ _780086) ^ [_866703, _866705] : [_866705 = _866703, -(c_member(_866705) = c_member(_866703))], (5664 ^ _780086) ^ [_866788, _866790, _866792, _866794, _866796, _866798] : [-(c_Set_Oimage(_866798, _866794, _866790) = c_Set_Oimage(_866796, _866792, _866788)), _866798 = _866796, _866794 = _866792, _866790 = _866788], (5678 ^ _780086) ^ [_867009, _867011, _867013, _867015, _867017, _867019] : [-(c_COMBS(_867019, _867015, _867011) = c_COMBS(_867017, _867013, _867009)), _867019 = _867017, _867015 = _867013, _867011 = _867009], (5692 ^ _780086) ^ [_867230, _867232, _867234, _867236, _867238, _867240] : [-(c_COMBB(_867240, _867236, _867232) = c_COMBB(_867238, _867234, _867230)), _867240 = _867238, _867236 = _867234, _867232 = _867230], (5706 ^ _780086) ^ [_867451, _867453] : [_867453 = _867451, -(c_Set_Oinsert(_867453) = c_Set_Oinsert(_867451))], (5712 ^ _780086) ^ [_867536, _867538] : [_867538 = _867536, -(c_Hoare__Mirabelle_Otriple_Otriple(_867538) = c_Hoare__Mirabelle_Otriple_Otriple(_867536))], (5718 ^ _780086) ^ [_867621, _867623, _867625, _867627] : [-(hAPP(_867627, _867623) = hAPP(_867625, _867621)), _867627 = _867625, _867623 = _867621], (5728 ^ _780086) ^ [_867770, _867772] : [_867772 = _867770, -(c_Orderings_Obot__class_Obot(_867772) = c_Orderings_Obot__class_Obot(_867770))], (5744 ^ _780086) ^ [_868000, _868002] : [_868002 = _868000, -(tc_Hoare__Mirabelle_Otriple(_868002) = tc_Hoare__Mirabelle_Otriple(_868000))], (5734 ^ _780086) ^ [_867855, _867857, _867859, _867861] : [-(tc_fun(_867861, _867857) = tc_fun(_867859, _867855)), _867861 = _867859, _867857 = _867855], (5750 ^ _780086) ^ [_870966, _870968] : [hAPP(_870966, 5751 ^ [_870966, _870968]) = hAPP(_870968, 5751 ^ [_870966, _870968]), -(_870966 = _870968)], (5757 ^ _780086) ^ [_871092, _871094] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_871092, _871094, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_871092), tc_HOL_Obool))))], (5759 ^ _780086) ^ [_871125, _871127] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_871125, _871127, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_871125), tc_HOL_Obool))))], (5761 ^ _780086) ^ [_871188, _871190, _871192, _871194, _871196, _871198, _871200] : [hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_871188), _871190), _871192), _871194) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_871188), _871196), _871198), _871200), 5764 ^ _780086 : [(5765 ^ _780086) ^ [] : [-(_871190 = _871196)], (5767 ^ _780086) ^ [] : [-(_871192 = _871198)], (5769 ^ _780086) ^ [] : [-(_871194 = _871200)]]], (5771 ^ _780086) ^ [_871365, _871367, _871369, _871371, _871373, _871375, _871377] : [-(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_871365), _871367), _871369), _871371) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_871365), _871373), _871375), _871377)), _871367 = _871373, _871369 = _871375, _871371 = _871377], (5785 ^ _780086) ^ [_871622, _871624, _871626, _871628] : [c_Hoare__Mirabelle_Ohoare__derivs(_871622, _871624, _871626), c_Hoare__Mirabelle_Ohoare__derivs(_871622, _871628, _871624), -(c_Hoare__Mirabelle_Ohoare__derivs(_871622, _871628, _871626))], (5795 ^ _780086) ^ [_871765, _871767, _871769, _871771] : [c_Hoare__Mirabelle_Ohoare__derivs(_871765, _871767, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_871765)), _871769), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_871765), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_871765, _871767, _871771), -(c_Hoare__Mirabelle_Ohoare__derivs(_871765, _871767, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_871765)), _871769), _871771)))], (5805 ^ _780086) ^ [_871962, _871964, _871966, _871968] : [c_Hoare__Mirabelle_Ohoare__derivs(_871962, _871964, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_871962)), _871966), _871968)), 5808 ^ _780086 : [(5809 ^ _780086) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_871962, _871964, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_871962)), _871966), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_871962), tc_HOL_Obool)))))], (5811 ^ _780086) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_871962, _871964, _871968))]]], (5813 ^ _780086) ^ [_872129, _872131, _872133, _872135] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_872129), _872131)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_872133), hAPP(c_Set_Oimage(_872129, _872133, _872135), _872131))))], (5819 ^ _780086) ^ [_872240, _872242, _872244] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_872240), _872242)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_872240), hAPP(hAPP(c_Set_Oinsert(_872240), _872244), _872242))))], (5825 ^ _780086) ^ [_872351] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_872351), c_Orderings_Obot__class_Obot(tc_fun(_872351, tc_HOL_Obool)))))], (5827 ^ _780086) ^ [_872383, _872385, _872387, _872389, _872391, _872393] : [_872383 = hAPP(_872385, _872387), hBOOL(hAPP(hAPP(c_member(_872389), _872387), _872391)), -(hBOOL(hAPP(hAPP(c_member(_872393), _872383), hAPP(c_Set_Oimage(_872389, _872393, _872385), _872391))))], (5837 ^ _780086) ^ [_872576, _872578, _872580, _872582] : [hBOOL(hAPP(hAPP(c_member(_872576), _872578), hAPP(hAPP(c_Set_Oinsert(_872576), _872580), _872582))), -(_872578 = _872580), -(hBOOL(hAPP(hAPP(c_member(_872576), _872578), _872582)))], (5847 ^ _780086) ^ [_872716, _872718, _872720, _872722] : [5848 ^ _780086 : [(5849 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_872716), _872718), _872720))], (5851 ^ _780086) ^ [] : [_872718 = _872722]], -(hBOOL(hAPP(hAPP(c_member(_872716), _872718), hAPP(hAPP(c_Set_Oinsert(_872716), _872722), _872720))))], (5855 ^ _780086) ^ [_872893, _872895] : [hBOOL(hAPP(hAPP(c_member(_872893), _872895), c_Orderings_Obot__class_Obot(tc_fun(_872893, tc_HOL_Obool))))], (5857 ^ _780086) ^ [_872930, _872932, _872934, _872936, _872938] : [hBOOL(hAPP(hAPP(c_member(_872930), _872932), _872934)), -(hAPP(c_Set_Oimage(_872930, _872936, hAPP(c_COMBK(_872936, _872930), _872938)), _872934) = hAPP(hAPP(c_Set_Oinsert(_872936), _872938), c_Orderings_Obot__class_Obot(tc_fun(_872936, tc_HOL_Obool))))], (5863 ^ _780086) ^ [_873094, _873096, _873098, _873100] : [_873094 = c_Orderings_Obot__class_Obot(tc_fun(_873096, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_873096, _873098, hAPP(c_COMBK(_873098, _873096), _873100)), _873094) = c_Orderings_Obot__class_Obot(tc_fun(_873098, tc_HOL_Obool)))], (5869 ^ _780086) ^ [_873215, _873217, _873219, _873221] : [-(_873215 = c_Orderings_Obot__class_Obot(tc_fun(_873217, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_873217, _873219, hAPP(c_COMBK(_873219, _873217), _873221)), _873215) = hAPP(hAPP(c_Set_Oinsert(_873219), _873221), c_Orderings_Obot__class_Obot(tc_fun(_873219, tc_HOL_Obool))))], (5875 ^ _780086) ^ [_873288, _873290, _873292, _873294, _873296] : [hBOOL(hAPP(hAPP(c_member(_873288), _873290), _873292)), -(hAPP(hAPP(c_Set_Oinsert(_873294), hAPP(_873296, _873290)), hAPP(c_Set_Oimage(_873288, _873294, _873296), _873292)) = hAPP(c_Set_Oimage(_873288, _873294, _873296), _873292))], (5881 ^ _780086) ^ [_873453, _873455, _873457] : [hBOOL(hAPP(hAPP(c_member(_873453), _873455), hAPP(hAPP(c_Set_Oinsert(_873453), _873457), c_Orderings_Obot__class_Obot(tc_fun(_873453, tc_HOL_Obool))))), -(_873455 = _873457)], (5887 ^ _780086) ^ [_873568, _873570, _873572] : [_873570 = _873572, -(hBOOL(hAPP(hAPP(c_member(_873568), _873570), hAPP(hAPP(c_Set_Oinsert(_873568), _873572), c_Orderings_Obot__class_Obot(tc_fun(_873568, tc_HOL_Obool))))))], (5893 ^ _780086) ^ [_873689, _873691, _873693] : [hBOOL(hAPP(hAPP(c_member(_873689), _873691), hAPP(hAPP(c_Set_Oinsert(_873689), _873693), c_Orderings_Obot__class_Obot(tc_fun(_873689, tc_HOL_Obool))))), -(_873691 = _873693)], (5899 ^ _780086) ^ [_873808, _873810, _873812, _873814] : [_873808 = _873810, 5904 ^ _780086 : [(5905 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_873812), _873814), _873808)))], (5907 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_873812), _873814), _873810)))]], 5908 ^ _780086 : [(5909 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_873812), _873814), _873808))], (5911 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_873812), _873814), _873810))]]], (5913 ^ _780086) ^ [_874071, _874073, _874075, _874077] : [_874071 = _874073, hBOOL(hAPP(hAPP(c_member(_874075), _874073), _874077)), -(hBOOL(hAPP(hAPP(c_member(_874075), _874071), _874077)))], (5923 ^ _780086) ^ [_874236, _874238, _874240, _874242] : [_874236 = _874238, 5926 ^ _780086 : [(5927 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_874240), _874236), _874242)), -(hBOOL(hAPP(hAPP(c_member(_874240), _874238), _874242)))], (5933 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_874240), _874238), _874242)), -(hBOOL(hAPP(hAPP(c_member(_874240), _874236), _874242)))]]], (5939 ^ _780086) ^ [_874497, _874499, _874501, _874503] : [_874497 = _874499, 5942 ^ _780086 : [(5943 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_874501), _874503), _874497)), -(hBOOL(hAPP(hAPP(c_member(_874501), _874503), _874499)))], (5949 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_874501), _874503), _874499)), -(hBOOL(hAPP(hAPP(c_member(_874501), _874503), _874497)))]]], (5955 ^ _780086) ^ [_874776, _874778, _874780] : [hBOOL(hAPP(hAPP(c_member(_874776), _874778), _874780)), -(hBOOL(hAPP(_874780, _874778)))], (5961 ^ _780086) ^ [_874869, _874871, _874873] : [hBOOL(hAPP(_874873, _874871)), -(hBOOL(hAPP(hAPP(c_member(_874869), _874871), _874873)))], (5967 ^ _780086) ^ [_874968, _874970] : [class_Finite__Set_Ofinite(_874968), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_874968), _874970)))], (5973 ^ _780086) ^ [_875051, _875053] : [class_Finite__Set_Ofinite(_875051), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_875051), _875053)))], (5989 ^ _780086) ^ [_875269, _875271, _875273, _875275] : [5990 ^ _780086 : [(5991 ^ _780086) ^ [] : [_875271 = _875275], (5993 ^ _780086) ^ [] : [hBOOL(hAPP(_875273, _875275))]], -(hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_875269), _875271), _875273), _875275)))], (5979 ^ _780086) ^ [_875155, _875157, _875159, _875161] : [hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_875155), _875157), _875159), _875161)), -(_875157 = _875161), -(hBOOL(hAPP(_875159, _875161)))], (5997 ^ _780086) ^ [_875414, _875416, _875418, _875420] : [-(hAPP(hAPP(c_Set_Oinsert(_875414), _875416), hAPP(hAPP(c_Set_Oinsert(_875414), _875418), _875420)) = hAPP(hAPP(c_Set_Oinsert(_875414), _875418), hAPP(hAPP(c_Set_Oinsert(_875414), _875416), _875420)))], (5999 ^ _780086) ^ [_875475, _875477, _875479] : [-(hAPP(hAPP(c_Set_Oinsert(_875475), _875477), hAPP(hAPP(c_Set_Oinsert(_875475), _875477), _875479)) = hAPP(hAPP(c_Set_Oinsert(_875475), _875477), _875479))], (6001 ^ _780086) ^ [_875526, _875528, _875530, _875532, _875534, _875536] : [-(hAPP(c_Set_Oimage(_875526, _875528, _875530), hAPP(c_Set_Oimage(_875532, _875526, _875534), _875536)) = hAPP(c_Set_Oimage(_875532, _875528, hAPP(hAPP(c_COMBB(_875526, _875528, _875532), _875530), _875534)), _875536))], (6003 ^ _780086) ^ [_875590, _875592, _875594] : [_875590 = c_Orderings_Obot__class_Obot(tc_fun(_875592, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(_875592), _875594), _875590))], (6009 ^ _780086) ^ [_875706, _875708] : [hBOOL(hAPP(hAPP(c_member(_875706), _875708), c_Orderings_Obot__class_Obot(tc_fun(_875706, tc_HOL_Obool))))], (6011 ^ _780086) ^ [_875758, _875760] : [6012 ^ _780086 : [(6013 ^ _780086) ^ [_875811] : [hBOOL(hAPP(hAPP(c_member(_875758), _875811), _875760))]], _875760 = c_Orderings_Obot__class_Obot(tc_fun(_875758, tc_HOL_Obool))], (6017 ^ _780086) ^ [_875867, _875869] : [-(_875869 = c_Orderings_Obot__class_Obot(tc_fun(_875867, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_875867), 6020 ^ [_875867, _875869]), _875869)))], (6024 ^ _780086) ^ [_875933, _875935] : [-(hBOOL(hAPP(hAPP(c_member(_875933), 6025 ^ [_875933, _875935]), _875935))), -(_875935 = c_Orderings_Obot__class_Obot(tc_fun(_875933, tc_HOL_Obool)))], (6031 ^ _780086) ^ [_875984, _875986] : [_875986 = c_Orderings_Obot__class_Obot(tc_fun(_875984, tc_HOL_Obool)), 6034 ^ _780086 : [(6035 ^ _780086) ^ [_876064] : [hBOOL(hAPP(hAPP(c_member(_875984), _876064), _875986))]]], (6037 ^ _780086) ^ [_876100, _876102, _876104] : [hBOOL(hAPP(hAPP(c_member(_876100), _876102), _876104)), -(hAPP(hAPP(c_Set_Oinsert(_876100), _876102), _876104) = _876104)], (6043 ^ _780086) ^ [_876209, _876211, _876213, _876215] : [hBOOL(hAPP(hAPP(c_member(_876209), _876211), _876213)), -(hBOOL(hAPP(hAPP(c_member(_876209), _876211), hAPP(hAPP(c_Set_Oinsert(_876209), _876215), _876213))))], (6049 ^ _780086) ^ [_876333, _876335, _876337, _876339] : [-(hBOOL(hAPP(hAPP(c_member(_876333), _876335), _876337))), -(hBOOL(hAPP(hAPP(c_member(_876333), _876335), _876339))), 6056 ^ _780086 : [(6057 ^ _780086) ^ [] : [hAPP(hAPP(c_Set_Oinsert(_876333), _876335), _876337) = hAPP(hAPP(c_Set_Oinsert(_876333), _876335), _876339), -(_876337 = _876339)], (6063 ^ _780086) ^ [] : [_876337 = _876339, -(hAPP(hAPP(c_Set_Oinsert(_876333), _876335), _876337) = hAPP(hAPP(c_Set_Oinsert(_876333), _876335), _876339))]]], (6079 ^ _780086) ^ [_876833, _876835, _876837, _876839] : [6080 ^ _780086 : [(6081 ^ _780086) ^ [] : [_876835 = _876837], (6083 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_876833), _876835), _876839))]], -(hBOOL(hAPP(hAPP(c_member(_876833), _876835), hAPP(hAPP(c_Set_Oinsert(_876833), _876837), _876839))))], (6069 ^ _780086) ^ [_876699, _876701, _876703, _876705] : [hBOOL(hAPP(hAPP(c_member(_876699), _876701), hAPP(hAPP(c_Set_Oinsert(_876699), _876703), _876705))), -(_876701 = _876703), -(hBOOL(hAPP(hAPP(c_member(_876699), _876701), _876705)))], (6087 ^ _780086) ^ [_876998, _877000, _877002] : [-(hBOOL(hAPP(hAPP(c_member(_876998), _877000), hAPP(hAPP(c_Set_Oinsert(_876998), _877000), _877002))))], (6089 ^ _780086) ^ [_877040, _877042, _877044, _877046, _877048, _877050] : [hBOOL(hAPP(hAPP(c_member(_877040), _877042), _877044)), _877046 = hAPP(_877048, _877042), -(hBOOL(hAPP(hAPP(c_member(_877050), _877046), hAPP(c_Set_Oimage(_877040, _877050, _877048), _877044))))], (6099 ^ _780086) ^ [_877233, _877235, _877237, _877239, _877241] : [hBOOL(hAPP(hAPP(c_member(_877233), _877235), _877237)), -(hBOOL(hAPP(hAPP(c_member(_877239), hAPP(_877241, _877235)), hAPP(c_Set_Oimage(_877233, _877239, _877241), _877237))))], (6105 ^ _780086) ^ [_877388, _877390, _877392, _877394, _877396] : [hBOOL(hAPP(hAPP(c_member(_877388), _877390), hAPP(c_Set_Oimage(_877392, _877388, _877394), _877396))), 6109 ^ _780086 : [(6110 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_877392), 6108 ^ [_877388, _877390, _877392, _877394, _877396]), _877396)))], (6112 ^ _780086) ^ [] : [-(_877390 = hAPP(_877394, 6108 ^ [_877388, _877390, _877392, _877394, _877396]))]]], (6114 ^ _780086) ^ [_877572, _877574, _877576, _877578, _877580] : [-(hBOOL(hAPP(hAPP(c_member(_877572), _877574), hAPP(c_Set_Oimage(_877576, _877572, _877578), _877580)))), 6115 ^ _780086 : [(6116 ^ _780086) ^ [_877642] : [hBOOL(hAPP(hAPP(c_member(_877576), _877642), _877580)), _877574 = hAPP(_877578, _877642)]]], (6124 ^ _780086) ^ [_877790] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_877790), c_Orderings_Obot__class_Obot(tc_fun(_877790, tc_HOL_Obool)))))], (6126 ^ _780086) ^ [_877822, _877824, _877826] : [hAPP(hAPP(c_Set_Oinsert(_877822), _877824), c_Orderings_Obot__class_Obot(tc_fun(_877822, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(_877822), _877826), c_Orderings_Obot__class_Obot(tc_fun(_877822, tc_HOL_Obool))), -(_877824 = _877826)], (6132 ^ _780086) ^ [_877977, _877979, _877981, _877983, _877985] : [hAPP(hAPP(c_Set_Oinsert(_877977), _877979), hAPP(hAPP(c_Set_Oinsert(_877977), _877981), c_Orderings_Obot__class_Obot(tc_fun(_877977, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_877977), _877983), hAPP(hAPP(c_Set_Oinsert(_877977), _877985), c_Orderings_Obot__class_Obot(tc_fun(_877977, tc_HOL_Obool)))), 6137 ^ _780086 : [(6138 ^ _780086) ^ [] : [-(_877979 = _877983)], (6140 ^ _780086) ^ [] : [-(_877981 = _877985)]], 6141 ^ _780086 : [(6142 ^ _780086) ^ [] : [-(_877979 = _877985)], (6144 ^ _780086) ^ [] : [-(_877981 = _877983)]]], (6146 ^ _780086) ^ [_878239, _878241, _878243, _878245, _878247] : [-(hAPP(hAPP(c_Set_Oinsert(_878239), _878241), hAPP(hAPP(c_Set_Oinsert(_878239), _878243), c_Orderings_Obot__class_Obot(tc_fun(_878239, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_878239), _878245), hAPP(hAPP(c_Set_Oinsert(_878239), _878247), c_Orderings_Obot__class_Obot(tc_fun(_878239, tc_HOL_Obool))))), 6147 ^ _780086 : [(6148 ^ _780086) ^ [] : [_878241 = _878245, _878243 = _878247], (6154 ^ _780086) ^ [] : [_878241 = _878247, _878243 = _878245]]], (6162 ^ _780086) ^ [_878570, _878572, _878574] : [hAPP(hAPP(c_Set_Oinsert(_878570), _878572), _878574) = c_Orderings_Obot__class_Obot(tc_fun(_878570, tc_HOL_Obool))], (6164 ^ _780086) ^ [_878625, _878627, _878629] : [c_Orderings_Obot__class_Obot(tc_fun(_878625, tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(_878625), _878627), _878629)], (6166 ^ _780086) ^ [_878683, _878685, _878687] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_878683), hAPP(hAPP(c_Set_Oinsert(_878683), _878685), _878687))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_878683), _878687)))], (6172 ^ _780086) ^ [_878790, _878792, _878794] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_878790), _878794)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_878790), hAPP(hAPP(c_Set_Oinsert(_878790), _878792), _878794))))], (6178 ^ _780086) ^ [_878924, _878926, _878928, _878930] : [hAPP(c_Set_Oimage(_878924, _878926, _878928), _878930) = c_Orderings_Obot__class_Obot(tc_fun(_878926, tc_HOL_Obool)), -(_878930 = c_Orderings_Obot__class_Obot(tc_fun(_878924, tc_HOL_Obool)))], (6184 ^ _780086) ^ [_879035, _879037, _879039, _879041] : [_879041 = c_Orderings_Obot__class_Obot(tc_fun(_879035, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_879035, _879037, _879039), _879041) = c_Orderings_Obot__class_Obot(tc_fun(_879037, tc_HOL_Obool)))], (6190 ^ _780086) ^ [_879152, _879154, _879156] : [-(hAPP(c_Set_Oimage(_879152, _879154, _879156), c_Orderings_Obot__class_Obot(tc_fun(_879152, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_879154, tc_HOL_Obool)))], (6192 ^ _780086) ^ [_879217, _879219, _879221, _879223] : [c_Orderings_Obot__class_Obot(tc_fun(_879217, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_879219, _879217, _879221), _879223), -(_879223 = c_Orderings_Obot__class_Obot(tc_fun(_879219, tc_HOL_Obool)))], (6198 ^ _780086) ^ [_879328, _879330, _879332, _879334] : [_879334 = c_Orderings_Obot__class_Obot(tc_fun(_879330, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(_879328, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_879330, _879328, _879332), _879334))], (6204 ^ _780086) ^ [_879445, _879447, _879449, _879451, _879453] : [-(hAPP(c_Set_Oimage(_879445, _879447, _879449), hAPP(hAPP(c_Set_Oinsert(_879445), _879451), _879453)) = hAPP(hAPP(c_Set_Oinsert(_879447), hAPP(_879449, _879451)), hAPP(c_Set_Oimage(_879445, _879447, _879449), _879453)))], (6206 ^ _780086) ^ [_879509, _879511] : [-(c_Set_Othe__elem(_879509, hAPP(hAPP(c_Set_Oinsert(_879509), _879511), c_Orderings_Obot__class_Obot(tc_fun(_879509, tc_HOL_Obool)))) = _879511)], (6208 ^ _780086) ^ [_879550, _879552, _879554] : [class_Orderings_Obot(_879550), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_879552, _879550)), _879554) = c_Orderings_Obot__class_Obot(_879550))], (6214 ^ _780086) ^ [_879662, _879664] : [hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_879662, tc_HOL_Obool)), _879664)), -(hBOOL(hAPP(hAPP(c_member(_879662), _879664), c_Orderings_Obot__class_Obot(tc_fun(_879662, tc_HOL_Obool)))))], (6220 ^ _780086) ^ [_879773, _879775] : [hBOOL(hAPP(hAPP(c_member(_879773), _879775), c_Orderings_Obot__class_Obot(tc_fun(_879773, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_879773, tc_HOL_Obool)), _879775)))], (6226 ^ _780086) ^ [_879890, _879892, _879894, _879896, _879898, _879900] : [-(c_Hoare__Mirabelle_Otriple_Otriple__case(_879890, _879892, _879894, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_879890), _879896), _879898), _879900)) = hAPP(hAPP(hAPP(_879894, _879896), _879898), _879900))], (6228 ^ _780086) ^ [_879948, _879950, _879952, _879954, _879956, _879958] : [-(c_Hoare__Mirabelle_Otriple_Otriple__rec(_879948, _879950, _879952, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_879948), _879954), _879956), _879958)) = hAPP(hAPP(hAPP(_879952, _879954), _879956), _879958))], (6230 ^ _780086) ^ [_880006, _880008, _880010, _880012, _880014] : [c_Finite__Set_Ofolding__one(_880006, _880008, _880010), hBOOL(hAPP(c_Finite__Set_Ofinite(_880006), _880012)), -(hBOOL(hAPP(hAPP(c_member(_880006), _880014), _880012))), -(_880012 = c_Orderings_Obot__class_Obot(tc_fun(_880006, tc_HOL_Obool))), -(hAPP(_880010, hAPP(hAPP(c_Set_Oinsert(_880006), _880014), _880012)) = hAPP(hAPP(_880008, _880014), hAPP(_880010, _880012)))], (6248 ^ _780086) ^ [_880251, _880253, _880255] : [class_Orderings_Obot(_880251), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_880253, _880251)), _880255) = c_Orderings_Obot__class_Obot(_880251))], (6254 ^ _780086) ^ [_880348, _880350, _880352, _880354, _880356] : [6257 ^ _780086 : [(6258 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(_880348, 6255 ^ [_880348, _880350, _880352, _880354, _880356]), 6256 ^ [_880348, _880350, _880352, _880354, _880356])))], (6260 ^ _780086) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(_880350, _880352, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_880350)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_880350), hAPP(c_COMBK(tc_fun(tc_Com_Ostate, tc_HOL_Obool), _880350), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Ostate, tc_HOL_Obool), c_fequal), 6256 ^ [_880348, _880350, _880352, _880354, _880356]))), _880354), hAPP(c_COMBK(tc_fun(tc_Com_Ostate, tc_HOL_Obool), _880350), hAPP(_880356, 6255 ^ [_880348, _880350, _880352, _880354, _880356])))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_880350), tc_HOL_Obool))))]], -(c_Hoare__Mirabelle_Ohoare__derivs(_880350, _880352, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_880350)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_880350), _880348), _880354), _880356)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_880350), tc_HOL_Obool)))))], (6264 ^ _780086) ^ [_880770, _880772, _880774, _880776, _880778] : [c_Finite__Set_Ofolding__one__idem(_880770, _880772, _880774), hBOOL(hAPP(c_Finite__Set_Ofinite(_880770), _880776)), -(_880776 = c_Orderings_Obot__class_Obot(tc_fun(_880770, tc_HOL_Obool))), -(hAPP(_880774, hAPP(hAPP(c_Set_Oinsert(_880770), _880778), _880776)) = hAPP(hAPP(_880772, _880778), hAPP(_880774, _880776)))], (6278 ^ _780086) ^ [_880986, _880988, _880990] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_880986, _880988, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_880986)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_880986), _880990), c_Com_Ocom_OSKIP), _880990)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_880986), tc_HOL_Obool)))))], (6280 ^ _780086) ^ [_881042, _881044, _881046] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_881042, _881044, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_881042)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_881042), _881046), c_Com_Ocom_OSKIP), _881046)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_881042), tc_HOL_Obool)))))], (6282 ^ _780086) ^ [_881098, _881100, _881102, _881104, _881106, _881108] : [c_Hoare__Mirabelle_Ohoare__derivs(_881098, _881100, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_881098)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_881098), _881102), _881104), _881106)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_881098), tc_HOL_Obool)))), 6289 ^ _780086 : [(6290 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(_881108, 6287 ^ [_881098, _881100, _881102, _881104, _881106, _881108]), 6288 ^ [_881098, _881100, _881102, _881104, _881106, _881108])))], (6292 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(_881102, 6287 ^ [_881098, _881100, _881102, _881104, _881106, _881108]), 6288 ^ [_881098, _881100, _881102, _881104, _881106, _881108]))]], -(c_Hoare__Mirabelle_Ohoare__derivs(_881098, _881100, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_881098)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_881098), _881108), _881104), _881106)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_881098), tc_HOL_Obool)))))], (6296 ^ _780086) ^ [_881527, _881529, _881531, _881533] : [c_Finite__Set_Ofolding__one__idem(_881527, _881529, _881531), -(hAPP(hAPP(_881529, _881533), _881533) = _881533)], (6302 ^ _780086) ^ [_881640, _881642, _881644] : [hBOOL(hAPP(hAPP(c_member(_881640), _881642), hAPP(c_fequal, _881644))), -(_881642 = _881644)], (6308 ^ _780086) ^ [_881735, _881737, _881739] : [_881737 = _881739, -(hBOOL(hAPP(hAPP(c_member(_881735), _881737), hAPP(c_fequal, _881739))))], (6314 ^ _780086) ^ [_881836, _881838, _881840, _881842] : [c_Finite__Set_Ofolding__one(_881836, _881838, _881840), -(hAPP(_881840, hAPP(hAPP(c_Set_Oinsert(_881836), _881842), c_Orderings_Obot__class_Obot(tc_fun(_881836, tc_HOL_Obool)))) = _881842)], (6320 ^ _780086) ^ [_881951, _881953, _881955, _881957, _881959] : [c_Finite__Set_Ofolding__one__idem(_881951, _881953, _881955), hBOOL(hAPP(c_Finite__Set_Ofinite(_881951), _881957)), hBOOL(hAPP(hAPP(c_member(_881951), _881959), _881957)), -(hAPP(hAPP(_881953, _881959), hAPP(_881955, _881957)) = hAPP(_881955, _881957))], (6334 ^ _780086) ^ [_882216, _882218, _882220] : [hAPP(hAPP(c_COMBC(_882216, tc_fun(_882216, tc_HOL_Obool), tc_HOL_Obool), c_member(_882216)), _882218) = hAPP(hAPP(c_COMBC(_882216, tc_fun(_882216, tc_HOL_Obool), tc_HOL_Obool), c_member(_882216)), _882220), -(_882218 = _882220)], (6340 ^ _780086) ^ [_882351, _882353, _882355] : [_882353 = _882355, -(hAPP(hAPP(c_COMBC(_882351, tc_fun(_882351, tc_HOL_Obool), tc_HOL_Obool), c_member(_882351)), _882353) = hAPP(hAPP(c_COMBC(_882351, tc_fun(_882351, tc_HOL_Obool), tc_HOL_Obool), c_member(_882351)), _882355))], (6346 ^ _780086) ^ [_882492, _882494, _882496, _882498] : [c_Finite__Set_Ofolding__one(_882492, _882494, _882496), hBOOL(hAPP(c_Finite__Set_Ofinite(_882492), _882498)), -(_882498 = c_Orderings_Obot__class_Obot(tc_fun(_882492, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_882492), hAPP(hAPP(_882494, 6359 ^ [_882492, _882494, _882496, _882498]), 6360 ^ [_882492, _882494, _882496, _882498])), hAPP(hAPP(c_Set_Oinsert(_882492), 6359 ^ [_882492, _882494, _882496, _882498]), hAPP(hAPP(c_Set_Oinsert(_882492), 6360 ^ [_882492, _882494, _882496, _882498]), c_Orderings_Obot__class_Obot(tc_fun(_882492, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_882492), hAPP(_882496, _882498)), _882498)))], (6366 ^ _780086) ^ [_882978, _882980, _882982, _882984, _882986, _882988] : [c_Hoare__Mirabelle_Ohoare__derivs(_882978, _882980, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_882978)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_882978), _882982), _882984), _882986)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_882978), tc_HOL_Obool)))), 6373 ^ _780086 : [(6374 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(_882986, 6371 ^ [_882978, _882980, _882982, _882984, _882986, _882988]), 6372 ^ [_882978, _882980, _882982, _882984, _882986, _882988])))], (6376 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(_882988, 6371 ^ [_882978, _882980, _882982, _882984, _882986, _882988]), 6372 ^ [_882978, _882980, _882982, _882984, _882986, _882988]))]], -(c_Hoare__Mirabelle_Ohoare__derivs(_882978, _882980, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_882978)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_882978), _882982), _882984), _882988)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_882978), tc_HOL_Obool)))))], (6380 ^ _780086) ^ [_883407, _883409, _883411, _883413, _883415, _883417, _883419] : [c_Hoare__Mirabelle_Ohoare__derivs(_883407, _883409, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_883407)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_883407), _883411), _883413), _883415)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_883407), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_883407, _883409, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_883407)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_883407), _883415), _883417), _883419)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_883407), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_883407, _883409, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_883407)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_883407), _883411), c_Com_Ocom_OSemi(_883413, _883417)), _883419)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_883407), tc_HOL_Obool)))))], (6390 ^ _780086) ^ [_883736, _883738] : [-(c_Set_Othe__elem(_883736, _883738) = c_HOL_OThe(_883736, hAPP(hAPP(c_COMBB(tc_fun(_883736, tc_HOL_Obool), tc_HOL_Obool, _883736), hAPP(c_fequal, _883738)), hAPP(hAPP(c_COMBC(_883736, tc_fun(_883736, tc_HOL_Obool), tc_fun(_883736, tc_HOL_Obool)), c_Set_Oinsert(_883736)), c_Orderings_Obot__class_Obot(tc_fun(_883736, tc_HOL_Obool))))))], (6392 ^ _780086) ^ [_883806, _883808, _883810, _883812, _883814] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_883806, _883808, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_883806)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_883806), hAPP(hAPP(c_COMBC(_883806, tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _883806), c_COMBS(tc_Com_Ostate, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _883806), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fconj)), _883810))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate), c_fNot), _883812))), c_Com_Ocom_OWhile(_883812, _883814)), _883810)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_883806), tc_HOL_Obool)))))], (6394 ^ _780086) ^ [_883902, _883904, _883906, _883908, _883910] : [c_Finite__Set_Ofolding__one__idem(_883902, _883904, _883906), hAPP(_883908, hAPP(hAPP(_883904, 6399 ^ [_883902, _883904, _883906, _883908, _883910]), 6400 ^ [_883902, _883904, _883906, _883908, _883910])) = hAPP(hAPP(_883904, hAPP(_883908, 6399 ^ [_883902, _883904, _883906, _883908, _883910])), hAPP(_883908, 6400 ^ [_883902, _883904, _883906, _883908, _883910])), hBOOL(hAPP(c_Finite__Set_Ofinite(_883902), _883910)), -(_883910 = c_Orderings_Obot__class_Obot(tc_fun(_883902, tc_HOL_Obool))), -(hAPP(_883908, hAPP(_883906, _883910)) = hAPP(_883906, hAPP(c_Set_Oimage(_883902, _883902, _883908), _883910)))], (6414 ^ _780086) ^ [_884337, _884339, _884341, _884343, _884345, _884347, _884349, _884351] : [c_Finite__Set_Ofolding__image__simple(_884337, _884339, _884341, _884343, _884345, _884347), hBOOL(hAPP(c_Finite__Set_Ofinite(_884339), _884349)), -(hBOOL(hAPP(hAPP(c_member(_884339), _884351), _884349))), -(hAPP(_884347, hAPP(hAPP(c_Set_Oinsert(_884339), _884351), _884349)) = hAPP(hAPP(_884341, hAPP(_884345, _884351)), hAPP(_884347, _884349)))], (6428 ^ _780086) ^ [_884581, _884583, _884585, _884587, _884589] : [c_Finite__Set_Ofolding__one(_884581, _884583, _884585), hBOOL(hAPP(c_Finite__Set_Ofinite(_884581), _884587)), hBOOL(hAPP(hAPP(c_member(_884581), _884589), _884587)), 6439 ^ _780086 : [(6440 ^ _780086) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_884581, tc_HOL_Obool)), _884587), hAPP(hAPP(c_Set_Oinsert(_884581), _884589), c_Orderings_Obot__class_Obot(tc_fun(_884581, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_884581, tc_HOL_Obool)), -(hAPP(_884585, _884587) = _884589)], (6446 ^ _780086) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_884581, tc_HOL_Obool)), _884587), hAPP(hAPP(c_Set_Oinsert(_884581), _884589), c_Orderings_Obot__class_Obot(tc_fun(_884581, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_884581, tc_HOL_Obool))), -(hAPP(_884585, _884587) = hAPP(hAPP(_884583, _884589), hAPP(_884585, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_884581, tc_HOL_Obool)), _884587), hAPP(hAPP(c_Set_Oinsert(_884581), _884589), c_Orderings_Obot__class_Obot(tc_fun(_884581, tc_HOL_Obool)))))))]]], (6452 ^ _780086) ^ [_885103, _885105, _885107, _885109, _885111, _885113, _885115, _885117] : [c_Finite__Set_Ofolding__image__simple__idem(_885103, _885105, _885107, _885109, _885111, _885113), hBOOL(hAPP(c_Finite__Set_Ofinite(_885105), _885115)), -(hAPP(_885113, hAPP(hAPP(c_Set_Oinsert(_885105), _885117), _885115)) = hAPP(hAPP(_885107, hAPP(_885111, _885117)), hAPP(_885113, _885115)))], (6462 ^ _780086) ^ [_885318, _885320, _885322] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_885318), _885320)), hBOOL(hAPP(_885322, c_Orderings_Obot__class_Obot(tc_fun(_885318, tc_HOL_Obool)))), 6473 ^ _780086 : [(6474 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_885318), 6472 ^ [_885318, _885320, _885322])))], (6476 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_885318), 6471 ^ [_885318, _885320, _885322]), 6472 ^ [_885318, _885320, _885322]))], (6478 ^ _780086) ^ [] : [-(hBOOL(hAPP(_885322, 6472 ^ [_885318, _885320, _885322])))], (6480 ^ _780086) ^ [] : [hBOOL(hAPP(_885322, hAPP(hAPP(c_Set_Oinsert(_885318), 6471 ^ [_885318, _885320, _885322]), 6472 ^ [_885318, _885320, _885322])))]], -(hBOOL(hAPP(_885322, _885320)))], (6484 ^ _780086) ^ [_885805, _885807, _885809, _885811, _885813, _885815, _885817, _885819] : [c_Finite__Set_Ofolding__image__simple__idem(_885805, _885807, _885809, _885811, _885813, _885815), hBOOL(hAPP(c_Finite__Set_Ofinite(_885807), _885817)), hBOOL(hAPP(hAPP(c_member(_885807), _885819), _885817)), -(hAPP(hAPP(_885809, hAPP(_885813, _885819)), hAPP(_885815, _885817)) = hAPP(_885815, _885817))], (6498 ^ _780086) ^ [_886082, _886084] : [-(hAPP(c_Set_Oimage(_886082, _886082, c_COMBI(_886082)), _886084) = _886084)], (6500 ^ _780086) ^ [_886116, _886118, _886120, _886122] : [hBOOL(hAPP(hAPP(c_member(_886116), _886118), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_886116, tc_HOL_Obool)), _886120), _886122))), 6503 ^ _780086 : [(6504 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_886116), _886118), _886120)))], (6506 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_886116), _886118), _886122))]]], (6508 ^ _780086) ^ [_886295, _886297, _886299, _886301] : [hBOOL(hAPP(hAPP(c_member(_886295), _886297), _886299)), -(hBOOL(hAPP(hAPP(c_member(_886295), _886297), _886301))), -(hBOOL(hAPP(hAPP(c_member(_886295), _886297), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_886295, tc_HOL_Obool)), _886299), _886301))))], (6518 ^ _780086) ^ [_886455, _886457, _886459] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_886455), _886457)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_886455), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_886455, tc_HOL_Obool)), _886457), _886459))))], (6524 ^ _780086) ^ [_886572, _886574, _886576] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_886572, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_886572, tc_HOL_Obool)), _886574), _886576)), _886576) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_886572, tc_HOL_Obool)), _886574), _886576))], (6526 ^ _780086) ^ [_886632, _886634, _886636, _886638, _886640, _886642, _886644] : [c_Finite__Set_Ofolding__image__simple__idem(_886632, _886634, _886636, _886638, _886640, _886642), -(hAPP(hAPP(_886636, _886644), _886644) = _886644)], (6532 ^ _780086) ^ [_886739, _886741, _886743, _886745] : [hBOOL(hAPP(hAPP(c_member(_886739), _886741), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_886739, tc_HOL_Obool)), _886743), _886745))), hBOOL(hAPP(hAPP(c_member(_886739), _886741), _886745))], (6538 ^ _780086) ^ [_886871, _886873, _886875, _886877] : [hBOOL(hAPP(hAPP(c_member(_886871), _886873), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_886871, tc_HOL_Obool)), _886875), _886877))), -(hBOOL(hAPP(hAPP(c_member(_886871), _886873), _886875)))], (6544 ^ _780086) ^ [_887023, _887025, _887027, _887029] : [hBOOL(hAPP(hAPP(c_member(_887023), _887025), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_887023, tc_HOL_Obool)), _887027), _887029))), 6547 ^ _780086 : [(6548 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_887023), _887025), _887027)))], (6550 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_887023), _887025), _887029))]]], (6552 ^ _780086) ^ [_887198, _887200, _887202, _887204] : [-(hBOOL(hAPP(hAPP(c_member(_887198), _887200), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_887198, tc_HOL_Obool)), _887202), _887204)))), hBOOL(hAPP(hAPP(c_member(_887198), _887200), _887202)), -(hBOOL(hAPP(hAPP(c_member(_887198), _887200), _887204)))], (6562 ^ _780086) ^ [_887404, _887406] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_887404, tc_HOL_Obool)), _887406), _887406) = c_Orderings_Obot__class_Obot(tc_fun(_887404, tc_HOL_Obool)))], (6564 ^ _780086) ^ [_887445, _887447] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_887445, tc_HOL_Obool)), _887447), c_Orderings_Obot__class_Obot(tc_fun(_887445, tc_HOL_Obool))) = _887447)], (6566 ^ _780086) ^ [_887486, _887488] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_887486, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_887486, tc_HOL_Obool))), _887488) = c_Orderings_Obot__class_Obot(tc_fun(_887486, tc_HOL_Obool)))], (6568 ^ _780086) ^ [_887532, _887534, _887536] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_887532), _887534)), 6571 ^ _780086 : [(6572 ^ _780086) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_887532), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_887532, tc_HOL_Obool)), _887536), _887534))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_887532), _887536)))], (6578 ^ _780086) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_887532), _887536)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_887532), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_887532, tc_HOL_Obool)), _887536), _887534))))]]], (6584 ^ _780086) ^ [_887810, _887812, _887814, _887816, _887818, _887820, _887822, _887824] : [c_Finite__Set_Ofolding__image__simple(_887810, _887812, _887814, _887816, _887818, _887820), hBOOL(hAPP(c_Finite__Set_Ofinite(_887812), _887822)), -(hAPP(_887820, hAPP(hAPP(c_Set_Oinsert(_887812), _887824), _887822)) = hAPP(hAPP(_887814, hAPP(_887818, _887824)), hAPP(_887820, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_887812, tc_HOL_Obool)), _887822), hAPP(hAPP(c_Set_Oinsert(_887812), _887824), c_Orderings_Obot__class_Obot(tc_fun(_887812, tc_HOL_Obool)))))))], (6594 ^ _780086) ^ [_888073, _888075, _888077, _888079] : [hBOOL(hAPP(hAPP(c_member(_888073), _888075), _888077)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_888073, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_888073), _888075), _888079)), _888077) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_888073, tc_HOL_Obool)), _888079), _888077))], (6600 ^ _780086) ^ [_888243, _888245, _888247, _888249] : [hBOOL(hAPP(hAPP(c_member(_888243), _888245), _888247)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_888243, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_888243), _888245), _888249)), _888247) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_888243, tc_HOL_Obool)), _888249), _888247))], (6606 ^ _780086) ^ [_888392, _888394, _888396, _888398] : [-(hBOOL(hAPP(hAPP(c_member(_888392), _888394), _888396))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_888392, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_888392), _888394), _888398)), _888396) = hAPP(hAPP(c_Set_Oinsert(_888392), _888394), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_888392, tc_HOL_Obool)), _888398), _888396)))], (6612 ^ _780086) ^ [_888479, _888481, _888483] : [-(hAPP(hAPP(c_Set_Oinsert(_888479), _888481), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_888479, tc_HOL_Obool)), _888483), hAPP(hAPP(c_Set_Oinsert(_888479), _888481), c_Orderings_Obot__class_Obot(tc_fun(_888479, tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(_888479), _888481), _888483))], (6614 ^ _780086) ^ [_888546, _888548, _888550, _888552] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_888546, tc_HOL_Obool)), _888548), hAPP(hAPP(c_Set_Oinsert(_888546), _888550), _888552)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_888546, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_888546, tc_HOL_Obool)), _888548), hAPP(hAPP(c_Set_Oinsert(_888546), _888550), c_Orderings_Obot__class_Obot(tc_fun(_888546, tc_HOL_Obool))))), _888552))], (6616 ^ _780086) ^ [_888629, _888631, _888633, _888635] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_888629, tc_HOL_Obool)), _888631), hAPP(hAPP(c_Set_Oinsert(_888629), _888633), _888635)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_888629, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_888629, tc_HOL_Obool)), _888631), _888635)), hAPP(hAPP(c_Set_Oinsert(_888629), _888633), c_Orderings_Obot__class_Obot(tc_fun(_888629, tc_HOL_Obool)))))], (6618 ^ _780086) ^ [_888733, _888735, _888737, _888739] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_888733), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_888733, tc_HOL_Obool)), _888735), hAPP(hAPP(c_Set_Oinsert(_888733), _888737), _888739)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_888733), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_888733, tc_HOL_Obool)), _888735), _888739))))], (6624 ^ _780086) ^ [_888886, _888888, _888890, _888892] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_888886), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_888886, tc_HOL_Obool)), _888888), _888892))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_888886), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_888886, tc_HOL_Obool)), _888888), hAPP(hAPP(c_Set_Oinsert(_888886), _888890), _888892)))))], (6630 ^ _780086) ^ [_889045, _889047, _889049, _889051, _889053, _889055] : [c_Finite__Set_Ofolding__image__simple(_889045, _889047, _889049, _889051, _889053, _889055), -(hAPP(_889055, c_Orderings_Obot__class_Obot(tc_fun(_889047, tc_HOL_Obool))) = _889051)], (6636 ^ _780086) ^ [_889154, _889156, _889158, _889160, _889162, _889164, _889166, _889168] : [c_Finite__Set_Ofolding__image__simple(_889154, _889156, _889158, _889160, _889162, _889164), hBOOL(hAPP(c_Finite__Set_Ofinite(_889156), _889166)), hBOOL(hAPP(hAPP(c_member(_889156), _889168), _889166)), -(hAPP(_889164, _889166) = hAPP(hAPP(_889158, hAPP(_889162, _889168)), hAPP(_889164, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_889156, tc_HOL_Obool)), _889166), hAPP(hAPP(c_Set_Oinsert(_889156), _889168), c_Orderings_Obot__class_Obot(tc_fun(_889156, tc_HOL_Obool)))))))], (6650 ^ _780086) ^ [_889479, _889481, _889483] : [hBOOL(hAPP(hAPP(c_member(_889479), _889481), _889483)), -(hAPP(hAPP(c_Set_Oinsert(_889479), _889481), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_889479, tc_HOL_Obool)), _889483), hAPP(hAPP(c_Set_Oinsert(_889479), _889481), c_Orderings_Obot__class_Obot(tc_fun(_889479, tc_HOL_Obool))))) = _889483)], (6656 ^ _780086) ^ [_889632, _889634, _889636] : [-(hBOOL(hAPP(hAPP(c_member(_889632), _889634), _889636))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_889632, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_889632), _889634), _889636)), hAPP(hAPP(c_Set_Oinsert(_889632), _889634), c_Orderings_Obot__class_Obot(tc_fun(_889632, tc_HOL_Obool)))) = _889636)], (6662 ^ _780086) ^ [_889709, _889711, _889713, _889715, _889717] : [c_Finite__Set_Ofolding__one(_889709, _889711, _889713), hBOOL(hAPP(c_Finite__Set_Ofinite(_889709), _889715)), 6669 ^ _780086 : [(6670 ^ _780086) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_889709, tc_HOL_Obool)), _889715), hAPP(hAPP(c_Set_Oinsert(_889709), _889717), c_Orderings_Obot__class_Obot(tc_fun(_889709, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_889709, tc_HOL_Obool)), -(hAPP(_889713, hAPP(hAPP(c_Set_Oinsert(_889709), _889717), _889715)) = _889717)], (6676 ^ _780086) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_889709, tc_HOL_Obool)), _889715), hAPP(hAPP(c_Set_Oinsert(_889709), _889717), c_Orderings_Obot__class_Obot(tc_fun(_889709, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_889709, tc_HOL_Obool))), -(hAPP(_889713, hAPP(hAPP(c_Set_Oinsert(_889709), _889717), _889715)) = hAPP(hAPP(_889711, _889717), hAPP(_889713, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_889709, tc_HOL_Obool)), _889715), hAPP(hAPP(c_Set_Oinsert(_889709), _889717), c_Orderings_Obot__class_Obot(tc_fun(_889709, tc_HOL_Obool)))))))]]], (6682 ^ _780086) ^ [_890191, _890193, _890195, _890197, _890199] : [class_Groups_Ominus(_890191), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_890193, _890191)), _890195), _890197), _890199) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_890191), hAPP(_890195, _890199)), hAPP(_890197, _890199)))], (6688 ^ _780086) ^ [_890340, _890342] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OSemi(_890340, _890342)], (6690 ^ _780086) ^ [_890380, _890382] : [c_Com_Ocom_OSemi(_890380, _890382) = c_Com_Ocom_OSKIP], (6692 ^ _780086) ^ [_890420, _890422] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OWhile(_890420, _890422)], (6694 ^ _780086) ^ [_890460, _890462] : [c_Com_Ocom_OWhile(_890460, _890462) = c_Com_Ocom_OSKIP], (6696 ^ _780086) ^ [_890506, _890508, _890510, _890512] : [c_Com_Ocom_OSemi(_890506, _890508) = c_Com_Ocom_OWhile(_890510, _890512)], (6698 ^ _780086) ^ [_890559, _890561, _890563, _890565] : [c_Com_Ocom_OWhile(_890559, _890561) = c_Com_Ocom_OSemi(_890563, _890565)], (6700 ^ _780086) ^ [_890594, _890596, _890598, _890600, _890602] : [class_Groups_Ominus(_890594), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_890596, _890594)), _890598), _890600), _890602) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_890594), hAPP(_890598, _890602)), hAPP(_890600, _890602)))], (6706 ^ _780086) ^ [_890752, _890754, _890756, _890758, _890760, _890762] : [hBOOL(hAPP(hAPP(c_member(_890752), _890754), _890756)), -(hAPP(c_Set_Oimage(_890752, _890758, c_Fun_Ofun__upd(_890752, _890758, _890760, _890754, _890762)), _890756) = hAPP(hAPP(c_Set_Oinsert(_890758), _890762), hAPP(c_Set_Oimage(_890752, _890758, _890760), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_890752, tc_HOL_Obool)), _890756), hAPP(hAPP(c_Set_Oinsert(_890752), _890754), c_Orderings_Obot__class_Obot(tc_fun(_890752, tc_HOL_Obool)))))))], (6712 ^ _780086) ^ [_890949, _890951, _890953, _890955, _890957, _890959] : [-(hBOOL(hAPP(hAPP(c_member(_890949), _890951), _890953))), -(hAPP(c_Set_Oimage(_890949, _890955, c_Fun_Ofun__upd(_890949, _890955, _890957, _890951, _890959)), _890953) = hAPP(c_Set_Oimage(_890949, _890955, _890957), _890953))], (6718 ^ _780086) ^ [_891022, _891024, _891026] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_891022), _891024)), hBOOL(hAPP(_891026, _891024)), 6729 ^ _780086 : [(6730 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_891022), 6728 ^ [_891022, _891024, _891026])))], (6732 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_891022), 6727 ^ [_891022, _891024, _891026]), 6728 ^ [_891022, _891024, _891026])))], (6734 ^ _780086) ^ [] : [-(hBOOL(hAPP(_891026, 6728 ^ [_891022, _891024, _891026])))], (6736 ^ _780086) ^ [] : [hBOOL(hAPP(_891026, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_891022, tc_HOL_Obool)), 6728 ^ [_891022, _891024, _891026]), hAPP(hAPP(c_Set_Oinsert(_891022), 6727 ^ [_891022, _891024, _891026]), c_Orderings_Obot__class_Obot(tc_fun(_891022, tc_HOL_Obool))))))]], -(hBOOL(hAPP(_891026, c_Orderings_Obot__class_Obot(tc_fun(_891022, tc_HOL_Obool)))))], (6740 ^ _780086) ^ [_891547] : [-(c_Finite__Set_Ofun__left__comm__idem(_891547, tc_fun(_891547, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_891547, tc_HOL_Obool), tc_fun(tc_fun(_891547, tc_HOL_Obool), tc_fun(_891547, tc_HOL_Obool)), _891547), hAPP(c_COMBC(tc_fun(_891547, tc_HOL_Obool), tc_fun(_891547, tc_HOL_Obool), tc_fun(_891547, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_891547, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_891547, tc_fun(_891547, tc_HOL_Obool), tc_fun(_891547, tc_HOL_Obool)), c_Set_Oinsert(_891547)), c_Orderings_Obot__class_Obot(tc_fun(_891547, tc_HOL_Obool))))))], (6742 ^ _780086) ^ [_891640, _891642] : [-(c_HOL_OThe(_891640, hAPP(c_fequal, _891642)) = _891642)], (6744 ^ _780086) ^ [_891671, _891673, _891675, _891677] : [-(c_Fun_Ofun__upd(_891671, _891673, _891675, _891677, hAPP(_891675, _891677)) = _891675)], (6746 ^ _780086) ^ [_891733, _891735, _891737, _891739, _891741] : [c_Fun_Ofun__upd(_891733, _891735, _891737, _891739, _891741) = _891737, -(hAPP(_891737, _891739) = _891741)], (6752 ^ _780086) ^ [_891830, _891832, _891834, _891836, _891838] : [hAPP(_891834, _891836) = _891838, -(c_Fun_Ofun__upd(_891830, _891832, _891834, _891836, _891838) = _891834)], (6758 ^ _780086) ^ [_891933, _891935, _891937, _891939, _891941, _891943] : [-(c_Fun_Ofun__upd(_891933, _891935, c_Fun_Ofun__upd(_891933, _891935, _891937, _891939, _891941), _891939, _891943) = c_Fun_Ofun__upd(_891933, _891935, _891937, _891939, _891943))], (6760 ^ _780086) ^ [_891984, _891986, _891988, _891990, _891992] : [-(hAPP(c_Fun_Ofun__upd(_891984, _891986, _891988, _891990, _891992), _891990) = _891992)], (6762 ^ _780086) ^ [_892045, _892047, _892049, _892051, _892053, _892055] : [_892045 = _892047, -(hAPP(c_Fun_Ofun__upd(_892049, _892051, _892053, _892047, _892055), _892045) = _892055)], (6768 ^ _780086) ^ [_892142, _892144, _892146, _892148, _892150, _892152] : [-(_892142 = _892144), -(hAPP(c_Fun_Ofun__upd(_892146, _892148, _892150, _892144, _892152), _892142) = hAPP(_892150, _892142))], (6774 ^ _780086) ^ [_892196, _892198, _892200, _892202, _892204, _892206, _892208] : [-(_892196 = _892198), -(c_Fun_Ofun__upd(_892200, _892202, c_Fun_Ofun__upd(_892200, _892202, _892204, _892196, _892206), _892198, _892208) = c_Fun_Ofun__upd(_892200, _892202, c_Fun_Ofun__upd(_892200, _892202, _892204, _892198, _892208), _892196, _892206))], (6780 ^ _780086) ^ [_892262, _892264, _892266, _892268, _892270, _892272] : [-(_892262 = _892264), -(hAPP(c_Fun_Ofun__upd(_892266, _892268, _892270, _892264, _892272), _892262) = hAPP(_892270, _892262))], (6786 ^ _780086) ^ [_892318, _892320, _892322, _892324, _892326] : [hAPP(_892318, _892320) = _892322, -(c_Fun_Ofun__upd(_892324, _892326, _892318, _892320, _892322) = _892318)], (6792 ^ _780086) ^ [_892419, _892421, _892423, _892425, _892427] : [c_Finite__Set_Ofun__left__comm__idem(_892419, _892421, _892423), -(hAPP(hAPP(_892423, _892425), hAPP(hAPP(_892423, _892425), _892427)) = hAPP(hAPP(_892423, _892425), _892427))], (6798 ^ _780086) ^ [_892561, _892563, _892565, _892567, _892569, _892571] : [_892561 = _892563, -(hAPP(c_Fun_Ofun__upd(_892565, _892567, _892569, _892563, _892571), _892561) = _892571)], (6804 ^ _780086) ^ [_892658, _892660, _892662, _892664, _892666, _892668] : [-(_892658 = _892660), -(hAPP(c_Fun_Ofun__upd(_892662, _892664, _892666, _892660, _892668), _892658) = hAPP(_892666, _892658))], (6810 ^ _780086) ^ [_892716, _892718, _892720, _892722, _892724] : [c_Finite__Set_Ofun__left__comm__idem(_892716, _892718, _892720), -(c_Finite__Set_Ofun__left__comm__idem(_892722, _892718, hAPP(hAPP(c_COMBB(_892716, tc_fun(_892718, _892718), _892722), _892720), _892724)))], (6816 ^ _780086) ^ [_892829] : [-(c_Finite__Set_Ofun__left__comm__idem(_892829, tc_fun(_892829, tc_HOL_Obool), c_Set_Oinsert(_892829)))], (6818 ^ _780086) ^ [_892879, _892881, _892883, _892885] : [c_Com_Ocom_OWhile(_892879, _892881) = c_Com_Ocom_OWhile(_892883, _892885), 6821 ^ _780086 : [(6822 ^ _780086) ^ [] : [-(_892879 = _892883)], (6824 ^ _780086) ^ [] : [-(_892881 = _892885)]]], (6826 ^ _780086) ^ [_892994, _892996, _892998, _893000] : [-(c_Com_Ocom_OWhile(_892994, _892996) = c_Com_Ocom_OWhile(_892998, _893000)), _892994 = _892998, _892996 = _893000], (6836 ^ _780086) ^ [_893166, _893168, _893170, _893172] : [c_Com_Ocom_OSemi(_893166, _893168) = c_Com_Ocom_OSemi(_893170, _893172), 6839 ^ _780086 : [(6840 ^ _780086) ^ [] : [-(_893166 = _893170)], (6842 ^ _780086) ^ [] : [-(_893168 = _893172)]]], (6844 ^ _780086) ^ [_893281, _893283, _893285, _893287] : [-(c_Com_Ocom_OSemi(_893281, _893283) = c_Com_Ocom_OSemi(_893285, _893287)), _893281 = _893285, _893283 = _893287], (6854 ^ _780086) ^ [_893432, _893434] : [-(c_HOL_OThe(_893432, hAPP(hAPP(c_COMBC(_893432, _893432, tc_HOL_Obool), c_fequal), _893434)) = _893434)], (6856 ^ _780086) ^ [_893470, _893472, _893474, _893476, _893478, _893480, _893482] : [hBOOL(hAPP(hAPP(c_member(_893470), _893472), _893474)), c_Nitpick_Ofold__graph_H(_893470, _893476, _893478, _893480, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_893470, tc_HOL_Obool)), _893474), hAPP(hAPP(c_Set_Oinsert(_893470), _893472), c_Orderings_Obot__class_Obot(tc_fun(_893470, tc_HOL_Obool)))), _893482), -(c_Nitpick_Ofold__graph_H(_893470, _893476, _893478, _893480, _893474, hAPP(hAPP(_893478, _893472), _893482)))], (6866 ^ _780086) ^ [_893709, _893711, _893713, _893715, _893717, _893719, _893721] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_893709, _893711, _893713, _893715, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_893709, tc_HOL_Obool)), _893717), hAPP(hAPP(c_Set_Oinsert(_893709), _893719), c_Orderings_Obot__class_Obot(tc_fun(_893709, tc_HOL_Obool))))), _893721)), hBOOL(hAPP(hAPP(c_member(_893709), _893719), _893717)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_893709, _893711, _893713, _893715, _893717), hAPP(hAPP(_893713, _893719), _893721))))], (6876 ^ _780086) ^ [_893988, _893990, _893992, _893994, _893996] : [c_Fun_Oinj__on(_893988, _893990, _893992, hAPP(hAPP(c_Set_Oinsert(_893988), _893994), _893996)), 6879 ^ _780086 : [(6880 ^ _780086) ^ [] : [-(c_Fun_Oinj__on(_893988, _893990, _893992, _893996))], (6882 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_893990), hAPP(_893992, _893994)), hAPP(c_Set_Oimage(_893988, _893990, _893992), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_893988, tc_HOL_Obool)), _893996), hAPP(hAPP(c_Set_Oinsert(_893988), _893994), c_Orderings_Obot__class_Obot(tc_fun(_893988, tc_HOL_Obool)))))))]]], (6884 ^ _780086) ^ [_894207, _894209, _894211, _894213, _894215] : [-(c_Fun_Oinj__on(_894207, _894209, _894211, hAPP(hAPP(c_Set_Oinsert(_894207), _894213), _894215))), c_Fun_Oinj__on(_894207, _894209, _894211, _894215), -(hBOOL(hAPP(hAPP(c_member(_894209), hAPP(_894211, _894213)), hAPP(c_Set_Oimage(_894207, _894209, _894211), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_894207, tc_HOL_Obool)), _894215), hAPP(hAPP(c_Set_Oinsert(_894207), _894213), c_Orderings_Obot__class_Obot(tc_fun(_894207, tc_HOL_Obool))))))))], (6894 ^ _780086) ^ [_894459, _894461, _894463, _894465, _894467] : [c_Finite__Set_Ofolding__one(_894459, _894461, _894463), hBOOL(hAPP(c_Finite__Set_Ofinite(_894459), _894465)), -(hBOOL(hAPP(hAPP(c_member(_894459), _894467), _894465))), -(hAPP(_894463, hAPP(hAPP(c_Set_Oinsert(_894459), _894467), _894465)) = hAPP(hAPP(c_Finite__Set_Ofold(_894459, _894459, _894461), _894467), _894465))], (6908 ^ _780086) ^ [_894681, _894683, _894685] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_894681), _894683)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_894681, tc_HOL_Obool)), _894685), _894683) = hAPP(hAPP(c_Finite__Set_Ofold(_894681, tc_fun(_894681, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_894681, tc_HOL_Obool), tc_fun(tc_fun(_894681, tc_HOL_Obool), tc_fun(_894681, tc_HOL_Obool)), _894681), hAPP(c_COMBC(tc_fun(_894681, tc_HOL_Obool), tc_fun(_894681, tc_HOL_Obool), tc_fun(_894681, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_894681, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_894681, tc_fun(_894681, tc_HOL_Obool), tc_fun(_894681, tc_HOL_Obool)), c_Set_Oinsert(_894681)), c_Orderings_Obot__class_Obot(tc_fun(_894681, tc_HOL_Obool))))), _894685), _894683))], (6914 ^ _780086) ^ [_894948, _894950, _894952, _894954, _894956] : [-(hAPP(c_Fun_Othe__inv__into(_894948, _894950, _894952, _894954), _894956) = c_HOL_OThe(_894948, hAPP(hAPP(c_COMBS(_894948, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _894948), c_fconj), hAPP(hAPP(c_COMBC(_894948, tc_fun(_894948, tc_HOL_Obool), tc_HOL_Obool), c_member(_894948)), _894952))), hAPP(hAPP(c_COMBC(_894948, _894950, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_894950, tc_fun(_894950, tc_HOL_Obool), _894948), c_fequal), _894954)), _894956))))], (6932 ^ _780086) ^ [_895401, _895403, _895405, _895407] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_895401, tc_HOL_Obool)), _895403), hAPP(hAPP(c_Set_Oinsert(_895401), _895405), _895407)))), 6935 ^ _780086 : [(6936 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_895401), _895405), _895403)))], (6938 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_895401, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_895401, tc_HOL_Obool)), _895403), hAPP(hAPP(c_Set_Oinsert(_895401), _895405), c_Orderings_Obot__class_Obot(tc_fun(_895401, tc_HOL_Obool))))), _895407))]], 6939 ^ _780086 : [(6940 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_895401), _895405), _895403))], (6942 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_895401, tc_HOL_Obool)), _895403), _895407))]]], (6916 ^ _780086) ^ [_895069, _895071, _895073, _895075] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_895069, tc_HOL_Obool)), _895071), hAPP(hAPP(c_Set_Oinsert(_895069), _895073), _895075))), 6919 ^ _780086 : [(6920 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_895069), _895073), _895071)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_895069, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_895069, tc_HOL_Obool)), _895071), hAPP(hAPP(c_Set_Oinsert(_895069), _895073), c_Orderings_Obot__class_Obot(tc_fun(_895069, tc_HOL_Obool))))), _895075)))], (6926 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_895069), _895073), _895071))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_895069, tc_HOL_Obool)), _895071), _895075)))]]], (6946 ^ _780086) ^ [_895765, _895767, _895769, _895771] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_895765, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_895765, tc_HOL_Obool)), _895767), hAPP(hAPP(c_Set_Oinsert(_895765), _895769), c_Orderings_Obot__class_Obot(tc_fun(_895765, tc_HOL_Obool))))), _895771)), hBOOL(hAPP(hAPP(c_member(_895765), _895769), _895767)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_895765, tc_HOL_Obool)), _895767), hAPP(hAPP(c_Set_Oinsert(_895765), _895769), _895771))))], (6956 ^ _780086) ^ [_896020, _896022, _896024, _896026, _896028] : [class_Groups_Oab__group__add(_896020), hBOOL(hAPP(c_Finite__Set_Ofinite(_896022), _896024)), 6963 ^ _780086 : [(6964 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_896022), _896026), _896024)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_896022, _896020), _896028), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_896022, tc_HOL_Obool)), _896024), hAPP(hAPP(c_Set_Oinsert(_896022), _896026), c_Orderings_Obot__class_Obot(tc_fun(_896022, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_896020), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_896022, _896020), _896028), _896024)), hAPP(_896028, _896026)))], (6970 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_896022), _896026), _896024))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_896022, _896020), _896028), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_896022, tc_HOL_Obool)), _896024), hAPP(hAPP(c_Set_Oinsert(_896022), _896026), c_Orderings_Obot__class_Obot(tc_fun(_896022, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_896022, _896020), _896028), _896024))]]], (6976 ^ _780086) ^ [_896490, _896492, _896494, _896496, _896498] : [class_Rings_Oring(_896490), hBOOL(hAPP(c_Finite__Set_Ofinite(_896492), _896494)), hBOOL(hAPP(hAPP(c_member(_896492), _896496), _896494)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_896492, _896490), _896498), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_896492, tc_HOL_Obool)), _896494), hAPP(hAPP(c_Set_Oinsert(_896492), _896496), c_Orderings_Obot__class_Obot(tc_fun(_896492, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_896490), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_896492, _896490), _896498), _896494)), hAPP(_896498, _896496)))], (6990 ^ _780086) ^ [_896836, _896838, _896840, _896842, _896844, _896846] : [hBOOL(hAPP(hAPP(c_member(_896836), _896838), _896840)), -(hAPP(c_Fun_Ooverride__on(_896836, _896842, _896844, _896846, _896840), _896838) = hAPP(_896846, _896838))], (6996 ^ _780086) ^ [_896953, _896955, _896957, _896959, _896961, _896963] : [-(hBOOL(hAPP(hAPP(c_member(_896953), _896955), _896957))), -(hAPP(c_Fun_Ooverride__on(_896953, _896959, _896961, _896963, _896957), _896955) = hAPP(_896961, _896955))], (7002 ^ _780086) ^ [_897018, _897020] : [class_Orderings_Opreorder(_897018), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_897018), _897020), _897020)))], (7008 ^ _780086) ^ [_897107, _897109, _897111] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_897107, tc_HOL_Obool)), _897109), _897111)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_897107, tc_HOL_Obool)), _897111), _897109)), -(_897109 = _897111)], (7018 ^ _780086) ^ [_897280, _897282, _897284, _897286] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_897280, tc_HOL_Obool)), _897282), _897284)), hBOOL(hAPP(hAPP(c_member(_897280), _897286), _897282)), -(hBOOL(hAPP(hAPP(c_member(_897280), _897286), _897284)))], (7028 ^ _780086) ^ [_897465, _897467] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_897465, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_897465, tc_HOL_Obool))), _897467)))], (7030 ^ _780086) ^ [_897505, _897507, _897509] : [-(c_Fun_Oinj__on(_897505, _897507, _897509, c_Orderings_Obot__class_Obot(tc_fun(_897505, tc_HOL_Obool))))], (7032 ^ _780086) ^ [_897539, _897541, _897543] : [class_Orderings_Olinorder(_897539), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_897539), _897541), _897543))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_897539), _897543), _897541)))], (7042 ^ _780086) ^ [_897659, _897661, _897663, _897665, _897667] : [class_Orderings_Oord(_897659), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_897661, _897659)), _897663), _897665)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_897659), hAPP(_897663, _897667)), hAPP(_897665, _897667))))], (7052 ^ _780086) ^ [_897844, _897846, _897848, _897850] : [class_Orderings_Oorder(_897844), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_897844), _897846), _897848)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_897844), _897850), _897846)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_897844), _897850), _897848)))], (7066 ^ _780086) ^ [_898077, _898079, _898081] : [class_Orderings_Oorder(_898077), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_898077), _898079), _898081)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_898077), _898081), _898079)), -(_898081 = _898079)], (7080 ^ _780086) ^ [_898290, _898292, _898294, _898296] : [class_Orderings_Opreorder(_898290), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_898290), _898292), _898294)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_898290), _898294), _898296)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_898290), _898292), _898296)))], (7094 ^ _780086) ^ [_898523, _898525, _898527] : [class_Orderings_Oorder(_898523), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_898523), _898525), _898527)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_898523), _898527), _898525)), -(_898525 = _898527)], (7108 ^ _780086) ^ [_898736, _898738, _898740, _898742] : [class_Orderings_Oorder(_898736), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_898736), _898738), _898740)), _898738 = _898742, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_898736), _898742), _898740)))], (7122 ^ _780086) ^ [_898955, _898957, _898959, _898961] : [class_Orderings_Oord(_898955), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_898955), _898957), _898959)), _898959 = _898961, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_898955), _898957), _898961)))], (7136 ^ _780086) ^ [_899174, _899176, _899178, _899180] : [class_Orderings_Oorder(_899174), _899176 = _899178, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899174), _899180), _899178)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899174), _899180), _899176)))], (7150 ^ _780086) ^ [_899393, _899395, _899397, _899399] : [class_Orderings_Oord(_899393), _899395 = _899397, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899393), _899397), _899399)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899393), _899395), _899399)))], (7164 ^ _780086) ^ [_899612, _899614, _899616, _899618] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_899612, tc_HOL_Obool)), _899614), _899616)), hBOOL(hAPP(_899614, _899618)), -(hBOOL(hAPP(_899616, _899618)))], (7174 ^ _780086) ^ [_899777, _899779, _899781] : [class_Orderings_Oorder(_899777), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899777), _899779), _899781)), 7181 ^ _780086 : [(7182 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899777), _899781), _899779)), -(_899781 = _899779)], (7188 ^ _780086) ^ [] : [_899781 = _899779, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899777), _899781), _899779)))]]], (7194 ^ _780086) ^ [_900077, _900079, _900081, _900083, _900085] : [class_Orderings_Oord(_900077), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_900079, _900077)), _900081), _900083)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900077), hAPP(_900081, _900085)), hAPP(_900083, _900085))))], (7204 ^ _780086) ^ [_900262, _900264, _900266] : [class_Orderings_Opreorder(_900262), _900264 = _900266, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900262), _900264), _900266)))], (7214 ^ _780086) ^ [_900407, _900409, _900411, _900413] : [hBOOL(hAPP(_900407, _900409)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_900411, tc_HOL_Obool)), _900407), _900413)), -(hBOOL(hAPP(_900413, _900409)))], (7224 ^ _780086) ^ [_900572, _900574, _900576] : [class_Orderings_Oorder(_900572), 7227 ^ _780086 : [(7228 ^ _780086) ^ [] : [_900574 = _900576, 7231 ^ _780086 : [(7232 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900572), _900574), _900576)))], (7234 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900572), _900576), _900574)))]]], (7236 ^ _780086) ^ [] : [-(_900574 = _900576), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900572), _900574), _900576)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900572), _900576), _900574))]]], (7246 ^ _780086) ^ [_900899, _900901, _900903] : [class_Orderings_Olinorder(_900899), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900899), _900901), _900903))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900899), _900903), _900901)))], (7256 ^ _780086) ^ [_901017, _901019, _901021, _901023] : [class_Orderings_Oord(_901017), 7259 ^ _780086 : [(7260 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901019, _901017)), _901021), _901023)), 7263 ^ _780086 : [(7264 ^ _780086) ^ [_901174] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901017), hAPP(_901021, _901174)), hAPP(_901023, _901174))))]]], (7266 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901017), hAPP(_901021, 7267 ^ [_901017, _901019, _901021, _901023])), hAPP(_901023, 7267 ^ [_901017, _901019, _901021, _901023]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901019, _901017)), _901021), _901023)))]]], (7273 ^ _780086) ^ [_901363, _901365, _901367, _901369, _901371, _901373] : [class_Groups_Ocomm__monoid__add(_901363), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_901365, _901363), hAPP(hAPP(c_COMBC(_901365, tc_fun(_901367, tc_HOL_Obool), _901363), hAPP(hAPP(c_COMBB(tc_fun(_901367, _901363), tc_fun(tc_fun(_901367, tc_HOL_Obool), _901363), _901365), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_901367, _901363)), _901369)), _901371)), _901373) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_901367, _901363), hAPP(hAPP(c_COMBC(_901367, tc_fun(_901365, tc_HOL_Obool), _901363), hAPP(hAPP(c_COMBB(tc_fun(_901365, _901363), tc_fun(tc_fun(_901365, tc_HOL_Obool), _901363), _901367), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_901365, _901363)), hAPP(c_COMBC(_901365, _901367, _901363), _901369))), _901373)), _901371))], (7279 ^ _780086) ^ [_901636, _901638, _901640] : [_901636 = _901638, 7282 ^ _780086 : [(7283 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901640, tc_HOL_Obool)), _901636), _901638)))], (7285 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901640, tc_HOL_Obool)), _901638), _901636)))]]], (7287 ^ _780086) ^ [_901785, _901787, _901789, _901791] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901785, tc_HOL_Obool)), _901787), _901789)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901785, tc_HOL_Obool)), _901789), _901791)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901785, tc_HOL_Obool)), _901787), _901791)))], (7297 ^ _780086) ^ [_901982, _901984, _901986] : [_901982 = _901984, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901986, tc_HOL_Obool)), _901984), _901982)))], (7303 ^ _780086) ^ [_902081, _902083, _902085] : [_902081 = _902083, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_902085, tc_HOL_Obool)), _902081), _902083)))], (7309 ^ _780086) ^ [_902198, _902200, _902202] : [_902198 = _902200, 7312 ^ _780086 : [(7313 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_902202, tc_HOL_Obool)), _902198), _902200)))], (7315 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_902202, tc_HOL_Obool)), _902200), _902198)))]]], (7317 ^ _780086) ^ [_902339, _902341, _902343] : [-(_902339 = _902341), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_902343, tc_HOL_Obool)), _902339), _902341)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_902343, tc_HOL_Obool)), _902341), _902339))], (7327 ^ _780086) ^ [_902514, _902516] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_902514, tc_HOL_Obool)), _902516), _902516)))], (7329 ^ _780086) ^ [_902549, _902551, _902553, _902555, _902557] : [c_Fun_Oinj__on(_902549, _902551, _902553, _902555), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_902549, tc_HOL_Obool)), _902557), _902555)), -(c_Fun_Oinj__on(_902549, _902551, _902553, _902557))], (7357 ^ _780086) ^ [_903124, _903126, _903128, _903130] : [7359 ^ _780086 : [(7360 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_903124), 7358 ^ [_903124, _903126, _903128, _903130]), _903130)))], (7363 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_903124), 7361 ^ [_903124, _903126, _903128, _903130]), _903130)))], (7365 ^ _780086) ^ [] : [-(hAPP(_903128, 7358 ^ [_903124, _903126, _903128, _903130]) = hAPP(_903128, 7361 ^ [_903124, _903126, _903128, _903130]))], (7367 ^ _780086) ^ [] : [7358 ^ [_903124, _903126, _903128, _903130] = 7361 ^ [_903124, _903126, _903128, _903130]]], -(c_Fun_Oinj__on(_903124, _903126, _903128, _903130))], (7339 ^ _780086) ^ [_902739, _902741, _902743, _902745] : [c_Fun_Oinj__on(_902739, _902741, _902743, _902745), 7342 ^ _780086 : [(7343 ^ _780086) ^ [_902847] : [hBOOL(hAPP(hAPP(c_member(_902739), _902847), _902745)), 7346 ^ _780086 : [(7347 ^ _780086) ^ [_902949] : [hBOOL(hAPP(hAPP(c_member(_902739), _902949), _902745)), hAPP(_902743, _902847) = hAPP(_902743, _902949), -(_902847 = _902949)]]]]], (7371 ^ _780086) ^ [_903516, _903518] : [-(c_Fun_Oinj__on(_903516, _903516, c_COMBI(_903516), _903518))], (7373 ^ _780086) ^ [_903545, _903547, _903549, _903551, _903553, _903555] : [c_Fun_Oinj__on(_903545, _903547, _903549, _903551), hAPP(_903549, _903553) = _903555, hBOOL(hAPP(hAPP(c_member(_903545), _903553), _903551)), -(hAPP(c_Fun_Othe__inv__into(_903545, _903547, _903551, _903549), _903555) = _903553)], (7387 ^ _780086) ^ [_903790, _903792, _903794, _903796, _903798] : [c_Fun_Oinj__on(_903790, _903792, _903794, _903796), hBOOL(hAPP(hAPP(c_member(_903790), _903798), _903796)), -(hAPP(c_Fun_Othe__inv__into(_903790, _903792, _903796, _903794), hAPP(_903794, _903798)) = _903798)], (7397 ^ _780086) ^ [_903971, _903973, _903975, _903977] : [c_Fun_Oinj__on(_903971, _903973, _903975, _903977), -(hAPP(c_Set_Oimage(_903973, _903971, c_Fun_Othe__inv__into(_903971, _903973, _903977, _903975)), hAPP(c_Set_Oimage(_903971, _903973, _903975), _903977)) = _903977)], (7403 ^ _780086) ^ [_904094, _904096, _904098, _904100] : [c_Fun_Oinj__on(_904094, _904096, _904098, _904100), -(c_Fun_Oinj__on(_904096, _904094, c_Fun_Othe__inv__into(_904094, _904096, _904100, _904098), hAPP(c_Set_Oimage(_904094, _904096, _904098), _904100)))], (7409 ^ _780086) ^ [_904207, _904209, _904211, _904213, _904215, _904217] : [c_Fun_Oinj__on(_904207, _904209, _904211, _904213), hBOOL(hAPP(hAPP(c_member(_904209), _904215), hAPP(c_Set_Oimage(_904207, _904209, _904211), _904213))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_904207, tc_HOL_Obool)), _904213), _904217)), -(hBOOL(hAPP(hAPP(c_member(_904207), hAPP(c_Fun_Othe__inv__into(_904207, _904209, _904213, _904211), _904215)), _904217)))], (7423 ^ _780086) ^ [_904494, _904496, _904498, _904500] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_904494), _904496)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_904494, tc_HOL_Obool)), _904496), _904498)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_904494, tc_Nat_Onat), _904500), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_904494, tc_HOL_Obool)), _904498), _904496)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_904494, tc_Nat_Onat), _904500), _904498)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_904494, tc_Nat_Onat), _904500), _904496)))], (7433 ^ _780086) ^ [_904747, _904749, _904751, _904753, _904755] : [class_Groups_Oab__group__add(_904747), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_904749, _904747), hAPP(hAPP(c_COMBS(_904749, _904747, _904747), hAPP(hAPP(c_COMBB(_904747, tc_fun(_904747, _904747), _904749), c_Groups_Ominus__class_Ominus(_904747)), _904751)), _904753)), _904755) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_904747), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_904749, _904747), _904751), _904755)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_904749, _904747), _904753), _904755)))], (7439 ^ _780086) ^ [_904948, _904950, _904952, _904954, _904956] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_904948, _904950, _904952), _904954), _904956) = c_HOL_OThe(_904950, c_Finite__Set_Ofold__graph(_904948, _904950, _904952, _904954, _904956)))], (7441 ^ _780086) ^ [_904998, _905000, _905002] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_904998), _905000)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_904998, tc_HOL_Obool)), hAPP(c_Set_Oimage(_904998, _904998, _905002), _905000)), _905000)), c_Fun_Oinj__on(_904998, _904998, _905002, _905000), -(hAPP(c_Set_Oimage(_904998, _904998, _905002), _905000) = _905000)], (7455 ^ _780086) ^ [_905245, _905247, _905249] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_905245), _905247)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_905245, tc_HOL_Obool)), _905247), hAPP(c_Set_Oimage(_905245, _905245, _905249), _905247))), -(c_Fun_Oinj__on(_905245, _905245, _905249, _905247))], (7465 ^ _780086) ^ [_905424, _905426, _905428, _905430, _905432, _905434] : [c_Fun_Oinj__on(_905424, _905426, _905428, _905430), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_905424, tc_HOL_Obool)), _905432), _905430)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_905424, tc_HOL_Obool)), _905434), _905430)), -(hAPP(c_Set_Oimage(_905424, _905426, _905428), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_905424, tc_HOL_Obool)), _905432), _905434)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_905426, tc_HOL_Obool)), hAPP(c_Set_Oimage(_905424, _905426, _905428), _905432)), hAPP(c_Set_Oimage(_905424, _905426, _905428), _905434)))], (7479 ^ _780086) ^ [_905759, _905761, _905763, _905765, _905767, _905769] : [c_Fun_Oinj__on(_905759, _905761, _905763, _905765), hAPP(_905763, _905767) = hAPP(_905763, _905769), hBOOL(hAPP(hAPP(c_member(_905759), _905767), _905765)), hBOOL(hAPP(hAPP(c_member(_905759), _905769), _905765)), -(_905767 = _905769)], (7497 ^ _780086) ^ [_906068, _906070, _906072, _906074, _906076, _906078] : [c_Fun_Oinj__on(_906068, _906070, _906072, _906074), hBOOL(hAPP(hAPP(c_member(_906068), _906076), _906074)), hBOOL(hAPP(hAPP(c_member(_906068), _906078), _906074)), 7508 ^ _780086 : [(7509 ^ _780086) ^ [] : [hAPP(_906072, _906076) = hAPP(_906072, _906078), -(_906076 = _906078)], (7515 ^ _780086) ^ [] : [_906076 = _906078, -(hAPP(_906072, _906076) = hAPP(_906072, _906078))]]], (7521 ^ _780086) ^ [_906469, _906471, _906473, _906475, _906477, _906479] : [c_Fun_Oinj__on(_906469, _906471, _906473, _906475), -(_906477 = _906479), hBOOL(hAPP(hAPP(c_member(_906469), _906477), _906475)), hBOOL(hAPP(hAPP(c_member(_906469), _906479), _906475)), hAPP(_906473, _906477) = hAPP(_906473, _906479)], (7539 ^ _780086) ^ [_906782, _906784, _906786, _906788, _906790] : [c_Fun_Oinj__on(_906782, _906784, _906786, _906788), -(c_Fun_Oinj__on(_906782, _906784, _906786, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_906782, tc_HOL_Obool)), _906788), _906790)))], (7545 ^ _780086) ^ [_906895, _906897, _906899, _906901, _906903] : [class_Groups_Oab__group__add(_906895), hBOOL(hAPP(c_Finite__Set_Ofinite(_906897), _906899)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_906897, tc_HOL_Obool)), _906901), _906899)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_906897, _906895), _906903), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_906897, tc_HOL_Obool)), _906899), _906901)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_906895), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_906897, _906895), _906903), _906899)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_906897, _906895), _906903), _906901)))], (7559 ^ _780086) ^ [_907212, _907214, _907216, _907218] : [-(c_Nitpick_Ofold__graph_H(_907212, _907214, _907216, _907218, c_Orderings_Obot__class_Obot(tc_fun(_907212, tc_HOL_Obool)), _907218))], (7561 ^ _780086) ^ [_907250, _907252, _907254, _907256] : [-(c_Nitpick_Ofold__graph_H(_907250, _907252, _907254, _907256, c_Orderings_Obot__class_Obot(tc_fun(_907250, tc_HOL_Obool)), _907256))], (7563 ^ _780086) ^ [_907288, _907290, _907292, _907294] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_907288, _907290, _907292), _907294), c_Orderings_Obot__class_Obot(tc_fun(_907288, tc_HOL_Obool))) = _907294)], (7565 ^ _780086) ^ [_907332, _907334, _907336, _907338, _907340] : [c_Fun_Oinj__on(_907332, _907334, _907336, _907338), hBOOL(hAPP(hAPP(c_member(_907334), _907340), hAPP(c_Set_Oimage(_907332, _907334, _907336), _907338))), -(hAPP(_907336, hAPP(c_Fun_Othe__inv__into(_907332, _907334, _907338, _907336), _907340)) = _907340)], (7575 ^ _780086) ^ [_907527, _907529, _907531, _907533] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_907527, tc_HOL_Obool)), _907529), _907531)), hBOOL(hAPP(hAPP(c_member(_907527), _907533), _907529)), -(hBOOL(hAPP(hAPP(c_member(_907527), _907533), _907531)))], (7585 ^ _780086) ^ [_907712, _907714, _907716, _907718] : [hBOOL(hAPP(hAPP(c_member(_907712), _907714), _907716)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_907712, tc_HOL_Obool)), _907716), _907718)), -(hBOOL(hAPP(hAPP(c_member(_907712), _907714), _907718)))], (7595 ^ _780086) ^ [_907897, _907899, _907901, _907903] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_907897, tc_HOL_Obool)), _907899), _907901)), hBOOL(hAPP(hAPP(c_member(_907897), _907903), _907899)), -(hBOOL(hAPP(hAPP(c_member(_907897), _907903), _907901)))], (7605 ^ _780086) ^ [_908082, _908084] : [class_Orderings_Obot(_908082), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908082), c_Orderings_Obot__class_Obot(_908082)), _908084)))], (7611 ^ _780086) ^ [_908190, _908192] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_908190, tc_HOL_Obool)), _908192), c_Orderings_Obot__class_Obot(tc_fun(_908190, tc_HOL_Obool)))), -(_908192 = c_Orderings_Obot__class_Obot(tc_fun(_908190, tc_HOL_Obool)))], (7617 ^ _780086) ^ [_908303, _908305] : [_908305 = c_Orderings_Obot__class_Obot(tc_fun(_908303, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_908303, tc_HOL_Obool)), _908305), c_Orderings_Obot__class_Obot(tc_fun(_908303, tc_HOL_Obool)))))], (7623 ^ _780086) ^ [_908422, _908424, _908426] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_908422, tc_HOL_Obool)), _908424), _908426)), hBOOL(hAPP(c_Finite__Set_Ofinite(_908422), _908426)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_908422), _908424)))], (7633 ^ _780086) ^ [_908591, _908593, _908595] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_908591), _908593)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_908591, tc_HOL_Obool)), _908595), _908593)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_908591), _908595)))], (7643 ^ _780086) ^ [_908760, _908762, _908764, _908766] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_908760, tc_HOL_Obool)), _908762), _908764)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_908760, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_908760), _908766), _908762)), hAPP(hAPP(c_Set_Oinsert(_908760), _908766), _908764))))], (7649 ^ _780086) ^ [_908913, _908915, _908917, _908919] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_908913, tc_HOL_Obool)), _908915), _908917)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_908913, tc_HOL_Obool)), _908915), hAPP(hAPP(c_Set_Oinsert(_908913), _908919), _908917))))], (7655 ^ _780086) ^ [_909050, _909052, _909054] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909050, tc_HOL_Obool)), _909052), hAPP(hAPP(c_Set_Oinsert(_909050), _909054), _909052))))], (7657 ^ _780086) ^ [_909095, _909097, _909099, _909101, _909103] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909095, tc_HOL_Obool)), _909097), _909099)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909101, tc_HOL_Obool)), hAPP(c_Set_Oimage(_909095, _909101, _909103), _909097)), hAPP(c_Set_Oimage(_909095, _909101, _909103), _909099))))], (7663 ^ _780086) ^ [_909270, _909272, _909274, _909276, _909278] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909270, tc_HOL_Obool)), _909272), hAPP(c_Set_Oimage(_909274, _909270, _909276), _909278))), 7667 ^ _780086 : [(7668 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909274, tc_HOL_Obool)), 7666 ^ [_909270, _909272, _909274, _909276, _909278]), _909278)))], (7670 ^ _780086) ^ [] : [-(_909272 = hAPP(c_Set_Oimage(_909274, _909270, _909276), 7666 ^ [_909270, _909272, _909274, _909276, _909278]))]]], (7672 ^ _780086) ^ [_909474, _909476, _909478, _909480, _909482] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909474, tc_HOL_Obool)), _909476), hAPP(c_Set_Oimage(_909478, _909474, _909480), _909482)))), 7673 ^ _780086 : [(7674 ^ _780086) ^ [_909554] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909478, tc_HOL_Obool)), _909554), _909482)), _909476 = hAPP(c_Set_Oimage(_909478, _909474, _909480), _909554)]]], (7682 ^ _780086) ^ [_909719, _909721, _909723, _909725] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909719, tc_HOL_Obool)), _909721), _909723)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909719, tc_HOL_Obool)), _909723), _909725)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_909719, tc_HOL_Obool)), _909723), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_909719, tc_HOL_Obool)), _909725), _909721)) = _909721)], (7692 ^ _780086) ^ [_909940, _909942, _909944, _909946, _909948] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909940, tc_HOL_Obool)), _909942), _909944)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909940, tc_HOL_Obool)), _909946), _909948)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909940, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_909940, tc_HOL_Obool)), _909942), _909948)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_909940, tc_HOL_Obool)), _909944), _909946))))], (7702 ^ _780086) ^ [_910185, _910187, _910189] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_910185, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_910185, tc_HOL_Obool)), _910187), _910189)), _910187)))], (7704 ^ _780086) ^ [_910233, _910235, _910237, _910239] : [c_Hoare__Mirabelle_Ohoare__derivs(_910233, _910235, _910237), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_910233), tc_HOL_Obool)), _910235), _910239)), -(c_Hoare__Mirabelle_Ohoare__derivs(_910233, _910239, _910237))], (7714 ^ _780086) ^ [_910398, _910400, _910402, _910404] : [c_Hoare__Mirabelle_Ohoare__derivs(_910398, _910400, _910402), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_910398), tc_HOL_Obool)), _910404), _910402)), -(c_Hoare__Mirabelle_Ohoare__derivs(_910398, _910400, _910404))], (7724 ^ _780086) ^ [_910563, _910565, _910567] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_910563), tc_HOL_Obool)), _910565), _910567)), -(c_Hoare__Mirabelle_Ohoare__derivs(_910563, _910567, _910565))], (7730 ^ _780086) ^ [_910668, _910670, _910672, _910674, _910676] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_910668, _910670, _910672, _910674, c_Orderings_Obot__class_Obot(tc_fun(_910668, tc_HOL_Obool))), _910676)), -(_910676 = _910674)], (7736 ^ _780086) ^ [_910777, _910779, _910781, _910783] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_910777, _910779, _910781, _910783, c_Orderings_Obot__class_Obot(tc_fun(_910777, tc_HOL_Obool))), _910783)))], (7738 ^ _780086) ^ [_910819, _910821, _910823, _910825] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_910819, _910821, _910823, _910825, c_Orderings_Obot__class_Obot(tc_fun(_910819, tc_HOL_Obool))), _910825)))], (7740 ^ _780086) ^ [_910861, _910863, _910865, _910867, _910869, _910871] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_910861, _910863, _910865, _910867, _910869), _910871)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_910861), _910869)))], (7746 ^ _780086) ^ [_910988, _910990, _910992] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_910988, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_910988, tc_fun(_910988, tc_HOL_Obool), tc_HOL_Obool), c_member(_910988)), _910990)), hAPP(hAPP(c_COMBC(_910988, tc_fun(_910988, tc_HOL_Obool), tc_HOL_Obool), c_member(_910988)), _910992))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_910988, tc_HOL_Obool)), _910990), _910992)))], (7752 ^ _780086) ^ [_911163, _911165, _911167] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911163, tc_HOL_Obool)), _911165), _911167)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911163, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_911163, tc_fun(_911163, tc_HOL_Obool), tc_HOL_Obool), c_member(_911163)), _911165)), hAPP(hAPP(c_COMBC(_911163, tc_fun(_911163, tc_HOL_Obool), tc_HOL_Obool), c_member(_911163)), _911167))))], (7758 ^ _780086) ^ [_911344, _911346, _911348, _911350] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_911344), hAPP(c_Set_Oimage(_911346, _911344, _911348), _911350))), c_Fun_Oinj__on(_911346, _911344, _911348, _911350), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_911346), _911350)))], (7768 ^ _780086) ^ [_911514, _911516, _911518, _911520] : [-(hBOOL(hAPP(hAPP(c_member(_911514), _911516), _911518))), 7771 ^ _780086 : [(7772 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911514, tc_HOL_Obool)), _911518), hAPP(hAPP(c_Set_Oinsert(_911514), _911516), _911520))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911514, tc_HOL_Obool)), _911518), _911520)))], (7778 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911514, tc_HOL_Obool)), _911518), _911520)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911514, tc_HOL_Obool)), _911518), hAPP(hAPP(c_Set_Oinsert(_911514), _911516), _911520))))]]], (7784 ^ _780086) ^ [_911843, _911845, _911847, _911849] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911843, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_911843), _911845), _911847)), _911849)), 7787 ^ _780086 : [(7788 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_911843), _911845), _911849)))], (7790 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911843, tc_HOL_Obool)), _911847), _911849)))]]], (7792 ^ _780086) ^ [_912016, _912018, _912020, _912022] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_912016, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_912016), _912018), _912020)), _912022))), hBOOL(hAPP(hAPP(c_member(_912016), _912018), _912022)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_912016, tc_HOL_Obool)), _912020), _912022))], (7802 ^ _780086) ^ [_912225, _912227, _912229] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_912225, tc_HOL_Obool)), _912227), hAPP(hAPP(c_Set_Oinsert(_912225), _912229), c_Orderings_Obot__class_Obot(tc_fun(_912225, tc_HOL_Obool))))), -(_912227 = c_Orderings_Obot__class_Obot(tc_fun(_912225, tc_HOL_Obool))), -(_912227 = hAPP(hAPP(c_Set_Oinsert(_912225), _912229), c_Orderings_Obot__class_Obot(tc_fun(_912225, tc_HOL_Obool))))], (7812 ^ _780086) ^ [_912399, _912401, _912403, _912405, _912407] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_912399), _912401)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_912403, tc_HOL_Obool)), _912405), hAPP(c_Set_Oimage(_912399, _912403, _912407), _912401))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_912403), _912405)))], (7822 ^ _780086) ^ [_912590, _912592, _912594, _912596, _912598] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_912590, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_912590, tc_HOL_Obool)), hAPP(c_Set_Oimage(_912592, _912590, _912594), _912596)), hAPP(c_Set_Oimage(_912592, _912590, _912594), _912598))), hAPP(c_Set_Oimage(_912592, _912590, _912594), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_912592, tc_HOL_Obool)), _912596), _912598)))))], (7824 ^ _780086) ^ [_912673, _912675, _912677, _912679, _912681, _912683, _912685] : [-(hBOOL(hAPP(hAPP(c_member(_912673), _912675), _912677))), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_912673, _912679, _912681, _912683, _912677), _912685)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_912673, _912679, _912681, _912683, hAPP(hAPP(c_Set_Oinsert(_912673), _912675), _912677)), hAPP(hAPP(_912681, _912675), _912685))))], (7834 ^ _780086) ^ [_912902, _912904, _912906, _912908] : [hBOOL(hAPP(hAPP(c_member(_912902), _912904), _912906)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_912902, tc_Nat_Onat), _912908), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_912902, tc_HOL_Obool)), _912906), hAPP(hAPP(c_Set_Oinsert(_912902), _912904), c_Orderings_Obot__class_Obot(tc_fun(_912902, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_912902, tc_Nat_Onat), _912908), _912906)), hAPP(_912908, _912904)))], (7840 ^ _780086) ^ [_913093, _913095, _913097, _913099] : [-(hBOOL(hAPP(hAPP(c_member(_913093), _913095), _913097))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_913093, tc_Nat_Onat), _913099), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_913093, tc_HOL_Obool)), _913097), hAPP(hAPP(c_Set_Oinsert(_913093), _913095), c_Orderings_Obot__class_Obot(tc_fun(_913093, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_913093, tc_Nat_Onat), _913099), _913097))], (7846 ^ _780086) ^ [_913184, _913186, _913188, _913190, _913192, _913194, _913196, _913198] : [c_Finite__Set_Ofolding__image__simple__idem(_913184, _913186, _913188, _913190, _913192, _913194), hBOOL(hAPP(c_Finite__Set_Ofinite(_913186), _913196)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_913186, tc_HOL_Obool)), _913198), _913196)), -(hAPP(hAPP(_913188, hAPP(_913194, _913198)), hAPP(_913194, _913196)) = hAPP(_913194, _913196))], (7860 ^ _780086) ^ [_913467, _913469, _913471, _913473, _913475, _913477] : [c_Fun_Oinj__on(_913467, _913469, _913471, _913473), -(hBOOL(hAPP(hAPP(c_member(_913469), _913475), hAPP(c_Set_Oimage(_913467, _913469, _913471), _913473)))), -(c_Fun_Oinj__on(_913467, _913469, c_Fun_Ofun__upd(_913467, _913469, _913471, _913477, _913475), _913473))], (7870 ^ _780086) ^ [_913615, _913617, _913619, _913621, _913623, _913625] : [hBOOL(hAPP(hAPP(c_member(_913615), _913617), _913619)), -(hAPP(c_Fun_Ooverride__on(_913615, _913621, _913623, _913625, _913619), _913617) = hAPP(_913625, _913617))], (7876 ^ _780086) ^ [_913734, _913736, _913738, _913740, _913742, _913744] : [-(hBOOL(hAPP(hAPP(c_member(_913734), _913736), _913738))), -(hAPP(c_Fun_Ooverride__on(_913734, _913740, _913742, _913744, _913738), _913736) = hAPP(_913742, _913736))], (7882 ^ _780086) ^ [_913797, _913799, _913801, _913803] : [-(c_Fun_Ooverride__on(_913797, _913799, _913801, _913803, c_Orderings_Obot__class_Obot(tc_fun(_913797, tc_HOL_Obool))) = _913801)], (7884 ^ _780086) ^ [_913837, _913839, _913841, _913843, _913845, _913847] : [c_Finite__Set_Ofun__left__comm__idem(_913837, _913839, _913841), hBOOL(hAPP(c_Finite__Set_Ofinite(_913837), _913843)), -(hAPP(hAPP(c_Finite__Set_Ofold(_913837, _913839, _913841), _913845), hAPP(hAPP(c_Set_Oinsert(_913837), _913847), _913843)) = hAPP(hAPP(c_Finite__Set_Ofold(_913837, _913839, _913841), hAPP(hAPP(_913841, _913847), _913845)), _913843))], (7894 ^ _780086) ^ [_914060, _914062, _914064, _914066, _914068, _914070] : [c_Finite__Set_Ofun__left__comm__idem(_914060, _914062, _914064), hBOOL(hAPP(c_Finite__Set_Ofinite(_914060), _914066)), -(hAPP(hAPP(c_Finite__Set_Ofold(_914060, _914062, _914064), _914068), hAPP(hAPP(c_Set_Oinsert(_914060), _914070), _914066)) = hAPP(hAPP(_914064, _914070), hAPP(hAPP(c_Finite__Set_Ofold(_914060, _914062, _914064), _914068), _914066)))], (7904 ^ _780086) ^ [_914283, _914285, _914287, _914289, _914291] : [c_Finite__Set_Ofolding__one__idem(_914283, _914285, _914287), hBOOL(hAPP(c_Finite__Set_Ofinite(_914283), _914289)), -(hAPP(_914287, hAPP(hAPP(c_Set_Oinsert(_914283), _914291), _914289)) = hAPP(hAPP(c_Finite__Set_Ofold(_914283, _914283, _914285), _914291), _914289))], (7914 ^ _780086) ^ [_914476, _914478, _914480, _914482, _914484] : [c_Finite__Set_Ofolding__one__idem(_914476, _914478, _914480), hBOOL(hAPP(c_Finite__Set_Ofinite(_914476), _914482)), -(_914484 = c_Orderings_Obot__class_Obot(tc_fun(_914476, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_914476, tc_HOL_Obool)), _914484), _914482)), -(hAPP(hAPP(_914478, hAPP(_914480, _914484)), hAPP(_914480, _914482)) = hAPP(_914480, _914482))], (7932 ^ _780086) ^ [_914805, _914807, _914809, _914811] : [-(_914805 = c_Orderings_Obot__class_Obot(tc_fun(_914807, tc_HOL_Obool))), 7935 ^ _780086 : [(7947 ^ _780086) ^ [] : [7948 ^ _780086 : [(7949 ^ _780086) ^ [_915138] : [hAPP(c_Set_Oimage(_914809, _914807, _915138), _914811) = _914805]], 7951 ^ _780086 : [(7952 ^ _780086) ^ [] : [-(c_Fun_Oinj__on(_914807, _914809, 7950 ^ [_914805, _914807, _914809, _914811], _914805))], (7954 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_914809, tc_HOL_Obool)), hAPP(c_Set_Oimage(_914807, _914809, 7950 ^ [_914805, _914807, _914809, _914811]), _914805)), _914811)))]]], (7936 ^ _780086) ^ [] : [-(hAPP(c_Set_Oimage(_914809, _914807, 7943 ^ [_914805, _914807, _914809, _914811]), _914811) = _914805), 7937 ^ _780086 : [(7938 ^ _780086) ^ [_914946] : [c_Fun_Oinj__on(_914807, _914809, _914946, _914805), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_914809, tc_HOL_Obool)), hAPP(c_Set_Oimage(_914807, _914809, _914946), _914805)), _914811))]]]]], (7956 ^ _780086) ^ [_915263, _915265, _915267, _915269, _915271, _915273] : [c_Finite__Set_Ofun__left__comm(_915263, _915265, _915267), hBOOL(hAPP(c_Finite__Set_Ofinite(_915263), _915269)), hBOOL(hAPP(hAPP(c_member(_915263), _915271), _915269)), -(hAPP(hAPP(c_Finite__Set_Ofold(_915263, _915265, _915267), _915273), _915269) = hAPP(hAPP(_915267, _915271), hAPP(hAPP(c_Finite__Set_Ofold(_915263, _915265, _915267), _915273), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_915263, tc_HOL_Obool)), _915269), hAPP(hAPP(c_Set_Oinsert(_915263), _915271), c_Orderings_Obot__class_Obot(tc_fun(_915263, tc_HOL_Obool)))))))], (7970 ^ _780086) ^ [_915592, _915594, _915596, _915598, _915600] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_915592, _915592, _915594, _915596, _915598), _915600)), -(hBOOL(hAPP(hAPP(c_member(_915592), _915596), _915598))), -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_915592, _915594, hAPP(hAPP(c_Set_Oinsert(_915592), _915596), _915598)), _915600)))], (7980 ^ _780086) ^ [_915760, _915762, _915764] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_915760, tc_HOL_Obool)), _915762), hAPP(hAPP(c_Set_Oinsert(_915760), _915764), c_Orderings_Obot__class_Obot(tc_fun(_915760, tc_HOL_Obool))))), -(c_Partial__Function_Oflat__lub(_915760, _915764, _915762) = _915764)], (7986 ^ _780086) ^ [_915887, _915889, _915891] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_915887, tc_HOL_Obool)), _915889), hAPP(hAPP(c_Set_Oinsert(_915887), _915891), c_Orderings_Obot__class_Obot(tc_fun(_915887, tc_HOL_Obool)))))), -(c_Partial__Function_Oflat__lub(_915887, _915891, _915889) = c_HOL_OThe(_915887, hAPP(hAPP(c_COMBC(_915887, tc_fun(_915887, tc_HOL_Obool), tc_HOL_Obool), c_member(_915887)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_915887, tc_HOL_Obool)), _915889), hAPP(hAPP(c_Set_Oinsert(_915887), _915891), c_Orderings_Obot__class_Obot(tc_fun(_915887, tc_HOL_Obool)))))))], (7992 ^ _780086) ^ [_915996, _915998, _916000, _916002, _916004, _916006] : [c_Finite__Set_Ofun__left__comm(_915996, _915998, _916000), hBOOL(hAPP(c_Finite__Set_Ofinite(_915996), _916002)), -(hAPP(hAPP(c_Finite__Set_Ofold(_915996, _915998, _916000), _916004), hAPP(hAPP(c_Set_Oinsert(_915996), _916006), _916002)) = hAPP(hAPP(_916000, _916006), hAPP(hAPP(c_Finite__Set_Ofold(_915996, _915998, _916000), _916004), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_915996, tc_HOL_Obool)), _916002), hAPP(hAPP(c_Set_Oinsert(_915996), _916006), c_Orderings_Obot__class_Obot(tc_fun(_915996, tc_HOL_Obool)))))))], (8002 ^ _780086) ^ [_916297, _916299, _916301, _916303, _916305, _916307, _916309] : [c_Nitpick_Ofold__graph_H(_916297, _916299, _916301, _916303, _916305, hAPP(hAPP(_916301, _916307), _916309)), 8007 ^ _780086 : [(8008 ^ _780086) ^ [] : [-(_916305 = c_Orderings_Obot__class_Obot(tc_fun(_916297, tc_HOL_Obool)))], (8010 ^ _780086) ^ [] : [-(hAPP(hAPP(_916301, _916307), _916309) = _916303)]], 8013 ^ _780086 : [(8014 ^ _780086) ^ [] : [-(hAPP(hAPP(_916301, _916307), _916309) = hAPP(hAPP(_916301, 8011 ^ [_916297, _916299, _916301, _916303, _916305, _916307, _916309]), 8012 ^ [_916297, _916299, _916301, _916303, _916305, _916307, _916309]))], (8016 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_916297), 8011 ^ [_916297, _916299, _916301, _916303, _916305, _916307, _916309]), _916305)))], (8018 ^ _780086) ^ [] : [-(c_Nitpick_Ofold__graph_H(_916297, _916299, _916301, _916303, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916297, tc_HOL_Obool)), _916305), hAPP(hAPP(c_Set_Oinsert(_916297), 8011 ^ [_916297, _916299, _916301, _916303, _916305, _916307, _916309]), c_Orderings_Obot__class_Obot(tc_fun(_916297, tc_HOL_Obool)))), 8012 ^ [_916297, _916299, _916301, _916303, _916305, _916307, _916309]))]]], (8020 ^ _780086) ^ [_916734, _916736, _916738, _916740, _916742, _916744, _916746] : [-(c_Nitpick_Ofold__graph_H(_916734, _916736, _916738, _916740, _916742, hAPP(hAPP(_916738, _916744), _916746))), 8021 ^ _780086 : [(8022 ^ _780086) ^ [] : [_916742 = c_Orderings_Obot__class_Obot(tc_fun(_916734, tc_HOL_Obool)), hAPP(hAPP(_916738, _916744), _916746) = _916740], (8028 ^ _780086) ^ [_916963, _916965] : [hAPP(hAPP(_916738, _916744), _916746) = hAPP(hAPP(_916738, _916965), _916963), hBOOL(hAPP(hAPP(c_member(_916734), _916965), _916742)), c_Nitpick_Ofold__graph_H(_916734, _916736, _916738, _916740, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916734, tc_HOL_Obool)), _916742), hAPP(hAPP(c_Set_Oinsert(_916734), _916965), c_Orderings_Obot__class_Obot(tc_fun(_916734, tc_HOL_Obool)))), _916963)]]], (8040 ^ _780086) ^ [_917255, _917257, _917259, _917261, _917263] : [class_Groups_Oordered__ab__group__add(_917255), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_917255), _917257), _917259) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_917255), _917261), _917263), 8047 ^ _780086 : [(8048 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_917255), _917257), _917259)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_917255), _917261), _917263)))], (8054 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_917255), _917261), _917263)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_917255), _917257), _917259)))]]], (8060 ^ _780086) ^ [_917610, _917612, _917614, _917616, _917618, _917620] : [c_Finite__Set_Ofun__left__comm(_917610, _917612, _917614), hBOOL(hAPP(c_Finite__Set_Ofinite(_917610), _917616)), -(hBOOL(hAPP(hAPP(c_member(_917610), _917618), _917616))), -(hAPP(hAPP(c_Finite__Set_Ofold(_917610, _917612, _917614), _917620), hAPP(hAPP(c_Set_Oinsert(_917610), _917618), _917616)) = hAPP(hAPP(c_Finite__Set_Ofold(_917610, _917612, _917614), hAPP(hAPP(_917614, _917618), _917620)), _917616))], (8074 ^ _780086) ^ [_917862, _917864, _917866, _917868, _917870, _917872] : [c_Finite__Set_Ofun__left__comm(_917862, _917864, _917866), hBOOL(hAPP(c_Finite__Set_Ofinite(_917862), _917868)), -(hBOOL(hAPP(hAPP(c_member(_917862), _917870), _917868))), -(hAPP(hAPP(c_Finite__Set_Ofold(_917862, _917864, _917866), _917872), hAPP(hAPP(c_Set_Oinsert(_917862), _917870), _917868)) = hAPP(hAPP(_917866, _917870), hAPP(hAPP(c_Finite__Set_Ofold(_917862, _917864, _917866), _917872), _917868)))], (8088 ^ _780086) ^ [_918114, _918116, _918118, _918120] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_918114), _918116)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_918114, tc_HOL_Obool)), _918116), _918118)), hBOOL(hAPP(_918120, c_Orderings_Obot__class_Obot(tc_fun(_918114, tc_HOL_Obool)))), 8103 ^ _780086 : [(8104 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_918114), 8102 ^ [_918114, _918116, _918118, _918120])))], (8106 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_918114), 8101 ^ [_918114, _918116, _918118, _918120]), _918118)))], (8108 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_918114), 8101 ^ [_918114, _918116, _918118, _918120]), 8102 ^ [_918114, _918116, _918118, _918120]))], (8110 ^ _780086) ^ [] : [-(hBOOL(hAPP(_918120, 8102 ^ [_918114, _918116, _918118, _918120])))], (8112 ^ _780086) ^ [] : [hBOOL(hAPP(_918120, hAPP(hAPP(c_Set_Oinsert(_918114), 8101 ^ [_918114, _918116, _918118, _918120]), 8102 ^ [_918114, _918116, _918118, _918120])))]], -(hBOOL(hAPP(_918120, _918116)))], (8116 ^ _780086) ^ [_918779, _918781, _918783, _918785, _918787] : [class_Groups_Ocomm__monoid__add(_918779), hBOOL(hAPP(c_Finite__Set_Ofinite(_918781), _918783)), hBOOL(hAPP(hAPP(c_member(_918781), _918785), _918783)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_918781, _918779), _918787), _918783) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_918779), hAPP(_918787, _918785)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_918781, _918779), _918787), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_918781, tc_HOL_Obool)), _918783), hAPP(hAPP(c_Set_Oinsert(_918781), _918785), c_Orderings_Obot__class_Obot(tc_fun(_918781, tc_HOL_Obool)))))))], (8130 ^ _780086) ^ [_919104, _919106, _919108, _919110, _919112, _919114] : [c_Finite__Set_Ofun__left__comm(_919104, _919106, _919108), -(hAPP(hAPP(_919108, _919110), hAPP(hAPP(_919108, _919112), _919114)) = hAPP(hAPP(_919108, _919112), hAPP(hAPP(_919108, _919110), _919114)))], (8136 ^ _780086) ^ [_919239, _919241, _919243, _919245] : [class_Groups_Ocancel__semigroup__add(_919239), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_919239), _919241), _919243) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_919239), _919245), _919243), -(_919241 = _919245)], (8146 ^ _780086) ^ [_919406, _919408, _919410, _919412] : [class_Groups_Ocancel__ab__semigroup__add(_919406), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_919406), _919408), _919410) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_919406), _919408), _919412), -(_919410 = _919412)], (8156 ^ _780086) ^ [_919573, _919575, _919577, _919579] : [class_Groups_Ocancel__semigroup__add(_919573), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_919573), _919575), _919577) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_919573), _919575), _919579), -(_919577 = _919579)], (8166 ^ _780086) ^ [_919740, _919742, _919744, _919746] : [class_Groups_Ocancel__semigroup__add(_919740), 8169 ^ _780086 : [(8170 ^ _780086) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_919740), _919742), _919744) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_919740), _919746), _919744), -(_919742 = _919746)], (8176 ^ _780086) ^ [] : [_919742 = _919746, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_919740), _919742), _919744) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_919740), _919746), _919744))]]], (8182 ^ _780086) ^ [_920005, _920007, _920009, _920011] : [class_Groups_Ocancel__semigroup__add(_920005), 8185 ^ _780086 : [(8186 ^ _780086) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920005), _920007), _920009) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920005), _920007), _920011), -(_920009 = _920011)], (8192 ^ _780086) ^ [] : [_920009 = _920011, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920005), _920007), _920009) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920005), _920007), _920011))]]], (8198 ^ _780086) ^ [_920270, _920272, _920274, _920276] : [class_Groups_Oab__semigroup__add(_920270), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920270), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920270), _920272), _920274)), _920276) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920270), _920272), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920270), _920274), _920276)))], (8204 ^ _780086) ^ [_920413, _920415, _920417, _920419] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_920413), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920413), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920413), _920415), _920417)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920413), _920415), _920419))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920413), _920417), _920419)))], (8214 ^ _780086) ^ [_920608, _920610, _920612, _920614] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_920608), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920608), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920608), _920610), _920612)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920608), _920614), _920612))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920608), _920610), _920614)))], (8224 ^ _780086) ^ [_920803, _920805, _920807, _920809, _920811] : [class_Groups_Oordered__ab__semigroup__add(_920803), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920803), _920805), _920807)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920803), _920809), _920811)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920803), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920803), _920805), _920809)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920803), _920807), _920811))))], (8238 ^ _780086) ^ [_921074, _921076, _921078, _921080] : [class_Groups_Oordered__ab__semigroup__add(_921074), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921074), _921076), _921078)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921074), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_921074), _921080), _921076)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_921074), _921080), _921078))))], (8248 ^ _780086) ^ [_921269, _921271, _921273, _921275] : [class_Groups_Oordered__ab__semigroup__add(_921269), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921269), _921271), _921273)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921269), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_921269), _921271), _921275)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_921269), _921273), _921275))))], (8258 ^ _780086) ^ [_921464, _921466, _921468, _921470] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_921464), 8261 ^ _780086 : [(8262 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921464), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_921464), _921466), _921468)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_921464), _921466), _921470))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921464), _921468), _921470)))], (8268 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921464), _921468), _921470)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921464), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_921464), _921466), _921468)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_921464), _921466), _921470))))]]], (8274 ^ _780086) ^ [_921771, _921773, _921775, _921777] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_921771), 8277 ^ _780086 : [(8278 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921771), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_921771), _921773), _921775)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_921771), _921777), _921775))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921771), _921773), _921777)))], (8284 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921771), _921773), _921777)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921771), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_921771), _921773), _921775)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_921771), _921777), _921775))))]]], (8290 ^ _780086) ^ [_922078, _922080, _922082] : [class_Groups_Ogroup__add(_922078), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_922078), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_922078), _922080), _922082)), _922082) = _922080)], (8296 ^ _780086) ^ [_922187, _922189, _922191] : [class_Groups_Ogroup__add(_922187), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_922187), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_922187), _922189), _922191)), _922191) = _922189)], (8302 ^ _780086) ^ [_922296, _922298, _922300, _922302, _922304] : [c_Finite__Set_Ofun__left__comm(_922296, _922298, _922300), -(c_Finite__Set_Ofun__left__comm(_922302, _922298, hAPP(hAPP(c_COMBB(_922296, tc_fun(_922298, _922298), _922302), _922300), _922304)))], (8308 ^ _780086) ^ [_922409, _922411, _922413, _922415, _922417] : [class_Groups_Ocomm__monoid__add(_922409), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_922411, _922409), hAPP(hAPP(c_COMBS(_922411, _922409, _922409), hAPP(hAPP(c_COMBB(_922409, tc_fun(_922409, _922409), _922411), c_Groups_Oplus__class_Oplus(_922409)), _922413)), _922415)), _922417) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_922409), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_922411, _922409), _922413), _922417)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_922411, _922409), _922415), _922417)))], (8314 ^ _780086) ^ [_922610, _922612, _922614, _922616, _922618, _922620, _922622] : [c_Finite__Set_Ofun__left__comm(_922610, _922612, _922614), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_922610, _922612, _922614, _922616, _922618), _922620)), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_922610, _922612, _922614, _922616, _922618), _922622)), -(_922622 = _922620)], (8328 ^ _780086) ^ [_922870, _922872, _922874] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_922870, _922872, c_Orderings_Obot__class_Obot(tc_fun(_922870, tc_HOL_Obool))), _922874))], (8330 ^ _780086) ^ [_922908, _922910, _922912, _922914] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_922908, _922910, _922912), _922914)), _922912 = c_Orderings_Obot__class_Obot(tc_fun(_922908, tc_HOL_Obool))], (8336 ^ _780086) ^ [_923012, _923014, _923016, _923018, _923020] : [class_Groups_Ocomm__monoid__add(_923012), hBOOL(hAPP(c_Finite__Set_Ofinite(_923014), _923016)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_923014, _923012), hAPP(hAPP(c_COMBS(_923014, _923012, _923012), hAPP(hAPP(c_COMBB(_923012, tc_fun(_923012, _923012), _923014), c_Groups_Oplus__class_Oplus(_923012)), _923018)), _923020)), _923016) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_923012), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_923014, _923012), _923018), _923016)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_923014, _923012), _923020), _923016)))], (8346 ^ _780086) ^ [_923279, _923281, _923283, _923285, _923287] : [class_Groups_Oab__group__add(_923279), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_923279), _923281), _923283) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_923279), _923285), _923287), 8353 ^ _780086 : [(8354 ^ _780086) ^ [] : [_923281 = _923283, -(_923285 = _923287)], (8360 ^ _780086) ^ [] : [_923285 = _923287, -(_923281 = _923283)]]], (8366 ^ _780086) ^ [_923592, _923594, _923596, _923598, _923600, _923602] : [c_Finite__Set_Ofun__left__comm(_923592, _923594, _923596), hBOOL(hAPP(c_Finite__Set_Ofinite(_923592), _923598)), -(hAPP(hAPP(_923596, _923600), hAPP(hAPP(c_Finite__Set_Ofold(_923592, _923594, _923596), _923602), _923598)) = hAPP(hAPP(c_Finite__Set_Ofold(_923592, _923594, _923596), hAPP(hAPP(_923596, _923600), _923602)), _923598))], (8376 ^ _780086) ^ [_923811, _923813, _923815, _923817, _923819, _923821] : [c_Finite__Set_Ofun__left__comm(_923811, _923813, _923815), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_923811, _923813, _923815, _923817, _923819), _923821)), -(hAPP(hAPP(c_Finite__Set_Ofold(_923811, _923813, _923815), _923817), _923819) = _923821)], (8386 ^ _780086) ^ [_924015, _924017, _924019, _924021] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_924015, _924017, hAPP(hAPP(c_Set_Oinsert(_924015), _924019), c_Orderings_Obot__class_Obot(tc_fun(_924015, tc_HOL_Obool)))), _924021)), -(_924019 = _924021)], (8392 ^ _780086) ^ [_924130, _924132, _924134, _924136] : [_924134 = _924136, -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_924130, _924132, hAPP(hAPP(c_Set_Oinsert(_924130), _924134), c_Orderings_Obot__class_Obot(tc_fun(_924130, tc_HOL_Obool)))), _924136)))], (8398 ^ _780086) ^ [_924251, _924253, _924255, _924257, _924259] : [class_Groups_Ocomm__monoid__add(_924251), hBOOL(hAPP(c_Finite__Set_Ofinite(_924253), _924255)), -(hBOOL(hAPP(hAPP(c_member(_924253), _924257), _924255))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_924253, _924251), _924259), hAPP(hAPP(c_Set_Oinsert(_924253), _924257), _924255)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924251), hAPP(_924259, _924257)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_924253, _924251), _924259), _924255)))], (8412 ^ _780086) ^ [_924501, _924503, _924505, _924507, _924509] : [class_Groups_Ocomm__monoid__add(_924501), hBOOL(hAPP(c_Finite__Set_Ofinite(_924503), _924505)), -(hBOOL(hAPP(hAPP(c_member(_924503), _924507), _924505))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_924503, _924501), _924509), hAPP(hAPP(c_Set_Oinsert(_924503), _924507), _924505)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924501), hAPP(_924509, _924507)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_924503, _924501), _924509), _924505)))], (8426 ^ _780086) ^ [_924751, _924753, _924755, _924757, _924759] : [class_Groups_Ocomm__monoid__add(_924751), hBOOL(hAPP(c_Finite__Set_Ofinite(_924753), _924755)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_924753, _924751), _924757), hAPP(hAPP(c_Set_Oinsert(_924753), _924759), _924755)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924751), hAPP(_924757, _924759)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_924753, _924751), _924757), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_924753, tc_HOL_Obool)), _924755), hAPP(hAPP(c_Set_Oinsert(_924753), _924759), c_Orderings_Obot__class_Obot(tc_fun(_924753, tc_HOL_Obool)))))))], (8436 ^ _780086) ^ [_925020, _925022, _925024, _925026, _925028] : [c_Finite__Set_Ofun__left__comm(_925020, _925022, _925024), hBOOL(hAPP(c_Finite__Set_Ofinite(_925020), _925026)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_925020, _925022, _925024, _925028, _925026), hAPP(hAPP(c_Finite__Set_Ofold(_925020, _925022, _925024), _925028), _925026))))], (8446 ^ _780086) ^ [_925207, _925209, _925211, _925213, _925215] : [class_Groups_Ocomm__monoid__add(_925207), hBOOL(hAPP(c_Finite__Set_Ofinite(_925209), _925211)), hBOOL(hAPP(hAPP(c_member(_925209), _925213), _925211)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_925209, _925207), _925215), _925211) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_925207), hAPP(_925215, _925213)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_925209, _925207), _925215), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_925209, tc_HOL_Obool)), _925211), hAPP(hAPP(c_Set_Oinsert(_925209), _925213), c_Orderings_Obot__class_Obot(tc_fun(_925209, tc_HOL_Obool)))))))], (8460 ^ _780086) ^ [_925532, _925534, _925536, _925538, _925540, _925542, _925544] : [c_Finite__Set_Ofun__left__comm(_925532, _925534, _925536), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_925532, _925534, _925536, _925538, _925540), _925542)), hBOOL(hAPP(hAPP(c_member(_925532), _925544), _925540)), 8472 ^ _780086 : [(8473 ^ _780086) ^ [] : [-(_925542 = hAPP(hAPP(_925536, _925544), 8471 ^ [_925532, _925534, _925536, _925538, _925540, _925542, _925544]))], (8475 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_925532, _925534, _925536, _925538, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_925532, tc_HOL_Obool)), _925540), hAPP(hAPP(c_Set_Oinsert(_925532), _925544), c_Orderings_Obot__class_Obot(tc_fun(_925532, tc_HOL_Obool))))), 8471 ^ [_925532, _925534, _925536, _925538, _925540, _925542, _925544])))]]], (8477 ^ _780086) ^ [_925940, _925942, _925944, _925946, _925948] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_925940, _925942, hAPP(hAPP(c_Set_Oinsert(_925940), _925944), _925946)), _925948)), 8482 ^ _780086 : [(8483 ^ _780086) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_925940), _925944), _925946) = hAPP(hAPP(c_Set_Oinsert(_925940), 8480 ^ [_925940, _925942, _925944, _925946, _925948]), 8481 ^ [_925940, _925942, _925944, _925946, _925948]))], (8485 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_925940, _925940, _925942, 8480 ^ [_925940, _925942, _925944, _925946, _925948], 8481 ^ [_925940, _925942, _925944, _925946, _925948]), _925948)))], (8487 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_925940), 8480 ^ [_925940, _925942, _925944, _925946, _925948]), 8481 ^ [_925940, _925942, _925944, _925946, _925948]))]]], (8489 ^ _780086) ^ [_926331, _926333, _926335, _926337, _926339] : [-(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_926331, _926333, hAPP(hAPP(c_Set_Oinsert(_926331), _926335), _926337)), _926339))), 8490 ^ _780086 : [(8491 ^ _780086) ^ [_926435, _926437] : [hAPP(hAPP(c_Set_Oinsert(_926331), _926335), _926337) = hAPP(hAPP(c_Set_Oinsert(_926331), _926437), _926435), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_926331, _926331, _926333, _926437, _926435), _926339)), -(hBOOL(hAPP(hAPP(c_member(_926331), _926437), _926435)))]]], (8503 ^ _780086) ^ [_926692, _926694, _926696, _926698, _926700] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_926692, _926694, hAPP(hAPP(c_Set_Oinsert(_926692), _926696), _926698)), _926700)), 8508 ^ _780086 : [(8509 ^ _780086) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_926692), _926696), _926698) = hAPP(hAPP(c_Set_Oinsert(_926692), 8506 ^ [_926692, _926694, _926696, _926698, _926700]), 8507 ^ [_926692, _926694, _926696, _926698, _926700]))], (8511 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_926692, _926692, _926694, 8506 ^ [_926692, _926694, _926696, _926698, _926700], 8507 ^ [_926692, _926694, _926696, _926698, _926700]), _926700)))], (8513 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_926692), 8506 ^ [_926692, _926694, _926696, _926698, _926700]), 8507 ^ [_926692, _926694, _926696, _926698, _926700]))]]], (8515 ^ _780086) ^ [_927085, _927087, _927089, _927091, _927093, _927095, _927097] : [c_Finite__Set_Ofun__left__comm(_927085, _927087, _927089), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_927085, _927087, _927089, _927091, hAPP(hAPP(c_Set_Oinsert(_927085), _927093), _927095)), _927097)), -(hBOOL(hAPP(hAPP(c_member(_927085), _927093), _927095))), 8527 ^ _780086 : [(8528 ^ _780086) ^ [] : [-(_927097 = hAPP(hAPP(_927089, _927093), 8526 ^ [_927085, _927087, _927089, _927091, _927093, _927095, _927097]))], (8530 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_927085, _927087, _927089, _927091, _927095), 8526 ^ [_927085, _927087, _927089, _927091, _927093, _927095, _927097])))]]], (8532 ^ _780086) ^ [_927411, _927413, _927415, _927417, _927419] : [class_Groups_Oab__semigroup__mult(_927411), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_927411, _927411, c_Groups_Otimes__class_Otimes(_927411), _927413, _927415), _927417)), hBOOL(hAPP(hAPP(c_member(_927411), _927419), _927415)), -(hBOOL(hAPP(hAPP(c_member(_927411), _927413), _927415))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_927411, _927411, c_Groups_Otimes__class_Otimes(_927411), _927419, hAPP(hAPP(c_Set_Oinsert(_927411), _927413), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_927411, tc_HOL_Obool)), _927415), hAPP(hAPP(c_Set_Oinsert(_927411), _927419), c_Orderings_Obot__class_Obot(tc_fun(_927411, tc_HOL_Obool)))))), _927417)))], (8550 ^ _780086) ^ [_927755, _927757, _927759, _927761, _927763, _927765, _927767, _927769] : [class_Groups_Ocomm__monoid__add(_927755), c_Fun_Oinj__on(_927757, _927759, _927761, _927763), _927765 = hAPP(c_Set_Oimage(_927757, _927759, _927761), _927763), 8564 ^ _780086 : [(8565 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_927757), 8563 ^ [_927755, _927757, _927759, _927761, _927763, _927765, _927767, _927769]), _927763)))], (8567 ^ _780086) ^ [] : [hAPP(_927767, 8563 ^ [_927755, _927757, _927759, _927761, _927763, _927765, _927767, _927769]) = hAPP(_927769, hAPP(_927761, 8563 ^ [_927755, _927757, _927759, _927761, _927763, _927765, _927767, _927769]))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_927759, _927755), _927769), _927765) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_927757, _927755), _927767), _927763))], (8597 ^ _780086) ^ [_928795, _928797, _928799, _928801] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_928795, tc_HOL_Obool)), _928797), hAPP(hAPP(c_Set_Oinsert(_928795), _928799), _928801)))), 8600 ^ _780086 : [(8601 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_928795), _928799), _928801)))], (8603 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_928795, tc_HOL_Obool)), _928797), _928801))]], 8604 ^ _780086 : [(8605 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_928795), _928799), _928801))], (8607 ^ _780086) ^ [] : [8608 ^ _780086 : [(8609 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_928795), _928799), _928797)))], (8611 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_928795, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_928795, tc_HOL_Obool)), _928797), hAPP(hAPP(c_Set_Oinsert(_928795), _928799), c_Orderings_Obot__class_Obot(tc_fun(_928795, tc_HOL_Obool))))), _928801))]], 8612 ^ _780086 : [(8613 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_928795), _928799), _928797))], (8615 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_928795, tc_HOL_Obool)), _928797), _928801))]]]]], (8571 ^ _780086) ^ [_928268, _928270, _928272, _928274] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_928268, tc_HOL_Obool)), _928270), hAPP(hAPP(c_Set_Oinsert(_928268), _928272), _928274))), 8574 ^ _780086 : [(8575 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_928268), _928272), _928274)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_928268, tc_HOL_Obool)), _928270), _928274)))], (8581 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_928268), _928272), _928274))), 8584 ^ _780086 : [(8585 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_928268), _928272), _928270)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_928268, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_928268, tc_HOL_Obool)), _928270), hAPP(hAPP(c_Set_Oinsert(_928268), _928272), c_Orderings_Obot__class_Obot(tc_fun(_928268, tc_HOL_Obool))))), _928274)))], (8591 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_928268), _928272), _928270))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_928268, tc_HOL_Obool)), _928270), _928274)))]]]]], (8619 ^ _780086) ^ [_929334, _929336, _929338, _929340, _929342, _929344, _929346] : [c_Big__Operators_Ocomm__monoid__big(_929334, _929336, _929338, _929340, _929342), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_929336), _929344))), -(hAPP(hAPP(_929342, _929346), _929344) = _929340)], (8629 ^ _780086) ^ [_929462, _929464, _929466] : [class_Orderings_Olinorder(_929462), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_929462, tc_HOL_Obool)), _929464), _929466)), -(_929464 = c_Orderings_Obot__class_Obot(tc_fun(_929462, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_929462), _929466)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_929462), c_Big__Operators_Olinorder__class_OMax(_929462, _929464)), c_Big__Operators_Olinorder__class_OMax(_929462, _929466))))], (8647 ^ _780086) ^ [_929768, _929770, _929772] : [class_Orderings_Olinorder(_929768), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_929768, tc_HOL_Obool)), _929770), _929772)), -(_929770 = c_Orderings_Obot__class_Obot(tc_fun(_929768, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_929768), _929772)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_929768), c_Big__Operators_Olinorder__class_OMin(_929768, _929772)), c_Big__Operators_Olinorder__class_OMin(_929768, _929770))))], (8665 ^ _780086) ^ [_930074, _930076, _930078] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_930074), _930076)), -(_930076 = c_Orderings_Obot__class_Obot(tc_fun(_930074, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_930074, _930078, _930076), 8672 ^ [_930074, _930076, _930078])))], (8676 ^ _780086) ^ [_930212, _930214, _930216, _930218] : [class_Groups_Oab__semigroup__mult(_930212), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930212), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930212), _930214), _930216)), _930218) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930212), _930214), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930212), _930216), _930218)))], (8682 ^ _780086) ^ [_930355, _930357, _930359] : [class_Lattices_Oab__semigroup__idem__mult(_930355), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930355), _930357), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930355), _930357), _930359)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930355), _930357), _930359))], (8688 ^ _780086) ^ [_930480, _930482] : [class_Lattices_Oab__semigroup__idem__mult(_930480), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930480), _930482), _930482) = _930482)], (8694 ^ _780086) ^ [_930571, _930573] : [class_Lattices_Oab__semigroup__idem__mult(_930571), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930571), _930573), _930573) = _930573)], (8700 ^ _780086) ^ [_930662, _930664, _930666] : [class_Orderings_Olinorder(_930662), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930662), _930664), _930666))), -(_930664 = _930666), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930662), _930666), _930664)))], (8714 ^ _780086) ^ [_930797, _930799, _930801] : [class_Orderings_Opreorder(_930797), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930797), _930799), _930801)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930797), _930801), _930799))], (8724 ^ _780086) ^ [_930957, _930959, _930961, _930963] : [class_Orderings_Oorder(_930957), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930957), _930959), _930961)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930957), _930963), _930959)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930957), _930963), _930961)))], (8738 ^ _780086) ^ [_931190, _931192, _931194, _931196] : [class_Orderings_Opreorder(_931190), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931190), _931192), _931194)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931190), _931194), _931196)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931190), _931192), _931196)))], (8752 ^ _780086) ^ [_931423, _931425, _931427, _931429] : [class_Orderings_Oorder(_931423), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931423), _931425), _931427)), _931425 = _931429, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931423), _931429), _931427)))], (8766 ^ _780086) ^ [_931642, _931644, _931646, _931648] : [class_Orderings_Oord(_931642), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931642), _931644), _931646)), _931646 = _931648, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931642), _931644), _931648)))], (8780 ^ _780086) ^ [_931861, _931863, _931865, _931867] : [class_Orderings_Oorder(_931861), _931863 = _931865, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931861), _931867), _931865)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931861), _931867), _931863)))], (8794 ^ _780086) ^ [_932080, _932082, _932084, _932086] : [class_Orderings_Oord(_932080), _932082 = _932084, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932080), _932084), _932086)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932080), _932082), _932086)))], (8808 ^ _780086) ^ [_932299, _932301, _932303] : [class_Orderings_Oorder(_932299), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932299), _932301), _932303)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932299), _932303), _932301))], (8818 ^ _780086) ^ [_932459, _932461, _932463] : [class_Orderings_Opreorder(_932459), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932459), _932461), _932463)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932459), _932463), _932461))], (8828 ^ _780086) ^ [_932619, _932621, _932623] : [class_Orderings_Oorder(_932619), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932619), _932621), _932623)), _932623 = _932621], (8838 ^ _780086) ^ [_932765, _932767, _932769] : [class_Orderings_Oorder(_932765), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932765), _932767), _932769)), _932767 = _932769], (8848 ^ _780086) ^ [_932911, _932913, _932915] : [class_Orderings_Opreorder(_932911), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932911), _932913), _932915)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932911), _932915), _932913))], (8858 ^ _780086) ^ [_933071, _933073, _933075] : [class_Orderings_Opreorder(_933071), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933071), _933073), _933075)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933071), _933075), _933073))], (8868 ^ _780086) ^ [_933231, _933233, _933235] : [class_Orderings_Oorder(_933231), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933231), _933233), _933235)), _933233 = _933235], (8878 ^ _780086) ^ [_933377, _933379, _933381] : [class_Orderings_Olinorder(_933377), -(_933379 = _933381), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933377), _933379), _933381))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933377), _933381), _933379)))], (8892 ^ _780086) ^ [_933512, _933514, _933516] : [class_Orderings_Olinorder(_933512), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933512), _933514), _933516))), 8899 ^ _780086 : [(8900 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933512), _933516), _933514))), -(_933516 = _933514)], (8906 ^ _780086) ^ [] : [_933516 = _933514, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933512), _933516), _933514))]]], (8912 ^ _780086) ^ [_933771, _933773, _933775] : [class_Orderings_Olinorder(_933771), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933771), _933773), _933775))), -(_933773 = _933775), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933771), _933775), _933773)))], (8926 ^ _780086) ^ [_933902, _933904, _933906] : [class_Orderings_Olinorder(_933902), 8929 ^ _780086 : [(8940 ^ _780086) ^ [] : [8941 ^ _780086 : [(8942 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933902), _933906), _933904))], (8944 ^ _780086) ^ [] : [_933904 = _933906]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933902), _933904), _933906))], (8930 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933902), _933904), _933906))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933902), _933906), _933904))), -(_933904 = _933906)]]], (8948 ^ _780086) ^ [_934156, _934158, _934160] : [class_Orderings_Olinorder(_934156), 8951 ^ _780086 : [(8962 ^ _780086) ^ [] : [8963 ^ _780086 : [(8964 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934156), _934158), _934160))], (8966 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934156), _934160), _934158))]], _934158 = _934160], (8952 ^ _780086) ^ [] : [-(_934158 = _934160), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934156), _934158), _934160))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934156), _934160), _934158)))]]], (8970 ^ _780086) ^ [_934410, _934412] : [class_Orderings_Opreorder(_934410), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934410), _934412), _934412))], (8976 ^ _780086) ^ [_934500, _934502, _934504, _934506] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_934500, tc_HOL_Obool)), _934502), _934504)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_934500, tc_HOL_Obool)), _934504), _934506)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_934500, tc_HOL_Obool)), _934502), _934506)))], (8986 ^ _780086) ^ [_934697, _934699, _934701, _934703] : [class_Orderings_Oord(_934697), 8989 ^ _780086 : [(8990 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_934699, _934697)), _934701), _934703)), 8993 ^ _780086 : [(8994 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_934699, _934697)), _934701), _934703)))], (8996 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_934699, _934697)), _934703), _934701))]]], (8998 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_934699, _934697)), _934701), _934703))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_934699, _934697)), _934701), _934703)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_934699, _934697)), _934703), _934701)))]]], (9008 ^ _780086) ^ [_935089, _935091, _935093, _935095] : [class_Orderings_Oorder(_935089), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935089), _935091), _935093)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935089), _935095), _935091)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935089), _935095), _935093)))], (9022 ^ _780086) ^ [_935322, _935324, _935326, _935328] : [class_Orderings_Opreorder(_935322), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935322), _935324), _935326)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935322), _935326), _935328)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935322), _935324), _935328)))], (9036 ^ _780086) ^ [_935555, _935557, _935559, _935561] : [class_Orderings_Oorder(_935555), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935555), _935557), _935559)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935555), _935561), _935557)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935555), _935561), _935559)))], (9050 ^ _780086) ^ [_935788, _935790, _935792, _935794] : [class_Orderings_Opreorder(_935788), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935788), _935790), _935792)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935788), _935792), _935794)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935788), _935790), _935794)))], (9064 ^ _780086) ^ [_936021, _936023, _936025] : [class_Orderings_Oorder(_936021), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936021), _936023), _936025)), -(_936025 = _936023), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936021), _936023), _936025)))], (9078 ^ _780086) ^ [_936195, _936197, _936199] : [class_Orderings_Oorder(_936195), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936195), _936197), _936199)), -(_936197 = _936199), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936195), _936197), _936199)))], (9092 ^ _780086) ^ [_936369, _936371, _936373] : [class_Orderings_Oorder(_936369), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936369), _936371), _936373)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936369), _936371), _936373))), -(_936371 = _936373)], (9106 ^ _780086) ^ [_936541, _936543, _936545] : [class_Orderings_Olinorder(_936541), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936541), _936543), _936545)), 9113 ^ _780086 : [(9114 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936541), _936543), _936545))), -(_936543 = _936545)], (9120 ^ _780086) ^ [] : [_936543 = _936545, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936541), _936543), _936545))]]], (9126 ^ _780086) ^ [_936797, _936799, _936801] : [class_Orderings_Opreorder(_936797), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936797), _936799), _936801)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936797), _936799), _936801)))], (9136 ^ _780086) ^ [_936956, _936958, _936960] : [class_Orderings_Olinorder(_936956), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936956), _936958), _936960)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936956), _936960), _936958))], (9146 ^ _780086) ^ [_937116, _937118, _937120] : [class_Orderings_Oorder(_937116), -(_937118 = _937120), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937116), _937120), _937118)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937116), _937120), _937118)))], (9160 ^ _780086) ^ [_937332, _937334, _937336] : [class_Orderings_Oorder(_937332), -(_937334 = _937336), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937332), _937334), _937336)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937332), _937334), _937336)))], (9174 ^ _780086) ^ [_937548, _937550, _937552] : [class_Orderings_Olinorder(_937548), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937548), _937550), _937552))), 9181 ^ _780086 : [(9182 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937548), _937550), _937552)), -(_937550 = _937552)], (9188 ^ _780086) ^ [] : [_937550 = _937552, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937548), _937550), _937552)))]]], (9194 ^ _780086) ^ [_937851, _937853, _937855] : [class_Orderings_Olinorder(_937851), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937851), _937853), _937855))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937851), _937855), _937853)))], (9204 ^ _780086) ^ [_937971, _937973, _937975] : [class_Orderings_Olinorder(_937971), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937971), _937973), _937975))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937971), _937975), _937973)))], (9214 ^ _780086) ^ [_938091, _938093, _938095] : [class_Orderings_Oorder(_938091), 9217 ^ _780086 : [(9228 ^ _780086) ^ [] : [9229 ^ _780086 : [(9230 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938091), _938093), _938095))], (9232 ^ _780086) ^ [] : [_938093 = _938095]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938091), _938093), _938095)))], (9218 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938091), _938093), _938095)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938091), _938093), _938095))), -(_938093 = _938095)]]], (9236 ^ _780086) ^ [_938389, _938391, _938393] : [class_Orderings_Opreorder(_938389), 9239 ^ _780086 : [(9240 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938389), _938391), _938393)), 9243 ^ _780086 : [(9244 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938389), _938391), _938393)))], (9246 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938389), _938393), _938391))]]], (9248 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938389), _938391), _938393))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938389), _938391), _938393)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938389), _938393), _938391)))]]], (9258 ^ _780086) ^ [_938746, _938748, _938750] : [class_Orderings_Oorder(_938746), 9261 ^ _780086 : [(9262 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938746), _938748), _938750)), 9265 ^ _780086 : [(9266 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938746), _938748), _938750)))], (9268 ^ _780086) ^ [] : [_938748 = _938750]]], (9270 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938746), _938748), _938750))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938746), _938748), _938750)), -(_938748 = _938750)]]], (9280 ^ _780086) ^ [_939082, _939084, _939086] : [class_Orderings_Olinorder(_939082), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939082), _939084), _939086))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939082), _939086), _939084)))], (9290 ^ _780086) ^ [_939200, _939202, _939204] : [class_Orderings_Olinorder(_939200), 9293 ^ _780086 : [(9294 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939200), _939202), _939204))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939200), _939204), _939202)))], (9300 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939200), _939204), _939202)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939200), _939202), _939204))]]], (9306 ^ _780086) ^ [_939409, _939411, _939413] : [class_Orderings_Olinorder(_939409), 9309 ^ _780086 : [(9310 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939409), _939411), _939413))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939409), _939413), _939411)))], (9316 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939409), _939413), _939411)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939409), _939411), _939413))]]], (9322 ^ _780086) ^ [_939618, _939620, _939622, _939624] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_939618, tc_HOL_Obool)), _939620), _939622)), hBOOL(hAPP(hAPP(c_member(_939618), _939624), _939620)), -(hBOOL(hAPP(hAPP(c_member(_939618), _939624), _939622)))], (9332 ^ _780086) ^ [_939803, _939805, _939807, _939809] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_939803), 9335 ^ _780086 : [(9336 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939803), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_939803), _939805), _939807)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_939803), _939809), _939807))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939803), _939805), _939809)))], (9342 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939803), _939805), _939809)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939803), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_939803), _939805), _939807)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_939803), _939809), _939807))))]]], (9348 ^ _780086) ^ [_940110, _940112, _940114, _940116] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_940110), 9351 ^ _780086 : [(9352 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940110), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940110), _940112), _940114)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940110), _940112), _940116))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940110), _940114), _940116)))], (9358 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940110), _940114), _940116)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940110), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940110), _940112), _940114)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940110), _940112), _940116))))]]], (9364 ^ _780086) ^ [_940417, _940419, _940421, _940423] : [class_Groups_Oordered__cancel__ab__semigroup__add(_940417), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940417), _940419), _940421)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940417), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940417), _940419), _940423)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940417), _940421), _940423))))], (9374 ^ _780086) ^ [_940612, _940614, _940616, _940618] : [class_Groups_Oordered__cancel__ab__semigroup__add(_940612), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940612), _940614), _940616)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940612), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940612), _940618), _940614)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940612), _940618), _940616))))], (9384 ^ _780086) ^ [_940807, _940809, _940811, _940813, _940815] : [class_Groups_Oordered__cancel__ab__semigroup__add(_940807), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940807), _940809), _940811)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940807), _940813), _940815)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940807), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940807), _940809), _940813)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940807), _940811), _940815))))], (9398 ^ _780086) ^ [_941078, _941080, _941082, _941084] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_941078), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941078), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_941078), _941080), _941082)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_941078), _941084), _941082))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941078), _941080), _941084)))], (9408 ^ _780086) ^ [_941273, _941275, _941277, _941279] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_941273), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941273), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_941273), _941275), _941277)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_941273), _941275), _941279))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941273), _941277), _941279)))], (9418 ^ _780086) ^ [_941480, _941482] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_941480, tc_HOL_Obool)), _941482), c_Orderings_Obot__class_Obot(tc_fun(_941480, tc_HOL_Obool))))], (9420 ^ _780086) ^ [_941520, _941522, _941524, _941526, _941528] : [class_Groups_Oordered__ab__group__add(_941520), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_941520), _941522), _941524) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_941520), _941526), _941528), 9427 ^ _780086 : [(9428 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941520), _941522), _941524)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941520), _941526), _941528)))], (9434 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941520), _941526), _941528)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941520), _941522), _941524)))]]], (9440 ^ _780086) ^ [_941875, _941877, _941879, _941881] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_941875, tc_HOL_Obool)), _941877), _941879)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_941875, tc_HOL_Obool)), _941879), _941881)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_941875, tc_HOL_Obool)), _941877), _941881)))], (9450 ^ _780086) ^ [_942072, _942074, _942076, _942078] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_942072, tc_HOL_Obool)), _942074), _942076)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_942072, tc_HOL_Obool)), _942076), _942078)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_942072, tc_HOL_Obool)), _942074), _942078)))], (9460 ^ _780086) ^ [_942269, _942271, _942273] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_942269, tc_HOL_Obool)), _942271), _942273)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_942269, tc_HOL_Obool)), _942271), _942273)))], (9476 ^ _780086) ^ [_942534, _942536, _942538] : [9477 ^ _780086 : [(9478 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_942534, tc_HOL_Obool)), _942536), _942538))], (9480 ^ _780086) ^ [] : [_942536 = _942538]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_942534, tc_HOL_Obool)), _942536), _942538)))], (9466 ^ _780086) ^ [_942406, _942408, _942410] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_942406, tc_HOL_Obool)), _942408), _942410)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_942406, tc_HOL_Obool)), _942408), _942410))), -(_942408 = _942410)], (9484 ^ _780086) ^ [_942711, _942713, _942715] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_942711, tc_HOL_Obool)), _942713), _942715)), 9487 ^ _780086 : [(9488 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_942711, tc_HOL_Obool)), _942713), _942715)))], (9490 ^ _780086) ^ [] : [_942713 = _942715]]], (9492 ^ _780086) ^ [_942860, _942862, _942864] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_942860, tc_HOL_Obool)), _942862), _942864))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_942860, tc_HOL_Obool)), _942862), _942864)), -(_942862 = _942864)], (9502 ^ _780086) ^ [_943038] : [class_Groups_Oab__semigroup__mult(_943038), -(c_Finite__Set_Ofun__left__comm(_943038, _943038, c_Groups_Otimes__class_Otimes(_943038)))], (9508 ^ _780086) ^ [_943117] : [class_Lattices_Oab__semigroup__idem__mult(_943117), -(c_Finite__Set_Ofun__left__comm__idem(_943117, _943117, c_Groups_Otimes__class_Otimes(_943117)))], (9514 ^ _780086) ^ [_943196, _943198, _943200, _943202, _943204] : [class_Rings_Osemiring__0(_943196), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_943196), _943198), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_943200, _943196), _943202), _943204)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_943200, _943196), hAPP(hAPP(c_COMBB(_943196, _943196, _943200), hAPP(c_Groups_Otimes__class_Otimes(_943196), _943198)), _943202)), _943204))], (9520 ^ _780086) ^ [_943359, _943361, _943363, _943365, _943367] : [class_Rings_Osemiring__0(_943359), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_943359), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_943361, _943359), _943363), _943365)), _943367) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_943361, _943359), hAPP(hAPP(c_COMBC(_943361, _943359, _943359), hAPP(hAPP(c_COMBB(_943359, tc_fun(_943359, _943359), _943361), c_Groups_Otimes__class_Otimes(_943359)), _943363)), _943367)), _943365))], (9526 ^ _780086) ^ [_943542, _943544, _943546, _943548, _943550, _943552, _943554] : [class_Rings_Osemiring__0(_943542), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_943542), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_943544, _943542), _943546), _943548)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_943550, _943542), _943552), _943554)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_943544, _943542), hAPP(hAPP(c_COMBC(_943544, tc_fun(_943550, tc_HOL_Obool), _943542), hAPP(hAPP(c_COMBB(tc_fun(_943550, _943542), tc_fun(tc_fun(_943550, tc_HOL_Obool), _943542), _943544), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_943550, _943542)), hAPP(hAPP(c_COMBC(_943544, tc_fun(_943550, _943542), tc_fun(_943550, _943542)), hAPP(hAPP(c_COMBB(tc_fun(_943542, _943542), tc_fun(tc_fun(_943550, _943542), tc_fun(_943550, _943542)), _943544), c_COMBB(_943542, _943542, _943550)), hAPP(hAPP(c_COMBB(_943542, tc_fun(_943542, _943542), _943544), c_Groups_Otimes__class_Otimes(_943542)), _943546))), _943552))), _943554)), _943548))], (9532 ^ _780086) ^ [_943881, _943883, _943885, _943887, _943889] : [class_Groups_Oordered__cancel__ab__semigroup__add(_943881), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943881), _943883), _943885)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943881), _943887), _943889)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943881), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_943881), _943883), _943887)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_943881), _943885), _943889))))], (9546 ^ _780086) ^ [_944152, _944154, _944156, _944158, _944160] : [class_Groups_Oordered__cancel__ab__semigroup__add(_944152), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944152), _944154), _944156)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944152), _944158), _944160)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944152), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_944152), _944154), _944158)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_944152), _944156), _944160))))], (9560 ^ _780086) ^ [_944423, _944425, _944427, _944429, _944431] : [c_Fun_Oinj__on(_944423, _944425, _944427, _944429), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_944423, tc_HOL_Obool)), _944431), _944429)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_944425, tc_HOL_Obool)), hAPP(c_Set_Oimage(_944423, _944425, _944427), _944431)), hAPP(c_Set_Oimage(_944423, _944425, _944427), _944429))))], (9570 ^ _780086) ^ [_944636, _944638] : [class_Orderings_Olinorder(_944636), -(c_Big__Operators_Olinorder__class_OMin(_944636, hAPP(hAPP(c_Set_Oinsert(_944636), _944638), c_Orderings_Obot__class_Obot(tc_fun(_944636, tc_HOL_Obool)))) = _944638)], (9576 ^ _780086) ^ [_944743, _944745] : [class_Orderings_Olinorder(_944743), -(c_Big__Operators_Olinorder__class_OMax(_944743, hAPP(hAPP(c_Set_Oinsert(_944743), _944745), c_Orderings_Obot__class_Obot(tc_fun(_944743, tc_HOL_Obool)))) = _944745)], (9582 ^ _780086) ^ [_944850, _944852, _944854, _944856, _944858] : [class_Groups_Oab__semigroup__mult(_944850), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_944850, _944850, c_Groups_Otimes__class_Otimes(_944850), _944852, _944854), _944856)), -(hBOOL(hAPP(hAPP(c_member(_944850), _944852), _944854))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_944850, _944850, c_Groups_Otimes__class_Otimes(_944850), _944858, hAPP(hAPP(c_Set_Oinsert(_944850), _944852), _944854)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_944850), _944858), _944856))))], (9596 ^ _780086) ^ [_945090, _945092, _945094] : [class_Orderings_Olinorder(_945090), hBOOL(hAPP(c_Finite__Set_Ofinite(_945090), _945092)), hBOOL(hAPP(hAPP(c_member(_945090), _945094), _945092)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_945090), c_Big__Operators_Olinorder__class_OMin(_945090, _945092)), _945094)))], (9610 ^ _780086) ^ [_945317, _945319, _945321] : [class_Orderings_Olinorder(_945317), hBOOL(hAPP(c_Finite__Set_Ofinite(_945317), _945319)), hBOOL(hAPP(hAPP(c_member(_945317), _945321), _945319)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_945317), _945321), c_Big__Operators_Olinorder__class_OMax(_945317, _945319))))], (9624 ^ _780086) ^ [_945544, _945546] : [class_Orderings_Olinorder(_945544), hBOOL(hAPP(c_Finite__Set_Ofinite(_945544), _945546)), -(_945546 = c_Orderings_Obot__class_Obot(tc_fun(_945544, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_945544), c_Big__Operators_Olinorder__class_OMin(_945544, _945546)), _945546)))], (9638 ^ _780086) ^ [_945724, _945726] : [class_Orderings_Olinorder(_945724), hBOOL(hAPP(c_Finite__Set_Ofinite(_945724), _945726)), -(_945726 = c_Orderings_Obot__class_Obot(tc_fun(_945724, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_945724), c_Big__Operators_Olinorder__class_OMax(_945724, _945726)), _945726)))], (9652 ^ _780086) ^ [_945904, _945906, _945908, _945910, _945912, _945914] : [class_Rings_Oordered__ring(_945904), 9655 ^ _780086 : [(9656 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945904), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_945904), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_945904), _945906), _945908)), _945910)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_945904), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_945904), _945912), _945908)), _945914))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945904), _945910), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_945904), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_945904), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_945904), _945912), _945906)), _945908)), _945914))))], (9662 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945904), _945910), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_945904), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_945904), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_945904), _945912), _945906)), _945908)), _945914))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945904), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_945904), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_945904), _945906), _945908)), _945910)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_945904), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_945904), _945912), _945908)), _945914))))]]], (9668 ^ _780086) ^ [_946343, _946345, _946347, _946349, _946351, _946353] : [class_Rings_Oordered__ring(_946343), 9671 ^ _780086 : [(9672 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946343), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946343), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_946343), _946345), _946347)), _946349)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946343), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_946343), _946351), _946347)), _946353))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946343), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946343), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_946343), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_946343), _946345), _946351)), _946347)), _946349)), _946353)))], (9678 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946343), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946343), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_946343), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_946343), _946345), _946351)), _946347)), _946349)), _946353)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946343), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946343), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_946343), _946345), _946347)), _946349)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946343), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_946343), _946351), _946347)), _946353))))]]], (9684 ^ _780086) ^ [_946782, _946784, _946786, _946788, _946790, _946792] : [class_Rings_Oordered__ring(_946782), 9687 ^ _780086 : [(9688 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_946782), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946782), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_946782), _946784), _946786)), _946788)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946782), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_946782), _946790), _946786)), _946792))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_946782), _946788), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946782), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_946782), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_946782), _946790), _946784)), _946786)), _946792))))], (9694 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_946782), _946788), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946782), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_946782), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_946782), _946790), _946784)), _946786)), _946792))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_946782), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946782), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_946782), _946784), _946786)), _946788)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946782), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_946782), _946790), _946786)), _946792))))]]], (9700 ^ _780086) ^ [_947221, _947223, _947225, _947227, _947229, _947231] : [class_Rings_Oordered__ring(_947221), 9703 ^ _780086 : [(9704 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947221), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947221), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_947221), _947223), _947225)), _947227)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947221), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_947221), _947229), _947225)), _947231))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947221), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947221), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_947221), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_947221), _947223), _947229)), _947225)), _947227)), _947231)))], (9710 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947221), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947221), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_947221), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_947221), _947223), _947229)), _947225)), _947227)), _947231)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947221), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947221), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_947221), _947223), _947225)), _947227)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947221), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_947221), _947229), _947225)), _947231))))]]], (9716 ^ _780086) ^ [_947660, _947662, _947664, _947666, _947668, _947670] : [class_Rings_Oring(_947660), 9719 ^ _780086 : [(9720 ^ _780086) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947660), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_947660), _947662), _947664)), _947666) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947660), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_947660), _947668), _947664)), _947670), -(_947666 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947660), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_947660), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_947660), _947668), _947662)), _947664)), _947670))], (9726 ^ _780086) ^ [] : [_947666 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947660), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_947660), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_947660), _947668), _947662)), _947664)), _947670), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947660), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_947660), _947662), _947664)), _947666) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947660), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_947660), _947668), _947664)), _947670))]]], (9732 ^ _780086) ^ [_948057, _948059, _948061, _948063, _948065, _948067] : [class_Rings_Oring(_948057), 9735 ^ _780086 : [(9736 ^ _780086) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948057), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948057), _948059), _948061)), _948063) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948057), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948057), _948065), _948061)), _948067), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948057), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948057), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_948057), _948059), _948065)), _948061)), _948063) = _948067)], (9742 ^ _780086) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948057), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948057), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_948057), _948059), _948065)), _948061)), _948063) = _948067, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948057), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948057), _948059), _948061)), _948063) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948057), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948057), _948065), _948061)), _948067))]]], (9748 ^ _780086) ^ [_948454, _948456, _948458, _948460] : [class_Rings_Ocomm__semiring__1(_948454), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948454), _948456), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948454), _948458), _948460)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948454), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948454), _948456), _948458)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948454), _948456), _948460)))], (9754 ^ _780086) ^ [_948613, _948615, _948617, _948619, _948621] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_948613), 9757 ^ _780086 : [(9768 ^ _780086) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948613), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948613), _948615), _948619)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948613), _948617), _948621)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948613), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948613), _948615), _948621)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948613), _948617), _948619))), 9771 ^ _780086 : [(9772 ^ _780086) ^ [] : [_948615 = _948617], (9774 ^ _780086) ^ [] : [_948619 = _948621]]], (9758 ^ _780086) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948613), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948613), _948615), _948619)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948613), _948617), _948621)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948613), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948613), _948615), _948621)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948613), _948617), _948619)), -(_948615 = _948617), -(_948619 = _948621)]]], (9776 ^ _780086) ^ [_949031, _949033, _949035, _949037] : [class_Rings_Ocomm__semiring(_949031), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949031), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949031), _949033), _949035)), _949037) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949031), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949031), _949033), _949037)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949031), _949035), _949037)))], (9782 ^ _780086) ^ [_949190, _949192, _949194, _949196] : [class_Rings_Ocomm__semiring__1(_949190), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949190), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949190), _949192), _949194)), _949196) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949190), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949190), _949192), _949196)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949190), _949194), _949196)))], (9788 ^ _780086) ^ [_949349, _949351, _949353] : [class_Rings_Olinordered__idom(_949349), -(_949351 = _949353), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_949349), _949351), _949353))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_949349), _949353), _949351)))], (9802 ^ _780086) ^ [_949484, _949486, _949488, _949490, _949492] : [class_Rings_Ocomm__semiring__1(_949484), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949484), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949484), _949486), _949488)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949484), _949490), _949492)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949484), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949484), _949486), _949490)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949484), _949488), _949492)))], (9808 ^ _780086) ^ [_949661, _949663, _949665, _949667] : [class_Rings_Ocomm__semiring__1(_949661), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949661), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949661), _949663), _949665)), _949667) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949661), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949661), _949663), _949667)), _949665))], (9814 ^ _780086) ^ [_949804, _949806, _949808, _949810] : [class_Rings_Ocomm__semiring__1(_949804), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949804), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949804), _949806), _949808)), _949810) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949804), _949806), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949804), _949808), _949810)))], (9820 ^ _780086) ^ [_949947, _949949, _949951, _949953] : [class_Rings_Ocomm__semiring__1(_949947), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949947), _949949), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949947), _949951), _949953)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949947), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949947), _949949), _949951)), _949953))], (9826 ^ _780086) ^ [_950090, _950092, _950094, _950096] : [class_Rings_Ocomm__semiring__1(_950090), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950090), _950092), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950090), _950094), _950096)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950090), _950094), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950090), _950092), _950096)))], (9832 ^ _780086) ^ [_950233, _950235, _950237] : [class_Rings_Ocomm__semiring__1(_950233), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950233), _950235), _950237) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950233), _950237), _950235))], (9838 ^ _780086) ^ [_950342, _950344, _950346, _950348, _950350] : [class_Rings_Ocomm__semiring__1(_950342), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950342), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950342), _950344), _950346)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950342), _950348), _950350)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950342), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950342), _950344), _950348)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950342), _950346), _950350)))], (9844 ^ _780086) ^ [_950519, _950521, _950523, _950525, _950527] : [class_Rings_Ocomm__semiring__1(_950519), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950519), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950519), _950521), _950523)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950519), _950525), _950527)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950519), _950525), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950519), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950519), _950521), _950523)), _950527)))], (9850 ^ _780086) ^ [_950696, _950698, _950700, _950702, _950704] : [class_Rings_Ocomm__semiring__1(_950696), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950696), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950696), _950698), _950700)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950696), _950702), _950704)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950696), _950698), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950696), _950700), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950696), _950702), _950704))))], (9856 ^ _780086) ^ [_950873, _950875, _950877, _950879] : [class_Rings_Ocomm__semiring__1(_950873), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950873), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950873), _950875), _950877)), _950879) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950873), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950873), _950875), _950879)), _950877))], (9862 ^ _780086) ^ [_951016, _951018, _951020, _951022] : [class_Rings_Ocomm__semiring__1(_951016), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951016), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951016), _951018), _951020)), _951022) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951016), _951018), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951016), _951020), _951022)))], (9868 ^ _780086) ^ [_951159, _951161, _951163, _951165] : [class_Rings_Ocomm__semiring__1(_951159), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951159), _951161), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951159), _951163), _951165)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951159), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951159), _951161), _951163)), _951165))], (9874 ^ _780086) ^ [_951302, _951304, _951306, _951308] : [class_Rings_Ocomm__semiring__1(_951302), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951302), _951304), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951302), _951306), _951308)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951302), _951306), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951302), _951304), _951308)))], (9880 ^ _780086) ^ [_951445, _951447, _951449] : [class_Rings_Ocomm__semiring__1(_951445), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951445), _951447), _951449) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951445), _951449), _951447))], (9886 ^ _780086) ^ [_951554, _951556, _951558, _951560, _951562] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_951554), 9889 ^ _780086 : [(9900 ^ _780086) ^ [] : [9901 ^ _780086 : [(9902 ^ _780086) ^ [] : [_951556 = _951560], (9904 ^ _780086) ^ [] : [_951558 = _951562]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_951554), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951554), _951556), _951558)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951554), _951560), _951562)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_951554), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951554), _951556), _951562)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951554), _951560), _951558)))], (9890 ^ _780086) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_951554), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951554), _951556), _951558)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951554), _951560), _951562)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_951554), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951554), _951556), _951562)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951554), _951560), _951558)), -(_951556 = _951560), -(_951558 = _951562)]]], (9908 ^ _780086) ^ [_951966, _951968, _951970, _951972, _951974] : [class_Rings_Osemiring(_951966), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_951966), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951966), _951968), _951970)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_951966), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951966), _951972), _951970)), _951974)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_951966), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951966), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_951966), _951968), _951972)), _951970)), _951974))], (9914 ^ _780086) ^ [_952159, _952161, _952163, _952165] : [class_Rings_Ocomm__semiring__1(_952159), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_952159), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_952159), _952161), _952163)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_952159), _952165), _952163)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_952159), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_952159), _952161), _952165)), _952163))], (9920 ^ _780086) ^ [_952318, _952320, _952322, _952324, _952326] : [class_Groups_Ocomm__monoid__add(_952318), class_Groups_Oordered__cancel__ab__semigroup__add(_952318), hBOOL(hAPP(c_Finite__Set_Ofinite(_952320), _952322)), -(_952322 = c_Orderings_Obot__class_Obot(tc_fun(_952320, tc_HOL_Obool))), 9938 ^ _780086 : [(9939 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_952320), 9937 ^ [_952318, _952320, _952322, _952324, _952326]), _952322)))], (9941 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952318), hAPP(_952324, 9937 ^ [_952318, _952320, _952322, _952324, _952326])), hAPP(_952326, 9937 ^ [_952318, _952320, _952322, _952324, _952326])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952318), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_952320, _952318), _952324), _952322)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_952320, _952318), _952326), _952322))))], (9945 ^ _780086) ^ [_952849, _952851, _952853] : [class_Orderings_Olinorder(_952849), hBOOL(hAPP(c_Finite__Set_Ofinite(_952849), _952851)), hBOOL(hAPP(hAPP(c_member(_952849), _952853), _952851)), 9956 ^ _780086 : [(9957 ^ _780086) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_952849, tc_HOL_Obool)), _952851), hAPP(hAPP(c_Set_Oinsert(_952849), _952853), c_Orderings_Obot__class_Obot(tc_fun(_952849, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_952849, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_952849, _952851) = _952853)], (9963 ^ _780086) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_952849, tc_HOL_Obool)), _952851), hAPP(hAPP(c_Set_Oinsert(_952849), _952853), c_Orderings_Obot__class_Obot(tc_fun(_952849, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_952849, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_952849, _952851) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_952849), _952853), c_Big__Operators_Olinorder__class_OMin(_952849, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_952849, tc_HOL_Obool)), _952851), hAPP(hAPP(c_Set_Oinsert(_952849), _952853), c_Orderings_Obot__class_Obot(tc_fun(_952849, tc_HOL_Obool)))))))]]], (9969 ^ _780086) ^ [_953355, _953357, _953359] : [class_Orderings_Olinorder(_953355), hBOOL(hAPP(c_Finite__Set_Ofinite(_953355), _953357)), hBOOL(hAPP(hAPP(c_member(_953355), _953359), _953357)), 9980 ^ _780086 : [(9981 ^ _780086) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_953355, tc_HOL_Obool)), _953357), hAPP(hAPP(c_Set_Oinsert(_953355), _953359), c_Orderings_Obot__class_Obot(tc_fun(_953355, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_953355, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_953355, _953357) = _953359)], (9987 ^ _780086) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_953355, tc_HOL_Obool)), _953357), hAPP(hAPP(c_Set_Oinsert(_953355), _953359), c_Orderings_Obot__class_Obot(tc_fun(_953355, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_953355, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_953355, _953357) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_953355), _953359), c_Big__Operators_Olinorder__class_OMax(_953355, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_953355, tc_HOL_Obool)), _953357), hAPP(hAPP(c_Set_Oinsert(_953355), _953359), c_Orderings_Obot__class_Obot(tc_fun(_953355, tc_HOL_Obool)))))))]]], (9993 ^ _780086) ^ [_953861, _953863, _953865] : [class_Groups_Oab__semigroup__mult(_953861), hBOOL(hAPP(c_Finite__Set_Ofinite(_953861), _953863)), -(hBOOL(hAPP(hAPP(c_member(_953861), _953865), _953863))), -(hAPP(c_Finite__Set_Ofold1(_953861, c_Groups_Otimes__class_Otimes(_953861)), hAPP(hAPP(c_Set_Oinsert(_953861), _953865), _953863)) = hAPP(hAPP(c_Finite__Set_Ofold(_953861, _953861, c_Groups_Otimes__class_Otimes(_953861)), _953865), _953863))], (10007 ^ _780086) ^ [_954085, _954087, _954089] : [class_Groups_Oab__semigroup__mult(_954085), -(_954087 = c_Orderings_Obot__class_Obot(tc_fun(_954085, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_954085), _954087)), -(hBOOL(hAPP(hAPP(c_member(_954085), _954089), _954087))), -(hAPP(c_Finite__Set_Ofold1(_954085, c_Groups_Otimes__class_Otimes(_954085)), hAPP(hAPP(c_Set_Oinsert(_954085), _954089), _954087)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954085), _954089), hAPP(c_Finite__Set_Ofold1(_954085, c_Groups_Otimes__class_Otimes(_954085)), _954087)))], (10025 ^ _780086) ^ [_954384, _954386, _954388, _954390, _954392] : [class_Groups_Ocomm__monoid__mult(_954384), hBOOL(hAPP(c_Finite__Set_Ofinite(_954386), _954388)), hBOOL(hAPP(hAPP(c_member(_954386), _954390), _954388)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_954386, _954384), _954392), _954388) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954384), hAPP(_954392, _954390)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_954386, _954384), _954392), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_954386, tc_HOL_Obool)), _954388), hAPP(hAPP(c_Set_Oinsert(_954386), _954390), c_Orderings_Obot__class_Obot(tc_fun(_954386, tc_HOL_Obool)))))))], (10039 ^ _780086) ^ [_954709, _954711, _954713] : [class_Orderings_Olinorder(_954709), hBOOL(hAPP(c_Finite__Set_Ofinite(_954709), _954711)), 10049 ^ _780086 : [(10050 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_954709), 10048 ^ [_954709, _954711, _954713]), _954711)))], (10052 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954709), _954713), 10048 ^ [_954709, _954711, _954713]))]], hBOOL(hAPP(hAPP(c_member(_954709), _954713), _954711)), -(c_Big__Operators_Olinorder__class_OMin(_954709, _954711) = _954713)], (10060 ^ _780086) ^ [_955081, _955083, _955085] : [class_Orderings_Olinorder(_955081), hBOOL(hAPP(c_Finite__Set_Ofinite(_955081), _955083)), 10070 ^ _780086 : [(10071 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_955081), 10069 ^ [_955081, _955083, _955085]), _955083)))], (10073 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955081), 10069 ^ [_955081, _955083, _955085]), _955085))]], hBOOL(hAPP(hAPP(c_member(_955081), _955085), _955083)), -(c_Big__Operators_Olinorder__class_OMax(_955081, _955083) = _955085)], (10081 ^ _780086) ^ [_955453, _955455] : [class_Groups_Olinordered__ab__group__add(_955453), hBOOL(hAPP(c_Finite__Set_Ofinite(_955453), _955455)), -(_955455 = c_Orderings_Obot__class_Obot(tc_fun(_955453, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_955453), c_Big__Operators_Olinorder__class_OMax(_955453, _955455)) = c_Big__Operators_Olinorder__class_OMin(_955453, hAPP(c_Set_Oimage(_955453, _955453, c_Groups_Ouminus__class_Ouminus(_955453)), _955455)))], (10095 ^ _780086) ^ [_955653, _955655] : [class_Groups_Olinordered__ab__group__add(_955653), hBOOL(hAPP(c_Finite__Set_Ofinite(_955653), _955655)), -(_955655 = c_Orderings_Obot__class_Obot(tc_fun(_955653, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_955653), c_Big__Operators_Olinorder__class_OMin(_955653, _955655)) = c_Big__Operators_Olinorder__class_OMax(_955653, hAPP(c_Set_Oimage(_955653, _955653, c_Groups_Ouminus__class_Ouminus(_955653)), _955655)))], (10109 ^ _780086) ^ [_955849, _955851, _955853] : [-(hBOOL(hAPP(hAPP(c_member(_955849), _955851), _955853))), -(hBOOL(hAPP(hAPP(c_member(_955849), _955851), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_955849, tc_HOL_Obool)), _955853))))], (10115 ^ _780086) ^ [_955909, _955911] : [class_Groups_Oordered__ab__group__add(_955909), -(c_Fun_Oinj__on(_955909, _955909, c_Groups_Ouminus__class_Ouminus(_955909), _955911))], (10121 ^ _780086) ^ [_955992, _955994, _955996] : [class_Groups_Ogroup__add(_955992), 10124 ^ _780086 : [(10125 ^ _780086) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_955992), _955994) = hAPP(c_Groups_Ouminus__class_Ouminus(_955992), _955996), -(_955994 = _955996)], (10131 ^ _780086) ^ [] : [_955994 = _955996, -(hAPP(c_Groups_Ouminus__class_Ouminus(_955992), _955994) = hAPP(c_Groups_Ouminus__class_Ouminus(_955992), _955996))]]], (10137 ^ _780086) ^ [_956233, _956235, _956237] : [class_Groups_Ogroup__add(_956233), 10140 ^ _780086 : [(10141 ^ _780086) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_956233), _956235) = _956237, -(hAPP(c_Groups_Ouminus__class_Ouminus(_956233), _956237) = _956235)], (10147 ^ _780086) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_956233), _956237) = _956235, -(hAPP(c_Groups_Ouminus__class_Ouminus(_956233), _956235) = _956237)]]], (10153 ^ _780086) ^ [_956474, _956476, _956478] : [class_Groups_Ogroup__add(_956474), 10156 ^ _780086 : [(10157 ^ _780086) ^ [] : [_956476 = hAPP(c_Groups_Ouminus__class_Ouminus(_956474), _956478), -(_956478 = hAPP(c_Groups_Ouminus__class_Ouminus(_956474), _956476))], (10163 ^ _780086) ^ [] : [_956478 = hAPP(c_Groups_Ouminus__class_Ouminus(_956474), _956476), -(_956476 = hAPP(c_Groups_Ouminus__class_Ouminus(_956474), _956478))]]], (10169 ^ _780086) ^ [_956715, _956717, _956719] : [class_Groups_Olinordered__ab__group__add(_956715), -(hAPP(c_Groups_Ouminus__class_Ouminus(_956715), hAPP(hAPP(c_Orderings_Oord__class_Omin(_956715), _956717), _956719)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_956715), hAPP(c_Groups_Ouminus__class_Ouminus(_956715), _956717)), hAPP(c_Groups_Ouminus__class_Ouminus(_956715), _956719)))], (10175 ^ _780086) ^ [_956854, _956856, _956858] : [class_Groups_Olinordered__ab__group__add(_956854), -(hAPP(c_Groups_Ouminus__class_Ouminus(_956854), hAPP(hAPP(c_Orderings_Oord__class_Omax(_956854), _956856), _956858)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_956854), hAPP(c_Groups_Ouminus__class_Ouminus(_956854), _956856)), hAPP(c_Groups_Ouminus__class_Ouminus(_956854), _956858)))], (10181 ^ _780086) ^ [_956993, _956995] : [class_Groups_Ogroup__add(_956993), -(hAPP(c_Groups_Ouminus__class_Ouminus(_956993), hAPP(c_Groups_Ouminus__class_Ouminus(_956993), _956995)) = _956995)], (10187 ^ _780086) ^ [_957088, _957090, _957092, _957094] : [class_Orderings_Olinorder(_957088), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957088), hAPP(hAPP(c_Orderings_Oord__class_Omax(_957088), _957090), hAPP(hAPP(c_Orderings_Oord__class_Omin(_957088), _957092), _957094))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_957088), hAPP(hAPP(c_Orderings_Oord__class_Omax(_957088), _957090), _957092)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_957088), _957090), _957094)))))], (10193 ^ _780086) ^ [_957261, _957263, _957265, _957267] : [class_Orderings_Olinorder(_957261), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957261), hAPP(hAPP(c_Orderings_Oord__class_Omax(_957261), hAPP(hAPP(c_Orderings_Oord__class_Omin(_957261), _957263), _957265)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_957261), _957263), _957267))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_957261), _957263), hAPP(hAPP(c_Orderings_Oord__class_Omax(_957261), _957265), _957267)))))], (10199 ^ _780086) ^ [_957434, _957436, _957438, _957440] : [class_Orderings_Olinorder(_957434), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_957434), hAPP(hAPP(c_Orderings_Oord__class_Omax(_957434), _957436), _957438)), _957440) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_957434), hAPP(hAPP(c_Orderings_Oord__class_Omin(_957434), _957436), _957440)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_957434), _957438), _957440)))], (10205 ^ _780086) ^ [_957593, _957595, _957597, _957599] : [class_Orderings_Olinorder(_957593), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_957593), hAPP(hAPP(c_Orderings_Oord__class_Omin(_957593), _957595), _957597)), _957599) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_957593), hAPP(hAPP(c_Orderings_Oord__class_Omax(_957593), _957595), _957599)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_957593), _957597), _957599)))], (10211 ^ _780086) ^ [_957752, _957754, _957756, _957758] : [class_Orderings_Olinorder(_957752), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_957752), hAPP(hAPP(c_Orderings_Oord__class_Omin(_957752), _957754), _957756)), _957758) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_957752), _957754), hAPP(hAPP(c_Orderings_Oord__class_Omin(_957752), _957756), _957758)))], (10217 ^ _780086) ^ [_957895, _957897, _957899, _957901] : [class_Orderings_Olinorder(_957895), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_957895), hAPP(hAPP(c_Orderings_Oord__class_Omin(_957895), _957897), _957899)), _957901) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_957895), _957897), hAPP(hAPP(c_Orderings_Oord__class_Omin(_957895), _957899), _957901)))], (10223 ^ _780086) ^ [_958038, _958040, _958042, _958044] : [class_Orderings_Olinorder(_958038), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_958038), hAPP(hAPP(c_Orderings_Oord__class_Omax(_958038), _958040), _958042)), _958044) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_958038), _958040), hAPP(hAPP(c_Orderings_Oord__class_Omax(_958038), _958042), _958044)))], (10229 ^ _780086) ^ [_958181, _958183, _958185, _958187] : [class_Orderings_Olinorder(_958181), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_958181), hAPP(hAPP(c_Orderings_Oord__class_Omax(_958181), _958183), _958185)), _958187) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_958181), _958183), hAPP(hAPP(c_Orderings_Oord__class_Omax(_958181), _958185), _958187)))], (10235 ^ _780086) ^ [_958324, _958326, _958328] : [class_Lattices_Oboolean__algebra(_958324), 10238 ^ _780086 : [(10239 ^ _780086) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_958324), _958326) = hAPP(c_Groups_Ouminus__class_Ouminus(_958324), _958328), -(_958326 = _958328)], (10245 ^ _780086) ^ [] : [_958326 = _958328, -(hAPP(c_Groups_Ouminus__class_Ouminus(_958324), _958326) = hAPP(c_Groups_Ouminus__class_Ouminus(_958324), _958328))]]], (10251 ^ _780086) ^ [_958565, _958567, _958569, _958571] : [class_Orderings_Olinorder(_958565), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_958565), _958567), hAPP(hAPP(c_Orderings_Oord__class_Omax(_958565), _958569), _958571)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_958565), hAPP(hAPP(c_Orderings_Oord__class_Omin(_958565), _958567), _958569)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_958565), _958567), _958571)))], (10257 ^ _780086) ^ [_958724, _958726, _958728, _958730] : [class_Orderings_Olinorder(_958724), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_958724), _958726), hAPP(hAPP(c_Orderings_Oord__class_Omin(_958724), _958728), _958730)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_958724), hAPP(hAPP(c_Orderings_Oord__class_Omax(_958724), _958726), _958728)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_958724), _958726), _958730)))], (10263 ^ _780086) ^ [_958883, _958885, _958887, _958889] : [class_Orderings_Olinorder(_958883), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_958883), _958885), hAPP(hAPP(c_Orderings_Oord__class_Omin(_958883), _958887), _958889)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_958883), _958887), hAPP(hAPP(c_Orderings_Oord__class_Omin(_958883), _958885), _958889)))], (10269 ^ _780086) ^ [_959026, _959028, _959030, _959032] : [class_Orderings_Olinorder(_959026), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_959026), _959028), hAPP(hAPP(c_Orderings_Oord__class_Omin(_959026), _959030), _959032)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_959026), _959030), hAPP(hAPP(c_Orderings_Oord__class_Omin(_959026), _959028), _959032)))], (10275 ^ _780086) ^ [_959169, _959171, _959173, _959175] : [class_Orderings_Olinorder(_959169), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_959169), _959171), hAPP(hAPP(c_Orderings_Oord__class_Omax(_959169), _959173), _959175)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_959169), _959173), hAPP(hAPP(c_Orderings_Oord__class_Omax(_959169), _959171), _959175)))], (10281 ^ _780086) ^ [_959312, _959314, _959316, _959318] : [class_Orderings_Olinorder(_959312), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_959312), _959314), hAPP(hAPP(c_Orderings_Oord__class_Omax(_959312), _959316), _959318)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_959312), _959316), hAPP(hAPP(c_Orderings_Oord__class_Omax(_959312), _959314), _959318)))], (10287 ^ _780086) ^ [_959455, _959457, _959459] : [class_Orderings_Olinorder(_959455), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_959455), _959457), hAPP(hAPP(c_Orderings_Oord__class_Omin(_959455), _959457), _959459)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_959455), _959457), _959459))], (10293 ^ _780086) ^ [_959580, _959582, _959584] : [class_Orderings_Olinorder(_959580), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_959580), _959582), hAPP(hAPP(c_Orderings_Oord__class_Omin(_959580), _959582), _959584)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_959580), _959582), _959584))], (10299 ^ _780086) ^ [_959705, _959707, _959709] : [class_Orderings_Olinorder(_959705), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_959705), _959707), hAPP(hAPP(c_Orderings_Oord__class_Omax(_959705), _959707), _959709)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_959705), _959707), _959709))], (10305 ^ _780086) ^ [_959830, _959832, _959834] : [class_Orderings_Olinorder(_959830), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_959830), _959832), hAPP(hAPP(c_Orderings_Oord__class_Omax(_959830), _959832), _959834)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_959830), _959832), _959834))], (10311 ^ _780086) ^ [_959955, _959957, _959959] : [class_Orderings_Olinorder(_959955), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_959955), _959957), hAPP(hAPP(c_Orderings_Oord__class_Omax(_959955), _959957), _959959)) = _959957)], (10317 ^ _780086) ^ [_960064, _960066, _960068] : [class_Orderings_Olinorder(_960064), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_960064), _960066), hAPP(hAPP(c_Orderings_Oord__class_Omin(_960064), _960066), _960068)) = _960066)], (10323 ^ _780086) ^ [_960173, _960175, _960177] : [class_Orderings_Olinorder(_960173), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_960173), _960175), _960177) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_960173), _960177), _960175))], (10329 ^ _780086) ^ [_960282, _960284, _960286] : [class_Orderings_Olinorder(_960282), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_960282), _960284), _960286) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_960282), _960286), _960284))], (10335 ^ _780086) ^ [_960391, _960393, _960395] : [class_Orderings_Olinorder(_960391), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_960391), _960393), _960395) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_960391), _960395), _960393))], (10341 ^ _780086) ^ [_960500, _960502, _960504] : [class_Orderings_Olinorder(_960500), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_960500), _960502), _960504) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_960500), _960504), _960502))], (10347 ^ _780086) ^ [_960609, _960611, _960613, _960615] : [class_Groups_Ouminus(_960609), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_960611, _960609)), _960613), _960615) = hAPP(c_Groups_Ouminus__class_Ouminus(_960609), hAPP(_960613, _960615)))], (10353 ^ _780086) ^ [_960726, _960728] : [class_Orderings_Olinorder(_960726), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_960726), _960728), _960728) = _960728)], (10359 ^ _780086) ^ [_960817, _960819] : [class_Orderings_Olinorder(_960817), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_960817), _960819), _960819) = _960819)], (10365 ^ _780086) ^ [_960908, _960910] : [class_Lattices_Oboolean__algebra(_960908), -(hAPP(c_Groups_Ouminus__class_Ouminus(_960908), hAPP(c_Groups_Ouminus__class_Ouminus(_960908), _960910)) = _960910)], (10371 ^ _780086) ^ [_961003, _961005, _961007, _961009] : [class_Groups_Ouminus(_961003), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_961005, _961003)), _961007), _961009) = hAPP(c_Groups_Ouminus__class_Ouminus(_961003), hAPP(_961007, _961009)))], (10377 ^ _780086) ^ [_961120, _961122] : [class_Orderings_Olinorder(_961120), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_961120), _961122), _961122) = _961122)], (10383 ^ _780086) ^ [_961211, _961213] : [class_Orderings_Olinorder(_961211), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_961211), _961213), _961213) = _961213)], (10389 ^ _780086) ^ [_961302, _961304, _961306, _961308] : [class_Orderings_Olinorder(_961302), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961302), hAPP(hAPP(c_Orderings_Oord__class_Omax(_961302), _961304), _961306)), _961308)), 10396 ^ _780086 : [(10397 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961302), _961304), _961308)))], (10399 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961302), _961306), _961308)))]]], (10401 ^ _780086) ^ [_961525, _961527, _961529, _961531, _961533] : [class_Orderings_Olinorder(_961525), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961525), _961527), _961529)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961525), _961531), _961533)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961525), hAPP(hAPP(c_Orderings_Oord__class_Omax(_961525), _961527), _961531)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_961525), _961529), _961533))))], (10415 ^ _780086) ^ [_961796, _961798, _961800, _961802] : [class_Orderings_Olinorder(_961796), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961796), _961798), _961800)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961796), _961802), _961800)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961796), hAPP(hAPP(c_Orderings_Oord__class_Omax(_961796), _961798), _961802)), _961800)))], (10429 ^ _780086) ^ [_962045, _962047, _962049, _962051] : [class_Orderings_Olinorder(_962045), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962045), _962047), _962049)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962045), _962051), _962049)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962045), hAPP(hAPP(c_Orderings_Oord__class_Omax(_962045), _962047), _962051)), _962049)))], (10443 ^ _780086) ^ [_962294, _962296, _962298] : [class_Orderings_Olinorder(_962294), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962294), _962296), _962298)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_962294), _962298), _962296) = _962298)], (10453 ^ _780086) ^ [_962455, _962457, _962459] : [class_Orderings_Olinorder(_962455), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962455), _962457), _962459)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_962455), _962457), _962459) = _962459)], (10463 ^ _780086) ^ [_962616, _962618, _962620, _962622] : [class_Orderings_Olinorder(_962616), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962616), _962618), _962620)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962616), _962618), hAPP(hAPP(c_Orderings_Oord__class_Omax(_962616), _962622), _962620))))], (10473 ^ _780086) ^ [_962795, _962797, _962799, _962801] : [class_Orderings_Olinorder(_962795), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962795), _962797), _962799)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962795), _962797), hAPP(hAPP(c_Orderings_Oord__class_Omax(_962795), _962799), _962801))))], (10483 ^ _780086) ^ [_962974, _962976, _962978, _962980] : [class_Orderings_Olinorder(_962974), 10486 ^ _780086 : [(10487 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962974), hAPP(hAPP(c_Orderings_Oord__class_Omax(_962974), _962976), _962978)), _962980)), 10490 ^ _780086 : [(10491 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962974), _962976), _962980)))], (10493 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962974), _962978), _962980)))]]], (10495 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962974), hAPP(hAPP(c_Orderings_Oord__class_Omax(_962974), _962976), _962978)), _962980))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962974), _962976), _962980)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962974), _962978), _962980))]]], (10505 ^ _780086) ^ [_963354, _963356, _963358] : [class_Orderings_Olinorder(_963354), 10508 ^ _780086 : [(10509 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963354), _963356), _963358)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_963354), _963356), _963358) = _963358)], (10515 ^ _780086) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omax(_963354), _963356), _963358) = _963358, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963354), _963356), _963358)))]]], (10521 ^ _780086) ^ [_963610, _963612, _963614] : [class_Orderings_Olinorder(_963610), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963610), _963612), hAPP(hAPP(c_Orderings_Oord__class_Omax(_963610), _963614), _963612))))], (10527 ^ _780086) ^ [_963717, _963719, _963721] : [class_Orderings_Olinorder(_963717), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963717), _963719), hAPP(hAPP(c_Orderings_Oord__class_Omax(_963717), _963719), _963721))))], (10533 ^ _780086) ^ [_963824, _963826, _963828, _963830] : [class_Orderings_Olinorder(_963824), 10536 ^ _780086 : [(10547 ^ _780086) ^ [] : [10548 ^ _780086 : [(10549 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963824), _963826), _963828))], (10551 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963824), _963826), _963830))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963824), _963826), hAPP(hAPP(c_Orderings_Oord__class_Omax(_963824), _963828), _963830))))], (10537 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963824), _963826), hAPP(hAPP(c_Orderings_Oord__class_Omax(_963824), _963828), _963830))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963824), _963826), _963828))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963824), _963826), _963830)))]]], (10555 ^ _780086) ^ [_964173, _964175, _964177] : [class_Lattices_Oboolean__algebra(_964173), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964173), _964175), _964177)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964173), hAPP(c_Groups_Ouminus__class_Ouminus(_964173), _964177)), hAPP(c_Groups_Ouminus__class_Ouminus(_964173), _964175))))], (10565 ^ _780086) ^ [_964352, _964354, _964356] : [class_Lattices_Oboolean__algebra(_964352), 10568 ^ _780086 : [(10569 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964352), hAPP(c_Groups_Ouminus__class_Ouminus(_964352), _964354)), hAPP(c_Groups_Ouminus__class_Ouminus(_964352), _964356))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964352), _964356), _964354)))], (10575 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964352), _964356), _964354)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964352), hAPP(c_Groups_Ouminus__class_Ouminus(_964352), _964354)), hAPP(c_Groups_Ouminus__class_Ouminus(_964352), _964356))))]]], (10581 ^ _780086) ^ [_964635, _964637, _964639] : [class_Groups_Oordered__ab__group__add(_964635), 10584 ^ _780086 : [(10585 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964635), _964637), hAPP(c_Groups_Ouminus__class_Ouminus(_964635), _964639))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964635), _964639), hAPP(c_Groups_Ouminus__class_Ouminus(_964635), _964637))))], (10591 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964635), _964639), hAPP(c_Groups_Ouminus__class_Ouminus(_964635), _964637))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964635), _964637), hAPP(c_Groups_Ouminus__class_Ouminus(_964635), _964639))))]]], (10597 ^ _780086) ^ [_964918, _964920, _964922] : [class_Groups_Oordered__ab__group__add(_964918), 10600 ^ _780086 : [(10601 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964918), hAPP(c_Groups_Ouminus__class_Ouminus(_964918), _964920)), _964922)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964918), hAPP(c_Groups_Ouminus__class_Ouminus(_964918), _964922)), _964920)))], (10607 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964918), hAPP(c_Groups_Ouminus__class_Ouminus(_964918), _964922)), _964920)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964918), hAPP(c_Groups_Ouminus__class_Ouminus(_964918), _964920)), _964922)))]]], (10613 ^ _780086) ^ [_965201, _965203, _965205] : [class_Groups_Oordered__ab__group__add(_965201), 10616 ^ _780086 : [(10617 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965201), hAPP(c_Groups_Ouminus__class_Ouminus(_965201), _965203)), hAPP(c_Groups_Ouminus__class_Ouminus(_965201), _965205))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965201), _965205), _965203)))], (10623 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965201), _965205), _965203)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965201), hAPP(c_Groups_Ouminus__class_Ouminus(_965201), _965203)), hAPP(c_Groups_Ouminus__class_Ouminus(_965201), _965205))))]]], (10629 ^ _780086) ^ [_965484, _965486, _965488] : [class_Groups_Oordered__ab__group__add(_965484), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965484), _965486), _965488)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965484), hAPP(c_Groups_Ouminus__class_Ouminus(_965484), _965488)), hAPP(c_Groups_Ouminus__class_Ouminus(_965484), _965486))))], (10639 ^ _780086) ^ [_965663, _965665, _965667, _965669] : [class_Orderings_Olinorder(_965663), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965663), _965665), hAPP(hAPP(c_Orderings_Oord__class_Omin(_965663), _965667), _965669))), 10646 ^ _780086 : [(10647 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965663), _965665), _965667)))], (10649 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965663), _965665), _965669)))]]], (10651 ^ _780086) ^ [_965886, _965888, _965890, _965892, _965894] : [class_Orderings_Olinorder(_965886), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965886), _965888), _965890)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965886), _965892), _965894)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965886), hAPP(hAPP(c_Orderings_Oord__class_Omin(_965886), _965888), _965892)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_965886), _965890), _965894))))], (10665 ^ _780086) ^ [_966157, _966159, _966161, _966163] : [class_Orderings_Olinorder(_966157), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966157), _966159), _966161)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966157), _966159), _966163)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966157), _966159), hAPP(hAPP(c_Orderings_Oord__class_Omin(_966157), _966161), _966163))))], (10679 ^ _780086) ^ [_966406, _966408, _966410, _966412] : [class_Orderings_Olinorder(_966406), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966406), _966408), _966410)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966406), _966408), _966412)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966406), _966408), hAPP(hAPP(c_Orderings_Oord__class_Omin(_966406), _966410), _966412))))], (10693 ^ _780086) ^ [_966655, _966657, _966659] : [class_Orderings_Olinorder(_966655), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966655), _966657), _966659)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_966655), _966659), _966657) = _966657)], (10703 ^ _780086) ^ [_966816, _966818, _966820] : [class_Orderings_Olinorder(_966816), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966816), _966818), _966820)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_966816), _966818), _966820) = _966818)], (10713 ^ _780086) ^ [_966977, _966979, _966981, _966983] : [class_Orderings_Olinorder(_966977), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966977), _966979), _966981)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966977), hAPP(hAPP(c_Orderings_Oord__class_Omin(_966977), _966983), _966979)), _966981)))], (10723 ^ _780086) ^ [_967156, _967158, _967160, _967162] : [class_Orderings_Olinorder(_967156), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967156), _967158), _967160)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967156), hAPP(hAPP(c_Orderings_Oord__class_Omin(_967156), _967158), _967162)), _967160)))], (10733 ^ _780086) ^ [_967335, _967337, _967339, _967341] : [class_Orderings_Olinorder(_967335), 10736 ^ _780086 : [(10737 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967335), _967337), hAPP(hAPP(c_Orderings_Oord__class_Omin(_967335), _967339), _967341))), 10740 ^ _780086 : [(10741 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967335), _967337), _967339)))], (10743 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967335), _967337), _967341)))]]], (10745 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967335), _967337), hAPP(hAPP(c_Orderings_Oord__class_Omin(_967335), _967339), _967341)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967335), _967337), _967339)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967335), _967337), _967341))]]], (10755 ^ _780086) ^ [_967715, _967717, _967719] : [class_Orderings_Olinorder(_967715), 10758 ^ _780086 : [(10759 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967715), _967717), _967719)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_967715), _967717), _967719) = _967717)], (10765 ^ _780086) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omin(_967715), _967717), _967719) = _967717, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967715), _967717), _967719)))]]], (10771 ^ _780086) ^ [_967971, _967973, _967975] : [class_Orderings_Olinorder(_967971), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967971), hAPP(hAPP(c_Orderings_Oord__class_Omin(_967971), _967973), _967975)), _967975)))], (10777 ^ _780086) ^ [_968078, _968080, _968082] : [class_Orderings_Olinorder(_968078), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968078), hAPP(hAPP(c_Orderings_Oord__class_Omin(_968078), _968080), _968082)), _968080)))], (10783 ^ _780086) ^ [_968185, _968187, _968189, _968191] : [class_Orderings_Olinorder(_968185), 10786 ^ _780086 : [(10797 ^ _780086) ^ [] : [10798 ^ _780086 : [(10799 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968185), _968187), _968191))], (10801 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968185), _968189), _968191))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968185), hAPP(hAPP(c_Orderings_Oord__class_Omin(_968185), _968187), _968189)), _968191)))], (10787 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968185), hAPP(hAPP(c_Orderings_Oord__class_Omin(_968185), _968187), _968189)), _968191)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968185), _968187), _968191))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968185), _968189), _968191)))]]], (10805 ^ _780086) ^ [_968534, _968536, _968538, _968540] : [class_Orderings_Olinorder(_968534), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_968534), _968536), _968538)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_968534), _968536), hAPP(hAPP(c_Orderings_Oord__class_Omax(_968534), _968540), _968538))))], (10815 ^ _780086) ^ [_968713, _968715, _968717, _968719] : [class_Orderings_Olinorder(_968713), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_968713), _968715), _968717)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_968713), _968715), hAPP(hAPP(c_Orderings_Oord__class_Omax(_968713), _968717), _968719))))], (10825 ^ _780086) ^ [_968892, _968894, _968896, _968898] : [class_Orderings_Olinorder(_968892), 10828 ^ _780086 : [(10829 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_968892), hAPP(hAPP(c_Orderings_Oord__class_Omax(_968892), _968894), _968896)), _968898)), 10832 ^ _780086 : [(10833 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_968892), _968894), _968898)))], (10835 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_968892), _968896), _968898)))]]], (10837 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_968892), hAPP(hAPP(c_Orderings_Oord__class_Omax(_968892), _968894), _968896)), _968898))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_968892), _968894), _968898)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_968892), _968896), _968898))]]], (10847 ^ _780086) ^ [_969272, _969274, _969276, _969278] : [class_Orderings_Olinorder(_969272), 10850 ^ _780086 : [(10861 ^ _780086) ^ [] : [10862 ^ _780086 : [(10863 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969272), _969274), _969276))], (10865 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969272), _969274), _969278))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969272), _969274), hAPP(hAPP(c_Orderings_Oord__class_Omax(_969272), _969276), _969278))))], (10851 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969272), _969274), hAPP(hAPP(c_Orderings_Oord__class_Omax(_969272), _969276), _969278))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969272), _969274), _969276))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969272), _969274), _969278)))]]], (10869 ^ _780086) ^ [_969621, _969623, _969625] : [class_Groups_Oordered__ab__group__add(_969621), 10872 ^ _780086 : [(10873 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969621), hAPP(c_Groups_Ouminus__class_Ouminus(_969621), _969623)), hAPP(c_Groups_Ouminus__class_Ouminus(_969621), _969625))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969621), _969625), _969623)))], (10879 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969621), _969625), _969623)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969621), hAPP(c_Groups_Ouminus__class_Ouminus(_969621), _969623)), hAPP(c_Groups_Ouminus__class_Ouminus(_969621), _969625))))]]], (10885 ^ _780086) ^ [_969904, _969906, _969908] : [class_Groups_Oordered__ab__group__add(_969904), 10888 ^ _780086 : [(10889 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969904), hAPP(c_Groups_Ouminus__class_Ouminus(_969904), _969906)), _969908)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969904), hAPP(c_Groups_Ouminus__class_Ouminus(_969904), _969908)), _969906)))], (10895 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969904), hAPP(c_Groups_Ouminus__class_Ouminus(_969904), _969908)), _969906)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969904), hAPP(c_Groups_Ouminus__class_Ouminus(_969904), _969906)), _969908)))]]], (10901 ^ _780086) ^ [_970187, _970189, _970191] : [class_Groups_Oordered__ab__group__add(_970187), 10904 ^ _780086 : [(10905 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970187), _970189), hAPP(c_Groups_Ouminus__class_Ouminus(_970187), _970191))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970187), _970191), hAPP(c_Groups_Ouminus__class_Ouminus(_970187), _970189))))], (10911 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970187), _970191), hAPP(c_Groups_Ouminus__class_Ouminus(_970187), _970189))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970187), _970189), hAPP(c_Groups_Ouminus__class_Ouminus(_970187), _970191))))]]], (10917 ^ _780086) ^ [_970470, _970472, _970474, _970476] : [class_Orderings_Olinorder(_970470), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970470), _970472), _970474)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970470), hAPP(hAPP(c_Orderings_Oord__class_Omin(_970470), _970476), _970472)), _970474)))], (10927 ^ _780086) ^ [_970649, _970651, _970653, _970655] : [class_Orderings_Olinorder(_970649), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970649), _970651), _970653)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970649), hAPP(hAPP(c_Orderings_Oord__class_Omin(_970649), _970651), _970655)), _970653)))], (10937 ^ _780086) ^ [_970828, _970830, _970832, _970834] : [class_Orderings_Olinorder(_970828), 10940 ^ _780086 : [(10951 ^ _780086) ^ [] : [10952 ^ _780086 : [(10953 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970828), _970830), _970834))], (10955 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970828), _970832), _970834))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970828), hAPP(hAPP(c_Orderings_Oord__class_Omin(_970828), _970830), _970832)), _970834)))], (10941 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970828), hAPP(hAPP(c_Orderings_Oord__class_Omin(_970828), _970830), _970832)), _970834)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970828), _970830), _970834))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970828), _970832), _970834)))]]], (10959 ^ _780086) ^ [_971177, _971179, _971181, _971183] : [class_Orderings_Olinorder(_971177), 10962 ^ _780086 : [(10963 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971177), _971179), hAPP(hAPP(c_Orderings_Oord__class_Omin(_971177), _971181), _971183))), 10966 ^ _780086 : [(10967 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971177), _971179), _971181)))], (10969 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971177), _971179), _971183)))]]], (10971 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971177), _971179), hAPP(hAPP(c_Orderings_Oord__class_Omin(_971177), _971181), _971183)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971177), _971179), _971181)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971177), _971179), _971183))]]], (10981 ^ _780086) ^ [_971557, _971559, _971561, _971563] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_971557), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971557), hAPP(hAPP(c_Orderings_Oord__class_Omax(_971557), _971559), _971561)), _971563) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_971557), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971557), _971559), _971563)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971557), _971561), _971563)))], (10987 ^ _780086) ^ [_971716, _971718, _971720] : [class_Groups_Oab__group__add(_971716), -(hAPP(c_Groups_Ouminus__class_Ouminus(_971716), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971716), _971718), _971720)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971716), hAPP(c_Groups_Ouminus__class_Ouminus(_971716), _971718)), hAPP(c_Groups_Ouminus__class_Ouminus(_971716), _971720)))], (10993 ^ _780086) ^ [_971855, _971857, _971859] : [class_Groups_Ogroup__add(_971855), -(hAPP(c_Groups_Ouminus__class_Ouminus(_971855), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971855), _971857), _971859)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971855), hAPP(c_Groups_Ouminus__class_Ouminus(_971855), _971859)), hAPP(c_Groups_Ouminus__class_Ouminus(_971855), _971857)))], (10999 ^ _780086) ^ [_971994, _971996, _971998] : [class_Groups_Ogroup__add(_971994), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971994), _971996), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971994), hAPP(c_Groups_Ouminus__class_Ouminus(_971994), _971996)), _971998)) = _971998)], (11005 ^ _780086) ^ [_972113, _972115, _972117] : [class_Groups_Ogroup__add(_972113), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972113), hAPP(c_Groups_Ouminus__class_Ouminus(_972113), _972115)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972113), _972115), _972117)) = _972117)], (11011 ^ _780086) ^ [_972232, _972234, _972236] : [class_Rings_Oring(_972232), -(hAPP(c_Groups_Ouminus__class_Ouminus(_972232), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972232), _972234), _972236)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972232), _972234), hAPP(c_Groups_Ouminus__class_Ouminus(_972232), _972236)))], (11017 ^ _780086) ^ [_972361, _972363, _972365] : [class_Rings_Oring(_972361), -(hAPP(c_Groups_Ouminus__class_Ouminus(_972361), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972361), _972363), _972365)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972361), hAPP(c_Groups_Ouminus__class_Ouminus(_972361), _972363)), _972365))], (11023 ^ _780086) ^ [_972490, _972492, _972494] : [class_Rings_Oring(_972490), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972490), hAPP(c_Groups_Ouminus__class_Ouminus(_972490), _972492)), _972494) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972490), _972492), hAPP(c_Groups_Ouminus__class_Ouminus(_972490), _972494)))], (11029 ^ _780086) ^ [_972619, _972621, _972623] : [class_Rings_Oring(_972619), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972619), hAPP(c_Groups_Ouminus__class_Ouminus(_972619), _972621)), hAPP(c_Groups_Ouminus__class_Ouminus(_972619), _972623)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972619), _972621), _972623))], (11035 ^ _780086) ^ [_972748, _972750, _972752] : [class_Rings_Oidom(_972748), 11038 ^ _780086 : [(11049 ^ _780086) ^ [] : [11050 ^ _780086 : [(11051 ^ _780086) ^ [] : [_972750 = _972752], (11053 ^ _780086) ^ [] : [_972750 = hAPP(c_Groups_Ouminus__class_Ouminus(_972748), _972752)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972748), _972750), _972750) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972748), _972752), _972752))], (11039 ^ _780086) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972748), _972750), _972750) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972748), _972752), _972752), -(_972750 = _972752), -(_972750 = hAPP(c_Groups_Ouminus__class_Ouminus(_972748), _972752))]]], (11057 ^ _780086) ^ [_973067, _973069, _973071, _973073] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_973067), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973067), hAPP(hAPP(c_Orderings_Oord__class_Omin(_973067), _973069), _973071)), _973073) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_973067), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973067), _973069), _973073)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973067), _973071), _973073)))], (11063 ^ _780086) ^ [_973226, _973228, _973230] : [hBOOL(hAPP(hAPP(c_member(_973226), _973228), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_973226, tc_HOL_Obool)), _973230))), hBOOL(hAPP(hAPP(c_member(_973226), _973228), _973230))], (11069 ^ _780086) ^ [_973350, _973352, _973354] : [hBOOL(hAPP(hAPP(c_member(_973350), _973352), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_973350, tc_HOL_Obool)), _973354))), hBOOL(hAPP(hAPP(c_member(_973350), _973352), _973354))], (11075 ^ _780086) ^ [_973492, _973494, _973496] : [hBOOL(hAPP(hAPP(c_member(_973492), _973494), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_973492, tc_HOL_Obool)), _973496))), hBOOL(hAPP(hAPP(c_member(_973492), _973494), _973496))], (11081 ^ _780086) ^ [_973610, _973612, _973614] : [-(hBOOL(hAPP(hAPP(c_member(_973610), _973612), _973614))), -(hBOOL(hAPP(hAPP(c_member(_973610), _973612), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_973610, tc_HOL_Obool)), _973614))))], (11087 ^ _780086) ^ [_973672, _973674] : [class_Orderings_Olinorder(_973672), hBOOL(hAPP(c_Finite__Set_Ofinite(_973672), _973674)), -(c_Big__Operators_Olinorder__class_OMax(_973672, _973674) = hAPP(c_Finite__Set_Ofold1(_973672, c_Orderings_Oord__class_Omax(_973672)), _973674))], (11097 ^ _780086) ^ [_973829, _973831] : [class_Orderings_Olinorder(_973829), hBOOL(hAPP(c_Finite__Set_Ofinite(_973829), _973831)), -(c_Big__Operators_Olinorder__class_OMin(_973829, _973831) = hAPP(c_Finite__Set_Ofold1(_973829, c_Orderings_Oord__class_Omin(_973829)), _973831))], (11107 ^ _780086) ^ [_973986, _973988, _973990, _973992] : [class_Groups_Oordered__ab__group__add(_973986), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_973986), hAPP(hAPP(c_Orderings_Oord__class_Omax(_973986), _973988), _973990)), _973992) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_973986), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_973986), _973988), _973992)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_973986), _973990), _973992)))], (11113 ^ _780086) ^ [_974145, _974147, _974149] : [class_Groups_Oab__group__add(_974145), -(hAPP(c_Groups_Ouminus__class_Ouminus(_974145), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_974145), _974147), _974149)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_974145), _974149), _974147))], (11119 ^ _780086) ^ [_974264, _974266, _974268, _974270] : [class_Groups_Oordered__ab__group__add(_974264), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_974264), hAPP(hAPP(c_Orderings_Oord__class_Omin(_974264), _974266), _974268)), _974270) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_974264), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_974264), _974266), _974270)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_974264), _974268), _974270)))], (11125 ^ _780086) ^ [_974423, _974425, _974427] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_974423, tc_HOL_Obool)), _974425), _974427)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_974423, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_974423, tc_HOL_Obool)), _974427)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_974423, tc_HOL_Obool)), _974425))))], (11131 ^ _780086) ^ [_974592, _974594, _974596] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_974592, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_974592, tc_HOL_Obool)), _974594)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_974592, tc_HOL_Obool)), _974596))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_974592, tc_HOL_Obool)), _974596), _974594)))], (11137 ^ _780086) ^ [_974739, _974741, _974743] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_974739, tc_HOL_Obool)), _974743), _974741)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_974739, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_974739, tc_HOL_Obool)), _974741)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_974739, tc_HOL_Obool)), _974743))))], (11143 ^ _780086) ^ [_974892, _974894, _974896, _974898, _974900] : [class_Groups_Ocomm__monoid__mult(_974892), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_974894, _974892), hAPP(hAPP(c_COMBS(_974894, _974892, _974892), hAPP(hAPP(c_COMBB(_974892, tc_fun(_974892, _974892), _974894), c_Groups_Otimes__class_Otimes(_974892)), _974896)), _974898)), _974900) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_974892), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_974894, _974892), _974896), _974900)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_974894, _974892), _974898), _974900)))], (11149 ^ _780086) ^ [_975093] : [class_Orderings_Olinorder(_975093), -(c_Finite__Set_Ofun__left__comm__idem(_975093, _975093, c_Orderings_Oord__class_Omax(_975093)))], (11155 ^ _780086) ^ [_975172] : [class_Orderings_Olinorder(_975172), -(c_Finite__Set_Ofun__left__comm__idem(_975172, _975172, c_Orderings_Oord__class_Omin(_975172)))], (11161 ^ _780086) ^ [_975251, _975253, _975255] : [class_Orderings_Olinorder(_975251), hBOOL(hAPP(c_Finite__Set_Ofinite(_975251), _975253)), hBOOL(hAPP(hAPP(c_member(_975251), _975255), _975253)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975251), hAPP(c_Finite__Set_Ofold1(_975251, c_Orderings_Oord__class_Omin(_975251)), _975253)), _975255)))], (11175 ^ _780086) ^ [_975488, _975490, _975492] : [class_Orderings_Olinorder(_975488), hBOOL(hAPP(c_Finite__Set_Ofinite(_975488), _975490)), -(_975490 = c_Orderings_Obot__class_Obot(tc_fun(_975488, tc_HOL_Obool))), 11186 ^ _780086 : [(11187 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975488), hAPP(c_Finite__Set_Ofold1(_975488, c_Orderings_Oord__class_Omin(_975488)), _975490)), _975492)), 11191 ^ _780086 : [(11192 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_975488), 11190 ^ [_975488, _975490, _975492]), _975490)))], (11194 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975488), 11190 ^ [_975488, _975490, _975492]), _975492)))]]], (11196 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975488), hAPP(c_Finite__Set_Ofold1(_975488, c_Orderings_Oord__class_Omin(_975488)), _975490)), _975492))), 11197 ^ _780086 : [(11198 ^ _780086) ^ [_975877] : [hBOOL(hAPP(hAPP(c_member(_975488), _975877), _975490)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975488), _975877), _975492))]]]]], (11206 ^ _780086) ^ [_976038, _976040, _976042] : [class_Orderings_Olinorder(_976038), hBOOL(hAPP(c_Finite__Set_Ofinite(_976038), _976040)), -(_976040 = c_Orderings_Obot__class_Obot(tc_fun(_976038, tc_HOL_Obool))), 11217 ^ _780086 : [(11228 ^ _780086) ^ [] : [11230 ^ _780086 : [(11231 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_976038), 11229 ^ [_976038, _976040, _976042]), _976040)))], (11233 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976038), _976042), 11229 ^ [_976038, _976040, _976042]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976038), _976042), hAPP(c_Finite__Set_Ofold1(_976038, c_Orderings_Oord__class_Omin(_976038)), _976040))))], (11218 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976038), _976042), hAPP(c_Finite__Set_Ofold1(_976038, c_Orderings_Oord__class_Omin(_976038)), _976040))), 11221 ^ _780086 : [(11222 ^ _780086) ^ [_976331] : [hBOOL(hAPP(hAPP(c_member(_976038), _976331), _976040)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976038), _976042), _976331)))]]]]], (11237 ^ _780086) ^ [_976616, _976618, _976620, _976622] : [class_Groups_Oab__group__add(_976616), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_976618, _976616), hAPP(hAPP(c_COMBB(_976616, _976616, _976618), c_Groups_Ouminus__class_Ouminus(_976616)), _976620)), _976622) = hAPP(c_Groups_Ouminus__class_Ouminus(_976616), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_976618, _976616), _976620), _976622)))], (11243 ^ _780086) ^ [_976765, _976767, _976769] : [class_Orderings_Olinorder(_976765), hBOOL(hAPP(c_Finite__Set_Ofinite(_976765), _976767)), -(_976767 = c_Orderings_Obot__class_Obot(tc_fun(_976765, tc_HOL_Obool))), 11254 ^ _780086 : [(11255 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_976765), hAPP(c_Finite__Set_Ofold1(_976765, c_Orderings_Oord__class_Omin(_976765)), _976767)), _976769)), 11259 ^ _780086 : [(11260 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_976765), 11258 ^ [_976765, _976767, _976769]), _976767)))], (11262 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_976765), 11258 ^ [_976765, _976767, _976769]), _976769)))]]], (11264 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_976765), hAPP(c_Finite__Set_Ofold1(_976765, c_Orderings_Oord__class_Omin(_976765)), _976767)), _976769))), 11265 ^ _780086 : [(11266 ^ _780086) ^ [_977154] : [hBOOL(hAPP(hAPP(c_member(_976765), _977154), _976767)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_976765), _977154), _976769))]]]]], (11274 ^ _780086) ^ [_977315, _977317, _977319] : [class_Orderings_Olinorder(_977315), hBOOL(hAPP(c_Finite__Set_Ofinite(_977315), _977317)), -(_977317 = c_Orderings_Obot__class_Obot(tc_fun(_977315, tc_HOL_Obool))), 11285 ^ _780086 : [(11296 ^ _780086) ^ [] : [11298 ^ _780086 : [(11299 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_977315), 11297 ^ [_977315, _977317, _977319]), _977317)))], (11301 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_977315), _977319), 11297 ^ [_977315, _977317, _977319]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_977315), _977319), hAPP(c_Finite__Set_Ofold1(_977315, c_Orderings_Oord__class_Omin(_977315)), _977317))))], (11286 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_977315), _977319), hAPP(c_Finite__Set_Ofold1(_977315, c_Orderings_Oord__class_Omin(_977315)), _977317))), 11289 ^ _780086 : [(11290 ^ _780086) ^ [_977608] : [hBOOL(hAPP(hAPP(c_member(_977315), _977608), _977317)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_977315), _977319), _977608)))]]]]], (11305 ^ _780086) ^ [_977893, _977895, _977897] : [class_Orderings_Olinorder(_977893), -(_977895 = c_Orderings_Obot__class_Obot(tc_fun(_977893, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_977893, tc_HOL_Obool)), _977895), _977897)), hBOOL(hAPP(c_Finite__Set_Ofinite(_977893), _977897)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977893), hAPP(c_Finite__Set_Ofold1(_977893, c_Orderings_Oord__class_Omin(_977893)), _977897)), hAPP(c_Finite__Set_Ofold1(_977893, c_Orderings_Oord__class_Omin(_977893)), _977895))))], (11323 ^ _780086) ^ [_978219, _978221, _978223] : [class_Groups_Ogroup__add(_978219), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_978219), _978221), _978223) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_978219), _978221), hAPP(c_Groups_Ouminus__class_Ouminus(_978219), _978223)))], (11329 ^ _780086) ^ [_978338, _978340, _978342] : [class_Groups_Oab__group__add(_978338), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_978338), _978340), _978342) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_978338), _978340), hAPP(c_Groups_Ouminus__class_Ouminus(_978338), _978342)))], (11335 ^ _780086) ^ [_978457, _978459, _978461] : [class_Groups_Ogroup__add(_978457), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_978457), _978459), hAPP(c_Groups_Ouminus__class_Ouminus(_978457), _978461)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_978457), _978459), _978461))], (11341 ^ _780086) ^ [_978576, _978578, _978580] : [class_Rings_Ocomm__ring__1(_978576), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_978576), _978578), _978580) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_978576), _978578), hAPP(c_Groups_Ouminus__class_Ouminus(_978576), _978580)))], (11347 ^ _780086) ^ [_978710, _978712] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_978710, tc_HOL_Obool)), _978712), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_978710, tc_HOL_Obool)), _978712))), -(_978712 = c_Orderings_Obot__class_Obot(tc_fun(_978710, tc_HOL_Obool)))], (11353 ^ _780086) ^ [_978829, _978831] : [_978831 = c_Orderings_Obot__class_Obot(tc_fun(_978829, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_978829, tc_HOL_Obool)), _978831), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_978829, tc_HOL_Obool)), _978831))))], (11359 ^ _780086) ^ [_978954, _978956, _978958, _978960, _978962] : [class_Groups_Ocomm__monoid__mult(_978954), hBOOL(hAPP(c_Finite__Set_Ofinite(_978956), _978958)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_978956, _978954), hAPP(hAPP(c_COMBS(_978956, _978954, _978954), hAPP(hAPP(c_COMBB(_978954, tc_fun(_978954, _978954), _978956), c_Groups_Otimes__class_Otimes(_978954)), _978960)), _978962)), _978958) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978954), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_978956, _978954), _978960), _978958)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_978956, _978954), _978962), _978958)))], (11369 ^ _780086) ^ [_979221, _979223, _979225, _979227] : [_979221 = c_Finite__Set_Ofold1(_979223, _979225), -(hAPP(_979221, hAPP(hAPP(c_Set_Oinsert(_979223), _979227), c_Orderings_Obot__class_Obot(tc_fun(_979223, tc_HOL_Obool)))) = _979227)], (11375 ^ _780086) ^ [_979340, _979342, _979344] : [-(hAPP(c_Finite__Set_Ofold1(_979340, _979342), hAPP(hAPP(c_Set_Oinsert(_979340), _979344), c_Orderings_Obot__class_Obot(tc_fun(_979340, tc_HOL_Obool)))) = _979344)], (11377 ^ _780086) ^ [_979386, _979388, _979390, _979392] : [c_Finite__Set_Ofolding__one(_979386, _979388, _979390), hBOOL(hAPP(c_Finite__Set_Ofinite(_979386), _979392)), -(hAPP(_979390, _979392) = hAPP(c_Finite__Set_Ofold1(_979386, _979388), _979392))], (11387 ^ _780086) ^ [_979551, _979553, _979555, _979557] : [class_Orderings_Olinorder(_979551), hBOOL(hAPP(c_Finite__Set_Ofinite(_979551), _979553)), -(hAPP(hAPP(c_Finite__Set_Ofold(_979551, _979551, c_Orderings_Oord__class_Omax(_979551)), _979555), hAPP(hAPP(c_Set_Oinsert(_979551), _979557), _979553)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_979551), _979557), hAPP(hAPP(c_Finite__Set_Ofold(_979551, _979551, c_Orderings_Oord__class_Omax(_979551)), _979555), _979553)))], (11397 ^ _780086) ^ [_979774, _979776, _979778] : [class_Orderings_Olinorder(_979774), hBOOL(hAPP(c_Finite__Set_Ofinite(_979774), _979776)), hBOOL(hAPP(hAPP(c_member(_979774), _979778), _979776)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_979774), _979778), c_Big__Operators_Olinorder__class_OMax(_979774, _979776)) = c_Big__Operators_Olinorder__class_OMax(_979774, _979776))], (11411 ^ _780086) ^ [_980009, _980011, _980013, _980015] : [class_Orderings_Olinorder(_980009), hBOOL(hAPP(c_Finite__Set_Ofinite(_980009), _980011)), -(hAPP(hAPP(c_Finite__Set_Ofold(_980009, _980009, c_Orderings_Oord__class_Omin(_980009)), _980013), hAPP(hAPP(c_Set_Oinsert(_980009), _980015), _980011)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_980009), _980015), hAPP(hAPP(c_Finite__Set_Ofold(_980009, _980009, c_Orderings_Oord__class_Omin(_980009)), _980013), _980011)))], (11421 ^ _780086) ^ [_980232, _980234, _980236] : [class_Orderings_Olinorder(_980232), hBOOL(hAPP(c_Finite__Set_Ofinite(_980232), _980234)), hBOOL(hAPP(hAPP(c_member(_980232), _980236), _980234)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_980232), _980236), c_Big__Operators_Olinorder__class_OMin(_980232, _980234)) = c_Big__Operators_Olinorder__class_OMin(_980232, _980234))], (11435 ^ _780086) ^ [_980467, _980469, _980471] : [-(hAPP(c_Finite__Set_Ofold1(_980467, _980469), _980471) = c_HOL_OThe(_980467, c_Finite__Set_Ofold1Set(_980467, _980469, _980471)))], (11437 ^ _780086) ^ [_980507, _980509, _980511, _980513, _980515] : [class_Groups_Ocomm__monoid__mult(_980507), hBOOL(hAPP(c_Finite__Set_Ofinite(_980509), _980511)), -(hBOOL(hAPP(hAPP(c_member(_980509), _980513), _980511))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_980509, _980507), _980515), hAPP(hAPP(c_Set_Oinsert(_980509), _980513), _980511)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980507), hAPP(_980515, _980513)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_980509, _980507), _980515), _980511)))], (11451 ^ _780086) ^ [_980757, _980759, _980761, _980763, _980765] : [class_Groups_Ocomm__monoid__mult(_980757), hBOOL(hAPP(c_Finite__Set_Ofinite(_980759), _980761)), -(hBOOL(hAPP(hAPP(c_member(_980759), _980763), _980761))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_980759, _980757), _980765), hAPP(hAPP(c_Set_Oinsert(_980759), _980763), _980761)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980757), hAPP(_980765, _980763)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_980759, _980757), _980765), _980761)))], (11465 ^ _780086) ^ [_981007, _981009, _981011, _981013] : [class_Orderings_Olinorder(_981007), hBOOL(hAPP(c_Finite__Set_Ofinite(_981007), _981009)), hBOOL(hAPP(hAPP(c_member(_981007), _981011), _981009)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981007), hAPP(hAPP(c_Orderings_Oord__class_Omax(_981007), _981011), _981013)), hAPP(hAPP(c_Finite__Set_Ofold(_981007, _981007, c_Orderings_Oord__class_Omax(_981007)), _981013), _981009))))], (11479 ^ _780086) ^ [_981274, _981276, _981278, _981280] : [class_Orderings_Olinorder(_981274), hBOOL(hAPP(c_Finite__Set_Ofinite(_981274), _981276)), hBOOL(hAPP(hAPP(c_member(_981274), _981278), _981276)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981274), hAPP(hAPP(c_Finite__Set_Ofold(_981274, _981274, c_Orderings_Oord__class_Omin(_981274)), _981280), _981276)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_981274), _981278), _981280))))], (11493 ^ _780086) ^ [_981541, _981543, _981545] : [class_Orderings_Olinorder(_981541), hBOOL(hAPP(c_Finite__Set_Ofinite(_981541), _981543)), -(_981543 = c_Orderings_Obot__class_Obot(tc_fun(_981541, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_981541, hAPP(hAPP(c_Set_Oinsert(_981541), _981545), _981543)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_981541), _981545), c_Big__Operators_Olinorder__class_OMax(_981541, _981543)))], (11507 ^ _780086) ^ [_981749, _981751, _981753] : [class_Orderings_Olinorder(_981749), hBOOL(hAPP(c_Finite__Set_Ofinite(_981749), _981751)), -(_981751 = c_Orderings_Obot__class_Obot(tc_fun(_981749, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_981749, hAPP(hAPP(c_Set_Oinsert(_981749), _981753), _981751)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_981749), _981753), c_Big__Operators_Olinorder__class_OMin(_981749, _981751)))], (11521 ^ _780086) ^ [_981957, _981959, _981961] : [class_Orderings_Olinorder(_981957), hBOOL(hAPP(c_Finite__Set_Ofinite(_981957), _981959)), -(_981961 = c_Orderings_Obot__class_Obot(tc_fun(_981957, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_981957, tc_HOL_Obool)), _981961), _981959)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_981957), c_Big__Operators_Olinorder__class_OMax(_981957, _981961)), c_Big__Operators_Olinorder__class_OMax(_981957, _981959)) = c_Big__Operators_Olinorder__class_OMax(_981957, _981959))], (11539 ^ _780086) ^ [_982271, _982273, _982275] : [class_Orderings_Olinorder(_982271), hBOOL(hAPP(c_Finite__Set_Ofinite(_982271), _982273)), -(_982275 = c_Orderings_Obot__class_Obot(tc_fun(_982271, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_982271, tc_HOL_Obool)), _982275), _982273)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_982271), c_Big__Operators_Olinorder__class_OMin(_982271, _982275)), c_Big__Operators_Olinorder__class_OMin(_982271, _982273)) = c_Big__Operators_Olinorder__class_OMin(_982271, _982273))], (11557 ^ _780086) ^ [_982585, _982587, _982589] : [class_Orderings_Olinorder(_982585), hBOOL(hAPP(c_Finite__Set_Ofinite(_982585), _982587)), -(c_Big__Operators_Olinorder__class_OMax(_982585, hAPP(hAPP(c_Set_Oinsert(_982585), _982589), _982587)) = hAPP(hAPP(c_Finite__Set_Ofold(_982585, _982585, c_Orderings_Oord__class_Omax(_982585)), _982589), _982587))], (11567 ^ _780086) ^ [_982770, _982772, _982774] : [class_Orderings_Olinorder(_982770), hBOOL(hAPP(c_Finite__Set_Ofinite(_982770), _982772)), -(c_Big__Operators_Olinorder__class_OMin(_982770, hAPP(hAPP(c_Set_Oinsert(_982770), _982774), _982772)) = hAPP(hAPP(c_Finite__Set_Ofold(_982770, _982770, c_Orderings_Oord__class_Omin(_982770)), _982774), _982772))], (11577 ^ _780086) ^ [_982955, _982957, _982959, _982961, _982963] : [class_Groups_Ocomm__monoid__mult(_982955), hBOOL(hAPP(c_Finite__Set_Ofinite(_982957), _982959)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_982957, _982955), _982961), hAPP(hAPP(c_Set_Oinsert(_982957), _982963), _982959)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982955), hAPP(_982961, _982963)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_982957, _982955), _982961), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_982957, tc_HOL_Obool)), _982959), hAPP(hAPP(c_Set_Oinsert(_982957), _982963), c_Orderings_Obot__class_Obot(tc_fun(_982957, tc_HOL_Obool)))))))], (11587 ^ _780086) ^ [_983224, _983226, _983228] : [class_Lattices_Oab__semigroup__idem__mult(_983224), -(_983226 = c_Orderings_Obot__class_Obot(tc_fun(_983224, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_983224), _983226)), -(hAPP(c_Finite__Set_Ofold1(_983224, c_Groups_Otimes__class_Otimes(_983224)), hAPP(hAPP(c_Set_Oinsert(_983224), _983228), _983226)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983224), _983228), hAPP(c_Finite__Set_Ofold1(_983224, c_Groups_Otimes__class_Otimes(_983224)), _983226)))], (11601 ^ _780086) ^ [_983494, _983496, _983498] : [class_Lattices_Oab__semigroup__idem__mult(_983494), hBOOL(hAPP(c_Finite__Set_Ofinite(_983494), _983496)), -(hAPP(c_Finite__Set_Ofold1(_983494, c_Groups_Otimes__class_Otimes(_983494)), hAPP(hAPP(c_Set_Oinsert(_983494), _983498), _983496)) = hAPP(hAPP(c_Finite__Set_Ofold(_983494, _983494, c_Groups_Otimes__class_Otimes(_983494)), _983498), _983496))], (11611 ^ _780086) ^ [_983689, _983691, _983693] : [class_Orderings_Olinorder(_983689), hBOOL(hAPP(c_Finite__Set_Ofinite(_983689), _983691)), -(hBOOL(hAPP(hAPP(c_member(_983689), _983693), _983691))), -(_983691 = c_Orderings_Obot__class_Obot(tc_fun(_983689, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_983689, hAPP(hAPP(c_Set_Oinsert(_983689), _983693), _983691)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_983689), _983693), c_Big__Operators_Olinorder__class_OMax(_983689, _983691)))], (11629 ^ _780086) ^ [_983926, _983928, _983930] : [class_Orderings_Olinorder(_983926), hBOOL(hAPP(c_Finite__Set_Ofinite(_983926), _983928)), -(hBOOL(hAPP(hAPP(c_member(_983926), _983930), _983928))), -(_983928 = c_Orderings_Obot__class_Obot(tc_fun(_983926, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_983926, hAPP(hAPP(c_Set_Oinsert(_983926), _983930), _983928)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_983926), _983930), c_Big__Operators_Olinorder__class_OMin(_983926, _983928)))], (11647 ^ _780086) ^ [_984163, _984165, _984167] : [class_Orderings_Olinorder(_984163), hBOOL(hAPP(c_Finite__Set_Ofinite(_984163), _984165)), 11654 ^ _780086 : [(11655 ^ _780086) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_984163, tc_HOL_Obool)), _984165), hAPP(hAPP(c_Set_Oinsert(_984163), _984167), c_Orderings_Obot__class_Obot(tc_fun(_984163, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_984163, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_984163, hAPP(hAPP(c_Set_Oinsert(_984163), _984167), _984165)) = _984167)], (11661 ^ _780086) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_984163, tc_HOL_Obool)), _984165), hAPP(hAPP(c_Set_Oinsert(_984163), _984167), c_Orderings_Obot__class_Obot(tc_fun(_984163, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_984163, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_984163, hAPP(hAPP(c_Set_Oinsert(_984163), _984167), _984165)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_984163), _984167), c_Big__Operators_Olinorder__class_OMax(_984163, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_984163, tc_HOL_Obool)), _984165), hAPP(hAPP(c_Set_Oinsert(_984163), _984167), c_Orderings_Obot__class_Obot(tc_fun(_984163, tc_HOL_Obool)))))))]]], (11667 ^ _780086) ^ [_984633, _984635, _984637] : [class_Orderings_Olinorder(_984633), hBOOL(hAPP(c_Finite__Set_Ofinite(_984633), _984635)), 11674 ^ _780086 : [(11675 ^ _780086) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_984633, tc_HOL_Obool)), _984635), hAPP(hAPP(c_Set_Oinsert(_984633), _984637), c_Orderings_Obot__class_Obot(tc_fun(_984633, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_984633, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_984633, hAPP(hAPP(c_Set_Oinsert(_984633), _984637), _984635)) = _984637)], (11681 ^ _780086) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_984633, tc_HOL_Obool)), _984635), hAPP(hAPP(c_Set_Oinsert(_984633), _984637), c_Orderings_Obot__class_Obot(tc_fun(_984633, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_984633, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_984633, hAPP(hAPP(c_Set_Oinsert(_984633), _984637), _984635)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_984633), _984637), c_Big__Operators_Olinorder__class_OMin(_984633, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_984633, tc_HOL_Obool)), _984635), hAPP(hAPP(c_Set_Oinsert(_984633), _984637), c_Orderings_Obot__class_Obot(tc_fun(_984633, tc_HOL_Obool)))))))]]], (11687 ^ _780086) ^ [_985103, _985105, _985107] : [class_Orderings_Olinorder(_985103), hBOOL(hAPP(c_Finite__Set_Ofinite(_985103), _985105)), -(hBOOL(hAPP(hAPP(c_member(_985103), _985107), _985105))), -(c_Big__Operators_Olinorder__class_OMax(_985103, hAPP(hAPP(c_Set_Oinsert(_985103), _985107), _985105)) = hAPP(hAPP(c_Finite__Set_Ofold(_985103, _985103, c_Orderings_Oord__class_Omax(_985103)), _985107), _985105))], (11701 ^ _780086) ^ [_985317, _985319, _985321] : [class_Orderings_Olinorder(_985317), hBOOL(hAPP(c_Finite__Set_Ofinite(_985317), _985319)), -(hBOOL(hAPP(hAPP(c_member(_985317), _985321), _985319))), -(c_Big__Operators_Olinorder__class_OMin(_985317, hAPP(hAPP(c_Set_Oinsert(_985317), _985321), _985319)) = hAPP(hAPP(c_Finite__Set_Ofold(_985317, _985317, c_Orderings_Oord__class_Omin(_985317)), _985321), _985319))], (11715 ^ _780086) ^ [_985531, _985533, _985535, _985537] : [c_Big__Operators_Osemilattice__big(_985531, _985533, _985535), hBOOL(hAPP(c_Finite__Set_Ofinite(_985531), _985537)), -(hAPP(_985535, _985537) = hAPP(c_Finite__Set_Ofold1(_985531, _985533), _985537))], (11725 ^ _780086) ^ [_985696] : [class_Orderings_Olinorder(_985696), -(c_Orderings_Oord_Omin(_985696, hAPP(c_COMBC(_985696, _985696, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_985696))) = c_Orderings_Oord__class_Omax(_985696))], (11731 ^ _780086) ^ [_985797] : [class_Orderings_Olinorder(_985797), -(c_Orderings_Oord_Omax(_985797, hAPP(c_COMBC(_985797, _985797, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_985797))) = c_Orderings_Oord__class_Omin(_985797))], (11737 ^ _780086) ^ [_985898] : [class_Orderings_Oord(_985898), -(c_Orderings_Oord__class_Omax(_985898) = c_Orderings_Oord_Omax(_985898, c_Orderings_Oord__class_Oless__eq(_985898)))], (11743 ^ _780086) ^ [_985985] : [class_Orderings_Oord(_985985), -(c_Orderings_Oord__class_Omin(_985985) = c_Orderings_Oord_Omin(_985985, c_Orderings_Oord__class_Oless__eq(_985985)))], (11749 ^ _780086) ^ [_986072, _986074] : [class_Orderings_Olinorder(_986072), hBOOL(hAPP(c_Finite__Set_Ofinite(_986072), _986074)), -(_986074 = c_Orderings_Obot__class_Obot(tc_fun(_986072, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_986072), hAPP(hAPP(c_Orderings_Oord__class_Omax(_986072), 11762 ^ [_986072, _986074]), 11763 ^ [_986072, _986074])), hAPP(hAPP(c_Set_Oinsert(_986072), 11762 ^ [_986072, _986074]), hAPP(hAPP(c_Set_Oinsert(_986072), 11763 ^ [_986072, _986074]), c_Orderings_Obot__class_Obot(tc_fun(_986072, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_986072), c_Big__Operators_Olinorder__class_OMax(_986072, _986074)), _986074)))], (11769 ^ _780086) ^ [_986516, _986518] : [class_Orderings_Olinorder(_986516), hBOOL(hAPP(c_Finite__Set_Ofinite(_986516), _986518)), -(_986518 = c_Orderings_Obot__class_Obot(tc_fun(_986516, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_986516), hAPP(hAPP(c_Orderings_Oord__class_Omin(_986516), 11782 ^ [_986516, _986518]), 11783 ^ [_986516, _986518])), hAPP(hAPP(c_Set_Oinsert(_986516), 11782 ^ [_986516, _986518]), hAPP(hAPP(c_Set_Oinsert(_986516), 11783 ^ [_986516, _986518]), c_Orderings_Obot__class_Obot(tc_fun(_986516, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_986516), c_Big__Operators_Olinorder__class_OMin(_986516, _986518)), _986518)))], (11789 ^ _780086) ^ [_986960, _986962] : [class_Groups_Oab__semigroup__mult(_986960), hBOOL(hAPP(c_Finite__Set_Ofinite(_986960), _986962)), -(_986962 = c_Orderings_Obot__class_Obot(tc_fun(_986960, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_986960), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986960), 11802 ^ [_986960, _986962]), 11803 ^ [_986960, _986962])), hAPP(hAPP(c_Set_Oinsert(_986960), 11802 ^ [_986960, _986962]), hAPP(hAPP(c_Set_Oinsert(_986960), 11803 ^ [_986960, _986962]), c_Orderings_Obot__class_Obot(tc_fun(_986960, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_986960), hAPP(c_Finite__Set_Ofold1(_986960, c_Groups_Otimes__class_Otimes(_986960)), _986962)), _986962)))], (11809 ^ _780086) ^ [_987414, _987416, _987418] : [class_Orderings_Olinorder(_987414), hBOOL(hAPP(c_Finite__Set_Ofinite(_987414), _987416)), hBOOL(hAPP(hAPP(c_member(_987414), _987418), _987416)), 11820 ^ _780086 : [(11821 ^ _780086) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_987414, tc_HOL_Obool)), _987416), hAPP(hAPP(c_Set_Oinsert(_987414), _987418), c_Orderings_Obot__class_Obot(tc_fun(_987414, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_987414, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_987414, c_Orderings_Oord__class_Omax(_987414), _987416) = _987418)], (11827 ^ _780086) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_987414, tc_HOL_Obool)), _987416), hAPP(hAPP(c_Set_Oinsert(_987414), _987418), c_Orderings_Obot__class_Obot(tc_fun(_987414, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_987414, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_987414, c_Orderings_Oord__class_Omax(_987414), _987416) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_987414), _987418), c_Big__Operators_Olattice_OSup__fin(_987414, c_Orderings_Oord__class_Omax(_987414), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_987414, tc_HOL_Obool)), _987416), hAPP(hAPP(c_Set_Oinsert(_987414), _987418), c_Orderings_Obot__class_Obot(tc_fun(_987414, tc_HOL_Obool)))))))]]], (11833 ^ _780086) ^ [_987938, _987940, _987942] : [class_Orderings_Olinorder(_987938), hBOOL(hAPP(c_Finite__Set_Ofinite(_987938), _987940)), hBOOL(hAPP(hAPP(c_member(_987938), _987942), _987940)), 11844 ^ _780086 : [(11845 ^ _780086) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_987938, tc_HOL_Obool)), _987940), hAPP(hAPP(c_Set_Oinsert(_987938), _987942), c_Orderings_Obot__class_Obot(tc_fun(_987938, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_987938, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_987938, c_Orderings_Oord__class_Omin(_987938), _987940) = _987942)], (11851 ^ _780086) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_987938, tc_HOL_Obool)), _987940), hAPP(hAPP(c_Set_Oinsert(_987938), _987942), c_Orderings_Obot__class_Obot(tc_fun(_987938, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_987938, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_987938, c_Orderings_Oord__class_Omin(_987938), _987940) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_987938), _987942), c_Big__Operators_Olattice_OInf__fin(_987938, c_Orderings_Oord__class_Omin(_987938), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_987938, tc_HOL_Obool)), _987940), hAPP(hAPP(c_Set_Oinsert(_987938), _987942), c_Orderings_Obot__class_Obot(tc_fun(_987938, tc_HOL_Obool)))))))]]], (11857 ^ _780086) ^ [_988480, _988482, _988484] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_988480, tc_HOL_Obool)), _988482) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_988480, tc_HOL_Obool)), _988484), -(_988482 = _988484)], (11863 ^ _780086) ^ [_988587, _988589, _988591] : [_988589 = _988591, -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_988587, tc_HOL_Obool)), _988589) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_988587, tc_HOL_Obool)), _988591))], (11869 ^ _780086) ^ [_988700, _988702] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_988700, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_988700, tc_HOL_Obool)), _988702)) = _988702)], (11871 ^ _780086) ^ [_988741, _988743] : [class_Orderings_Olinorder(_988741), hBOOL(hAPP(c_Finite__Set_Ofinite(_988741), _988743)), -(_988743 = c_Orderings_Obot__class_Obot(tc_fun(_988741, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_988741), c_Big__Operators_Olattice_OInf__fin(_988741, c_Orderings_Oord__class_Omin(_988741), _988743)), c_Big__Operators_Olattice_OSup__fin(_988741, c_Orderings_Oord__class_Omax(_988741), _988743))))], (11885 ^ _780086) ^ [_988939, _988941, _988943] : [class_Orderings_Olinorder(_988939), hBOOL(hAPP(c_Finite__Set_Ofinite(_988939), _988941)), hBOOL(hAPP(hAPP(c_member(_988939), _988943), _988941)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_988939), _988943), c_Big__Operators_Olattice_OInf__fin(_988939, c_Orderings_Oord__class_Omin(_988939), _988941)) = c_Big__Operators_Olattice_OInf__fin(_988939, c_Orderings_Oord__class_Omin(_988939), _988941))], (11899 ^ _780086) ^ [_989186, _989188, _989190] : [class_Orderings_Olinorder(_989186), hBOOL(hAPP(c_Finite__Set_Ofinite(_989186), _989188)), hBOOL(hAPP(hAPP(c_member(_989186), _989190), _989188)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_989186), _989190), c_Big__Operators_Olattice_OSup__fin(_989186, c_Orderings_Oord__class_Omax(_989186), _989188)) = c_Big__Operators_Olattice_OSup__fin(_989186, c_Orderings_Oord__class_Omax(_989186), _989188))], (11913 ^ _780086) ^ [_989433, _989435] : [class_Orderings_Olinorder(_989433), -(c_Big__Operators_Olattice_OInf__fin(_989433, c_Orderings_Oord__class_Omin(_989433), hAPP(hAPP(c_Set_Oinsert(_989433), _989435), c_Orderings_Obot__class_Obot(tc_fun(_989433, tc_HOL_Obool)))) = _989435)], (11919 ^ _780086) ^ [_989546, _989548] : [class_Orderings_Olinorder(_989546), -(c_Big__Operators_Olattice_OSup__fin(_989546, c_Orderings_Oord__class_Omax(_989546), hAPP(hAPP(c_Set_Oinsert(_989546), _989548), c_Orderings_Obot__class_Obot(tc_fun(_989546, tc_HOL_Obool)))) = _989548)], (11925 ^ _780086) ^ [_989659, _989661] : [class_Orderings_Olinorder(_989659), hBOOL(hAPP(c_Finite__Set_Ofinite(_989659), _989661)), -(c_Big__Operators_Olattice_OInf__fin(_989659, c_Orderings_Oord__class_Omin(_989659), _989661) = hAPP(c_Finite__Set_Ofold1(_989659, c_Orderings_Oord__class_Omin(_989659)), _989661))], (11935 ^ _780086) ^ [_989822, _989824] : [class_Orderings_Olinorder(_989822), hBOOL(hAPP(c_Finite__Set_Ofinite(_989822), _989824)), -(c_Big__Operators_Olattice_OSup__fin(_989822, c_Orderings_Oord__class_Omax(_989822), _989824) = hAPP(c_Finite__Set_Ofold1(_989822, c_Orderings_Oord__class_Omax(_989822)), _989824))], (11945 ^ _780086) ^ [_989985, _989987, _989989] : [class_Orderings_Olinorder(_989985), hBOOL(hAPP(c_Finite__Set_Ofinite(_989985), _989987)), -(_989987 = c_Orderings_Obot__class_Obot(tc_fun(_989985, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_989985, c_Orderings_Oord__class_Omin(_989985), hAPP(hAPP(c_Set_Oinsert(_989985), _989989), _989987)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_989985), _989989), c_Big__Operators_Olattice_OInf__fin(_989985, c_Orderings_Oord__class_Omin(_989985), _989987)))], (11959 ^ _780086) ^ [_990205, _990207, _990209] : [class_Orderings_Olinorder(_990205), hBOOL(hAPP(c_Finite__Set_Ofinite(_990205), _990207)), -(_990207 = c_Orderings_Obot__class_Obot(tc_fun(_990205, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_990205, c_Orderings_Oord__class_Omax(_990205), hAPP(hAPP(c_Set_Oinsert(_990205), _990209), _990207)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_990205), _990209), c_Big__Operators_Olattice_OSup__fin(_990205, c_Orderings_Oord__class_Omax(_990205), _990207)))], (11973 ^ _780086) ^ [_990425, _990427, _990429] : [class_Orderings_Olinorder(_990425), hBOOL(hAPP(c_Finite__Set_Ofinite(_990425), _990427)), -(_990429 = c_Orderings_Obot__class_Obot(tc_fun(_990425, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_990425, tc_HOL_Obool)), _990429), _990427)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_990425), c_Big__Operators_Olattice_OInf__fin(_990425, c_Orderings_Oord__class_Omin(_990425), _990429)), c_Big__Operators_Olattice_OInf__fin(_990425, c_Orderings_Oord__class_Omin(_990425), _990427)) = c_Big__Operators_Olattice_OInf__fin(_990425, c_Orderings_Oord__class_Omin(_990425), _990427))], (11991 ^ _780086) ^ [_990757, _990759, _990761] : [class_Orderings_Olinorder(_990757), hBOOL(hAPP(c_Finite__Set_Ofinite(_990757), _990759)), -(_990761 = c_Orderings_Obot__class_Obot(tc_fun(_990757, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_990757, tc_HOL_Obool)), _990761), _990759)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_990757), c_Big__Operators_Olattice_OSup__fin(_990757, c_Orderings_Oord__class_Omax(_990757), _990761)), c_Big__Operators_Olattice_OSup__fin(_990757, c_Orderings_Oord__class_Omax(_990757), _990759)) = c_Big__Operators_Olattice_OSup__fin(_990757, c_Orderings_Oord__class_Omax(_990757), _990759))], (12009 ^ _780086) ^ [_991089, _991091, _991093] : [class_Orderings_Olinorder(_991089), hBOOL(hAPP(c_Finite__Set_Ofinite(_991089), _991091)), hBOOL(hAPP(hAPP(c_member(_991089), _991093), _991091)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_991089), _991093), c_Big__Operators_Olattice_OSup__fin(_991089, c_Orderings_Oord__class_Omax(_991089), _991091)) = _991093)], (12023 ^ _780086) ^ [_991324, _991326, _991328] : [class_Orderings_Olinorder(_991324), hBOOL(hAPP(c_Finite__Set_Ofinite(_991324), _991326)), hBOOL(hAPP(hAPP(c_member(_991324), _991328), _991326)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_991324), _991328), c_Big__Operators_Olattice_OInf__fin(_991324, c_Orderings_Oord__class_Omin(_991324), _991326)) = _991328)], (12037 ^ _780086) ^ [_991559, _991561, _991563] : [class_Orderings_Olinorder(_991559), hBOOL(hAPP(c_Finite__Set_Ofinite(_991559), _991561)), -(c_Big__Operators_Olattice_OInf__fin(_991559, c_Orderings_Oord__class_Omin(_991559), hAPP(hAPP(c_Set_Oinsert(_991559), _991563), _991561)) = hAPP(hAPP(c_Finite__Set_Ofold(_991559, _991559, c_Orderings_Oord__class_Omin(_991559)), _991563), _991561))], (12047 ^ _780086) ^ [_991750, _991752, _991754] : [class_Orderings_Olinorder(_991750), hBOOL(hAPP(c_Finite__Set_Ofinite(_991750), _991752)), -(c_Big__Operators_Olattice_OSup__fin(_991750, c_Orderings_Oord__class_Omax(_991750), hAPP(hAPP(c_Set_Oinsert(_991750), _991754), _991752)) = hAPP(hAPP(c_Finite__Set_Ofold(_991750, _991750, c_Orderings_Oord__class_Omax(_991750)), _991754), _991752))], (12057 ^ _780086) ^ [_991941, _991943, _991945] : [class_Orderings_Olinorder(_991941), hBOOL(hAPP(c_Finite__Set_Ofinite(_991941), _991943)), -(hBOOL(hAPP(hAPP(c_member(_991941), _991945), _991943))), -(_991943 = c_Orderings_Obot__class_Obot(tc_fun(_991941, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_991941, c_Orderings_Oord__class_Omin(_991941), hAPP(hAPP(c_Set_Oinsert(_991941), _991945), _991943)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_991941), _991945), c_Big__Operators_Olattice_OInf__fin(_991941, c_Orderings_Oord__class_Omin(_991941), _991943)))], (12075 ^ _780086) ^ [_992190, _992192, _992194] : [class_Orderings_Olinorder(_992190), hBOOL(hAPP(c_Finite__Set_Ofinite(_992190), _992192)), -(hBOOL(hAPP(hAPP(c_member(_992190), _992194), _992192))), -(_992192 = c_Orderings_Obot__class_Obot(tc_fun(_992190, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_992190, c_Orderings_Oord__class_Omax(_992190), hAPP(hAPP(c_Set_Oinsert(_992190), _992194), _992192)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_992190), _992194), c_Big__Operators_Olattice_OSup__fin(_992190, c_Orderings_Oord__class_Omax(_992190), _992192)))], (12093 ^ _780086) ^ [_992439, _992441, _992443] : [class_Orderings_Olinorder(_992439), hBOOL(hAPP(c_Finite__Set_Ofinite(_992439), _992441)), 12100 ^ _780086 : [(12101 ^ _780086) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_992439, tc_HOL_Obool)), _992441), hAPP(hAPP(c_Set_Oinsert(_992439), _992443), c_Orderings_Obot__class_Obot(tc_fun(_992439, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_992439, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_992439, c_Orderings_Oord__class_Omin(_992439), hAPP(hAPP(c_Set_Oinsert(_992439), _992443), _992441)) = _992443)], (12107 ^ _780086) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_992439, tc_HOL_Obool)), _992441), hAPP(hAPP(c_Set_Oinsert(_992439), _992443), c_Orderings_Obot__class_Obot(tc_fun(_992439, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_992439, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_992439, c_Orderings_Oord__class_Omin(_992439), hAPP(hAPP(c_Set_Oinsert(_992439), _992443), _992441)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_992439), _992443), c_Big__Operators_Olattice_OInf__fin(_992439, c_Orderings_Oord__class_Omin(_992439), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_992439, tc_HOL_Obool)), _992441), hAPP(hAPP(c_Set_Oinsert(_992439), _992443), c_Orderings_Obot__class_Obot(tc_fun(_992439, tc_HOL_Obool)))))))]]], (12113 ^ _780086) ^ [_992927, _992929, _992931] : [class_Orderings_Olinorder(_992927), hBOOL(hAPP(c_Finite__Set_Ofinite(_992927), _992929)), 12120 ^ _780086 : [(12121 ^ _780086) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_992927, tc_HOL_Obool)), _992929), hAPP(hAPP(c_Set_Oinsert(_992927), _992931), c_Orderings_Obot__class_Obot(tc_fun(_992927, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_992927, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_992927, c_Orderings_Oord__class_Omax(_992927), hAPP(hAPP(c_Set_Oinsert(_992927), _992931), _992929)) = _992931)], (12127 ^ _780086) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_992927, tc_HOL_Obool)), _992929), hAPP(hAPP(c_Set_Oinsert(_992927), _992931), c_Orderings_Obot__class_Obot(tc_fun(_992927, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_992927, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_992927, c_Orderings_Oord__class_Omax(_992927), hAPP(hAPP(c_Set_Oinsert(_992927), _992931), _992929)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_992927), _992931), c_Big__Operators_Olattice_OSup__fin(_992927, c_Orderings_Oord__class_Omax(_992927), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_992927, tc_HOL_Obool)), _992929), hAPP(hAPP(c_Set_Oinsert(_992927), _992931), c_Orderings_Obot__class_Obot(tc_fun(_992927, tc_HOL_Obool)))))))]]], (12133 ^ _780086) ^ [_993415, _993417, _993419] : [class_Orderings_Olinorder(_993415), hBOOL(hAPP(c_Finite__Set_Ofinite(_993415), _993417)), -(hBOOL(hAPP(hAPP(c_member(_993415), _993419), _993417))), -(c_Big__Operators_Olattice_OInf__fin(_993415, c_Orderings_Oord__class_Omin(_993415), hAPP(hAPP(c_Set_Oinsert(_993415), _993419), _993417)) = hAPP(hAPP(c_Finite__Set_Ofold(_993415, _993415, c_Orderings_Oord__class_Omin(_993415)), _993419), _993417))], (12147 ^ _780086) ^ [_993635, _993637, _993639] : [class_Orderings_Olinorder(_993635), hBOOL(hAPP(c_Finite__Set_Ofinite(_993635), _993637)), -(hBOOL(hAPP(hAPP(c_member(_993635), _993639), _993637))), -(c_Big__Operators_Olattice_OSup__fin(_993635, c_Orderings_Oord__class_Omax(_993635), hAPP(hAPP(c_Set_Oinsert(_993635), _993639), _993637)) = hAPP(hAPP(c_Finite__Set_Ofold(_993635, _993635, c_Orderings_Oord__class_Omax(_993635)), _993639), _993637))], (12161 ^ _780086) ^ [_993855, _993857] : [class_Orderings_Olinorder(_993855), hBOOL(hAPP(c_Finite__Set_Ofinite(_993855), _993857)), -(_993857 = c_Orderings_Obot__class_Obot(tc_fun(_993855, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_993855), hAPP(hAPP(c_Orderings_Oord__class_Omax(_993855), 12174 ^ [_993855, _993857]), 12175 ^ [_993855, _993857])), hAPP(hAPP(c_Set_Oinsert(_993855), 12174 ^ [_993855, _993857]), hAPP(hAPP(c_Set_Oinsert(_993855), 12175 ^ [_993855, _993857]), c_Orderings_Obot__class_Obot(tc_fun(_993855, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_993855), c_Big__Operators_Olattice_OSup__fin(_993855, c_Orderings_Oord__class_Omax(_993855), _993857)), _993857)))], (12181 ^ _780086) ^ [_994305, _994307] : [class_Orderings_Olinorder(_994305), hBOOL(hAPP(c_Finite__Set_Ofinite(_994305), _994307)), -(_994307 = c_Orderings_Obot__class_Obot(tc_fun(_994305, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_994305), hAPP(hAPP(c_Orderings_Oord__class_Omin(_994305), 12194 ^ [_994305, _994307]), 12195 ^ [_994305, _994307])), hAPP(hAPP(c_Set_Oinsert(_994305), 12194 ^ [_994305, _994307]), hAPP(hAPP(c_Set_Oinsert(_994305), 12195 ^ [_994305, _994307]), c_Orderings_Obot__class_Obot(tc_fun(_994305, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_994305), c_Big__Operators_Olattice_OInf__fin(_994305, c_Orderings_Oord__class_Omin(_994305), _994307)), _994307)))], (12201 ^ _780086) ^ [_994755, _994757, _994759] : [class_Orderings_Olinorder(_994755), hAPP(_994757, hAPP(hAPP(c_Orderings_Oord__class_Omax(_994755), 12206 ^ [_994755, _994757, _994759]), 12207 ^ [_994755, _994757, _994759])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_994755), hAPP(_994757, 12206 ^ [_994755, _994757, _994759])), hAPP(_994757, 12207 ^ [_994755, _994757, _994759])), hBOOL(hAPP(c_Finite__Set_Ofinite(_994755), _994759)), -(_994759 = c_Orderings_Obot__class_Obot(tc_fun(_994755, tc_HOL_Obool))), -(hAPP(_994757, c_Big__Operators_Olattice_OSup__fin(_994755, c_Orderings_Oord__class_Omax(_994755), _994759)) = c_Big__Operators_Olattice_OSup__fin(_994755, c_Orderings_Oord__class_Omax(_994755), hAPP(c_Set_Oimage(_994755, _994755, _994757), _994759)))], (12221 ^ _780086) ^ [_995170, _995172, _995174] : [class_Orderings_Olinorder(_995170), hAPP(_995172, hAPP(hAPP(c_Orderings_Oord__class_Omin(_995170), 12226 ^ [_995170, _995172, _995174]), 12227 ^ [_995170, _995172, _995174])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_995170), hAPP(_995172, 12226 ^ [_995170, _995172, _995174])), hAPP(_995172, 12227 ^ [_995170, _995172, _995174])), hBOOL(hAPP(c_Finite__Set_Ofinite(_995170), _995174)), -(_995174 = c_Orderings_Obot__class_Obot(tc_fun(_995170, tc_HOL_Obool))), -(hAPP(_995172, c_Big__Operators_Olattice_OInf__fin(_995170, c_Orderings_Oord__class_Omin(_995170), _995174)) = c_Big__Operators_Olattice_OInf__fin(_995170, c_Orderings_Oord__class_Omin(_995170), hAPP(c_Set_Oimage(_995170, _995170, _995172), _995174)))], (12241 ^ _780086) ^ [_995585, _995587, _995589] : [class_Orderings_Olinorder(_995585), hAPP(_995587, hAPP(hAPP(c_Orderings_Oord__class_Omax(_995585), 12246 ^ [_995585, _995587, _995589]), 12247 ^ [_995585, _995587, _995589])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_995585), hAPP(_995587, 12246 ^ [_995585, _995587, _995589])), hAPP(_995587, 12247 ^ [_995585, _995587, _995589])), hBOOL(hAPP(c_Finite__Set_Ofinite(_995585), _995589)), -(_995589 = c_Orderings_Obot__class_Obot(tc_fun(_995585, tc_HOL_Obool))), -(hAPP(_995587, c_Big__Operators_Olinorder__class_OMax(_995585, _995589)) = c_Big__Operators_Olinorder__class_OMax(_995585, hAPP(c_Set_Oimage(_995585, _995585, _995587), _995589)))], (12261 ^ _780086) ^ [_995988, _995990, _995992] : [class_Orderings_Olinorder(_995988), hAPP(_995990, hAPP(hAPP(c_Orderings_Oord__class_Omin(_995988), 12266 ^ [_995988, _995990, _995992]), 12267 ^ [_995988, _995990, _995992])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_995988), hAPP(_995990, 12266 ^ [_995988, _995990, _995992])), hAPP(_995990, 12267 ^ [_995988, _995990, _995992])), hBOOL(hAPP(c_Finite__Set_Ofinite(_995988), _995992)), -(_995992 = c_Orderings_Obot__class_Obot(tc_fun(_995988, tc_HOL_Obool))), -(hAPP(_995990, c_Big__Operators_Olinorder__class_OMin(_995988, _995992)) = c_Big__Operators_Olinorder__class_OMin(_995988, hAPP(c_Set_Oimage(_995988, _995988, _995990), _995992)))], (12281 ^ _780086) ^ [_996391, _996393, _996395] : [class_Lattices_Oab__semigroup__idem__mult(_996391), hAPP(_996393, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_996391), 12286 ^ [_996391, _996393, _996395]), 12287 ^ [_996391, _996393, _996395])) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_996391), hAPP(_996393, 12286 ^ [_996391, _996393, _996395])), hAPP(_996393, 12287 ^ [_996391, _996393, _996395])), hBOOL(hAPP(c_Finite__Set_Ofinite(_996391), _996395)), -(_996395 = c_Orderings_Obot__class_Obot(tc_fun(_996391, tc_HOL_Obool))), -(hAPP(_996393, hAPP(c_Finite__Set_Ofold1(_996391, c_Groups_Otimes__class_Otimes(_996391)), _996395)) = hAPP(c_Finite__Set_Ofold1(_996391, c_Groups_Otimes__class_Otimes(_996391)), hAPP(c_Set_Oimage(_996391, _996391, _996393), _996395)))], (12301 ^ _780086) ^ [_996814, _996816, _996818, _996820] : [class_Orderings_Olinorder(_996814), hBOOL(hAPP(c_Finite__Set_Ofinite(_996814), _996816)), 12311 ^ _780086 : [(12312 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_996814), 12310 ^ [_996814, _996816, _996818, _996820]), _996816)))], (12314 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996814), 12310 ^ [_996814, _996816, _996818, _996820]), _996818))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996814), hAPP(hAPP(c_Finite__Set_Ofold(_996814, _996814, c_Orderings_Oord__class_Omax(_996814)), _996820), _996816)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_996814), _996818), _996820))))], (12318 ^ _780086) ^ [_997178, _997180, _997182, _997184] : [class_Orderings_Olinorder(_997178), hBOOL(hAPP(c_Finite__Set_Ofinite(_997178), _997180)), 12328 ^ _780086 : [(12329 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_997178), 12327 ^ [_997178, _997180, _997182, _997184]), _997180)))], (12331 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997178), _997182), 12327 ^ [_997178, _997180, _997182, _997184]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997178), hAPP(hAPP(c_Orderings_Oord__class_Omin(_997178), _997182), _997184)), hAPP(hAPP(c_Finite__Set_Ofold(_997178, _997178, c_Orderings_Oord__class_Omin(_997178)), _997184), _997180))))], (12335 ^ _780086) ^ [_997542, _997544, _997546, _997548] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_997542), _997544)), hBOOL(hAPP(hAPP(c_member(_997542), _997546), _997544)), hBOOL(hAPP(hAPP(c_member(_997542), _997548), _997544)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_997542), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_997542, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_997542, tc_HOL_Obool)), _997544), hAPP(hAPP(c_Set_Oinsert(_997542), _997546), c_Orderings_Obot__class_Obot(tc_fun(_997542, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_997542), _997548), c_Orderings_Obot__class_Obot(tc_fun(_997542, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_997542), _997544))))], (12349 ^ _780086) ^ [_997897, _997899, _997901] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_997897), _997899)), hBOOL(hAPP(hAPP(c_member(_997897), _997901), _997899)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_997897), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_997897, tc_HOL_Obool)), _997899), hAPP(hAPP(c_Set_Oinsert(_997897), _997901), c_Orderings_Obot__class_Obot(tc_fun(_997897, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_997897), _997899))))], (12359 ^ _780086) ^ [_998130, _998132, _998134, _998136] : [c_Fun_Oinj__on(_998130, _998132, _998134, c_Orderings_Otop__class_Otop(tc_fun(_998130, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_998132, tc_HOL_Obool)), hAPP(c_Set_Oimage(_998130, _998132, _998134), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_998130, tc_HOL_Obool)), _998136))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_998132, tc_HOL_Obool)), hAPP(c_Set_Oimage(_998130, _998132, _998134), _998136)))))], (12365 ^ _780086) ^ [_998305, _998307, _998309, _998311, _998313, _998315] : [class_Groups_Oab__semigroup__mult(_998305), hBOOL(hAPP(c_Finite__Set_Ofinite(_998307), _998309)), -(hBOOL(hAPP(hAPP(c_member(_998307), _998311), _998309))), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_998305, _998307, c_Groups_Otimes__class_Otimes(_998305)), _998313), _998315), hAPP(hAPP(c_Set_Oinsert(_998307), _998311), _998309)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_998305), hAPP(_998313, _998311)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_998305, _998307, c_Groups_Otimes__class_Otimes(_998305)), _998313), _998315), _998309)))], (12379 ^ _780086) ^ [_998583, _998585, _998587, _998589, _998591] : [class_Groups_Ocomm__monoid__add(_998583), class_Groups_Oordered__ab__semigroup__add(_998583), 12389 ^ _780086 : [(12390 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_998585), 12388 ^ [_998583, _998585, _998587, _998589, _998591]), _998587)))], (12392 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998583), hAPP(_998589, 12388 ^ [_998583, _998585, _998587, _998589, _998591])), hAPP(_998591, 12388 ^ [_998583, _998585, _998587, _998589, _998591])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998583), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_998585, _998583), _998589), _998587)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_998585, _998583), _998591), _998587))))], (12396 ^ _780086) ^ [_998977, _998979, _998981] : [class_Orderings_Olinorder(_998977), hBOOL(hAPP(c_Finite__Set_Ofinite(_998977), _998979)), -(_998979 = c_Orderings_Obot__class_Obot(tc_fun(_998977, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_998977), _998981)), -(_998981 = c_Orderings_Obot__class_Obot(tc_fun(_998977, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_998977, c_Orderings_Oord__class_Omax(_998977), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_998977, tc_HOL_Obool)), _998979), _998981)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_998977), c_Big__Operators_Olattice_OSup__fin(_998977, c_Orderings_Oord__class_Omax(_998977), _998979)), c_Big__Operators_Olattice_OSup__fin(_998977, c_Orderings_Oord__class_Omax(_998977), _998981)))], (12418 ^ _780086) ^ [_999344, _999346, _999348] : [class_Orderings_Olinorder(_999344), hBOOL(hAPP(c_Finite__Set_Ofinite(_999344), _999346)), -(_999346 = c_Orderings_Obot__class_Obot(tc_fun(_999344, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_999344), _999348)), -(_999348 = c_Orderings_Obot__class_Obot(tc_fun(_999344, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_999344, c_Orderings_Oord__class_Omin(_999344), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_999344, tc_HOL_Obool)), _999346), _999348)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_999344), c_Big__Operators_Olattice_OInf__fin(_999344, c_Orderings_Oord__class_Omin(_999344), _999346)), c_Big__Operators_Olattice_OInf__fin(_999344, c_Orderings_Oord__class_Omin(_999344), _999348)))], (12440 ^ _780086) ^ [_999711, _999713, _999715] : [class_Orderings_Olinorder(_999711), hBOOL(hAPP(c_Finite__Set_Ofinite(_999711), _999713)), -(_999713 = c_Orderings_Obot__class_Obot(tc_fun(_999711, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_999711), _999715)), -(_999715 = c_Orderings_Obot__class_Obot(tc_fun(_999711, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_999711, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_999711, tc_HOL_Obool)), _999713), _999715)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_999711), c_Big__Operators_Olinorder__class_OMax(_999711, _999713)), c_Big__Operators_Olinorder__class_OMax(_999711, _999715)))], (12462 ^ _780086) ^ [_1000060, _1000062, _1000064] : [class_Orderings_Olinorder(_1000060), hBOOL(hAPP(c_Finite__Set_Ofinite(_1000060), _1000062)), -(_1000062 = c_Orderings_Obot__class_Obot(tc_fun(_1000060, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1000060), _1000064)), -(_1000064 = c_Orderings_Obot__class_Obot(tc_fun(_1000060, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1000060, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1000060, tc_HOL_Obool)), _1000062), _1000064)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1000060), c_Big__Operators_Olinorder__class_OMin(_1000060, _1000062)), c_Big__Operators_Olinorder__class_OMin(_1000060, _1000064)))], (12484 ^ _780086) ^ [_1000409, _1000411] : [-(hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1000409, tc_HOL_Obool)), _1000411)))], (12486 ^ _780086) ^ [_1000441, _1000443, _1000445, _1000447] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1000441, tc_HOL_Obool)), _1000443), _1000445), _1000447)), -(hBOOL(hAPP(_1000443, _1000447))), -(hBOOL(hAPP(_1000445, _1000447)))], (12496 ^ _780086) ^ [_1000571, _1000573, _1000575, _1000577] : [12497 ^ _780086 : [(12498 ^ _780086) ^ [] : [hBOOL(hAPP(_1000571, _1000573))], (12500 ^ _780086) ^ [] : [hBOOL(hAPP(_1000575, _1000573))]], -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1000577, tc_HOL_Obool)), _1000575), _1000571), _1000573)))], (12504 ^ _780086) ^ [_1000726, _1000728] : [-(hBOOL(hAPP(hAPP(c_member(_1000726), _1000728), c_Orderings_Otop__class_Otop(tc_fun(_1000726, tc_HOL_Obool)))))], (12506 ^ _780086) ^ [_1000763, _1000765, _1000767, _1000769] : [hBOOL(hAPP(hAPP(c_member(_1000763), _1000765), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1000763, tc_HOL_Obool)), _1000767), _1000769))), -(hBOOL(hAPP(hAPP(c_member(_1000763), _1000765), _1000767))), -(hBOOL(hAPP(hAPP(c_member(_1000763), _1000765), _1000769)))], (12516 ^ _780086) ^ [_1000923, _1000925, _1000927, _1000929] : [12517 ^ _780086 : [(12518 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1000923), _1000925), _1000927))], (12520 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1000923), _1000925), _1000929))]], -(hBOOL(hAPP(hAPP(c_member(_1000923), _1000925), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1000923, tc_HOL_Obool)), _1000929), _1000927))))], (12524 ^ _780086) ^ [_1001120] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1001120)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1001120), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1001120), c_Orderings_Otop__class_Otop(tc_fun(_1001120, tc_HOL_Obool)))))], (12530 ^ _780086) ^ [_1001235] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1001235), c_Orderings_Otop__class_Otop(tc_fun(_1001235, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1001235)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1001235), tc_HOL_Obool)))))], (12536 ^ _780086) ^ [_1001371, _1001373] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1001371, _1001373)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1001371, _1001373), tc_HOL_Obool)))), 12539 ^ _780086 : [(12540 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1001371), c_Orderings_Otop__class_Otop(tc_fun(_1001371, tc_HOL_Obool)))))], (12542 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1001373), c_Orderings_Otop__class_Otop(tc_fun(_1001373, tc_HOL_Obool)))))]]], (12544 ^ _780086) ^ [_1001536, _1001538] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1001536, _1001538)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1001536, _1001538), tc_HOL_Obool))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1001536), c_Orderings_Otop__class_Otop(tc_fun(_1001536, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1001538), c_Orderings_Otop__class_Otop(tc_fun(_1001538, tc_HOL_Obool))))], (12554 ^ _780086) ^ [_1001733, _1001735] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1001733), c_Orderings_Otop__class_Otop(tc_fun(_1001733, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1001735), c_Orderings_Otop__class_Otop(tc_fun(_1001735, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1001733, _1001735)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1001733, _1001735), tc_HOL_Obool)))))], (12564 ^ _780086) ^ [_1001928, _1001930] : [class_Lattices_Olattice(_1001928), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1001928), _1001930), _1001930) = _1001930)], (12570 ^ _780086) ^ [_1002019, _1002021] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1002019, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1002019, tc_HOL_Obool))), _1002021) = c_Orderings_Otop__class_Otop(tc_fun(_1002019, tc_HOL_Obool)))], (12572 ^ _780086) ^ [_1002065, _1002067] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1002065, tc_HOL_Obool)), _1002067), c_Orderings_Otop__class_Otop(tc_fun(_1002065, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1002065, tc_HOL_Obool)))], (12574 ^ _780086) ^ [_1002111, _1002113] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1002111, tc_HOL_Obool)), _1002113), _1002113) = _1002113)], (12576 ^ _780086) ^ [_1002147, _1002149, _1002151] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1002147, tc_HOL_Obool)), _1002149), _1002151) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1002147, tc_HOL_Obool)), _1002151), _1002149))], (12578 ^ _780086) ^ [_1002196, _1002198, _1002200] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1002196, tc_HOL_Obool)), _1002198), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1002196, tc_HOL_Obool)), _1002198), _1002200)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1002196, tc_HOL_Obool)), _1002198), _1002200))], (12580 ^ _780086) ^ [_1002256, _1002258, _1002260, _1002262] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1002256, tc_HOL_Obool)), _1002258), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1002256, tc_HOL_Obool)), _1002260), _1002262)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1002256, tc_HOL_Obool)), _1002260), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1002256, tc_HOL_Obool)), _1002258), _1002262)))], (12582 ^ _780086) ^ [_1002329, _1002331, _1002333, _1002335] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1002329, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1002329, tc_HOL_Obool)), _1002331), _1002333)), _1002335) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1002329, tc_HOL_Obool)), _1002331), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1002329, tc_HOL_Obool)), _1002333), _1002335)))], (12584 ^ _780086) ^ [_1002423, _1002425, _1002427, _1002429] : [12585 ^ _780086 : [(12586 ^ _780086) ^ [_1002533] : [hBOOL(hAPP(hAPP(c_member(_1002423), _1002533), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1002423, tc_HOL_Obool)), _1002425), _1002427))), hBOOL(hAPP(_1002429, _1002533))]], 12594 ^ _780086 : [(12595 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1002423), 12593 ^ [_1002423, _1002425, _1002427, _1002429]), _1002425)))], (12597 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1002429, 12593 ^ [_1002423, _1002425, _1002427, _1002429])))]], 12599 ^ _780086 : [(12600 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1002423), 12598 ^ [_1002423, _1002425, _1002427, _1002429]), _1002427)))], (12602 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1002429, 12598 ^ [_1002423, _1002425, _1002427, _1002429])))]]], (12604 ^ _780086) ^ [_1002822, _1002824, _1002826, _1002828] : [12618 ^ _780086 : [(12619 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1002822), 12617 ^ [_1002822, _1002824, _1002826, _1002828]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1002822, tc_HOL_Obool)), _1002824), _1002826))))], (12621 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1002828, 12617 ^ [_1002822, _1002824, _1002826, _1002828])))]], 12605 ^ _780086 : [(12606 ^ _780086) ^ [_1002935] : [hBOOL(hAPP(hAPP(c_member(_1002822), _1002935), _1002824)), hBOOL(hAPP(_1002828, _1002935))], (12612 ^ _780086) ^ [_1003031] : [hBOOL(hAPP(hAPP(c_member(_1002822), _1003031), _1002826)), hBOOL(hAPP(_1002828, _1003031))]]], (12642 ^ _780086) ^ [_1003668, _1003670, _1003672, _1003674] : [12646 ^ _780086 : [(12647 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1003668), 12645 ^ [_1003668, _1003670, _1003672, _1003674]), _1003670)))], (12649 ^ _780086) ^ [] : [hBOOL(hAPP(_1003674, 12645 ^ [_1003668, _1003670, _1003672, _1003674]))]], 12651 ^ _780086 : [(12652 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1003668), 12650 ^ [_1003668, _1003670, _1003672, _1003674]), _1003672)))], (12654 ^ _780086) ^ [] : [hBOOL(hAPP(_1003674, 12650 ^ [_1003668, _1003670, _1003672, _1003674]))]], 12655 ^ _780086 : [(12656 ^ _780086) ^ [_1004001] : [hBOOL(hAPP(hAPP(c_member(_1003668), _1004001), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1003668, tc_HOL_Obool)), _1003670), _1003672))), -(hBOOL(hAPP(_1003674, _1004001)))]]], (12623 ^ _780086) ^ [_1003246, _1003248, _1003250, _1003252] : [12625 ^ _780086 : [(12626 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1003246), 12624 ^ [_1003246, _1003248, _1003250, _1003252]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1003246, tc_HOL_Obool)), _1003248), _1003250))))], (12628 ^ _780086) ^ [] : [hBOOL(hAPP(_1003252, 12624 ^ [_1003246, _1003248, _1003250, _1003252]))]], 12629 ^ _780086 : [(12630 ^ _780086) ^ [_1003466] : [hBOOL(hAPP(hAPP(c_member(_1003246), _1003466), _1003248)), -(hBOOL(hAPP(_1003252, _1003466)))], (12636 ^ _780086) ^ [_1003563] : [hBOOL(hAPP(hAPP(c_member(_1003246), _1003563), _1003250)), -(hBOOL(hAPP(_1003252, _1003563)))]]], (12662 ^ _780086) ^ [_1004132, _1004134, _1004136] : [class_Orderings_Otop(_1004132), -(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1004134, _1004132)), _1004136) = c_Orderings_Otop__class_Otop(_1004132))], (12668 ^ _780086) ^ [_1004229, _1004231, _1004233, _1004235] : [hBOOL(hAPP(_1004229, _1004231)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1004233, tc_HOL_Obool)), _1004229), _1004235), _1004231)))], (12674 ^ _780086) ^ [_1004340, _1004342, _1004344, _1004346] : [hBOOL(hAPP(_1004340, _1004342)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1004344, tc_HOL_Obool)), _1004346), _1004340), _1004342)))], (12680 ^ _780086) ^ [_1004451, _1004453] : [class_Lattices_Obounded__lattice__top(_1004451), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1004451), c_Orderings_Otop__class_Otop(_1004451)), _1004453) = c_Orderings_Otop__class_Otop(_1004451))], (12686 ^ _780086) ^ [_1004550, _1004552] : [class_Lattices_Obounded__lattice__top(_1004550), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1004550), _1004552), c_Orderings_Otop__class_Otop(_1004550)) = c_Orderings_Otop__class_Otop(_1004550))], (12692 ^ _780086) ^ [_1004649, _1004651] : [class_Lattices_Osemilattice__sup(_1004649), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1004649), _1004651), _1004651) = _1004651)], (12698 ^ _780086) ^ [_1004740, _1004742] : [class_Lattices_Osemilattice__sup(_1004740), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1004740), _1004742), _1004742) = _1004742)], (12704 ^ _780086) ^ [_1004831, _1004833, _1004835, _1004837, _1004839] : [class_Lattices_Olattice(_1004831), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1004833, _1004831)), _1004835), _1004837), _1004839) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1004831), hAPP(_1004835, _1004839)), hAPP(_1004837, _1004839)))], (12710 ^ _780086) ^ [_1004968, _1004970, _1004972] : [class_Lattices_Osemilattice__sup(_1004968), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1004968), _1004970), _1004972) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1004968), _1004972), _1004970))], (12716 ^ _780086) ^ [_1005077, _1005079, _1005081] : [class_Lattices_Olattice(_1005077), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1005077), _1005079), _1005081) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1005077), _1005081), _1005079))], (12722 ^ _780086) ^ [_1005186, _1005188, _1005190] : [class_Lattices_Osemilattice__sup(_1005186), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1005186), _1005188), _1005190) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1005186), _1005190), _1005188))], (12728 ^ _780086) ^ [_1005295, _1005297, _1005299] : [class_Lattices_Osemilattice__sup(_1005295), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1005295), _1005297), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1005295), _1005297), _1005299)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1005295), _1005297), _1005299))], (12734 ^ _780086) ^ [_1005420, _1005422, _1005424] : [class_Lattices_Olattice(_1005420), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1005420), _1005422), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1005420), _1005422), _1005424)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1005420), _1005422), _1005424))], (12740 ^ _780086) ^ [_1005545, _1005547, _1005549] : [class_Lattices_Osemilattice__sup(_1005545), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1005545), _1005547), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1005545), _1005547), _1005549)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1005545), _1005547), _1005549))], (12746 ^ _780086) ^ [_1005670, _1005672, _1005674, _1005676] : [class_Lattices_Osemilattice__sup(_1005670), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1005670), _1005672), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1005670), _1005674), _1005676)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1005670), _1005674), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1005670), _1005672), _1005676)))], (12752 ^ _780086) ^ [_1005813, _1005815, _1005817, _1005819] : [class_Lattices_Olattice(_1005813), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1005813), _1005815), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1005813), _1005817), _1005819)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1005813), _1005817), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1005813), _1005815), _1005819)))], (12758 ^ _780086) ^ [_1005956, _1005958, _1005960, _1005962] : [class_Lattices_Osemilattice__sup(_1005956), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1005956), _1005958), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1005956), _1005960), _1005962)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1005956), _1005960), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1005956), _1005958), _1005962)))], (12764 ^ _780086) ^ [_1006099, _1006101, _1006103, _1006105] : [class_Lattices_Osemilattice__sup(_1006099), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1006099), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1006099), _1006101), _1006103)), _1006105) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1006099), _1006101), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1006099), _1006103), _1006105)))], (12770 ^ _780086) ^ [_1006242, _1006244, _1006246, _1006248] : [class_Lattices_Olattice(_1006242), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1006242), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1006242), _1006244), _1006246)), _1006248) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1006242), _1006244), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1006242), _1006246), _1006248)))], (12776 ^ _780086) ^ [_1006385, _1006387, _1006389, _1006391] : [class_Lattices_Osemilattice__sup(_1006385), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1006385), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1006385), _1006387), _1006389)), _1006391) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1006385), _1006387), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1006385), _1006389), _1006391)))], (12782 ^ _780086) ^ [_1006528, _1006530, _1006532, _1006534, _1006536] : [class_Lattices_Olattice(_1006528), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1006530, _1006528)), _1006532), _1006534), _1006536) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1006528), hAPP(_1006532, _1006536)), hAPP(_1006534, _1006536)))], (12788 ^ _780086) ^ [_1006665, _1006667] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1006665, _1006667)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1006665, _1006667), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1006667), c_Orderings_Otop__class_Otop(tc_fun(_1006667, tc_HOL_Obool)))))], (12794 ^ _780086) ^ [_1006790, _1006792] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1006790), c_Orderings_Otop__class_Otop(tc_fun(_1006790, tc_HOL_Obool)))), hAPP(c_Finite__Set_Ocard(_1006790), _1006792) = hAPP(c_Finite__Set_Ocard(_1006790), c_Orderings_Otop__class_Otop(tc_fun(_1006790, tc_HOL_Obool))), -(_1006792 = c_Orderings_Otop__class_Otop(tc_fun(_1006790, tc_HOL_Obool)))], (12804 ^ _780086) ^ [_1006977, _1006979] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1006977, tc_HOL_Obool)), _1006979), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1006977, tc_HOL_Obool)), _1006979)) = c_Orderings_Otop__class_Otop(tc_fun(_1006977, tc_HOL_Obool)))], (12806 ^ _780086) ^ [_1007026, _1007028] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1007026, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1007026, tc_HOL_Obool)), _1007028)), _1007028) = c_Orderings_Otop__class_Otop(tc_fun(_1007026, tc_HOL_Obool)))], (12808 ^ _780086) ^ [_1007075, _1007077] : [class_Lattices_Oboolean__algebra(_1007075), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1007075), _1007077), hAPP(c_Groups_Ouminus__class_Ouminus(_1007075), _1007077)) = c_Orderings_Otop__class_Otop(_1007075))], (12814 ^ _780086) ^ [_1007180, _1007182] : [class_Lattices_Oboolean__algebra(_1007180), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1007180), hAPP(c_Groups_Ouminus__class_Ouminus(_1007180), _1007182)), _1007182) = c_Orderings_Otop__class_Otop(_1007180))], (12820 ^ _780086) ^ [_1007285, _1007287, _1007289] : [class_Lattices_Olattice(_1007285), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007285), _1007287), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1007285), _1007287), _1007289))))], (12826 ^ _780086) ^ [_1007392, _1007394, _1007396] : [class_Lattices_Osemilattice__sup(_1007392), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007392), _1007394), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1007392), _1007394), _1007396))))], (12832 ^ _780086) ^ [_1007499, _1007501, _1007503] : [class_Lattices_Olattice(_1007499), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007499), _1007501), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1007499), _1007503), _1007501))))], (12838 ^ _780086) ^ [_1007606, _1007608, _1007610] : [class_Lattices_Osemilattice__sup(_1007606), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007606), _1007608), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1007606), _1007610), _1007608))))], (12844 ^ _780086) ^ [_1007713, _1007715, _1007717] : [class_Lattices_Osemilattice__sup(_1007713), 12847 ^ _780086 : [(12848 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007713), _1007715), _1007717)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1007713), _1007715), _1007717) = _1007717)], (12854 ^ _780086) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1007713), _1007715), _1007717) = _1007717, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007713), _1007715), _1007717)))]]], (12860 ^ _780086) ^ [_1007969, _1007971, _1007973, _1007975] : [class_Lattices_Osemilattice__sup(_1007969), 12863 ^ _780086 : [(12864 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007969), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1007969), _1007971), _1007973)), _1007975)), 12867 ^ _780086 : [(12868 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007969), _1007971), _1007975)))], (12870 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007969), _1007973), _1007975)))]]], (12872 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007969), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1007969), _1007971), _1007973)), _1007975))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007969), _1007971), _1007975)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007969), _1007973), _1007975))]]], (12882 ^ _780086) ^ [_1008349, _1008351, _1008353, _1008355] : [class_Lattices_Osemilattice__sup(_1008349), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008349), _1008351), _1008353)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008349), _1008351), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1008349), _1008353), _1008355))))], (12892 ^ _780086) ^ [_1008528, _1008530, _1008532, _1008534] : [class_Lattices_Osemilattice__sup(_1008528), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008528), _1008530), _1008532)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008528), _1008530), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1008528), _1008534), _1008532))))], (12902 ^ _780086) ^ [_1008707, _1008709, _1008711] : [class_Lattices_Osemilattice__sup(_1008707), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008707), _1008709), _1008711)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1008707), _1008709), _1008711) = _1008711)], (12912 ^ _780086) ^ [_1008868, _1008870, _1008872] : [class_Lattices_Osemilattice__sup(_1008868), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008868), _1008870), _1008872)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1008868), _1008872), _1008870) = _1008872)], (12922 ^ _780086) ^ [_1009029, _1009031, _1009033, _1009035] : [class_Lattices_Osemilattice__sup(_1009029), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009029), _1009031), _1009033)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009029), _1009035), _1009033)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009029), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1009029), _1009031), _1009035)), _1009033)))], (12936 ^ _780086) ^ [_1009278, _1009280, _1009282, _1009284] : [class_Lattices_Osemilattice__sup(_1009278), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009278), _1009280), _1009282)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009278), _1009284), _1009282)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009278), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1009278), _1009280), _1009284)), _1009282)))], (12950 ^ _780086) ^ [_1009527, _1009529, _1009531, _1009533, _1009535] : [class_Lattices_Osemilattice__sup(_1009527), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009527), _1009529), _1009531)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009527), _1009533), _1009535)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009527), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1009527), _1009529), _1009533)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1009527), _1009531), _1009535))))], (12964 ^ _780086) ^ [_1009798, _1009800, _1009802, _1009804] : [class_Lattices_Osemilattice__sup(_1009798), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009798), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1009798), _1009800), _1009802)), _1009804)), 12971 ^ _780086 : [(12972 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009798), _1009800), _1009804)))], (12974 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009798), _1009802), _1009804)))]]], (12976 ^ _780086) ^ [_1010021, _1010023, _1010025, _1010027] : [class_Lattices_Osemilattice__sup(_1010021), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1010021), _1010023), _1010025)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1010021), _1010023), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1010021), _1010025), _1010027))))], (12986 ^ _780086) ^ [_1010200, _1010202, _1010204, _1010206] : [class_Lattices_Osemilattice__sup(_1010200), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1010200), _1010202), _1010204)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1010200), _1010202), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1010200), _1010206), _1010204))))], (12996 ^ _780086) ^ [_1010379, _1010381] : [class_Lattices_Obounded__lattice__bot(_1010379), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1010379), c_Orderings_Obot__class_Obot(_1010379)), _1010381) = _1010381)], (13002 ^ _780086) ^ [_1010474, _1010476] : [class_Lattices_Obounded__lattice__bot(_1010474), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1010474), _1010476), c_Orderings_Obot__class_Obot(_1010474)) = _1010476)], (13008 ^ _780086) ^ [_1010569, _1010571, _1010573] : [class_Lattices_Obounded__lattice__bot(_1010569), 13011 ^ _780086 : [(13012 ^ _780086) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1010569), _1010571), _1010573) = c_Orderings_Obot__class_Obot(_1010569), 13015 ^ _780086 : [(13016 ^ _780086) ^ [] : [-(_1010571 = c_Orderings_Obot__class_Obot(_1010569))], (13018 ^ _780086) ^ [] : [-(_1010573 = c_Orderings_Obot__class_Obot(_1010569))]]], (13020 ^ _780086) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1010569), _1010571), _1010573) = c_Orderings_Obot__class_Obot(_1010569)), _1010571 = c_Orderings_Obot__class_Obot(_1010569), _1010573 = c_Orderings_Obot__class_Obot(_1010569)]]], (13040 ^ _780086) ^ [_1011071, _1011073, _1011075, _1011077] : [13041 ^ _780086 : [(13042 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1011071), _1011073), _1011075))], (13044 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1011071), _1011073), _1011077))]], -(hBOOL(hAPP(hAPP(c_member(_1011071), _1011073), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1011071, tc_HOL_Obool)), _1011075), _1011077))))], (13030 ^ _780086) ^ [_1010917, _1010919, _1010921, _1010923] : [hBOOL(hAPP(hAPP(c_member(_1010917), _1010919), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1010917, tc_HOL_Obool)), _1010921), _1010923))), -(hBOOL(hAPP(hAPP(c_member(_1010917), _1010919), _1010921))), -(hBOOL(hAPP(hAPP(c_member(_1010917), _1010919), _1010923)))], (13048 ^ _780086) ^ [_1011256, _1011258, _1011260, _1011262] : [hBOOL(hAPP(hAPP(c_member(_1011256), _1011258), _1011260)), -(hBOOL(hAPP(hAPP(c_member(_1011256), _1011258), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1011256, tc_HOL_Obool)), _1011260), _1011262))))], (13054 ^ _780086) ^ [_1011387, _1011389, _1011391, _1011393] : [hBOOL(hAPP(hAPP(c_member(_1011387), _1011389), _1011391)), -(hBOOL(hAPP(hAPP(c_member(_1011387), _1011389), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1011387, tc_HOL_Obool)), _1011393), _1011391))))], (13060 ^ _780086) ^ [_1011518] : [-(c_Lattices_Osemilattice__sup__class_Osup(_1011518) = c_Orderings_Oord__class_Omax(_1011518)), class_Lattices_Osemilattice__sup(_1011518), class_Orderings_Olinorder(_1011518)], (13070 ^ _780086) ^ [_1011647, _1011649] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1011647, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1011647, tc_HOL_Obool))), _1011649) = _1011649)], (13072 ^ _780086) ^ [_1011688, _1011690] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1011688, tc_HOL_Obool)), _1011690), c_Orderings_Obot__class_Obot(tc_fun(_1011688, tc_HOL_Obool))) = _1011690)], (13074 ^ _780086) ^ [_1011747, _1011749, _1011751] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1011747, tc_HOL_Obool)), _1011749), _1011751) = c_Orderings_Obot__class_Obot(tc_fun(_1011747, tc_HOL_Obool)), 13077 ^ _780086 : [(13078 ^ _780086) ^ [] : [-(_1011749 = c_Orderings_Obot__class_Obot(tc_fun(_1011747, tc_HOL_Obool)))], (13080 ^ _780086) ^ [] : [-(_1011751 = c_Orderings_Obot__class_Obot(tc_fun(_1011747, tc_HOL_Obool)))]]], (13082 ^ _780086) ^ [_1011900, _1011902, _1011904] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1011900, tc_HOL_Obool)), _1011902), _1011904) = c_Orderings_Obot__class_Obot(tc_fun(_1011900, tc_HOL_Obool))), _1011902 = c_Orderings_Obot__class_Obot(tc_fun(_1011900, tc_HOL_Obool)), _1011904 = c_Orderings_Obot__class_Obot(tc_fun(_1011900, tc_HOL_Obool))], (13092 ^ _780086) ^ [_1012105, _1012107, _1012109] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1012105), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1012105, tc_HOL_Obool)), _1012107), _1012109))), 13095 ^ _780086 : [(13096 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1012105), _1012107)))], (13098 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1012105), _1012109)))]]], (13100 ^ _780086) ^ [_1012252, _1012254, _1012256] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1012252), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1012252, tc_HOL_Obool)), _1012254), _1012256)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1012252), _1012254)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1012252), _1012256))], (13110 ^ _780086) ^ [_1012433, _1012435, _1012437] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1012433), _1012435)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1012433), _1012437)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1012433), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1012433, tc_HOL_Obool)), _1012435), _1012437))))], (13120 ^ _780086) ^ [_1012612, _1012614, _1012616, _1012618] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1012612, tc_HOL_Obool)), _1012614), hAPP(hAPP(c_Set_Oinsert(_1012612), _1012616), _1012618)) = hAPP(hAPP(c_Set_Oinsert(_1012612), _1012616), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1012612, tc_HOL_Obool)), _1012614), _1012618)))], (13122 ^ _780086) ^ [_1012679, _1012681, _1012683, _1012685] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1012679, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1012679), _1012681), _1012683)), _1012685) = hAPP(hAPP(c_Set_Oinsert(_1012679), _1012681), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1012679, tc_HOL_Obool)), _1012683), _1012685)))], (13124 ^ _780086) ^ [_1012746, _1012748, _1012750] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1012746, tc_HOL_Obool)), _1012748), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1012746, tc_HOL_Obool)), _1012748), _1012750))))], (13126 ^ _780086) ^ [_1012794, _1012796, _1012798] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1012794, tc_HOL_Obool)), _1012796), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1012794, tc_HOL_Obool)), _1012798), _1012796))))], (13128 ^ _780086) ^ [_1012860, _1012862, _1012864] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1012860, tc_HOL_Obool)), _1012862), _1012864)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1012860, tc_HOL_Obool)), _1012862), _1012864) = _1012864)], (13134 ^ _780086) ^ [_1012977, _1012979, _1012981] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1012977, tc_HOL_Obool)), _1012979), _1012981) = _1012981, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1012977, tc_HOL_Obool)), _1012979), _1012981)))], (13140 ^ _780086) ^ [_1013100, _1013102, _1013104] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1013100, tc_HOL_Obool)), _1013102), _1013104)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1013100, tc_HOL_Obool)), _1013102), _1013104) = _1013104)], (13146 ^ _780086) ^ [_1013221, _1013223, _1013225] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1013221, tc_HOL_Obool)), _1013223), _1013225)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1013221, tc_HOL_Obool)), _1013225), _1013223) = _1013225)], (13152 ^ _780086) ^ [_1013342, _1013344, _1013346, _1013348] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1013342, tc_HOL_Obool)), _1013344), _1013346)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1013342, tc_HOL_Obool)), _1013348), _1013346)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1013342, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1013342, tc_HOL_Obool)), _1013344), _1013348)), _1013346)))], (13162 ^ _780086) ^ [_1013561, _1013563, _1013565, _1013567, _1013569] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1013561, tc_HOL_Obool)), _1013563), _1013565)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1013561, tc_HOL_Obool)), _1013567), _1013569)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1013561, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1013561, tc_HOL_Obool)), _1013563), _1013567)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1013561, tc_HOL_Obool)), _1013565), _1013569))))], (13172 ^ _780086) ^ [_1013806, _1013808, _1013810, _1013812, _1013814] : [-(hAPP(c_Set_Oimage(_1013806, _1013808, _1013810), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1013806, tc_HOL_Obool)), _1013812), _1013814)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1013808, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1013806, _1013808, _1013810), _1013812)), hAPP(c_Set_Oimage(_1013806, _1013808, _1013810), _1013814)))], (13174 ^ _780086) ^ [_1013880, _1013882, _1013884] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1013880, tc_HOL_Obool)), _1013882), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1013880, tc_HOL_Obool)), _1013884), _1013882)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1013880, tc_HOL_Obool)), _1013882), _1013884))], (13176 ^ _780086) ^ [_1013940, _1013942, _1013944] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1013940, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1013940, tc_HOL_Obool)), _1013942), _1013944)), _1013944) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1013940, tc_HOL_Obool)), _1013942), _1013944))], (13178 ^ _780086) ^ [_1014000, _1014002, _1014004, _1014006] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1014000, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1014000, tc_HOL_Obool)), _1014002), _1014004)), _1014006) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1014000, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1014000, tc_HOL_Obool)), _1014002), _1014006)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1014000, tc_HOL_Obool)), _1014004), _1014006)))], (13180 ^ _780086) ^ [_1014093] : [c_Orderings_Otop__class_Otop(tc_fun(_1014093, tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(_1014093, tc_HOL_Obool))], (13182 ^ _780086) ^ [_1014126] : [class_Finite__Set_Ofinite(_1014126), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1014126), c_Orderings_Otop__class_Otop(tc_fun(_1014126, tc_HOL_Obool)))))], (13188 ^ _780086) ^ [_1014217, _1014219] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1014217, tc_HOL_Obool)), _1014219), c_Orderings_Otop__class_Otop(tc_fun(_1014217, tc_HOL_Obool)))))], (13190 ^ _780086) ^ [_1014257, _1014259, _1014261, _1014263, _1014265] : [c_Fun_Oinj__on(_1014257, _1014259, _1014261, c_Orderings_Otop__class_Otop(tc_fun(_1014257, tc_HOL_Obool))), 13193 ^ _780086 : [(13194 ^ _780086) ^ [] : [hAPP(_1014261, _1014263) = hAPP(_1014261, _1014265), -(_1014263 = _1014265)], (13200 ^ _780086) ^ [] : [_1014263 = _1014265, -(hAPP(_1014261, _1014263) = hAPP(_1014261, _1014265))]]], (13206 ^ _780086) ^ [_1014514, _1014516, _1014518, _1014520, _1014522] : [c_Fun_Oinj__on(_1014514, _1014516, _1014518, c_Orderings_Otop__class_Otop(tc_fun(_1014514, tc_HOL_Obool))), hAPP(_1014518, _1014520) = hAPP(_1014518, _1014522), -(_1014520 = _1014522)], (13216 ^ _780086) ^ [_1014681, _1014683, _1014685, _1014687, _1014689] : [-(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1014681, _1014683, _1014685), _1014687), _1014689), c_Orderings_Obot__class_Obot(tc_fun(_1014683, tc_HOL_Obool))) = _1014689)], (13218 ^ _780086) ^ [_1014730] : [class_Lattices_Osemilattice__sup(_1014730), -(c_Finite__Set_Ofun__left__comm__idem(_1014730, _1014730, c_Lattices_Osemilattice__sup__class_Osup(_1014730)))], (13224 ^ _780086) ^ [_1014830, _1014832, _1014834, _1014836] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1014830, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1014830, tc_fun(_1014830, tc_HOL_Obool), tc_HOL_Obool), c_member(_1014830)), _1014832)), hAPP(hAPP(c_COMBC(_1014830, tc_fun(_1014830, tc_HOL_Obool), tc_HOL_Obool), c_member(_1014830)), _1014834)), _1014836)), -(hBOOL(hAPP(hAPP(c_member(_1014830), _1014836), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1014830, tc_HOL_Obool)), _1014832), _1014834))))], (13230 ^ _780086) ^ [_1015029, _1015031, _1015033, _1015035] : [hBOOL(hAPP(hAPP(c_member(_1015029), _1015035), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1015029, tc_HOL_Obool)), _1015031), _1015033))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1015029, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1015029, tc_fun(_1015029, tc_HOL_Obool), tc_HOL_Obool), c_member(_1015029)), _1015031)), hAPP(hAPP(c_COMBC(_1015029, tc_fun(_1015029, tc_HOL_Obool), tc_HOL_Obool), c_member(_1015029)), _1015033)), _1015035)))], (13236 ^ _780086) ^ [_1015234, _1015236, _1015238, _1015240, _1015242] : [-(hAPP(c_Set_Oimage(_1015234, _1015236, hAPP(hAPP(c_COMBB(_1015238, _1015236, _1015234), _1015240), _1015242)), c_Orderings_Otop__class_Otop(tc_fun(_1015234, tc_HOL_Obool))) = hAPP(c_Set_Oimage(_1015238, _1015236, _1015240), hAPP(c_Set_Oimage(_1015234, _1015238, _1015242), c_Orderings_Otop__class_Otop(tc_fun(_1015234, tc_HOL_Obool)))))], (13238 ^ _780086) ^ [_1015306, _1015308, _1015310, _1015312] : [c_Fun_Oinj__on(_1015306, _1015308, _1015310, c_Orderings_Otop__class_Otop(tc_fun(_1015306, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1015306, tc_fun(_1015312, _1015308), hAPP(hAPP(c_COMBB(_1015308, tc_fun(_1015312, _1015308), _1015306), c_COMBK(_1015308, _1015312)), _1015310), c_Orderings_Otop__class_Otop(tc_fun(_1015306, tc_HOL_Obool))))], (13244 ^ _780086) ^ [_1015453, _1015455] : [class_Orderings_Otop(_1015453), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1015453), _1015455), c_Orderings_Otop__class_Otop(_1015453))))], (13250 ^ _780086) ^ [_1015546, _1015548, _1015550, _1015552] : [-(hAPP(c_Finite__Set_Ofold__image(_1015546, _1015548, _1015550), _1015552) = c_Finite__Set_Ofold(_1015548, _1015546, hAPP(hAPP(c_COMBB(_1015546, tc_fun(_1015546, _1015546), _1015548), _1015550), _1015552)))], (13252 ^ _780086) ^ [_1015599, _1015601, _1015603] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1015599), _1015601)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1015599), _1015601)), hAPP(c_Finite__Set_Ocard(_1015599), hAPP(hAPP(c_Set_Oinsert(_1015599), _1015603), _1015601)))))], (13258 ^ _780086) ^ [_1015732, _1015734, _1015736] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1015732), _1015734)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1015732, tc_HOL_Obool)), _1015736), _1015734)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1015732), _1015736)), hAPP(c_Finite__Set_Ocard(_1015732), _1015734))))], (13268 ^ _780086) ^ [_1015923, _1015925, _1015927] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1015923), _1015925)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1015923, tc_HOL_Obool)), _1015927), _1015925)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1015923), _1015925)), hAPP(c_Finite__Set_Ocard(_1015923), _1015927))), -(_1015927 = _1015925)], (13282 ^ _780086) ^ [_1016168, _1016170, _1016172, _1016174] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1016168), _1016170)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1016172), hAPP(c_Set_Oimage(_1016168, _1016172, _1016174), _1016170))), hAPP(c_Finite__Set_Ocard(_1016168), _1016170))))], (13288 ^ _780086) ^ [_1016301, _1016303, _1016305, _1016307] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1016301), hAPP(c_Set_Oimage(_1016303, _1016301, _1016305), _1016307))), hAPP(c_Finite__Set_Ocard(_1016303), _1016307))), c_Fun_Oinj__on(_1016303, _1016301, _1016305, _1016307)], (13294 ^ _780086) ^ [_1016431, _1016433, _1016435, _1016437] : [c_Fun_Oinj__on(_1016431, _1016433, _1016435, _1016437), -(hAPP(c_Finite__Set_Ocard(_1016433), hAPP(c_Set_Oimage(_1016431, _1016433, _1016435), _1016437)) = hAPP(c_Finite__Set_Ocard(_1016431), _1016437))], (13300 ^ _780086) ^ [_1016550, _1016552, _1016554] : [-(hAPP(hAPP(c_Set_Oinsert(_1016550), _1016552), _1016554) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1016550, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1016550), _1016552), c_Orderings_Obot__class_Obot(tc_fun(_1016550, tc_HOL_Obool)))), _1016554))], (13302 ^ _780086) ^ [_1016630, _1016632, _1016634, _1016636] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1016630, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1016630, tc_HOL_Obool)), _1016632), _1016634)), _1016636)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1016630, tc_HOL_Obool)), _1016632), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1016630, tc_HOL_Obool)), _1016634), _1016636))))], (13308 ^ _780086) ^ [_1016791, _1016793, _1016795, _1016797] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1016791, tc_HOL_Obool)), _1016793), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1016791, tc_HOL_Obool)), _1016795), _1016797))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1016791, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1016791, tc_HOL_Obool)), _1016793), _1016795)), _1016797)))], (13314 ^ _780086) ^ [_1016958, _1016960, _1016962] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1016958, tc_HOL_Obool)), _1016960), _1016962)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1016958, tc_HOL_Obool)), _1016960), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1016958, tc_HOL_Obool)), _1016962), _1016960)) = _1016962)], (13320 ^ _780086) ^ [_1017101, _1017103, _1017105] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1017101), _1017103)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1017101, tc_HOL_Obool)), _1017105), _1017103)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1017101), _1017105)), hAPP(c_Finite__Set_Ocard(_1017101), _1017103))))], (13330 ^ _780086) ^ [_1017292, _1017294, _1017296, _1017298, _1017300] : [c_Fun_Oinj__on(_1017292, _1017294, _1017296, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1017292, tc_HOL_Obool)), _1017298), _1017300)), 13333 ^ _780086 : [(13334 ^ _780086) ^ [] : [hAPP(c_Set_Oimage(_1017292, _1017294, _1017296), _1017298) = hAPP(c_Set_Oimage(_1017292, _1017294, _1017296), _1017300), -(_1017298 = _1017300)], (13340 ^ _780086) ^ [] : [_1017298 = _1017300, -(hAPP(c_Set_Oimage(_1017292, _1017294, _1017296), _1017298) = hAPP(c_Set_Oimage(_1017292, _1017294, _1017296), _1017300))]]], (13346 ^ _780086) ^ [_1017585, _1017587, _1017589, _1017591] : [-(hBOOL(hAPP(hAPP(c_member(_1017585), hAPP(_1017587, _1017589)), hAPP(c_Set_Oimage(_1017591, _1017585, _1017587), c_Orderings_Otop__class_Otop(tc_fun(_1017591, tc_HOL_Obool))))))], (13348 ^ _780086) ^ [_1017636, _1017638, _1017640, _1017642, _1017644] : [_1017636 = hAPP(_1017638, _1017640), -(hBOOL(hAPP(hAPP(c_member(_1017642), _1017636), hAPP(c_Set_Oimage(_1017644, _1017642, _1017638), c_Orderings_Otop__class_Otop(tc_fun(_1017644, tc_HOL_Obool))))))], (13354 ^ _780086) ^ [_1017763, _1017765, _1017767, _1017769] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1017763), _1017765)), -(hAPP(c_Set_Oimage(_1017763, _1017767, _1017769), _1017765) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(_1017767, tc_HOL_Obool), _1017763, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1017767, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1017763, tc_fun(_1017767, tc_HOL_Obool), tc_fun(_1017767, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1017767, tc_fun(tc_fun(_1017767, tc_HOL_Obool), tc_fun(_1017767, tc_HOL_Obool)), _1017763), c_Set_Oinsert(_1017767)), _1017769)), c_Orderings_Obot__class_Obot(tc_fun(_1017767, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(_1017767, tc_HOL_Obool))), _1017765))], (13360 ^ _780086) ^ [_1018002, _1018004] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1018002, tc_HOL_Obool)), _1018004), c_Orderings_Otop__class_Otop(tc_fun(_1018002, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1018002, tc_HOL_Obool)))], (13362 ^ _780086) ^ [_1018048, _1018050, _1018052] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1018048, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1018048, tc_HOL_Obool)), _1018050), _1018052)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1018048, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1018048, tc_HOL_Obool)), _1018050)), _1018052))], (13364 ^ _780086) ^ [_1018113, _1018115, _1018117, _1018119, _1018121] : [c_Fun_Oinj__on(_1018113, _1018115, _1018117, c_Orderings_Otop__class_Otop(tc_fun(_1018113, tc_HOL_Obool))), 13367 ^ _780086 : [(13368 ^ _780086) ^ [] : [hAPP(c_Set_Oimage(_1018113, _1018115, _1018117), _1018119) = hAPP(c_Set_Oimage(_1018113, _1018115, _1018117), _1018121), -(_1018119 = _1018121)], (13374 ^ _780086) ^ [] : [_1018119 = _1018121, -(hAPP(c_Set_Oimage(_1018113, _1018115, _1018117), _1018119) = hAPP(c_Set_Oimage(_1018113, _1018115, _1018117), _1018121))]]], (13380 ^ _780086) ^ [_1018394] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1018394, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1018394, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1018394, tc_HOL_Obool)))], (13382 ^ _780086) ^ [_1018435] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1018435, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1018435, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1018435, tc_HOL_Obool)))], (13384 ^ _780086) ^ [_1018476, _1018478] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1018476), _1018478)), 13387 ^ _780086 : [(13388 ^ _780086) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1018476), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1018476, tc_HOL_Obool)), _1018478))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1018476), c_Orderings_Otop__class_Otop(tc_fun(_1018476, tc_HOL_Obool)))))], (13394 ^ _780086) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1018476), c_Orderings_Otop__class_Otop(tc_fun(_1018476, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1018476), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1018476, tc_HOL_Obool)), _1018478))))]]], (13400 ^ _780086) ^ [_1018754, _1018756] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1018754, tc_HOL_Obool)), _1018756) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1018754, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1018754, tc_HOL_Obool))), _1018756))], (13402 ^ _780086) ^ [_1018803] : [-(c_Fun_Oinj__on(_1018803, tc_fun(_1018803, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1018803, tc_fun(_1018803, tc_HOL_Obool), tc_fun(_1018803, tc_HOL_Obool)), c_Set_Oinsert(_1018803)), c_Orderings_Obot__class_Obot(tc_fun(_1018803, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1018803, tc_HOL_Obool))))], (13404 ^ _780086) ^ [_1018859, _1018861, _1018863, _1018865, _1018867] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1018859), hAPP(c_Set_Oimage(_1018861, _1018859, _1018863), c_Orderings_Otop__class_Otop(tc_fun(_1018861, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1018865), hAPP(c_Set_Oimage(_1018861, _1018865, hAPP(hAPP(c_COMBB(_1018859, _1018865, _1018861), _1018867), _1018863)), c_Orderings_Otop__class_Otop(tc_fun(_1018861, tc_HOL_Obool))))))], (13410 ^ _780086) ^ [_1019026, _1019028, _1019030, _1019032] : [c_Fun_Oinj__on(_1019026, _1019028, _1019030, c_Orderings_Otop__class_Otop(tc_fun(_1019026, tc_HOL_Obool))), -(hAPP(c_Fun_Othe__inv__into(_1019026, _1019028, c_Orderings_Otop__class_Otop(tc_fun(_1019026, tc_HOL_Obool)), _1019030), hAPP(_1019030, _1019032)) = _1019032)], (13416 ^ _780086) ^ [_1019153, _1019155, _1019157, _1019159, _1019161, _1019163, _1019165, _1019167] : [c_Finite__Set_Ofolding__image__simple__idem(_1019153, _1019155, _1019157, _1019159, _1019161, _1019163), hBOOL(hAPP(c_Finite__Set_Ofinite(_1019155), _1019165)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1019155), _1019167)), -(hAPP(_1019163, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1019155, tc_HOL_Obool)), _1019165), _1019167)) = hAPP(hAPP(_1019157, hAPP(_1019163, _1019165)), hAPP(_1019163, _1019167)))], (13430 ^ _780086) ^ [_1019446, _1019448, _1019450, _1019452, _1019454, _1019456, _1019458] : [c_Finite__Set_Ofolding__image__simple(_1019446, _1019448, _1019450, _1019452, _1019454, _1019456), hBOOL(hAPP(c_Finite__Set_Ofinite(_1019448), _1019458)), -(hAPP(_1019456, _1019458) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1019446, _1019448, _1019450), _1019454), _1019452), _1019458))], (13440 ^ _780086) ^ [_1019643, _1019645, _1019647, _1019649] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1019643), _1019645)), 13443 ^ _780086 : [(13444 ^ _780086) ^ [] : [c_Fun_Oinj__on(_1019643, _1019647, _1019649, _1019645), -(hAPP(c_Finite__Set_Ocard(_1019647), hAPP(c_Set_Oimage(_1019643, _1019647, _1019649), _1019645)) = hAPP(c_Finite__Set_Ocard(_1019643), _1019645))], (13450 ^ _780086) ^ [] : [hAPP(c_Finite__Set_Ocard(_1019647), hAPP(c_Set_Oimage(_1019643, _1019647, _1019649), _1019645)) = hAPP(c_Finite__Set_Ocard(_1019643), _1019645), -(c_Fun_Oinj__on(_1019643, _1019647, _1019649, _1019645))]]], (13456 ^ _780086) ^ [_1019927, _1019929, _1019931, _1019933] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1019927), _1019929)), hAPP(c_Finite__Set_Ocard(_1019931), hAPP(c_Set_Oimage(_1019927, _1019931, _1019933), _1019929)) = hAPP(c_Finite__Set_Ocard(_1019927), _1019929), -(c_Fun_Oinj__on(_1019927, _1019931, _1019933, _1019929))], (13466 ^ _780086) ^ [_1020110, _1020112, _1020114] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1020110), _1020112)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1020110), _1020114)), hAPP(c_Finite__Set_Ocard(_1020110), _1020112))), hAPP(c_Finite__Set_Ocard(_1020110), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1020110, tc_HOL_Obool)), _1020114), _1020112)))))], (13472 ^ _780086) ^ [_1020271, _1020273, _1020275, _1020277] : [class_Lattices_Osemilattice__sup(_1020271), hBOOL(hAPP(c_Finite__Set_Ofinite(_1020271), _1020273)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1020271, _1020271, c_Lattices_Osemilattice__sup__class_Osup(_1020271)), _1020275), hAPP(hAPP(c_Set_Oinsert(_1020271), _1020277), _1020273)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1020271), _1020277), hAPP(hAPP(c_Finite__Set_Ofold(_1020271, _1020271, c_Lattices_Osemilattice__sup__class_Osup(_1020271)), _1020275), _1020273)))], (13482 ^ _780086) ^ [_1020494, _1020496, _1020498] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1020494), _1020496)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1020494, tc_HOL_Obool)), _1020498), _1020496)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1020494), _1020498)), hAPP(c_Finite__Set_Ocard(_1020494), _1020496))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1020494, tc_HOL_Obool)), _1020498), _1020496)))], (13496 ^ _780086) ^ [_1020759] : [class_Lattices_Oboolean__algebra(_1020759), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1020759), c_Orderings_Otop__class_Otop(_1020759)) = c_Orderings_Obot__class_Obot(_1020759))], (13502 ^ _780086) ^ [_1020850] : [class_Lattices_Oboolean__algebra(_1020850), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1020850), c_Orderings_Obot__class_Obot(_1020850)) = c_Orderings_Otop__class_Otop(_1020850))], (13508 ^ _780086) ^ [_1020941, _1020943, _1020945, _1020947] : [c_Fun_Oinj__on(_1020941, _1020943, _1020945, c_Orderings_Otop__class_Otop(tc_fun(_1020941, tc_HOL_Obool))), 13511 ^ _780086 : [(13512 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1020943), _1020947), hAPP(c_Set_Oimage(_1020941, _1020943, _1020945), c_Orderings_Otop__class_Otop(tc_fun(_1020941, tc_HOL_Obool))))), 13516 ^ _780086 : [(13517 ^ _780086) ^ [] : [-(_1020947 = hAPP(_1020945, 13515 ^ [_1020941, _1020943, _1020945, _1020947]))], (13519 ^ _780086) ^ [_1021206] : [_1020947 = hAPP(_1020945, _1021206), -(_1021206 = 13515 ^ [_1020941, _1020943, _1020945, _1020947])]]], (13525 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1020943), _1020947), hAPP(c_Set_Oimage(_1020941, _1020943, _1020945), c_Orderings_Otop__class_Otop(tc_fun(_1020941, tc_HOL_Obool)))))), 13526 ^ _780086 : [(13527 ^ _780086) ^ [_1021344] : [_1020947 = hAPP(_1020945, _1021344), 13531 ^ _780086 : [(13532 ^ _780086) ^ [] : [-(_1020947 = hAPP(_1020945, 13530 ^ [_1020941, _1020943, _1020945, _1020947, _1021344]))], (13534 ^ _780086) ^ [] : [13530 ^ [_1020941, _1020943, _1020945, _1020947, _1021344] = _1021344]]]]]]], (13538 ^ _780086) ^ [_1021572, _1021574, _1021576, _1021578, _1021580] : [c_Fun_Oinj__on(_1021572, _1021574, _1021576, c_Orderings_Otop__class_Otop(tc_fun(_1021572, tc_HOL_Obool))), 13541 ^ _780086 : [(13542 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1021574), hAPP(_1021576, _1021578)), hAPP(c_Set_Oimage(_1021572, _1021574, _1021576), _1021580))), -(hBOOL(hAPP(hAPP(c_member(_1021572), _1021578), _1021580)))], (13548 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1021572), _1021578), _1021580)), -(hBOOL(hAPP(hAPP(c_member(_1021574), hAPP(_1021576, _1021578)), hAPP(c_Set_Oimage(_1021572, _1021574, _1021576), _1021580))))]]], (13554 ^ _780086) ^ [_1021883, _1021885] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1021883), c_Orderings_Otop__class_Otop(tc_fun(_1021883, tc_HOL_Obool)))), c_Fun_Oinj__on(_1021883, _1021883, _1021885, c_Orderings_Otop__class_Otop(tc_fun(_1021883, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1021883, _1021883, _1021885), c_Orderings_Otop__class_Otop(tc_fun(_1021883, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1021883, tc_HOL_Obool)))], (13564 ^ _780086) ^ [_1022078, _1022080] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1022078), c_Orderings_Otop__class_Otop(tc_fun(_1022078, tc_HOL_Obool)))), hAPP(c_Set_Oimage(_1022078, _1022078, _1022080), c_Orderings_Otop__class_Otop(tc_fun(_1022078, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1022078, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1022078, _1022078, _1022080, c_Orderings_Otop__class_Otop(tc_fun(_1022078, tc_HOL_Obool))))], (13574 ^ _780086) ^ [_1022273, _1022275, _1022277, _1022279, _1022281] : [c_Fun_Oinj__on(_1022273, _1022275, _1022277, c_Orderings_Otop__class_Otop(tc_fun(_1022273, tc_HOL_Obool))), 13577 ^ _780086 : [(13578 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1022275, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1022273, _1022275, _1022277), _1022279)), hAPP(c_Set_Oimage(_1022273, _1022275, _1022277), _1022281))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1022273, tc_HOL_Obool)), _1022279), _1022281)))], (13584 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1022273, tc_HOL_Obool)), _1022279), _1022281)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1022275, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1022273, _1022275, _1022277), _1022279)), hAPP(c_Set_Oimage(_1022273, _1022275, _1022277), _1022281))))]]], (13590 ^ _780086) ^ [_1022614, _1022616, _1022618, _1022620, _1022622] : [c_Fun_Oinj__on(_1022614, _1022616, _1022618, c_Orderings_Otop__class_Otop(tc_fun(_1022614, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1022614, _1022616, _1022618), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1022614, tc_HOL_Obool)), _1022620), _1022622)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1022616, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1022614, _1022616, _1022618), _1022620)), hAPP(c_Set_Oimage(_1022614, _1022616, _1022618), _1022622)))], (13596 ^ _780086) ^ [_1022797, _1022799, _1022801, _1022803] : [hAPP(c_Set_Oimage(_1022797, _1022799, _1022801), c_Orderings_Otop__class_Otop(tc_fun(_1022797, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1022799, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1022799, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1022799, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1022797, _1022799, _1022801), _1022803))), hAPP(c_Set_Oimage(_1022797, _1022799, _1022801), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1022797, tc_HOL_Obool)), _1022803)))))], (13602 ^ _780086) ^ [_1022992, _1022994, _1022996, _1022998, _1023000] : [c_Finite__Set_Ofolding__one__idem(_1022992, _1022994, _1022996), hBOOL(hAPP(c_Finite__Set_Ofinite(_1022992), _1022998)), -(_1022998 = c_Orderings_Obot__class_Obot(tc_fun(_1022992, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1022992), _1023000)), -(_1023000 = c_Orderings_Obot__class_Obot(tc_fun(_1022992, tc_HOL_Obool))), -(hAPP(_1022996, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1022992, tc_HOL_Obool)), _1022998), _1023000)) = hAPP(hAPP(_1022994, hAPP(_1022996, _1022998)), hAPP(_1022996, _1023000)))], (13624 ^ _780086) ^ [_1023357, _1023359, _1023361, _1023363, _1023365, _1023367, _1023369] : [c_Big__Operators_Ocomm__monoid__big(_1023357, _1023359, _1023361, _1023363, _1023365), 13627 ^ _780086 : [(13628 ^ _780086) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1023359), _1023367)), -(hAPP(hAPP(_1023365, _1023369), _1023367) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1023357, _1023359, _1023361), _1023369), _1023363), _1023367))], (13634 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1023359), _1023367))), -(hAPP(hAPP(_1023365, _1023369), _1023367) = _1023363)]]], (13640 ^ _780086) ^ [_1023625, _1023627, _1023629] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1023625), _1023627)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1023625), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1023625, tc_HOL_Obool)), _1023627), hAPP(hAPP(c_Set_Oinsert(_1023625), _1023629), c_Orderings_Obot__class_Obot(tc_fun(_1023625, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1023625), _1023627))))], (13646 ^ _780086) ^ [_1023790, _1023792, _1023794, _1023796] : [class_Lattices_Osemilattice__sup(_1023790), hBOOL(hAPP(c_Finite__Set_Ofinite(_1023790), _1023792)), hBOOL(hAPP(hAPP(c_member(_1023790), _1023794), _1023792)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1023790), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1023790), _1023794), _1023796)), hAPP(hAPP(c_Finite__Set_Ofold(_1023790, _1023790, c_Lattices_Osemilattice__sup__class_Osup(_1023790)), _1023796), _1023792))))], (13660 ^ _780086) ^ [_1024057, _1024059, _1024061, _1024063, _1024065] : [c_Fun_Oinj__on(_1024057, _1024059, _1024061, _1024063), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1024059, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1024057, _1024059, _1024061), _1024063)), _1024065)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1024059), _1024065)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1024057), _1024063)), hAPP(c_Finite__Set_Ocard(_1024059), _1024065))))], (13674 ^ _780086) ^ [_1024332, _1024334, _1024336, _1024338, _1024340, _1024342] : [c_Fun_Oinj__on(_1024332, _1024334, _1024336, _1024338), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1024334, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1024332, _1024334, _1024336), _1024338)), _1024340)), c_Fun_Oinj__on(_1024334, _1024332, _1024342, _1024340), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1024332, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1024334, _1024332, _1024342), _1024340)), _1024338)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1024332), _1024338)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1024334), _1024340)), -(hAPP(c_Finite__Set_Ocard(_1024332), _1024338) = hAPP(c_Finite__Set_Ocard(_1024334), _1024340))], (13700 ^ _780086) ^ [_1024829, _1024831, _1024833] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1024829), _1024831)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1024829, tc_HOL_Obool)), _1024831), _1024833)), -(hAPP(c_Finite__Set_Ocard(_1024829), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1024829, tc_HOL_Obool)), _1024833), _1024831)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1024829), _1024833)), hAPP(c_Finite__Set_Ocard(_1024829), _1024831)))], (13710 ^ _780086) ^ [_1025054, _1025056, _1025058] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1025054), _1025056)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1025054, tc_HOL_Obool)), _1025056), _1025058) = hAPP(hAPP(c_Finite__Set_Ofold(_1025054, tc_fun(_1025054, tc_HOL_Obool), c_Set_Oinsert(_1025054)), _1025058), _1025056))], (13716 ^ _780086) ^ [_1025193, _1025195, _1025197] : [class_Lattices_Oab__semigroup__idem__mult(_1025193), hBOOL(hAPP(c_Finite__Set_Ofinite(_1025193), _1025195)), -(_1025195 = c_Orderings_Obot__class_Obot(tc_fun(_1025193, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1025193), _1025197)), -(_1025197 = c_Orderings_Obot__class_Obot(tc_fun(_1025193, tc_HOL_Obool))), -(hAPP(c_Finite__Set_Ofold1(_1025193, c_Groups_Otimes__class_Otimes(_1025193)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1025193, tc_HOL_Obool)), _1025195), _1025197)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025193), hAPP(c_Finite__Set_Ofold1(_1025193, c_Groups_Otimes__class_Otimes(_1025193)), _1025195)), hAPP(c_Finite__Set_Ofold1(_1025193, c_Groups_Otimes__class_Otimes(_1025193)), _1025197)))], (13738 ^ _780086) ^ [_1025572, _1025574, _1025576, _1025578] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1025572), _1025574)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1025576), _1025578)), 13745 ^ _780086 : [(13756 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1025572), _1025574)), hAPP(c_Finite__Set_Ocard(_1025576), _1025578))), 13760 ^ _780086 : [(13761 ^ _780086) ^ [] : [-(c_Fun_Oinj__on(_1025572, _1025576, 13759 ^ [_1025572, _1025574, _1025576, _1025578], _1025574))], (13763 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1025576, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1025572, _1025576, 13759 ^ [_1025572, _1025574, _1025576, _1025578]), _1025574)), _1025578)))]]], (13746 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1025572), _1025574)), hAPP(c_Finite__Set_Ocard(_1025576), _1025578)))), 13747 ^ _780086 : [(13748 ^ _780086) ^ [_1025783] : [c_Fun_Oinj__on(_1025572, _1025576, _1025783, _1025574), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1025576, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1025572, _1025576, _1025783), _1025574)), _1025578))]]]]], (13765 ^ _780086) ^ [_1026099, _1026101, _1026103] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1026099), _1026101)), 13768 ^ _780086 : [(13769 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1026099), _1026103), _1026101)), -(hAPP(c_Finite__Set_Ocard(_1026099), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1026099, tc_HOL_Obool)), _1026101), hAPP(hAPP(c_Set_Oinsert(_1026099), _1026103), c_Orderings_Obot__class_Obot(tc_fun(_1026099, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1026099), _1026101)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (13775 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1026099), _1026103), _1026101))), -(hAPP(c_Finite__Set_Ocard(_1026099), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1026099, tc_HOL_Obool)), _1026101), hAPP(hAPP(c_Set_Oinsert(_1026099), _1026103), c_Orderings_Obot__class_Obot(tc_fun(_1026099, tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(_1026099), _1026101))]]], (13781 ^ _780086) ^ [_1026463, _1026465, _1026467] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1026463), _1026465)), hBOOL(hAPP(hAPP(c_member(_1026463), _1026467), _1026465)), -(hAPP(c_Finite__Set_Ocard(_1026463), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1026463, tc_HOL_Obool)), _1026465), hAPP(hAPP(c_Set_Oinsert(_1026463), _1026467), c_Orderings_Obot__class_Obot(tc_fun(_1026463, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1026463), _1026465)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (13791 ^ _780086) ^ [_1026698, _1026700, _1026702] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1026698), _1026700)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1026702), _1026698)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1026698), _1026702)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1026700), _1026702))))], (13801 ^ _780086) ^ [_1026885, _1026887, _1026889] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1026885), _1026887)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1026885), _1026889)), 13808 ^ _780086 : [(13809 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1026887), _1026885)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1026889), _1026885))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1026887), _1026889)))], (13815 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1026887), _1026889)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1026887), _1026885)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1026889), _1026885))))]]], (13821 ^ _780086) ^ [_1027238, _1027240, _1027242] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027238), _1027240)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027238), _1027242)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1027242), _1027240)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1027242), _1027238))))], (13831 ^ _780086) ^ [_1027425, _1027427, _1027429] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027425), _1027427)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1027425), _1027429)), _1027427)))], (13837 ^ _780086) ^ [_1027532, _1027534] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027532), _1027534))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1027534), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1027532), _1027534)) = _1027532)], (13843 ^ _780086) ^ [_1027603, _1027605, _1027607] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027603), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1027605), _1027607))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1027603), _1027607)), _1027605)))], (13849 ^ _780086) ^ [_1027722, _1027724, _1027726] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1027722), _1027726)), _1027724)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027722), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1027724), _1027726))))], (13855 ^ _780086) ^ [] : [-(hAPP(c_Finite__Set_Ocard(tc_Product__Type_Ounit), c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (13857 ^ _780086) ^ [_1027865] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1027865), _1027865)))], (13859 ^ _780086) ^ [_1027893, _1027895] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1027893), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1027895), _1027893))))], (13861 ^ _780086) ^ [_1027929, _1027931] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1027929), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1027929), _1027931))))], (13863 ^ _780086) ^ [_1027965, _1027967] : [-(c_Fun_Oinj__on(tc_Nat_Onat, tc_Nat_Onat, hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1027965), _1027967))], (13865 ^ _780086) ^ [_1028010, _1028012] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028010), _1028012)), -(_1028012 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1028010), 13868 ^ [_1028010, _1028012]))], (13872 ^ _780086) ^ [_1028117, _1028119] : [13873 ^ _780086 : [(13874 ^ _780086) ^ [_1028167] : [_1028119 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1028117), _1028167)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028117), _1028119)))], (13878 ^ _780086) ^ [_1028227, _1028229] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028227), _1028229))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028229), _1028227)))], (13884 ^ _780086) ^ [_1028291, _1028293, _1028295] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1028291), _1028293)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1028291), _1028295))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028293), _1028295)))], (13890 ^ _780086) ^ [_1028410, _1028412, _1028414] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028412), _1028414)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1028410), _1028412)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1028410), _1028414))))], (13896 ^ _780086) ^ [_1028535, _1028537] : [_1028535 = _1028537, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028535), _1028537)))], (13902 ^ _780086) ^ [_1028622, _1028624, _1028626] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028622), _1028624)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028622), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1028624), _1028626))))], (13908 ^ _780086) ^ [_1028733, _1028735, _1028737] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028733), _1028735)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028733), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1028737), _1028735))))], (13914 ^ _780086) ^ [_1028844, _1028846, _1028848] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028844), _1028846)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1028844), _1028848)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1028846), _1028848))))], (13920 ^ _780086) ^ [_1028967, _1028969, _1028971] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028967), _1028969)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028969), _1028971)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028967), _1028971)))], (13930 ^ _780086) ^ [_1029130, _1029132] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1029130), _1029132)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1029132), _1029130)), -(_1029130 = _1029132)], (13940 ^ _780086) ^ [_1029279, _1029281, _1029283, _1029285] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1029279), _1029281)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1029283), _1029285)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1029279), _1029283)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1029281), _1029285))))], (13950 ^ _780086) ^ [_1029470, _1029472, _1029474] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1029470), _1029472)), _1029474)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1029472), _1029474)))], (13956 ^ _780086) ^ [_1029581, _1029583, _1029585] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1029581), _1029583)), _1029585)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1029581), _1029585)))], (13962 ^ _780086) ^ [_1029692, _1029694, _1029696] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1029692), _1029694)), _1029696)), 13965 ^ _780086 : [(13966 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1029692), _1029696)))], (13968 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1029694), _1029696)))]]], (13981 ^ _780086) ^ [_1030042] : [13983 ^ _780086 : [(13984 ^ _780086) ^ [_1030118] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 13982 ^ [_1030042, _1030118]), _1030042)))], (13986 ^ _780086) ^ [_1030152] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 13982 ^ [_1030042, _1030152]), _1030152))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1030042)))], (13970 ^ _780086) ^ [_1029855] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1029855)), 13974 ^ _780086 : [(13975 ^ _780086) ^ [_1029935] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1029935), _1029855)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1029935), 13973 ^ [_1029855])))]]], (13990 ^ _780086) ^ [_1030239, _1030241, _1030243] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1030239), _1030241) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1030243), _1030241), -(_1030239 = _1030243)], (13996 ^ _780086) ^ [_1030338, _1030340, _1030342] : [_1030338 = _1030342, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1030338), _1030340) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1030342), _1030340))], (14002 ^ _780086) ^ [_1030461, _1030463, _1030465] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1030461), _1030463) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1030461), _1030465), -(_1030463 = _1030465)], (14008 ^ _780086) ^ [_1030560, _1030562, _1030564] : [_1030562 = _1030564, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1030560), _1030562) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1030560), _1030564))], (14014 ^ _780086) ^ [_1030665, _1030667, _1030669] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1030665), _1030667)), _1030669) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1030665), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1030667), _1030669)))], (14016 ^ _780086) ^ [_1030716, _1030718, _1030720] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1030716), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1030718), _1030720)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1030718), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1030716), _1030720)))], (14018 ^ _780086) ^ [_1030767, _1030769] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1030767), _1030769) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1030769), _1030767))], (14020 ^ _780086) ^ [_1030804, _1030806] : [class_Groups_Oone(_1030804), 14023 ^ _780086 : [(14024 ^ _780086) ^ [] : [c_Groups_Oone__class_Oone(_1030804) = _1030806, -(_1030806 = c_Groups_Oone__class_Oone(_1030804))], (14030 ^ _780086) ^ [] : [_1030806 = c_Groups_Oone__class_Oone(_1030804), -(c_Groups_Oone__class_Oone(_1030804) = _1030806)]]], (14036 ^ _780086) ^ [_1031036, _1031038] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1031036), _1031038) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 14039 ^ _780086 : [(14040 ^ _780086) ^ [] : [-(_1031036 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (14042 ^ _780086) ^ [] : [-(_1031038 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (14044 ^ _780086) ^ [_1031147, _1031149] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1031147), _1031149) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1031147 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _1031149 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (14054 ^ _780086) ^ [_1031290] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1031290), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1031290)], (14056 ^ _780086) ^ [_1031334, _1031336] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1031334), _1031336), 14059 ^ _780086 : [(14060 ^ _780086) ^ [] : [-(_1031334 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (14062 ^ _780086) ^ [] : [-(_1031336 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (14064 ^ _780086) ^ [_1031445, _1031447] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1031445), _1031447)), _1031445 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _1031447 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (14074 ^ _780086) ^ [_1031588] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1031588) = _1031588)], (14076 ^ _780086) ^ [_1031614, _1031616, _1031618] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1031614), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1031616), _1031618)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1031614), _1031616)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1031614), _1031618)))], (14078 ^ _780086) ^ [_1031671, _1031673, _1031675] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1031671), _1031673)), _1031675) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1031671), _1031675)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1031673), _1031675)))], (14080 ^ _780086) ^ [_1031728, _1031730, _1031732, _1031734] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1031728), _1031730)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1031732), _1031734)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1031728), _1031732)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1031730), _1031734))))], (14090 ^ _780086) ^ [_1031919, _1031921, _1031923] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1031919), _1031921)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1031923), _1031919)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1031923), _1031921))))], (14096 ^ _780086) ^ [_1032042, _1032044, _1032046] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1032042), _1032044)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1032042), _1032046)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1032044), _1032046))))], (14102 ^ _780086) ^ [_1032165] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1032165), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1032165), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1032165), _1032165)))))], (14104 ^ _780086) ^ [_1032205] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1032205), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1032205), _1032205))))], (14106 ^ _780086) ^ [_1032239, _1032241] : [class_Groups_Ocomm__monoid__mult(_1032239), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1032239), _1032241), c_Groups_Oone__class_Oone(_1032239)) = _1032241)], (14112 ^ _780086) ^ [_1032334, _1032336] : [class_Groups_Omonoid__mult(_1032334), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1032334), _1032336), c_Groups_Oone__class_Oone(_1032334)) = _1032336)], (14118 ^ _780086) ^ [_1032429, _1032431] : [class_Groups_Ocomm__monoid__mult(_1032429), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1032429), c_Groups_Oone__class_Oone(_1032429)), _1032431) = _1032431)], (14124 ^ _780086) ^ [_1032524, _1032526] : [class_Groups_Omonoid__mult(_1032524), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1032524), c_Groups_Oone__class_Oone(_1032524)), _1032526) = _1032526)], (14130 ^ _780086) ^ [_1032619, _1032621] : [class_Rings_Ocomm__semiring__1(_1032619), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1032619), c_Groups_Oone__class_Oone(_1032619)), _1032621) = _1032621)], (14136 ^ _780086) ^ [_1032714, _1032716] : [class_Rings_Ocomm__semiring__1(_1032714), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1032714), _1032716), c_Groups_Oone__class_Oone(_1032714)) = _1032716)], (14142 ^ _780086) ^ [_1032809, _1032811, _1032813] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1032809), _1032811)), 14145 ^ _780086 : [(14156 ^ _780086) ^ [] : [14158 ^ _780086 : [(14159 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1032809), 14157 ^ [_1032809, _1032811, _1032813]), _1032811)))], (14161 ^ _780086) ^ [] : [hAPP(_1032813, 14157 ^ [_1032809, _1032811, _1032813]) = c_Groups_Oone__class_Oone(tc_Nat_Onat)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1032809, tc_Nat_Onat), _1032813), _1032811) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (14146 ^ _780086) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1032809, tc_Nat_Onat), _1032813), _1032811) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 14149 ^ _780086 : [(14150 ^ _780086) ^ [_1032971] : [hBOOL(hAPP(hAPP(c_member(_1032809), _1032971), _1032811)), -(hAPP(_1032813, _1032971) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]]]], (14165 ^ _780086) ^ [_1033229, _1033231, _1033233] : [class_Groups_Ocomm__monoid__mult(_1033229), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1033231, _1033229), hAPP(c_COMBK(_1033229, _1033231), c_Groups_Oone__class_Oone(_1033229))), _1033233) = c_Groups_Oone__class_Oone(_1033229))], (14171 ^ _780086) ^ [_1033344, _1033346] : [class_Rings_Olinordered__semidom(_1033344), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033344), _1033346), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033344), _1033346), c_Groups_Oone__class_Oone(_1033344)))))], (14177 ^ _780086) ^ [_1033453, _1033455, _1033457] : [class_Rings_Olinordered__semidom(_1033453), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033453), c_Groups_Oone__class_Oone(_1033453)), _1033455)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033453), c_Groups_Oone__class_Oone(_1033453)), _1033457)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033453), c_Groups_Oone__class_Oone(_1033453)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033453), _1033455), _1033457))))], (14191 ^ _780086) ^ [_1033708, _1033710, _1033712] : [class_Rings_Ocomm__semiring__1(_1033708), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033708), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033708), _1033710), _1033712)), _1033712) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033708), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033708), _1033710), c_Groups_Oone__class_Oone(_1033708))), _1033712))], (14197 ^ _780086) ^ [_1033853, _1033855, _1033857] : [class_Rings_Ocomm__semiring__1(_1033853), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033853), _1033855), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033853), _1033857), _1033855)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033853), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033853), _1033857), c_Groups_Oone__class_Oone(_1033853))), _1033855))], (14203 ^ _780086) ^ [_1033998, _1034000] : [class_Rings_Ocomm__semiring__1(_1033998), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033998), _1034000), _1034000) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033998), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033998), c_Groups_Oone__class_Oone(_1033998)), c_Groups_Oone__class_Oone(_1033998))), _1034000))], (14209 ^ _780086) ^ [_1034129, _1034131] : [class_Rings_Ocomm__ring__1(_1034129), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1034129), _1034131) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034129), hAPP(c_Groups_Ouminus__class_Ouminus(_1034129), c_Groups_Oone__class_Oone(_1034129))), _1034131))], (14215 ^ _780086) ^ [_1034244, _1034246] : [class_Rings_Oring__1__no__zero__divisors(_1034244), 14218 ^ _780086 : [(14229 ^ _780086) ^ [] : [14230 ^ _780086 : [(14231 ^ _780086) ^ [] : [_1034246 = c_Groups_Oone__class_Oone(_1034244)], (14233 ^ _780086) ^ [] : [_1034246 = hAPP(c_Groups_Ouminus__class_Ouminus(_1034244), c_Groups_Oone__class_Oone(_1034244))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034244), _1034246), _1034246) = c_Groups_Oone__class_Oone(_1034244))], (14219 ^ _780086) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034244), _1034246), _1034246) = c_Groups_Oone__class_Oone(_1034244), -(_1034246 = c_Groups_Oone__class_Oone(_1034244)), -(_1034246 = hAPP(c_Groups_Ouminus__class_Ouminus(_1034244), c_Groups_Oone__class_Oone(_1034244)))]]], (14237 ^ _780086) ^ [_1034551, _1034553, _1034555] : [class_Groups_Ocomm__monoid__mult(_1034551), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1034553, _1034551), _1034555), c_Orderings_Obot__class_Obot(tc_fun(_1034553, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1034551))], (14243 ^ _780086) ^ [_1034660, _1034662, _1034664] : [class_Groups_Ocomm__monoid__mult(_1034660), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1034662, _1034660), _1034664), c_Orderings_Obot__class_Obot(tc_fun(_1034662, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1034660))], (14249 ^ _780086) ^ [_1034769, _1034771, _1034773, _1034775] : [class_Groups_Ocomm__monoid__mult(_1034769), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1034771), _1034773))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1034771, _1034769), _1034775), _1034773) = c_Groups_Oone__class_Oone(_1034769))], (14259 ^ _780086) ^ [_1034893, _1034895, _1034897, _1034899] : [class_Groups_Ocomm__monoid__mult(_1034893), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1034895), _1034897))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1034895, _1034893), _1034899), _1034897) = c_Groups_Oone__class_Oone(_1034893))], (14269 ^ _780086) ^ [_1035017, _1035019] : [-(hAPP(c_Finite__Set_Ocard(_1035017), _1035019) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1035017, tc_Nat_Onat), hAPP(c_COMBK(tc_Nat_Onat, _1035017), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1035019))], (14271 ^ _780086) ^ [_1035077, _1035079] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1035077), _1035079)), 14274 ^ _780086 : [(14275 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1035077), _1035079)))], (14277 ^ _780086) ^ [] : [_1035077 = _1035079]]], (14279 ^ _780086) ^ [_1035204, _1035206] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1035204), _1035206))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1035204), _1035206)), -(_1035204 = _1035206)], (14299 ^ _780086) ^ [_1035479, _1035481] : [14300 ^ _780086 : [(14301 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1035479), _1035481))], (14303 ^ _780086) ^ [] : [_1035479 = _1035481]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1035479), _1035481)))], (14289 ^ _780086) ^ [_1035373, _1035375] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1035373), _1035375)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1035373), _1035375))), -(_1035373 = _1035375)], (14307 ^ _780086) ^ [_1035616, _1035618] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1035616), _1035618)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1035616), _1035618)))], (14313 ^ _780086) ^ [_1035713, _1035715] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1035713), _1035715)), -(_1035713 = _1035715), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1035713), _1035715)))], (14323 ^ _780086) ^ [_1035825, _1035827] : [14324 ^ _780086 : [(14325 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1035825), _1035827))], (14327 ^ _780086) ^ [] : [_1035825 = _1035827]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1035825), _1035827)))], (14331 ^ _780086) ^ [_1035960, _1035962, _1035964] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1035960), _1035962)), _1035964)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1035960), _1035964)))], (14337 ^ _780086) ^ [_1036071, _1036073, _1036075, _1036077] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1036071), _1036073)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1036075), _1036073) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1036071), _1036077), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1036075), _1036077)))], (14347 ^ _780086) ^ [_1036252, _1036254, _1036256, _1036258] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1036252), _1036254)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1036256), _1036258)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1036252), _1036256)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1036254), _1036258))))], (14357 ^ _780086) ^ [_1036443, _1036445, _1036447] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1036443), _1036445)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1036443), _1036447)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1036445), _1036447))))], (14363 ^ _780086) ^ [_1036566, _1036568, _1036570] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1036566), _1036568)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1036566), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1036570), _1036568))))], (14369 ^ _780086) ^ [_1036677, _1036679, _1036681] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1036677), _1036679)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1036677), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1036679), _1036681))))], (14375 ^ _780086) ^ [_1036806, _1036808, _1036810] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1036806), _1036808)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1036806), _1036810))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1036808), _1036810)))], (14381 ^ _780086) ^ [_1036925, _1036927, _1036929] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1036927), _1036929)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1036925), _1036927)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1036925), _1036929))))], (14387 ^ _780086) ^ [_1037062, _1037064] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1037062), _1037064)), _1037064))], (14389 ^ _780086) ^ [_1037110, _1037112] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1037110), _1037112)), _1037110))], (14391 ^ _780086) ^ [_1037155] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1037155), _1037155))], (14403 ^ _780086) ^ [_1037241, _1037243] : [14404 ^ _780086 : [(14405 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1037241), _1037243))], (14407 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1037243), _1037241))]], _1037241 = _1037243], (14393 ^ _780086) ^ [_1037192, _1037194] : [-(_1037192 = _1037194), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1037192), _1037194))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1037194), _1037192)))], (14411 ^ _780086) ^ [_1037375, _1037377] : [-(_1037375 = _1037377), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1037375), _1037377))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1037377), _1037375)))], (14421 ^ _780086) ^ [_1037437] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1037437), _1037437))], (14423 ^ _780086) ^ [_1037465, _1037467] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1037465), _1037467)), _1037467 = _1037465], (14429 ^ _780086) ^ [_1037553, _1037555] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1037553), _1037555)), _1037553 = _1037555], (14435 ^ _780086) ^ [_1037641, _1037643, _1037645] : [14436 ^ _780086 : [(14437 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1037641), _1037643)))], (14439 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(_1037645, _1037643), _1037641))]], 14442 ^ _780086 : [(14443 ^ _780086) ^ [] : [-(_1037641 = _1037643)], (14445 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(_1037645, _1037643), _1037641))]], 14448 ^ _780086 : [(14449 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1037643), _1037641)))], (14451 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(_1037645, _1037643), _1037641))]], -(hBOOL(hAPP(hAPP(_1037645, _1037643), _1037641)))], (14466 ^ _780086) ^ [_1038186] : [14468 ^ _780086 : [(14469 ^ _780086) ^ [_1038262] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 14467 ^ [_1038186, _1038262]), _1038186)))], (14471 ^ _780086) ^ [_1038296] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 14467 ^ [_1038186, _1038296]), _1038296))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1038186)))], (14455 ^ _780086) ^ [_1037999] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1037999)), 14459 ^ _780086 : [(14460 ^ _780086) ^ [_1038079] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1038079), _1037999)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1038079), 14458 ^ [_1037999])))]]], (14475 ^ _780086) ^ [_1038365, _1038367, _1038369, _1038371, _1038373] : [class_Groups_Ocomm__monoid__mult(_1038365), hBOOL(hAPP(c_Finite__Set_Ofinite(_1038367), _1038369)), 14482 ^ _780086 : [(14483 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1038367), _1038371), _1038369)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1038367, _1038365), hAPP(hAPP(c_COMBC(_1038367, _1038365, _1038365), hAPP(hAPP(c_COMBS(_1038367, _1038365, tc_fun(_1038365, _1038365)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1038365, tc_fun(_1038365, _1038365)), _1038367), c_If(_1038365)), hAPP(hAPP(c_COMBC(_1038367, _1038367, tc_HOL_Obool), c_fequal), _1038371))), _1038373)), c_Groups_Oone__class_Oone(_1038365))), _1038369) = hAPP(_1038373, _1038371))], (14489 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1038367), _1038371), _1038369))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1038367, _1038365), hAPP(hAPP(c_COMBC(_1038367, _1038365, _1038365), hAPP(hAPP(c_COMBS(_1038367, _1038365, tc_fun(_1038365, _1038365)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1038365, tc_fun(_1038365, _1038365)), _1038367), c_If(_1038365)), hAPP(hAPP(c_COMBC(_1038367, _1038367, tc_HOL_Obool), c_fequal), _1038371))), _1038373)), c_Groups_Oone__class_Oone(_1038365))), _1038369) = c_Groups_Oone__class_Oone(_1038365))]]], (14495 ^ _780086) ^ [_1038903, _1038905, _1038907, _1038909, _1038911] : [class_Groups_Ocomm__monoid__mult(_1038903), hBOOL(hAPP(c_Finite__Set_Ofinite(_1038905), _1038907)), 14502 ^ _780086 : [(14503 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1038905), _1038909), _1038907)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1038905, _1038903), hAPP(hAPP(c_COMBC(_1038905, _1038903, _1038903), hAPP(hAPP(c_COMBS(_1038905, _1038903, tc_fun(_1038903, _1038903)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1038903, tc_fun(_1038903, _1038903)), _1038905), c_If(_1038903)), hAPP(c_fequal, _1038909))), _1038911)), c_Groups_Oone__class_Oone(_1038903))), _1038907) = hAPP(_1038911, _1038909))], (14509 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1038905), _1038909), _1038907))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1038905, _1038903), hAPP(hAPP(c_COMBC(_1038905, _1038903, _1038903), hAPP(hAPP(c_COMBS(_1038905, _1038903, tc_fun(_1038903, _1038903)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1038903, tc_fun(_1038903, _1038903)), _1038905), c_If(_1038903)), hAPP(c_fequal, _1038909))), _1038911)), c_Groups_Oone__class_Oone(_1038903))), _1038907) = c_Groups_Oone__class_Oone(_1038903))]]], (14515 ^ _780086) ^ [_1039413, _1039415] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1039413), _1039415)), _1039415) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1039413), _1039415))], (14517 ^ _780086) ^ [_1039456, _1039458, _1039460] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1039456), _1039458)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1039460), _1039458)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1039456), _1039460)), _1039458))], (14519 ^ _780086) ^ [_1039513, _1039515, _1039517] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1039513), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1039515), _1039517)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1039513), _1039515)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1039513), _1039517)))], (14521 ^ _780086) ^ [_1039570, _1039572, _1039574] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1039570), _1039572)), _1039574) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1039570), _1039574)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1039572), _1039574)))], (14523 ^ _780086) ^ [_1039627, _1039629] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1039627), _1039629)), _1039629) = _1039627)], (14525 ^ _780086) ^ [_1039664, _1039666] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1039664), _1039666)), _1039664) = _1039666)], (14527 ^ _780086) ^ [_1039701, _1039703, _1039705] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1039701), _1039703)), _1039705) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1039701), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1039703), _1039705)))], (14529 ^ _780086) ^ [_1039752, _1039754, _1039756] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1039752), _1039754)), _1039756) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1039752), _1039756)), _1039754))], (14531 ^ _780086) ^ [_1039803, _1039805, _1039807] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1039803), _1039805)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1039803), _1039807)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1039805), _1039807))], (14533 ^ _780086) ^ [_1039854, _1039856, _1039858] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1039854), _1039856)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1039858), _1039856)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1039854), _1039858))], (14535 ^ _780086) ^ [_1039905, _1039907, _1039909] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1039905), _1039907)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1039905), _1039909)), 14542 ^ _780086 : [(14543 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1039907), _1039905)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1039909), _1039905))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1039907), _1039909)))], (14549 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1039907), _1039909)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1039907), _1039905)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1039909), _1039905))))]]], (14555 ^ _780086) ^ [_1040258, _1040260, _1040262] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1040258), _1040260)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1040258), _1040262)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040260), _1040258)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040262), _1040258)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040260), _1040262))], (14565 ^ _780086) ^ [_1040459, _1040461, _1040463] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1040459), _1040461)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1040459), _1040463)), 14572 ^ _780086 : [(14573 ^ _780086) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040461), _1040459) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040463), _1040459), -(_1040461 = _1040463)], (14579 ^ _780086) ^ [] : [_1040461 = _1040463, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040461), _1040459) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040463), _1040459))]]], (14585 ^ _780086) ^ [_1040782, _1040784, _1040786] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1040782), _1040784)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1040784), _1040786)), _1040782) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040784), _1040782)), _1040786))], (14591 ^ _780086) ^ [_1040919, _1040921, _1040923] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1040919), _1040921)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040921), _1040919)), _1040923) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1040921), _1040923)), _1040919))], (14597 ^ _780086) ^ [_1041056, _1041058, _1041060] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041056), _1041058)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1041060), _1041058)), _1041056) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1041060), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041058), _1041056)))], (14603 ^ _780086) ^ [_1041193, _1041195, _1041197] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041193), _1041195)), 14606 ^ _780086 : [(14607 ^ _780086) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041195), _1041193) = _1041197, -(_1041195 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1041197), _1041193))], (14613 ^ _780086) ^ [] : [_1041195 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1041197), _1041193), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041195), _1041193) = _1041197)]]], (14619 ^ _780086) ^ [_1041452, _1041454] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041452), _1041454)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041454), _1041452)), _1041452) = _1041454)], (14625 ^ _780086) ^ [_1041563, _1041565, _1041567] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041563), _1041565)), 14628 ^ _780086 : [(14629 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041567), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041565), _1041563))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1041567), _1041563)), _1041565)))], (14635 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1041567), _1041563)), _1041565)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041567), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041565), _1041563))))]]], (14641 ^ _780086) ^ [_1041852, _1041854, _1041856] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041852), _1041854)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1041856), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041854), _1041852)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1041856), _1041854)), _1041852))], (14647 ^ _780086) ^ [_1041989, _1041991] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041989), _1041991)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1041989), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041991), _1041989)) = _1041991)], (14653 ^ _780086) ^ [_1042100, _1042102] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042100), _1042102)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042102), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042102), _1042100)) = _1042100)], (14659 ^ _780086) ^ [_1042211, _1042213, _1042215] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042211), _1042213)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042211), _1042215)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042213), _1042215))))], (14665 ^ _780086) ^ [_1042334, _1042336, _1042338] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042334), _1042336)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042338), _1042336)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042338), _1042334))))], (14671 ^ _780086) ^ [_1042457, _1042459, _1042461] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042457), _1042459)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042461), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042459), _1042461)), _1042457))))], (14677 ^ _780086) ^ [_1042598, _1042600, _1042602] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042598), _1042600)), _1042602)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042598), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042602), _1042600))))], (14683 ^ _780086) ^ [_1042717, _1042719, _1042721] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042717), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042721), _1042719))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042717), _1042719)), _1042721)))], (14689 ^ _780086) ^ [_1042842, _1042844, _1042846] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042842), _1042844)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042846), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042844), _1042842)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042846), _1042842)), _1042844))], (14695 ^ _780086) ^ [_1042979, _1042981] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042979), _1042981)), _1042979)))], (14697 ^ _780086) ^ [_1043015, _1043017, _1043019, _1043021, _1043023] : [class_Groups_Ocomm__monoid__mult(_1043015), hBOOL(hAPP(c_Finite__Set_Ofinite(_1043017), _1043019)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1043015, _1043017, c_Groups_Otimes__class_Otimes(_1043015)), hAPP(hAPP(c_COMBS(_1043017, _1043015, _1043015), hAPP(hAPP(c_COMBB(_1043015, tc_fun(_1043015, _1043015), _1043017), c_Groups_Otimes__class_Otimes(_1043015)), _1043021)), _1043023)), c_Groups_Oone__class_Oone(_1043015)), _1043019) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043015), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1043015, _1043017, c_Groups_Otimes__class_Otimes(_1043015)), _1043021), c_Groups_Oone__class_Oone(_1043015)), _1043019)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1043015, _1043017, c_Groups_Otimes__class_Otimes(_1043015)), _1043023), c_Groups_Oone__class_Oone(_1043015)), _1043019)))], (14707 ^ _780086) ^ [_1043330, _1043332, _1043334] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1043330), _1043332)), -(hBOOL(hAPP(hAPP(c_member(_1043330), _1043334), _1043332))), -(hAPP(c_Finite__Set_Ocard(_1043330), hAPP(hAPP(c_Set_Oinsert(_1043330), _1043334), _1043332)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1043330), _1043332)))], (14717 ^ _780086) ^ [_1043488, _1043490, _1043492, _1043494] : [class_Groups_Ocomm__monoid__mult(_1043488), 14720 ^ _780086 : [(14721 ^ _780086) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1043490), _1043492)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1043490, _1043488), _1043494), _1043492) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1043488, _1043490, c_Groups_Otimes__class_Otimes(_1043488)), _1043494), c_Groups_Oone__class_Oone(_1043488)), _1043492))], (14727 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1043490), _1043492))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1043490, _1043488), _1043494), _1043492) = c_Groups_Oone__class_Oone(_1043488))]]], (14733 ^ _780086) ^ [_1043760, _1043762, _1043764, _1043766] : [class_Groups_Ocomm__monoid__mult(_1043760), hBOOL(hAPP(c_Finite__Set_Ofinite(_1043762), _1043764)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1043762, _1043760), _1043766), _1043764) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1043760, _1043762, c_Groups_Otimes__class_Otimes(_1043760)), _1043766), c_Groups_Oone__class_Oone(_1043760)), _1043764))], (14743 ^ _780086) ^ [_1043955, _1043957, _1043959] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1043955), _1043957)), -(hAPP(c_Finite__Set_Ocard(_1043955), hAPP(hAPP(c_Set_Oinsert(_1043955), _1043959), _1043957)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1043955), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1043955, tc_HOL_Obool)), _1043957), hAPP(hAPP(c_Set_Oinsert(_1043955), _1043959), c_Orderings_Obot__class_Obot(tc_fun(_1043955, tc_HOL_Obool)))))))], (14749 ^ _780086) ^ [_1044132, _1044134, _1044136] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1044132), _1044134)), hBOOL(hAPP(hAPP(c_member(_1044132), _1044136), _1044134)), -(hAPP(c_Finite__Set_Ocard(_1044132), _1044134) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1044132), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1044132, tc_HOL_Obool)), _1044134), hAPP(hAPP(c_Set_Oinsert(_1044132), _1044136), c_Orderings_Obot__class_Obot(tc_fun(_1044132, tc_HOL_Obool)))))))], (14759 ^ _780086) ^ [_1044361, _1044363, _1044365, _1044367] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1044361), _1044363)), hBOOL(hAPP(hAPP(c_member(_1044361), _1044365), _1044363)), -(hBOOL(hAPP(hAPP(c_member(_1044361), _1044365), _1044367))), -(hAPP(c_Finite__Set_Ocard(_1044361), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1044361, tc_HOL_Obool)), _1044363), hAPP(hAPP(c_Set_Oinsert(_1044361), _1044365), _1044367))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1044361), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1044361, tc_HOL_Obool)), _1044363), _1044367))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (14773 ^ _780086) ^ [_1044641, _1044643, _1044645, _1044647, _1044649] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1044641), _1044643)), 14776 ^ _780086 : [(14777 ^ _780086) ^ [] : [hBOOL(hAPP(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), _1044641), _1044645)), _1044647)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1044643), _1044645)), _1044649))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1044647), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044643), _1044641)), _1044645)), _1044649))))], (14783 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1044647), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1044643), _1044641)), _1044645)), _1044649))), -(hBOOL(hAPP(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), _1044641), _1044645)), _1044647)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1044643), _1044645)), _1044649))))]]], (14789 ^ _780086) ^ [_1045032, _1045034, _1045036, _1045038, _1045040] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1045032), _1045034)), 14792 ^ _780086 : [(14793 ^ _780086) ^ [] : [hBOOL(hAPP(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), _1045034), _1045036)), _1045038)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1045032), _1045036)), _1045040))), -(hBOOL(hAPP(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), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1045034), _1045032)), _1045036)), _1045038)), _1045040)))], (14799 ^ _780086) ^ [] : [hBOOL(hAPP(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), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1045034), _1045032)), _1045036)), _1045038)), _1045040)), -(hBOOL(hAPP(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), _1045034), _1045036)), _1045038)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1045032), _1045036)), _1045040))))]]], (14805 ^ _780086) ^ [_1045423, _1045425, _1045427, _1045429, _1045431] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1045423), _1045425)), 14808 ^ _780086 : [(14809 ^ _780086) ^ [] : [hBOOL(hAPP(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), _1045425), _1045427)), _1045429)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1045423), _1045427)), _1045431))), -(hBOOL(hAPP(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), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1045425), _1045423)), _1045427)), _1045429)), _1045431)))], (14815 ^ _780086) ^ [] : [hBOOL(hAPP(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), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1045425), _1045423)), _1045427)), _1045429)), _1045431)), -(hBOOL(hAPP(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), _1045425), _1045427)), _1045429)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1045423), _1045427)), _1045431))))]]], (14821 ^ _780086) ^ [_1045814, _1045816, _1045818, _1045820, _1045822] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1045814), _1045816)), -(hAPP(hAPP(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), _1045816), _1045818)), _1045820)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1045814), _1045818)), _1045822)) = hAPP(hAPP(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), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1045816), _1045814)), _1045818)), _1045820)), _1045822))], (14827 ^ _780086) ^ [_1046015, _1046017, _1046019, _1046021, _1046023] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1046015), _1046017)), 14830 ^ _780086 : [(14831 ^ _780086) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1046017), _1046019)), _1046021) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1046015), _1046019)), _1046023), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046017), _1046015)), _1046019)), _1046021) = _1046023)], (14837 ^ _780086) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046017), _1046015)), _1046019)), _1046021) = _1046023, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1046017), _1046019)), _1046021) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1046015), _1046019)), _1046023))]]], (14843 ^ _780086) ^ [_1046376, _1046378, _1046380, _1046382, _1046384] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1046376), _1046378)), 14846 ^ _780086 : [(14847 ^ _780086) ^ [] : [hBOOL(hAPP(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), _1046376), _1046380)), _1046382)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1046378), _1046380)), _1046384))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1046382), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046378), _1046376)), _1046380)), _1046384))))], (14853 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1046382), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046378), _1046376)), _1046380)), _1046384))), -(hBOOL(hAPP(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), _1046376), _1046380)), _1046382)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1046378), _1046380)), _1046384))))]]], (14859 ^ _780086) ^ [_1046767, _1046769, _1046771, _1046773, _1046775] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1046767), _1046769)), -(hAPP(hAPP(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), _1046767), _1046771)), _1046773)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1046769), _1046771)), _1046775)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046773), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046769), _1046767)), _1046771)), _1046775)))], (14865 ^ _780086) ^ [_1046968, _1046970, _1046972, _1046974, _1046976] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1046968), _1046970)), 14868 ^ _780086 : [(14869 ^ _780086) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1046968), _1046972)), _1046974) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1046970), _1046972)), _1046976), -(_1046974 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046970), _1046968)), _1046972)), _1046976))], (14875 ^ _780086) ^ [] : [_1046974 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046970), _1046968)), _1046972)), _1046976), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1046968), _1046972)), _1046974) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1046970), _1046972)), _1046976))]]], (14881 ^ _780086) ^ [] : [-(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat))], (14883 ^ _780086) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (14885 ^ _780086) ^ [_1047371, _1047373, _1047375] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1047371), _1047373)), _1047375) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1047371), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1047373), _1047375)))], (14887 ^ _780086) ^ [_1047422, _1047424] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1047422), _1047424) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1047424), _1047422))], (14889 ^ _780086) ^ [_1047459, _1047461, _1047463, _1047465] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1047459), _1047461)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1047463), _1047461)), _1047465)) = 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), _1047459), _1047463)), _1047461)), _1047465))], (14891 ^ _780086) ^ [_1047551, _1047553, _1047555, _1047557] : [hBOOL(hAPP(hAPP(c_member(_1047551), _1047553), c_SetInterval_Oord_OatMost(_1047551, _1047555, _1047557))), -(hBOOL(hAPP(hAPP(_1047555, _1047553), _1047557)))], (14897 ^ _780086) ^ [_1047660, _1047662, _1047664, _1047666] : [hBOOL(hAPP(hAPP(_1047664, _1047662), _1047666)), -(hBOOL(hAPP(hAPP(c_member(_1047660), _1047662), c_SetInterval_Oord_OatMost(_1047660, _1047664, _1047666))))], (14903 ^ _780086) ^ [_1047796, _1047798, _1047800, _1047802] : [hBOOL(hAPP(hAPP(c_member(_1047796), _1047798), c_SetInterval_Oord_OatLeast(_1047796, _1047800, _1047802))), -(hBOOL(hAPP(hAPP(_1047800, _1047802), _1047798)))], (14909 ^ _780086) ^ [_1047905, _1047907, _1047909, _1047911] : [hBOOL(hAPP(hAPP(_1047909, _1047911), _1047907)), -(hBOOL(hAPP(hAPP(c_member(_1047905), _1047907), c_SetInterval_Oord_OatLeast(_1047905, _1047909, _1047911))))], (14915 ^ _780086) ^ [_1048041, _1048043, _1048045, _1048047] : [hBOOL(hAPP(hAPP(c_member(_1048041), _1048043), c_SetInterval_Oord_OlessThan(_1048041, _1048045, _1048047))), -(hBOOL(hAPP(hAPP(_1048045, _1048043), _1048047)))], (14921 ^ _780086) ^ [_1048150, _1048152, _1048154, _1048156] : [hBOOL(hAPP(hAPP(_1048154, _1048152), _1048156)), -(hBOOL(hAPP(hAPP(c_member(_1048150), _1048152), c_SetInterval_Oord_OlessThan(_1048150, _1048154, _1048156))))], (14927 ^ _780086) ^ [_1048286, _1048288, _1048290, _1048292] : [hBOOL(hAPP(hAPP(c_member(_1048286), _1048288), c_SetInterval_Oord_OgreaterThan(_1048286, _1048290, _1048292))), -(hBOOL(hAPP(hAPP(_1048290, _1048292), _1048288)))], (14933 ^ _780086) ^ [_1048395, _1048397, _1048399, _1048401] : [hBOOL(hAPP(hAPP(_1048399, _1048401), _1048397)), -(hBOOL(hAPP(hAPP(c_member(_1048395), _1048397), c_SetInterval_Oord_OgreaterThan(_1048395, _1048399, _1048401))))], (14939 ^ _780086) ^ [_1048534, _1048536, _1048538, _1048540, _1048542] : [hBOOL(hAPP(hAPP(c_member(_1048534), _1048536), c_SetInterval_Oord_OatLeastAtMost(_1048534, _1048538, _1048540, _1048542))), 14942 ^ _780086 : [(14943 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(_1048538, _1048540), _1048536)))], (14945 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(_1048538, _1048536), _1048542)))]]], (14947 ^ _780086) ^ [_1048683, _1048685, _1048687, _1048689, _1048691] : [-(hBOOL(hAPP(hAPP(c_member(_1048683), _1048685), c_SetInterval_Oord_OatLeastAtMost(_1048683, _1048687, _1048689, _1048691)))), hBOOL(hAPP(hAPP(_1048687, _1048689), _1048685)), hBOOL(hAPP(hAPP(_1048687, _1048685), _1048691))], (14957 ^ _780086) ^ [_1048894, _1048896, _1048898, _1048900, _1048902] : [hBOOL(hAPP(hAPP(c_member(_1048894), _1048896), c_SetInterval_Oord_OgreaterThanLessThan(_1048894, _1048898, _1048900, _1048902))), 14960 ^ _780086 : [(14961 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(_1048898, _1048900), _1048896)))], (14963 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(_1048898, _1048896), _1048902)))]]], (14965 ^ _780086) ^ [_1049043, _1049045, _1049047, _1049049, _1049051] : [-(hBOOL(hAPP(hAPP(c_member(_1049043), _1049045), c_SetInterval_Oord_OgreaterThanLessThan(_1049043, _1049047, _1049049, _1049051)))), hBOOL(hAPP(hAPP(_1049047, _1049049), _1049045)), hBOOL(hAPP(hAPP(_1049047, _1049045), _1049051))], (14975 ^ _780086) ^ [_1049257, _1049259, _1049261, _1049263, _1049265, _1049267] : [hBOOL(hAPP(hAPP(c_member(_1049257), _1049259), c_SetInterval_Oord_OatLeastLessThan(_1049257, _1049261, _1049263, _1049265, _1049267))), 14978 ^ _780086 : [(14979 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(_1049261, _1049265), _1049259)))], (14981 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(_1049263, _1049259), _1049267)))]]], (14983 ^ _780086) ^ [_1049410, _1049412, _1049414, _1049416, _1049418, _1049420] : [-(hBOOL(hAPP(hAPP(c_member(_1049410), _1049412), c_SetInterval_Oord_OatLeastLessThan(_1049410, _1049414, _1049416, _1049418, _1049420)))), hBOOL(hAPP(hAPP(_1049414, _1049418), _1049412)), hBOOL(hAPP(hAPP(_1049416, _1049412), _1049420))], (14993 ^ _780086) ^ [_1049630, _1049632, _1049634, _1049636, _1049638, _1049640] : [hBOOL(hAPP(hAPP(c_member(_1049630), _1049632), c_SetInterval_Oord_OgreaterThanAtMost(_1049630, _1049634, _1049636, _1049638, _1049640))), 14996 ^ _780086 : [(14997 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(_1049636, _1049638), _1049632)))], (14999 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(_1049634, _1049632), _1049640)))]]], (15001 ^ _780086) ^ [_1049783, _1049785, _1049787, _1049789, _1049791, _1049793] : [-(hBOOL(hAPP(hAPP(c_member(_1049783), _1049785), c_SetInterval_Oord_OgreaterThanAtMost(_1049783, _1049787, _1049789, _1049791, _1049793)))), hBOOL(hAPP(hAPP(_1049789, _1049791), _1049785)), hBOOL(hAPP(hAPP(_1049787, _1049785), _1049793))], (15011 ^ _780086) ^ [_1049976, _1049978, _1049980, _1049982, _1049984, _1049986] : [class_Groups_Ocomm__monoid__mult(_1049976), hBOOL(hAPP(c_Finite__Set_Ofinite(_1049978), _1049980)), 15018 ^ _780086 : [(15019 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1049978), _1049982), _1049980)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1049978, _1049976), hAPP(hAPP(c_COMBC(_1049978, _1049976, _1049976), hAPP(hAPP(c_COMBS(_1049978, _1049976, tc_fun(_1049976, _1049976)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1049976, tc_fun(_1049976, _1049976)), _1049978), c_If(_1049976)), hAPP(hAPP(c_COMBC(_1049978, _1049978, tc_HOL_Obool), c_fequal), _1049982))), _1049984)), _1049986)), _1049980) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1049976), hAPP(_1049984, _1049982)), hAPP(hAPP(c_Power_Opower__class_Opower(_1049976), _1049986), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1049978), _1049980)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (15025 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1049978), _1049982), _1049980))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1049978, _1049976), hAPP(hAPP(c_COMBC(_1049978, _1049976, _1049976), hAPP(hAPP(c_COMBS(_1049978, _1049976, tc_fun(_1049976, _1049976)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1049976, tc_fun(_1049976, _1049976)), _1049978), c_If(_1049976)), hAPP(hAPP(c_COMBC(_1049978, _1049978, tc_HOL_Obool), c_fequal), _1049982))), _1049984)), _1049986)), _1049980) = hAPP(hAPP(c_Power_Opower__class_Opower(_1049976), _1049986), hAPP(c_Finite__Set_Ocard(_1049978), _1049980)))]]], (15031 ^ _780086) ^ [_1050588, _1050590, _1050592] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1050588), _1050590)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1050588), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1050590), _1050592))))], (15037 ^ _780086) ^ [_1050699, _1050701, _1050703] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1050699), _1050701)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1050699), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1050703), _1050701))))], (15043 ^ _780086) ^ [_1050810, _1050812] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1050810), _1050812)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1050810), _1050812)))], (15049 ^ _780086) ^ [_1050907, _1050909, _1050911] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1050907), _1050909)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1050907), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1050911), _1050909))))], (15055 ^ _780086) ^ [_1051018, _1051020, _1051022] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1051018), _1051020)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1051018), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1051020), _1051022))))], (15061 ^ _780086) ^ [_1051129, _1051131, _1051133] : [class_Lattices_Olattice(_1051129), hBOOL(hAPP(c_Finite__Set_Ofinite(_1051129), _1051131)), hBOOL(hAPP(hAPP(c_member(_1051129), _1051133), _1051131)), 15072 ^ _780086 : [(15073 ^ _780086) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1051129, tc_HOL_Obool)), _1051131), hAPP(hAPP(c_Set_Oinsert(_1051129), _1051133), c_Orderings_Obot__class_Obot(tc_fun(_1051129, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1051129, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1051129, _1051131) = _1051133)], (15079 ^ _780086) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1051129, tc_HOL_Obool)), _1051131), hAPP(hAPP(c_Set_Oinsert(_1051129), _1051133), c_Orderings_Obot__class_Obot(tc_fun(_1051129, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1051129, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1051129, _1051131) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1051129), _1051133), c_Big__Operators_Olattice__class_OSup__fin(_1051129, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1051129, tc_HOL_Obool)), _1051131), hAPP(hAPP(c_Set_Oinsert(_1051129), _1051133), c_Orderings_Obot__class_Obot(tc_fun(_1051129, tc_HOL_Obool)))))))]]], (15085 ^ _780086) ^ [_1051635, _1051637] : [-(hBOOL(hAPP(hAPP(c_member(_1051635), _1051637), c_Orderings_Otop__class_Otop(tc_fun(_1051635, tc_HOL_Obool)))))], (15087 ^ _780086) ^ [_1051672, _1051674, _1051676, _1051678] : [class_Rings_Ocomm__semiring__1(_1051672), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1051672), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1051672), _1051674), _1051676)), _1051678) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1051672), hAPP(hAPP(c_Power_Opower__class_Opower(_1051672), _1051674), _1051678)), hAPP(hAPP(c_Power_Opower__class_Opower(_1051672), _1051676), _1051678)))], (15093 ^ _780086) ^ [_1051831, _1051833, _1051835, _1051837] : [class_Rings_Ocomm__semiring__1(_1051831), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1051831), hAPP(hAPP(c_Power_Opower__class_Opower(_1051831), _1051833), _1051835)), _1051837) = hAPP(hAPP(c_Power_Opower__class_Opower(_1051831), _1051833), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1051835), _1051837)))], (15099 ^ _780086) ^ [_1051970, _1051972] : [class_Rings_Ocomm__semiring__1(_1051970), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1051970), _1051972), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1051972)], (15105 ^ _780086) ^ [_1052061, _1052063, _1052065, _1052067] : [class_Rings_Ocomm__semiring__1(_1052061), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1052061), hAPP(hAPP(c_Power_Opower__class_Opower(_1052061), _1052063), _1052065)), hAPP(hAPP(c_Power_Opower__class_Opower(_1052061), _1052063), _1052067)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1052061), _1052063), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1052065), _1052067)))], (15111 ^ _780086) ^ [_1052216, _1052218] : [class_Lattices_Olattice(_1052216), -(c_Big__Operators_Olattice__class_OSup__fin(_1052216, hAPP(hAPP(c_Set_Oinsert(_1052216), _1052218), c_Orderings_Obot__class_Obot(tc_fun(_1052216, tc_HOL_Obool)))) = _1052218)], (15117 ^ _780086) ^ [_1052323, _1052325, _1052327, _1052329] : [class_Groups_Ocomm__monoid__mult(_1052323), hBOOL(hAPP(c_Finite__Set_Ofinite(_1052325), _1052327)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1052325, _1052323), hAPP(c_COMBK(_1052323, _1052325), _1052329)), _1052327) = hAPP(hAPP(c_Power_Opower__class_Opower(_1052323), _1052329), hAPP(c_Finite__Set_Ocard(_1052325), _1052327)))], (15127 ^ _780086) ^ [_1052522, _1052524, _1052526] : [class_Lattices_Olattice(_1052522), hBOOL(hAPP(c_Finite__Set_Ofinite(_1052522), _1052524)), hBOOL(hAPP(hAPP(c_member(_1052522), _1052526), _1052524)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1052522), _1052526), c_Big__Operators_Olattice__class_OSup__fin(_1052522, _1052524)) = c_Big__Operators_Olattice__class_OSup__fin(_1052522, _1052524))], (15141 ^ _780086) ^ [_1052757, _1052759] : [class_Lattices_Olattice(_1052757), hBOOL(hAPP(c_Finite__Set_Ofinite(_1052757), _1052759)), -(c_Big__Operators_Olattice__class_OSup__fin(_1052757, _1052759) = hAPP(c_Finite__Set_Ofold1(_1052757, c_Lattices_Osemilattice__sup__class_Osup(_1052757)), _1052759))], (15151 ^ _780086) ^ [_1052914, _1052916, _1052918] : [class_Lattices_Olattice(_1052914), hBOOL(hAPP(c_Finite__Set_Ofinite(_1052914), _1052916)), -(_1052916 = c_Orderings_Obot__class_Obot(tc_fun(_1052914, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1052914, hAPP(hAPP(c_Set_Oinsert(_1052914), _1052918), _1052916)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1052914), _1052918), c_Big__Operators_Olattice__class_OSup__fin(_1052914, _1052916)))], (15165 ^ _780086) ^ [_1053122, _1053124, _1053126] : [class_Lattices_Olattice(_1053122), hBOOL(hAPP(c_Finite__Set_Ofinite(_1053122), _1053124)), -(_1053126 = c_Orderings_Obot__class_Obot(tc_fun(_1053122, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1053122, tc_HOL_Obool)), _1053126), _1053124)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1053122), c_Big__Operators_Olattice__class_OSup__fin(_1053122, _1053126)), c_Big__Operators_Olattice__class_OSup__fin(_1053122, _1053124)) = c_Big__Operators_Olattice__class_OSup__fin(_1053122, _1053124))], (15183 ^ _780086) ^ [_1053436, _1053438, _1053440] : [class_Lattices_Olattice(_1053436), hBOOL(hAPP(c_Finite__Set_Ofinite(_1053436), _1053438)), -(_1053438 = c_Orderings_Obot__class_Obot(tc_fun(_1053436, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1053436), _1053440)), -(_1053440 = c_Orderings_Obot__class_Obot(tc_fun(_1053436, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1053436, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1053436, tc_HOL_Obool)), _1053438), _1053440)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1053436), c_Big__Operators_Olattice__class_OSup__fin(_1053436, _1053438)), c_Big__Operators_Olattice__class_OSup__fin(_1053436, _1053440)))], (15205 ^ _780086) ^ [_1053785, _1053787, _1053789] : [class_Lattices_Olattice(_1053785), hBOOL(hAPP(c_Finite__Set_Ofinite(_1053785), _1053787)), -(c_Big__Operators_Olattice__class_OSup__fin(_1053785, hAPP(hAPP(c_Set_Oinsert(_1053785), _1053789), _1053787)) = hAPP(hAPP(c_Finite__Set_Ofold(_1053785, _1053785, c_Lattices_Osemilattice__sup__class_Osup(_1053785)), _1053789), _1053787))], (15215 ^ _780086) ^ [_1053970, _1053972, _1053974] : [class_Lattices_Olattice(_1053970), hBOOL(hAPP(c_Finite__Set_Ofinite(_1053970), _1053972)), -(hBOOL(hAPP(hAPP(c_member(_1053970), _1053974), _1053972))), -(_1053972 = c_Orderings_Obot__class_Obot(tc_fun(_1053970, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1053970, hAPP(hAPP(c_Set_Oinsert(_1053970), _1053974), _1053972)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1053970), _1053974), c_Big__Operators_Olattice__class_OSup__fin(_1053970, _1053972)))], (15233 ^ _780086) ^ [_1054207, _1054209, _1054211] : [class_Lattices_Olattice(_1054207), hBOOL(hAPP(c_Finite__Set_Ofinite(_1054207), _1054209)), 15240 ^ _780086 : [(15241 ^ _780086) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1054207, tc_HOL_Obool)), _1054209), hAPP(hAPP(c_Set_Oinsert(_1054207), _1054211), c_Orderings_Obot__class_Obot(tc_fun(_1054207, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1054207, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1054207, hAPP(hAPP(c_Set_Oinsert(_1054207), _1054211), _1054209)) = _1054211)], (15247 ^ _780086) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1054207, tc_HOL_Obool)), _1054209), hAPP(hAPP(c_Set_Oinsert(_1054207), _1054211), c_Orderings_Obot__class_Obot(tc_fun(_1054207, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1054207, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1054207, hAPP(hAPP(c_Set_Oinsert(_1054207), _1054211), _1054209)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1054207), _1054211), c_Big__Operators_Olattice__class_OSup__fin(_1054207, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1054207, tc_HOL_Obool)), _1054209), hAPP(hAPP(c_Set_Oinsert(_1054207), _1054211), c_Orderings_Obot__class_Obot(tc_fun(_1054207, tc_HOL_Obool)))))))]]], (15253 ^ _780086) ^ [_1054677, _1054679, _1054681] : [class_Lattices_Olattice(_1054677), hBOOL(hAPP(c_Finite__Set_Ofinite(_1054677), _1054679)), -(hBOOL(hAPP(hAPP(c_member(_1054677), _1054681), _1054679))), -(c_Big__Operators_Olattice__class_OSup__fin(_1054677, hAPP(hAPP(c_Set_Oinsert(_1054677), _1054681), _1054679)) = hAPP(hAPP(c_Finite__Set_Ofold(_1054677, _1054677, c_Lattices_Osemilattice__sup__class_Osup(_1054677)), _1054681), _1054679))], (15267 ^ _780086) ^ [_1054891, _1054893, _1054895, _1054897] : [class_Rings_Olinordered__semidom(_1054891), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1054891), c_Groups_Oone__class_Oone(_1054891)), _1054893)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1054891), hAPP(hAPP(c_Power_Opower__class_Opower(_1054891), _1054893), _1054895)), hAPP(hAPP(c_Power_Opower__class_Opower(_1054891), _1054893), _1054897))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1054895), _1054897)))], (15281 ^ _780086) ^ [_1055156, _1055158, _1055160, _1055162] : [class_Rings_Olinordered__semidom(_1055156), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1055156), c_Groups_Oone__class_Oone(_1055156)), _1055158)), 15288 ^ _780086 : [(15289 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055156), hAPP(hAPP(c_Power_Opower__class_Opower(_1055156), _1055158), _1055160)), hAPP(hAPP(c_Power_Opower__class_Opower(_1055156), _1055158), _1055162))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1055160), _1055162)))], (15295 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1055160), _1055162)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055156), hAPP(hAPP(c_Power_Opower__class_Opower(_1055156), _1055158), _1055160)), hAPP(hAPP(c_Power_Opower__class_Opower(_1055156), _1055158), _1055162))))]]], (15301 ^ _780086) ^ [_1055531, _1055533, _1055535] : [class_Rings_Oring__1(_1055531), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1055531), hAPP(c_Groups_Ouminus__class_Ouminus(_1055531), _1055533)), _1055535) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055531), hAPP(hAPP(c_Power_Opower__class_Opower(_1055531), hAPP(c_Groups_Ouminus__class_Ouminus(_1055531), c_Groups_Oone__class_Oone(_1055531))), _1055535)), hAPP(hAPP(c_Power_Opower__class_Opower(_1055531), _1055533), _1055535)))], (15307 ^ _780086) ^ [_1055696, _1055698, _1055700, _1055702] : [class_Rings_Olinordered__semidom(_1055696), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1055698), _1055700)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055696), c_Groups_Oone__class_Oone(_1055696)), _1055702)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055696), hAPP(hAPP(c_Power_Opower__class_Opower(_1055696), _1055702), _1055698)), hAPP(hAPP(c_Power_Opower__class_Opower(_1055696), _1055702), _1055700))))], (15321 ^ _780086) ^ [_1055961, _1055963, _1055965, _1055967] : [class_Rings_Olinordered__semidom(_1055961), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1055963), _1055965)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1055961), c_Groups_Oone__class_Oone(_1055961)), _1055967)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1055961), hAPP(hAPP(c_Power_Opower__class_Opower(_1055961), _1055967), _1055963)), hAPP(hAPP(c_Power_Opower__class_Opower(_1055961), _1055967), _1055965))))], (15335 ^ _780086) ^ [_1056226, _1056228, _1056230, _1056232] : [class_Rings_Olinordered__semidom(_1056226), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1056226), c_Groups_Oone__class_Oone(_1056226)), _1056228)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1056226), hAPP(hAPP(c_Power_Opower__class_Opower(_1056226), _1056228), _1056230)), hAPP(hAPP(c_Power_Opower__class_Opower(_1056226), _1056228), _1056232))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1056230), _1056232)))], (15349 ^ _780086) ^ [_1056491, _1056493, _1056495, _1056497] : [class_Rings_Olinordered__semidom(_1056491), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1056491), c_Groups_Oone__class_Oone(_1056491)), _1056493)), 15356 ^ _780086 : [(15357 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1056491), hAPP(hAPP(c_Power_Opower__class_Opower(_1056491), _1056493), _1056495)), hAPP(hAPP(c_Power_Opower__class_Opower(_1056491), _1056493), _1056497))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1056495), _1056497)))], (15363 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1056495), _1056497)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1056491), hAPP(hAPP(c_Power_Opower__class_Opower(_1056491), _1056493), _1056495)), hAPP(hAPP(c_Power_Opower__class_Opower(_1056491), _1056493), _1056497))))]]], (15369 ^ _780086) ^ [_1056866, _1056868, _1056870] : [class_Rings_Olinordered__semidom(_1056866), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1056866), c_Groups_Oone__class_Oone(_1056866)), _1056868)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1056866), hAPP(hAPP(c_Power_Opower__class_Opower(_1056866), _1056868), _1056870)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056866), _1056868), hAPP(hAPP(c_Power_Opower__class_Opower(_1056866), _1056868), _1056870)))))], (15379 ^ _780086) ^ [_1057077, _1057079, _1057081] : [class_Groups_Omonoid__mult(_1057077), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1057077), hAPP(hAPP(c_Power_Opower__class_Opower(_1057077), _1057079), _1057081)), _1057079) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1057077), _1057079), hAPP(hAPP(c_Power_Opower__class_Opower(_1057077), _1057079), _1057081)))], (15385 ^ _780086) ^ [_1057218, _1057220, _1057222, _1057224] : [class_Groups_Ocomm__monoid__mult(_1057218), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1057218), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1057218), _1057220), _1057222)), _1057224) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1057218), hAPP(hAPP(c_Power_Opower__class_Opower(_1057218), _1057220), _1057224)), hAPP(hAPP(c_Power_Opower__class_Opower(_1057218), _1057222), _1057224)))], (15391 ^ _780086) ^ [_1057377, _1057379] : [class_Groups_Omonoid__mult(_1057377), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1057377), c_Groups_Oone__class_Oone(_1057377)), _1057379) = c_Groups_Oone__class_Oone(_1057377))], (15397 ^ _780086) ^ [_1057476, _1057478, _1057480, _1057482] : [class_Groups_Omonoid__mult(_1057476), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1057476), _1057478), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1057480), _1057482)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1057476), hAPP(hAPP(c_Power_Opower__class_Opower(_1057476), _1057478), _1057480)), _1057482))], (15403 ^ _780086) ^ [_1057615, _1057617] : [class_Groups_Omonoid__mult(_1057615), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1057615), _1057617), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1057617)], (15409 ^ _780086) ^ [_1057706, _1057708, _1057710] : [class_Rings_Olinordered__semidom(_1057706), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1057706), c_Groups_Oone__class_Oone(_1057706)), _1057708)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1057706), c_Groups_Oone__class_Oone(_1057706)), hAPP(hAPP(c_Power_Opower__class_Opower(_1057706), _1057708), _1057710))))], (15419 ^ _780086) ^ [_1057889, _1057891, _1057893, _1057895] : [class_Rings_Olinordered__semidom(_1057889), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1057889), c_Groups_Oone__class_Oone(_1057889)), _1057891)), 15426 ^ _780086 : [(15427 ^ _780086) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1057889), _1057891), _1057893) = hAPP(hAPP(c_Power_Opower__class_Opower(_1057889), _1057891), _1057895), -(_1057893 = _1057895)], (15433 ^ _780086) ^ [] : [_1057893 = _1057895, -(hAPP(hAPP(c_Power_Opower__class_Opower(_1057889), _1057891), _1057893) = hAPP(hAPP(c_Power_Opower__class_Opower(_1057889), _1057891), _1057895))]]], (15439 ^ _780086) ^ [_1058228, _1058230, _1058232, _1058234] : [class_Groups_Omonoid__mult(_1058228), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1058228), _1058230), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1058232), _1058234)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1058228), hAPP(hAPP(c_Power_Opower__class_Opower(_1058228), _1058230), _1058232)), hAPP(hAPP(c_Power_Opower__class_Opower(_1058228), _1058230), _1058234)))], (15445 ^ _780086) ^ [_1058383, _1058385, _1058387] : [class_Rings_Olinordered__semidom(_1058383), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058383), c_Groups_Oone__class_Oone(_1058383)), _1058385)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058383), c_Groups_Oone__class_Oone(_1058383)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1058383), _1058385), hAPP(hAPP(c_Power_Opower__class_Opower(_1058383), _1058385), _1058387)))))], (15455 ^ _780086) ^ [_1058582] : [class_Power_Opower(_1058582), -(c_Power_Opower__class_Opower(_1058582) = c_Power_Opower_Opower(_1058582, c_Groups_Oone__class_Oone(_1058582), c_Groups_Otimes__class_Otimes(_1058582)))], (15461 ^ _780086) ^ [_1058675, _1058677] : [class_Lattices_Olattice(_1058675), hBOOL(hAPP(c_Finite__Set_Ofinite(_1058675), _1058677)), -(_1058677 = c_Orderings_Obot__class_Obot(tc_fun(_1058675, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1058675), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1058675), 15474 ^ [_1058675, _1058677]), 15475 ^ [_1058675, _1058677])), hAPP(hAPP(c_Set_Oinsert(_1058675), 15474 ^ [_1058675, _1058677]), hAPP(hAPP(c_Set_Oinsert(_1058675), 15475 ^ [_1058675, _1058677]), c_Orderings_Obot__class_Obot(tc_fun(_1058675, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1058675), c_Big__Operators_Olattice__class_OSup__fin(_1058675, _1058677)), _1058677)))], (15481 ^ _780086) ^ [_1059119, _1059121, _1059123, _1059125] : [c_Fun_Oinj__on(_1059119, _1059121, _1059123, c_Orderings_Otop__class_Otop(tc_fun(_1059119, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1059119, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1059119, _1059121, _1059123), hAPP(hAPP(c_Set_Oinsert(_1059121), _1059125), c_Orderings_Obot__class_Obot(tc_fun(_1059121, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1059119), c_HOL_OThe(_1059119, hAPP(hAPP(c_COMBC(_1059119, _1059121, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1059121, tc_fun(_1059121, tc_HOL_Obool), _1059119), c_fequal), _1059123)), _1059125))), c_Orderings_Obot__class_Obot(tc_fun(_1059119, tc_HOL_Obool))))))], (15487 ^ _780086) ^ [_1059352, _1059354, _1059356] : [class_Lattices_Olattice(_1059352), hAPP(_1059354, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1059352), 15492 ^ [_1059352, _1059354, _1059356]), 15493 ^ [_1059352, _1059354, _1059356])) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1059352), hAPP(_1059354, 15492 ^ [_1059352, _1059354, _1059356])), hAPP(_1059354, 15493 ^ [_1059352, _1059354, _1059356])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1059352), _1059356)), -(_1059356 = c_Orderings_Obot__class_Obot(tc_fun(_1059352, tc_HOL_Obool))), -(hAPP(_1059354, c_Big__Operators_Olattice__class_OSup__fin(_1059352, _1059356)) = c_Big__Operators_Olattice__class_OSup__fin(_1059352, hAPP(c_Set_Oimage(_1059352, _1059352, _1059354), _1059356)))], (15507 ^ _780086) ^ [_1059755, _1059757, _1059759, _1059761] : [class_Complete__Lattice_Ocomplete__lattice(_1059755), hBOOL(hAPP(c_Finite__Set_Ofinite(_1059757), _1059759)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1059757, _1059755), _1059759), _1059761) = hAPP(hAPP(c_Finite__Set_Ofold(_1059757, _1059755, hAPP(hAPP(c_COMBB(_1059755, tc_fun(_1059755, _1059755), _1059757), c_Lattices_Osemilattice__sup__class_Osup(_1059755)), _1059761)), c_Orderings_Obot__class_Obot(_1059755)), _1059759))], (15517 ^ _780086) ^ [_1059970, _1059972, _1059974, _1059976, _1059978] : [class_Groups_Ocomm__monoid__mult(_1059970), hBOOL(hAPP(c_Finite__Set_Ofinite(_1059972), _1059974)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1059972, tc_HOL_Obool)), _1059976), _1059974)), 15531 ^ _780086 : [(15532 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1059972), 15530 ^ [_1059970, _1059972, _1059974, _1059976, _1059978]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1059972, tc_HOL_Obool)), _1059974), _1059976))))], (15534 ^ _780086) ^ [] : [hAPP(_1059978, 15530 ^ [_1059970, _1059972, _1059974, _1059976, _1059978]) = c_Groups_Oone__class_Oone(_1059970)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1059972, _1059970), _1059978), _1059974) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1059972, _1059970), _1059978), _1059976))], (15538 ^ _780086) ^ [_1060421, _1060423, _1060425, _1060427, _1060429] : [class_Groups_Ocomm__monoid__mult(_1060421), hBOOL(hAPP(c_Finite__Set_Ofinite(_1060423), _1060425)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1060423, tc_HOL_Obool)), _1060427), _1060425)), 15552 ^ _780086 : [(15553 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1060423), 15551 ^ [_1060421, _1060423, _1060425, _1060427, _1060429]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1060423, tc_HOL_Obool)), _1060425), _1060427))))], (15555 ^ _780086) ^ [] : [hAPP(_1060429, 15551 ^ [_1060421, _1060423, _1060425, _1060427, _1060429]) = c_Groups_Oone__class_Oone(_1060421)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1060423, _1060421), _1060429), _1060427) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1060423, _1060421), _1060429), _1060425))], (15559 ^ _780086) ^ [_1060872, _1060874, _1060876, _1060878, _1060880] : [class_Groups_Ocomm__monoid__mult(_1060872), hBOOL(hAPP(c_Finite__Set_Ofinite(_1060874), _1060876)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1060874), _1060878)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1060874, tc_HOL_Obool)), _1060876), _1060878) = c_Orderings_Obot__class_Obot(tc_fun(_1060874, tc_HOL_Obool)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1060872, _1060874, c_Groups_Otimes__class_Otimes(_1060872)), _1060880), c_Groups_Oone__class_Oone(_1060872)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1060874, tc_HOL_Obool)), _1060876), _1060878)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060872), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1060872, _1060874, c_Groups_Otimes__class_Otimes(_1060872)), _1060880), c_Groups_Oone__class_Oone(_1060872)), _1060876)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1060872, _1060874, c_Groups_Otimes__class_Otimes(_1060872)), _1060880), c_Groups_Oone__class_Oone(_1060872)), _1060878)))], (15577 ^ _780086) ^ [_1061315, _1061317, _1061319, _1061321] : [hBOOL(hAPP(_1061315, _1061317)), hBOOL(hAPP(_1061319, _1061317)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1061321, tc_HOL_Obool)), _1061315), _1061319), _1061317)))], (15587 ^ _780086) ^ [_1061486, _1061488, _1061490, _1061492] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1061486, tc_HOL_Obool)), _1061488), _1061490), _1061492)), 15590 ^ _780086 : [(15591 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1061488, _1061492)))], (15593 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1061490, _1061492)))]]], (15595 ^ _780086) ^ [_1061631, _1061633, _1061635, _1061637, _1061639, _1061641] : [hBOOL(hAPP(hAPP(c_member(_1061631), _1061633), _1061635)), hBOOL(hAPP(hAPP(_1061637, _1061633), _1061639)), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1061631, tc_fun(_1061641, tc_HOL_Obool)), _1061635), _1061637), _1061639)))], (15605 ^ _780086) ^ [_1061828, _1061830, _1061832, _1061834, _1061836, _1061838, _1061840, _1061842] : [hBOOL(hAPP(hAPP(c_member(_1061828), _1061830), _1061832)), hBOOL(hAPP(hAPP(hAPP(_1061834, _1061830), _1061836), _1061838)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1061828, tc_fun(_1061840, tc_fun(_1061842, tc_HOL_Obool))), _1061832), _1061834), _1061836), _1061838)))], (15615 ^ _780086) ^ [_1062051, _1062053, _1062055, _1062057] : [hBOOL(hAPP(hAPP(c_member(_1062051), _1062053), _1062055)), hBOOL(hAPP(hAPP(c_member(_1062051), _1062053), _1062057)), -(hBOOL(hAPP(hAPP(c_member(_1062051), _1062053), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1062051, tc_HOL_Obool)), _1062055), _1062057))))], (15625 ^ _780086) ^ [_1062252, _1062254, _1062256, _1062258] : [hBOOL(hAPP(hAPP(c_member(_1062252), _1062254), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1062252, tc_HOL_Obool)), _1062256), _1062258))), 15628 ^ _780086 : [(15629 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1062252), _1062254), _1062256)))], (15631 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1062252), _1062254), _1062258)))]]], (15633 ^ _780086) ^ [_1062427, _1062429, _1062431] : [15634 ^ _780086 : [(15635 ^ _780086) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1062427), _1062429))], (15637 ^ _780086) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1062427), _1062431))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1062427), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1062427, tc_HOL_Obool)), _1062429), _1062431))))], (15641 ^ _780086) ^ [_1062590, _1062592, _1062594, _1062596, _1062598, _1062600] : [hAPP(_1062590, _1062592) = _1062594, hBOOL(hAPP(hAPP(c_member(_1062596), _1062594), _1062598)), -(hBOOL(hAPP(hAPP(c_member(_1062600), _1062592), hAPP(c_Set_Ovimage(_1062600, _1062596, _1062590), _1062598))))], (15651 ^ _780086) ^ [_1062783, _1062785] : [class_Lattices_Olattice(_1062783), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1062783), _1062785), _1062785) = _1062785)], (15657 ^ _780086) ^ [_1062874, _1062876] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1062874, tc_HOL_Obool)), _1062876), _1062876) = _1062876)], (15659 ^ _780086) ^ [_1062910, _1062912, _1062914] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1062910, tc_HOL_Obool)), _1062912), _1062914) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1062910, tc_HOL_Obool)), _1062914), _1062912))], (15661 ^ _780086) ^ [_1062959, _1062961, _1062963] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1062959, tc_HOL_Obool)), _1062961), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1062959, tc_HOL_Obool)), _1062961), _1062963)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1062959, tc_HOL_Obool)), _1062961), _1062963))], (15663 ^ _780086) ^ [_1063019, _1063021, _1063023, _1063025] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1063019, tc_HOL_Obool)), _1063021), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1063019, tc_HOL_Obool)), _1063023), _1063025)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1063019, tc_HOL_Obool)), _1063023), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1063019, tc_HOL_Obool)), _1063021), _1063025)))], (15665 ^ _780086) ^ [_1063092, _1063094, _1063096, _1063098, _1063100] : [-(hAPP(c_Set_Ovimage(_1063092, _1063094, _1063096), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1063094, tc_HOL_Obool)), _1063098), _1063100)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1063092, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1063092, _1063094, _1063096), _1063098)), hAPP(c_Set_Ovimage(_1063092, _1063094, _1063096), _1063100)))], (15667 ^ _780086) ^ [_1063166, _1063168, _1063170, _1063172] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1063166, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1063166, tc_HOL_Obool)), _1063168), _1063170)), _1063172) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1063166, tc_HOL_Obool)), _1063168), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1063166, tc_HOL_Obool)), _1063170), _1063172)))], (15669 ^ _780086) ^ [_1063263, _1063265, _1063267, _1063269, _1063271] : [hBOOL(hAPP(hAPP(c_Set_Ovimage(_1063263, _1063265, _1063267), _1063269), _1063271)), -(hBOOL(hAPP(_1063269, hAPP(_1063267, _1063271))))], (15675 ^ _780086) ^ [_1063370, _1063372, _1063374, _1063376, _1063378] : [hBOOL(hAPP(_1063376, hAPP(_1063374, _1063378))), -(hBOOL(hAPP(hAPP(c_Set_Ovimage(_1063370, _1063372, _1063374), _1063376), _1063378)))], (15681 ^ _780086) ^ [_1063483, _1063485, _1063487, _1063489] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1063483, tc_HOL_Obool)), _1063485), _1063487), _1063489)), -(hBOOL(hAPP(_1063485, _1063489)))], (15687 ^ _780086) ^ [_1063594, _1063596, _1063598, _1063600] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1063594, tc_HOL_Obool)), _1063596), _1063598), _1063600)), -(hBOOL(hAPP(_1063598, _1063600)))], (15693 ^ _780086) ^ [_1063705, _1063707] : [class_Lattices_Osemilattice__inf(_1063705), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1063705), _1063707), _1063707) = _1063707)], (15699 ^ _780086) ^ [_1063796, _1063798] : [class_Lattices_Osemilattice__inf(_1063796), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1063796), _1063798), _1063798) = _1063798)], (15705 ^ _780086) ^ [_1063887, _1063889, _1063891, _1063893, _1063895] : [class_Lattices_Olattice(_1063887), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1063889, _1063887)), _1063891), _1063893), _1063895) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1063887), hAPP(_1063891, _1063895)), hAPP(_1063893, _1063895)))], (15711 ^ _780086) ^ [_1064024, _1064026, _1064028] : [class_Lattices_Osemilattice__inf(_1064024), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1064024), _1064026), _1064028) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1064024), _1064028), _1064026))], (15717 ^ _780086) ^ [_1064133, _1064135, _1064137] : [class_Lattices_Olattice(_1064133), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1064133), _1064135), _1064137) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1064133), _1064137), _1064135))], (15723 ^ _780086) ^ [_1064242, _1064244, _1064246] : [class_Lattices_Osemilattice__inf(_1064242), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1064242), _1064244), _1064246) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1064242), _1064246), _1064244))], (15729 ^ _780086) ^ [_1064351, _1064353, _1064355] : [class_Lattices_Osemilattice__inf(_1064351), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1064351), _1064353), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1064351), _1064353), _1064355)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1064351), _1064353), _1064355))], (15735 ^ _780086) ^ [_1064476, _1064478, _1064480] : [class_Lattices_Olattice(_1064476), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1064476), _1064478), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1064476), _1064478), _1064480)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1064476), _1064478), _1064480))], (15741 ^ _780086) ^ [_1064601, _1064603, _1064605] : [class_Lattices_Osemilattice__inf(_1064601), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1064601), _1064603), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1064601), _1064603), _1064605)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1064601), _1064603), _1064605))], (15747 ^ _780086) ^ [_1064726, _1064728, _1064730, _1064732] : [class_Lattices_Osemilattice__inf(_1064726), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1064726), _1064728), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1064726), _1064730), _1064732)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1064726), _1064730), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1064726), _1064728), _1064732)))], (15753 ^ _780086) ^ [_1064869, _1064871, _1064873, _1064875] : [class_Lattices_Olattice(_1064869), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1064869), _1064871), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1064869), _1064873), _1064875)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1064869), _1064873), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1064869), _1064871), _1064875)))], (15759 ^ _780086) ^ [_1065012, _1065014, _1065016, _1065018] : [class_Lattices_Osemilattice__inf(_1065012), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1065012), _1065014), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1065012), _1065016), _1065018)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1065012), _1065016), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1065012), _1065014), _1065018)))], (15765 ^ _780086) ^ [_1065155, _1065157, _1065159, _1065161] : [class_Lattices_Osemilattice__inf(_1065155), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1065155), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1065155), _1065157), _1065159)), _1065161) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1065155), _1065157), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1065155), _1065159), _1065161)))], (15771 ^ _780086) ^ [_1065298, _1065300, _1065302, _1065304] : [class_Lattices_Olattice(_1065298), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1065298), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1065298), _1065300), _1065302)), _1065304) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1065298), _1065300), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1065298), _1065302), _1065304)))], (15777 ^ _780086) ^ [_1065441, _1065443, _1065445, _1065447] : [class_Lattices_Osemilattice__inf(_1065441), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1065441), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1065441), _1065443), _1065445)), _1065447) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1065441), _1065443), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1065441), _1065445), _1065447)))], (15783 ^ _780086) ^ [_1065584, _1065586, _1065588, _1065590, _1065592] : [class_Lattices_Olattice(_1065584), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1065586, _1065584)), _1065588), _1065590), _1065592) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1065584), hAPP(_1065588, _1065592)), hAPP(_1065590, _1065592)))], (15789 ^ _780086) ^ [_1065721, _1065723] : [-(hAPP(c_Set_Ovimage(_1065721, _1065721, c_COMBI(_1065721)), _1065723) = _1065723)], (15791 ^ _780086) ^ [_1065755, _1065757, _1065759, _1065761] : [-(hAPP(c_Set_Oimage(_1065755, _1065757, _1065759), hAPP(c_Set_Ovimage(_1065755, _1065757, _1065759), _1065761)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1065757, tc_HOL_Obool)), _1065761), hAPP(c_Set_Oimage(_1065755, _1065757, _1065759), c_Orderings_Otop__class_Otop(tc_fun(_1065755, tc_HOL_Obool)))))], (15793 ^ _780086) ^ [_1065821, _1065823, _1065825, _1065827] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1065821), _1065823)), 15796 ^ _780086 : [(15807 ^ _780086) ^ [] : [15809 ^ _780086 : [(15810 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1065821), 15808 ^ [_1065821, _1065823, _1065825, _1065827]), _1065823)))], (15812 ^ _780086) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1065825), hAPP(_1065827, 15808 ^ [_1065821, _1065823, _1065825, _1065827])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1065825), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1065821, tc_fun(_1065825, tc_HOL_Obool)), _1065823), _1065827))))], (15797 ^ _780086) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1065825), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1065821, tc_fun(_1065825, tc_HOL_Obool)), _1065823), _1065827))), 15800 ^ _780086 : [(15801 ^ _780086) ^ [_1066005] : [hBOOL(hAPP(hAPP(c_member(_1065821), _1066005), _1065823)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1065825), hAPP(_1065827, _1066005))))]]]]], (15816 ^ _780086) ^ [_1066296, _1066298, _1066300] : [class_Lattices_Olattice(_1066296), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066296), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1066296), _1066298), _1066300)), _1066298)))], (15822 ^ _780086) ^ [_1066403, _1066405, _1066407] : [class_Lattices_Osemilattice__inf(_1066403), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066403), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1066403), _1066405), _1066407)), _1066405)))], (15828 ^ _780086) ^ [_1066510, _1066512, _1066514] : [class_Lattices_Olattice(_1066510), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066510), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1066510), _1066512), _1066514)), _1066514)))], (15834 ^ _780086) ^ [_1066617, _1066619, _1066621] : [class_Lattices_Osemilattice__inf(_1066617), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066617), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1066617), _1066619), _1066621)), _1066621)))], (15840 ^ _780086) ^ [_1066724, _1066726, _1066728] : [class_Lattices_Osemilattice__inf(_1066724), 15843 ^ _780086 : [(15844 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066724), _1066726), _1066728)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1066724), _1066726), _1066728) = _1066726)], (15850 ^ _780086) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1066724), _1066726), _1066728) = _1066726, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066724), _1066726), _1066728)))]]], (15856 ^ _780086) ^ [_1066980, _1066982, _1066984, _1066986] : [class_Lattices_Osemilattice__inf(_1066980), 15859 ^ _780086 : [(15860 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066980), _1066982), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1066980), _1066984), _1066986))), 15863 ^ _780086 : [(15864 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066980), _1066982), _1066984)))], (15866 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066980), _1066982), _1066986)))]]], (15868 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066980), _1066982), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1066980), _1066984), _1066986)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066980), _1066982), _1066984)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066980), _1066982), _1066986))]]], (15878 ^ _780086) ^ [_1067360, _1067362, _1067364, _1067366] : [class_Lattices_Osemilattice__inf(_1067360), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067360), _1067362), _1067364)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067360), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1067360), _1067362), _1067366)), _1067364)))], (15888 ^ _780086) ^ [_1067539, _1067541, _1067543, _1067545] : [class_Lattices_Osemilattice__inf(_1067539), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067539), _1067541), _1067543)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067539), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1067539), _1067545), _1067541)), _1067543)))], (15898 ^ _780086) ^ [_1067718, _1067720, _1067722] : [class_Lattices_Osemilattice__inf(_1067718), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067718), _1067720), _1067722)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1067718), _1067720), _1067722) = _1067720)], (15908 ^ _780086) ^ [_1067879, _1067881, _1067883] : [class_Lattices_Osemilattice__inf(_1067879), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067879), _1067881), _1067883)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1067879), _1067883), _1067881) = _1067881)], (15918 ^ _780086) ^ [_1068040, _1068042, _1068044, _1068046] : [class_Lattices_Osemilattice__inf(_1068040), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068040), _1068042), _1068044)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068040), _1068042), _1068046)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068040), _1068042), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1068040), _1068044), _1068046))))], (15932 ^ _780086) ^ [_1068289, _1068291, _1068293, _1068295] : [class_Lattices_Osemilattice__inf(_1068289), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068289), _1068291), _1068293)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068289), _1068291), _1068295)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068289), _1068291), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1068289), _1068293), _1068295))))], (15946 ^ _780086) ^ [_1068538, _1068540, _1068542, _1068544, _1068546] : [class_Lattices_Osemilattice__inf(_1068538), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068538), _1068540), _1068542)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068538), _1068544), _1068546)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068538), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1068538), _1068540), _1068544)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1068538), _1068542), _1068546))))], (15960 ^ _780086) ^ [_1068809, _1068811, _1068813, _1068815] : [class_Lattices_Osemilattice__inf(_1068809), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068809), _1068811), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1068809), _1068813), _1068815))), 15967 ^ _780086 : [(15968 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068809), _1068811), _1068813)))], (15970 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068809), _1068811), _1068815)))]]], (15972 ^ _780086) ^ [_1069032, _1069034, _1069036, _1069038] : [class_Lattices_Osemilattice__inf(_1069032), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1069032), _1069034), _1069036)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1069032), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1069032), _1069034), _1069038)), _1069036)))], (15982 ^ _780086) ^ [_1069211, _1069213, _1069215, _1069217] : [class_Lattices_Osemilattice__inf(_1069211), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1069211), _1069213), _1069215)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1069211), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1069211), _1069217), _1069213)), _1069215)))], (15992 ^ _780086) ^ [_1069390, _1069392] : [class_Lattices_Obounded__lattice__bot(_1069390), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1069390), c_Orderings_Obot__class_Obot(_1069390)), _1069392) = c_Orderings_Obot__class_Obot(_1069390))], (15998 ^ _780086) ^ [_1069489, _1069491] : [class_Lattices_Obounded__lattice__bot(_1069489), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1069489), _1069491), c_Orderings_Obot__class_Obot(_1069489)) = c_Orderings_Obot__class_Obot(_1069489))], (16004 ^ _780086) ^ [_1069588, _1069590, _1069592] : [class_Lattices_Olattice(_1069588), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1069588), _1069590), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1069588), _1069590), _1069592)) = _1069590)], (16010 ^ _780086) ^ [_1069697, _1069699, _1069701] : [class_Lattices_Olattice(_1069697), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1069697), _1069699), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1069697), _1069699), _1069701)) = _1069699)], (16016 ^ _780086) ^ [_1069806, _1069808, _1069810, _1069812] : [class_Lattices_Odistrib__lattice(_1069806), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1069806), _1069808), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1069806), _1069810), _1069812)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1069806), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1069806), _1069808), _1069810)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1069806), _1069808), _1069812)))], (16022 ^ _780086) ^ [_1069965, _1069967, _1069969, _1069971] : [class_Lattices_Odistrib__lattice(_1069965), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1069965), _1069967), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1069965), _1069969), _1069971)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1069965), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1069965), _1069967), _1069969)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1069965), _1069967), _1069971)))], (16028 ^ _780086) ^ [_1070124, _1070126, _1070128, _1070130] : [class_Lattices_Odistrib__lattice(_1070124), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1070124), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1070124), _1070126), _1070128)), _1070130) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1070124), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1070124), _1070126), _1070130)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1070124), _1070128), _1070130)))], (16034 ^ _780086) ^ [_1070283, _1070285, _1070287, _1070289] : [class_Lattices_Odistrib__lattice(_1070283), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1070283), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1070283), _1070285), _1070287)), _1070289) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1070283), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1070283), _1070285), _1070289)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1070283), _1070287), _1070289)))], (16040 ^ _780086) ^ [_1070442, _1070444] : [class_Lattices_Obounded__lattice__top(_1070442), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1070442), c_Orderings_Otop__class_Otop(_1070442)), _1070444) = _1070444)], (16046 ^ _780086) ^ [_1070537, _1070539] : [class_Lattices_Obounded__lattice__top(_1070537), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1070537), _1070539), c_Orderings_Otop__class_Otop(_1070537)) = _1070539)], (16052 ^ _780086) ^ [_1070632, _1070634, _1070636] : [class_Lattices_Obounded__lattice__top(_1070632), 16055 ^ _780086 : [(16056 ^ _780086) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1070632), _1070634), _1070636) = c_Orderings_Otop__class_Otop(_1070632), 16059 ^ _780086 : [(16060 ^ _780086) ^ [] : [-(_1070634 = c_Orderings_Otop__class_Otop(_1070632))], (16062 ^ _780086) ^ [] : [-(_1070636 = c_Orderings_Otop__class_Otop(_1070632))]]], (16064 ^ _780086) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1070632), _1070634), _1070636) = c_Orderings_Otop__class_Otop(_1070632)), _1070634 = c_Orderings_Otop__class_Otop(_1070632), _1070636 = c_Orderings_Otop__class_Otop(_1070632)]]], (16074 ^ _780086) ^ [_1070983, _1070985, _1070987, _1070989, _1070991] : [hBOOL(hAPP(hAPP(c_member(_1070983), _1070985), hAPP(c_Set_Ovimage(_1070983, _1070987, _1070989), _1070991))), -(hBOOL(hAPP(hAPP(c_member(_1070987), hAPP(_1070989, _1070985)), _1070991)))], (16080 ^ _780086) ^ [_1071110, _1071112, _1071114, _1071116, _1071118] : [hBOOL(hAPP(hAPP(c_member(_1071114), hAPP(_1071116, _1071112)), _1071118)), -(hBOOL(hAPP(hAPP(c_member(_1071110), _1071112), hAPP(c_Set_Ovimage(_1071110, _1071114, _1071116), _1071118))))], (16086 ^ _780086) ^ [_1071243, _1071245, _1071247, _1071249, _1071251] : [hBOOL(hAPP(hAPP(c_member(_1071243), _1071245), hAPP(c_Set_Ovimage(_1071243, _1071247, _1071249), _1071251))), -(hBOOL(hAPP(hAPP(c_member(_1071247), hAPP(_1071249, _1071245)), _1071251)))], (16092 ^ _780086) ^ [_1071374, _1071376, _1071378, _1071380, _1071382] : [hBOOL(hAPP(hAPP(c_member(_1071374), hAPP(_1071376, _1071378)), _1071380)), -(hBOOL(hAPP(hAPP(c_member(_1071382), _1071378), hAPP(c_Set_Ovimage(_1071382, _1071374, _1071376), _1071380))))], (16098 ^ _780086) ^ [_1071526, _1071528, _1071530, _1071532] : [hBOOL(hAPP(hAPP(c_member(_1071526), _1071528), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1071526, tc_HOL_Obool)), _1071530), _1071532))), 16101 ^ _780086 : [(16102 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1071526), _1071528), _1071530)))], (16104 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1071526), _1071528), _1071532)))]]], (16106 ^ _780086) ^ [_1071693, _1071695, _1071697, _1071699] : [-(hBOOL(hAPP(hAPP(c_member(_1071693), _1071695), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1071693, tc_HOL_Obool)), _1071697), _1071699)))), hBOOL(hAPP(hAPP(c_member(_1071693), _1071695), _1071697)), hBOOL(hAPP(hAPP(c_member(_1071693), _1071695), _1071699))], (16116 ^ _780086) ^ [_1071896, _1071898, _1071900, _1071902] : [hBOOL(hAPP(hAPP(c_member(_1071896), _1071898), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1071896, tc_HOL_Obool)), _1071900), _1071902))), -(hBOOL(hAPP(hAPP(c_member(_1071896), _1071898), _1071900)))], (16122 ^ _780086) ^ [_1072027, _1072029, _1072031, _1072033] : [hBOOL(hAPP(hAPP(c_member(_1072027), _1072029), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1072027, tc_HOL_Obool)), _1072031), _1072033))), -(hBOOL(hAPP(hAPP(c_member(_1072027), _1072029), _1072033)))], (16128 ^ _780086) ^ [_1072158] : [-(c_Lattices_Osemilattice__inf__class_Oinf(_1072158) = c_Orderings_Oord__class_Omin(_1072158)), class_Lattices_Osemilattice__inf(_1072158), class_Orderings_Olinorder(_1072158)], (16138 ^ _780086) ^ [_1072287, _1072289, _1072291] : [-(hAPP(c_Set_Ovimage(_1072287, _1072289, _1072291), c_Orderings_Obot__class_Obot(tc_fun(_1072289, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1072287, tc_HOL_Obool)))], (16140 ^ _780086) ^ [_1072331, _1072333] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1072331, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1072331, tc_HOL_Obool))), _1072333) = c_Orderings_Obot__class_Obot(tc_fun(_1072331, tc_HOL_Obool)))], (16142 ^ _780086) ^ [_1072377, _1072379] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1072377, tc_HOL_Obool)), _1072379), c_Orderings_Obot__class_Obot(tc_fun(_1072377, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1072377, tc_HOL_Obool)))], (16158 ^ _780086) ^ [_1072755, _1072757, _1072759] : [16160 ^ _780086 : [(16161 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1072755), 16159 ^ [_1072755, _1072757, _1072759]), _1072757)))], (16164 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1072755), 16162 ^ [_1072755, _1072757, _1072759]), _1072759)))], (16166 ^ _780086) ^ [] : [-(16159 ^ [_1072755, _1072757, _1072759] = 16162 ^ [_1072755, _1072757, _1072759])]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1072755, tc_HOL_Obool)), _1072757), _1072759) = c_Orderings_Obot__class_Obot(tc_fun(_1072755, tc_HOL_Obool)))], (16144 ^ _780086) ^ [_1072441, _1072443, _1072445] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1072441, tc_HOL_Obool)), _1072443), _1072445) = c_Orderings_Obot__class_Obot(tc_fun(_1072441, tc_HOL_Obool)), 16147 ^ _780086 : [(16148 ^ _780086) ^ [_1072565] : [hBOOL(hAPP(hAPP(c_member(_1072441), _1072565), _1072443)), 16151 ^ _780086 : [(16152 ^ _780086) ^ [_1072655] : [hBOOL(hAPP(hAPP(c_member(_1072441), _1072655), _1072445)), _1072565 = _1072655]]]]], (16170 ^ _780086) ^ [_1072916, _1072918, _1072920, _1072922, _1072924] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1072916, tc_HOL_Obool)), _1072918), _1072920)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1072922, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1072922, _1072916, _1072924), _1072918)), hAPP(c_Set_Ovimage(_1072922, _1072916, _1072924), _1072920))))], (16176 ^ _780086) ^ [_1073067, _1073069, _1073071] : [-(hAPP(c_Set_Ovimage(_1073067, _1073069, _1073071), c_Orderings_Otop__class_Otop(tc_fun(_1073069, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1073067, tc_HOL_Obool)))], (16178 ^ _780086) ^ [_1073111, _1073113, _1073115, _1073117] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1073111, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1073111), _1073113), _1073115)), hAPP(hAPP(c_Set_Oinsert(_1073111), _1073113), _1073117)) = hAPP(hAPP(c_Set_Oinsert(_1073111), _1073113), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1073111, tc_HOL_Obool)), _1073115), _1073117)))], (16180 ^ _780086) ^ [_1073186, _1073188, _1073190, _1073192, _1073194] : [-(hAPP(c_Set_Ovimage(_1073186, _1073188, _1073190), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1073188, tc_HOL_Obool)), _1073192), _1073194)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1073186, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1073186, _1073188, _1073190), _1073192)), hAPP(c_Set_Ovimage(_1073186, _1073188, _1073190), _1073194)))], (16182 ^ _780086) ^ [_1073260, _1073262, _1073264] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1073260, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1073260, tc_HOL_Obool)), _1073262), _1073264)), _1073262)))], (16184 ^ _780086) ^ [_1073308, _1073310, _1073312] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1073308, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1073308, tc_HOL_Obool)), _1073310), _1073312)), _1073312)))], (16186 ^ _780086) ^ [_1073356, _1073358, _1073360] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1073356, tc_HOL_Obool)), _1073358), _1073360)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1073356, tc_HOL_Obool)), _1073358), _1073360) = _1073358)], (16192 ^ _780086) ^ [_1073477, _1073479, _1073481] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1073477, tc_HOL_Obool)), _1073479), _1073481)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1073477, tc_HOL_Obool)), _1073481), _1073479) = _1073479)], (16198 ^ _780086) ^ [_1073598, _1073600, _1073602, _1073604] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1073598, tc_HOL_Obool)), _1073600), _1073602)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1073598, tc_HOL_Obool)), _1073600), _1073604)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1073598, tc_HOL_Obool)), _1073600), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1073598, tc_HOL_Obool)), _1073602), _1073604))))], (16208 ^ _780086) ^ [_1073817, _1073819, _1073821, _1073823, _1073825] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1073817, tc_HOL_Obool)), _1073819), _1073821)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1073817, tc_HOL_Obool)), _1073823), _1073825)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1073817, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1073817, tc_HOL_Obool)), _1073819), _1073823)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1073817, tc_HOL_Obool)), _1073821), _1073825))))], (16218 ^ _780086) ^ [_1074062, _1074064] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074062, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1074062, tc_HOL_Obool))), _1074064) = _1074064)], (16220 ^ _780086) ^ [_1074103, _1074105] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074103, tc_HOL_Obool)), _1074105), c_Orderings_Otop__class_Otop(tc_fun(_1074103, tc_HOL_Obool))) = _1074105)], (16222 ^ _780086) ^ [_1074144, _1074146, _1074148, _1074150] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074144, tc_HOL_Obool)), _1074146), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1074144, tc_HOL_Obool)), _1074148), _1074150)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1074144, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074144, tc_HOL_Obool)), _1074146), _1074148)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074144, tc_HOL_Obool)), _1074146), _1074150)))], (16224 ^ _780086) ^ [_1074228, _1074230, _1074232, _1074234] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1074228, tc_HOL_Obool)), _1074230), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074228, tc_HOL_Obool)), _1074232), _1074234)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074228, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1074228, tc_HOL_Obool)), _1074230), _1074232)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1074228, tc_HOL_Obool)), _1074230), _1074234)))], (16226 ^ _780086) ^ [_1074312, _1074314, _1074316, _1074318] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074312, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1074312, tc_HOL_Obool)), _1074314), _1074316)), _1074318) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1074312, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074312, tc_HOL_Obool)), _1074314), _1074318)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074312, tc_HOL_Obool)), _1074316), _1074318)))], (16228 ^ _780086) ^ [_1074396, _1074398, _1074400, _1074402] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1074396, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074396, tc_HOL_Obool)), _1074398), _1074400)), _1074402) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074396, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1074396, tc_HOL_Obool)), _1074398), _1074402)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1074396, tc_HOL_Obool)), _1074400), _1074402)))], (16230 ^ _780086) ^ [_1074480, _1074482, _1074484, _1074486] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1074480, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1074480, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074480, tc_HOL_Obool)), _1074482), _1074484)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074480, tc_HOL_Obool)), _1074484), _1074486))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074480, tc_HOL_Obool)), _1074486), _1074482)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074480, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074480, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1074480, tc_HOL_Obool)), _1074482), _1074484)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1074480, tc_HOL_Obool)), _1074484), _1074486))), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1074480, tc_HOL_Obool)), _1074486), _1074482)))], (16232 ^ _780086) ^ [_1074619, _1074621, _1074623, _1074625, _1074627] : [-(hAPP(c_Set_Ovimage(_1074619, _1074621, _1074623), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1074621, tc_HOL_Obool)), _1074625), _1074627)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1074619, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1074619, _1074621, _1074623), _1074625)), hAPP(c_Set_Ovimage(_1074619, _1074621, _1074623), _1074627)))], (16234 ^ _780086) ^ [_1074693, _1074695, _1074697, _1074699] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074693, tc_HOL_Obool)), _1074695), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1074693, tc_HOL_Obool)), _1074697), _1074699)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1074693, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074693, tc_HOL_Obool)), _1074695), _1074697)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074693, tc_HOL_Obool)), _1074695), _1074699)))], (16236 ^ _780086) ^ [_1074777, _1074779, _1074781, _1074783] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1074777, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074777, tc_HOL_Obool)), _1074779), _1074781)), _1074783) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074777, tc_HOL_Obool)), _1074779), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1074777, tc_HOL_Obool)), _1074781), _1074783)))], (16238 ^ _780086) ^ [_1074850, _1074852, _1074854, _1074856] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074850, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1074850, tc_HOL_Obool)), _1074852), _1074854)), _1074856) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1074850, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074850, tc_HOL_Obool)), _1074852), _1074856)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074850, tc_HOL_Obool)), _1074854), _1074856)))], (16240 ^ _780086) ^ [_1074934, _1074936, _1074938, _1074940] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1074934, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074934, tc_HOL_Obool)), _1074936), _1074938)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074934, tc_HOL_Obool)), _1074940), _1074938)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1074934, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074934, tc_HOL_Obool)), _1074936), _1074938)), _1074940))], (16242 ^ _780086) ^ [_1075018, _1075020, _1075022, _1075024, _1075026] : [c_Fun_Oinj__on(_1075018, _1075020, _1075022, _1075024), c_Fun_Oinj__on(_1075018, _1075020, _1075022, _1075026), -(c_Fun_Oinj__on(_1075018, _1075020, _1075022, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1075018, tc_HOL_Obool)), _1075024), _1075026)))], (16252 ^ _780086) ^ [_1075193, _1075195, _1075197, _1075199] : [-(hAPP(c_Set_Ovimage(_1075193, _1075195, _1075197), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1075195, tc_HOL_Obool)), _1075199)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1075193, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1075193, _1075195, _1075197), _1075199)))], (16254 ^ _780086) ^ [_1075252] : [class_Lattices_Osemilattice__inf(_1075252), -(c_Finite__Set_Ofun__left__comm__idem(_1075252, _1075252, c_Lattices_Osemilattice__inf__class_Oinf(_1075252)))], (16260 ^ _780086) ^ [_1075352, _1075354, _1075356, _1075358] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1075352, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1075352, tc_fun(_1075352, tc_HOL_Obool), tc_HOL_Obool), c_member(_1075352)), _1075354)), hAPP(hAPP(c_COMBC(_1075352, tc_fun(_1075352, tc_HOL_Obool), tc_HOL_Obool), c_member(_1075352)), _1075356)), _1075358)), -(hBOOL(hAPP(hAPP(c_member(_1075352), _1075358), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1075352, tc_HOL_Obool)), _1075354), _1075356))))], (16266 ^ _780086) ^ [_1075551, _1075553, _1075555, _1075557] : [hBOOL(hAPP(hAPP(c_member(_1075551), _1075557), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1075551, tc_HOL_Obool)), _1075553), _1075555))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1075551, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1075551, tc_fun(_1075551, tc_HOL_Obool), tc_HOL_Obool), c_member(_1075551)), _1075553)), hAPP(hAPP(c_COMBC(_1075551, tc_fun(_1075551, tc_HOL_Obool), tc_HOL_Obool), c_member(_1075551)), _1075555)), _1075557)))], (16272 ^ _780086) ^ [_1075756, _1075758, _1075760, _1075762] : [class_Lattices_Olattice(_1075756), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1075756), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1075756), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1075756), _1075758), _1075760)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1075756), _1075758), _1075762))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1075756), _1075758), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1075756), _1075760), _1075762)))))], (16278 ^ _780086) ^ [_1075929, _1075931, _1075933, _1075935] : [class_Lattices_Olattice(_1075929), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1075929), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1075929), _1075931), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1075929), _1075933), _1075935))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1075929), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1075929), _1075931), _1075933)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1075929), _1075931), _1075935)))))], (16284 ^ _780086) ^ [_1076102, _1076104] : [class_Lattices_Oboolean__algebra(_1076102), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1076102), _1076104), hAPP(c_Groups_Ouminus__class_Ouminus(_1076102), _1076104)) = c_Orderings_Obot__class_Obot(_1076102))], (16290 ^ _780086) ^ [_1076207, _1076209] : [class_Lattices_Oboolean__algebra(_1076207), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1076207), hAPP(c_Groups_Ouminus__class_Ouminus(_1076207), _1076209)), _1076209) = c_Orderings_Obot__class_Obot(_1076207))], (16296 ^ _780086) ^ [_1076312, _1076314, _1076316] : [class_Lattices_Oboolean__algebra(_1076312), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1076312), _1076314), _1076316) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1076312), _1076314), hAPP(c_Groups_Ouminus__class_Ouminus(_1076312), _1076316)))], (16302 ^ _780086) ^ [_1076431, _1076433, _1076435] : [class_Lattices_Oboolean__algebra(_1076431), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1076431), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1076431), _1076433), _1076435)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1076431), hAPP(c_Groups_Ouminus__class_Ouminus(_1076431), _1076433)), hAPP(c_Groups_Ouminus__class_Ouminus(_1076431), _1076435)))], (16308 ^ _780086) ^ [_1076570, _1076572, _1076574] : [class_Lattices_Oboolean__algebra(_1076570), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1076570), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1076570), _1076572), _1076574)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1076570), hAPP(c_Groups_Ouminus__class_Ouminus(_1076570), _1076572)), hAPP(c_Groups_Ouminus__class_Ouminus(_1076570), _1076574)))], (16314 ^ _780086) ^ [_1076724, _1076726, _1076728, _1076730] : [hBOOL(hAPP(hAPP(c_member(_1076724), _1076726), _1076728)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1076724, tc_HOL_Obool)), _1076728), hAPP(hAPP(c_Set_Oinsert(_1076724), _1076726), _1076730)) = hAPP(hAPP(c_Set_Oinsert(_1076724), _1076726), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1076724, tc_HOL_Obool)), _1076728), _1076730)))], (16320 ^ _780086) ^ [_1076889, _1076891, _1076893, _1076895] : [-(hBOOL(hAPP(hAPP(c_member(_1076889), _1076891), _1076893))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1076889, tc_HOL_Obool)), _1076893), hAPP(hAPP(c_Set_Oinsert(_1076889), _1076891), _1076895)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1076889, tc_HOL_Obool)), _1076893), _1076895))], (16326 ^ _780086) ^ [_1076983, _1076985, _1076987, _1076989] : [hBOOL(hAPP(hAPP(c_member(_1076983), _1076985), _1076987)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1076983, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1076983), _1076985), _1076989)), _1076987) = hAPP(hAPP(c_Set_Oinsert(_1076983), _1076985), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1076983, tc_HOL_Obool)), _1076989), _1076987)))], (16332 ^ _780086) ^ [_1077148, _1077150, _1077152, _1077154] : [-(hBOOL(hAPP(hAPP(c_member(_1077148), _1077150), _1077152))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1077148, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1077148), _1077150), _1077154)), _1077152) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1077148, tc_HOL_Obool)), _1077154), _1077152))], (16338 ^ _780086) ^ [_1077223, _1077225, _1077227, _1077229] : [-(hBOOL(hAPP(hAPP(c_member(_1077223), _1077225), _1077227))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1077223, tc_HOL_Obool)), _1077227), hAPP(hAPP(c_Set_Oinsert(_1077223), _1077225), _1077229)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1077223, tc_HOL_Obool)), _1077227), _1077229))], (16344 ^ _780086) ^ [_1077296, _1077298, _1077300, _1077302] : [-(hBOOL(hAPP(hAPP(c_member(_1077296), _1077298), _1077300))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1077296, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1077296), _1077298), _1077302)), _1077300) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1077296, tc_HOL_Obool)), _1077302), _1077300))], (16350 ^ _780086) ^ [_1077373, _1077375, _1077377, _1077379] : [hBOOL(hAPP(hAPP(c_member(_1077373), _1077375), _1077377)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1077373, tc_HOL_Obool)), _1077377), hAPP(hAPP(c_Set_Oinsert(_1077373), _1077375), _1077379)) = hAPP(hAPP(c_Set_Oinsert(_1077373), _1077375), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1077373, tc_HOL_Obool)), _1077377), _1077379)))], (16356 ^ _780086) ^ [_1077544, _1077546, _1077548, _1077550] : [hBOOL(hAPP(hAPP(c_member(_1077544), _1077546), _1077548)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1077544, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1077544), _1077546), _1077550)), _1077548) = hAPP(hAPP(c_Set_Oinsert(_1077544), _1077546), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1077544, tc_HOL_Obool)), _1077550), _1077548)))], (16362 ^ _780086) ^ [_1077715, _1077717, _1077719, _1077721] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1077715, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1077717, _1077715, _1077719), hAPP(c_Set_Ovimage(_1077717, _1077715, _1077719), _1077721))), _1077721)))], (16364 ^ _780086) ^ [_1077768, _1077770, _1077772, _1077774] : [hAPP(c_Set_Oimage(_1077768, _1077770, _1077772), c_Orderings_Otop__class_Otop(tc_fun(_1077768, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1077770, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1077768, _1077770, _1077772), hAPP(c_Set_Ovimage(_1077768, _1077770, _1077772), _1077774)) = _1077774)], (16370 ^ _780086) ^ [_1077911, _1077913, _1077915, _1077917, _1077919] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1077911, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1077913, _1077911, _1077915), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1077913, tc_HOL_Obool)), _1077917), _1077919))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1077911, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1077913, _1077911, _1077915), _1077917)), hAPP(c_Set_Oimage(_1077913, _1077911, _1077915), _1077919)))))], (16372 ^ _780086) ^ [_1077995, _1077997, _1077999] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1077995, tc_HOL_Obool)), _1077997), _1077999) = c_Orderings_Obot__class_Obot(tc_fun(_1077995, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1077995, tc_HOL_Obool)), _1077997), _1077999) = _1077997)], (16378 ^ _780086) ^ [_1078128, _1078130, _1078132] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1078128, tc_HOL_Obool)), _1078130), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1078128, tc_HOL_Obool)), _1078132), _1078130)) = c_Orderings_Obot__class_Obot(tc_fun(_1078128, tc_HOL_Obool)))], (16380 ^ _780086) ^ [_1078203, _1078205, _1078207, _1078209] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1078203, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1078203, tc_HOL_Obool)), _1078205), _1078207)), _1078209) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1078203, tc_HOL_Obool)), _1078205), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1078203, tc_HOL_Obool)), _1078207), _1078209)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1078203, tc_HOL_Obool)), _1078209), _1078205)))], (16386 ^ _780086) ^ [_1078388, _1078390, _1078392, _1078394] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1078388, tc_HOL_Obool)), _1078394), _1078390)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1078388, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1078388, tc_HOL_Obool)), _1078390), _1078392)), _1078394) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1078388, tc_HOL_Obool)), _1078390), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1078388, tc_HOL_Obool)), _1078392), _1078394)))], (16392 ^ _780086) ^ [_1078579, _1078581, _1078583] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1078579, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1078579, tc_HOL_Obool)), _1078581), _1078583)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1078579, tc_HOL_Obool)), _1078581), _1078583)) = _1078581)], (16394 ^ _780086) ^ [_1078639, _1078641, _1078643, _1078645] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1078639, tc_HOL_Obool)), _1078641), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1078639, tc_HOL_Obool)), _1078643), _1078645)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1078639, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1078639, tc_HOL_Obool)), _1078641), _1078643)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1078639, tc_HOL_Obool)), _1078641), _1078645)))], (16396 ^ _780086) ^ [_1078723, _1078725, _1078727, _1078729] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1078723, tc_HOL_Obool)), _1078725), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1078723, tc_HOL_Obool)), _1078727), _1078729)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1078723, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1078723, tc_HOL_Obool)), _1078725), _1078727)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1078723, tc_HOL_Obool)), _1078725), _1078729)))], (16398 ^ _780086) ^ [_1078828, _1078830, _1078832, _1078834] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1078828, tc_fun(_1078830, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1078828, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1078830, tc_HOL_Obool), tc_fun(_1078830, tc_HOL_Obool), _1078828), hAPP(c_COMBC(_1078830, tc_fun(_1078830, tc_HOL_Obool), tc_HOL_Obool), c_member(_1078830))), _1078832)), _1078834)), -(hBOOL(hAPP(hAPP(c_member(_1078830), _1078834), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1078828, tc_fun(_1078830, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1078828, tc_HOL_Obool))), _1078832))))], (16404 ^ _780086) ^ [_1079047, _1079049, _1079051, _1079053] : [hBOOL(hAPP(hAPP(c_member(_1079049), _1079053), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1079047, tc_fun(_1079049, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1079047, tc_HOL_Obool))), _1079051))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1079047, tc_fun(_1079049, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1079047, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1079049, tc_HOL_Obool), tc_fun(_1079049, tc_HOL_Obool), _1079047), hAPP(c_COMBC(_1079049, tc_fun(_1079049, tc_HOL_Obool), tc_HOL_Obool), c_member(_1079049))), _1079051)), _1079053)))], (16410 ^ _780086) ^ [_1079272, _1079274] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1079272, tc_HOL_Obool)), _1079274), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1079272, tc_HOL_Obool)), _1079274)) = c_Orderings_Obot__class_Obot(tc_fun(_1079272, tc_HOL_Obool)))], (16412 ^ _780086) ^ [_1079321, _1079323] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1079321, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1079321, tc_HOL_Obool)), _1079323)), _1079323) = c_Orderings_Obot__class_Obot(tc_fun(_1079321, tc_HOL_Obool)))], (16414 ^ _780086) ^ [_1079370, _1079372, _1079374] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1079370, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1079370, tc_HOL_Obool)), _1079372), _1079374)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1079370, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1079370, tc_HOL_Obool)), _1079372)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1079370, tc_HOL_Obool)), _1079374)))], (16416 ^ _780086) ^ [_1079443, _1079445, _1079447] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1079443, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1079443, tc_HOL_Obool)), _1079445), _1079447)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1079443, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1079443, tc_HOL_Obool)), _1079445)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1079443, tc_HOL_Obool)), _1079447)))], (16418 ^ _780086) ^ [_1079516, _1079518, _1079520] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1079516, tc_HOL_Obool)), _1079518), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1079516, tc_HOL_Obool)), _1079520)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1079516, tc_HOL_Obool)), _1079518), _1079520))], (16420 ^ _780086) ^ [_1079573, _1079575, _1079577] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1079573, tc_HOL_Obool)), _1079575), _1079577) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1079573, tc_HOL_Obool)), _1079575), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1079573, tc_HOL_Obool)), _1079577)))], (16422 ^ _780086) ^ [_1079654, _1079656, _1079658, _1079660, _1079662] : [hBOOL(hAPP(hAPP(c_member(_1079654), _1079656), hAPP(c_Set_Ovimage(_1079654, _1079658, _1079660), hAPP(hAPP(c_Set_Oinsert(_1079658), _1079662), c_Orderings_Obot__class_Obot(tc_fun(_1079658, tc_HOL_Obool)))))), -(hAPP(_1079660, _1079656) = _1079662)], (16428 ^ _780086) ^ [_1079793, _1079795, _1079797, _1079799, _1079801] : [hAPP(_1079799, _1079795) = _1079801, -(hBOOL(hAPP(hAPP(c_member(_1079793), _1079795), hAPP(c_Set_Ovimage(_1079793, _1079797, _1079799), hAPP(hAPP(c_Set_Oinsert(_1079797), _1079801), c_Orderings_Obot__class_Obot(tc_fun(_1079797, tc_HOL_Obool)))))))], (16434 ^ _780086) ^ [_1079938, _1079940, _1079942, _1079944] : [class_Lattices_Osemilattice__inf(_1079938), hBOOL(hAPP(c_Finite__Set_Ofinite(_1079938), _1079940)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1079938, _1079938, c_Lattices_Osemilattice__inf__class_Oinf(_1079938)), _1079942), hAPP(hAPP(c_Set_Oinsert(_1079938), _1079944), _1079940)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1079938), _1079944), hAPP(hAPP(c_Finite__Set_Ofold(_1079938, _1079938, c_Lattices_Osemilattice__inf__class_Oinf(_1079938)), _1079942), _1079940)))], (16444 ^ _780086) ^ [_1080161, _1080163, _1080165] : [class_Lattices_Olattice(_1080161), hBOOL(hAPP(c_Finite__Set_Ofinite(_1080161), _1080163)), hBOOL(hAPP(hAPP(c_member(_1080161), _1080165), _1080163)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1080161), _1080165), c_Big__Operators_Olattice__class_OSup__fin(_1080161, _1080163)) = _1080165)], (16458 ^ _780086) ^ [_1080390, _1080392, _1080394, _1080396, _1080398] : [-(hAPP(c_Set_Ovimage(_1080390, _1080392, _1080394), hAPP(hAPP(c_Set_Oinsert(_1080392), _1080396), _1080398)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1080390, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1080390, _1080392, _1080394), hAPP(hAPP(c_Set_Oinsert(_1080392), _1080396), c_Orderings_Obot__class_Obot(tc_fun(_1080392, tc_HOL_Obool))))), hAPP(c_Set_Ovimage(_1080390, _1080392, _1080394), _1080398)))], (16460 ^ _780086) ^ [_1080474, _1080476, _1080478, _1080480] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1080474), hAPP(c_Set_Ovimage(_1080474, _1080476, _1080478), _1080480))), hAPP(c_Set_Oimage(_1080474, _1080476, _1080478), c_Orderings_Otop__class_Otop(tc_fun(_1080474, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1080476, tc_HOL_Obool)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1080476), _1080480)))], (16470 ^ _780086) ^ [_1080675, _1080677, _1080679, _1080681, _1080683] : [hAPP(c_Set_Oimage(_1080675, _1080677, _1080679), c_Orderings_Otop__class_Otop(tc_fun(_1080675, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1080677, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1080675, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1080675, _1080677, _1080679), _1080681)), _1080683)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1080677, tc_HOL_Obool)), _1080681), hAPP(c_Set_Oimage(_1080675, _1080677, _1080679), _1080683))))], (16480 ^ _780086) ^ [_1080918, _1080920, _1080922, _1080924] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1080918), _1080920)), c_Fun_Oinj__on(_1080922, _1080918, _1080924, c_Orderings_Otop__class_Otop(tc_fun(_1080922, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1080922), hAPP(c_Set_Ovimage(_1080922, _1080918, _1080924), _1080920))))], (16490 ^ _780086) ^ [_1081099, _1081101, _1081103, _1081105] : [c_Fun_Oinj__on(_1081099, _1081101, _1081103, c_Orderings_Otop__class_Otop(tc_fun(_1081099, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_1081099, _1081101, _1081103), hAPP(c_Set_Oimage(_1081099, _1081101, _1081103), _1081105)) = _1081105)], (16496 ^ _780086) ^ [_1081222, _1081224, _1081226, _1081228, _1081230, _1081232] : [c_Fun_Oinj__on(_1081222, _1081224, _1081226, _1081228), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1081222, tc_HOL_Obool)), _1081230), _1081228)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1081222, tc_HOL_Obool)), _1081232), _1081228)), -(hAPP(c_Set_Oimage(_1081222, _1081224, _1081226), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1081222, tc_HOL_Obool)), _1081230), _1081232)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1081224, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1081222, _1081224, _1081226), _1081230)), hAPP(c_Set_Oimage(_1081222, _1081224, _1081226), _1081232)))], (16510 ^ _780086) ^ [_1081557, _1081559, _1081561, _1081563, _1081565] : [c_Fun_Oinj__on(_1081557, _1081559, _1081561, c_Orderings_Otop__class_Otop(tc_fun(_1081557, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1081557, _1081559, _1081561), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1081557, tc_HOL_Obool)), _1081563), _1081565)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1081559, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1081557, _1081559, _1081561), _1081563)), hAPP(c_Set_Oimage(_1081557, _1081559, _1081561), _1081565)))], (16516 ^ _780086) ^ [_1081758, _1081760, _1081762] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1081758, tc_HOL_Obool)), _1081760), _1081762) = c_Orderings_Obot__class_Obot(tc_fun(_1081758, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1081758, tc_HOL_Obool)), _1081760), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1081758, tc_HOL_Obool)), _1081762))))], (16522 ^ _780086) ^ [_1081901, _1081903, _1081905] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1081901, tc_HOL_Obool)), _1081903), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1081901, tc_HOL_Obool)), _1081905))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1081901, tc_HOL_Obool)), _1081903), _1081905) = c_Orderings_Obot__class_Obot(tc_fun(_1081901, tc_HOL_Obool)))], (16528 ^ _780086) ^ [_1082065, _1082067, _1082069, _1082071] : [hBOOL(hAPP(hAPP(c_member(_1082065), _1082067), _1082069)), -(hAPP(c_Set_Ovimage(_1082071, _1082065, hAPP(c_COMBK(_1082065, _1082071), _1082067)), _1082069) = c_Orderings_Otop__class_Otop(tc_fun(_1082071, tc_HOL_Obool)))], (16534 ^ _780086) ^ [_1082190, _1082192, _1082194, _1082196] : [-(hBOOL(hAPP(hAPP(c_member(_1082190), _1082192), _1082194))), -(hAPP(c_Set_Ovimage(_1082196, _1082190, hAPP(c_COMBK(_1082190, _1082196), _1082192)), _1082194) = c_Orderings_Obot__class_Obot(tc_fun(_1082196, tc_HOL_Obool)))], (16540 ^ _780086) ^ [_1082257, _1082259, _1082261, _1082263, _1082265, _1082267, _1082269, _1082271] : [c_Finite__Set_Ofolding__image__simple(_1082257, _1082259, _1082261, _1082263, _1082265, _1082267), hBOOL(hAPP(c_Finite__Set_Ofinite(_1082259), _1082269)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1082259), _1082271)), -(hAPP(hAPP(_1082261, hAPP(_1082267, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1082259, tc_HOL_Obool)), _1082269), _1082271))), hAPP(_1082267, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1082259, tc_HOL_Obool)), _1082269), _1082271))) = hAPP(hAPP(_1082261, hAPP(_1082267, _1082269)), hAPP(_1082267, _1082271)))], (16554 ^ _780086) ^ [_1082590, _1082592, _1082594] : [class_Lattices_Oboolean__algebra(_1082590), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1082590), _1082592), _1082594) = c_Orderings_Obot__class_Obot(_1082590), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1082590), _1082592), _1082594) = c_Orderings_Otop__class_Otop(_1082590), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1082590), _1082592) = _1082594)], (16568 ^ _780086) ^ [_1082825, _1082827, _1082829, _1082831] : [class_Lattices_Osemilattice__inf(_1082825), hBOOL(hAPP(c_Finite__Set_Ofinite(_1082825), _1082827)), hBOOL(hAPP(hAPP(c_member(_1082825), _1082829), _1082827)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082825), hAPP(hAPP(c_Finite__Set_Ofold(_1082825, _1082825, c_Lattices_Osemilattice__inf__class_Oinf(_1082825)), _1082831), _1082827)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1082825), _1082829), _1082831))))], (16582 ^ _780086) ^ [_1083092, _1083094, _1083096] : [class_Lattices_Osemilattice__inf(_1083092), hBOOL(hAPP(c_Finite__Set_Ofinite(_1083092), _1083094)), hBOOL(hAPP(hAPP(c_member(_1083092), _1083096), _1083094)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083092), hAPP(c_Finite__Set_Ofold1(_1083092, c_Lattices_Osemilattice__inf__class_Oinf(_1083092)), _1083094)), _1083096)))], (16596 ^ _780086) ^ [_1083329, _1083331, _1083333] : [class_Lattices_Osemilattice__inf(_1083329), hBOOL(hAPP(c_Finite__Set_Ofinite(_1083329), _1083331)), -(_1083331 = c_Orderings_Obot__class_Obot(tc_fun(_1083329, tc_HOL_Obool))), 16607 ^ _780086 : [(16618 ^ _780086) ^ [] : [16620 ^ _780086 : [(16621 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1083329), 16619 ^ [_1083329, _1083331, _1083333]), _1083331)))], (16623 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083329), _1083333), 16619 ^ [_1083329, _1083331, _1083333]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083329), _1083333), hAPP(c_Finite__Set_Ofold1(_1083329, c_Lattices_Osemilattice__inf__class_Oinf(_1083329)), _1083331))))], (16608 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083329), _1083333), hAPP(c_Finite__Set_Ofold1(_1083329, c_Lattices_Osemilattice__inf__class_Oinf(_1083329)), _1083331))), 16611 ^ _780086 : [(16612 ^ _780086) ^ [_1083622] : [hBOOL(hAPP(hAPP(c_member(_1083329), _1083622), _1083331)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083329), _1083333), _1083622)))]]]]], (16627 ^ _780086) ^ [_1083907, _1083909, _1083911, _1083913, _1083915] : [class_Groups_Ocomm__monoid__add(_1083907), hBOOL(hAPP(c_Finite__Set_Ofinite(_1083909), _1083911)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1083909), _1083913)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1083907), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1083909, _1083907), _1083915), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1083909, tc_HOL_Obool)), _1083911), _1083913))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1083909, _1083907), _1083915), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1083909, tc_HOL_Obool)), _1083911), _1083913))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1083907), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1083909, _1083907), _1083915), _1083911)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1083909, _1083907), _1083915), _1083913)))], (16641 ^ _780086) ^ [_1084268, _1084270, _1084272, _1084274, _1084276] : [c_Fun_Oinj__on(_1084268, _1084270, _1084272, c_Orderings_Otop__class_Otop(tc_fun(_1084268, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1084270, tc_HOL_Obool)), _1084274), hAPP(c_Set_Oimage(_1084268, _1084270, _1084272), _1084276))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1084268, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1084268, _1084270, _1084272), _1084274)), _1084276)))], (16651 ^ _780086) ^ [_1084491, _1084493, _1084495, _1084497, _1084499] : [class_Groups_Ocomm__monoid__mult(_1084491), hBOOL(hAPP(c_Finite__Set_Ofinite(_1084493), _1084495)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1084493), _1084497)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084491), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1084493, _1084491), _1084499), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1084493, tc_HOL_Obool)), _1084495), _1084497))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1084493, _1084491), _1084499), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1084493, tc_HOL_Obool)), _1084495), _1084497))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084491), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1084493, _1084491), _1084499), _1084495)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1084493, _1084491), _1084499), _1084497)))], (16665 ^ _780086) ^ [_1084852, _1084854, _1084856, _1084858, _1084860] : [class_Groups_Ocomm__monoid__mult(_1084852), hBOOL(hAPP(c_Finite__Set_Ofinite(_1084854), _1084856)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1084854), _1084858)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084852), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1084854, _1084852), _1084860), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1084854, tc_HOL_Obool)), _1084856), _1084858))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1084854, _1084852), _1084860), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1084854, tc_HOL_Obool)), _1084856), _1084858))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084852), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1084854, _1084852), _1084860), _1084856)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1084854, _1084852), _1084860), _1084858)))], (16679 ^ _780086) ^ [_1085213, _1085215, _1085217] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1085213), _1085215)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1085213), _1085217)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1085213), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1085213, tc_HOL_Obool)), _1085215), _1085217))), hAPP(c_Finite__Set_Ocard(_1085213), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1085213, tc_HOL_Obool)), _1085215), _1085217))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1085213), _1085215)), hAPP(c_Finite__Set_Ocard(_1085213), _1085217)))], (16689 ^ _780086) ^ [_1085470, _1085472, _1085474] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1085470), _1085472)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1085470), _1085474)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1085470), _1085472)), hAPP(c_Finite__Set_Ocard(_1085470), _1085474)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1085470), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1085470, tc_HOL_Obool)), _1085472), _1085474))), hAPP(c_Finite__Set_Ocard(_1085470), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1085470, tc_HOL_Obool)), _1085472), _1085474))))], (16699 ^ _780086) ^ [_1085727, _1085729, _1085731] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1085727), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1085727, tc_HOL_Obool)), _1085729), _1085731))), -(hAPP(c_Finite__Set_Ocard(_1085727), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1085727, tc_HOL_Obool)), _1085729), _1085731)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1085727), _1085729)), hAPP(c_Finite__Set_Ocard(_1085727), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1085727, tc_HOL_Obool)), _1085729), _1085731))))], (16705 ^ _780086) ^ [_1085943, _1085945, _1085947, _1085949, _1085951, _1085953] : [hBOOL(hAPP(hAPP(c_member(_1085943), _1085945), _1085947)), 16708 ^ _780086 : [(16709 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1085943), _1085949), _1085947)), -(hAPP(c_Set_Ovimage(_1085951, _1085943, hAPP(hAPP(c_COMBC(_1085951, _1085943, _1085943), hAPP(hAPP(c_COMBC(_1085951, _1085943, tc_fun(_1085943, _1085943)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1085943, tc_fun(_1085943, _1085943)), _1085951), c_If(_1085943)), hAPP(hAPP(c_COMBC(_1085951, tc_fun(_1085951, tc_HOL_Obool), tc_HOL_Obool), c_member(_1085951)), _1085953))), _1085945)), _1085949)), _1085947) = c_Orderings_Otop__class_Otop(tc_fun(_1085951, tc_HOL_Obool)))], (16715 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1085943), _1085949), _1085947))), -(hAPP(c_Set_Ovimage(_1085951, _1085943, hAPP(hAPP(c_COMBC(_1085951, _1085943, _1085943), hAPP(hAPP(c_COMBC(_1085951, _1085943, tc_fun(_1085943, _1085943)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1085943, tc_fun(_1085943, _1085943)), _1085951), c_If(_1085943)), hAPP(hAPP(c_COMBC(_1085951, tc_fun(_1085951, tc_HOL_Obool), tc_HOL_Obool), c_member(_1085951)), _1085953))), _1085945)), _1085949)), _1085947) = _1085953)]]], (16721 ^ _780086) ^ [_1086434, _1086436, _1086438, _1086440, _1086442, _1086444] : [-(hBOOL(hAPP(hAPP(c_member(_1086434), _1086436), _1086438))), 16724 ^ _780086 : [(16725 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1086434), _1086440), _1086438)), -(hAPP(c_Set_Ovimage(_1086442, _1086434, hAPP(hAPP(c_COMBC(_1086442, _1086434, _1086434), hAPP(hAPP(c_COMBC(_1086442, _1086434, tc_fun(_1086434, _1086434)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1086434, tc_fun(_1086434, _1086434)), _1086442), c_If(_1086434)), hAPP(hAPP(c_COMBC(_1086442, tc_fun(_1086442, tc_HOL_Obool), tc_HOL_Obool), c_member(_1086442)), _1086444))), _1086436)), _1086440)), _1086438) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1086442, tc_HOL_Obool)), _1086444))], (16731 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1086434), _1086440), _1086438))), -(hAPP(c_Set_Ovimage(_1086442, _1086434, hAPP(hAPP(c_COMBC(_1086442, _1086434, _1086434), hAPP(hAPP(c_COMBC(_1086442, _1086434, tc_fun(_1086434, _1086434)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1086434, tc_fun(_1086434, _1086434)), _1086442), c_If(_1086434)), hAPP(hAPP(c_COMBC(_1086442, tc_fun(_1086442, tc_HOL_Obool), tc_HOL_Obool), c_member(_1086442)), _1086444))), _1086436)), _1086440)), _1086438) = c_Orderings_Obot__class_Obot(tc_fun(_1086442, tc_HOL_Obool)))]]], (16737 ^ _780086) ^ [_1086939, _1086941, _1086943, _1086945, _1086947] : [c_Finite__Set_Ofolding__one(_1086939, _1086941, _1086943), hBOOL(hAPP(c_Finite__Set_Ofinite(_1086939), _1086945)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1086939), _1086947)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1086939, tc_HOL_Obool)), _1086945), _1086947) = c_Orderings_Obot__class_Obot(tc_fun(_1086939, tc_HOL_Obool))), -(hAPP(hAPP(_1086941, hAPP(_1086943, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1086939, tc_HOL_Obool)), _1086945), _1086947))), hAPP(_1086943, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1086939, tc_HOL_Obool)), _1086945), _1086947))) = hAPP(hAPP(_1086941, hAPP(_1086943, _1086945)), hAPP(_1086943, _1086947)))], (16755 ^ _780086) ^ [_1087295, _1087297, _1087299, _1087301, _1087303] : [c_Finite__Set_Ofolding__one(_1087295, _1087297, _1087299), hBOOL(hAPP(c_Finite__Set_Ofinite(_1087295), _1087301)), -(_1087301 = c_Orderings_Obot__class_Obot(tc_fun(_1087295, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1087295), _1087303)), -(_1087303 = c_Orderings_Obot__class_Obot(tc_fun(_1087295, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1087295, tc_HOL_Obool)), _1087301), _1087303) = c_Orderings_Obot__class_Obot(tc_fun(_1087295, tc_HOL_Obool)), -(hAPP(_1087299, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1087295, tc_HOL_Obool)), _1087301), _1087303)) = hAPP(hAPP(_1087297, hAPP(_1087299, _1087301)), hAPP(_1087299, _1087303)))], (16781 ^ _780086) ^ [_1087796, _1087798, _1087800, _1087802, _1087804, _1087806, _1087808, _1087810] : [c_Finite__Set_Ofolding__image__simple(_1087796, _1087798, _1087800, _1087802, _1087804, _1087806), hBOOL(hAPP(c_Finite__Set_Ofinite(_1087798), _1087808)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1087798), _1087810)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1087798, tc_HOL_Obool)), _1087808), _1087810) = c_Orderings_Obot__class_Obot(tc_fun(_1087798, tc_HOL_Obool)), -(hAPP(_1087806, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1087798, tc_HOL_Obool)), _1087808), _1087810)) = hAPP(hAPP(_1087800, hAPP(_1087806, _1087808)), hAPP(_1087806, _1087810)))], (16799 ^ _780086) ^ [_1088185, _1088187, _1088189, _1088191, _1088193] : [class_Groups_Ocomm__monoid__add(_1088185), hBOOL(hAPP(c_Finite__Set_Ofinite(_1088187), _1088189)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1088187), _1088191)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1088187, tc_HOL_Obool)), _1088189), _1088191) = c_Orderings_Obot__class_Obot(tc_fun(_1088187, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1088187, _1088185), _1088193), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1088187, tc_HOL_Obool)), _1088189), _1088191)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1088185), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1088187, _1088185), _1088193), _1088189)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1088187, _1088185), _1088193), _1088191)))], (16817 ^ _780086) ^ [_1088580, _1088582, _1088584, _1088586, _1088588] : [class_Groups_Oab__group__add(_1088580), hBOOL(hAPP(c_Finite__Set_Ofinite(_1088582), _1088584)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1088582), _1088586)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1088582, _1088580), _1088588), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1088582, tc_HOL_Obool)), _1088584), _1088586)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1088580), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1088580), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1088582, _1088580), _1088588), _1088584)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1088582, _1088580), _1088588), _1088586))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1088582, _1088580), _1088588), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1088582, tc_HOL_Obool)), _1088584), _1088586))))], (16831 ^ _780086) ^ [_1088941, _1088943, _1088945, _1088947, _1088949] : [class_Groups_Ocomm__monoid__mult(_1088941), hBOOL(hAPP(c_Finite__Set_Ofinite(_1088943), _1088945)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1088943), _1088947)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1088943, tc_HOL_Obool)), _1088945), _1088947) = c_Orderings_Obot__class_Obot(tc_fun(_1088943, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1088943, _1088941), _1088949), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1088943, tc_HOL_Obool)), _1088945), _1088947)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1088941), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1088943, _1088941), _1088949), _1088945)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1088943, _1088941), _1088949), _1088947)))], (16849 ^ _780086) ^ [_1089336, _1089338, _1089340, _1089342, _1089344] : [class_Groups_Ocomm__monoid__mult(_1089336), hBOOL(hAPP(c_Finite__Set_Ofinite(_1089338), _1089340)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1089338), _1089342)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1089338, tc_HOL_Obool)), _1089340), _1089342) = c_Orderings_Obot__class_Obot(tc_fun(_1089338, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1089338, _1089336), _1089344), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1089338, tc_HOL_Obool)), _1089340), _1089342)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1089336), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1089338, _1089336), _1089344), _1089340)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1089338, _1089336), _1089344), _1089342)))], (16867 ^ _780086) ^ [_1089731, _1089733, _1089735, _1089737, _1089739] : [class_Complete__Lattice_Ocomplete__lattice(_1089731), hBOOL(hAPP(c_Finite__Set_Ofinite(_1089733), _1089735)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1089731), _1089737), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1089733, _1089731), _1089735), _1089739)) = hAPP(hAPP(c_Finite__Set_Ofold(_1089733, _1089731, hAPP(hAPP(c_COMBB(_1089731, tc_fun(_1089731, _1089731), _1089733), c_Lattices_Osemilattice__sup__class_Osup(_1089731)), _1089739)), _1089737), _1089735))], (16877 ^ _780086) ^ [_1089962, _1089964, _1089966] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1089962), _1089964)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1089962), _1089966)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1089962, tc_HOL_Obool)), _1089964), _1089966) = c_Orderings_Obot__class_Obot(tc_fun(_1089962, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ocard(_1089962), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1089962, tc_HOL_Obool)), _1089964), _1089966)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1089962), _1089964)), hAPP(c_Finite__Set_Ocard(_1089962), _1089966)))], (16891 ^ _780086) ^ [_1090285, _1090287, _1090289, _1090291, _1090293] : [c_Fun_Oinj__on(_1090285, _1090287, _1090289, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1090285, tc_HOL_Obool)), _1090291), _1090293)), 16894 ^ _780086 : [(16895 ^ _780086) ^ [] : [-(c_Fun_Oinj__on(_1090285, _1090287, _1090289, _1090291))], (16897 ^ _780086) ^ [] : [-(c_Fun_Oinj__on(_1090285, _1090287, _1090289, _1090293))], (16899 ^ _780086) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1090287, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1090285, _1090287, _1090289), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1090285, tc_HOL_Obool)), _1090291), _1090293))), hAPP(c_Set_Oimage(_1090285, _1090287, _1090289), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1090285, tc_HOL_Obool)), _1090293), _1090291))) = c_Orderings_Obot__class_Obot(tc_fun(_1090287, tc_HOL_Obool)))]]], (16901 ^ _780086) ^ [_1090552, _1090554, _1090556, _1090558, _1090560] : [-(c_Fun_Oinj__on(_1090552, _1090554, _1090556, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1090552, tc_HOL_Obool)), _1090558), _1090560))), c_Fun_Oinj__on(_1090552, _1090554, _1090556, _1090558), c_Fun_Oinj__on(_1090552, _1090554, _1090556, _1090560), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1090554, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1090552, _1090554, _1090556), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1090552, tc_HOL_Obool)), _1090558), _1090560))), hAPP(c_Set_Oimage(_1090552, _1090554, _1090556), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1090552, tc_HOL_Obool)), _1090560), _1090558))) = c_Orderings_Obot__class_Obot(tc_fun(_1090554, tc_HOL_Obool))], (16915 ^ _780086) ^ [_1090891, _1090893, _1090895, _1090897, _1090899] : [class_Groups_Ocomm__monoid__mult(_1090891), hBOOL(hAPP(c_Finite__Set_Ofinite(_1090893), _1090895)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1090893), _1090897)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090891), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1090891, _1090893, c_Groups_Otimes__class_Otimes(_1090891)), _1090899), c_Groups_Oone__class_Oone(_1090891)), _1090895)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1090891, _1090893, c_Groups_Otimes__class_Otimes(_1090891)), _1090899), c_Groups_Oone__class_Oone(_1090891)), _1090897)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090891), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1090891, _1090893, c_Groups_Otimes__class_Otimes(_1090891)), _1090899), c_Groups_Oone__class_Oone(_1090891)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1090893, tc_HOL_Obool)), _1090895), _1090897))), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1090891, _1090893, c_Groups_Otimes__class_Otimes(_1090891)), _1090899), c_Groups_Oone__class_Oone(_1090891)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1090893, tc_HOL_Obool)), _1090895), _1090897))))], (16929 ^ _780086) ^ [_1091316, _1091318, _1091320] : [class_Groups_Oab__semigroup__mult(_1091316), hBOOL(hAPP(c_Finite__Set_Ofinite(_1091316), _1091318)), -(_1091318 = c_Orderings_Obot__class_Obot(tc_fun(_1091316, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1091316), _1091320)), -(_1091320 = c_Orderings_Obot__class_Obot(tc_fun(_1091316, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1091316, tc_HOL_Obool)), _1091318), _1091320) = c_Orderings_Obot__class_Obot(tc_fun(_1091316, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ofold1(_1091316, c_Groups_Otimes__class_Otimes(_1091316)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1091316, tc_HOL_Obool)), _1091318), _1091320)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091316), hAPP(c_Finite__Set_Ofold1(_1091316, c_Groups_Otimes__class_Otimes(_1091316)), _1091318)), hAPP(c_Finite__Set_Ofold1(_1091316, c_Groups_Otimes__class_Otimes(_1091316)), _1091320)))], (16955 ^ _780086) ^ [_1091823, _1091825, _1091827] : [class_Lattices_Olattice(_1091823), hBOOL(hAPP(c_Finite__Set_Ofinite(_1091823), _1091825)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1091823), _1091827)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1091823, tc_HOL_Obool)), _1091825), _1091827) = c_Orderings_Obot__class_Obot(tc_fun(_1091823, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1091823), c_Big__Operators_Olattice__class_OSup__fin(_1091823, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1091823, tc_HOL_Obool)), _1091825), _1091827))), c_Big__Operators_Olattice__class_OSup__fin(_1091823, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1091823, tc_HOL_Obool)), _1091825), _1091827))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1091823), c_Big__Operators_Olattice__class_OSup__fin(_1091823, _1091825)), c_Big__Operators_Olattice__class_OSup__fin(_1091823, _1091827)))], (16973 ^ _780086) ^ [_1092171, _1092173, _1092175] : [class_Lattices_Olattice(_1092171), hBOOL(hAPP(c_Finite__Set_Ofinite(_1092171), _1092173)), -(_1092173 = c_Orderings_Obot__class_Obot(tc_fun(_1092171, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1092171), _1092175)), -(_1092175 = c_Orderings_Obot__class_Obot(tc_fun(_1092171, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1092171, tc_HOL_Obool)), _1092173), _1092175) = c_Orderings_Obot__class_Obot(tc_fun(_1092171, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1092171, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1092171, tc_HOL_Obool)), _1092173), _1092175)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1092171), c_Big__Operators_Olattice__class_OSup__fin(_1092171, _1092173)), c_Big__Operators_Olattice__class_OSup__fin(_1092171, _1092175)))], (16999 ^ _780086) ^ [_1092648, _1092650, _1092652] : [class_Orderings_Olinorder(_1092648), hBOOL(hAPP(c_Finite__Set_Ofinite(_1092648), _1092650)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1092648), _1092652)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1092648, tc_HOL_Obool)), _1092650), _1092652) = c_Orderings_Obot__class_Obot(tc_fun(_1092648, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1092648), c_Big__Operators_Olinorder__class_OMin(_1092648, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1092648, tc_HOL_Obool)), _1092650), _1092652))), c_Big__Operators_Olinorder__class_OMin(_1092648, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1092648, tc_HOL_Obool)), _1092650), _1092652))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1092648), c_Big__Operators_Olinorder__class_OMin(_1092648, _1092650)), c_Big__Operators_Olinorder__class_OMin(_1092648, _1092652)))], (17017 ^ _780086) ^ [_1092996, _1092998, _1093000] : [class_Orderings_Olinorder(_1092996), hBOOL(hAPP(c_Finite__Set_Ofinite(_1092996), _1092998)), -(_1092998 = c_Orderings_Obot__class_Obot(tc_fun(_1092996, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1092996), _1093000)), -(_1093000 = c_Orderings_Obot__class_Obot(tc_fun(_1092996, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1092996, tc_HOL_Obool)), _1092998), _1093000) = c_Orderings_Obot__class_Obot(tc_fun(_1092996, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1092996, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1092996, tc_HOL_Obool)), _1092998), _1093000)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1092996), c_Big__Operators_Olinorder__class_OMin(_1092996, _1092998)), c_Big__Operators_Olinorder__class_OMin(_1092996, _1093000)))], (17043 ^ _780086) ^ [_1093473, _1093475, _1093477] : [class_Orderings_Olinorder(_1093473), hBOOL(hAPP(c_Finite__Set_Ofinite(_1093473), _1093475)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1093473), _1093477)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1093473, tc_HOL_Obool)), _1093475), _1093477) = c_Orderings_Obot__class_Obot(tc_fun(_1093473, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1093473), c_Big__Operators_Olinorder__class_OMax(_1093473, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1093473, tc_HOL_Obool)), _1093475), _1093477))), c_Big__Operators_Olinorder__class_OMax(_1093473, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1093473, tc_HOL_Obool)), _1093475), _1093477))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1093473), c_Big__Operators_Olinorder__class_OMax(_1093473, _1093475)), c_Big__Operators_Olinorder__class_OMax(_1093473, _1093477)))], (17061 ^ _780086) ^ [_1093821, _1093823, _1093825] : [class_Orderings_Olinorder(_1093821), hBOOL(hAPP(c_Finite__Set_Ofinite(_1093821), _1093823)), -(_1093823 = c_Orderings_Obot__class_Obot(tc_fun(_1093821, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1093821), _1093825)), -(_1093825 = c_Orderings_Obot__class_Obot(tc_fun(_1093821, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1093821, tc_HOL_Obool)), _1093823), _1093825) = c_Orderings_Obot__class_Obot(tc_fun(_1093821, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1093821, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1093821, tc_HOL_Obool)), _1093823), _1093825)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1093821), c_Big__Operators_Olinorder__class_OMax(_1093821, _1093823)), c_Big__Operators_Olinorder__class_OMax(_1093821, _1093825)))], (17087 ^ _780086) ^ [_1094298, _1094300, _1094302] : [class_Orderings_Olinorder(_1094298), hBOOL(hAPP(c_Finite__Set_Ofinite(_1094298), _1094300)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1094298), _1094302)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1094298, tc_HOL_Obool)), _1094300), _1094302) = c_Orderings_Obot__class_Obot(tc_fun(_1094298, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1094298), c_Big__Operators_Olattice_OInf__fin(_1094298, c_Orderings_Oord__class_Omin(_1094298), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1094298, tc_HOL_Obool)), _1094300), _1094302))), c_Big__Operators_Olattice_OInf__fin(_1094298, c_Orderings_Oord__class_Omin(_1094298), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1094298, tc_HOL_Obool)), _1094300), _1094302))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1094298), c_Big__Operators_Olattice_OInf__fin(_1094298, c_Orderings_Oord__class_Omin(_1094298), _1094300)), c_Big__Operators_Olattice_OInf__fin(_1094298, c_Orderings_Oord__class_Omin(_1094298), _1094302)))], (17105 ^ _780086) ^ [_1094670, _1094672, _1094674] : [class_Orderings_Olinorder(_1094670), hBOOL(hAPP(c_Finite__Set_Ofinite(_1094670), _1094672)), -(_1094672 = c_Orderings_Obot__class_Obot(tc_fun(_1094670, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1094670), _1094674)), -(_1094674 = c_Orderings_Obot__class_Obot(tc_fun(_1094670, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1094670, tc_HOL_Obool)), _1094672), _1094674) = c_Orderings_Obot__class_Obot(tc_fun(_1094670, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1094670, c_Orderings_Oord__class_Omin(_1094670), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1094670, tc_HOL_Obool)), _1094672), _1094674)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1094670), c_Big__Operators_Olattice_OInf__fin(_1094670, c_Orderings_Oord__class_Omin(_1094670), _1094672)), c_Big__Operators_Olattice_OInf__fin(_1094670, c_Orderings_Oord__class_Omin(_1094670), _1094674)))], (17131 ^ _780086) ^ [_1095165, _1095167, _1095169] : [class_Orderings_Olinorder(_1095165), hBOOL(hAPP(c_Finite__Set_Ofinite(_1095165), _1095167)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1095165), _1095169)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1095165, tc_HOL_Obool)), _1095167), _1095169) = c_Orderings_Obot__class_Obot(tc_fun(_1095165, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1095165), c_Big__Operators_Olattice_OSup__fin(_1095165, c_Orderings_Oord__class_Omax(_1095165), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1095165, tc_HOL_Obool)), _1095167), _1095169))), c_Big__Operators_Olattice_OSup__fin(_1095165, c_Orderings_Oord__class_Omax(_1095165), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1095165, tc_HOL_Obool)), _1095167), _1095169))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1095165), c_Big__Operators_Olattice_OSup__fin(_1095165, c_Orderings_Oord__class_Omax(_1095165), _1095167)), c_Big__Operators_Olattice_OSup__fin(_1095165, c_Orderings_Oord__class_Omax(_1095165), _1095169)))], (17149 ^ _780086) ^ [_1095537, _1095539, _1095541] : [class_Orderings_Olinorder(_1095537), hBOOL(hAPP(c_Finite__Set_Ofinite(_1095537), _1095539)), -(_1095539 = c_Orderings_Obot__class_Obot(tc_fun(_1095537, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1095537), _1095541)), -(_1095541 = c_Orderings_Obot__class_Obot(tc_fun(_1095537, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1095537, tc_HOL_Obool)), _1095539), _1095541) = c_Orderings_Obot__class_Obot(tc_fun(_1095537, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1095537, c_Orderings_Oord__class_Omax(_1095537), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1095537, tc_HOL_Obool)), _1095539), _1095541)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1095537), c_Big__Operators_Olattice_OSup__fin(_1095537, c_Orderings_Oord__class_Omax(_1095537), _1095539)), c_Big__Operators_Olattice_OSup__fin(_1095537, c_Orderings_Oord__class_Omax(_1095537), _1095541)))], (17175 ^ _780086) ^ [_1096032, _1096034, _1096036, _1096038] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1096032), _1096034)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1096032), _1096036)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1096032, tc_Nat_Onat), _1096038), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1096032, tc_HOL_Obool)), _1096034), _1096036)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1096032, tc_Nat_Onat), _1096038), _1096034)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1096032, tc_Nat_Onat), _1096038), _1096036))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1096032, tc_Nat_Onat), _1096038), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1096032, tc_HOL_Obool)), _1096034), _1096036))))], (17185 ^ _780086) ^ [_1096325, _1096327, _1096329, _1096331] : [-(hAPP(c_Set_Ovimage(_1096325, _1096327, _1096329), _1096331) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1096327, tc_fun(_1096325, tc_HOL_Obool)), _1096331), hAPP(hAPP(c_COMBB(tc_fun(_1096327, tc_HOL_Obool), tc_fun(_1096325, tc_HOL_Obool), _1096327), c_Set_Ovimage(_1096325, _1096327, _1096329)), hAPP(hAPP(c_COMBC(_1096327, tc_fun(_1096327, tc_HOL_Obool), tc_fun(_1096327, tc_HOL_Obool)), c_Set_Oinsert(_1096327)), c_Orderings_Obot__class_Obot(tc_fun(_1096327, tc_HOL_Obool))))))], (17187 ^ _780086) ^ [_1096416, _1096418, _1096420, _1096422] : [-(hAPP(c_Set_Oimage(_1096416, _1096418, _1096420), _1096422) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1096416, tc_fun(_1096418, tc_HOL_Obool)), _1096422), hAPP(hAPP(c_COMBC(_1096416, tc_fun(_1096418, tc_HOL_Obool), tc_fun(_1096418, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1096418, tc_fun(tc_fun(_1096418, tc_HOL_Obool), tc_fun(_1096418, tc_HOL_Obool)), _1096416), c_Set_Oinsert(_1096418)), _1096420)), c_Orderings_Obot__class_Obot(tc_fun(_1096418, tc_HOL_Obool)))))], (17189 ^ _780086) ^ [_1096506, _1096508, _1096510, _1096512, _1096514, _1096516] : [hBOOL(hAPP(hAPP(c_member(_1096506), _1096508), _1096510)), hBOOL(hAPP(hAPP(c_member(_1096512), _1096514), hAPP(_1096516, _1096508))), -(hBOOL(hAPP(hAPP(c_member(_1096512), _1096514), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1096506, tc_fun(_1096512, tc_HOL_Obool)), _1096510), _1096516))))], (17199 ^ _780086) ^ [_1096723, _1096725, _1096727, _1096729, _1096731] : [class_Complete__Lattice_Ocomplete__lattice(_1096723), hBOOL(hAPP(hAPP(c_member(_1096725), _1096727), _1096729)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096723), hAPP(_1096731, _1096727)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1096725, _1096723), _1096729), _1096731))))], (17209 ^ _780086) ^ [_1096914, _1096916, _1096918, _1096920, _1096922] : [class_Complete__Lattice_Ocomplete__lattice(_1096914), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1096916, tc_HOL_Obool)), _1096918), _1096920)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096914), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1096916, _1096914), _1096918), _1096922)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1096916, _1096914), _1096920), _1096922))))], (17219 ^ _780086) ^ [_1097123, _1097125, _1097127, _1097129] : [class_Complete__Lattice_Ocomplete__lattice(_1097123), -(_1097125 = c_Orderings_Obot__class_Obot(tc_fun(_1097127, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1097127, _1097123), _1097125), hAPP(c_COMBK(_1097123, _1097127), _1097129)) = _1097129)], (17229 ^ _780086) ^ [_1097257, _1097259, _1097261, _1097263, _1097265] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1097257, tc_fun(_1097259, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1097257), _1097261), _1097263)), _1097265) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1097259, tc_HOL_Obool)), hAPP(_1097265, _1097261)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1097257, tc_fun(_1097259, tc_HOL_Obool)), _1097263), _1097265)))], (17231 ^ _780086) ^ [_1097352, _1097354, _1097356, _1097358, _1097360] : [_1097352 = c_Orderings_Obot__class_Obot(tc_fun(_1097354, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1097354, tc_fun(_1097356, tc_HOL_Obool)), _1097352), hAPP(hAPP(c_COMBB(tc_fun(_1097356, tc_HOL_Obool), tc_fun(_1097356, tc_HOL_Obool), _1097354), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1097356, tc_HOL_Obool)), _1097358)), _1097360)) = c_Orderings_Obot__class_Obot(tc_fun(_1097356, tc_HOL_Obool)))], (17237 ^ _780086) ^ [_1097521, _1097523, _1097525, _1097527, _1097529] : [-(_1097521 = c_Orderings_Obot__class_Obot(tc_fun(_1097523, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1097523, tc_fun(_1097525, tc_HOL_Obool)), _1097521), hAPP(hAPP(c_COMBB(tc_fun(_1097525, tc_HOL_Obool), tc_fun(_1097525, tc_HOL_Obool), _1097523), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1097525, tc_HOL_Obool)), _1097527)), _1097529)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1097525, tc_HOL_Obool)), _1097527), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1097523, tc_fun(_1097525, tc_HOL_Obool)), _1097521), _1097529)))], (17243 ^ _780086) ^ [_1097629, _1097631, _1097633, _1097635, _1097637, _1097639] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1097629, tc_fun(_1097631, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1097633, tc_fun(_1097629, tc_HOL_Obool)), _1097635), _1097637)), _1097639) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1097633, tc_fun(_1097631, tc_HOL_Obool)), _1097635), hAPP(hAPP(c_COMBC(_1097633, tc_fun(_1097629, tc_fun(_1097631, tc_HOL_Obool)), tc_fun(_1097631, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1097629, tc_HOL_Obool), tc_fun(tc_fun(_1097629, tc_fun(_1097631, tc_HOL_Obool)), tc_fun(_1097631, tc_HOL_Obool)), _1097633), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1097629, tc_fun(_1097631, tc_HOL_Obool))), _1097637)), _1097639)))], (17245 ^ _780086) ^ [_1097748, _1097750, _1097752, _1097754, _1097756, _1097758] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1097748, tc_fun(_1097750, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1097752, tc_fun(_1097748, tc_HOL_Obool)), _1097754), _1097756)), _1097758) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1097752, tc_fun(_1097750, tc_HOL_Obool)), _1097754), hAPP(hAPP(c_COMBC(_1097752, tc_fun(_1097748, tc_fun(_1097750, tc_HOL_Obool)), tc_fun(_1097750, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1097748, tc_HOL_Obool), tc_fun(tc_fun(_1097748, tc_fun(_1097750, tc_HOL_Obool)), tc_fun(_1097750, tc_HOL_Obool)), _1097752), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1097748, tc_fun(_1097750, tc_HOL_Obool))), _1097756)), _1097758)))], (17264 ^ _780086) ^ [_1098327, _1098329, _1098331, _1098333, _1098335] : [17266 ^ _780086 : [(17267 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1098329), 17265 ^ [_1098327, _1098329, _1098331, _1098333, _1098335]), _1098331)))], (17270 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1098327), 17268 ^ [_1098327, _1098329, _1098331, _1098333, _1098335]), hAPP(_1098333, 17265 ^ [_1098327, _1098329, _1098331, _1098333, _1098335]))))], (17272 ^ _780086) ^ [] : [hBOOL(hAPP(_1098335, 17268 ^ [_1098327, _1098329, _1098331, _1098333, _1098335]))]], 17273 ^ _780086 : [(17274 ^ _780086) ^ [_1098637] : [hBOOL(hAPP(hAPP(c_member(_1098327), _1098637), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1098329, tc_fun(_1098327, tc_HOL_Obool)), _1098331), _1098333))), -(hBOOL(hAPP(_1098335, _1098637)))]]], (17247 ^ _780086) ^ [_1097891, _1097893, _1097895, _1097897, _1097899] : [17249 ^ _780086 : [(17250 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1097891), 17248 ^ [_1097891, _1097893, _1097895, _1097897, _1097899]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1097893, tc_fun(_1097891, tc_HOL_Obool)), _1097895), _1097897))))], (17252 ^ _780086) ^ [] : [hBOOL(hAPP(_1097899, 17248 ^ [_1097891, _1097893, _1097895, _1097897, _1097899]))]], 17253 ^ _780086 : [(17254 ^ _780086) ^ [_1098113] : [hBOOL(hAPP(hAPP(c_member(_1097893), _1098113), _1097895)), 17257 ^ _780086 : [(17258 ^ _780086) ^ [_1098210] : [hBOOL(hAPP(hAPP(c_member(_1097891), _1098210), hAPP(_1097897, _1098113))), -(hBOOL(hAPP(_1097899, _1098210)))]]]]], (17280 ^ _780086) ^ [_1098772, _1098774, _1098776, _1098778, _1098780, _1098782] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1098772, tc_fun(_1098774, tc_HOL_Obool)), _1098776), hAPP(hAPP(c_COMBC(_1098772, tc_fun(_1098778, tc_fun(_1098774, tc_HOL_Obool)), tc_fun(_1098774, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1098778, tc_HOL_Obool), tc_fun(tc_fun(_1098778, tc_fun(_1098774, tc_HOL_Obool)), tc_fun(_1098774, tc_HOL_Obool)), _1098772), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1098778, tc_fun(_1098774, tc_HOL_Obool))), _1098780)), _1098782)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1098778, tc_fun(_1098774, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1098772, tc_fun(_1098778, tc_HOL_Obool)), _1098776), _1098780)), _1098782))], (17282 ^ _780086) ^ [_1098915, _1098917, _1098919, _1098921, _1098923] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1098915, tc_fun(_1098917, tc_HOL_Obool)), _1098919), _1098921), _1098923)), 17286 ^ _780086 : [(17287 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1098915), 17285 ^ [_1098915, _1098917, _1098919, _1098921, _1098923]), _1098919)))], (17289 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(_1098921, 17285 ^ [_1098915, _1098917, _1098919, _1098921, _1098923]), _1098923)))]]], (17291 ^ _780086) ^ [_1099103, _1099105, _1099107, _1099109, _1099111] : [-(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1099103, tc_fun(_1099105, tc_HOL_Obool)), _1099107), _1099109), _1099111))), 17292 ^ _780086 : [(17293 ^ _780086) ^ [_1099175] : [hBOOL(hAPP(hAPP(c_member(_1099103), _1099175), _1099107)), hBOOL(hAPP(hAPP(_1099109, _1099175), _1099111))]]], (17301 ^ _780086) ^ [_1099357, _1099359, _1099361, _1099363, _1099365, _1099367, _1099369] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1099357, tc_fun(_1099359, tc_fun(_1099361, tc_HOL_Obool))), _1099363), _1099365), _1099367), _1099369)), 17305 ^ _780086 : [(17306 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1099357), 17304 ^ [_1099357, _1099359, _1099361, _1099363, _1099365, _1099367, _1099369]), _1099363)))], (17308 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1099365, 17304 ^ [_1099357, _1099359, _1099361, _1099363, _1099365, _1099367, _1099369]), _1099367), _1099369)))]]], (17310 ^ _780086) ^ [_1099575, _1099577, _1099579, _1099581, _1099583, _1099585, _1099587] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1099575, tc_fun(_1099577, tc_fun(_1099579, tc_HOL_Obool))), _1099581), _1099583), _1099585), _1099587))), 17311 ^ _780086 : [(17312 ^ _780086) ^ [_1099660] : [hBOOL(hAPP(hAPP(c_member(_1099575), _1099660), _1099581)), hBOOL(hAPP(hAPP(hAPP(_1099583, _1099660), _1099585), _1099587))]]], (17320 ^ _780086) ^ [] : [-(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat))], (17322 ^ _780086) ^ [_1099870, _1099872, _1099874, _1099876, _1099878] : [hBOOL(hAPP(hAPP(c_member(_1099870), _1099872), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1099874, tc_fun(_1099870, tc_HOL_Obool)), _1099876), _1099878))), 17326 ^ _780086 : [(17327 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1099874), 17325 ^ [_1099870, _1099872, _1099874, _1099876, _1099878]), _1099876)))], (17329 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1099870), _1099872), hAPP(_1099878, 17325 ^ [_1099870, _1099872, _1099874, _1099876, _1099878]))))]]], (17331 ^ _780086) ^ [_1100078, _1100080, _1100082, _1100084, _1100086] : [-(hBOOL(hAPP(hAPP(c_member(_1100078), _1100080), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1100082, tc_fun(_1100078, tc_HOL_Obool)), _1100084), _1100086)))), 17332 ^ _780086 : [(17333 ^ _780086) ^ [_1100160] : [hBOOL(hAPP(hAPP(c_member(_1100082), _1100160), _1100084)), hBOOL(hAPP(hAPP(c_member(_1100078), _1100080), hAPP(_1100086, _1100160)))]]], (17351 ^ _780086) ^ [_1100577, _1100579, _1100581, _1100583] : [17353 ^ _780086 : [(17354 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1100577), 17352 ^ [_1100577, _1100579, _1100581, _1100583]), _1100581)))], (17356 ^ _780086) ^ [] : [hAPP(_1100583, 17352 ^ [_1100577, _1100579, _1100581, _1100583]) = c_Orderings_Obot__class_Obot(tc_fun(_1100579, tc_HOL_Obool))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1100577, tc_fun(_1100579, tc_HOL_Obool)), _1100581), _1100583) = c_Orderings_Obot__class_Obot(tc_fun(_1100579, tc_HOL_Obool)))], (17341 ^ _780086) ^ [_1100348, _1100350, _1100352, _1100354] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1100348, tc_fun(_1100350, tc_HOL_Obool)), _1100352), _1100354) = c_Orderings_Obot__class_Obot(tc_fun(_1100350, tc_HOL_Obool)), 17344 ^ _780086 : [(17345 ^ _780086) ^ [_1100464] : [hBOOL(hAPP(hAPP(c_member(_1100348), _1100464), _1100352)), -(hAPP(_1100354, _1100464) = c_Orderings_Obot__class_Obot(tc_fun(_1100350, tc_HOL_Obool)))]]], (17360 ^ _780086) ^ [_1100822, _1100824, _1100826, _1100828] : [_1100822 = c_Orderings_Obot__class_Obot(tc_fun(_1100824, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1100824, tc_fun(_1100826, tc_HOL_Obool)), _1100822), hAPP(c_COMBK(tc_fun(_1100826, tc_HOL_Obool), _1100824), _1100828)) = c_Orderings_Obot__class_Obot(tc_fun(_1100826, tc_HOL_Obool)))], (17366 ^ _780086) ^ [_1100959, _1100961, _1100963, _1100965] : [-(_1100959 = c_Orderings_Obot__class_Obot(tc_fun(_1100961, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1100961, tc_fun(_1100963, tc_HOL_Obool)), _1100959), hAPP(c_COMBK(tc_fun(_1100963, tc_HOL_Obool), _1100961), _1100965)) = _1100965)], (17372 ^ _780086) ^ [_1101027, _1101029, _1101031] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1101027, tc_fun(_1101029, tc_HOL_Obool)), _1101031), hAPP(c_COMBK(tc_fun(_1101029, tc_HOL_Obool), _1101027), c_Orderings_Obot__class_Obot(tc_fun(_1101029, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1101029, tc_HOL_Obool)))], (17384 ^ _780086) ^ [_1101335, _1101337, _1101339, _1101341] : [17386 ^ _780086 : [(17387 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1101337), 17385 ^ [_1101335, _1101337, _1101339, _1101341]), _1101339)))], (17389 ^ _780086) ^ [] : [hAPP(_1101341, 17385 ^ [_1101335, _1101337, _1101339, _1101341]) = c_Orderings_Obot__class_Obot(tc_fun(_1101335, tc_HOL_Obool))]], -(c_Orderings_Obot__class_Obot(tc_fun(_1101335, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1101337, tc_fun(_1101335, tc_HOL_Obool)), _1101339), _1101341))], (17374 ^ _780086) ^ [_1101106, _1101108, _1101110, _1101112] : [c_Orderings_Obot__class_Obot(tc_fun(_1101106, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1101108, tc_fun(_1101106, tc_HOL_Obool)), _1101110), _1101112), 17377 ^ _780086 : [(17378 ^ _780086) ^ [_1101222] : [hBOOL(hAPP(hAPP(c_member(_1101108), _1101222), _1101110)), -(hAPP(_1101112, _1101222) = c_Orderings_Obot__class_Obot(tc_fun(_1101106, tc_HOL_Obool)))]]], (17403 ^ _780086) ^ [_1101847, _1101849, _1101851, _1101853, _1101855] : [17405 ^ _780086 : [(17406 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1101849), 17404 ^ [_1101847, _1101849, _1101851, _1101853, _1101855]), _1101851)))], (17408 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1101847, tc_HOL_Obool)), hAPP(_1101853, 17404 ^ [_1101847, _1101849, _1101851, _1101853, _1101855])), _1101855))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1101847, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1101849, tc_fun(_1101847, tc_HOL_Obool)), _1101851), _1101853)), _1101855)))], (17393 ^ _780086) ^ [_1101589, _1101591, _1101593, _1101595, _1101597] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1101589, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1101591, tc_fun(_1101589, tc_HOL_Obool)), _1101593), _1101595)), _1101597)), 17396 ^ _780086 : [(17397 ^ _780086) ^ [_1101722] : [hBOOL(hAPP(hAPP(c_member(_1101591), _1101722), _1101593)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1101589, tc_HOL_Obool)), hAPP(_1101595, _1101722)), _1101597)))]]], (17412 ^ _780086) ^ [_1102110, _1102112, _1102114, _1102116, _1102118, _1102120] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1102110, tc_fun(_1102112, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1102114, _1102110, _1102116), _1102118)), _1102120) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1102114, tc_fun(_1102112, tc_HOL_Obool)), _1102118), hAPP(hAPP(c_COMBB(_1102110, tc_fun(_1102112, tc_HOL_Obool), _1102114), _1102120), _1102116)))], (17414 ^ _780086) ^ [_1102187, _1102189, _1102191, _1102193, _1102195, _1102197] : [-(hAPP(c_Set_Oimage(_1102187, _1102189, _1102191), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1102193, tc_fun(_1102187, tc_HOL_Obool)), _1102195), _1102197)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1102193, tc_fun(_1102189, tc_HOL_Obool)), _1102195), hAPP(hAPP(c_COMBB(tc_fun(_1102187, tc_HOL_Obool), tc_fun(_1102189, tc_HOL_Obool), _1102193), c_Set_Oimage(_1102187, _1102189, _1102191)), _1102197)))], (17416 ^ _780086) ^ [_1102271, _1102273, _1102275, _1102277, _1102279, _1102281] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1102271, tc_fun(_1102273, tc_HOL_Obool)), _1102275), hAPP(hAPP(c_COMBB(_1102277, tc_fun(_1102273, tc_HOL_Obool), _1102271), _1102279), _1102281)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1102277, tc_fun(_1102273, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1102271, _1102277, _1102281), _1102275)), _1102279))], (17418 ^ _780086) ^ [_1102348, _1102350, _1102352, _1102354, _1102356] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1102348, tc_fun(_1102350, tc_HOL_Obool)), _1102352), hAPP(hAPP(c_COMBS(_1102348, tc_fun(_1102350, tc_HOL_Obool), tc_fun(_1102350, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1102350, tc_HOL_Obool), tc_fun(tc_fun(_1102350, tc_HOL_Obool), tc_fun(_1102350, tc_HOL_Obool)), _1102348), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1102350, tc_HOL_Obool))), _1102354)), _1102356)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1102350, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1102348, tc_fun(_1102350, tc_HOL_Obool)), _1102352), _1102354)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1102348, tc_fun(_1102350, tc_HOL_Obool)), _1102352), _1102356)))], (17420 ^ _780086) ^ [_1102469, _1102471, _1102473, _1102475, _1102477] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1102469, tc_fun(_1102471, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1102469, tc_HOL_Obool)), _1102473), _1102475)), _1102477) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1102471, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1102469, tc_fun(_1102471, tc_HOL_Obool)), _1102473), _1102477)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1102469, tc_fun(_1102471, tc_HOL_Obool)), _1102475), _1102477)))], (17422 ^ _780086) ^ [_1102558, _1102560, _1102562, _1102564, _1102566] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1102558, tc_fun(_1102560, tc_HOL_Obool)), _1102562), hAPP(hAPP(c_COMBB(tc_fun(_1102560, tc_HOL_Obool), tc_fun(_1102560, tc_HOL_Obool), _1102558), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1102560, tc_HOL_Obool)), _1102564)), _1102566)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1102560, tc_HOL_Obool)), _1102564), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1102558, tc_fun(_1102560, tc_HOL_Obool)), _1102562), _1102566)))], (17424 ^ _780086) ^ [_1102648, _1102650, _1102652, _1102654, _1102656] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1102648, tc_fun(_1102650, tc_HOL_Obool)), _1102652), hAPP(hAPP(c_COMBC(_1102648, tc_fun(_1102650, tc_HOL_Obool), tc_fun(_1102650, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1102650, tc_HOL_Obool), tc_fun(tc_fun(_1102650, tc_HOL_Obool), tc_fun(_1102650, tc_HOL_Obool)), _1102648), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1102650, tc_HOL_Obool))), _1102654)), _1102656)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1102650, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1102648, tc_fun(_1102650, tc_HOL_Obool)), _1102652), _1102654)), _1102656))], (17426 ^ _780086) ^ [_1102757, _1102759, _1102761, _1102763, _1102765] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1102757, tc_HOL_Obool)), _1102759), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1102761, tc_fun(_1102757, tc_HOL_Obool)), _1102763), _1102765)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1102761, tc_fun(_1102757, tc_HOL_Obool)), _1102763), hAPP(hAPP(c_COMBB(tc_fun(_1102757, tc_HOL_Obool), tc_fun(_1102757, tc_HOL_Obool), _1102761), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1102757, tc_HOL_Obool)), _1102759)), _1102765)))], (17428 ^ _780086) ^ [_1102847, _1102849, _1102851, _1102853, _1102855] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1102847, tc_HOL_Obool)), _1102849), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1102851, tc_fun(_1102847, tc_HOL_Obool)), _1102853), _1102855)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1102851, tc_fun(_1102847, tc_HOL_Obool)), _1102853), hAPP(hAPP(c_COMBB(tc_fun(_1102847, tc_HOL_Obool), tc_fun(_1102847, tc_HOL_Obool), _1102851), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1102847, tc_HOL_Obool)), _1102849)), _1102855)))], (17430 ^ _780086) ^ [_1102937, _1102939, _1102941, _1102943, _1102945] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1102937, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1102939, tc_fun(_1102937, tc_HOL_Obool)), _1102941), _1102943)), _1102945) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1102939, tc_fun(_1102937, tc_HOL_Obool)), _1102941), hAPP(hAPP(c_COMBC(_1102939, tc_fun(_1102937, tc_HOL_Obool), tc_fun(_1102937, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1102937, tc_HOL_Obool), tc_fun(tc_fun(_1102937, tc_HOL_Obool), tc_fun(_1102937, tc_HOL_Obool)), _1102939), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1102937, tc_HOL_Obool))), _1102943)), _1102945)))], (17432 ^ _780086) ^ [_1103046, _1103048, _1103050, _1103052, _1103054, _1103056, _1103058] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1103046, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1103048, tc_fun(_1103046, tc_HOL_Obool)), _1103050), _1103052)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1103054, tc_fun(_1103046, tc_HOL_Obool)), _1103056), _1103058)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1103048, tc_fun(_1103046, tc_HOL_Obool)), _1103050), hAPP(hAPP(c_COMBB(tc_fun(_1103054, tc_fun(_1103046, tc_HOL_Obool)), tc_fun(_1103046, tc_HOL_Obool), _1103048), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1103054, tc_fun(_1103046, tc_HOL_Obool)), _1103056)), hAPP(hAPP(c_COMBC(_1103048, tc_fun(_1103054, tc_fun(_1103046, tc_HOL_Obool)), tc_fun(_1103054, tc_fun(_1103046, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1103046, tc_HOL_Obool), tc_fun(_1103046, tc_HOL_Obool)), tc_fun(tc_fun(_1103054, tc_fun(_1103046, tc_HOL_Obool)), tc_fun(_1103054, tc_fun(_1103046, tc_HOL_Obool))), _1103048), c_COMBB(tc_fun(_1103046, tc_HOL_Obool), tc_fun(_1103046, tc_HOL_Obool), _1103054)), hAPP(hAPP(c_COMBB(tc_fun(_1103046, tc_HOL_Obool), tc_fun(tc_fun(_1103046, tc_HOL_Obool), tc_fun(_1103046, tc_HOL_Obool)), _1103048), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1103046, tc_HOL_Obool))), _1103052))), _1103058))))], (17434 ^ _780086) ^ [_1103249, _1103251, _1103253, _1103255, _1103257, _1103259] : [class_Complete__Lattice_Ocomplete__lattice(_1103249), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1103251, _1103249), _1103253), hAPP(hAPP(c_COMBB(tc_fun(_1103255, _1103249), _1103249, _1103251), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1103255, _1103249), _1103257)), _1103259)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1103255, _1103249), _1103257), hAPP(hAPP(c_COMBB(tc_fun(_1103251, _1103249), _1103249, _1103255), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1103251, _1103249), _1103253)), hAPP(c_COMBC(_1103251, _1103255, _1103249), _1103259))))], (17440 ^ _780086) ^ [_1103458, _1103460, _1103462, _1103464, _1103466, _1103468] : [class_Complete__Lattice_Ocomplete__lattice(_1103458), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1103460, tc_fun(_1103462, _1103458)), _1103464), _1103466), _1103468) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1103460, _1103458), _1103464), hAPP(hAPP(c_COMBC(_1103460, _1103462, _1103458), _1103466), _1103468)))], (17446 ^ _780086) ^ [_1103609, _1103611, _1103613, _1103615, _1103617] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1103609, tc_fun(_1103611, tc_HOL_Obool)), _1103613), hAPP(hAPP(c_COMBC(_1103609, tc_fun(_1103611, tc_HOL_Obool), tc_fun(_1103611, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1103611, tc_HOL_Obool), tc_fun(tc_fun(_1103611, tc_HOL_Obool), tc_fun(_1103611, tc_HOL_Obool)), _1103609), c_Groups_Ominus__class_Ominus(tc_fun(_1103611, tc_HOL_Obool))), _1103615)), _1103617)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1103611, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1103609, tc_fun(_1103611, tc_HOL_Obool)), _1103613), _1103615)), _1103617))], (17448 ^ _780086) ^ [_1103718, _1103720, _1103722, _1103724, _1103726] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1103718, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1103720, tc_fun(_1103718, tc_HOL_Obool)), _1103722), _1103724)), _1103726) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1103720, tc_fun(_1103718, tc_HOL_Obool)), _1103722), hAPP(hAPP(c_COMBC(_1103720, tc_fun(_1103718, tc_HOL_Obool), tc_fun(_1103718, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1103718, tc_HOL_Obool), tc_fun(tc_fun(_1103718, tc_HOL_Obool), tc_fun(_1103718, tc_HOL_Obool)), _1103720), c_Groups_Ominus__class_Ominus(tc_fun(_1103718, tc_HOL_Obool))), _1103724)), _1103726)))], (17450 ^ _780086) ^ [_1103827, _1103829, _1103831, _1103833, _1103835, _1103837] : [-(hAPP(c_Set_Ovimage(_1103827, _1103829, _1103831), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1103833, tc_fun(_1103829, tc_HOL_Obool)), _1103835), _1103837)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1103833, tc_fun(_1103827, tc_HOL_Obool)), _1103835), hAPP(hAPP(c_COMBB(tc_fun(_1103829, tc_HOL_Obool), tc_fun(_1103827, tc_HOL_Obool), _1103833), c_Set_Ovimage(_1103827, _1103829, _1103831)), _1103837)))], (17452 ^ _780086) ^ [_1103911, _1103913, _1103915, _1103917, _1103919, _1103921] : [hBOOL(hAPP(hAPP(c_member(_1103911), _1103913), _1103915)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1103911, tc_fun(_1103917, tc_HOL_Obool)), _1103915), hAPP(hAPP(c_COMBB(tc_fun(_1103917, tc_HOL_Obool), tc_fun(_1103917, tc_HOL_Obool), _1103911), hAPP(c_Set_Oinsert(_1103917), _1103919)), _1103921)) = hAPP(hAPP(c_Set_Oinsert(_1103917), _1103919), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1103911, tc_fun(_1103917, tc_HOL_Obool)), _1103915), _1103921)))], (17458 ^ _780086) ^ [_1104116, _1104118, _1104120, _1104122, _1104124] : [hBOOL(hAPP(hAPP(c_member(_1104116), _1104118), _1104120)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1104122, tc_HOL_Obool)), hAPP(_1104124, _1104118)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1104116, tc_fun(_1104122, tc_HOL_Obool)), _1104120), _1104124))))], (17464 ^ _780086) ^ [_1104263, _1104265, _1104267, _1104269, _1104271] : [hBOOL(hAPP(hAPP(c_member(_1104263), _1104265), _1104267)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1104269, tc_HOL_Obool)), hAPP(_1104271, _1104265)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1104263, tc_fun(_1104269, tc_HOL_Obool)), _1104267), _1104271)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1104263, tc_fun(_1104269, tc_HOL_Obool)), _1104267), _1104271))], (17470 ^ _780086) ^ [_1104454, _1104456, _1104458, _1104460, _1104462] : [_1104454 = c_Orderings_Obot__class_Obot(tc_fun(_1104456, tc_HOL_Obool)), -(hAPP(hAPP(c_Set_Oinsert(_1104458), _1104460), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1104456, tc_fun(_1104458, tc_HOL_Obool)), _1104454), _1104462)) = hAPP(hAPP(c_Set_Oinsert(_1104458), _1104460), c_Orderings_Obot__class_Obot(tc_fun(_1104458, tc_HOL_Obool))))], (17476 ^ _780086) ^ [_1104607, _1104609, _1104611, _1104613, _1104615] : [-(_1104607 = c_Orderings_Obot__class_Obot(tc_fun(_1104609, tc_HOL_Obool))), -(hAPP(hAPP(c_Set_Oinsert(_1104611), _1104613), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1104609, tc_fun(_1104611, tc_HOL_Obool)), _1104607), _1104615)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1104609, tc_fun(_1104611, tc_HOL_Obool)), _1104607), hAPP(hAPP(c_COMBB(tc_fun(_1104611, tc_HOL_Obool), tc_fun(_1104611, tc_HOL_Obool), _1104609), hAPP(c_Set_Oinsert(_1104611), _1104613)), _1104615)))], (17482 ^ _780086) ^ [_1104709, _1104711] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1104709, tc_fun(_1104709, tc_HOL_Obool)), _1104711), hAPP(hAPP(c_COMBC(_1104709, tc_fun(_1104709, tc_HOL_Obool), tc_fun(_1104709, tc_HOL_Obool)), c_Set_Oinsert(_1104709)), c_Orderings_Obot__class_Obot(tc_fun(_1104709, tc_HOL_Obool)))) = _1104711)], (17484 ^ _780086) ^ [_1104787, _1104789, _1104791, _1104793, _1104795] : [_1104787 = c_Orderings_Obot__class_Obot(tc_fun(_1104789, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1104789, tc_fun(_1104791, tc_HOL_Obool)), _1104787), hAPP(hAPP(c_COMBB(tc_fun(_1104791, tc_HOL_Obool), tc_fun(_1104791, tc_HOL_Obool), _1104789), hAPP(c_Set_Oinsert(_1104791), _1104793)), _1104795)) = c_Orderings_Obot__class_Obot(tc_fun(_1104791, tc_HOL_Obool)))], (17490 ^ _780086) ^ [_1104950, _1104952, _1104954, _1104956, _1104958] : [-(_1104950 = c_Orderings_Obot__class_Obot(tc_fun(_1104952, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1104952, tc_fun(_1104954, tc_HOL_Obool)), _1104950), hAPP(hAPP(c_COMBB(tc_fun(_1104954, tc_HOL_Obool), tc_fun(_1104954, tc_HOL_Obool), _1104952), hAPP(c_Set_Oinsert(_1104954), _1104956)), _1104958)) = hAPP(hAPP(c_Set_Oinsert(_1104954), _1104956), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1104952, tc_fun(_1104954, tc_HOL_Obool)), _1104950), _1104958)))], (17496 ^ _780086) ^ [_1105052, _1105054, _1105056, _1105058, _1105060] : [class_Complete__Lattice_Ocomplete__lattice(_1105052), 17499 ^ _780086 : [(17510 ^ _780086) ^ [] : [17512 ^ _780086 : [(17513 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1105054), 17511 ^ [_1105052, _1105054, _1105056, _1105058, _1105060]), _1105056)))], (17515 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1105052), hAPP(_1105058, 17511 ^ [_1105052, _1105054, _1105056, _1105058, _1105060])), _1105060))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1105052), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1105054, _1105052), _1105056), _1105058)), _1105060)))], (17500 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1105052), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1105054, _1105052), _1105056), _1105058)), _1105060)), 17503 ^ _780086 : [(17504 ^ _780086) ^ [_1105233] : [hBOOL(hAPP(hAPP(c_member(_1105054), _1105233), _1105056)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1105052), hAPP(_1105058, _1105233)), _1105060)))]]]]], (17519 ^ _780086) ^ [_1105546, _1105548, _1105550, _1105552, _1105554] : [class_Complete__Lattice_Ocomplete__lattice(_1105546), class_Orderings_Olinorder(_1105546), 17526 ^ _780086 : [(17527 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105546), _1105548), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1105550, _1105546), _1105552), _1105554))), 17531 ^ _780086 : [(17532 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1105550), 17530 ^ [_1105546, _1105548, _1105550, _1105552, _1105554]), _1105552)))], (17534 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105546), _1105548), hAPP(_1105554, 17530 ^ [_1105546, _1105548, _1105550, _1105552, _1105554]))))]]], (17536 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105546), _1105548), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1105550, _1105546), _1105552), _1105554)))), 17537 ^ _780086 : [(17538 ^ _780086) ^ [_1105894] : [hBOOL(hAPP(hAPP(c_member(_1105550), _1105894), _1105552)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105546), _1105548), hAPP(_1105554, _1105894)))]]]]], (17546 ^ _780086) ^ [_1106082, _1106084, _1106086, _1106088, _1106090] : [_1106082 = c_Orderings_Obot__class_Obot(tc_fun(_1106084, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1106086, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1106084, tc_fun(_1106086, tc_HOL_Obool)), _1106082), _1106088)), _1106090) = _1106090)], (17552 ^ _780086) ^ [_1106215, _1106217, _1106219, _1106221, _1106223] : [-(_1106215 = c_Orderings_Obot__class_Obot(tc_fun(_1106217, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1106219, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1106217, tc_fun(_1106219, tc_HOL_Obool)), _1106215), _1106221)), _1106223) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1106217, tc_fun(_1106219, tc_HOL_Obool)), _1106215), hAPP(hAPP(c_COMBC(_1106217, tc_fun(_1106219, tc_HOL_Obool), tc_fun(_1106219, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1106219, tc_HOL_Obool), tc_fun(tc_fun(_1106219, tc_HOL_Obool), tc_fun(_1106219, tc_HOL_Obool)), _1106217), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1106219, tc_HOL_Obool))), _1106221)), _1106223)))], (17558 ^ _780086) ^ [_1106360, _1106362, _1106364, _1106366, _1106368] : [_1106360 = c_Orderings_Obot__class_Obot(tc_fun(_1106362, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1106364, tc_HOL_Obool)), _1106366), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1106362, tc_fun(_1106364, tc_HOL_Obool)), _1106360), _1106368)) = _1106366)], (17564 ^ _780086) ^ [_1106493, _1106495, _1106497, _1106499, _1106501] : [-(_1106493 = c_Orderings_Obot__class_Obot(tc_fun(_1106495, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1106497, tc_HOL_Obool)), _1106499), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1106495, tc_fun(_1106497, tc_HOL_Obool)), _1106493), _1106501)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1106495, tc_fun(_1106497, tc_HOL_Obool)), _1106493), hAPP(hAPP(c_COMBB(tc_fun(_1106497, tc_HOL_Obool), tc_fun(_1106497, tc_HOL_Obool), _1106495), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1106497, tc_HOL_Obool)), _1106499)), _1106501)))], (17570 ^ _780086) ^ [_1106619, _1106621, _1106623, _1106625, _1106627] : [_1106619 = c_Orderings_Obot__class_Obot(tc_fun(_1106621, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1106621, tc_fun(_1106623, tc_HOL_Obool)), _1106619), hAPP(hAPP(c_COMBC(_1106621, tc_fun(_1106623, tc_HOL_Obool), tc_fun(_1106623, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1106623, tc_HOL_Obool), tc_fun(tc_fun(_1106623, tc_HOL_Obool), tc_fun(_1106623, tc_HOL_Obool)), _1106621), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1106623, tc_HOL_Obool))), _1106625)), _1106627)) = c_Orderings_Obot__class_Obot(tc_fun(_1106623, tc_HOL_Obool)))], (17576 ^ _780086) ^ [_1106826, _1106828, _1106830, _1106832, _1106834] : [-(_1106826 = c_Orderings_Obot__class_Obot(tc_fun(_1106828, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1106828, tc_fun(_1106830, tc_HOL_Obool)), _1106826), hAPP(hAPP(c_COMBC(_1106828, tc_fun(_1106830, tc_HOL_Obool), tc_fun(_1106830, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1106830, tc_HOL_Obool), tc_fun(tc_fun(_1106830, tc_HOL_Obool), tc_fun(_1106830, tc_HOL_Obool)), _1106828), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1106830, tc_HOL_Obool))), _1106832)), _1106834)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1106830, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1106828, tc_fun(_1106830, tc_HOL_Obool)), _1106826), _1106832)), _1106834))], (17582 ^ _780086) ^ [_1106953, _1106955, _1106957, _1106959, _1106961] : [class_Groups_Ocomm__monoid__mult(_1106953), hBOOL(hAPP(c_Finite__Set_Ofinite(_1106955), _1106957)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1106955), _1106959)), 17596 ^ _780086 : [(17597 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1106955), 17595 ^ [_1106953, _1106955, _1106957, _1106959, _1106961]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1106955, tc_HOL_Obool)), _1106957), _1106959))))], (17599 ^ _780086) ^ [] : [hAPP(_1106961, 17595 ^ [_1106953, _1106955, _1106957, _1106959, _1106961]) = c_Groups_Oone__class_Oone(_1106953)]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1106953, _1106955, c_Groups_Otimes__class_Otimes(_1106953)), _1106961), c_Groups_Oone__class_Oone(_1106953)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1106955, tc_HOL_Obool)), _1106957), _1106959)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1106953), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1106953, _1106955, c_Groups_Otimes__class_Otimes(_1106953)), _1106961), c_Groups_Oone__class_Oone(_1106953)), _1106957)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1106953, _1106955, c_Groups_Otimes__class_Otimes(_1106953)), _1106961), c_Groups_Oone__class_Oone(_1106953)), _1106959)))], (17603 ^ _780086) ^ [_1107496, _1107498, _1107500, _1107502, _1107504] : [class_Groups_Ocomm__monoid__mult(_1107496), hBOOL(hAPP(c_Finite__Set_Ofinite(_1107498), _1107500)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1107498), _1107502)), 17617 ^ _780086 : [(17618 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1107498), 17616 ^ [_1107496, _1107498, _1107500, _1107502, _1107504]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1107498, tc_HOL_Obool)), _1107500), _1107502))))], (17620 ^ _780086) ^ [] : [hAPP(_1107504, 17616 ^ [_1107496, _1107498, _1107500, _1107502, _1107504]) = c_Groups_Oone__class_Oone(_1107496)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1107498, _1107496), _1107504), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1107498, tc_HOL_Obool)), _1107500), _1107502)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107496), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1107498, _1107496), _1107504), _1107500)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1107498, _1107496), _1107504), _1107502)))], (17624 ^ _780086) ^ [_1107991, _1107993, _1107995, _1107997, _1107999] : [class_Groups_Ocomm__monoid__mult(_1107991), hBOOL(hAPP(c_Finite__Set_Ofinite(_1107993), _1107995)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1107993), _1107997)), 17638 ^ _780086 : [(17639 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1107993), 17637 ^ [_1107991, _1107993, _1107995, _1107997, _1107999]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1107993, tc_HOL_Obool)), _1107995), _1107997))))], (17641 ^ _780086) ^ [] : [hAPP(_1107999, 17637 ^ [_1107991, _1107993, _1107995, _1107997, _1107999]) = c_Groups_Oone__class_Oone(_1107991)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1107993, _1107991), _1107999), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1107993, tc_HOL_Obool)), _1107995), _1107997)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107991), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1107993, _1107991), _1107999), _1107995)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1107993, _1107991), _1107999), _1107997)))], (17645 ^ _780086) ^ [_1108486, _1108488, _1108490] : [class_Lattices_Olattice(_1108486), hBOOL(hAPP(c_Finite__Set_Ofinite(_1108486), _1108488)), hBOOL(hAPP(hAPP(c_member(_1108486), _1108490), _1108488)), 17656 ^ _780086 : [(17657 ^ _780086) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1108486, tc_HOL_Obool)), _1108488), hAPP(hAPP(c_Set_Oinsert(_1108486), _1108490), c_Orderings_Obot__class_Obot(tc_fun(_1108486, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1108486, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1108486, _1108488) = _1108490)], (17663 ^ _780086) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1108486, tc_HOL_Obool)), _1108488), hAPP(hAPP(c_Set_Oinsert(_1108486), _1108490), c_Orderings_Obot__class_Obot(tc_fun(_1108486, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1108486, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1108486, _1108488) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1108486), _1108490), c_Big__Operators_Olattice__class_OInf__fin(_1108486, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1108486, tc_HOL_Obool)), _1108488), hAPP(hAPP(c_Set_Oinsert(_1108486), _1108490), c_Orderings_Obot__class_Obot(tc_fun(_1108486, tc_HOL_Obool)))))))]]], (17669 ^ _780086) ^ [_1108992, _1108994, _1108996, _1108998] : [class_Complete__Lattice_Ocomplete__lattice(_1108992), hBOOL(hAPP(c_Finite__Set_Ofinite(_1108994), _1108996)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1108994, _1108992), _1108996), _1108998) = hAPP(hAPP(c_Finite__Set_Ofold(_1108994, _1108992, hAPP(hAPP(c_COMBB(_1108992, tc_fun(_1108992, _1108992), _1108994), c_Lattices_Osemilattice__inf__class_Oinf(_1108992)), _1108998)), c_Orderings_Otop__class_Otop(_1108992)), _1108996))], (17679 ^ _780086) ^ [_1109207, _1109209, _1109211] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1109207), _1109209)), hBOOL(hAPP(hAPP(c_member(_1109207), _1109211), _1109209)), -(hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1109207), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1109207, tc_HOL_Obool)), _1109209), hAPP(hAPP(c_Set_Oinsert(_1109207), _1109211), c_Orderings_Obot__class_Obot(tc_fun(_1109207, tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(_1109207), _1109209))], (17689 ^ _780086) ^ [_1109436, _1109438] : [class_Complete__Lattice_Ocomplete__lattice(_1109436), hBOOL(hAPP(c_Finite__Set_Ofinite(_1109436), _1109438)), -(c_Complete__Lattice_OInf__class_OInf(_1109436, _1109438) = hAPP(hAPP(c_Finite__Set_Ofold(_1109436, _1109436, c_Lattices_Osemilattice__inf__class_Oinf(_1109436)), c_Orderings_Otop__class_Otop(_1109436)), _1109438))], (17699 ^ _780086) ^ [_1109605, _1109607, _1109609, _1109611] : [hBOOL(hAPP(hAPP(c_member(_1109605), _1109607), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1109605, tc_HOL_Obool), _1109609))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1109605, tc_HOL_Obool)), _1109611), _1109609)), -(hBOOL(hAPP(hAPP(c_member(_1109605), _1109607), _1109611)))], (17709 ^ _780086) ^ [_1109802, _1109804, _1109806, _1109808] : [hBOOL(hAPP(hAPP(c_member(_1109802), _1109804), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1109802, tc_HOL_Obool), _1109806))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1109802, tc_HOL_Obool)), _1109808), _1109806)), -(hBOOL(hAPP(hAPP(c_member(_1109802), _1109804), _1109808)))], (17719 ^ _780086) ^ [_1109999, _1110001] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1109999), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1109999, tc_HOL_Obool), _1110001)))), 17720 ^ _780086 : [(17721 ^ _780086) ^ [_1110063] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1109999, tc_HOL_Obool)), _1110063), _1110001)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1109999), _1110063))]]], (17729 ^ _780086) ^ [_1110207, _1110209, _1110211, _1110213, _1110215, _1110217] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1110207, tc_fun(_1110209, tc_HOL_Obool)), _1110211), _1110213), _1110215)), hBOOL(hAPP(hAPP(c_member(_1110207), _1110217), _1110211)), -(hBOOL(hAPP(hAPP(_1110213, _1110217), _1110215)))], (17739 ^ _780086) ^ [_1110404, _1110406, _1110408, _1110410, _1110412, _1110414] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1110404, tc_fun(_1110406, tc_HOL_Obool)), _1110408), _1110410), _1110412)), -(hBOOL(hAPP(hAPP(_1110410, _1110414), _1110412))), hBOOL(hAPP(hAPP(c_member(_1110404), _1110414), _1110408))], (17749 ^ _780086) ^ [_1110605, _1110607, _1110609, _1110611, _1110613, _1110615] : [hBOOL(hAPP(hAPP(c_member(_1110605), _1110607), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1110609, tc_fun(_1110605, tc_HOL_Obool)), _1110611), _1110613))), hBOOL(hAPP(hAPP(c_member(_1110609), _1110615), _1110611)), -(hBOOL(hAPP(hAPP(c_member(_1110605), _1110607), hAPP(_1110613, _1110615))))], (17759 ^ _780086) ^ [_1110822, _1110824, _1110826, _1110828, _1110830, _1110832] : [hBOOL(hAPP(hAPP(c_member(_1110822), _1110824), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1110826, tc_fun(_1110822, tc_HOL_Obool)), _1110828), _1110830))), -(hBOOL(hAPP(hAPP(c_member(_1110822), _1110824), hAPP(_1110830, _1110832)))), hBOOL(hAPP(hAPP(c_member(_1110826), _1110832), _1110828))], (17769 ^ _780086) ^ [_1111043, _1111045, _1111047, _1111049, _1111051, _1111053, _1111055, _1111057] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1111043, tc_fun(_1111045, tc_fun(_1111047, tc_HOL_Obool))), _1111049), _1111051), _1111053), _1111055)), hBOOL(hAPP(hAPP(c_member(_1111043), _1111057), _1111049)), -(hBOOL(hAPP(hAPP(hAPP(_1111051, _1111057), _1111053), _1111055)))], (17779 ^ _780086) ^ [_1111266, _1111268, _1111270, _1111272, _1111274, _1111276, _1111278, _1111280] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1111266, tc_fun(_1111268, tc_fun(_1111270, tc_HOL_Obool))), _1111272), _1111274), _1111276), _1111278)), -(hBOOL(hAPP(hAPP(hAPP(_1111274, _1111280), _1111276), _1111278))), hBOOL(hAPP(hAPP(c_member(_1111266), _1111280), _1111272))], (17789 ^ _780086) ^ [_1111493, _1111495, _1111497, _1111499] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1111497), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1111493, tc_fun(_1111497, tc_HOL_Obool)), _1111495), _1111499)))), 17790 ^ _780086 : [(17791 ^ _780086) ^ [_1111567] : [hBOOL(hAPP(hAPP(c_member(_1111493), _1111567), _1111495)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1111497), hAPP(_1111499, _1111567)))]]], (17799 ^ _780086) ^ [_1111721, _1111723] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111721), _1111723)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1111721)), hAPP(c_Nat_OSuc, _1111723))))], (17805 ^ _780086) ^ [_1111830] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111830), hAPP(c_Nat_OSuc, _1111830))))], (17807 ^ _780086) ^ [_1111861, _1111863, _1111865, _1111867, _1111869] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1111861, tc_fun(_1111863, tc_HOL_Obool)), _1111865), hAPP(hAPP(c_COMBS(_1111861, tc_fun(_1111863, tc_HOL_Obool), tc_fun(_1111863, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1111863, tc_HOL_Obool), tc_fun(tc_fun(_1111863, tc_HOL_Obool), tc_fun(_1111863, tc_HOL_Obool)), _1111861), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1111863, tc_HOL_Obool))), _1111867)), _1111869)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1111863, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1111863, tc_HOL_Obool), hAPP(c_Set_Oimage(_1111861, tc_fun(_1111863, tc_HOL_Obool), _1111867), _1111865))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1111863, tc_HOL_Obool), hAPP(c_Set_Oimage(_1111861, tc_fun(_1111863, tc_HOL_Obool), _1111869), _1111865))))], (17809 ^ _780086) ^ [_1111990, _1111992, _1111994, _1111996, _1111998, _1112000] : [class_Complete__Lattice_Ocomplete__lattice(_1111990), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1111992, tc_fun(_1111994, _1111990)), _1111996), _1111998), _1112000) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1111992, _1111990), _1111996), hAPP(hAPP(c_COMBC(_1111992, _1111994, _1111990), _1111998), _1112000)))], (17815 ^ _780086) ^ [_1112141, _1112143, _1112145] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1112141, tc_HOL_Obool)), _1112143), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1112141, tc_HOL_Obool), _1112145)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1112141, tc_HOL_Obool), tc_fun(_1112141, tc_HOL_Obool)), _1112145), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1112141, tc_HOL_Obool)), _1112143)))], (17817 ^ _780086) ^ [_1112217] : [_1112217 = hAPP(c_Nat_OSuc, _1112217)], (17819 ^ _780086) ^ [_1112252] : [hAPP(c_Nat_OSuc, _1112252) = _1112252], (17821 ^ _780086) ^ [_1112293, _1112295] : [hAPP(c_Nat_OSuc, _1112293) = hAPP(c_Nat_OSuc, _1112295), -(_1112293 = _1112295)], (17827 ^ _780086) ^ [_1112378, _1112380] : [_1112378 = _1112380, -(hAPP(c_Nat_OSuc, _1112378) = hAPP(c_Nat_OSuc, _1112380))], (17833 ^ _780086) ^ [_1112469, _1112471] : [hAPP(c_Nat_OSuc, _1112469) = hAPP(c_Nat_OSuc, _1112471), -(_1112469 = _1112471)], (17839 ^ _780086) ^ [_1112558, _1112560, _1112562, _1112564, _1112566, _1112568] : [class_Complete__Lattice_Ocomplete__lattice(_1112558), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1112560, _1112558), _1112562), hAPP(hAPP(c_COMBB(tc_fun(_1112564, _1112558), _1112558, _1112560), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1112564, _1112558), _1112566)), _1112568)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1112564, _1112558), _1112566), hAPP(hAPP(c_COMBB(tc_fun(_1112560, _1112558), _1112558, _1112564), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1112560, _1112558), _1112562)), hAPP(c_COMBC(_1112560, _1112564, _1112558), _1112568))))], (17845 ^ _780086) ^ [_1112767, _1112769] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1112767)), hAPP(c_Nat_OSuc, _1112769))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1112767), _1112769)))], (17851 ^ _780086) ^ [_1112876, _1112878] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1112876)), _1112878)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1112876), _1112878)))], (17857 ^ _780086) ^ [_1112979, _1112981] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1112979), hAPP(c_Nat_OSuc, _1112981))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1112979), _1112981))), -(_1112979 = _1112981)], (17867 ^ _780086) ^ [_1113097, _1113099, _1113101] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113097), _1113099)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113099), _1113101)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1113097)), _1113101)))], (17877 ^ _780086) ^ [_1113266, _1113268] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113266), _1113268)), -(hAPP(c_Nat_OSuc, _1113266) = _1113268), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1113266)), _1113268)))], (17887 ^ _780086) ^ [_1113390, _1113392] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113390), _1113392)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113390), hAPP(c_Nat_OSuc, _1113392))))], (17893 ^ _780086) ^ [_1113492, _1113494] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113492), _1113494))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113492), hAPP(c_Nat_OSuc, _1113494))), -(_1113494 = _1113492)], (17903 ^ _780086) ^ [_1113639, _1113641] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113639), _1113641))), 17906 ^ _780086 : [(17907 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113639), hAPP(c_Nat_OSuc, _1113641))), -(_1113639 = _1113641)], (17913 ^ _780086) ^ [] : [_1113639 = _1113641, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113639), hAPP(c_Nat_OSuc, _1113641))))]]], (17919 ^ _780086) ^ [_1113888, _1113890] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1113888)), hAPP(c_Nat_OSuc, _1113890))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113888), _1113890)))], (17925 ^ _780086) ^ [_1113993, _1113995] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113993), _1113995)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1113993)), hAPP(c_Nat_OSuc, _1113995))))], (17941 ^ _780086) ^ [_1114231, _1114233] : [17942 ^ _780086 : [(17943 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114231), _1114233))], (17945 ^ _780086) ^ [] : [_1114231 = _1114233]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114231), hAPP(c_Nat_OSuc, _1114233))))], (17931 ^ _780086) ^ [_1114119, _1114121] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114119), hAPP(c_Nat_OSuc, _1114121))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114119), _1114121))), -(_1114119 = _1114121)], (17949 ^ _780086) ^ [_1114383, _1114385] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114383), _1114385))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114385), hAPP(c_Nat_OSuc, _1114383))))], (17955 ^ _780086) ^ [_1114428, _1114430] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114430), hAPP(c_Nat_OSuc, _1114428))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114428), _1114430))], (17961 ^ _780086) ^ [_1114534, _1114536] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1114534), hAPP(c_Nat_OSuc, _1114536)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1114534), _1114536)))], (17963 ^ _780086) ^ [_1114577, _1114579] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1114577)), _1114579) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1114577), _1114579)))], (17965 ^ _780086) ^ [_1114620, _1114622] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1114620)), _1114622) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1114620), hAPP(c_Nat_OSuc, _1114622)))], (17967 ^ _780086) ^ [_1114663, _1114665] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1114663)), _1114665)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1114663), _1114665)))], (17973 ^ _780086) ^ [_1114766, _1114768] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1114766), hAPP(c_Nat_OSuc, _1114768))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1114766), _1114768))), -(_1114766 = hAPP(c_Nat_OSuc, _1114768))], (17983 ^ _780086) ^ [_1114890, _1114892] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1114890), _1114892)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1114890), hAPP(c_Nat_OSuc, _1114892))))], (17989 ^ _780086) ^ [_1115008, _1115010] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1115008)), hAPP(c_Nat_OSuc, _1115010))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115008), _1115010)))], (17995 ^ _780086) ^ [_1115113, _1115115] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115113), _1115115)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1115113)), hAPP(c_Nat_OSuc, _1115115))))], (18011 ^ _780086) ^ [_1115357, _1115359] : [18012 ^ _780086 : [(18013 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115357), _1115359))], (18015 ^ _780086) ^ [] : [_1115357 = hAPP(c_Nat_OSuc, _1115359)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115357), hAPP(c_Nat_OSuc, _1115359))))], (18001 ^ _780086) ^ [_1115239, _1115241] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115239), hAPP(c_Nat_OSuc, _1115241))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115239), _1115241))), -(_1115239 = hAPP(c_Nat_OSuc, _1115241))], (18019 ^ _780086) ^ [_1115515, _1115517] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115515), _1115517))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1115517)), _1115515)))], (18025 ^ _780086) ^ [_1115560, _1115562] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1115562)), _1115560)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115560), _1115562))], (18031 ^ _780086) ^ [_1115675] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1115675)), _1115675))], (18033 ^ _780086) ^ [_1115706, _1115708, _1115710] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1115706)), _1115708)), hAPP(c_Nat_OSuc, _1115710)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1115706), _1115708)), _1115710))], (18035 ^ _780086) ^ [_1115763, _1115765] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1115763)), hAPP(c_Nat_OSuc, _1115765)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1115763), _1115765))], (18037 ^ _780086) ^ [_1115824, _1115826, _1115828] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1115824)), _1115826) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1115824)), _1115828), -(_1115826 = _1115828)], (18043 ^ _780086) ^ [_1115935, _1115937, _1115939] : [_1115937 = _1115939, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1115935)), _1115937) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1115935)), _1115939))], (18049 ^ _780086) ^ [_1116052] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1116052, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1116052, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1116052, tc_HOL_Obool)))], (18051 ^ _780086) ^ [_1116094, _1116096] : [class_Complete__Lattice_Ocomplete__lattice(_1116094), hBOOL(hAPP(c_Finite__Set_Ofinite(_1116094), _1116096)), -(_1116096 = c_Orderings_Obot__class_Obot(tc_fun(_1116094, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1116094, _1116096) = c_Complete__Lattice_OInf__class_OInf(_1116094, _1116096))], (18065 ^ _780086) ^ [_1116266, _1116268, _1116270] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1116266, tc_HOL_Obool), tc_HOL_Obool)), _1116268), _1116270)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1116266, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1116266, tc_HOL_Obool), _1116270)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1116266, tc_HOL_Obool), _1116268))))], (18071 ^ _780086) ^ [_1116415, _1116417, _1116419] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1116415, tc_HOL_Obool)), _1116417), _1116419)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1116415, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1116415, tc_HOL_Obool), _1116419)), _1116417)))], (18077 ^ _780086) ^ [_1116546] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1116546, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1116546, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1116546, tc_HOL_Obool)))], (18079 ^ _780086) ^ [_1116588, _1116590, _1116592] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1116588, tc_HOL_Obool)), _1116590), _1116592) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1116588, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1116588, tc_HOL_Obool)), _1116590), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1116588, tc_HOL_Obool)), _1116592), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1116588, tc_HOL_Obool), tc_HOL_Obool))))))], (18081 ^ _780086) ^ [_1116662, _1116664, _1116666] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1116662, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1116662, tc_HOL_Obool)), _1116664), _1116666)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1116662, tc_HOL_Obool)), _1116664), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1116662, tc_HOL_Obool), _1116666)))], (18083 ^ _780086) ^ [_1116723, _1116725, _1116727] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1116723, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1116723, tc_HOL_Obool), tc_HOL_Obool)), _1116725), _1116727)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1116723, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1116723, tc_HOL_Obool), _1116725)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1116723, tc_HOL_Obool), _1116727)))], (18095 ^ _780086) ^ [_1117060, _1117062, _1117064, _1117066, _1117068] : [18097 ^ _780086 : [(18098 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1117064), 18096 ^ [_1117060, _1117062, _1117064, _1117066, _1117068]), _1117066)))], (18100 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1117060), _1117062), hAPP(_1117068, 18096 ^ [_1117060, _1117062, _1117064, _1117066, _1117068])))]], -(hBOOL(hAPP(hAPP(c_member(_1117060), _1117062), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1117064, tc_fun(_1117060, tc_HOL_Obool)), _1117066), _1117068))))], (18085 ^ _780086) ^ [_1116817, _1116819, _1116821, _1116823, _1116825] : [hBOOL(hAPP(hAPP(c_member(_1116817), _1116819), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1116821, tc_fun(_1116817, tc_HOL_Obool)), _1116823), _1116825))), 18088 ^ _780086 : [(18089 ^ _780086) ^ [_1116941] : [hBOOL(hAPP(hAPP(c_member(_1116821), _1116941), _1116823)), -(hBOOL(hAPP(hAPP(c_member(_1116817), _1116819), hAPP(_1116825, _1116941))))]]], (18104 ^ _780086) ^ [_1117308, _1117310, _1117312, _1117314, _1117316] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1117308, tc_fun(_1117310, tc_HOL_Obool)), _1117312), hAPP(hAPP(c_COMBB(tc_fun(_1117310, tc_HOL_Obool), tc_fun(_1117310, tc_HOL_Obool), _1117308), hAPP(c_Set_Oinsert(_1117310), _1117314)), _1117316)) = hAPP(hAPP(c_Set_Oinsert(_1117310), _1117314), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1117308, tc_fun(_1117310, tc_HOL_Obool)), _1117312), _1117316)))], (18106 ^ _780086) ^ [_1117392, _1117394, _1117396, _1117398, _1117400] : [-(hAPP(hAPP(c_Set_Oinsert(_1117392), _1117394), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1117396, tc_fun(_1117392, tc_HOL_Obool)), _1117398), _1117400)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1117396, tc_fun(_1117392, tc_HOL_Obool)), _1117398), hAPP(hAPP(c_COMBB(tc_fun(_1117392, tc_HOL_Obool), tc_fun(_1117392, tc_HOL_Obool), _1117396), hAPP(c_Set_Oinsert(_1117392), _1117394)), _1117400)))], (18118 ^ _780086) ^ [_1117758, _1117760, _1117762, _1117764, _1117766] : [18120 ^ _780086 : [(18121 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1117762), 18119 ^ [_1117758, _1117760, _1117762, _1117764, _1117766]), _1117764)))], (18123 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1117758, tc_HOL_Obool)), _1117760), hAPP(_1117766, 18119 ^ [_1117758, _1117760, _1117762, _1117764, _1117766])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1117758, tc_HOL_Obool)), _1117760), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1117762, tc_fun(_1117758, tc_HOL_Obool)), _1117764), _1117766))))], (18108 ^ _780086) ^ [_1117500, _1117502, _1117504, _1117506, _1117508] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1117500, tc_HOL_Obool)), _1117502), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1117504, tc_fun(_1117500, tc_HOL_Obool)), _1117506), _1117508))), 18111 ^ _780086 : [(18112 ^ _780086) ^ [_1117633] : [hBOOL(hAPP(hAPP(c_member(_1117504), _1117633), _1117506)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1117500, tc_HOL_Obool)), _1117502), hAPP(_1117508, _1117633))))]]], (18137 ^ _780086) ^ [_1118271, _1118273, _1118275, _1118277] : [18139 ^ _780086 : [(18140 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1118271), 18138 ^ [_1118271, _1118273, _1118275, _1118277]), _1118275)))], (18142 ^ _780086) ^ [] : [hAPP(_1118277, 18138 ^ [_1118271, _1118273, _1118275, _1118277]) = c_Orderings_Otop__class_Otop(tc_fun(_1118273, tc_HOL_Obool))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1118271, tc_fun(_1118273, tc_HOL_Obool)), _1118275), _1118277) = c_Orderings_Otop__class_Otop(tc_fun(_1118273, tc_HOL_Obool)))], (18127 ^ _780086) ^ [_1118042, _1118044, _1118046, _1118048] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1118042, tc_fun(_1118044, tc_HOL_Obool)), _1118046), _1118048) = c_Orderings_Otop__class_Otop(tc_fun(_1118044, tc_HOL_Obool)), 18130 ^ _780086 : [(18131 ^ _780086) ^ [_1118158] : [hBOOL(hAPP(hAPP(c_member(_1118042), _1118158), _1118046)), -(hAPP(_1118048, _1118158) = c_Orderings_Otop__class_Otop(tc_fun(_1118044, tc_HOL_Obool)))]]], (18156 ^ _780086) ^ [_1118751, _1118753, _1118755, _1118757] : [18158 ^ _780086 : [(18159 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1118753), 18157 ^ [_1118751, _1118753, _1118755, _1118757]), _1118755)))], (18161 ^ _780086) ^ [] : [hAPP(_1118757, 18157 ^ [_1118751, _1118753, _1118755, _1118757]) = c_Orderings_Otop__class_Otop(tc_fun(_1118751, tc_HOL_Obool))]], -(c_Orderings_Otop__class_Otop(tc_fun(_1118751, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1118753, tc_fun(_1118751, tc_HOL_Obool)), _1118755), _1118757))], (18146 ^ _780086) ^ [_1118522, _1118524, _1118526, _1118528] : [c_Orderings_Otop__class_Otop(tc_fun(_1118522, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1118524, tc_fun(_1118522, tc_HOL_Obool)), _1118526), _1118528), 18149 ^ _780086 : [(18150 ^ _780086) ^ [_1118638] : [hBOOL(hAPP(hAPP(c_member(_1118524), _1118638), _1118526)), -(hAPP(_1118528, _1118638) = c_Orderings_Otop__class_Otop(tc_fun(_1118522, tc_HOL_Obool)))]]], (18165 ^ _780086) ^ [_1118981, _1118983, _1118985, _1118987, _1118989, _1118991] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1118981, tc_fun(_1118983, tc_HOL_Obool)), _1118985), hAPP(hAPP(c_COMBB(_1118987, tc_fun(_1118983, tc_HOL_Obool), _1118981), _1118989), _1118991)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1118987, tc_fun(_1118983, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1118981, _1118987, _1118991), _1118985)), _1118989))], (18167 ^ _780086) ^ [_1119058, _1119060, _1119062, _1119064, _1119066, _1119068] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1119058, tc_fun(_1119060, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1119062, _1119058, _1119064), _1119066)), _1119068) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1119062, tc_fun(_1119060, tc_HOL_Obool)), _1119066), hAPP(hAPP(c_COMBB(_1119058, tc_fun(_1119060, tc_HOL_Obool), _1119062), _1119068), _1119064)))], (18169 ^ _780086) ^ [_1119135, _1119137, _1119139, _1119141, _1119143, _1119145, _1119147] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1119135, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1119137, tc_fun(_1119135, tc_HOL_Obool)), _1119139), _1119141)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1119143, tc_fun(_1119135, tc_HOL_Obool)), _1119145), _1119147)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1119137, tc_fun(_1119135, tc_HOL_Obool)), _1119139), hAPP(hAPP(c_COMBB(tc_fun(_1119143, tc_fun(_1119135, tc_HOL_Obool)), tc_fun(_1119135, tc_HOL_Obool), _1119137), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1119143, tc_fun(_1119135, tc_HOL_Obool)), _1119145)), hAPP(hAPP(c_COMBC(_1119137, tc_fun(_1119143, tc_fun(_1119135, tc_HOL_Obool)), tc_fun(_1119143, tc_fun(_1119135, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1119135, tc_HOL_Obool), tc_fun(_1119135, tc_HOL_Obool)), tc_fun(tc_fun(_1119143, tc_fun(_1119135, tc_HOL_Obool)), tc_fun(_1119143, tc_fun(_1119135, tc_HOL_Obool))), _1119137), c_COMBB(tc_fun(_1119135, tc_HOL_Obool), tc_fun(_1119135, tc_HOL_Obool), _1119143)), hAPP(hAPP(c_COMBB(tc_fun(_1119135, tc_HOL_Obool), tc_fun(tc_fun(_1119135, tc_HOL_Obool), tc_fun(_1119135, tc_HOL_Obool)), _1119137), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1119135, tc_HOL_Obool))), _1119141))), _1119147))))], (18171 ^ _780086) ^ [_1119338, _1119340, _1119342, _1119344, _1119346] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1119338, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1119340, tc_fun(_1119338, tc_HOL_Obool)), _1119342), _1119344)), _1119346) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1119340, tc_fun(_1119338, tc_HOL_Obool)), _1119342), hAPP(hAPP(c_COMBC(_1119340, tc_fun(_1119338, tc_HOL_Obool), tc_fun(_1119338, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1119338, tc_HOL_Obool), tc_fun(tc_fun(_1119338, tc_HOL_Obool), tc_fun(_1119338, tc_HOL_Obool)), _1119340), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1119338, tc_HOL_Obool))), _1119344)), _1119346)))], (18173 ^ _780086) ^ [_1119447, _1119449, _1119451, _1119453, _1119455] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1119447, tc_HOL_Obool)), _1119449), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1119451, tc_fun(_1119447, tc_HOL_Obool)), _1119453), _1119455)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1119451, tc_fun(_1119447, tc_HOL_Obool)), _1119453), hAPP(hAPP(c_COMBB(tc_fun(_1119447, tc_HOL_Obool), tc_fun(_1119447, tc_HOL_Obool), _1119451), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1119447, tc_HOL_Obool)), _1119449)), _1119455)))], (18175 ^ _780086) ^ [_1119537, _1119539, _1119541, _1119543, _1119545] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1119537, tc_HOL_Obool)), _1119539), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1119541, tc_fun(_1119537, tc_HOL_Obool)), _1119543), _1119545)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1119541, tc_fun(_1119537, tc_HOL_Obool)), _1119543), hAPP(hAPP(c_COMBB(tc_fun(_1119537, tc_HOL_Obool), tc_fun(_1119537, tc_HOL_Obool), _1119541), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1119537, tc_HOL_Obool)), _1119539)), _1119545)))], (18177 ^ _780086) ^ [_1119627, _1119629, _1119631, _1119633, _1119635] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1119627, tc_fun(_1119629, tc_HOL_Obool)), _1119631), hAPP(hAPP(c_COMBC(_1119627, tc_fun(_1119629, tc_HOL_Obool), tc_fun(_1119629, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1119629, tc_HOL_Obool), tc_fun(tc_fun(_1119629, tc_HOL_Obool), tc_fun(_1119629, tc_HOL_Obool)), _1119627), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1119629, tc_HOL_Obool))), _1119633)), _1119635)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1119629, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1119627, tc_fun(_1119629, tc_HOL_Obool)), _1119631), _1119633)), _1119635))], (18179 ^ _780086) ^ [_1119736, _1119738, _1119740, _1119742, _1119744] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1119736, tc_fun(_1119738, tc_HOL_Obool)), _1119740), hAPP(hAPP(c_COMBB(tc_fun(_1119738, tc_HOL_Obool), tc_fun(_1119738, tc_HOL_Obool), _1119736), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1119738, tc_HOL_Obool)), _1119742)), _1119744)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1119738, tc_HOL_Obool)), _1119742), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1119736, tc_fun(_1119738, tc_HOL_Obool)), _1119740), _1119744)))], (18181 ^ _780086) ^ [_1119826, _1119828, _1119830, _1119832, _1119834] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1119826, tc_fun(_1119828, tc_HOL_Obool)), _1119830), hAPP(hAPP(c_COMBS(_1119826, tc_fun(_1119828, tc_HOL_Obool), tc_fun(_1119828, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1119828, tc_HOL_Obool), tc_fun(tc_fun(_1119828, tc_HOL_Obool), tc_fun(_1119828, tc_HOL_Obool)), _1119826), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1119828, tc_HOL_Obool))), _1119832)), _1119834)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1119828, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1119826, tc_fun(_1119828, tc_HOL_Obool)), _1119830), _1119832)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1119826, tc_fun(_1119828, tc_HOL_Obool)), _1119830), _1119834)))], (18183 ^ _780086) ^ [_1119947, _1119949, _1119951, _1119953, _1119955, _1119957] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1119947, tc_fun(_1119949, tc_HOL_Obool)), _1119951), hAPP(hAPP(c_COMBC(_1119947, tc_fun(_1119953, tc_fun(_1119949, tc_HOL_Obool)), tc_fun(_1119949, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1119953, tc_HOL_Obool), tc_fun(tc_fun(_1119953, tc_fun(_1119949, tc_HOL_Obool)), tc_fun(_1119949, tc_HOL_Obool)), _1119947), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1119953, tc_fun(_1119949, tc_HOL_Obool))), _1119955)), _1119957)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1119953, tc_fun(_1119949, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1119947, tc_fun(_1119953, tc_HOL_Obool)), _1119951), _1119955)), _1119957))], (18185 ^ _780086) ^ [_1120066, _1120068, _1120070, _1120072, _1120074, _1120076] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1120066, tc_fun(_1120068, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1120070, tc_fun(_1120066, tc_HOL_Obool)), _1120072), _1120074)), _1120076) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1120070, tc_fun(_1120068, tc_HOL_Obool)), _1120072), hAPP(hAPP(c_COMBC(_1120070, tc_fun(_1120066, tc_fun(_1120068, tc_HOL_Obool)), tc_fun(_1120068, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1120066, tc_HOL_Obool), tc_fun(tc_fun(_1120066, tc_fun(_1120068, tc_HOL_Obool)), tc_fun(_1120068, tc_HOL_Obool)), _1120070), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1120066, tc_fun(_1120068, tc_HOL_Obool))), _1120074)), _1120076)))], (18187 ^ _780086) ^ [_1120185, _1120187] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1120185)), hAPP(c_Nat_OSuc, _1120187)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1120185), _1120187)))], (18189 ^ _780086) ^ [_1120231, _1120233] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1120231)), hAPP(c_Nat_OSuc, _1120233)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1120231), _1120233)))], (18191 ^ _780086) ^ [_1120277, _1120279, _1120281, _1120283, _1120285, _1120287] : [-(hAPP(c_Set_Ovimage(_1120277, _1120279, _1120281), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1120283, tc_fun(_1120279, tc_HOL_Obool)), _1120285), _1120287)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1120283, tc_fun(_1120277, tc_HOL_Obool)), _1120285), hAPP(hAPP(c_COMBB(tc_fun(_1120279, tc_HOL_Obool), tc_fun(_1120277, tc_HOL_Obool), _1120283), c_Set_Ovimage(_1120277, _1120279, _1120281)), _1120287)))], (18193 ^ _780086) ^ [_1120361, _1120363, _1120365] : [class_Complete__Lattice_Ocomplete__lattice(_1120361), 18196 ^ _780086 : [(18207 ^ _780086) ^ [] : [18209 ^ _780086 : [(18210 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1120361), 18208 ^ [_1120361, _1120363, _1120365]), _1120365)))], (18212 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1120361), _1120363), 18208 ^ [_1120361, _1120363, _1120365]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1120361), _1120363), c_Complete__Lattice_OInf__class_OInf(_1120361, _1120365))))], (18197 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1120361), _1120363), c_Complete__Lattice_OInf__class_OInf(_1120361, _1120365))), 18200 ^ _780086 : [(18201 ^ _780086) ^ [_1120519] : [hBOOL(hAPP(hAPP(c_member(_1120361), _1120519), _1120365)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1120361), _1120363), _1120519)))]]]]], (18216 ^ _780086) ^ [_1120795, _1120797, _1120799] : [class_Complete__Lattice_Ocomplete__lattice(_1120795), class_Orderings_Olinorder(_1120795), 18223 ^ _780086 : [(18224 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1120795), c_Complete__Lattice_OInf__class_OInf(_1120795, _1120797)), _1120799)), 18228 ^ _780086 : [(18229 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1120795), 18227 ^ [_1120795, _1120797, _1120799]), _1120797)))], (18231 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1120795), 18227 ^ [_1120795, _1120797, _1120799]), _1120799)))]]], (18233 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1120795), c_Complete__Lattice_OInf__class_OInf(_1120795, _1120797)), _1120799))), 18234 ^ _780086 : [(18235 ^ _780086) ^ [_1121101] : [hBOOL(hAPP(hAPP(c_member(_1120795), _1121101), _1120797)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1120795), _1121101), _1120799))]]]]], (18243 ^ _780086) ^ [_1121255, _1121257, _1121259, _1121261, _1121263] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1121255, _1121257, _1121259), _1121261), hAPP(c_Nat_OSuc, _1121263)) = hAPP(hAPP(_1121259, _1121261), hAPP(hAPP(c_Power_Opower_Opower(_1121255, _1121257, _1121259), _1121261), _1121263)))], (18245 ^ _780086) ^ [_1121315] : [-(c_Fun_Oinj__on(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc, _1121315))], (18247 ^ _780086) ^ [_1121340, _1121342, _1121344] : [class_Rings_Ocomm__semiring__1(_1121340), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1121340), _1121342), hAPP(c_Nat_OSuc, _1121344)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1121340), _1121342), hAPP(hAPP(c_Power_Opower__class_Opower(_1121340), _1121342), _1121344)))], (18253 ^ _780086) ^ [_1121471, _1121473, _1121475] : [class_Rings_Ocomm__semiring__1(_1121471), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1121471), _1121473), hAPP(hAPP(c_Power_Opower__class_Opower(_1121471), _1121473), _1121475)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1121471), _1121473), hAPP(c_Nat_OSuc, _1121475)))], (18259 ^ _780086) ^ [_1121602, _1121604, _1121606] : [class_Rings_Ocomm__semiring__1(_1121602), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1121602), hAPP(hAPP(c_Power_Opower__class_Opower(_1121602), _1121604), _1121606)), _1121604) = hAPP(hAPP(c_Power_Opower__class_Opower(_1121602), _1121604), hAPP(c_Nat_OSuc, _1121606)))], (18265 ^ _780086) ^ [_1121733, _1121735, _1121737] : [class_Groups_Omonoid__mult(_1121733), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1121733), _1121735), hAPP(c_Nat_OSuc, _1121737)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1121733), hAPP(hAPP(c_Power_Opower__class_Opower(_1121733), _1121735), _1121737)), _1121735))], (18271 ^ _780086) ^ [_1121864, _1121866, _1121868] : [class_Power_Opower(_1121864), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1121864), _1121866), hAPP(c_Nat_OSuc, _1121868)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1121864), _1121866), hAPP(hAPP(c_Power_Opower__class_Opower(_1121864), _1121866), _1121868)))], (18277 ^ _780086) ^ [_1121995, _1121997] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1121995), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1121995), _1121997)))))], (18279 ^ _780086) ^ [_1122034, _1122036] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1122034), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1122036), _1122034)))))], (18281 ^ _780086) ^ [_1122088, _1122090] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1122088), _1122090)), -(_1122090 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1122088), 18284 ^ [_1122088, _1122090])))], (18288 ^ _780086) ^ [_1122201, _1122203] : [18289 ^ _780086 : [(18290 ^ _780086) ^ [_1122254] : [_1122203 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1122201), _1122254))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1122201), _1122203)))], (18294 ^ _780086) ^ [_1122321, _1122323, _1122325, _1122327, _1122329] : [class_Complete__Lattice_Ocomplete__lattice(_1122321), 18297 ^ _780086 : [(18308 ^ _780086) ^ [] : [18310 ^ _780086 : [(18311 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1122325), 18309 ^ [_1122321, _1122323, _1122325, _1122327, _1122329]), _1122327)))], (18313 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1122321), _1122323), hAPP(_1122329, 18309 ^ [_1122321, _1122323, _1122325, _1122327, _1122329])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1122321), _1122323), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1122325, _1122321), _1122327), _1122329))))], (18298 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1122321), _1122323), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1122325, _1122321), _1122327), _1122329))), 18301 ^ _780086 : [(18302 ^ _780086) ^ [_1122502] : [hBOOL(hAPP(hAPP(c_member(_1122325), _1122502), _1122327)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1122321), _1122323), hAPP(_1122329, _1122502))))]]]]], (18317 ^ _780086) ^ [_1122815, _1122817] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1122815)), _1122817)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1122815), _1122817)))], (18323 ^ _780086) ^ [_1122918, _1122920] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1122918), _1122920)), 18326 ^ _780086 : [(18327 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1122920), hAPP(c_Nat_OSuc, _1122918))), -(_1122920 = _1122918)], (18333 ^ _780086) ^ [] : [_1122920 = _1122918, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1122920), hAPP(c_Nat_OSuc, _1122918))))]]], (18339 ^ _780086) ^ [_1123159, _1123161] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1123159), _1123161)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1123159)), _1123161)))], (18345 ^ _780086) ^ [_1123262, _1123264] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1123262), _1123264)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1123262), hAPP(c_Nat_OSuc, _1123264))))], (18351 ^ _780086) ^ [_1123380, _1123382] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1123380)), _1123382)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1123380), _1123382)))], (18357 ^ _780086) ^ [_1123479, _1123481] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1123479), _1123481)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1123479)), _1123481)))], (18363 ^ _780086) ^ [_1123599, _1123601] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1123599), hAPP(c_Nat_OSuc, _1123601))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1123599), _1123601)))], (18369 ^ _780086) ^ [_1123698, _1123700] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1123698), _1123700)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1123698), hAPP(c_Nat_OSuc, _1123700))))], (18375 ^ _780086) ^ [_1123818, _1123820] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1123818), _1123820)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1123818)), _1123820)))], (18381 ^ _780086) ^ [_1123917, _1123919] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1123917)), _1123919)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1123917), _1123919)))], (18387 ^ _780086) ^ [_1124022, _1124024, _1124026, _1124028, _1124030] : [class_Complete__Lattice_Ocomplete__lattice(_1124022), class_Orderings_Olinorder(_1124022), 18394 ^ _780086 : [(18395 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1124022), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1124024, _1124022), _1124026), _1124028)), _1124030)), 18399 ^ _780086 : [(18400 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1124024), 18398 ^ [_1124022, _1124024, _1124026, _1124028, _1124030]), _1124026)))], (18402 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1124022), hAPP(_1124028, 18398 ^ [_1124022, _1124024, _1124026, _1124028, _1124030])), _1124030)))]]], (18404 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1124022), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1124024, _1124022), _1124026), _1124028)), _1124030))), 18405 ^ _780086 : [(18406 ^ _780086) ^ [_1124370] : [hBOOL(hAPP(hAPP(c_member(_1124024), _1124370), _1124026)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1124022), hAPP(_1124028, _1124370)), _1124030))]]]]], (18414 ^ _780086) ^ [_1124540, _1124542, _1124544, _1124546, _1124548, _1124550] : [hBOOL(hAPP(hAPP(c_member(_1124540), _1124542), _1124544)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1124540, tc_fun(_1124546, tc_HOL_Obool)), _1124544), hAPP(hAPP(c_COMBB(tc_fun(_1124546, tc_HOL_Obool), tc_fun(_1124546, tc_HOL_Obool), _1124540), hAPP(c_Set_Oinsert(_1124546), _1124548)), _1124550)) = hAPP(hAPP(c_Set_Oinsert(_1124546), _1124548), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1124540, tc_fun(_1124546, tc_HOL_Obool)), _1124544), _1124550)))], (18420 ^ _780086) ^ [_1124745, _1124747] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1124745), _1124747)), hAPP(c_Nat_OSuc, _1124745))))], (18422 ^ _780086) ^ [_1124802, _1124804, _1124806] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1124802)), _1124804)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1124802)), _1124806))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1124804), _1124806)))], (18428 ^ _780086) ^ [_1124933, _1124935, _1124937] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1124935), _1124937)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1124933)), _1124935)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1124933)), _1124937))))], (18434 ^ _780086) ^ [_1125070, _1125072, _1125074, _1125076, _1125078] : [hBOOL(hAPP(hAPP(c_member(_1125070), _1125072), _1125074)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1125076, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1125070, tc_fun(_1125076, tc_HOL_Obool)), _1125074), _1125078)), hAPP(_1125078, _1125072))))], (18440 ^ _780086) ^ [_1125238, _1125240, _1125242, _1125244] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1125238, tc_fun(_1125240, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1125238, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1125240, tc_HOL_Obool), tc_fun(_1125240, tc_HOL_Obool), _1125238), hAPP(c_COMBC(_1125240, tc_fun(_1125240, tc_HOL_Obool), tc_HOL_Obool), c_member(_1125240))), _1125242)), _1125244)), -(hBOOL(hAPP(hAPP(c_member(_1125240), _1125244), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1125238, tc_fun(_1125240, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1125238, tc_HOL_Obool))), _1125242))))], (18446 ^ _780086) ^ [_1125457, _1125459, _1125461, _1125463] : [hBOOL(hAPP(hAPP(c_member(_1125459), _1125463), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1125457, tc_fun(_1125459, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1125457, tc_HOL_Obool))), _1125461))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1125457, tc_fun(_1125459, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1125457, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1125459, tc_HOL_Obool), tc_fun(_1125459, tc_HOL_Obool), _1125457), hAPP(c_COMBC(_1125459, tc_fun(_1125459, tc_HOL_Obool), tc_HOL_Obool), c_member(_1125459))), _1125461)), _1125463)))], (18452 ^ _780086) ^ [_1125682, _1125684] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1125682)), _1125684) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1125684), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1125682), _1125684)))], (18454 ^ _780086) ^ [_1125728, _1125730] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1125728), hAPP(c_Nat_OSuc, _1125730)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1125728), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1125728), _1125730)))], (18456 ^ _780086) ^ [_1125774, _1125776, _1125778, _1125780, _1125782] : [hBOOL(hAPP(hAPP(c_member(_1125774), _1125776), _1125778)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1125780, tc_HOL_Obool)), hAPP(_1125782, _1125776)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1125774, tc_fun(_1125780, tc_HOL_Obool)), _1125778), _1125782)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1125774, tc_fun(_1125780, tc_HOL_Obool)), _1125778), _1125782))], (18462 ^ _780086) ^ [_1125947, _1125949, _1125951, _1125953] : [class_Complete__Lattice_Ocomplete__lattice(_1125947), -(_1125949 = c_Orderings_Obot__class_Obot(tc_fun(_1125951, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1125951, _1125947), _1125949), hAPP(c_COMBK(_1125947, _1125951), _1125953)) = _1125953)], (18472 ^ _780086) ^ [_1126081, _1126083] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1126081), _1126083)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1126083)), _1126081) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1126083), _1126081)))], (18478 ^ _780086) ^ [_1126222, _1126224, _1126226] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1126222)), _1126224)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1126222)), _1126226))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1126224), _1126226)))], (18484 ^ _780086) ^ [_1126353, _1126355, _1126357] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1126355), _1126357)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1126353)), _1126355)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1126353)), _1126357))))], (18490 ^ _780086) ^ [_1126505, _1126507, _1126509, _1126511] : [_1126505 = c_Orderings_Obot__class_Obot(tc_fun(_1126507, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1126507, tc_fun(_1126509, tc_HOL_Obool)), _1126505), hAPP(c_COMBK(tc_fun(_1126509, tc_HOL_Obool), _1126507), _1126511)) = c_Orderings_Otop__class_Otop(tc_fun(_1126509, tc_HOL_Obool)))], (18496 ^ _780086) ^ [_1126642, _1126644, _1126646, _1126648] : [-(_1126642 = c_Orderings_Obot__class_Obot(tc_fun(_1126644, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1126644, tc_fun(_1126646, tc_HOL_Obool)), _1126642), hAPP(c_COMBK(tc_fun(_1126646, tc_HOL_Obool), _1126644), _1126648)) = _1126648)], (18502 ^ _780086) ^ [_1126710, _1126712, _1126714] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1126710, tc_fun(_1126712, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1126710, tc_HOL_Obool))), _1126714) = c_Orderings_Otop__class_Otop(tc_fun(_1126712, tc_HOL_Obool)))], (18504 ^ _780086) ^ [_1126777, _1126779, _1126781, _1126783, _1126785] : [_1126777 = c_Orderings_Obot__class_Obot(tc_fun(_1126779, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1126781, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1126779, tc_fun(_1126781, tc_HOL_Obool)), _1126777), _1126783)), _1126785) = _1126785)], (18510 ^ _780086) ^ [_1126910, _1126912, _1126914, _1126916, _1126918] : [-(_1126910 = c_Orderings_Obot__class_Obot(tc_fun(_1126912, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1126914, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1126912, tc_fun(_1126914, tc_HOL_Obool)), _1126910), _1126916)), _1126918) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1126912, tc_fun(_1126914, tc_HOL_Obool)), _1126910), hAPP(hAPP(c_COMBC(_1126912, tc_fun(_1126914, tc_HOL_Obool), tc_fun(_1126914, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1126914, tc_HOL_Obool), tc_fun(tc_fun(_1126914, tc_HOL_Obool), tc_fun(_1126914, tc_HOL_Obool)), _1126912), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1126914, tc_HOL_Obool))), _1126916)), _1126918)))], (18516 ^ _780086) ^ [_1127055, _1127057, _1127059, _1127061, _1127063] : [_1127055 = c_Orderings_Obot__class_Obot(tc_fun(_1127057, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1127059, tc_HOL_Obool)), _1127061), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1127057, tc_fun(_1127059, tc_HOL_Obool)), _1127055), _1127063)) = _1127061)], (18522 ^ _780086) ^ [_1127188, _1127190, _1127192, _1127194, _1127196] : [-(_1127188 = c_Orderings_Obot__class_Obot(tc_fun(_1127190, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1127192, tc_HOL_Obool)), _1127194), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1127190, tc_fun(_1127192, tc_HOL_Obool)), _1127188), _1127196)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1127190, tc_fun(_1127192, tc_HOL_Obool)), _1127188), hAPP(hAPP(c_COMBB(tc_fun(_1127192, tc_HOL_Obool), tc_fun(_1127192, tc_HOL_Obool), _1127190), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1127192, tc_HOL_Obool)), _1127194)), _1127196)))], (18528 ^ _780086) ^ [_1127296, _1127298, _1127300, _1127302, _1127304] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1127296, tc_fun(_1127298, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1127296), _1127300), _1127302)), _1127304) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1127298, tc_HOL_Obool)), hAPP(_1127304, _1127300)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1127296, tc_fun(_1127298, tc_HOL_Obool)), _1127302), _1127304)))], (18530 ^ _780086) ^ [_1127373, _1127375, _1127377, _1127379, _1127381] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1127373, tc_fun(_1127375, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1127373, tc_HOL_Obool)), _1127377), _1127379)), _1127381) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1127375, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1127373, tc_fun(_1127375, tc_HOL_Obool)), _1127377), _1127381)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1127373, tc_fun(_1127375, tc_HOL_Obool)), _1127379), _1127381)))], (18532 ^ _780086) ^ [_1127462] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1127462)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1127462)], (18534 ^ _780086) ^ [_1127494, _1127496, _1127498, _1127500, _1127502] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1127494, tc_fun(_1127496, tc_HOL_Obool)), _1127498), hAPP(hAPP(c_COMBB(tc_fun(_1127496, tc_HOL_Obool), tc_fun(_1127496, tc_HOL_Obool), _1127494), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1127496, tc_HOL_Obool)), _1127500)), _1127502)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1127496, tc_HOL_Obool)), _1127500), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1127494, tc_fun(_1127496, tc_HOL_Obool)), _1127498), _1127502)))], (18536 ^ _780086) ^ [_1127584, _1127586, _1127588, _1127590, _1127592] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1127584, tc_HOL_Obool)), _1127586), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1127588, tc_fun(_1127584, tc_HOL_Obool)), _1127590), _1127592)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1127588, tc_fun(_1127584, tc_HOL_Obool)), _1127590), hAPP(hAPP(c_COMBB(tc_fun(_1127584, tc_HOL_Obool), tc_fun(_1127584, tc_HOL_Obool), _1127588), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1127584, tc_HOL_Obool)), _1127586)), _1127592)))], (18538 ^ _780086) ^ [_1127674, _1127676, _1127678] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1127674, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1127674, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1127674, tc_HOL_Obool), _1127676)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1127674, tc_HOL_Obool), _1127678))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1127674, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1127674, tc_HOL_Obool), tc_HOL_Obool)), _1127676), _1127678)))))], (18540 ^ _780086) ^ [_1127754, _1127756, _1127758, _1127760] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1127754, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1127756, tc_fun(_1127754, tc_HOL_Obool)), _1127758), _1127760)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1127756, tc_fun(_1127754, tc_HOL_Obool)), _1127758), hAPP(hAPP(c_COMBB(tc_fun(_1127754, tc_HOL_Obool), tc_fun(_1127754, tc_HOL_Obool), _1127756), c_Groups_Ouminus__class_Ouminus(tc_fun(_1127754, tc_HOL_Obool))), _1127760)))], (18542 ^ _780086) ^ [_1127836, _1127838, _1127840, _1127842] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1127836, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1127838, tc_fun(_1127836, tc_HOL_Obool)), _1127840), _1127842)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1127838, tc_fun(_1127836, tc_HOL_Obool)), _1127840), hAPP(hAPP(c_COMBB(tc_fun(_1127836, tc_HOL_Obool), tc_fun(_1127836, tc_HOL_Obool), _1127838), c_Groups_Ouminus__class_Ouminus(tc_fun(_1127836, tc_HOL_Obool))), _1127842)))], (18544 ^ _780086) ^ [_1127918, _1127920] : [class_Lattices_Olattice(_1127918), -(c_Big__Operators_Olattice__class_OInf__fin(_1127918, hAPP(hAPP(c_Set_Oinsert(_1127918), _1127920), c_Orderings_Obot__class_Obot(tc_fun(_1127918, tc_HOL_Obool)))) = _1127920)], (18550 ^ _780086) ^ [_1128025] : [-(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1128025) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1128025)))], (18552 ^ _780086) ^ [_1128057, _1128059, _1128061] : [class_Complete__Lattice_Ocomplete__lattice(_1128057), hBOOL(hAPP(hAPP(c_member(_1128057), _1128059), _1128061)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1128057), c_Complete__Lattice_OInf__class_OInf(_1128057, _1128061)), _1128059)))], (18562 ^ _780086) ^ [_1128222, _1128224, _1128226, _1128228, _1128230] : [class_Complete__Lattice_Ocomplete__lattice(_1128222), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1128224, tc_HOL_Obool)), _1128226), _1128228)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1128222), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1128224, _1128222), _1128228), _1128230)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1128224, _1128222), _1128226), _1128230))))], (18572 ^ _780086) ^ [_1128431, _1128433] : [class_Complete__Lattice_Ocomplete__lattice(_1128431), -(c_Complete__Lattice_OInf__class_OInf(_1128431, hAPP(hAPP(c_Set_Oinsert(_1128431), _1128433), c_Orderings_Obot__class_Obot(tc_fun(_1128431, tc_HOL_Obool)))) = _1128433)], (18578 ^ _780086) ^ [_1128538] : [class_Complete__Lattice_Ocomplete__lattice(_1128538), -(c_Complete__Lattice_OInf__class_OInf(_1128538, c_Orderings_Obot__class_Obot(tc_fun(_1128538, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1128538))], (18584 ^ _780086) ^ [_1128631] : [class_Complete__Lattice_Ocomplete__lattice(_1128631), -(c_Complete__Lattice_OInf__class_OInf(_1128631, c_Orderings_Otop__class_Otop(tc_fun(_1128631, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1128631))], (18590 ^ _780086) ^ [_1128724, _1128726, _1128728] : [class_Complete__Lattice_Ocomplete__lattice(_1128724), -(c_Complete__Lattice_OInf__class_OInf(_1128724, hAPP(hAPP(c_Set_Oinsert(_1128724), _1128726), _1128728)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1128724), _1128726), c_Complete__Lattice_OInf__class_OInf(_1128724, _1128728)))], (18596 ^ _780086) ^ [_1128863, _1128865, _1128867, _1128869, _1128871] : [_1128863 = c_Orderings_Obot__class_Obot(tc_fun(_1128865, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1128865, tc_fun(_1128867, tc_HOL_Obool)), _1128863), hAPP(hAPP(c_COMBC(_1128865, tc_fun(_1128867, tc_HOL_Obool), tc_fun(_1128867, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1128867, tc_HOL_Obool), tc_fun(tc_fun(_1128867, tc_HOL_Obool), tc_fun(_1128867, tc_HOL_Obool)), _1128865), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1128867, tc_HOL_Obool))), _1128869)), _1128871)) = c_Orderings_Otop__class_Otop(tc_fun(_1128867, tc_HOL_Obool)))], (18602 ^ _780086) ^ [_1129070, _1129072, _1129074, _1129076, _1129078] : [-(_1129070 = c_Orderings_Obot__class_Obot(tc_fun(_1129072, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1129072, tc_fun(_1129074, tc_HOL_Obool)), _1129070), hAPP(hAPP(c_COMBC(_1129072, tc_fun(_1129074, tc_HOL_Obool), tc_fun(_1129074, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1129074, tc_HOL_Obool), tc_fun(tc_fun(_1129074, tc_HOL_Obool), tc_fun(_1129074, tc_HOL_Obool)), _1129072), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1129074, tc_HOL_Obool))), _1129076)), _1129078)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1129074, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1129072, tc_fun(_1129074, tc_HOL_Obool)), _1129070), _1129076)), _1129078))], (18608 ^ _780086) ^ [_1129215, _1129217, _1129219, _1129221, _1129223] : [_1129215 = c_Orderings_Obot__class_Obot(tc_fun(_1129217, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1129217, tc_fun(_1129219, tc_HOL_Obool)), _1129215), hAPP(hAPP(c_COMBB(tc_fun(_1129219, tc_HOL_Obool), tc_fun(_1129219, tc_HOL_Obool), _1129217), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1129219, tc_HOL_Obool)), _1129221)), _1129223)) = c_Orderings_Otop__class_Otop(tc_fun(_1129219, tc_HOL_Obool)))], (18614 ^ _780086) ^ [_1129384, _1129386, _1129388, _1129390, _1129392] : [-(_1129384 = c_Orderings_Obot__class_Obot(tc_fun(_1129386, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1129386, tc_fun(_1129388, tc_HOL_Obool)), _1129384), hAPP(hAPP(c_COMBB(tc_fun(_1129388, tc_HOL_Obool), tc_fun(_1129388, tc_HOL_Obool), _1129386), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1129388, tc_HOL_Obool)), _1129390)), _1129392)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1129388, tc_HOL_Obool)), _1129390), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1129386, tc_fun(_1129388, tc_HOL_Obool)), _1129384), _1129392)))], (18620 ^ _780086) ^ [_1129492, _1129494, _1129496] : [class_Rings_Olinordered__semidom(_1129492), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129492), c_Groups_Oone__class_Oone(_1129492)), _1129494)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129492), c_Groups_Oone__class_Oone(_1129492)), hAPP(hAPP(c_Power_Opower__class_Opower(_1129492), _1129494), hAPP(c_Nat_OSuc, _1129496)))))], (18630 ^ _780086) ^ [_1129699, _1129701, _1129703, _1129705, _1129707] : [_1129699 = c_Orderings_Obot__class_Obot(tc_fun(_1129701, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1129703, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1129701, tc_fun(_1129703, tc_HOL_Obool)), _1129699), _1129705)), _1129707) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1129703, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1129703, tc_HOL_Obool))), _1129707))], (18636 ^ _780086) ^ [_1129864, _1129866, _1129868, _1129870, _1129872] : [-(_1129864 = c_Orderings_Obot__class_Obot(tc_fun(_1129866, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1129868, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1129866, tc_fun(_1129868, tc_HOL_Obool)), _1129864), _1129870)), _1129872) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1129866, tc_fun(_1129868, tc_HOL_Obool)), _1129864), hAPP(hAPP(c_COMBC(_1129866, tc_fun(_1129868, tc_HOL_Obool), tc_fun(_1129868, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1129868, tc_HOL_Obool), tc_fun(tc_fun(_1129868, tc_HOL_Obool), tc_fun(_1129868, tc_HOL_Obool)), _1129866), c_Groups_Ominus__class_Ominus(tc_fun(_1129868, tc_HOL_Obool))), _1129870)), _1129872)))], (18642 ^ _780086) ^ [_1130009, _1130011, _1130013, _1130015, _1130017] : [_1130009 = c_Orderings_Obot__class_Obot(tc_fun(_1130011, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1130011, tc_fun(_1130013, tc_HOL_Obool)), _1130009), hAPP(hAPP(c_COMBC(_1130011, tc_fun(_1130013, tc_HOL_Obool), tc_fun(_1130013, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1130013, tc_HOL_Obool), tc_fun(tc_fun(_1130013, tc_HOL_Obool), tc_fun(_1130013, tc_HOL_Obool)), _1130011), c_Groups_Ominus__class_Ominus(tc_fun(_1130013, tc_HOL_Obool))), _1130015)), _1130017)) = c_Orderings_Otop__class_Otop(tc_fun(_1130013, tc_HOL_Obool)))], (18648 ^ _780086) ^ [_1130216, _1130218, _1130220, _1130222, _1130224] : [-(_1130216 = c_Orderings_Obot__class_Obot(tc_fun(_1130218, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1130218, tc_fun(_1130220, tc_HOL_Obool)), _1130216), hAPP(hAPP(c_COMBC(_1130218, tc_fun(_1130220, tc_HOL_Obool), tc_fun(_1130220, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1130220, tc_HOL_Obool), tc_fun(tc_fun(_1130220, tc_HOL_Obool), tc_fun(_1130220, tc_HOL_Obool)), _1130218), c_Groups_Ominus__class_Ominus(tc_fun(_1130220, tc_HOL_Obool))), _1130222)), _1130224)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1130220, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1130218, tc_fun(_1130220, tc_HOL_Obool)), _1130216), _1130222)), _1130224))], (18654 ^ _780086) ^ [_1130361, _1130363, _1130365, _1130367, _1130369] : [_1130361 = c_Orderings_Obot__class_Obot(tc_fun(_1130363, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1130365, tc_HOL_Obool)), _1130367), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1130363, tc_fun(_1130365, tc_HOL_Obool)), _1130361), _1130369)) = _1130367)], (18660 ^ _780086) ^ [_1130494, _1130496, _1130498, _1130500, _1130502] : [-(_1130494 = c_Orderings_Obot__class_Obot(tc_fun(_1130496, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1130498, tc_HOL_Obool)), _1130500), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1130496, tc_fun(_1130498, tc_HOL_Obool)), _1130494), _1130502)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1130496, tc_fun(_1130498, tc_HOL_Obool)), _1130494), hAPP(hAPP(c_COMBB(tc_fun(_1130498, tc_HOL_Obool), tc_fun(_1130498, tc_HOL_Obool), _1130496), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1130498, tc_HOL_Obool)), _1130500)), _1130502)))], (18666 ^ _780086) ^ [_1130602, _1130604, _1130606] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1130602), _1130604)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1130606), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1130604), _1130602))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1130606), _1130602)), hAPP(c_Nat_OSuc, _1130604)))], (18672 ^ _780086) ^ [_1130751, _1130753, _1130755] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1130751), _1130753)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1130753), _1130751))), _1130755) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1130753)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1130751), _1130755)))], (18678 ^ _780086) ^ [_1130900, _1130902, _1130904, _1130906, _1130908] : [class_Complete__Lattice_Ocomplete__lattice(_1130900), hBOOL(hAPP(hAPP(c_member(_1130902), _1130904), _1130906)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1130900), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1130902, _1130900), _1130906), _1130908)), hAPP(_1130908, _1130904))))], (18688 ^ _780086) ^ [_1131091, _1131093, _1131095] : [class_Lattices_Olattice(_1131091), hBOOL(hAPP(c_Finite__Set_Ofinite(_1131091), _1131093)), hBOOL(hAPP(hAPP(c_member(_1131091), _1131095), _1131093)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1131091), _1131095), c_Big__Operators_Olattice__class_OInf__fin(_1131091, _1131093)) = _1131095)], (18702 ^ _780086) ^ [_1131320, _1131322, _1131324] : [class_Lattices_Olattice(_1131320), hBOOL(hAPP(c_Finite__Set_Ofinite(_1131320), _1131322)), hBOOL(hAPP(hAPP(c_member(_1131320), _1131324), _1131322)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1131320), _1131324), c_Big__Operators_Olattice__class_OInf__fin(_1131320, _1131322)) = c_Big__Operators_Olattice__class_OInf__fin(_1131320, _1131322))], (18716 ^ _780086) ^ [_1131555, _1131557] : [class_Lattices_Olattice(_1131555), hBOOL(hAPP(c_Finite__Set_Ofinite(_1131555), _1131557)), -(c_Big__Operators_Olattice__class_OInf__fin(_1131555, _1131557) = hAPP(c_Finite__Set_Ofold1(_1131555, c_Lattices_Osemilattice__inf__class_Oinf(_1131555)), _1131557))], (18726 ^ _780086) ^ [_1131730, _1131732, _1131734, _1131736, _1131738] : [_1131730 = c_Orderings_Obot__class_Obot(tc_fun(_1131732, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1131732, tc_fun(_1131734, tc_HOL_Obool)), _1131730), hAPP(hAPP(c_COMBB(tc_fun(_1131734, tc_HOL_Obool), tc_fun(_1131734, tc_HOL_Obool), _1131732), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1131734, tc_HOL_Obool)), _1131736)), _1131738)) = c_Orderings_Otop__class_Otop(tc_fun(_1131734, tc_HOL_Obool)))], (18732 ^ _780086) ^ [_1131899, _1131901, _1131903, _1131905, _1131907] : [-(_1131899 = c_Orderings_Obot__class_Obot(tc_fun(_1131901, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1131901, tc_fun(_1131903, tc_HOL_Obool)), _1131899), hAPP(hAPP(c_COMBB(tc_fun(_1131903, tc_HOL_Obool), tc_fun(_1131903, tc_HOL_Obool), _1131901), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1131903, tc_HOL_Obool)), _1131905)), _1131907)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1131903, tc_HOL_Obool)), _1131905), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1131901, tc_fun(_1131903, tc_HOL_Obool)), _1131899), _1131907)))], (18738 ^ _780086) ^ [_1132007, _1132009, _1132011] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1132007), _1132009)), 18741 ^ _780086 : [(18742 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1132007), _1132011), _1132009)), -(hAPP(c_Finite__Set_Ocard(_1132007), hAPP(hAPP(c_Set_Oinsert(_1132007), _1132011), _1132009)) = hAPP(c_Finite__Set_Ocard(_1132007), _1132009))], (18748 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1132007), _1132011), _1132009))), -(hAPP(c_Finite__Set_Ocard(_1132007), hAPP(hAPP(c_Set_Oinsert(_1132007), _1132011), _1132009)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1132007), _1132009)))]]], (18754 ^ _780086) ^ [_1132301, _1132303, _1132305] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1132301), _1132303)), -(hBOOL(hAPP(hAPP(c_member(_1132301), _1132305), _1132303))), -(hAPP(c_Finite__Set_Ocard(_1132301), hAPP(hAPP(c_Set_Oinsert(_1132301), _1132305), _1132303)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1132301), _1132303)))], (18764 ^ _780086) ^ [_1132459, _1132461, _1132463] : [class_Complete__Lattice_Ocomplete__lattice(_1132459), -(c_Complete__Lattice_OInf__class_OInf(_1132459, hAPP(hAPP(c_Set_Oinsert(_1132459), _1132461), hAPP(hAPP(c_Set_Oinsert(_1132459), _1132463), c_Orderings_Obot__class_Obot(tc_fun(_1132459, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1132459), _1132461), _1132463))], (18770 ^ _780086) ^ [_1132600, _1132602, _1132604] : [class_Complete__Lattice_Ocomplete__lattice(_1132600), hBOOL(hAPP(c_Finite__Set_Ofinite(_1132600), _1132602)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1132600), _1132604), c_Complete__Lattice_OInf__class_OInf(_1132600, _1132602)) = hAPP(hAPP(c_Finite__Set_Ofold(_1132600, _1132600, c_Lattices_Osemilattice__inf__class_Oinf(_1132600)), _1132604), _1132602))], (18780 ^ _780086) ^ [_1132785, _1132787, _1132789] : [class_Lattices_Olattice(_1132785), hBOOL(hAPP(c_Finite__Set_Ofinite(_1132785), _1132787)), -(_1132787 = c_Orderings_Obot__class_Obot(tc_fun(_1132785, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1132785, hAPP(hAPP(c_Set_Oinsert(_1132785), _1132789), _1132787)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1132785), _1132789), c_Big__Operators_Olattice__class_OInf__fin(_1132785, _1132787)))], (18794 ^ _780086) ^ [_1132993, _1132995, _1132997] : [class_Lattices_Olattice(_1132993), hBOOL(hAPP(c_Finite__Set_Ofinite(_1132993), _1132995)), -(_1132997 = c_Orderings_Obot__class_Obot(tc_fun(_1132993, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1132993, tc_HOL_Obool)), _1132997), _1132995)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1132993), c_Big__Operators_Olattice__class_OInf__fin(_1132993, _1132997)), c_Big__Operators_Olattice__class_OInf__fin(_1132993, _1132995)) = c_Big__Operators_Olattice__class_OInf__fin(_1132993, _1132995))], (18812 ^ _780086) ^ [_1133307, _1133309, _1133311] : [class_Lattices_Olattice(_1133307), hBOOL(hAPP(c_Finite__Set_Ofinite(_1133307), _1133309)), -(_1133309 = c_Orderings_Obot__class_Obot(tc_fun(_1133307, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1133307), _1133311)), -(_1133311 = c_Orderings_Obot__class_Obot(tc_fun(_1133307, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1133307, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1133307, tc_HOL_Obool)), _1133309), _1133311)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1133307), c_Big__Operators_Olattice__class_OInf__fin(_1133307, _1133309)), c_Big__Operators_Olattice__class_OInf__fin(_1133307, _1133311)))], (18834 ^ _780086) ^ [_1133656, _1133658] : [class_Lattices_Olattice(_1133656), hBOOL(hAPP(c_Finite__Set_Ofinite(_1133656), _1133658)), -(_1133658 = c_Orderings_Obot__class_Obot(tc_fun(_1133656, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133656), c_Big__Operators_Olattice__class_OInf__fin(_1133656, _1133658)), c_Big__Operators_Olattice__class_OSup__fin(_1133656, _1133658))))], (18848 ^ _780086) ^ [_1133842, _1133844, _1133846] : [class_Lattices_Olattice(_1133842), hBOOL(hAPP(c_Finite__Set_Ofinite(_1133842), _1133844)), -(c_Big__Operators_Olattice__class_OInf__fin(_1133842, hAPP(hAPP(c_Set_Oinsert(_1133842), _1133846), _1133844)) = hAPP(hAPP(c_Finite__Set_Ofold(_1133842, _1133842, c_Lattices_Osemilattice__inf__class_Oinf(_1133842)), _1133846), _1133844))], (18858 ^ _780086) ^ [_1134027, _1134029, _1134031, _1134033, _1134035] : [class_Complete__Lattice_Ocomplete__lattice(_1134027), hBOOL(hAPP(c_Finite__Set_Ofinite(_1134029), _1134031)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1134027), _1134033), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1134029, _1134027), _1134031), _1134035)) = hAPP(hAPP(c_Finite__Set_Ofold(_1134029, _1134027, hAPP(hAPP(c_COMBB(_1134027, tc_fun(_1134027, _1134027), _1134029), c_Lattices_Osemilattice__inf__class_Oinf(_1134027)), _1134035)), _1134033), _1134031))], (18868 ^ _780086) ^ [_1134258, _1134260, _1134262] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1134258), _1134260)), -(hAPP(c_Finite__Set_Ocard(_1134258), hAPP(hAPP(c_Set_Oinsert(_1134258), _1134262), _1134260)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1134258), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1134258, tc_HOL_Obool)), _1134260), hAPP(hAPP(c_Set_Oinsert(_1134258), _1134262), c_Orderings_Obot__class_Obot(tc_fun(_1134258, tc_HOL_Obool)))))))], (18874 ^ _780086) ^ [_1134435, _1134437, _1134439] : [class_Lattices_Olattice(_1134435), hBOOL(hAPP(c_Finite__Set_Ofinite(_1134435), _1134437)), -(hBOOL(hAPP(hAPP(c_member(_1134435), _1134439), _1134437))), -(_1134437 = c_Orderings_Obot__class_Obot(tc_fun(_1134435, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1134435, hAPP(hAPP(c_Set_Oinsert(_1134435), _1134439), _1134437)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1134435), _1134439), c_Big__Operators_Olattice__class_OInf__fin(_1134435, _1134437)))], (18892 ^ _780086) ^ [_1134672, _1134674, _1134676] : [class_Lattices_Olattice(_1134672), hBOOL(hAPP(c_Finite__Set_Ofinite(_1134672), _1134674)), 18899 ^ _780086 : [(18900 ^ _780086) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1134672, tc_HOL_Obool)), _1134674), hAPP(hAPP(c_Set_Oinsert(_1134672), _1134676), c_Orderings_Obot__class_Obot(tc_fun(_1134672, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1134672, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1134672, hAPP(hAPP(c_Set_Oinsert(_1134672), _1134676), _1134674)) = _1134676)], (18906 ^ _780086) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1134672, tc_HOL_Obool)), _1134674), hAPP(hAPP(c_Set_Oinsert(_1134672), _1134676), c_Orderings_Obot__class_Obot(tc_fun(_1134672, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1134672, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1134672, hAPP(hAPP(c_Set_Oinsert(_1134672), _1134676), _1134674)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1134672), _1134676), c_Big__Operators_Olattice__class_OInf__fin(_1134672, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1134672, tc_HOL_Obool)), _1134674), hAPP(hAPP(c_Set_Oinsert(_1134672), _1134676), c_Orderings_Obot__class_Obot(tc_fun(_1134672, tc_HOL_Obool)))))))]]], (18912 ^ _780086) ^ [_1135142, _1135144, _1135146] : [class_Lattices_Olattice(_1135142), hBOOL(hAPP(c_Finite__Set_Ofinite(_1135142), _1135144)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1135142), _1135146)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1135142, tc_HOL_Obool)), _1135144), _1135146) = c_Orderings_Obot__class_Obot(tc_fun(_1135142, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1135142), c_Big__Operators_Olattice__class_OInf__fin(_1135142, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1135142, tc_HOL_Obool)), _1135144), _1135146))), c_Big__Operators_Olattice__class_OInf__fin(_1135142, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1135142, tc_HOL_Obool)), _1135144), _1135146))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1135142), c_Big__Operators_Olattice__class_OInf__fin(_1135142, _1135144)), c_Big__Operators_Olattice__class_OInf__fin(_1135142, _1135146)))], (18930 ^ _780086) ^ [_1135490, _1135492, _1135494] : [class_Lattices_Olattice(_1135490), hBOOL(hAPP(c_Finite__Set_Ofinite(_1135490), _1135492)), -(_1135492 = c_Orderings_Obot__class_Obot(tc_fun(_1135490, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1135490), _1135494)), -(_1135494 = c_Orderings_Obot__class_Obot(tc_fun(_1135490, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1135490, tc_HOL_Obool)), _1135492), _1135494) = c_Orderings_Obot__class_Obot(tc_fun(_1135490, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1135490, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1135490, tc_HOL_Obool)), _1135492), _1135494)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1135490), c_Big__Operators_Olattice__class_OInf__fin(_1135490, _1135492)), c_Big__Operators_Olattice__class_OInf__fin(_1135490, _1135494)))], (18956 ^ _780086) ^ [_1135967, _1135969, _1135971] : [class_Lattices_Olattice(_1135967), hBOOL(hAPP(c_Finite__Set_Ofinite(_1135967), _1135969)), -(hBOOL(hAPP(hAPP(c_member(_1135967), _1135971), _1135969))), -(c_Big__Operators_Olattice__class_OInf__fin(_1135967, hAPP(hAPP(c_Set_Oinsert(_1135967), _1135971), _1135969)) = hAPP(hAPP(c_Finite__Set_Ofold(_1135967, _1135967, c_Lattices_Osemilattice__inf__class_Oinf(_1135967)), _1135971), _1135969))], (18970 ^ _780086) ^ [_1136181, _1136183] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1136181), hAPP(c_Nat_OSuc, _1136183)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1136181), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1136183))], (18972 ^ _780086) ^ [_1136227] : [-(hAPP(c_Nat_OSuc, _1136227) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1136227))], (18974 ^ _780086) ^ [_1136256] : [-(hAPP(c_Nat_OSuc, _1136256) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1136256), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (18976 ^ _780086) ^ [_1136288, _1136290] : [class_Lattices_Olattice(_1136288), hBOOL(hAPP(c_Finite__Set_Ofinite(_1136288), _1136290)), -(_1136290 = c_Orderings_Obot__class_Obot(tc_fun(_1136288, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1136288), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1136288), 18989 ^ [_1136288, _1136290]), 18990 ^ [_1136288, _1136290])), hAPP(hAPP(c_Set_Oinsert(_1136288), 18989 ^ [_1136288, _1136290]), hAPP(hAPP(c_Set_Oinsert(_1136288), 18990 ^ [_1136288, _1136290]), c_Orderings_Obot__class_Obot(tc_fun(_1136288, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1136288), c_Big__Operators_Olattice__class_OInf__fin(_1136288, _1136290)), _1136290)))], (18996 ^ _780086) ^ [_1136732, _1136734] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1136732, _1136734)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1136732, _1136734), tc_HOL_Obool)))), -(hAPP(c_Finite__Set_Ocard(_1136734), c_Orderings_Otop__class_Otop(tc_fun(_1136734, tc_HOL_Obool))) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1136732), c_Orderings_Otop__class_Otop(tc_fun(_1136732, tc_HOL_Obool)))))], (19006 ^ _780086) ^ [_1136892, _1136894, _1136896] : [class_Lattices_Olattice(_1136892), hAPP(_1136894, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1136892), 19011 ^ [_1136892, _1136894, _1136896]), 19012 ^ [_1136892, _1136894, _1136896])) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1136892), hAPP(_1136894, 19011 ^ [_1136892, _1136894, _1136896])), hAPP(_1136894, 19012 ^ [_1136892, _1136894, _1136896])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1136892), _1136896)), -(_1136896 = c_Orderings_Obot__class_Obot(tc_fun(_1136892, tc_HOL_Obool))), -(hAPP(_1136894, c_Big__Operators_Olattice__class_OInf__fin(_1136892, _1136896)) = c_Big__Operators_Olattice__class_OInf__fin(_1136892, hAPP(c_Set_Oimage(_1136892, _1136892, _1136894), _1136896)))], (19026 ^ _780086) ^ [_1137304] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1137304), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (19028 ^ _780086) ^ [_1137332] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1137332)))], (19030 ^ _780086) ^ [_1137357] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Nat_OSuc, _1137357))))], (19032 ^ _780086) ^ [_1137385, _1137387] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1137385, tc_HOL_Obool), _1137387) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1137385, tc_HOL_Obool), tc_fun(_1137385, tc_HOL_Obool)), _1137387), c_COMBI(tc_fun(_1137385, tc_HOL_Obool))))], (19034 ^ _780086) ^ [_1137436, _1137438, _1137440, _1137442] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1137436, tc_fun(_1137438, tc_HOL_Obool)), _1137440), _1137442) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1137438, tc_HOL_Obool), hAPP(c_Set_Oimage(_1137436, tc_fun(_1137438, tc_HOL_Obool), _1137442), _1137440)))], (19036 ^ _780086) ^ [_1137493, _1137495, _1137497, _1137499] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1137493, tc_HOL_Obool), hAPP(c_Set_Oimage(_1137495, tc_fun(_1137493, tc_HOL_Obool), _1137497), _1137499)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1137495, tc_fun(_1137493, tc_HOL_Obool)), _1137499), _1137497))], (19048 ^ _780086) ^ [_1137827, _1137829, _1137831, _1137833, _1137835, _1137837, _1137839] : [19050 ^ _780086 : [(19051 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1137827), 19049 ^ [_1137827, _1137829, _1137831, _1137833, _1137835, _1137837, _1137839]), _1137833)))], (19053 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1137835, 19049 ^ [_1137827, _1137829, _1137831, _1137833, _1137835, _1137837, _1137839]), _1137837), _1137839))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1137827, tc_fun(_1137829, tc_fun(_1137831, tc_HOL_Obool))), _1137833), _1137835), _1137837), _1137839)))], (19038 ^ _780086) ^ [_1137580, _1137582, _1137584, _1137586, _1137588, _1137590, _1137592] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1137580, tc_fun(_1137582, tc_fun(_1137584, tc_HOL_Obool))), _1137586), _1137588), _1137590), _1137592)), 19041 ^ _780086 : [(19042 ^ _780086) ^ [_1137708] : [hBOOL(hAPP(hAPP(c_member(_1137580), _1137708), _1137586)), -(hBOOL(hAPP(hAPP(hAPP(_1137588, _1137708), _1137590), _1137592)))]]], (19067 ^ _780086) ^ [_1138329, _1138331, _1138333, _1138335, _1138337] : [19069 ^ _780086 : [(19070 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1138329), 19068 ^ [_1138329, _1138331, _1138333, _1138335, _1138337]), _1138333)))], (19072 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(_1138335, 19068 ^ [_1138329, _1138331, _1138333, _1138335, _1138337]), _1138337))]], -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1138329, tc_fun(_1138331, tc_HOL_Obool)), _1138333), _1138335), _1138337)))], (19057 ^ _780086) ^ [_1138111, _1138113, _1138115, _1138117, _1138119] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1138111, tc_fun(_1138113, tc_HOL_Obool)), _1138115), _1138117), _1138119)), 19060 ^ _780086 : [(19061 ^ _780086) ^ [_1138220] : [hBOOL(hAPP(hAPP(c_member(_1138111), _1138220), _1138115)), -(hBOOL(hAPP(hAPP(_1138117, _1138220), _1138119)))]]], (19076 ^ _780086) ^ [_1138552, _1138554] : [class_Groups_Ozero(_1138552), 19079 ^ _780086 : [(19080 ^ _780086) ^ [] : [c_Groups_Ozero__class_Ozero(_1138552) = _1138554, -(_1138554 = c_Groups_Ozero__class_Ozero(_1138552))], (19086 ^ _780086) ^ [] : [_1138554 = c_Groups_Ozero__class_Ozero(_1138552), -(c_Groups_Ozero__class_Ozero(_1138552) = _1138554)]]], (19092 ^ _780086) ^ [] : [-(c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19094 ^ _780086) ^ [_1138787, _1138789, _1138791] : [class_Power_Opower(_1138787), class_Rings_Omult__zero(_1138787), class_Rings_Ono__zero__divisors(_1138787), class_Rings_Ozero__neq__one(_1138787), 19109 ^ _780086 : [(19110 ^ _780086) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1138787), _1138789), _1138791) = c_Groups_Ozero__class_Ozero(_1138787), 19113 ^ _780086 : [(19114 ^ _780086) ^ [] : [-(_1138789 = c_Groups_Ozero__class_Ozero(_1138787))], (19116 ^ _780086) ^ [] : [_1138791 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (19118 ^ _780086) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1138787), _1138789), _1138791) = c_Groups_Ozero__class_Ozero(_1138787)), _1138789 = c_Groups_Ozero__class_Ozero(_1138787), -(_1138791 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (19128 ^ _780086) ^ [_1139279, _1139281] : [class_Power_Opower(_1139279), class_Rings_Osemiring__0(_1139279), 19135 ^ _780086 : [(19136 ^ _780086) ^ [] : [_1139281 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1139279), c_Groups_Ozero__class_Ozero(_1139279)), _1139281) = c_Groups_Oone__class_Oone(_1139279))], (19142 ^ _780086) ^ [] : [-(_1139281 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1139279), c_Groups_Ozero__class_Ozero(_1139279)), _1139281) = c_Groups_Ozero__class_Ozero(_1139279))]]], (19148 ^ _780086) ^ [_1139553, _1139555] : [class_Groups_Omonoid__add(_1139553), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1139553), c_Groups_Ozero__class_Ozero(_1139553)), _1139555) = _1139555)], (19154 ^ _780086) ^ [_1139648, _1139650] : [class_Groups_Ocomm__monoid__add(_1139648), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1139648), c_Groups_Ozero__class_Ozero(_1139648)), _1139650) = _1139650)], (19160 ^ _780086) ^ [_1139743, _1139745] : [class_Groups_Olinordered__ab__group__add(_1139743), 19163 ^ _780086 : [(19164 ^ _780086) ^ [] : [c_Groups_Ozero__class_Ozero(_1139743) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1139743), _1139745), _1139745), -(_1139745 = c_Groups_Ozero__class_Ozero(_1139743))], (19170 ^ _780086) ^ [] : [_1139745 = c_Groups_Ozero__class_Ozero(_1139743), -(c_Groups_Ozero__class_Ozero(_1139743) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1139743), _1139745), _1139745))]]], (19176 ^ _780086) ^ [_1139984, _1139986] : [class_Groups_Omonoid__add(_1139984), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1139984), _1139986), c_Groups_Ozero__class_Ozero(_1139984)) = _1139986)], (19182 ^ _780086) ^ [_1140079, _1140081] : [class_Groups_Ocomm__monoid__add(_1140079), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1140079), _1140081), c_Groups_Ozero__class_Ozero(_1140079)) = _1140081)], (19188 ^ _780086) ^ [_1140174, _1140176] : [class_Rings_Ocomm__semiring__1(_1140174), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1140174), c_Groups_Ozero__class_Ozero(_1140174)), _1140176) = _1140176)], (19194 ^ _780086) ^ [_1140269, _1140271] : [class_Rings_Ocomm__semiring__1(_1140269), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1140269), _1140271), c_Groups_Ozero__class_Ozero(_1140269)) = _1140271)], (19200 ^ _780086) ^ [_1140364, _1140366, _1140368] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1140364), 19203 ^ _780086 : [(19204 ^ _780086) ^ [] : [_1140366 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1140364), _1140366), _1140368), -(_1140368 = c_Groups_Ozero__class_Ozero(_1140364))], (19210 ^ _780086) ^ [] : [_1140368 = c_Groups_Ozero__class_Ozero(_1140364), -(_1140366 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1140364), _1140366), _1140368))]]], (19216 ^ _780086) ^ [_1140605, _1140607] : [class_Rings_Omult__zero(_1140605), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140605), c_Groups_Ozero__class_Ozero(_1140605)), _1140607) = c_Groups_Ozero__class_Ozero(_1140605))], (19222 ^ _780086) ^ [_1140704, _1140706] : [class_Rings_Ocomm__semiring__1(_1140704), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140704), c_Groups_Ozero__class_Ozero(_1140704)), _1140706) = c_Groups_Ozero__class_Ozero(_1140704))], (19228 ^ _780086) ^ [_1140803, _1140805] : [class_Rings_Omult__zero(_1140803), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140803), _1140805), c_Groups_Ozero__class_Ozero(_1140803)) = c_Groups_Ozero__class_Ozero(_1140803))], (19234 ^ _780086) ^ [_1140902, _1140904] : [class_Rings_Ocomm__semiring__1(_1140902), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140902), _1140904), c_Groups_Ozero__class_Ozero(_1140902)) = c_Groups_Ozero__class_Ozero(_1140902))], (19240 ^ _780086) ^ [_1141001, _1141003, _1141005] : [class_Rings_Oring__no__zero__divisors(_1141001), 19243 ^ _780086 : [(19254 ^ _780086) ^ [] : [19255 ^ _780086 : [(19256 ^ _780086) ^ [] : [_1141003 = c_Groups_Ozero__class_Ozero(_1141001)], (19258 ^ _780086) ^ [] : [_1141005 = c_Groups_Ozero__class_Ozero(_1141001)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141001), _1141003), _1141005) = c_Groups_Ozero__class_Ozero(_1141001))], (19244 ^ _780086) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141001), _1141003), _1141005) = c_Groups_Ozero__class_Ozero(_1141001), -(_1141003 = c_Groups_Ozero__class_Ozero(_1141001)), -(_1141005 = c_Groups_Ozero__class_Ozero(_1141001))]]], (19262 ^ _780086) ^ [_1141299, _1141301, _1141303] : [class_Rings_Ono__zero__divisors(_1141299), -(_1141301 = c_Groups_Ozero__class_Ozero(_1141299)), -(_1141303 = c_Groups_Ozero__class_Ozero(_1141299)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141299), _1141301), _1141303) = c_Groups_Ozero__class_Ozero(_1141299)], (19276 ^ _780086) ^ [_1141519, _1141521, _1141523] : [class_Rings_Ono__zero__divisors(_1141519), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141519), _1141521), _1141523) = c_Groups_Ozero__class_Ozero(_1141519), -(_1141521 = c_Groups_Ozero__class_Ozero(_1141519)), -(_1141523 = c_Groups_Ozero__class_Ozero(_1141519))], (19290 ^ _780086) ^ [_1141691, _1141693] : [class_Groups_Ogroup__add(_1141691), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1141691), _1141693), c_Groups_Ozero__class_Ozero(_1141691)) = _1141693)], (19296 ^ _780086) ^ [_1141786, _1141788] : [class_Groups_Ogroup__add(_1141786), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1141786), _1141788), _1141788) = c_Groups_Ozero__class_Ozero(_1141786))], (19302 ^ _780086) ^ [_1141881, _1141883, _1141885] : [class_Groups_Oab__group__add(_1141881), 19305 ^ _780086 : [(19306 ^ _780086) ^ [] : [_1141883 = _1141885, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1141881), _1141883), _1141885) = c_Groups_Ozero__class_Ozero(_1141881))], (19312 ^ _780086) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1141881), _1141883), _1141885) = c_Groups_Ozero__class_Ozero(_1141881), -(_1141883 = _1141885)]]], (19318 ^ _780086) ^ [_1142122, _1142124, _1142126] : [class_Groups_Ogroup__add(_1142122), 19321 ^ _780086 : [(19322 ^ _780086) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1142122), _1142124), _1142126) = c_Groups_Ozero__class_Ozero(_1142122), -(_1142124 = _1142126)], (19328 ^ _780086) ^ [] : [_1142124 = _1142126, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1142122), _1142124), _1142126) = c_Groups_Ozero__class_Ozero(_1142122))]]], (19334 ^ _780086) ^ [_1142363] : [class_Rings_Ozero__neq__one(_1142363), c_Groups_Ozero__class_Ozero(_1142363) = c_Groups_Oone__class_Oone(_1142363)], (19340 ^ _780086) ^ [_1142445] : [class_Rings_Ozero__neq__one(_1142445), c_Groups_Oone__class_Oone(_1142445) = c_Groups_Ozero__class_Ozero(_1142445)], (19346 ^ _780086) ^ [_1142527, _1142529] : [class_Groups_Olinordered__ab__group__add(_1142527), 19349 ^ _780086 : [(19350 ^ _780086) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1142527), _1142529) = _1142529, -(_1142529 = c_Groups_Ozero__class_Ozero(_1142527))], (19356 ^ _780086) ^ [] : [_1142529 = c_Groups_Ozero__class_Ozero(_1142527), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1142527), _1142529) = _1142529)]]], (19362 ^ _780086) ^ [_1142753, _1142755] : [class_Groups_Ogroup__add(_1142753), 19365 ^ _780086 : [(19366 ^ _780086) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1142753), _1142755) = c_Groups_Ozero__class_Ozero(_1142753), -(_1142755 = c_Groups_Ozero__class_Ozero(_1142753))], (19372 ^ _780086) ^ [] : [_1142755 = c_Groups_Ozero__class_Ozero(_1142753), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1142753), _1142755) = c_Groups_Ozero__class_Ozero(_1142753))]]], (19378 ^ _780086) ^ [_1142985, _1142987] : [class_Groups_Olinordered__ab__group__add(_1142985), 19381 ^ _780086 : [(19382 ^ _780086) ^ [] : [_1142987 = hAPP(c_Groups_Ouminus__class_Ouminus(_1142985), _1142987), -(_1142987 = c_Groups_Ozero__class_Ozero(_1142985))], (19388 ^ _780086) ^ [] : [_1142987 = c_Groups_Ozero__class_Ozero(_1142985), -(_1142987 = hAPP(c_Groups_Ouminus__class_Ouminus(_1142985), _1142987))]]], (19394 ^ _780086) ^ [_1143211, _1143213] : [class_Groups_Ogroup__add(_1143211), 19397 ^ _780086 : [(19398 ^ _780086) ^ [] : [c_Groups_Ozero__class_Ozero(_1143211) = hAPP(c_Groups_Ouminus__class_Ouminus(_1143211), _1143213), -(c_Groups_Ozero__class_Ozero(_1143211) = _1143213)], (19404 ^ _780086) ^ [] : [c_Groups_Ozero__class_Ozero(_1143211) = _1143213, -(c_Groups_Ozero__class_Ozero(_1143211) = hAPP(c_Groups_Ouminus__class_Ouminus(_1143211), _1143213))]]], (19410 ^ _780086) ^ [_1143443] : [class_Groups_Ogroup__add(_1143443), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1143443), c_Groups_Ozero__class_Ozero(_1143443)) = c_Groups_Ozero__class_Ozero(_1143443))], (19416 ^ _780086) ^ [_1143543] : [hAPP(c_Nat_OSuc, _1143543) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (19418 ^ _780086) ^ [_1143578] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _1143578)], (19420 ^ _780086) ^ [_1143613] : [hAPP(c_Nat_OSuc, _1143613) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (19422 ^ _780086) ^ [_1143648] : [hAPP(c_Nat_OSuc, _1143648) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (19424 ^ _780086) ^ [_1143683] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _1143683)], (19426 ^ _780086) ^ [_1143718] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _1143718)], (19428 ^ _780086) ^ [_1143744] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1143744) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (19440 ^ _780086) ^ [_1143883, _1143885] : [19441 ^ _780086 : [(19442 ^ _780086) ^ [] : [_1143885 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (19444 ^ _780086) ^ [] : [_1143883 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1143883), _1143885) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (19430 ^ _780086) ^ [_1143785, _1143787] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1143785), _1143787) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1143787 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1143785 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (19448 ^ _780086) ^ [_1144012, _1144014, _1144016] : [class_Rings_Oring__1__no__zero__divisors(_1144012), -(_1144014 = c_Groups_Ozero__class_Ozero(_1144012)), hAPP(hAPP(c_Power_Opower__class_Opower(_1144012), _1144014), _1144016) = c_Groups_Ozero__class_Ozero(_1144012)], (19468 ^ _780086) ^ [_1144292, _1144294] : [19469 ^ _780086 : [(19470 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1144292))], (19472 ^ _780086) ^ [] : [_1144294 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hBOOL(hAPP(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), _1144292), _1144294))))], (19458 ^ _780086) ^ [_1144186, _1144188] : [hBOOL(hAPP(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), _1144186), _1144188))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1144186))), -(_1144188 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19476 ^ _780086) ^ [_1144429, _1144431, _1144433] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1144429)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1144429), _1144431)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1144429), _1144433))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1144431), _1144433)))], (19486 ^ _780086) ^ [_1144619] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1144619), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (19488 ^ _780086) ^ [_1144653] : [-(_1144653 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1144653)))], (19494 ^ _780086) ^ [_1144685] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1144685)), _1144685 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (19500 ^ _780086) ^ [_1144776] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1144776), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (19502 ^ _780086) ^ [_1144804, _1144806] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1144804), _1144806)), _1144806 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (19508 ^ _780086) ^ [_1144888] : [-(_1144888 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1144888)))], (19514 ^ _780086) ^ [_1144924, _1144926] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1144924), _1144926) = _1144924, -(_1144926 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19520 ^ _780086) ^ [_1145028, _1145030] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1145028), _1145030) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 19523 ^ _780086 : [(19524 ^ _780086) ^ [] : [-(_1145028 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19526 ^ _780086) ^ [] : [-(_1145030 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (19528 ^ _780086) ^ [_1145139, _1145141] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1145139), _1145141) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1145139 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1145141 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (19538 ^ _780086) ^ [_1145282] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1145282), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1145282)], (19540 ^ _780086) ^ [_1145311] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1145311) = _1145311)], (19542 ^ _780086) ^ [_1145337] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1145337)))], (19544 ^ _780086) ^ [_1145374] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1145374), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_1145374 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19550 ^ _780086) ^ [_1145455] : [_1145455 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1145455), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (19556 ^ _780086) ^ [_1145542] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1145542) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19558 ^ _780086) ^ [_1145568] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1145568), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1145568)], (19560 ^ _780086) ^ [_1145597] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1145597), _1145597) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19562 ^ _780086) ^ [_1145626, _1145628] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1145626), _1145628) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1145628), _1145626) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1145626 = _1145628)], (19582 ^ _780086) ^ [_1145909, _1145911, _1145913] : [19583 ^ _780086 : [(19584 ^ _780086) ^ [] : [_1145909 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (19586 ^ _780086) ^ [] : [_1145911 = _1145913]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1145909), _1145911) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1145909), _1145913))], (19572 ^ _780086) ^ [_1145797, _1145799, _1145801] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1145797), _1145799) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1145797), _1145801), -(_1145797 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1145799 = _1145801)], (19590 ^ _780086) ^ [_1146052] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1146052) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19592 ^ _780086) ^ [_1146078] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146078), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19604 ^ _780086) ^ [_1146220, _1146222] : [19605 ^ _780086 : [(19606 ^ _780086) ^ [] : [_1146220 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (19608 ^ _780086) ^ [] : [_1146222 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146220), _1146222) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19594 ^ _780086) ^ [_1146122, _1146124] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146122), _1146124) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1146122 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1146124 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19622 ^ _780086) ^ [_1146479, _1146481, _1146483] : [19623 ^ _780086 : [(19624 ^ _780086) ^ [] : [_1146481 = _1146483], (19626 ^ _780086) ^ [] : [_1146479 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146479), _1146481) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146479), _1146483))], (19612 ^ _780086) ^ [_1146367, _1146369, _1146371] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146367), _1146369) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146367), _1146371), -(_1146369 = _1146371), -(_1146367 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19640 ^ _780086) ^ [_1146752, _1146754, _1146756] : [19641 ^ _780086 : [(19642 ^ _780086) ^ [] : [_1146752 = _1146756], (19644 ^ _780086) ^ [] : [_1146754 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146752), _1146754) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146756), _1146754))], (19630 ^ _780086) ^ [_1146640, _1146642, _1146644] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146640), _1146642) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146644), _1146642), -(_1146640 = _1146644), -(_1146642 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19648 ^ _780086) ^ [_1146895, _1146897, _1146899] : [class_Rings_Olinordered__ring__strict(_1146895), 19651 ^ _780086 : [(19652 ^ _780086) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1146895), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146895), _1146897), _1146897)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146895), _1146899), _1146899)) = c_Groups_Ozero__class_Ozero(_1146895), 19655 ^ _780086 : [(19656 ^ _780086) ^ [] : [-(_1146897 = c_Groups_Ozero__class_Ozero(_1146895))], (19658 ^ _780086) ^ [] : [-(_1146899 = c_Groups_Ozero__class_Ozero(_1146895))]]], (19660 ^ _780086) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1146895), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146895), _1146897), _1146897)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146895), _1146899), _1146899)) = c_Groups_Ozero__class_Ozero(_1146895)), _1146897 = c_Groups_Ozero__class_Ozero(_1146895), _1146899 = c_Groups_Ozero__class_Ozero(_1146895)]]], (19670 ^ _780086) ^ [_1147270] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1147270) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19672 ^ _780086) ^ [_1147296] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1147296), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19674 ^ _780086) ^ [_1147325] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1147325) = _1147325)], (19676 ^ _780086) ^ [_1147351] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1147351), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1147351)], (19678 ^ _780086) ^ [_1147380, _1147382, _1147384, _1147386] : [class_Rings_Olinordered__semidom(_1147380), hAPP(hAPP(c_Power_Opower__class_Opower(_1147380), _1147382), _1147384) = hAPP(hAPP(c_Power_Opower__class_Opower(_1147380), _1147386), _1147384), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147380), c_Groups_Ozero__class_Ozero(_1147380)), _1147382)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147380), c_Groups_Ozero__class_Ozero(_1147380)), _1147386)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1147384)), -(_1147382 = _1147386)], (19700 ^ _780086) ^ [_1147755, _1147757, _1147759] : [class_Groups_Ocomm__monoid__add(_1147755), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1147757, _1147755), hAPP(c_COMBK(_1147755, _1147757), c_Groups_Ozero__class_Ozero(_1147755))), _1147759) = c_Groups_Ozero__class_Ozero(_1147755))], (19706 ^ _780086) ^ [_1147870, _1147872, _1147874, _1147876] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1147870, _1147872, _1147874), _1147876), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1147872)], (19708 ^ _780086) ^ [_1147909, _1147911, _1147913, _1147915] : [class_Rings_Olinordered__semidom(_1147909), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147909), _1147911), _1147913)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147909), c_Groups_Ozero__class_Ozero(_1147909)), _1147911)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1147915)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147909), hAPP(hAPP(c_Power_Opower__class_Opower(_1147909), _1147911), _1147915)), hAPP(hAPP(c_Power_Opower__class_Opower(_1147909), _1147913), _1147915))))], (19726 ^ _780086) ^ [_1148238, _1148240, _1148242] : [class_Rings_Olinordered__ring__strict(_1148238), 19729 ^ _780086 : [(19730 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1148238), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1148238), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148238), _1148240), _1148240)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148238), _1148242), _1148242))), c_Groups_Ozero__class_Ozero(_1148238))), 19733 ^ _780086 : [(19734 ^ _780086) ^ [] : [-(_1148240 = c_Groups_Ozero__class_Ozero(_1148238))], (19736 ^ _780086) ^ [] : [-(_1148242 = c_Groups_Ozero__class_Ozero(_1148238))]]], (19738 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1148238), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1148238), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148238), _1148240), _1148240)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148238), _1148242), _1148242))), c_Groups_Ozero__class_Ozero(_1148238)))), _1148240 = c_Groups_Ozero__class_Ozero(_1148238), _1148242 = c_Groups_Ozero__class_Ozero(_1148238)]]], (19748 ^ _780086) ^ [_1148634, _1148636, _1148638] : [class_Rings_Olinordered__ring(_1148634), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1148634), c_Groups_Ozero__class_Ozero(_1148634)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1148634), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148634), _1148636), _1148636)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148634), _1148638), _1148638)))))], (19754 ^ _780086) ^ [_1148777, _1148779, _1148781] : [class_Rings_Olinordered__ring__strict(_1148777), 19757 ^ _780086 : [(19768 ^ _780086) ^ [] : [19769 ^ _780086 : [(19770 ^ _780086) ^ [] : [-(_1148779 = c_Groups_Ozero__class_Ozero(_1148777))], (19772 ^ _780086) ^ [] : [-(_1148781 = c_Groups_Ozero__class_Ozero(_1148777))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148777), c_Groups_Ozero__class_Ozero(_1148777)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1148777), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148777), _1148779), _1148779)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148777), _1148781), _1148781)))))], (19758 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148777), c_Groups_Ozero__class_Ozero(_1148777)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1148777), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148777), _1148779), _1148779)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148777), _1148781), _1148781)))), _1148779 = c_Groups_Ozero__class_Ozero(_1148777), _1148781 = c_Groups_Ozero__class_Ozero(_1148777)]]], (19776 ^ _780086) ^ [_1149152, _1149154, _1149156] : [class_Rings_Olinordered__ring(_1149152), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149152), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1149152), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149152), _1149154), _1149154)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149152), _1149156), _1149156))), c_Groups_Ozero__class_Ozero(_1149152)))], (19782 ^ _780086) ^ [_1149296, _1149298, _1149300] : [class_Groups_Oordered__comm__monoid__add(_1149296), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149296), _1149298), c_Groups_Ozero__class_Ozero(_1149296))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149296), _1149300), c_Groups_Ozero__class_Ozero(_1149296))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149296), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1149296), _1149298), _1149300)), c_Groups_Ozero__class_Ozero(_1149296))))], (19796 ^ _780086) ^ [_1149551, _1149553, _1149555, _1149557] : [class_Groups_Oordered__comm__monoid__add(_1149551), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149551), c_Groups_Ozero__class_Ozero(_1149551)), _1149553)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149551), _1149555), _1149557)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149551), _1149555), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1149551), _1149557), _1149553))))], (19810 ^ _780086) ^ [_1149804, _1149806, _1149808, _1149810] : [class_Groups_Oordered__comm__monoid__add(_1149804), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149804), c_Groups_Ozero__class_Ozero(_1149804)), _1149806)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149804), _1149808), _1149810)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149804), _1149808), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1149804), _1149806), _1149810))))], (19824 ^ _780086) ^ [_1150057, _1150059, _1150061] : [class_Groups_Oordered__comm__monoid__add(_1150057), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150057), c_Groups_Ozero__class_Ozero(_1150057)), _1150059)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150057), c_Groups_Ozero__class_Ozero(_1150057)), _1150061)), 19835 ^ _780086 : [(19836 ^ _780086) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1150057), _1150059), _1150061) = c_Groups_Ozero__class_Ozero(_1150057), 19839 ^ _780086 : [(19840 ^ _780086) ^ [] : [-(_1150059 = c_Groups_Ozero__class_Ozero(_1150057))], (19842 ^ _780086) ^ [] : [-(_1150061 = c_Groups_Ozero__class_Ozero(_1150057))]]], (19844 ^ _780086) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1150057), _1150059), _1150061) = c_Groups_Ozero__class_Ozero(_1150057)), _1150059 = c_Groups_Ozero__class_Ozero(_1150057), _1150061 = c_Groups_Ozero__class_Ozero(_1150057)]]], (19854 ^ _780086) ^ [_1150528, _1150530, _1150532] : [class_Groups_Oordered__comm__monoid__add(_1150528), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150528), c_Groups_Ozero__class_Ozero(_1150528)), _1150530)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150528), c_Groups_Ozero__class_Ozero(_1150528)), _1150532)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150528), c_Groups_Ozero__class_Ozero(_1150528)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1150528), _1150530), _1150532))))], (19868 ^ _780086) ^ [_1150783, _1150785] : [class_Groups_Olinordered__ab__group__add(_1150783), 19871 ^ _780086 : [(19872 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150783), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1150783), _1150785), _1150785)), c_Groups_Ozero__class_Ozero(_1150783))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150783), _1150785), c_Groups_Ozero__class_Ozero(_1150783))))], (19878 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150783), _1150785), c_Groups_Ozero__class_Ozero(_1150783))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150783), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1150783), _1150785), _1150785)), c_Groups_Ozero__class_Ozero(_1150783))))]]], (19884 ^ _780086) ^ [_1151066, _1151068] : [class_Groups_Olinordered__ab__group__add(_1151066), 19887 ^ _780086 : [(19888 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151066), c_Groups_Ozero__class_Ozero(_1151066)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1151066), _1151068), _1151068))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151066), c_Groups_Ozero__class_Ozero(_1151066)), _1151068)))], (19894 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151066), c_Groups_Ozero__class_Ozero(_1151066)), _1151068)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151066), c_Groups_Ozero__class_Ozero(_1151066)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1151066), _1151068), _1151068))))]]], (19900 ^ _780086) ^ [_1151349, _1151351] : [class_Rings_Olinordered__ring(_1151349), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151349), c_Groups_Ozero__class_Ozero(_1151349)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151349), _1151351), _1151351))))], (19906 ^ _780086) ^ [_1151458, _1151460, _1151462] : [class_Rings_Olinordered__ring__strict(_1151458), 19909 ^ _780086 : [(19910 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151458), c_Groups_Ozero__class_Ozero(_1151458)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151458), _1151460), _1151462))), 19915 ^ _780086 : [(19916 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151458), c_Groups_Ozero__class_Ozero(_1151458)), _1151460)))], (19918 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151458), c_Groups_Ozero__class_Ozero(_1151458)), _1151462)))]], 19919 ^ _780086 : [(19920 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151458), _1151460), c_Groups_Ozero__class_Ozero(_1151458))))], (19922 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151458), _1151462), c_Groups_Ozero__class_Ozero(_1151458))))]]], (19924 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151458), c_Groups_Ozero__class_Ozero(_1151458)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151458), _1151460), _1151462)))), 19925 ^ _780086 : [(19926 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151458), c_Groups_Ozero__class_Ozero(_1151458)), _1151460)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151458), c_Groups_Ozero__class_Ozero(_1151458)), _1151462))], (19932 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151458), _1151460), c_Groups_Ozero__class_Ozero(_1151458))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151458), _1151462), c_Groups_Ozero__class_Ozero(_1151458)))]]]]], (19940 ^ _780086) ^ [_1152048, _1152050, _1152052] : [class_Rings_Olinordered__ring__strict(_1152048), 19943 ^ _780086 : [(19944 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152048), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152048), _1152050), _1152052)), c_Groups_Ozero__class_Ozero(_1152048))), 19949 ^ _780086 : [(19950 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152048), c_Groups_Ozero__class_Ozero(_1152048)), _1152050)))], (19952 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152048), _1152052), c_Groups_Ozero__class_Ozero(_1152048))))]], 19953 ^ _780086 : [(19954 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152048), _1152050), c_Groups_Ozero__class_Ozero(_1152048))))], (19956 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152048), c_Groups_Ozero__class_Ozero(_1152048)), _1152052)))]]], (19958 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152048), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152048), _1152050), _1152052)), c_Groups_Ozero__class_Ozero(_1152048)))), 19959 ^ _780086 : [(19960 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152048), c_Groups_Ozero__class_Ozero(_1152048)), _1152050)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152048), _1152052), c_Groups_Ozero__class_Ozero(_1152048)))], (19966 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152048), _1152050), c_Groups_Ozero__class_Ozero(_1152048))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152048), c_Groups_Ozero__class_Ozero(_1152048)), _1152052))]]]]], (19974 ^ _780086) ^ [_1152638, _1152640, _1152642] : [class_Rings_Oordered__cancel__semiring(_1152638), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152638), c_Groups_Ozero__class_Ozero(_1152638)), _1152640)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152638), c_Groups_Ozero__class_Ozero(_1152638)), _1152642)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152638), c_Groups_Ozero__class_Ozero(_1152638)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152638), _1152640), _1152642))))], (19988 ^ _780086) ^ [_1152893, _1152895, _1152897] : [class_Rings_Oordered__cancel__semiring(_1152893), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152893), c_Groups_Ozero__class_Ozero(_1152893)), _1152895)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152893), _1152897), c_Groups_Ozero__class_Ozero(_1152893))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152893), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152893), _1152895), _1152897)), c_Groups_Ozero__class_Ozero(_1152893))))], (20002 ^ _780086) ^ [_1153148, _1153150, _1153152] : [class_Rings_Oordered__cancel__semiring(_1153148), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153148), c_Groups_Ozero__class_Ozero(_1153148)), _1153150)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153148), _1153152), c_Groups_Ozero__class_Ozero(_1153148))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153148), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153148), _1153152), _1153150)), c_Groups_Ozero__class_Ozero(_1153148))))], (20016 ^ _780086) ^ [_1153403, _1153405, _1153407] : [class_Rings_Oordered__cancel__semiring(_1153403), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153403), _1153405), c_Groups_Ozero__class_Ozero(_1153403))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153403), c_Groups_Ozero__class_Ozero(_1153403)), _1153407)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153403), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153403), _1153405), _1153407)), c_Groups_Ozero__class_Ozero(_1153403))))], (20030 ^ _780086) ^ [_1153658, _1153660, _1153662] : [class_Rings_Oordered__ring(_1153658), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153658), _1153660), c_Groups_Ozero__class_Ozero(_1153658))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153658), _1153662), c_Groups_Ozero__class_Ozero(_1153658))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153658), c_Groups_Ozero__class_Ozero(_1153658)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153658), _1153660), _1153662))))], (20044 ^ _780086) ^ [_1153913, _1153915, _1153917, _1153919] : [class_Rings_Oordered__semiring(_1153913), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153913), _1153915), _1153917)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153913), c_Groups_Ozero__class_Ozero(_1153913)), _1153919)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153913), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153913), _1153915), _1153919)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153913), _1153917), _1153919))))], (20058 ^ _780086) ^ [_1154182, _1154184, _1154186, _1154188] : [class_Rings_Oordered__semiring(_1154182), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154182), _1154184), _1154186)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154182), c_Groups_Ozero__class_Ozero(_1154182)), _1154188)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154182), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154182), _1154188), _1154184)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154182), _1154188), _1154186))))], (20072 ^ _780086) ^ [_1154451, _1154453, _1154455, _1154457] : [class_Rings_Oordered__comm__semiring(_1154451), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154451), _1154453), _1154455)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154451), c_Groups_Ozero__class_Ozero(_1154451)), _1154457)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154451), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154451), _1154457), _1154453)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154451), _1154457), _1154455))))], (20086 ^ _780086) ^ [_1154720, _1154722, _1154724, _1154726] : [class_Rings_Oordered__ring(_1154720), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154720), _1154722), _1154724)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154720), _1154726), c_Groups_Ozero__class_Ozero(_1154720))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154720), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154720), _1154724), _1154726)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154720), _1154722), _1154726))))], (20100 ^ _780086) ^ [_1154989, _1154991, _1154993, _1154995] : [class_Rings_Oordered__ring(_1154989), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154989), _1154991), _1154993)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154989), _1154995), c_Groups_Ozero__class_Ozero(_1154989))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154989), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154989), _1154995), _1154993)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154989), _1154995), _1154991))))], (20114 ^ _780086) ^ [_1155258, _1155260, _1155262, _1155264, _1155266] : [class_Rings_Oordered__semiring(_1155258), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155258), _1155260), _1155262)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155258), _1155264), _1155266)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155258), c_Groups_Ozero__class_Ozero(_1155258)), _1155260)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155258), c_Groups_Ozero__class_Ozero(_1155258)), _1155264)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155258), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155258), _1155260), _1155264)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155258), _1155262), _1155266))))], (20136 ^ _780086) ^ [_1155681, _1155683, _1155685, _1155687, _1155689] : [class_Rings_Oordered__semiring(_1155681), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155681), _1155683), _1155685)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155681), _1155687), _1155689)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155681), c_Groups_Ozero__class_Ozero(_1155681)), _1155685)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155681), c_Groups_Ozero__class_Ozero(_1155681)), _1155687)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155681), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155681), _1155683), _1155687)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155681), _1155685), _1155689))))], (20158 ^ _780086) ^ [_1156104, _1156106, _1156108] : [class_Rings_Oordered__ring(_1156104), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156104), c_Groups_Ozero__class_Ozero(_1156104)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156104), _1156106), _1156108)))), 20163 ^ _780086 : [(20164 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156104), c_Groups_Ozero__class_Ozero(_1156104)), _1156106)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156104), c_Groups_Ozero__class_Ozero(_1156104)), _1156108))], (20170 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156104), _1156106), c_Groups_Ozero__class_Ozero(_1156104))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156104), _1156108), c_Groups_Ozero__class_Ozero(_1156104)))]]], (20178 ^ _780086) ^ [_1156480, _1156482, _1156484] : [class_Rings_Oordered__cancel__semiring(_1156480), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156480), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156480), _1156482), _1156484)), c_Groups_Ozero__class_Ozero(_1156480)))), 20183 ^ _780086 : [(20184 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156480), c_Groups_Ozero__class_Ozero(_1156480)), _1156482)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156480), _1156484), c_Groups_Ozero__class_Ozero(_1156480)))], (20190 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156480), _1156482), c_Groups_Ozero__class_Ozero(_1156480))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156480), c_Groups_Ozero__class_Ozero(_1156480)), _1156484))]]], (20198 ^ _780086) ^ [_1156856, _1156858] : [class_Groups_Olinordered__ab__group__add(_1156856), 20201 ^ _780086 : [(20202 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156856), c_Groups_Ozero__class_Ozero(_1156856)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1156856), _1156858), _1156858))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156856), c_Groups_Ozero__class_Ozero(_1156856)), _1156858)))], (20208 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156856), c_Groups_Ozero__class_Ozero(_1156856)), _1156858)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156856), c_Groups_Ozero__class_Ozero(_1156856)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1156856), _1156858), _1156858))))]]], (20214 ^ _780086) ^ [_1157139, _1157141] : [class_Groups_Olinordered__ab__group__add(_1157139), 20217 ^ _780086 : [(20218 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157139), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1157139), _1157141), _1157141)), c_Groups_Ozero__class_Ozero(_1157139))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157139), _1157141), c_Groups_Ozero__class_Ozero(_1157139))))], (20224 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157139), _1157141), c_Groups_Ozero__class_Ozero(_1157139))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157139), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1157139), _1157141), _1157141)), c_Groups_Ozero__class_Ozero(_1157139))))]]], (20230 ^ _780086) ^ [_1157422, _1157424, _1157426] : [class_Groups_Oordered__comm__monoid__add(_1157422), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157422), c_Groups_Ozero__class_Ozero(_1157422)), _1157424)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157422), c_Groups_Ozero__class_Ozero(_1157422)), _1157426)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157422), c_Groups_Ozero__class_Ozero(_1157422)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1157422), _1157424), _1157426))))], (20244 ^ _780086) ^ [_1157677, _1157679, _1157681] : [class_Groups_Oordered__comm__monoid__add(_1157677), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157677), _1157679), c_Groups_Ozero__class_Ozero(_1157677))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157677), _1157681), c_Groups_Ozero__class_Ozero(_1157677))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157677), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1157677), _1157679), _1157681)), c_Groups_Ozero__class_Ozero(_1157677))))], (20258 ^ _780086) ^ [_1157932, _1157934, _1157936, _1157938] : [class_Rings_Olinordered__semidom(_1157932), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157932), c_Groups_Ozero__class_Ozero(_1157932)), _1157934)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157932), _1157936), _1157938)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157932), _1157936), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1157932), _1157934), _1157938))))], (20272 ^ _780086) ^ [_1158185, _1158187] : [class_Rings_Olinordered__ring(_1158185), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158185), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158185), _1158187), _1158187)), c_Groups_Ozero__class_Ozero(_1158185)))], (20278 ^ _780086) ^ [_1158295, _1158297, _1158299, _1158301] : [class_Rings_Olinordered__ring__strict(_1158295), 20281 ^ _780086 : [(20282 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158295), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158295), _1158297), _1158299)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158295), _1158301), _1158299))), 20287 ^ _780086 : [(20288 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158295), c_Groups_Ozero__class_Ozero(_1158295)), _1158299)))], (20290 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158295), _1158297), _1158301)))]], 20291 ^ _780086 : [(20292 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158295), _1158299), c_Groups_Ozero__class_Ozero(_1158295))))], (20294 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158295), _1158301), _1158297)))]]], (20296 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158295), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158295), _1158297), _1158299)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158295), _1158301), _1158299)))), 20297 ^ _780086 : [(20298 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158295), c_Groups_Ozero__class_Ozero(_1158295)), _1158299)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158295), _1158297), _1158301))], (20304 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158295), _1158299), c_Groups_Ozero__class_Ozero(_1158295))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158295), _1158301), _1158297))]]]]], (20312 ^ _780086) ^ [_1158901, _1158903, _1158905, _1158907] : [class_Rings_Olinordered__ring__strict(_1158901), 20315 ^ _780086 : [(20316 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158901), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158901), _1158903), _1158905)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158901), _1158903), _1158907))), 20321 ^ _780086 : [(20322 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158901), c_Groups_Ozero__class_Ozero(_1158901)), _1158903)))], (20324 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158901), _1158905), _1158907)))]], 20325 ^ _780086 : [(20326 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158901), _1158903), c_Groups_Ozero__class_Ozero(_1158901))))], (20328 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158901), _1158907), _1158905)))]]], (20330 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158901), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158901), _1158903), _1158905)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158901), _1158903), _1158907)))), 20331 ^ _780086 : [(20332 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158901), c_Groups_Ozero__class_Ozero(_1158901)), _1158903)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158901), _1158905), _1158907))], (20338 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158901), _1158903), c_Groups_Ozero__class_Ozero(_1158901))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158901), _1158907), _1158905))]]]]], (20346 ^ _780086) ^ [_1159507, _1159509, _1159511, _1159513] : [class_Rings_Olinordered__ring__strict(_1159507), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159507), c_Groups_Ozero__class_Ozero(_1159507)), _1159509)), 20353 ^ _780086 : [(20354 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159507), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159507), _1159509), _1159511)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159507), _1159509), _1159513))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159507), _1159511), _1159513)))], (20360 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159507), _1159511), _1159513)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159507), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159507), _1159509), _1159511)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159507), _1159509), _1159513))))]]], (20366 ^ _780086) ^ [_1159888, _1159890, _1159892] : [class_Rings_Olinordered__semiring__strict(_1159888), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159888), c_Groups_Ozero__class_Ozero(_1159888)), _1159890)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159888), c_Groups_Ozero__class_Ozero(_1159888)), _1159892)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159888), c_Groups_Ozero__class_Ozero(_1159888)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159888), _1159890), _1159892))))], (20380 ^ _780086) ^ [_1160143, _1160145, _1160147] : [class_Rings_Olinordered__semiring__strict(_1160143), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160143), c_Groups_Ozero__class_Ozero(_1160143)), _1160145)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160143), _1160147), c_Groups_Ozero__class_Ozero(_1160143))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160143), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160143), _1160145), _1160147)), c_Groups_Ozero__class_Ozero(_1160143))))], (20394 ^ _780086) ^ [_1160398, _1160400, _1160402] : [class_Rings_Olinordered__semiring__strict(_1160398), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160398), c_Groups_Ozero__class_Ozero(_1160398)), _1160400)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160398), _1160402), c_Groups_Ozero__class_Ozero(_1160398))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160398), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160398), _1160402), _1160400)), c_Groups_Ozero__class_Ozero(_1160398))))], (20408 ^ _780086) ^ [_1160653, _1160655, _1160657] : [class_Rings_Olinordered__semiring__strict(_1160653), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160653), c_Groups_Ozero__class_Ozero(_1160653)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160653), _1160655), _1160657))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160653), c_Groups_Ozero__class_Ozero(_1160653)), _1160655)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160653), c_Groups_Ozero__class_Ozero(_1160653)), _1160657)))], (20422 ^ _780086) ^ [_1160908, _1160910, _1160912] : [class_Rings_Olinordered__semiring__strict(_1160908), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160908), c_Groups_Ozero__class_Ozero(_1160908)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160908), _1160910), _1160912))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160908), c_Groups_Ozero__class_Ozero(_1160908)), _1160912)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160908), c_Groups_Ozero__class_Ozero(_1160908)), _1160910)))], (20436 ^ _780086) ^ [_1161163, _1161165, _1161167, _1161169] : [class_Rings_Olinordered__ring__strict(_1161163), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161163), _1161165), c_Groups_Ozero__class_Ozero(_1161163))), 20443 ^ _780086 : [(20444 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161163), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161163), _1161165), _1161167)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161163), _1161165), _1161169))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161163), _1161169), _1161167)))], (20450 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161163), _1161169), _1161167)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161163), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161163), _1161165), _1161167)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161163), _1161165), _1161169))))]]], (20456 ^ _780086) ^ [_1161544, _1161546, _1161548] : [class_Rings_Olinordered__semiring__strict(_1161544), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161544), _1161546), c_Groups_Ozero__class_Ozero(_1161544))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161544), c_Groups_Ozero__class_Ozero(_1161544)), _1161548)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161544), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161544), _1161546), _1161548)), c_Groups_Ozero__class_Ozero(_1161544))))], (20470 ^ _780086) ^ [_1161799, _1161801, _1161803] : [class_Rings_Olinordered__ring__strict(_1161799), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161799), _1161801), c_Groups_Ozero__class_Ozero(_1161799))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161799), _1161803), c_Groups_Ozero__class_Ozero(_1161799))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161799), c_Groups_Ozero__class_Ozero(_1161799)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161799), _1161801), _1161803))))], (20484 ^ _780086) ^ [_1162054, _1162056, _1162058, _1162060] : [class_Rings_Olinordered__semiring__strict(_1162054), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162054), _1162056), _1162058)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162054), c_Groups_Ozero__class_Ozero(_1162054)), _1162060)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162054), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162054), _1162056), _1162060)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162054), _1162058), _1162060))))], (20498 ^ _780086) ^ [_1162323, _1162325, _1162327, _1162329] : [class_Rings_Olinordered__semiring__strict(_1162323), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162323), _1162325), _1162327)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162323), c_Groups_Ozero__class_Ozero(_1162323)), _1162329)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162323), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162323), _1162329), _1162325)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162323), _1162329), _1162327))))], (20512 ^ _780086) ^ [_1162592, _1162594, _1162596, _1162598] : [class_Rings_Olinordered__comm__semiring__strict(_1162592), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162592), _1162594), _1162596)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162592), c_Groups_Ozero__class_Ozero(_1162592)), _1162598)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162592), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162592), _1162598), _1162594)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162592), _1162598), _1162596))))], (20526 ^ _780086) ^ [_1162861, _1162863, _1162865, _1162867] : [class_Rings_Olinordered__ring__strict(_1162861), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162861), _1162863), _1162865)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162861), _1162867), c_Groups_Ozero__class_Ozero(_1162861))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162861), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162861), _1162865), _1162867)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162861), _1162863), _1162867))))], (20540 ^ _780086) ^ [_1163130, _1163132, _1163134, _1163136] : [class_Rings_Olinordered__ring__strict(_1163130), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163130), _1163132), _1163134)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163130), _1163136), c_Groups_Ozero__class_Ozero(_1163130))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163130), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163130), _1163136), _1163134)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163130), _1163136), _1163132))))], (20554 ^ _780086) ^ [_1163399, _1163401, _1163403] : [class_Groups_Oordered__ab__group__add(_1163399), 20557 ^ _780086 : [(20558 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163399), _1163401), _1163403)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163399), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1163399), _1163401), _1163403)), c_Groups_Ozero__class_Ozero(_1163399))))], (20564 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163399), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1163399), _1163401), _1163403)), c_Groups_Ozero__class_Ozero(_1163399))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163399), _1163401), _1163403)))]]], (20570 ^ _780086) ^ [_1163682, _1163684, _1163686] : [class_Groups_Oordered__ab__group__add(_1163682), 20573 ^ _780086 : [(20574 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163682), _1163684), _1163686)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163682), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1163682), _1163684), _1163686)), c_Groups_Ozero__class_Ozero(_1163682))))], (20580 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163682), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1163682), _1163684), _1163686)), c_Groups_Ozero__class_Ozero(_1163682))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163682), _1163684), _1163686)))]]], (20586 ^ _780086) ^ [_1163965, _1163967, _1163969, _1163971, _1163973, _1163975] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1163965), -(_1163967 = c_Groups_Ozero__class_Ozero(_1163965)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1163965), _1163969), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163965), _1163967), _1163973)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1163965), _1163971), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163965), _1163967), _1163975)), _1163969 = _1163971, -(_1163973 = _1163975)], (20604 ^ _780086) ^ [_1164303] : [class_Rings_Olinordered__semidom(_1164303), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164303), c_Groups_Ozero__class_Ozero(_1164303)), c_Groups_Oone__class_Oone(_1164303))))], (20610 ^ _780086) ^ [_1164398] : [class_Rings_Olinordered__semidom(_1164398), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164398), c_Groups_Oone__class_Oone(_1164398)), c_Groups_Ozero__class_Ozero(_1164398)))], (20616 ^ _780086) ^ [_1164494] : [class_Rings_Olinordered__semidom(_1164494), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164494), c_Groups_Ozero__class_Ozero(_1164494)), c_Groups_Oone__class_Oone(_1164494))))], (20622 ^ _780086) ^ [_1164589] : [class_Rings_Olinordered__semidom(_1164589), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164589), c_Groups_Oone__class_Oone(_1164589)), c_Groups_Ozero__class_Ozero(_1164589)))], (20628 ^ _780086) ^ [_1164685, _1164687] : [class_Groups_Oordered__ab__group__add(_1164685), 20631 ^ _780086 : [(20632 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164685), c_Groups_Ozero__class_Ozero(_1164685)), hAPP(c_Groups_Ouminus__class_Ouminus(_1164685), _1164687))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164685), _1164687), c_Groups_Ozero__class_Ozero(_1164685))))], (20638 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164685), _1164687), c_Groups_Ozero__class_Ozero(_1164685))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164685), c_Groups_Ozero__class_Ozero(_1164685)), hAPP(c_Groups_Ouminus__class_Ouminus(_1164685), _1164687))))]]], (20644 ^ _780086) ^ [_1164959, _1164961] : [class_Groups_Olinordered__ab__group__add(_1164959), 20647 ^ _780086 : [(20648 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164959), _1164961), hAPP(c_Groups_Ouminus__class_Ouminus(_1164959), _1164961))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164959), _1164961), c_Groups_Ozero__class_Ozero(_1164959))))], (20654 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164959), _1164961), c_Groups_Ozero__class_Ozero(_1164959))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164959), _1164961), hAPP(c_Groups_Ouminus__class_Ouminus(_1164959), _1164961))))]]], (20660 ^ _780086) ^ [_1165227, _1165229] : [class_Groups_Oordered__ab__group__add(_1165227), 20663 ^ _780086 : [(20664 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165227), hAPP(c_Groups_Ouminus__class_Ouminus(_1165227), _1165229)), c_Groups_Ozero__class_Ozero(_1165227))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165227), c_Groups_Ozero__class_Ozero(_1165227)), _1165229)))], (20670 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165227), c_Groups_Ozero__class_Ozero(_1165227)), _1165229)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165227), hAPP(c_Groups_Ouminus__class_Ouminus(_1165227), _1165229)), c_Groups_Ozero__class_Ozero(_1165227))))]]], (20676 ^ _780086) ^ [_1165501, _1165503] : [class_Groups_Olinordered__ab__group__add(_1165501), 20679 ^ _780086 : [(20680 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165501), hAPP(c_Groups_Ouminus__class_Ouminus(_1165501), _1165503)), _1165503)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165501), c_Groups_Ozero__class_Ozero(_1165501)), _1165503)))], (20686 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165501), c_Groups_Ozero__class_Ozero(_1165501)), _1165503)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165501), hAPP(c_Groups_Ouminus__class_Ouminus(_1165501), _1165503)), _1165503)))]]], (20692 ^ _780086) ^ [_1165769, _1165771] : [class_Rings_Olinordered__idom(_1165769), 20695 ^ _780086 : [(20696 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165769), _1165771), hAPP(c_Groups_Ouminus__class_Ouminus(_1165769), _1165771))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165769), _1165771), c_Groups_Ozero__class_Ozero(_1165769))))], (20702 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165769), _1165771), c_Groups_Ozero__class_Ozero(_1165769))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165769), _1165771), hAPP(c_Groups_Ouminus__class_Ouminus(_1165769), _1165771))))]]], (20708 ^ _780086) ^ [_1166037, _1166039] : [class_Groups_Oordered__ab__group__add(_1166037), 20711 ^ _780086 : [(20712 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166037), c_Groups_Ozero__class_Ozero(_1166037)), hAPP(c_Groups_Ouminus__class_Ouminus(_1166037), _1166039))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166037), _1166039), c_Groups_Ozero__class_Ozero(_1166037))))], (20718 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166037), _1166039), c_Groups_Ozero__class_Ozero(_1166037))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166037), c_Groups_Ozero__class_Ozero(_1166037)), hAPP(c_Groups_Ouminus__class_Ouminus(_1166037), _1166039))))]]], (20724 ^ _780086) ^ [_1166311, _1166313] : [class_Groups_Oordered__ab__group__add(_1166311), 20727 ^ _780086 : [(20728 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166311), hAPP(c_Groups_Ouminus__class_Ouminus(_1166311), _1166313)), c_Groups_Ozero__class_Ozero(_1166311))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166311), c_Groups_Ozero__class_Ozero(_1166311)), _1166313)))], (20734 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166311), c_Groups_Ozero__class_Ozero(_1166311)), _1166313)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166311), hAPP(c_Groups_Ouminus__class_Ouminus(_1166311), _1166313)), c_Groups_Ozero__class_Ozero(_1166311))))]]], (20740 ^ _780086) ^ [_1166585, _1166587] : [class_Groups_Olinordered__ab__group__add(_1166585), 20743 ^ _780086 : [(20744 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166585), hAPP(c_Groups_Ouminus__class_Ouminus(_1166585), _1166587)), _1166587)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166585), c_Groups_Ozero__class_Ozero(_1166585)), _1166587)))], (20750 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166585), c_Groups_Ozero__class_Ozero(_1166585)), _1166587)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166585), hAPP(c_Groups_Ouminus__class_Ouminus(_1166585), _1166587)), _1166587)))]]], (20756 ^ _780086) ^ [_1166853, _1166855, _1166857] : [class_Groups_Ogroup__add(_1166853), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1166853), _1166855), _1166857) = c_Groups_Ozero__class_Ozero(_1166853), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1166853), _1166855) = _1166857)], (20766 ^ _780086) ^ [_1167014, _1167016] : [class_Groups_Oab__group__add(_1167014), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1167014), hAPP(c_Groups_Ouminus__class_Ouminus(_1167014), _1167016)), _1167016) = c_Groups_Ozero__class_Ozero(_1167014))], (20772 ^ _780086) ^ [_1167119, _1167121] : [class_Groups_Ogroup__add(_1167119), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1167119), hAPP(c_Groups_Ouminus__class_Ouminus(_1167119), _1167121)), _1167121) = c_Groups_Ozero__class_Ozero(_1167119))], (20778 ^ _780086) ^ [_1167224, _1167226, _1167228] : [class_Groups_Ogroup__add(_1167224), 20781 ^ _780086 : [(20782 ^ _780086) ^ [] : [_1167226 = hAPP(c_Groups_Ouminus__class_Ouminus(_1167224), _1167228), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1167224), _1167226), _1167228) = c_Groups_Ozero__class_Ozero(_1167224))], (20788 ^ _780086) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1167224), _1167226), _1167228) = c_Groups_Ozero__class_Ozero(_1167224), -(_1167226 = hAPP(c_Groups_Ouminus__class_Ouminus(_1167224), _1167228))]]], (20794 ^ _780086) ^ [_1167480, _1167482] : [class_Groups_Ogroup__add(_1167480), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1167480), _1167482), hAPP(c_Groups_Ouminus__class_Ouminus(_1167480), _1167482)) = c_Groups_Ozero__class_Ozero(_1167480))], (20800 ^ _780086) ^ [_1167585, _1167587, _1167589, _1167591] : [class_Rings_Olinordered__semidom(_1167585), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167585), _1167587), _1167589)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167585), c_Groups_Ozero__class_Ozero(_1167585)), _1167587)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167585), hAPP(hAPP(c_Power_Opower__class_Opower(_1167585), _1167587), _1167591)), hAPP(hAPP(c_Power_Opower__class_Opower(_1167585), _1167589), _1167591))))], (20814 ^ _780086) ^ [_1167854, _1167856, _1167858] : [class_Rings_Olinordered__semidom(_1167854), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167854), c_Groups_Ozero__class_Ozero(_1167854)), _1167856)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167854), c_Groups_Ozero__class_Ozero(_1167854)), hAPP(hAPP(c_Power_Opower__class_Opower(_1167854), _1167856), _1167858))))], (20824 ^ _780086) ^ [_1168037, _1168039, _1168041] : [class_Rings_Olinordered__semidom(_1168037), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168037), c_Groups_Ozero__class_Ozero(_1168037)), _1168039)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168037), c_Groups_Ozero__class_Ozero(_1168037)), hAPP(hAPP(c_Power_Opower__class_Opower(_1168037), _1168039), _1168041))))], (20834 ^ _780086) ^ [_1168220, _1168222] : [class_Groups_Ogroup__add(_1168220), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1168220), c_Groups_Ozero__class_Ozero(_1168220)), _1168222) = hAPP(c_Groups_Ouminus__class_Ouminus(_1168220), _1168222))], (20840 ^ _780086) ^ [_1168325, _1168327, _1168329] : [class_Groups_Ocomm__monoid__add(_1168325), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1168327, _1168325), _1168329), c_Orderings_Obot__class_Obot(tc_fun(_1168327, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1168325))], (20846 ^ _780086) ^ [_1168434, _1168436, _1168438] : [class_Groups_Ocomm__monoid__add(_1168434), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1168436, _1168434), _1168438), c_Orderings_Obot__class_Obot(tc_fun(_1168436, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1168434))], (20852 ^ _780086) ^ [_1168543, _1168545, _1168547, _1168549] : [class_Groups_Ocomm__monoid__add(_1168543), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1168545), _1168547))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1168545, _1168543), _1168549), _1168547) = c_Groups_Ozero__class_Ozero(_1168543))], (20862 ^ _780086) ^ [_1168667, _1168669, _1168671, _1168673] : [class_Groups_Ocomm__monoid__add(_1168667), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1168669), _1168671))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1168669, _1168667), _1168673), _1168671) = c_Groups_Ozero__class_Ozero(_1168667))], (20872 ^ _780086) ^ [_1168791, _1168793] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1168791), c_Groups_Ozero__class_Ozero(_1168791)), hAPP(c_Nat_OSuc, _1168793)) = c_Groups_Ozero__class_Ozero(_1168791)), class_Power_Opower(_1168791), class_Rings_Osemiring__0(_1168791)], (20882 ^ _780086) ^ [_1168946, _1168948, _1168950, _1168952] : [class_Rings_Ocomm__semiring__1(_1168946), class_Rings_Ono__zero__divisors(_1168946), hBOOL(hAPP(c_Finite__Set_Ofinite(_1168948), _1168950)), 20893 ^ _780086 : [(20894 ^ _780086) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1168948, _1168946), _1168952), _1168950) = c_Groups_Ozero__class_Ozero(_1168946), 20898 ^ _780086 : [(20899 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1168948), 20897 ^ [_1168946, _1168948, _1168950, _1168952]), _1168950)))], (20901 ^ _780086) ^ [] : [-(hAPP(_1168952, 20897 ^ [_1168946, _1168948, _1168950, _1168952]) = c_Groups_Ozero__class_Ozero(_1168946))]]], (20903 ^ _780086) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1168948, _1168946), _1168952), _1168950) = c_Groups_Ozero__class_Ozero(_1168946)), 20904 ^ _780086 : [(20905 ^ _780086) ^ [_1169324] : [hBOOL(hAPP(hAPP(c_member(_1168948), _1169324), _1168950)), hAPP(_1168952, _1169324) = c_Groups_Ozero__class_Ozero(_1168946)]]]]], (20913 ^ _780086) ^ [_1169479, _1169481, _1169483, _1169485] : [class_Rings_Ocomm__semiring__1(_1169479), hBOOL(hAPP(c_Finite__Set_Ofinite(_1169481), _1169483)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1169481, _1169479), _1169485), _1169483) = c_Groups_Ozero__class_Ozero(_1169479)), 20922 ^ _780086 : [(20923 ^ _780086) ^ [_1169660] : [hBOOL(hAPP(hAPP(c_member(_1169481), _1169660), _1169483)), hAPP(_1169485, _1169660) = c_Groups_Ozero__class_Ozero(_1169479)]]], (20931 ^ _780086) ^ [_1169821] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1169821)), -(_1169821 = hAPP(c_Nat_OSuc, 20934 ^ [_1169821]))], (20938 ^ _780086) ^ [_1169912] : [20939 ^ _780086 : [(20940 ^ _780086) ^ [_1169954] : [_1169912 = hAPP(c_Nat_OSuc, _1169954)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1169912)))], (20944 ^ _780086) ^ [_1170024] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1170024), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_1170024 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20950 ^ _780086) ^ [_1170105] : [_1170105 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1170105), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (20956 ^ _780086) ^ [_1170207, _1170209] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1170207), hAPP(c_Nat_OSuc, _1170209))), -(_1170207 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 20964 ^ _780086 : [(20965 ^ _780086) ^ [] : [-(_1170207 = hAPP(c_Nat_OSuc, 20963 ^ [_1170207, _1170209]))], (20967 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 20963 ^ [_1170207, _1170209]), _1170209)))]]], (20969 ^ _780086) ^ [_1170387, _1170389] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1170387), hAPP(c_Nat_OSuc, _1170389)))), 20970 ^ _780086 : [(20971 ^ _780086) ^ [] : [_1170387 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (20973 ^ _780086) ^ [_1170475] : [_1170387 = hAPP(c_Nat_OSuc, _1170475), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1170475), _1170389))]]], (20981 ^ _780086) ^ [_1170624, _1170626] : [hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1170624), _1170626), 20986 ^ _780086 : [(20987 ^ _780086) ^ [] : [-(_1170624 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (20989 ^ _780086) ^ [] : [-(_1170626 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 20990 ^ _780086 : [(20991 ^ _780086) ^ [] : [-(_1170624 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20993 ^ _780086) ^ [] : [-(_1170626 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (20995 ^ _780086) ^ [_1170808, _1170810] : [-(hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1170808), _1170810)), 20996 ^ _780086 : [(20997 ^ _780086) ^ [] : [_1170808 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1170810 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (21003 ^ _780086) ^ [] : [_1170808 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1170810 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (21011 ^ _780086) ^ [_1171049, _1171051] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1171049), _1171051) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 21016 ^ _780086 : [(21017 ^ _780086) ^ [] : [-(_1171049 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (21019 ^ _780086) ^ [] : [-(_1171051 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 21020 ^ _780086 : [(21021 ^ _780086) ^ [] : [-(_1171049 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21023 ^ _780086) ^ [] : [-(_1171051 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (21025 ^ _780086) ^ [_1171233, _1171235] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1171233), _1171235) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 21026 ^ _780086 : [(21027 ^ _780086) ^ [] : [_1171233 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1171235 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (21033 ^ _780086) ^ [] : [_1171233 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1171235 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (21051 ^ _780086) ^ [_1171584, _1171586] : [21052 ^ _780086 : [(21053 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1171584))], (21055 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1171586))]], -(hBOOL(hAPP(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), _1171584), _1171586))))], (21041 ^ _780086) ^ [_1171474, _1171476] : [hBOOL(hAPP(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), _1171474), _1171476))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1171474))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1171476)))], (21059 ^ _780086) ^ [_1171725, _1171727] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1171725)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1171725), _1171727))))], (21065 ^ _780086) ^ [_1171822, _1171824] : [class_Power_Opower(_1171822), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1171822), _1171824), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1171822))], (21071 ^ _780086) ^ [_1171917, _1171919] : [class_Rings_Ocomm__semiring__1(_1171917), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1171917), _1171919), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1171917))], (21077 ^ _780086) ^ [_1172012] : [-(hAPP(c_Finite__Set_Ocard(_1172012), c_Orderings_Obot__class_Obot(tc_fun(_1172012, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21079 ^ _780086) ^ [_1172041, _1172043] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1172041), _1172043))), -(hAPP(c_Finite__Set_Ocard(_1172041), _1172043) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21085 ^ _780086) ^ [_1172101, _1172103] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1172101), _1172103) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 21088 ^ _780086 : [(21089 ^ _780086) ^ [] : [-(_1172101 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (21091 ^ _780086) ^ [] : [-(_1172103 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (21093 ^ _780086) ^ [_1172212, _1172214] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1172212), _1172214) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1172212 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1172214 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21103 ^ _780086) ^ [_1172370, _1172372] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1172370), _1172372))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1172372), _1172370)))], (21109 ^ _780086) ^ [_1172469, _1172471] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1172471), _1172469)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1172469), _1172471))))], (21115 ^ _780086) ^ [_1172574, _1172576] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1172574)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1172576)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1172576), _1172574)), _1172576)))], (21125 ^ _780086) ^ [_1172748, _1172750] : [hBOOL(hAPP(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), _1172748), _1172750))), 21128 ^ _780086 : [(21129 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1172748)))], (21131 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1172750)))]]], (21133 ^ _780086) ^ [_1172871, _1172873] : [-(hBOOL(hAPP(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), _1172871), _1172873)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1172871)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1172873))], (21143 ^ _780086) ^ [_1173044, _1173046, _1173048] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1173044), _1173046)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1173044), _1173048))), 21146 ^ _780086 : [(21147 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1173044)))], (21149 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1173046), _1173048)))]]], (21151 ^ _780086) ^ [_1173193, _1173195, _1173197] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1173193), _1173195)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1173193), _1173197)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1173193)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1173195), _1173197))], (21161 ^ _780086) ^ [_1173394, _1173396, _1173398] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1173394), _1173396)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1173398), _1173396))), 21164 ^ _780086 : [(21165 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1173396)))], (21167 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1173394), _1173398)))]]], (21169 ^ _780086) ^ [_1173543, _1173545, _1173547] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1173543), _1173545)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1173547), _1173545)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1173545)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1173543), _1173547))], (21179 ^ _780086) ^ [_1173726, _1173728, _1173730] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1173726), _1173728)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1173730)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1173726), _1173730)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1173728), _1173730))))], (21189 ^ _780086) ^ [_1173907, _1173909, _1173911] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1173907), _1173909)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1173911)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1173911), _1173907)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1173911), _1173909))))], (21199 ^ _780086) ^ [_1174088, _1174090, _1174092] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1174088)), 21202 ^ _780086 : [(21203 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1174088), _1174090)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1174088), _1174092))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1174090), _1174092)))], (21209 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1174090), _1174092)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1174088), _1174090)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1174088), _1174092))))]]], (21215 ^ _780086) ^ [_1174371, _1174373, _1174375] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1174371)), 21218 ^ _780086 : [(21219 ^ _780086) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1174371), _1174373) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1174371), _1174375), -(_1174373 = _1174375)], (21225 ^ _780086) ^ [] : [_1174373 = _1174375, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1174371), _1174373) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1174371), _1174375))]]], (21231 ^ _780086) ^ [_1174624, _1174626] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1174624), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1174624), _1174626)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21233 ^ _780086) ^ [_1174670, _1174672] : [_1174670 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1174672), _1174670) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (21239 ^ _780086) ^ [_1174753, _1174755] : [-(_1174753 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1174755), _1174753) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1174755), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1174755), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1174753), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (21245 ^ _780086) ^ [_1174815, _1174817] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1174815), _1174817)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1174815), _1174817) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21251 ^ _780086) ^ [_1174929, _1174931] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1174929), _1174931) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1174929), _1174931)))], (21257 ^ _780086) ^ [_1175024, _1175026] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1175024), _1175026)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1175024), _1175026) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21263 ^ _780086) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (21265 ^ _780086) ^ [_1175143, _1175145] : [_1175143 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1175143), _1175145), -(_1175145 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_1175143 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21275 ^ _780086) ^ [_1175245, _1175247, _1175249] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1175245), _1175247)), 21278 ^ _780086 : [(21289 ^ _780086) ^ [] : [21291 ^ _780086 : [(21292 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1175245), 21290 ^ [_1175245, _1175247, _1175249]), _1175247)))], (21294 ^ _780086) ^ [] : [hAPP(_1175249, 21290 ^ [_1175245, _1175247, _1175249]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1175245, tc_Nat_Onat), _1175249), _1175247) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21279 ^ _780086) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1175245, tc_Nat_Onat), _1175249), _1175247) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 21282 ^ _780086 : [(21283 ^ _780086) ^ [_1175407] : [hBOOL(hAPP(hAPP(c_member(_1175245), _1175407), _1175247)), -(hAPP(_1175249, _1175407) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]]]], (21298 ^ _780086) ^ [_1175665] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1175665)), -(_1175665 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1175665), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (21304 ^ _780086) ^ [_1175771, _1175773] : [_1175771 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1175771), _1175773) = _1175773)], (21310 ^ _780086) ^ [_1175854, _1175856] : [-(_1175854 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1175854), _1175856) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1175854), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1175856)))], (21316 ^ _780086) ^ [_1175913, _1175915, _1175917] : [class_Groups_Oordered__comm__monoid__add(_1175913), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1175913), _1175915), c_Groups_Ozero__class_Ozero(_1175913))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175913), _1175917), c_Groups_Ozero__class_Ozero(_1175913))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175913), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1175913), _1175915), _1175917)), c_Groups_Ozero__class_Ozero(_1175913))))], (21330 ^ _780086) ^ [_1176168, _1176170, _1176172] : [class_Groups_Oordered__comm__monoid__add(_1176168), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176168), _1176170), c_Groups_Ozero__class_Ozero(_1176168))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1176168), _1176172), c_Groups_Ozero__class_Ozero(_1176168))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176168), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1176168), _1176170), _1176172)), c_Groups_Ozero__class_Ozero(_1176168))))], (21344 ^ _780086) ^ [_1176423, _1176425, _1176427, _1176429] : [class_Groups_Oordered__comm__monoid__add(_1176423), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1176423), c_Groups_Ozero__class_Ozero(_1176423)), _1176425)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176423), _1176427), _1176429)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176423), _1176427), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1176423), _1176425), _1176429))))], (21358 ^ _780086) ^ [_1176676, _1176678, _1176680, _1176682] : [class_Groups_Oordered__comm__monoid__add(_1176676), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176676), c_Groups_Ozero__class_Ozero(_1176676)), _1176678)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1176676), _1176680), _1176682)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176676), _1176680), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1176676), _1176678), _1176682))))], (21372 ^ _780086) ^ [_1176929, _1176931, _1176933] : [class_Groups_Oordered__comm__monoid__add(_1176929), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1176929), c_Groups_Ozero__class_Ozero(_1176929)), _1176931)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176929), c_Groups_Ozero__class_Ozero(_1176929)), _1176933)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176929), c_Groups_Ozero__class_Ozero(_1176929)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1176929), _1176931), _1176933))))], (21386 ^ _780086) ^ [_1177184, _1177186, _1177188] : [class_Groups_Oordered__comm__monoid__add(_1177184), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1177184), c_Groups_Ozero__class_Ozero(_1177184)), _1177186)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1177184), c_Groups_Ozero__class_Ozero(_1177184)), _1177188)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1177184), c_Groups_Ozero__class_Ozero(_1177184)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1177184), _1177186), _1177188))))], (21400 ^ _780086) ^ [_1177439, _1177441, _1177443, _1177445] : [class_Rings_Olinordered__ring__strict(_1177439), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1177439), c_Groups_Ozero__class_Ozero(_1177439)), _1177441)), 21407 ^ _780086 : [(21408 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1177439), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1177439), _1177441), _1177443)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1177439), _1177441), _1177445))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1177439), _1177443), _1177445)))], (21414 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1177439), _1177443), _1177445)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1177439), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1177439), _1177441), _1177443)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1177439), _1177441), _1177445))))]]], (21420 ^ _780086) ^ [_1177820, _1177822, _1177824, _1177826] : [class_Rings_Olinordered__ring__strict(_1177820), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1177820), _1177822), c_Groups_Ozero__class_Ozero(_1177820))), 21427 ^ _780086 : [(21428 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1177820), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1177820), _1177822), _1177824)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1177820), _1177822), _1177826))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1177820), _1177826), _1177824)))], (21434 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1177820), _1177826), _1177824)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1177820), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1177820), _1177822), _1177824)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1177820), _1177822), _1177826))))]]], (21440 ^ _780086) ^ [_1178201, _1178203, _1178205, _1178207, _1178209] : [class_Rings_Olinordered__semiring__strict(_1178201), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1178201), _1178203), _1178205)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1178201), _1178207), _1178209)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1178201), c_Groups_Ozero__class_Ozero(_1178201)), _1178205)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1178201), c_Groups_Ozero__class_Ozero(_1178201)), _1178207)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1178201), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1178201), _1178203), _1178207)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1178201), _1178205), _1178209))))], (21462 ^ _780086) ^ [_1178624, _1178626, _1178628, _1178630, _1178632] : [class_Rings_Olinordered__semiring__strict(_1178624), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1178624), _1178626), _1178628)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1178624), _1178630), _1178632)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1178624), c_Groups_Ozero__class_Ozero(_1178624)), _1178626)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1178624), c_Groups_Ozero__class_Ozero(_1178624)), _1178630)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1178624), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1178624), _1178626), _1178630)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1178624), _1178628), _1178632))))], (21484 ^ _780086) ^ [_1179047, _1179049, _1179051, _1179053, _1179055] : [class_Rings_Olinordered__semiring__strict(_1179047), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1179047), _1179049), _1179051)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1179047), _1179053), _1179055)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1179047), c_Groups_Ozero__class_Ozero(_1179047)), _1179049)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1179047), c_Groups_Ozero__class_Ozero(_1179047)), _1179053)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1179047), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1179047), _1179049), _1179053)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1179047), _1179051), _1179055))))], (21506 ^ _780086) ^ [_1179470, _1179472, _1179474, _1179476, _1179478] : [class_Rings_Olinordered__semiring__strict(_1179470), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1179470), _1179472), _1179474)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1179470), _1179476), _1179478)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1179470), c_Groups_Ozero__class_Ozero(_1179470)), _1179472)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1179470), c_Groups_Ozero__class_Ozero(_1179470)), _1179476)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1179470), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1179470), _1179472), _1179476)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1179470), _1179474), _1179478))))], (21528 ^ _780086) ^ [_1179893, _1179895, _1179897, _1179899] : [class_Rings_Olinordered__semiring(_1179893), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1179893), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1179893), _1179895), _1179897)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1179893), _1179899), _1179897))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1179893), c_Groups_Ozero__class_Ozero(_1179893)), _1179897)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1179893), _1179895), _1179899)))], (21542 ^ _780086) ^ [_1180162, _1180164, _1180166, _1180168] : [class_Rings_Olinordered__semiring__strict(_1180162), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1180162), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1180162), _1180164), _1180166)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1180162), _1180168), _1180166))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1180162), c_Groups_Ozero__class_Ozero(_1180162)), _1180166)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1180162), _1180164), _1180168)))], (21556 ^ _780086) ^ [_1180431, _1180433, _1180435, _1180437] : [class_Rings_Olinordered__semiring(_1180431), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1180431), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1180431), _1180433), _1180435)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1180431), _1180433), _1180437))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1180431), c_Groups_Ozero__class_Ozero(_1180431)), _1180433)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1180431), _1180435), _1180437)))], (21570 ^ _780086) ^ [_1180700, _1180702, _1180704, _1180706] : [class_Rings_Olinordered__semiring__strict(_1180700), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1180700), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1180700), _1180702), _1180704)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1180700), _1180702), _1180706))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1180700), c_Groups_Ozero__class_Ozero(_1180700)), _1180702)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1180700), _1180704), _1180706)))], (21584 ^ _780086) ^ [_1180969, _1180971, _1180973, _1180975] : [class_Rings_Olinordered__semiring__strict(_1180969), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1180969), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1180969), _1180971), _1180973)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1180969), _1180975), _1180973))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1180969), c_Groups_Ozero__class_Ozero(_1180969)), _1180973)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1180969), _1180971), _1180975)))], (21598 ^ _780086) ^ [_1181238, _1181240, _1181242, _1181244] : [class_Rings_Olinordered__semiring__strict(_1181238), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181238), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1181238), _1181240), _1181242)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1181238), _1181240), _1181244))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1181238), c_Groups_Ozero__class_Ozero(_1181238)), _1181240)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181238), _1181242), _1181244)))], (21612 ^ _780086) ^ [_1181516, _1181518] : [_1181516 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1181516), _1181518) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21618 ^ _780086) ^ [_1181599, _1181601] : [-(_1181599 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1181599), _1181601) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1181601), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1181599), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1181601)))], (21624 ^ _780086) ^ [_1181661, _1181663, _1181665] : [class_Rings_Olinordered__idom(_1181661), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181661), c_Groups_Ozero__class_Ozero(_1181661)), _1181663)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181661), c_Groups_Ozero__class_Ozero(_1181661)), _1181665)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181661), _1181665), c_Groups_Oone__class_Oone(_1181661))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181661), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1181661), _1181663), _1181665)), _1181663)))], (21642 ^ _780086) ^ [_1181984, _1181986, _1181988] : [class_Rings_Olinordered__idom(_1181984), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181984), c_Groups_Ozero__class_Ozero(_1181984)), _1181986)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181984), c_Groups_Ozero__class_Ozero(_1181984)), _1181988)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181984), _1181988), c_Groups_Oone__class_Oone(_1181984))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181984), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1181984), _1181988), _1181986)), _1181986)))], (21660 ^ _780086) ^ [_1182307] : [class_Rings_Olinordered__semidom(_1182307), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1182307), c_Groups_Ozero__class_Ozero(_1182307)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1182307), c_Groups_Oone__class_Oone(_1182307)), c_Groups_Oone__class_Oone(_1182307)))))], (21666 ^ _780086) ^ [_1182422, _1182424, _1182426, _1182428] : [class_Rings_Olinordered__semidom(_1182422), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1182422), hAPP(hAPP(c_Power_Opower__class_Opower(_1182422), _1182424), _1182426)), hAPP(hAPP(c_Power_Opower__class_Opower(_1182422), _1182428), _1182426))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182422), c_Groups_Ozero__class_Ozero(_1182422)), _1182428)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1182422), _1182424), _1182428)))], (21680 ^ _780086) ^ [_1182691, _1182693, _1182695, _1182697] : [class_Rings_Olinordered__semidom(_1182691), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182691), hAPP(hAPP(c_Power_Opower__class_Opower(_1182691), _1182693), hAPP(c_Nat_OSuc, _1182695))), hAPP(hAPP(c_Power_Opower__class_Opower(_1182691), _1182697), hAPP(c_Nat_OSuc, _1182695)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182691), c_Groups_Ozero__class_Ozero(_1182691)), _1182697)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182691), _1182693), _1182697)))], (21694 ^ _780086) ^ [_1182972, _1182974, _1182976, _1182978] : [class_Rings_Olinordered__semidom(_1182972), hAPP(hAPP(c_Power_Opower__class_Opower(_1182972), _1182974), hAPP(c_Nat_OSuc, _1182976)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1182972), _1182978), hAPP(c_Nat_OSuc, _1182976)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182972), c_Groups_Ozero__class_Ozero(_1182972)), _1182974)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182972), c_Groups_Ozero__class_Ozero(_1182972)), _1182978)), -(_1182974 = _1182978)], (21722 ^ _780086) ^ [_1183469, _1183471] : [21723 ^ _780086 : [(21724 ^ _780086) ^ [] : [_1183471 = c_Orderings_Obot__class_Obot(tc_fun(_1183469, tc_HOL_Obool))], (21726 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1183469), _1183471)))]], -(hAPP(c_Finite__Set_Ocard(_1183469), _1183471) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21712 ^ _780086) ^ [_1183314, _1183316] : [hAPP(c_Finite__Set_Ocard(_1183314), _1183316) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1183316 = c_Orderings_Obot__class_Obot(tc_fun(_1183314, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1183314), _1183316))], (21730 ^ _780086) ^ [_1183613, _1183615] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1183613), _1183615))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1183613), _1183615)))], (21736 ^ _780086) ^ [_1183712, _1183714] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1183712)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1183712), hAPP(c_Nat_OSuc, _1183714))), _1183712)))], (21742 ^ _780086) ^ [_1183821] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1183821)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1183821), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = _1183821)], (21748 ^ _780086) ^ [_1183918, _1183920] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1183918)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1183920)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1183918), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1183920), _1183918))))], (21758 ^ _780086) ^ [_1184077, _1184079] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1184077)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1184079)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1184077), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1184077), _1184079))))], (21768 ^ _780086) ^ [_1184236, _1184238] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1184236)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1184238)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1184238), _1184236))))], (21794 ^ _780086) ^ [_1184699, _1184701, _1184703] : [-(hBOOL(hAPP(_1184699, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1184701), _1184703)))), 21797 ^ _780086 : [(21798 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1184701), _1184703)))], (21800 ^ _780086) ^ [] : [hBOOL(hAPP(_1184699, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 21802 ^ _780086 : [(21803 ^ _780086) ^ [] : [-(_1184701 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1184703), 21801 ^ [_1184699, _1184701, _1184703]))], (21805 ^ _780086) ^ [] : [hBOOL(hAPP(_1184699, 21801 ^ [_1184699, _1184701, _1184703]))]]], (21778 ^ _780086) ^ [_1184407, _1184409, _1184411] : [hBOOL(hAPP(_1184407, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1184409), _1184411))), 21781 ^ _780086 : [(21782 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1184409), _1184411)), -(hBOOL(hAPP(_1184407, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (21788 ^ _780086) ^ [_1184598] : [_1184409 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1184411), _1184598), -(hBOOL(hAPP(_1184407, _1184598)))]]], (21825 ^ _780086) ^ [_1185294, _1185296, _1185298] : [-(hBOOL(hAPP(_1185294, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1185296), _1185298)))), 21828 ^ _780086 : [(21829 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1185296), _1185298)))], (21831 ^ _780086) ^ [] : [hBOOL(hAPP(_1185294, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 21833 ^ _780086 : [(21834 ^ _780086) ^ [] : [-(_1185296 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1185298), 21832 ^ [_1185294, _1185296, _1185298]))], (21836 ^ _780086) ^ [] : [hBOOL(hAPP(_1185294, 21832 ^ [_1185294, _1185296, _1185298]))]]], (21809 ^ _780086) ^ [_1185010, _1185012, _1185014] : [hBOOL(hAPP(_1185010, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1185012), _1185014))), 21812 ^ _780086 : [(21813 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1185012), _1185014)), -(hBOOL(hAPP(_1185010, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (21819 ^ _780086) ^ [_1185195] : [_1185012 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1185014), _1185195), -(hBOOL(hAPP(_1185010, _1185195)))]]], (21840 ^ _780086) ^ [_1185594, _1185596] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1185594), _1185596))), 21843 ^ _780086 : [(21844 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1185594)))], (21846 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1185596)))]]], (21848 ^ _780086) ^ [_1185717, _1185719] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1185717), _1185719)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1185717)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1185719))], (21868 ^ _780086) ^ [_1186067, _1186069, _1186071] : [21869 ^ _780086 : [(21870 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1186067)))], (21872 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1186069), _1186071))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1186067), _1186069)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1186067), _1186071))))], (21858 ^ _780086) ^ [_1185890, _1185892, _1185894] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1185890), _1185892)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1185890), _1185894))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1185890)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1185892), _1185894)))], (21886 ^ _780086) ^ [_1186424, _1186426, _1186428] : [21887 ^ _780086 : [(21888 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1186426)))], (21890 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1186424), _1186428))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1186424), _1186426)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1186428), _1186426))))], (21876 ^ _780086) ^ [_1186247, _1186249, _1186251] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1186247), _1186249)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1186251), _1186249))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1186249)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1186247), _1186251)))], (21894 ^ _780086) ^ [_1186586, _1186588, _1186590] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1186586)), 21897 ^ _780086 : [(21898 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1186586), _1186588)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1186586), _1186590))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1186588), _1186590)))], (21904 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1186588), _1186590)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1186586), _1186588)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1186586), _1186590))))]]], (21910 ^ _780086) ^ [_1186869, _1186871, _1186873] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1186869), _1186871)), 21913 ^ _780086 : [(21914 ^ _780086) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1186869, tc_Nat_Onat), _1186873), _1186871) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 21918 ^ _780086 : [(21919 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1186869), 21917 ^ [_1186869, _1186871, _1186873]), _1186871)))], (21921 ^ _780086) ^ [] : [-(hAPP(_1186873, 21917 ^ [_1186869, _1186871, _1186873]) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (21923 ^ _780086) ^ [_1187189] : [hBOOL(hAPP(hAPP(c_member(_1186869), _1187189), _1186871)), -(21917 ^ [_1186869, _1186871, _1186873] = _1187189), -(hAPP(_1186873, _1187189) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (21933 ^ _780086) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1186869, tc_Nat_Onat), _1186873), _1186871) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 21934 ^ _780086 : [(21935 ^ _780086) ^ [_1187350] : [hBOOL(hAPP(hAPP(c_member(_1186869), _1187350), _1186871)), hAPP(_1186873, _1187350) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 21943 ^ _780086 : [(21944 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1186869), 21942 ^ [_1186869, _1186871, _1186873, _1187350]), _1186871)))], (21946 ^ _780086) ^ [] : [_1187350 = 21942 ^ [_1186869, _1186871, _1186873, _1187350]], (21948 ^ _780086) ^ [] : [hAPP(_1186873, 21942 ^ [_1186869, _1186871, _1186873, _1187350]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]]]]]], (21952 ^ _780086) ^ [_1187703, _1187705, _1187707] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1187703), _1187705)), 21955 ^ _780086 : [(21956 ^ _780086) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1187703, tc_Nat_Onat), _1187707), _1187705) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 21960 ^ _780086 : [(21961 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1187703), 21959 ^ [_1187703, _1187705, _1187707]), _1187705)))], (21963 ^ _780086) ^ [] : [-(hAPP(_1187707, 21959 ^ [_1187703, _1187705, _1187707]) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (21965 ^ _780086) ^ [_1188023] : [hBOOL(hAPP(hAPP(c_member(_1187703), _1188023), _1187705)), -(21959 ^ [_1187703, _1187705, _1187707] = _1188023), -(hAPP(_1187707, _1188023) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (21975 ^ _780086) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1187703, tc_Nat_Onat), _1187707), _1187705) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), 21976 ^ _780086 : [(21977 ^ _780086) ^ [_1188184] : [hBOOL(hAPP(hAPP(c_member(_1187703), _1188184), _1187705)), hAPP(_1187707, _1188184) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 21985 ^ _780086 : [(21986 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1187703), 21984 ^ [_1187703, _1187705, _1187707, _1188184]), _1187705)))], (21988 ^ _780086) ^ [] : [_1188184 = 21984 ^ [_1187703, _1187705, _1187707, _1188184]], (21990 ^ _780086) ^ [] : [hAPP(_1187707, 21984 ^ [_1187703, _1187705, _1187707, _1188184]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]]]]]], (21994 ^ _780086) ^ [_1188537, _1188539, _1188541, _1188543, _1188545] : [class_Groups_Ocomm__monoid__add(_1188537), hBOOL(hAPP(c_Finite__Set_Ofinite(_1188539), _1188541)), 22001 ^ _780086 : [(22002 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1188539), _1188543), _1188541)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1188539, _1188537), hAPP(hAPP(c_COMBC(_1188539, _1188537, _1188537), hAPP(hAPP(c_COMBS(_1188539, _1188537, tc_fun(_1188537, _1188537)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1188537, tc_fun(_1188537, _1188537)), _1188539), c_If(_1188537)), hAPP(hAPP(c_COMBC(_1188539, _1188539, tc_HOL_Obool), c_fequal), _1188543))), _1188545)), c_Groups_Ozero__class_Ozero(_1188537))), _1188541) = hAPP(_1188545, _1188543))], (22008 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1188539), _1188543), _1188541))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1188539, _1188537), hAPP(hAPP(c_COMBC(_1188539, _1188537, _1188537), hAPP(hAPP(c_COMBS(_1188539, _1188537, tc_fun(_1188537, _1188537)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1188537, tc_fun(_1188537, _1188537)), _1188539), c_If(_1188537)), hAPP(hAPP(c_COMBC(_1188539, _1188539, tc_HOL_Obool), c_fequal), _1188543))), _1188545)), c_Groups_Ozero__class_Ozero(_1188537))), _1188541) = c_Groups_Ozero__class_Ozero(_1188537))]]], (22014 ^ _780086) ^ [_1189075, _1189077, _1189079, _1189081, _1189083] : [class_Groups_Ocomm__monoid__add(_1189075), hBOOL(hAPP(c_Finite__Set_Ofinite(_1189077), _1189079)), 22021 ^ _780086 : [(22022 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1189077), _1189081), _1189079)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1189077, _1189075), hAPP(hAPP(c_COMBC(_1189077, _1189075, _1189075), hAPP(hAPP(c_COMBS(_1189077, _1189075, tc_fun(_1189075, _1189075)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1189075, tc_fun(_1189075, _1189075)), _1189077), c_If(_1189075)), hAPP(c_fequal, _1189081))), _1189083)), c_Groups_Ozero__class_Ozero(_1189075))), _1189079) = hAPP(_1189083, _1189081))], (22028 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1189077), _1189081), _1189079))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1189077, _1189075), hAPP(hAPP(c_COMBC(_1189077, _1189075, _1189075), hAPP(hAPP(c_COMBS(_1189077, _1189075, tc_fun(_1189075, _1189075)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1189075, tc_fun(_1189075, _1189075)), _1189077), c_If(_1189075)), hAPP(c_fequal, _1189081))), _1189083)), c_Groups_Ozero__class_Ozero(_1189075))), _1189079) = c_Groups_Ozero__class_Ozero(_1189075))]]], (22034 ^ _780086) ^ [_1189585, _1189587, _1189589] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1189585), _1189587)), 22037 ^ _780086 : [(22048 ^ _780086) ^ [] : [22050 ^ _780086 : [(22051 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1189585), 22049 ^ [_1189585, _1189587, _1189589]), _1189587)))], (22053 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1189589, 22049 ^ [_1189585, _1189587, _1189589])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1189585, tc_Nat_Onat), _1189589), _1189587))))], (22038 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1189585, tc_Nat_Onat), _1189589), _1189587))), 22041 ^ _780086 : [(22042 ^ _780086) ^ [_1189753] : [hBOOL(hAPP(hAPP(c_member(_1189585), _1189753), _1189587)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1189589, _1189753))))]]]]], (22057 ^ _780086) ^ [_1190021, _1190023, _1190025, _1190027, _1190029, _1190031] : [class_Rings_Olinordered__semiring__1(_1190021), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190021), _1190023), _1190025)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190021), _1190027), _1190025)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190021), c_Groups_Ozero__class_Ozero(_1190021)), _1190029)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190021), c_Groups_Ozero__class_Ozero(_1190021)), _1190031)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1190021), _1190029), _1190031) = c_Groups_Oone__class_Oone(_1190021), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190021), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1190021), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1190021), _1190029), _1190023)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1190021), _1190031), _1190027))), _1190025)))], (22083 ^ _780086) ^ [_1190550, _1190552, _1190554] : [class_Rings_Olinordered__semidom(_1190550), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190550), c_Groups_Ozero__class_Ozero(_1190550)), _1190552)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190550), _1190552), c_Groups_Oone__class_Oone(_1190550))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190550), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1190550), _1190552), hAPP(hAPP(c_Power_Opower__class_Opower(_1190550), _1190552), _1190554))), hAPP(hAPP(c_Power_Opower__class_Opower(_1190550), _1190552), _1190554))))], (22097 ^ _780086) ^ [_1190833, _1190835, _1190837] : [class_Rings_Olinordered__semidom(_1190833), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190833), c_Groups_Ozero__class_Ozero(_1190833)), _1190835)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190833), _1190835), c_Groups_Oone__class_Oone(_1190833))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190833), hAPP(hAPP(c_Power_Opower__class_Opower(_1190833), _1190835), hAPP(c_Nat_OSuc, _1190837))), c_Groups_Oone__class_Oone(_1190833))))], (22111 ^ _780086) ^ [_1191094, _1191096, _1191098, _1191100] : [class_Rings_Olinordered__semidom(_1191094), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1191096), _1191098)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191094), c_Groups_Ozero__class_Ozero(_1191094)), _1191100)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191094), _1191100), c_Groups_Oone__class_Oone(_1191094))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191094), hAPP(hAPP(c_Power_Opower__class_Opower(_1191094), _1191100), _1191098)), hAPP(hAPP(c_Power_Opower__class_Opower(_1191094), _1191100), _1191096))))], (22129 ^ _780086) ^ [_1191433, _1191435, _1191437, _1191439] : [class_Rings_Olinordered__semidom(_1191433), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1191435), _1191437)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1191433), c_Groups_Ozero__class_Ozero(_1191433)), _1191439)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1191433), _1191439), c_Groups_Oone__class_Oone(_1191433))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1191433), hAPP(hAPP(c_Power_Opower__class_Opower(_1191433), _1191439), _1191437)), hAPP(hAPP(c_Power_Opower__class_Opower(_1191433), _1191439), _1191435))))], (22147 ^ _780086) ^ [_1191772, _1191774, _1191776] : [class_Rings_Olinordered__semidom(_1191772), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191772), c_Groups_Oone__class_Oone(_1191772)), _1191774)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1191776)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191772), c_Groups_Oone__class_Oone(_1191772)), hAPP(hAPP(c_Power_Opower__class_Opower(_1191772), _1191774), _1191776))))], (22161 ^ _780086) ^ [_1192028, _1192030] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1192028), _1192030))), 22164 ^ _780086 : [(22165 ^ _780086) ^ [] : [_1192030 = c_Orderings_Obot__class_Obot(tc_fun(_1192028, tc_HOL_Obool))], (22167 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1192028), _1192030)))]]], (22169 ^ _780086) ^ [_1192169, _1192171] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1192169), _1192171)))), -(_1192171 = c_Orderings_Obot__class_Obot(tc_fun(_1192169, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1192169), _1192171))], (22179 ^ _780086) ^ [_1192335] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1192335), c_Orderings_Otop__class_Otop(tc_fun(_1192335, tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1192335), c_Orderings_Otop__class_Otop(tc_fun(_1192335, tc_HOL_Obool))))))], (22185 ^ _780086) ^ [_1192452, _1192454, _1192456, _1192458] : [class_Groups_Ocomm__monoid__add(_1192452), hBOOL(hAPP(c_Finite__Set_Ofinite(_1192454), _1192456)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1192454, _1192452), _1192458), _1192456) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1192452, _1192454, c_Groups_Oplus__class_Oplus(_1192452)), _1192458), c_Groups_Ozero__class_Ozero(_1192452)), _1192456))], (22195 ^ _780086) ^ [_1192647, _1192649, _1192651, _1192653] : [class_Groups_Ocomm__monoid__add(_1192647), 22198 ^ _780086 : [(22199 ^ _780086) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1192649), _1192651)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1192649, _1192647), _1192653), _1192651) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1192647, _1192649, c_Groups_Oplus__class_Oplus(_1192647)), _1192653), c_Groups_Ozero__class_Ozero(_1192647)), _1192651))], (22205 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1192649), _1192651))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1192649, _1192647), _1192653), _1192651) = c_Groups_Ozero__class_Ozero(_1192647))]]], (22211 ^ _780086) ^ [_1192919] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1192919)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1192919), c_Groups_Oone__class_Oone(tc_Nat_Onat))) = _1192919)], (22217 ^ _780086) ^ [_1193016, _1193018, _1193020, _1193022, _1193024] : [class_Groups_Ocomm__monoid__add(_1193016), hBOOL(hAPP(c_Finite__Set_Ofinite(_1193018), _1193020)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1193018, _1193016), _1193022), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1193018, tc_HOL_Obool)), _1193020), _1193024)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1193018, _1193016), hAPP(hAPP(c_COMBC(_1193018, _1193016, _1193016), hAPP(hAPP(c_COMBS(_1193018, _1193016, tc_fun(_1193016, _1193016)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1193016, tc_fun(_1193016, _1193016)), _1193018), c_If(_1193016)), hAPP(hAPP(c_COMBC(_1193018, tc_fun(_1193018, tc_HOL_Obool), tc_HOL_Obool), c_member(_1193018)), _1193024))), _1193022)), c_Groups_Ozero__class_Ozero(_1193016))), _1193020))], (22227 ^ _780086) ^ [_1193346, _1193348] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1193346), _1193348)), -(hAPP(c_Finite__Set_Ocard(_1193346), _1193348) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1193346, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1193346), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1193348))], (22233 ^ _780086) ^ [_1193473, _1193475] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1193473), _1193475))), -(hAPP(c_Finite__Set_Ocard(_1193473), _1193475) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22239 ^ _780086) ^ [_1193520, _1193522] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1193520), _1193522)), -(hAPP(c_Finite__Set_Ocard(_1193520), _1193522) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1193520, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1193520), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1193522))], (22245 ^ _780086) ^ [_1193653, _1193655, _1193657, _1193659, _1193661, _1193663] : [class_Rings_Olinordered__semiring__1__strict(_1193653), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1193653), _1193655), _1193657)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1193653), _1193659), _1193657)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193653), c_Groups_Ozero__class_Ozero(_1193653)), _1193661)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193653), c_Groups_Ozero__class_Ozero(_1193653)), _1193663)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1193653), _1193661), _1193663) = c_Groups_Oone__class_Oone(_1193653), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1193653), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1193653), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1193653), _1193661), _1193655)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1193653), _1193663), _1193659))), _1193657)))], (22271 ^ _780086) ^ [_1194182, _1194184, _1194186, _1194188, _1194190] : [-(c_Hoare__Mirabelle_Otriple_Otriple__size(_1194182, _1194184, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1194182), _1194186), _1194188), _1194190)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22273 ^ _780086) ^ [_1194228, _1194230] : [class_Rings_Olinordered__idom(_1194228), 22276 ^ _780086 : [(22277 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194228), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1194228), _1194230), _1194230)), c_Groups_Ozero__class_Ozero(_1194228))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194228), _1194230), c_Groups_Ozero__class_Ozero(_1194228))))], (22283 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194228), _1194230), c_Groups_Ozero__class_Ozero(_1194228))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194228), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1194228), _1194230), _1194230)), c_Groups_Ozero__class_Ozero(_1194228))))]]], (22289 ^ _780086) ^ [_1194511, _1194513, _1194515, _1194517] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(_1194511)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1194511), _1194513), _1194515), _1194517)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22291 ^ _780086) ^ [_1194558, _1194560, _1194562] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1194558), _1194560)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1194558), _1194562)), 22301 ^ _780086 : [(22302 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1194558), 22300 ^ [_1194558, _1194560, _1194562]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1194558, tc_HOL_Obool)), _1194560), _1194562))))], (22304 ^ _780086) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(c_Finite__Set_Ocard(_1194558), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1194558, tc_HOL_Obool)), _1194560), _1194562)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1194558), _1194560)), hAPP(c_Finite__Set_Ocard(_1194558), _1194562)))], (22308 ^ _780086) ^ [_1194902, _1194904, _1194906, _1194908, _1194910] : [class_Groups_Oordered__comm__monoid__add(_1194902), hBOOL(hAPP(c_Finite__Set_Ofinite(_1194904), _1194906)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1194904, tc_HOL_Obool)), _1194908), _1194906)), 22322 ^ _780086 : [(22323 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1194904), 22321 ^ [_1194902, _1194904, _1194906, _1194908, _1194910]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1194904, tc_HOL_Obool)), _1194906), _1194908))))], (22325 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194902), c_Groups_Ozero__class_Ozero(_1194902)), hAPP(_1194910, 22321 ^ [_1194902, _1194904, _1194906, _1194908, _1194910])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194902), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1194904, _1194902), _1194910), _1194908)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1194904, _1194902), _1194910), _1194906))))], (22329 ^ _780086) ^ [_1195388, _1195390, _1195392] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1195388)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Otimes__class_Otimes(tc_Nat_Onat)), _1195390))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1195392))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1195392), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1195388), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1195388), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1195392), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1195390)))))], (22331 ^ _780086) ^ [_1195469] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1195469))))], (22333 ^ _780086) ^ [_1195497, _1195499, _1195501] : [class_Orderings_Olinorder(_1195497), 22336 ^ _780086 : [(22337 ^ _780086) ^ [] : [hAPP(c_SetInterval_Oord__class_OlessThan(_1195497), _1195499) = hAPP(c_SetInterval_Oord__class_OlessThan(_1195497), _1195501), -(_1195499 = _1195501)], (22343 ^ _780086) ^ [] : [_1195499 = _1195501, -(hAPP(c_SetInterval_Oord__class_OlessThan(_1195497), _1195499) = hAPP(c_SetInterval_Oord__class_OlessThan(_1195497), _1195501))]]], (22349 ^ _780086) ^ [_1195738] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1195738)) = _1195738)], (22351 ^ _780086) ^ [] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (22353 ^ _780086) ^ [_1195785] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1195785)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1195785), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1195785)))], (22355 ^ _780086) ^ [] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (22357 ^ _780086) ^ [_1195841] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1195841)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1195841))))], (22359 ^ _780086) ^ [_1195879, _1195881, _1195883] : [class_Groups_Ocomm__monoid__add(_1195879), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1195879), _1195881), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1195883))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1195879), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1195879), _1195881), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1195883))), hAPP(_1195881, _1195883)))], (22365 ^ _780086) ^ [_1196032, _1196034, _1196036] : [class_Orderings_Oord(_1196032), 22368 ^ _780086 : [(22369 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1196032), _1196034), hAPP(c_SetInterval_Oord__class_OlessThan(_1196032), _1196036))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196032), _1196034), _1196036)))], (22375 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196032), _1196034), _1196036)), -(hBOOL(hAPP(hAPP(c_member(_1196032), _1196034), hAPP(c_SetInterval_Oord__class_OlessThan(_1196032), _1196036))))]]], (22381 ^ _780086) ^ [_1196300, _1196302, _1196304] : [class_Orderings_Olinorder(_1196300), 22384 ^ _780086 : [(22385 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1196300, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1196300), _1196302)), hAPP(c_SetInterval_Oord__class_OlessThan(_1196300), _1196304))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1196300), _1196302), _1196304)))], (22391 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1196300), _1196302), _1196304)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1196300, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1196300), _1196302)), hAPP(c_SetInterval_Oord__class_OlessThan(_1196300), _1196304))))]]], (22397 ^ _780086) ^ [_1196592, _1196594, _1196596] : [class_Orderings_Olinorder(_1196592), 22400 ^ _780086 : [(22401 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1196592, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1196592), _1196594)), hAPP(c_SetInterval_Oord__class_OlessThan(_1196592), _1196596))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196592), _1196594), _1196596)))], (22407 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196592), _1196594), _1196596)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1196592, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1196592), _1196594)), hAPP(c_SetInterval_Oord__class_OlessThan(_1196592), _1196596))))]]], (22413 ^ _780086) ^ [_1196884, _1196886, _1196888] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1196884), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1196886), _1196888)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1196884), _1196886)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1196884), _1196888)))], (22415 ^ _780086) ^ [_1196941, _1196943, _1196945] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1196941), _1196943)), _1196945) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1196941), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1196943), _1196945)))], (22417 ^ _780086) ^ [_1196992, _1196994] : [class_Orderings_Oorder(_1196992), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1196992, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1196992), _1196994), c_Orderings_Obot__class_Obot(tc_fun(_1196992, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OlessThan(_1196992), _1196994)) = hAPP(hAPP(c_Set_Oinsert(_1196992), _1196994), c_Orderings_Obot__class_Obot(tc_fun(_1196992, tc_HOL_Obool))))], (22423 ^ _780086) ^ [_1197151, _1197153] : [class_Groups_Olinordered__ab__group__add(_1197151), 22426 ^ _780086 : [(22427 ^ _780086) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1197151), _1197153), _1197153) = c_Groups_Ozero__class_Ozero(_1197151), -(_1197153 = c_Groups_Ozero__class_Ozero(_1197151))], (22433 ^ _780086) ^ [] : [_1197153 = c_Groups_Ozero__class_Ozero(_1197151), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1197151), _1197153), _1197153) = c_Groups_Ozero__class_Ozero(_1197151))]]], (22439 ^ _780086) ^ [_1197392, _1197394, _1197396, _1197398] : [class_Rings_Ocomm__semiring__1(_1197392), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1197392), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1197392), c_Groups_Oone__class_Oone(_1197392)), c_Groups_Oone__class_Oone(_1197392))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1197392), hAPP(hAPP(c_COMBB(_1197392, _1197392, tc_Nat_Onat), hAPP(c_Groups_Oplus__class_Oplus(_1197392), _1197394)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1197392, _1197392), hAPP(hAPP(c_COMBB(_1197392, tc_fun(_1197392, _1197392), tc_Nat_Onat), c_Groups_Otimes__class_Otimes(_1197392)), c_Nat_Osemiring__1__class_Oof__nat(_1197392))), _1197396))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1197398))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1197392), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1197392), _1197398)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1197392), _1197394), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1197392), _1197394), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1197392), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1197392), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1197398), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1197396)))))], (22445 ^ _780086) ^ [_1197715, _1197717, _1197719, _1197721, _1197723] : [class_Groups_Ocomm__monoid__add(_1197715), hBOOL(hAPP(c_Finite__Set_Ofinite(_1197717), _1197719)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1197717), _1197721)), 22459 ^ _780086 : [(22460 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1197717), 22458 ^ [_1197715, _1197717, _1197719, _1197721, _1197723]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1197717, tc_HOL_Obool)), _1197719), _1197721))))], (22462 ^ _780086) ^ [] : [hAPP(_1197723, 22458 ^ [_1197715, _1197717, _1197719, _1197721, _1197723]) = c_Groups_Ozero__class_Ozero(_1197715)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1197717, _1197715), _1197723), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1197717, tc_HOL_Obool)), _1197719), _1197721)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1197715), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1197717, _1197715), _1197723), _1197719)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1197717, _1197715), _1197723), _1197721)))], (22466 ^ _780086) ^ [_1198210, _1198212, _1198214, _1198216, _1198218] : [class_Groups_Ocomm__monoid__add(_1198210), hBOOL(hAPP(c_Finite__Set_Ofinite(_1198212), _1198214)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1198212), _1198216)), 22480 ^ _780086 : [(22481 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1198212), 22479 ^ [_1198210, _1198212, _1198214, _1198216, _1198218]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1198212, tc_HOL_Obool)), _1198214), _1198216))))], (22483 ^ _780086) ^ [] : [hAPP(_1198218, 22479 ^ [_1198210, _1198212, _1198214, _1198216, _1198218]) = c_Groups_Ozero__class_Ozero(_1198210)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1198212, _1198210), _1198218), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1198212, tc_HOL_Obool)), _1198214), _1198216)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1198210), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1198212, _1198210), _1198218), _1198214)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1198212, _1198210), _1198218), _1198216)))], (22487 ^ _780086) ^ [_1198723, _1198725, _1198727] : [hAPP(c_Finite__Set_Ocard(_1198723), _1198725) = hAPP(c_Nat_OSuc, _1198727), 22492 ^ _780086 : [(22493 ^ _780086) ^ [] : [-(_1198725 = hAPP(hAPP(c_Set_Oinsert(_1198723), 22490 ^ [_1198723, _1198725, _1198727]), 22491 ^ [_1198723, _1198725, _1198727]))], (22495 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1198723), 22490 ^ [_1198723, _1198725, _1198727]), 22491 ^ [_1198723, _1198725, _1198727]))], (22497 ^ _780086) ^ [] : [-(hAPP(c_Finite__Set_Ocard(_1198723), 22491 ^ [_1198723, _1198725, _1198727]) = _1198727)], (22499 ^ _780086) ^ [] : [_1198727 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(22491 ^ [_1198723, _1198725, _1198727] = c_Orderings_Obot__class_Obot(tc_fun(_1198723, tc_HOL_Obool)))]]], (22505 ^ _780086) ^ [_1199141, _1199143, _1199145] : [-(hAPP(c_Finite__Set_Ocard(_1199141), _1199143) = hAPP(c_Nat_OSuc, _1199145)), 22506 ^ _780086 : [(22507 ^ _780086) ^ [_1199241, _1199243] : [_1199143 = hAPP(hAPP(c_Set_Oinsert(_1199141), _1199243), _1199241), -(hBOOL(hAPP(hAPP(c_member(_1199141), _1199243), _1199241))), hAPP(c_Finite__Set_Ocard(_1199141), _1199241) = _1199145, 22518 ^ _780086 : [(22519 ^ _780086) ^ [] : [-(_1199145 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22521 ^ _780086) ^ [] : [_1199241 = c_Orderings_Obot__class_Obot(tc_fun(_1199141, tc_HOL_Obool))]]]]], (22525 ^ _780086) ^ [_1199563, _1199565, _1199567, _1199569, _1199571] : [class_Groups_Ocomm__monoid__add(_1199563), class_Groups_Oordered__ab__semigroup__add(_1199563), hBOOL(hAPP(c_Finite__Set_Ofinite(_1199565), _1199567)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1199565, tc_HOL_Obool)), _1199569), _1199567)), 22543 ^ _780086 : [(22544 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1199565), 22542 ^ [_1199563, _1199565, _1199567, _1199569, _1199571]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1199565, tc_HOL_Obool)), _1199567), _1199569))))], (22546 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1199563), c_Groups_Ozero__class_Ozero(_1199563)), hAPP(_1199571, 22542 ^ [_1199563, _1199565, _1199567, _1199569, _1199571])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1199563), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1199565, _1199563), _1199571), _1199569)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1199565, _1199563), _1199571), _1199567))))], (22550 ^ _780086) ^ [_1200107, _1200109] : [class_Rings_Olinordered__idom(_1200107), hBOOL(hAPP(hAPP(c_member(_1200107), _1200109), c_Int_Oring__1__class_OInts(_1200107))), 22557 ^ _780086 : [(22558 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1200107), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1200107), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1200107), c_Groups_Oone__class_Oone(_1200107)), _1200109)), _1200109)), c_Groups_Ozero__class_Ozero(_1200107))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1200107), _1200109), c_Groups_Ozero__class_Ozero(_1200107))))], (22564 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1200107), _1200109), c_Groups_Ozero__class_Ozero(_1200107))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1200107), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1200107), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1200107), c_Groups_Oone__class_Oone(_1200107)), _1200109)), _1200109)), c_Groups_Ozero__class_Ozero(_1200107))))]]], (22570 ^ _780086) ^ [_1200490, _1200492] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1200490)))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1200492))))], (22572 ^ _780086) ^ [_1200532, _1200534] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1200532)), 22575 ^ _780086 : [(22576 ^ _780086) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1200532), _1200534) = c_Groups_Oone__class_Oone(tc_Int_Oint), 22579 ^ _780086 : [(22580 ^ _780086) ^ [] : [-(_1200532 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (22582 ^ _780086) ^ [] : [-(_1200534 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (22584 ^ _780086) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1200532), _1200534) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _1200532 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1200534 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (22594 ^ _780086) ^ [_1200833, _1200835, _1200837] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1200833), _1200835)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1200837)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1200837), _1200833)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1200837), _1200835))))], (22604 ^ _780086) ^ [_1201014, _1201016] : [class_Rings_Oring__1(_1201014), -(hBOOL(hAPP(hAPP(c_member(_1201014), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1201014), _1201016)), c_Int_Oring__1__class_OInts(_1201014))))], (22610 ^ _780086) ^ [_1201117, _1201119] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1201117)), _1201119) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1201117), _1201119)))], (22612 ^ _780086) ^ [_1201160, _1201162, _1201164] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1201160), _1201162)), _1201164) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1201160), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1201162), _1201164)))], (22614 ^ _780086) ^ [_1201211, _1201213] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1201211), _1201213) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1201213), _1201211))], (22616 ^ _780086) ^ [_1201248, _1201250, _1201252] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1201248), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1201250), _1201252)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1201248), _1201250)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1201248), _1201252)))], (22618 ^ _780086) ^ [_1201305, _1201307, _1201309] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1201305), _1201307)), _1201309) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1201305), _1201309)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1201307), _1201309)))], (22620 ^ _780086) ^ [_1201362, _1201364, _1201366] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1201362), _1201364)), _1201366) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1201362), _1201366)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1201364), _1201366)))], (22622 ^ _780086) ^ [_1201419, _1201421, _1201423] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1201419), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1201421), _1201423)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1201419), _1201421)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1201419), _1201423)))], (22624 ^ _780086) ^ [_1201476] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1201476) = _1201476)], (22626 ^ _780086) ^ [_1201502] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1201502), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _1201502)], (22628 ^ _780086) ^ [_1201531, _1201533, _1201535] : [class_Nat_Osemiring__char__0(_1201531), 22631 ^ _780086 : [(22632 ^ _780086) ^ [] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1201531), _1201533) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1201531), _1201535), -(_1201533 = _1201535)], (22638 ^ _780086) ^ [] : [_1201533 = _1201535, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1201531), _1201533) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1201531), _1201535))]]], (22644 ^ _780086) ^ [_1201787, _1201789] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1201787)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1201789)))), 22647 ^ _780086 : [(22648 ^ _780086) ^ [] : [-(_1201787 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22650 ^ _780086) ^ [] : [-(_1201789 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (22652 ^ _780086) ^ [_1201914, _1201916] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1201914)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1201916))))), _1201914 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1201916 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (22662 ^ _780086) ^ [_1202085] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1202085)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1202085 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22668 ^ _780086) ^ [_1202172] : [_1202172 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1202172)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22674 ^ _780086) ^ [_1202277] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1202277) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1202277 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22680 ^ _780086) ^ [_1202354] : [_1202354 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1202354) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (22686 ^ _780086) ^ [] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (22688 ^ _780086) ^ [_1202470, _1202472] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1202470)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1202472), 22691 ^ _780086 : [(22692 ^ _780086) ^ [] : [-(_1202470 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22694 ^ _780086) ^ [] : [-(_1202472 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (22696 ^ _780086) ^ [_1202587, _1202589] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1202587)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1202589)), _1202587 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1202589 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (22706 ^ _780086) ^ [_1202751, _1202753] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1202751), _1202753)), -(_1202753 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1202751), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 22709 ^ [_1202751, _1202753]))))], (22713 ^ _780086) ^ [_1202870, _1202872] : [22714 ^ _780086 : [(22715 ^ _780086) ^ [_1202926] : [_1202872 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1202870), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1202926)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1202870), _1202872)))], (22719 ^ _780086) ^ [_1202996] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1202996)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1202996)))], (22721 ^ _780086) ^ [_1203031] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1203031)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22723 ^ _780086) ^ [_1203077] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1203077)))))], (22725 ^ _780086) ^ [_1203126, _1203128] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1203126)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1203128))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1203126), _1203128)))], (22731 ^ _780086) ^ [_1203231, _1203233] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1203231), _1203233)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1203231)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1203233))))], (22737 ^ _780086) ^ [_1203342, _1203344] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1203342)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1203344)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1203342), _1203344)))], (22739 ^ _780086) ^ [_1203388, _1203390, _1203392] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1203388)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1203390)), _1203392)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1203388), _1203390))), _1203392))], (22741 ^ _780086) ^ [_1203463, _1203465] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1203463)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1203465))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1203463), _1203465)))], (22747 ^ _780086) ^ [_1203568, _1203570] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1203568), _1203570)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1203568)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1203570))))], (22753 ^ _780086) ^ [_1203679, _1203681] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1203679), _1203681)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1203679)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1203681)))], (22755 ^ _780086) ^ [_1203725, _1203727] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1203725)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1203727)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1203725), _1203727)))], (22757 ^ _780086) ^ [] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (22759 ^ _780086) ^ [] : [-(c_Fun_Oinj__on(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (22761 ^ _780086) ^ [_1203807, _1203809] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1203807)), _1203809) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1203807), _1203809)))], (22763 ^ _780086) ^ [_1203850, _1203852] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1203850), _1203852)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1203850)), _1203852))], (22765 ^ _780086) ^ [_1203893, _1203895, _1203897] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1203893, tc_Nat_Onat), _1203895), _1203897)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1203893, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1203893), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1203895)), _1203897))], (22767 ^ _780086) ^ [_1203951, _1203953, _1203955] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1203951, tc_Nat_Onat), _1203953), _1203955)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1203951, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1203951), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1203953)), _1203955))], (22769 ^ _780086) ^ [] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (22771 ^ _780086) ^ [_1204027, _1204029, _1204031] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1204027), _1204029)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1204031)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1204031)), _1204027)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1204031)), _1204029))))], (22781 ^ _780086) ^ [_1204232] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1204232))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1204232)))], (22787 ^ _780086) ^ [_1204317] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1204317)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1204317))))], (22793 ^ _780086) ^ [_1204408, _1204410] : [class_Rings_Olinordered__semidom(_1204408), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1204408), c_Groups_Ozero__class_Ozero(_1204408)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1204408), _1204410))))], (22799 ^ _780086) ^ [_1204511, _1204513] : [class_Rings_Olinordered__semidom(_1204511), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1204511), c_Groups_Ozero__class_Ozero(_1204511)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1204511), _1204513))))], (22805 ^ _780086) ^ [_1204614, _1204616] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1204614), _1204616)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1204616)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1204614)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1204616), _1204614)))], (22811 ^ _780086) ^ [_1204743, _1204745] : [class_Rings_Olinordered__semidom(_1204743), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1204743), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1204743), _1204745)), c_Groups_Ozero__class_Ozero(_1204743)))], (22817 ^ _780086) ^ [_1204847] : [class_Rings_Osemiring__1(_1204847), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1204847), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1204847))], (22823 ^ _780086) ^ [_1204934, _1204936, _1204938] : [class_Rings_Olinordered__semidom(_1204934), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1204934), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1204934), _1204936)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1204934), _1204938))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1204936), _1204938)))], (22833 ^ _780086) ^ [_1205109, _1205111, _1205113] : [class_Rings_Olinordered__semidom(_1205109), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1205111), _1205113)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1205109), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1205109), _1205111)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1205109), _1205113))))], (22843 ^ _780086) ^ [_1205284, _1205286, _1205288] : [class_Rings_Olinordered__semidom(_1205284), 22846 ^ _780086 : [(22847 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1205284), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1205284), _1205286)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1205284), _1205288))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1205286), _1205288)))], (22853 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1205286), _1205288)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1205284), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1205284), _1205286)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1205284), _1205288))))]]], (22859 ^ _780086) ^ [_1205561, _1205563, _1205565] : [class_Rings_Olinordered__semidom(_1205561), 22862 ^ _780086 : [(22863 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1205561), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1205561), _1205563)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1205561), _1205565))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1205563), _1205565)))], (22869 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1205563), _1205565)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1205561), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1205561), _1205563)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1205561), _1205565))))]]], (22875 ^ _780086) ^ [_1205838, _1205840, _1205842] : [class_Rings_Osemiring__1(_1205838), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1205838), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1205840), _1205842)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1205838), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1205838), _1205840)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1205838), _1205842)))], (22881 ^ _780086) ^ [_1205973, _1205975, _1205977] : [class_Rings_Osemiring__1(_1205973), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1205973), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1205975), _1205977)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1205973), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1205973), _1205975)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1205973), _1205977)))], (22887 ^ _780086) ^ [_1206108] : [class_Rings_Osemiring__1(_1206108), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1206108), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1206108))], (22893 ^ _780086) ^ [_1206195, _1206197, _1206199] : [class_Rings_Osemiring__1(_1206195), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1206195), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1206197), _1206199)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1206195), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1206195), _1206197)), _1206199))], (22899 ^ _780086) ^ [_1206320, _1206322, _1206324, _1206326] : [class_Rings_Osemiring__1(_1206320), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1206320), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1206322, tc_Nat_Onat), _1206324), _1206326)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1206322, _1206320), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1206320, _1206322), c_Nat_Osemiring__1__class_Oof__nat(_1206320)), _1206324)), _1206326))], (22905 ^ _780086) ^ [_1206469] : [class_Nat_Osemiring__char__0(_1206469), -(c_Fun_Oinj__on(tc_Nat_Onat, _1206469, c_Nat_Osemiring__1__class_Oof__nat(_1206469), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (22911 ^ _780086) ^ [_1206550] : [class_Rings_Oring__1(_1206550), -(hBOOL(hAPP(hAPP(c_member(_1206550), c_Groups_Ozero__class_Ozero(_1206550)), c_Int_Oring__1__class_OInts(_1206550))))], (22917 ^ _780086) ^ [_1206645, _1206647, _1206649] : [class_Rings_Oring__1(_1206645), hBOOL(hAPP(hAPP(c_member(_1206645), _1206647), c_Int_Oring__1__class_OInts(_1206645))), hBOOL(hAPP(hAPP(c_member(_1206645), _1206649), c_Int_Oring__1__class_OInts(_1206645))), -(hBOOL(hAPP(hAPP(c_member(_1206645), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1206645), _1206647), _1206649)), c_Int_Oring__1__class_OInts(_1206645))))], (22931 ^ _780086) ^ [_1206900, _1206902, _1206904] : [class_Rings_Oring__1(_1206900), hBOOL(hAPP(hAPP(c_member(_1206900), _1206902), c_Int_Oring__1__class_OInts(_1206900))), hBOOL(hAPP(hAPP(c_member(_1206900), _1206904), c_Int_Oring__1__class_OInts(_1206900))), -(hBOOL(hAPP(hAPP(c_member(_1206900), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1206900), _1206902), _1206904)), c_Int_Oring__1__class_OInts(_1206900))))], (22945 ^ _780086) ^ [_1207155, _1207157, _1207159] : [class_Rings_Oring__1(_1207155), hBOOL(hAPP(hAPP(c_member(_1207155), _1207157), c_Int_Oring__1__class_OInts(_1207155))), hBOOL(hAPP(hAPP(c_member(_1207155), _1207159), c_Int_Oring__1__class_OInts(_1207155))), -(hBOOL(hAPP(hAPP(c_member(_1207155), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1207155), _1207157), _1207159)), c_Int_Oring__1__class_OInts(_1207155))))], (22959 ^ _780086) ^ [_1207410] : [class_Rings_Oring__1(_1207410), -(hBOOL(hAPP(hAPP(c_member(_1207410), c_Groups_Oone__class_Oone(_1207410)), c_Int_Oring__1__class_OInts(_1207410))))], (22965 ^ _780086) ^ [_1207505, _1207507] : [class_Rings_Oring__1(_1207505), hBOOL(hAPP(hAPP(c_member(_1207505), _1207507), c_Int_Oring__1__class_OInts(_1207505))), -(hBOOL(hAPP(hAPP(c_member(_1207505), hAPP(c_Groups_Ouminus__class_Ouminus(_1207505), _1207507)), c_Int_Oring__1__class_OInts(_1207505))))], (22975 ^ _780086) ^ [_1207678, _1207680, _1207682] : [class_Rings_Oring__1(_1207678), hBOOL(hAPP(hAPP(c_member(_1207678), _1207680), c_Int_Oring__1__class_OInts(_1207678))), -(hBOOL(hAPP(hAPP(c_member(_1207678), hAPP(hAPP(c_Power_Opower__class_Opower(_1207678), _1207680), _1207682)), c_Int_Oring__1__class_OInts(_1207678))))], (22985 ^ _780086) ^ [_1207861, _1207863, _1207865, _1207867] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1207861), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1207863, tc_Nat_Onat), _1207865), _1207867)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1207863, _1207861), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1207861, _1207863), c_Nat_Osemiring__1__class_Oof__nat(_1207861)), _1207865)), _1207867)), class_Groups_Ocomm__monoid__mult(_1207861), class_Rings_Osemiring__1(_1207861)], (22995 ^ _780086) ^ [_1208064, _1208066] : [class_Rings_Osemiring__1(_1208064), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1208064), hAPP(c_Nat_OSuc, _1208066)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1208064), c_Groups_Oone__class_Oone(_1208064)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1208064), _1208066)))], (23001 ^ _780086) ^ [_1208185, _1208187, _1208189] : [class_Rings_Oring__1(_1208185), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1208187), _1208189)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1208185), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1208189), _1208187)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1208185), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1208185), _1208189)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1208185), _1208187)))], (23011 ^ _780086) ^ [_1208384, _1208386, _1208388, _1208390] : [class_Rings_Osemiring__1(_1208384), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1208386, _1208384), hAPP(c_COMBK(_1208384, _1208386), _1208388)), _1208390) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1208384), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1208384), hAPP(c_Finite__Set_Ocard(_1208386), _1208390))), _1208388))], (23017 ^ _780086) ^ [_1208529, _1208531] : [class_Rings_Olinordered__semidom(_1208529), 23020 ^ _780086 : [(23021 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1208529), c_Groups_Ozero__class_Ozero(_1208529)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1208529), _1208531))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1208531)))], (23027 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1208531)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1208529), c_Groups_Ozero__class_Ozero(_1208529)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1208529), _1208531))))]]], (23033 ^ _780086) ^ [_1208782, _1208784] : [class_Int_Oring__char__0(_1208782), hBOOL(hAPP(hAPP(c_member(_1208782), _1208784), c_Int_Oring__1__class_OInts(_1208782))), 23040 ^ _780086 : [(23041 ^ _780086) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1208782), _1208784), _1208784) = c_Groups_Ozero__class_Ozero(_1208782), -(_1208784 = c_Groups_Ozero__class_Ozero(_1208782))], (23047 ^ _780086) ^ [] : [_1208784 = c_Groups_Ozero__class_Ozero(_1208782), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1208782), _1208784), _1208784) = c_Groups_Ozero__class_Ozero(_1208782))]]], (23053 ^ _780086) ^ [_1209093, _1209095] : [class_Int_Oring__char__0(_1209093), hBOOL(hAPP(hAPP(c_member(_1209093), _1209095), c_Int_Oring__1__class_OInts(_1209093))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1209093), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1209093), c_Groups_Oone__class_Oone(_1209093)), _1209095)), _1209095) = c_Groups_Ozero__class_Ozero(_1209093)], (23063 ^ _780086) ^ [_1209279, _1209281] : [class_Rings_Osemiring__1(_1209279), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1209279), _1209281) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1209279, hAPP(hAPP(c_COMBC(_1209279, _1209279, _1209279), c_Groups_Oplus__class_Oplus(_1209279)), c_Groups_Oone__class_Oone(_1209279)), _1209281, c_Groups_Ozero__class_Ozero(_1209279)))], (23085 ^ _780086) ^ [_1209713, _1209715, _1209717] : [-(hBOOL(hAPP(_1209713, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1209715), _1209717))))), 23088 ^ _780086 : [(23089 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1209717), _1209715)))], (23091 ^ _780086) ^ [] : [hBOOL(hAPP(_1209713, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1209715)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1209717))))]], 23092 ^ _780086 : [(23093 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1209715), _1209717)))], (23095 ^ _780086) ^ [] : [hBOOL(hAPP(_1209713, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (23069 ^ _780086) ^ [_1209424, _1209426, _1209428] : [hBOOL(hAPP(_1209424, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1209426), _1209428)))), 23072 ^ _780086 : [(23073 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1209428), _1209426)), -(hBOOL(hAPP(_1209424, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1209426)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1209428)))))], (23079 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1209426), _1209428)), -(hBOOL(hAPP(_1209424, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (23099 ^ _780086) ^ [_1209988, _1209990] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1209988)), _1209990) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1209988), _1209990)))], (23101 ^ _780086) ^ [_1210031, _1210033, _1210035, _1210037, _1210039] : [class_Groups_Oordered__ab__semigroup__add(_1210031), class_Rings_Osemiring__1(_1210031), 23111 ^ _780086 : [(23112 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1210033), 23110 ^ [_1210031, _1210033, _1210035, _1210037, _1210039]), _1210035)))], (23114 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1210031), hAPP(_1210037, 23110 ^ [_1210031, _1210033, _1210035, _1210037, _1210039])), _1210039))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1210031), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1210033, _1210031), _1210037), _1210035)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1210031), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1210031), hAPP(c_Finite__Set_Ocard(_1210033), _1210035))), _1210039))))], (23118 ^ _780086) ^ [_1210421, _1210423] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1210421)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1210423)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1210421), _1210423)))], (23120 ^ _780086) ^ [_1210479, _1210481, _1210483] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1210479), _1210481)), -(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat)), _1210479)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1210483), _1210481)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1210483), _1210479)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1210481), _1210479)))], (23126 ^ _780086) ^ [_1210631, _1210633, _1210635] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1210631), _1210633))), 23129 ^ _780086 : [(23130 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1210635), _1210633)), -(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat)), _1210631)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1210635), _1210633)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (23136 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1210635), _1210633))), -(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat)), _1210631)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1210635), _1210633)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))]]], (23142 ^ _780086) ^ [_1210900, _1210902] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1210900), _1210902))))], (23144 ^ _780086) ^ [_1210933, _1210935] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1210933))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1210935))))], (23146 ^ _780086) ^ [_1210981] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1210981)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (23148 ^ _780086) ^ [_1211027, _1211029] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1211027), _1211029)), -(_1211029 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1211027), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 23151 ^ [_1211027, _1211029])))], (23155 ^ _780086) ^ [_1211140, _1211142] : [23156 ^ _780086 : [(23157 ^ _780086) ^ [_1211193] : [_1211142 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1211140), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1211193))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1211140), _1211142)))], (23161 ^ _780086) ^ [_1211272] : [23163 ^ _780086 : [(23164 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23162 ^ [_1211272])))], (23166 ^ _780086) ^ [] : [hBOOL(hAPP(_1211272, 23162 ^ [_1211272]))]], 23167 ^ _780086 : [(23168 ^ _780086) ^ [_1211399] : [-(hBOOL(hAPP(_1211272, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1211399))))]]], (23170 ^ _780086) ^ [_1211429] : [hBOOL(hAPP(_1211429, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 23171 ^ [_1211429]))), 23174 ^ _780086 : [(23175 ^ _780086) ^ [_1211529] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1211529)), -(hBOOL(hAPP(_1211429, _1211529)))]]], (23192 ^ _780086) ^ [_1211802] : [23193 ^ _780086 : [(23194 ^ _780086) ^ [_1211859] : [hBOOL(hAPP(_1211802, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1211859)))]], 23196 ^ _780086 : [(23197 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23195 ^ [_1211802])))], (23199 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1211802, 23195 ^ [_1211802])))]]], (23181 ^ _780086) ^ [_1211632] : [-(hBOOL(hAPP(_1211632, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 23188 ^ [_1211632])))), 23182 ^ _780086 : [(23183 ^ _780086) ^ [_1211684] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1211684)), hBOOL(hAPP(_1211632, _1211684))]]], (23201 ^ _780086) ^ [_1211951] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1211951))))], (23203 ^ _780086) ^ [_1211979] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1211979))))], (23205 ^ _780086) ^ [_1212007] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1212007))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23207 ^ _780086) ^ [_1212056, _1212058] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1212056) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1212058), -(_1212056 = _1212058)], (23213 ^ _780086) ^ [_1212141, _1212143] : [_1212141 = _1212143, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1212141) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1212143))], (23219 ^ _780086) ^ [_1212244, _1212246] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1212244)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1212246))))], (23221 ^ _780086) ^ [_1212298, _1212300] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1212298) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1212300), -(_1212298 = _1212300)], (23227 ^ _780086) ^ [_1212383, _1212385] : [_1212383 = _1212385, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1212383) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1212385))], (23233 ^ _780086) ^ [_1212489, _1212491] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1212489), _1212491)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1212489)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1212491))))], (23239 ^ _780086) ^ [_1212594, _1212596] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1212594)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1212596))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1212594), _1212596)))], (23245 ^ _780086) ^ [_1212720, _1212722] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1212720), _1212722)), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1212720)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1212722))))], (23251 ^ _780086) ^ [_1212825, _1212827] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1212825)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1212827))), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1212825), _1212827)))], (23257 ^ _780086) ^ [_1212951, _1212953] : [_1212951 = _1212953, -(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1212951) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1212953))], (23263 ^ _780086) ^ [_1213036, _1213038] : [hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1213036) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1213038), -(_1213036 = _1213038)], (23269 ^ _780086) ^ [_1213142, _1213144] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1213142), _1213144)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1213142)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1213144))))], (23275 ^ _780086) ^ [_1213247, _1213249] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1213247)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1213249))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1213247), _1213249)))], (23291 ^ _780086) ^ [_1213491, _1213493] : [23292 ^ _780086 : [(23293 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1213491), _1213493))], (23295 ^ _780086) ^ [] : [_1213491 = _1213493]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1213491), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1213493), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (23281 ^ _780086) ^ [_1213373, _1213375] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1213373), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1213375), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1213373), _1213375))), -(_1213373 = _1213375)], (23299 ^ _780086) ^ [_1213636, _1213638] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1213636), _1213638))), -(_1213636 = _1213638), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1213638), _1213636)))], (23309 ^ _780086) ^ [_1213689] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1213689)) = _1213689)], (23311 ^ _780086) ^ [_1213718, _1213720] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1213718), _1213720) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1213720), _1213718))], (23313 ^ _780086) ^ [_1213755, _1213757, _1213759] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1213755), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1213757), _1213759)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1213757), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1213755), _1213759)))], (23315 ^ _780086) ^ [_1213806, _1213808, _1213810] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1213806), _1213808)), _1213810) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1213806), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1213808), _1213810)))], (23317 ^ _780086) ^ [_1213857, _1213859] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1213857), _1213859) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1213857), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1213859)))], (23319 ^ _780086) ^ [_1213897, _1213899] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1213897), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1213899)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1213897), _1213899))], (23321 ^ _780086) ^ [_1213937, _1213939] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1213937), _1213939)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1213937)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1213939)))], (23323 ^ _780086) ^ [_1213983, _1213985, _1213987] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1213983), _1213985)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1213983), _1213987)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1213985), _1213987))))], (23329 ^ _780086) ^ [_1214106, _1214108, _1214110, _1214112] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1214106), _1214108)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1214110), _1214112)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1214106), _1214110)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1214108), _1214112))))], (23339 ^ _780086) ^ [_1214312, _1214314] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1214312), _1214314)), 23342 ^ _780086 : [(23343 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1214312), _1214314)))], (23345 ^ _780086) ^ [] : [_1214312 = _1214314]]], (23347 ^ _780086) ^ [_1214439, _1214441] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1214439), _1214441))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1214439), _1214441)), -(_1214439 = _1214441)], (23357 ^ _780086) ^ [_1214593] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1214593)), _1214593) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (23359 ^ _780086) ^ [] : [-(hBOOL(hAPP(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))))], (23361 ^ _780086) ^ [_1214643] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1214643), _1214643)))], (23363 ^ _780086) ^ [_1214667, _1214669] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1214667), _1214669))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1214669), _1214667)))], (23369 ^ _780086) ^ [_1214713, _1214715] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1214713)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1214715)), -(hBOOL(hAPP(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), _1214713), _1214715))))], (23379 ^ _780086) ^ [_1214866, _1214868, _1214870] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1214866), _1214868)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1214870), _1214866)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1214870), _1214868))))], (23385 ^ _780086) ^ [_1214989, _1214991, _1214993] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1214989), _1214991)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1214991), _1214993)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1214989), _1214993)))], (23395 ^ _780086) ^ [_1215152, _1215154] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1215152), _1215154)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1215154), _1215152)), -(_1215152 = _1215154)], (23405 ^ _780086) ^ [_1215301] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1215301), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1215301)], (23407 ^ _780086) ^ [_1215330] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1215330) = _1215330)], (23409 ^ _780086) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (23411 ^ _780086) ^ [_1215389, _1215391] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1215389), _1215391)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1215389), _1215391)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23417 ^ _780086) ^ [_1215494, _1215496] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1215494), _1215496)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1215494), _1215496)))], (23423 ^ _780086) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (23425 ^ _780086) ^ [_1215638] : [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)), _1215638)), _1215638) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (23427 ^ _780086) ^ [] : [-(hBOOL(hAPP(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))))], (23429 ^ _780086) ^ [_1215703, _1215705] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1215703), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1215705), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1215703), _1215705)))], (23435 ^ _780086) ^ [_1215808, _1215810] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1215808), _1215810)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1215808), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1215810), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (23441 ^ _780086) ^ [_1215931] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1215931)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1215931)))], (23447 ^ _780086) ^ [_1216010] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1216010)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1216010)))], (23453 ^ _780086) ^ [_1216110, _1216112] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1216110), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1216112), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1216110), _1216112)))], (23459 ^ _780086) ^ [_1216215, _1216217] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1216215), _1216217)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1216215), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1216217), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (23465 ^ _780086) ^ [_1216341, _1216343] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1216341), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1216343)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1216341), _1216343)))], (23471 ^ _780086) ^ [_1216446, _1216448] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1216446), _1216448)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1216446), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1216448)))], (23477 ^ _780086) ^ [_1216557] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1216557)), -(hBOOL(hAPP(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)), _1216557))))], (23483 ^ _780086) ^ [_1216646, _1216648] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1216646), _1216648)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1216646), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1216648)))], (23489 ^ _780086) ^ [_1216767] : [hBOOL(hAPP(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)), _1216767)), _1216767)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1216767), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23495 ^ _780086) ^ [_1216876] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1216876), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(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)), _1216876)), _1216876)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23501 ^ _780086) ^ [] : [-(hBOOL(hAPP(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))))], (23503 ^ _780086) ^ [_1217009, _1217011, _1217013, _1217015, _1217017] : [class_Orderings_Olinorder(_1217009), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1217009, _1217011), _1217013) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1217009, _1217015), _1217017), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1217009), _1217011), _1217013)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1217009), _1217015), _1217017)), -(_1217013 = _1217017)], (23521 ^ _780086) ^ [_1217316, _1217318, _1217320, _1217322, _1217324] : [class_Orderings_Olinorder(_1217316), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1217316, _1217318), _1217320) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1217316, _1217322), _1217324), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1217316), _1217318), _1217320)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1217316), _1217322), _1217324)), -(_1217318 = _1217322)], (23539 ^ _780086) ^ [_1217623, _1217625, _1217627, _1217629, _1217631] : [class_Orderings_Olinorder(_1217623), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1217623), _1217625), _1217627)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1217623), _1217629), _1217631)), 23550 ^ _780086 : [(23551 ^ _780086) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1217623, _1217625), _1217627) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1217623, _1217629), _1217631), 23554 ^ _780086 : [(23555 ^ _780086) ^ [] : [-(_1217625 = _1217629)], (23557 ^ _780086) ^ [] : [-(_1217627 = _1217631)]]], (23559 ^ _780086) ^ [] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1217623, _1217625), _1217627) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1217623, _1217629), _1217631)), _1217625 = _1217629, _1217627 = _1217631]]], (23569 ^ _780086) ^ [_1218104, _1218106, _1218108] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1218104), _1218106)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1218104), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1218106), _1218108)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1218104), _1218106)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1218106), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1218106), _1218108))))], (23575 ^ _780086) ^ [_1218265] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1218265), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (23577 ^ _780086) ^ [_1218294] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1218294) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1218294))], (23579 ^ _780086) ^ [_1218323, _1218325] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1218323), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1218325), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1218325), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1218323))))), -(_1218323 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1218325), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1218325), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1218323))))], (23585 ^ _780086) ^ [_1218470, _1218472] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1218470), _1218472)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1218472), _1218470))], (23587 ^ _780086) ^ [_1218510, _1218512] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1218510), _1218512)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1218510)), hAPP(c_Nat_OSuc, _1218512)))], (23589 ^ _780086) ^ [_1218556, _1218558, _1218560] : [class_Orderings_Oorder(_1218556), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1218556), _1218558), _1218560)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1218556, _1218560), _1218558) = c_Orderings_Obot__class_Obot(tc_fun(_1218556, tc_HOL_Obool)))], (23599 ^ _780086) ^ [_1218723, _1218725, _1218727] : [class_Orderings_Oorder(_1218723), 23602 ^ _780086 : [(23603 ^ _780086) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1218723, _1218725), _1218727) = c_Orderings_Obot__class_Obot(tc_fun(_1218723, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1218723), _1218725), _1218727))], (23609 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1218723), _1218725), _1218727))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1218723, _1218725), _1218727) = c_Orderings_Obot__class_Obot(tc_fun(_1218723, tc_HOL_Obool)))]]], (23615 ^ _780086) ^ [_1218948, _1218950, _1218952] : [class_Orderings_Oorder(_1218948), 23618 ^ _780086 : [(23619 ^ _780086) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1218948, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1218948, _1218950), _1218952), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1218948), _1218950), _1218952))], (23625 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1218948), _1218950), _1218952))), -(c_Orderings_Obot__class_Obot(tc_fun(_1218948, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1218948, _1218950), _1218952))]]], (23631 ^ _780086) ^ [_1219173, _1219175, _1219177, _1219179, _1219181] : [class_Orderings_Olinorder(_1219173), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1219173, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1219173, _1219175), _1219177)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1219173, _1219179), _1219181))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219173), _1219177), _1219175))), 23642 ^ _780086 : [(23643 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219173), _1219179), _1219175)))], (23645 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219173), _1219177), _1219181)))]]], (23647 ^ _780086) ^ [_1219454, _1219456, _1219458, _1219460] : [class_Groups_Ocomm__monoid__add(_1219454), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1219454), _1219456), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1219458)), hAPP(c_Nat_OSuc, _1219460))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1219454), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1219454, tc_Nat_Onat), _1219456), c_Nat_OSuc)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1219458), _1219460)))], (23653 ^ _780086) ^ [_1219625, _1219627, _1219629, _1219631] : [class_Orderings_Olinorder(_1219625), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219625), _1219627), _1219629)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219625), _1219629), _1219631)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1219625, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1219625, _1219627), _1219629)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1219625, _1219629), _1219631)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1219625, _1219627), _1219631))], (23667 ^ _780086) ^ [_1219902, _1219904, _1219906, _1219908, _1219910] : [class_Groups_Ocomm__monoid__add(_1219902), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1219902), _1219904), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1219906), _1219908)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1219910), _1219908))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1219902), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1219902, tc_Nat_Onat), _1219904), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1219908))), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1219906), _1219910)))], (23673 ^ _780086) ^ [_1220093, _1220095, _1220097, _1220099] : [class_Orderings_Olinorder(_1220093), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220093), _1220095), _1220097)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1220093, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1220093, _1220095), _1220099)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1220093, _1220095), _1220097)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1220093, _1220097), _1220099))], (23683 ^ _780086) ^ [_1220300, _1220302, _1220304, _1220306] : [class_Orderings_Oorder(_1220300), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1220300, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1220300, _1220302), _1220304)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1220300, _1220304), _1220306)) = c_Orderings_Obot__class_Obot(tc_fun(_1220300, tc_HOL_Obool)))], (23689 ^ _780086) ^ [_1220435, _1220437, _1220439] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1220435)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1220437), _1220439)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1220437), _1220435)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1220439), _1220435)))], (23691 ^ _780086) ^ [_1220496, _1220498, _1220500, _1220502, _1220504] : [class_Groups_Ocomm__monoid__add(_1220496), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1220498), _1220500)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1220500), _1220502)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1220496), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1220496), _1220504), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1220498), _1220500))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1220496), _1220504), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1220500), _1220502))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1220496), _1220504), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1220498), _1220502)))], (23705 ^ _780086) ^ [_1220819, _1220821, _1220823, _1220825, _1220827] : [class_Groups_Oab__group__add(_1220819), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1220821), _1220823)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1220823), _1220825)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1220819), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1220819), _1220827), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1220821), _1220825))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1220819), _1220827), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1220821), _1220823))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1220819), _1220827), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1220823), _1220825)))], (23719 ^ _780086) ^ [_1221142, _1221144, _1221146] : [class_Rings_Osemiring__1(_1221142), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_1221142, _1221144, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1221146) = _1221146)], (23725 ^ _780086) ^ [_1221229, _1221231, _1221233, _1221235] : [class_Rings_Osemiring__1(_1221229), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_1221229, _1221231, hAPP(c_Nat_OSuc, _1221233), _1221235) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1221229, _1221231, _1221233, hAPP(_1221231, _1221235)))], (23731 ^ _780086) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (23733 ^ _780086) ^ [_1221358] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1221358), hAPP(c_Nat_OSuc, _1221358)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1221358), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (23735 ^ _780086) ^ [_1221411, _1221413] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1221411)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1221413))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1221411), _1221413)))], (23741 ^ _780086) ^ [_1221516, _1221518] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1221516), _1221518)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1221516)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1221518))))], (23747 ^ _780086) ^ [_1221627, _1221629] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1221627)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1221629)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1221627), _1221629)))], (23749 ^ _780086) ^ [_1221688, _1221690] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1221688)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1221690))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1221688), _1221690)))], (23755 ^ _780086) ^ [_1221793, _1221795] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1221793), _1221795)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1221793)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1221795))))], (23761 ^ _780086) ^ [_1221904, _1221906] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1221904)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1221906)), -(hBOOL(hAPP(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), _1221904), _1221906))))], (23771 ^ _780086) ^ [_1222057, _1222059] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1222057, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_fun(_1222057, tc_HOL_Obool)), tc_fun(_1222057, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_fun(_1222057, tc_HOL_Obool)), tc_fun(_1222057, tc_HOL_Obool)), tc_Nat_Onat), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1222057, tc_HOL_Obool))), c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), _1222059)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1222057, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1222059))], (23773 ^ _780086) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (23775 ^ _780086) ^ [_1222171, _1222173, _1222175, _1222177, _1222179] : [class_Orderings_Olinorder(_1222171), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1222171, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1222171, _1222173), _1222175)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1222171, _1222177), _1222179)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1222171, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1222171), _1222173), _1222177)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1222171), _1222175), _1222179)))], (23781 ^ _780086) ^ [_1222342, _1222344, _1222346] : [class_Orderings_Olinorder(_1222342), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1222342), _1222344), _1222346)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1222342, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1222342), _1222344)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1222342, _1222344), _1222346)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1222342), _1222346))], (23791 ^ _780086) ^ [_1222541, _1222543, _1222545] : [class_Orderings_Oorder(_1222541), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1222541, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1222541), _1222543)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1222541, _1222543), _1222545)) = c_Orderings_Obot__class_Obot(tc_fun(_1222541, tc_HOL_Obool)))], (23797 ^ _780086) ^ [_1222672, _1222674, _1222676] : [class_Groups_Ocomm__monoid__add(_1222672), hAPP(_1222674, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1222672), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1222672), _1222674), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1222676)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1222672), _1222674), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1222676)))], (23807 ^ _780086) ^ [_1222861, _1222863, _1222865, _1222867] : [class_Groups_Ocomm__monoid__add(_1222861), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1222863), _1222865)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1222861), _1222867), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1222863), _1222865)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1222861), hAPP(_1222867, _1222863)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1222861), _1222867), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1222863)), _1222865))))], (23817 ^ _780086) ^ [] : [-(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (23819 ^ _780086) ^ [_1223112, _1223114] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1223112)), -(hBOOL(hAPP(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), _1223112), _1223114))))], (23825 ^ _780086) ^ [_1223218, _1223220] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1223218), _1223220)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1223218), hAPP(c_Nat_OSuc, _1223220)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1223220), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1223218), _1223220)))], (23831 ^ _780086) ^ [_1223341, _1223343] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1223341), _1223343))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1223341), hAPP(c_Nat_OSuc, _1223343)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (23837 ^ _780086) ^ [_1223393] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1223393) = hAPP(c_Finite__Set_Ocard(tc_Int_Oint), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1223393)))], (23839 ^ _780086) ^ [_1223437] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1223437)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1223437))))], (23845 ^ _780086) ^ [_1223522] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1223522))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1223522)))], (23851 ^ _780086) ^ [_1223613, _1223615, _1223617, _1223619] : [class_Groups_Ocomm__monoid__add(_1223613), 23854 ^ _780086 : [(23855 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1223615), _1223617)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1223613), _1223619), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1223617), hAPP(c_Nat_OSuc, _1223615))) = c_Groups_Ozero__class_Ozero(_1223613))], (23861 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1223615), _1223617))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1223613), _1223619), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1223617), hAPP(c_Nat_OSuc, _1223615))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1223613), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1223613), _1223619), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1223617), _1223615))), hAPP(_1223619, _1223615)))]]], (23867 ^ _780086) ^ [_1223943, _1223945, _1223947] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1223943)), _1223943 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1223945), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1223943), _1223947)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1223945)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1223947), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (23881 ^ _780086) ^ [_1224172, _1224174, _1224176] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1224172)), _1224172 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1224174), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1224172), _1224176)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1224174), _1224172)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1224176)))], (23895 ^ _780086) ^ [_1224401, _1224403, _1224405] : [hBOOL(hAPP(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), _1224401), _1224403)), _1224405))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1224405), _1224401)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1224401)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1224403)))], (23909 ^ _780086) ^ [_1224634, _1224636, _1224638] : [hBOOL(hAPP(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), _1224634), _1224636)), _1224638)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1224638)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1224634)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1224636), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23923 ^ _780086) ^ [_1224873, _1224875, _1224877, _1224879, _1224881] : [hBOOL(hAPP(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), _1224873), _1224875)), _1224877)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1224873), _1224879)), _1224881))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1224877)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1224877), _1224873)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1224881), _1224873)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1224875), _1224879)))], (23941 ^ _780086) ^ [_1225222, _1225224, _1225226, _1225228, _1225230, _1225232] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1225222), _1225224)), _1225226) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1225228), _1225230)), _1225232), hBOOL(hAPP(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), _1225228), _1225230)), _1225232))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1225232), _1225228)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1225226)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1225228)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1225228), _1225222)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1225224), _1225230)))], (23967 ^ _780086) ^ [_1225721, _1225723] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1225721), _1225723))))], (23969 ^ _780086) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (23971 ^ _780086) ^ [_1225778] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1225778))))], (23973 ^ _780086) ^ [_1225806, _1225808] : [-(hAPP(c_Set_Oimage(tc_Int_Oint, tc_Int_Oint, hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint)), _1225806)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1225808), _1225806))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1225806), _1225808))], (23975 ^ _780086) ^ [_1225856, _1225858, _1225860, _1225862, _1225864, _1225866] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1225856), _1225858)), _1225860) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1225862), _1225864)), _1225866), hBOOL(hAPP(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), _1225862), _1225864)), _1225866)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1225860), _1225856)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1225866)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1225862)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1225862), _1225856)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1225864), _1225858)))], (24001 ^ _780086) ^ [_1226361, _1226363, _1226365, _1226367, _1226369] : [hBOOL(hAPP(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), _1226361), _1226363)), _1226365)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1226361), _1226367)), _1226369))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1226369), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1226361), _1226369)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1226361), _1226365)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1226367), _1226363)))], (24019 ^ _780086) ^ [_1226731, _1226733] : [24021 ^ _780086 : [(24022 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 24020 ^ [_1226731, _1226733]), _1226731)))], (24024 ^ _780086) ^ [] : [hBOOL(hAPP(_1226733, 24020 ^ [_1226731, _1226733]))]], 24025 ^ _780086 : [(24026 ^ _780086) ^ [_1226881] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1226881), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1226731))), -(hBOOL(hAPP(_1226733, _1226881)))]]], (24032 ^ _780086) ^ [_1226982, _1226984] : [24034 ^ _780086 : [(24035 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 24033 ^ [_1226982, _1226984]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1226982))))], (24037 ^ _780086) ^ [] : [hBOOL(hAPP(_1226984, 24033 ^ [_1226982, _1226984]))]], 24038 ^ _780086 : [(24039 ^ _780086) ^ [_1227135] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1227135), _1226982)), -(hBOOL(hAPP(_1226984, _1227135)))]]], (24045 ^ _780086) ^ [_1227251, _1227253] : [24053 ^ _780086 : [(24054 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 24052 ^ [_1227251, _1227253]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1227251))))], (24056 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1227253, 24052 ^ [_1227251, _1227253])))]], 24046 ^ _780086 : [(24047 ^ _780086) ^ [_1227319] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1227319), _1227251)), hBOOL(hAPP(_1227253, _1227319))]]], (24058 ^ _780086) ^ [_1227479, _1227481] : [24066 ^ _780086 : [(24067 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 24065 ^ [_1227479, _1227481]), _1227479)))], (24069 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1227481, 24065 ^ [_1227479, _1227481])))]], 24059 ^ _780086 : [(24060 ^ _780086) ^ [_1227547] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1227547), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1227479))), hBOOL(hAPP(_1227481, _1227547))]]], (24071 ^ _780086) ^ [_1227716, _1227718, _1227720, _1227722] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1227716, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1227716, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 24072 ^ [_1227716, _1227718, _1227720, _1227722])), _1227718)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1227716, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 24072 ^ [_1227716, _1227718, _1227720, _1227722]), _1227720))), _1227722))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1227716, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1227716, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1227718)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1227716, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1227722))))], (24078 ^ _780086) ^ [_1228046, _1228048, _1228050, _1228052] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1228046, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 24079 ^ [_1228046, _1228048, _1228050, _1228052])), _1228048) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1228046, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 24079 ^ [_1228046, _1228048, _1228050, _1228052]), _1228050))), _1228052), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1228046, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1228048) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1228046, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1228052))], (24085 ^ _780086) ^ [_1228326, _1228328, _1228330] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1228326, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1228326, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 24086 ^ [_1228326, _1228328, _1228330])), _1228328)), _1228330)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1228326, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1228326, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1228328)), _1228330)))], (24092 ^ _780086) ^ [_1228561, _1228563] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1228561), _1228563)), -(c_Nat__Transfer_Otsub(_1228563, _1228561) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1228563), _1228561))], (24098 ^ _780086) ^ [_1228660, _1228662] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1228660), _1228662))), -(c_Nat__Transfer_Otsub(_1228662, _1228660) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (24104 ^ _780086) ^ [_1228706, _1228708, _1228710] : [class_Orderings_Olinorder(_1228706), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1228706), _1228708), _1228710)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1228706, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1228706), _1228708), c_Orderings_Obot__class_Obot(tc_fun(_1228706, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanLessThan(_1228706, _1228708, _1228710)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1228706, _1228708), _1228710))], (24114 ^ _780086) ^ [_1228919, _1228921] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1228919)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1228921)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1228921), _1228919)), _1228921) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1228921), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1228919), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (24124 ^ _780086) ^ [_1229104, _1229106, _1229108, _1229110, _1229112, _1229114, _1229116, _1229118] : [c_Fun_Oinj__on(_1229104, _1229106, _1229108, _1229110), 24130 ^ _780086 : [(24131 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1229112), 24129 ^ [_1229104, _1229106, _1229108, _1229110, _1229112, _1229114, _1229116, _1229118]), _1229114)))], (24133 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1229104, tc_HOL_Obool)), hAPP(_1229116, 24129 ^ [_1229104, _1229106, _1229108, _1229110, _1229112, _1229114, _1229116, _1229118])), _1229110))]], hBOOL(hAPP(hAPP(c_member(_1229112), _1229118), _1229114)), -(hAPP(c_Set_Oimage(_1229104, _1229106, _1229108), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1229112, tc_fun(_1229104, tc_HOL_Obool)), _1229114), _1229116)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1229112, tc_fun(_1229106, tc_HOL_Obool)), _1229114), hAPP(hAPP(c_COMBB(tc_fun(_1229104, tc_HOL_Obool), tc_fun(_1229106, tc_HOL_Obool), _1229112), c_Set_Oimage(_1229104, _1229106, _1229108)), _1229116)))], (24141 ^ _780086) ^ [_1229593, _1229595] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(_1229593, _1229595)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_1229593)), c_Com_Ocom_Ocom__size(_1229595))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (24143 ^ _780086) ^ [_1229639, _1229641] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1229639, _1229641))))], (24145 ^ _780086) ^ [_1229670, _1229672] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1229670, _1229672))))], (24147 ^ _780086) ^ [_1229701] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229701) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (24149 ^ _780086) ^ [_1229727, _1229729] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1229727)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1229729)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1229727), _1229729))], (24151 ^ _780086) ^ [_1229770, _1229772] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1229770), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1229772)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1229770)), _1229772))], (24153 ^ _780086) ^ [_1229813, _1229815] : [class_Divides_Osemiring__div(_1229813), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1229813), _1229815), c_Groups_Ozero__class_Ozero(_1229813)) = c_Groups_Ozero__class_Ozero(_1229813))], (24159 ^ _780086) ^ [_1229912, _1229914] : [class_Divides_Osemiring__div(_1229912), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1229912), c_Groups_Ozero__class_Ozero(_1229912)), _1229914) = c_Groups_Ozero__class_Ozero(_1229912))], (24165 ^ _780086) ^ [_1230011, _1230013] : [class_Divides_Osemiring__div(_1230011), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1230011), _1230013), c_Groups_Oone__class_Oone(_1230011)) = _1230013)], (24171 ^ _780086) ^ [_1230106, _1230108] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230106)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230108)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1230106), _1230108))))], (24181 ^ _780086) ^ [_1230259, _1230261] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1230259), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230261)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1230259), _1230261)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24191 ^ _780086) ^ [_1230424, _1230426] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1230424), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 24194 ^ _780086 : [(24195 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1230426), _1230424)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230426)))], (24201 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230426)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1230426), _1230424)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (24207 ^ _780086) ^ [_1230680, _1230682] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230680)), 24210 ^ _780086 : [(24211 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1230682), _1230680)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1230682), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24217 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1230682), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1230682), _1230680)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (24223 ^ _780086) ^ [_1230935] : [-(_1230935 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1230935), _1230935) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (24229 ^ _780086) ^ [_1230975, _1230977, _1230979, _1230981] : [class_Divides_Osemiring__div(_1230975), 24232 ^ _780086 : [(24233 ^ _780086) ^ [] : [_1230977 = c_Groups_Ozero__class_Ozero(_1230975), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1230975), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1230975), _1230977), _1230979)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1230975), _1230977), _1230981)) = c_Groups_Ozero__class_Ozero(_1230975))], (24239 ^ _780086) ^ [] : [-(_1230977 = c_Groups_Ozero__class_Ozero(_1230975)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1230975), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1230975), _1230977), _1230979)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1230975), _1230977), _1230981)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1230975), _1230979), _1230981))]]], (24245 ^ _780086) ^ [_1231281, _1231283, _1231285] : [class_Divides_Osemiring__div(_1231281), -(_1231283 = c_Groups_Ozero__class_Ozero(_1231281)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1231281), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1231281), _1231285), _1231283)), _1231283) = _1231285)], (24255 ^ _780086) ^ [_1231409, _1231411, _1231413] : [class_Divides_Osemiring__div(_1231409), -(_1231411 = c_Groups_Ozero__class_Ozero(_1231409)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1231409), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1231409), _1231411), _1231413)), _1231411) = _1231413)], (24265 ^ _780086) ^ [_1231537, _1231539, _1231541, _1231543] : [class_Divides_Osemiring__div(_1231537), -(_1231539 = c_Groups_Ozero__class_Ozero(_1231537)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1231537), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1231537), _1231541), _1231539)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1231537), _1231543), _1231539)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1231537), _1231541), _1231543))], (24275 ^ _780086) ^ [_1231699, _1231701, _1231703, _1231705] : [class_Divides_Osemiring__div(_1231699), -(_1231701 = c_Groups_Ozero__class_Ozero(_1231699)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1231699), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1231699), _1231701), _1231703)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1231699), _1231701), _1231705)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1231699), _1231703), _1231705))], (24285 ^ _780086) ^ [_1231861, _1231863] : [class_Divides_Osemiring__div(_1231861), -(_1231863 = c_Groups_Ozero__class_Ozero(_1231861)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1231861), _1231863), _1231863) = c_Groups_Oone__class_Oone(_1231861))], (24295 ^ _780086) ^ [_1231975, _1231977, _1231979] : [class_Orderings_Oorder(_1231975), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1231975), _1231977), _1231979)), -(c_SetInterval_Oord__class_OgreaterThanLessThan(_1231975, _1231979, _1231977) = c_Orderings_Obot__class_Obot(tc_fun(_1231975, tc_HOL_Obool)))], (24305 ^ _780086) ^ [_1232153, _1232155] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1232153), _1232155) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1232155 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 24314 ^ _780086 : [(24315 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232153)))], (24317 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1232153), _1232155)))]], 24318 ^ _780086 : [(24319 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1232153), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24321 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1232155), _1232153)))]]], (24323 ^ _780086) ^ [_1232384, _1232386] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1232384), _1232386) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 24324 ^ _780086 : [(24325 ^ _780086) ^ [] : [_1232386 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (24327 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232384)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1232384), _1232386))], (24333 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1232384), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1232386), _1232384))]]], (24341 ^ _780086) ^ [_1232679, _1232681] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232679)), 24344 ^ _780086 : [(24345 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1232681), _1232679))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232681)))], (24351 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232681)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1232681), _1232679))))]]], (24357 ^ _780086) ^ [_1232920, _1232922] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232920)), 24360 ^ _780086 : [(24361 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1232922), _1232920))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1232920), _1232922)))], (24367 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1232920), _1232922)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1232922), _1232920))))]]], (24373 ^ _780086) ^ [_1233170, _1233172] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233170)), 24376 ^ _780086 : [(24377 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1233170), _1233172))), 24380 ^ _780086 : [(24381 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1233172), _1233170)))], (24383 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233172)))]]], (24385 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1233170), _1233172)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1233172), _1233170)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233172))]]], (24395 ^ _780086) ^ [_1233498, _1233500, _1233502] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233498)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233500)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1233500), _1233502)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1233498), _1233502)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1233498), _1233500))))], (24409 ^ _780086) ^ [_1233737, _1233739] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233737)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1233739), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1233737), _1233739)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24419 ^ _780086) ^ [_1233902, _1233904] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233902)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1233902), _1233904)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1233902), _1233904) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (24429 ^ _780086) ^ [_1234057, _1234059] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1234057), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 24432 ^ _780086 : [(24433 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1234059), _1234057))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1234059), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24439 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1234059), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1234059), _1234057))))]]], (24445 ^ _780086) ^ [_1234313, _1234315] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1234313), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1234315)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1234313), _1234315)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24455 ^ _780086) ^ [_1234478, _1234480, _1234482] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1234478), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1234480)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1234480), _1234482)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1234478), _1234480)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1234478), _1234482))))], (24469 ^ _780086) ^ [_1234723, _1234725] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1234723), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1234725), _1234723)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1234723), _1234725) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (24479 ^ _780086) ^ [_1234884, _1234886, _1234888] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1234884), _1234886)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1234888)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1234884), _1234888)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1234886), _1234888))))], (24489 ^ _780086) ^ [_1235065, _1235067, _1235069] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1235065), _1235067)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1235069), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1235067), _1235069)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1235065), _1235069))))], (24499 ^ _780086) ^ [_1235252, _1235254] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1235252)), _1235254) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1235252, _1235254))], (24501 ^ _780086) ^ [_1235290, _1235292, _1235294] : [class_Groups_Oordered__ab__group__add(_1235290), -(hAPP(c_Set_Oimage(_1235290, _1235290, c_Groups_Ouminus__class_Ouminus(_1235290)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1235290, _1235292, _1235294)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1235290, hAPP(c_Groups_Ouminus__class_Ouminus(_1235290), _1235294), hAPP(c_Groups_Ouminus__class_Ouminus(_1235290), _1235292)))], (24507 ^ _780086) ^ [_1235421, _1235423] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1235421)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1235423)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1235421), _1235423)), _1235421)))], (24517 ^ _780086) ^ [_1235580, _1235582, _1235584] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1235580)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1235582), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1235584), _1235580)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1235582), _1235584)), _1235580))], (24523 ^ _780086) ^ [_1235711, _1235713, _1235715, _1235717] : [class_Divides_Osemiring__div(_1235711), -(_1235713 = c_Groups_Ozero__class_Ozero(_1235711)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1235711), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1235711), _1235715), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1235711), _1235713), _1235717))), _1235713) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1235711), _1235717), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1235711), _1235715), _1235713)))], (24533 ^ _780086) ^ [_1235889, _1235891, _1235893, _1235895] : [class_Divides_Osemiring__div(_1235889), -(_1235891 = c_Groups_Ozero__class_Ozero(_1235889)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1235889), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1235889), _1235893), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1235889), _1235895), _1235891))), _1235891) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1235889), _1235895), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1235889), _1235893), _1235891)))], (24543 ^ _780086) ^ [_1236067, _1236069, _1236071] : [class_Divides_Osemiring__div(_1236067), -(_1236069 = c_Groups_Ozero__class_Ozero(_1236067)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1236067), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1236067), _1236071), _1236069)), _1236069) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1236067), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1236067), _1236071), _1236069)), c_Groups_Oone__class_Oone(_1236067)))], (24553 ^ _780086) ^ [_1236231, _1236233, _1236235] : [class_Divides_Osemiring__div(_1236231), -(_1236233 = c_Groups_Ozero__class_Ozero(_1236231)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1236231), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1236231), _1236233), _1236235)), _1236233) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1236231), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1236231), _1236235), _1236233)), c_Groups_Oone__class_Oone(_1236231)))], (24563 ^ _780086) ^ [] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24565 ^ _780086) ^ [_1236413, _1236415, _1236417, _1236419] : [class_Orderings_Oorder(_1236413), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1236413, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1236413, _1236415, _1236417)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1236413, _1236417), _1236419)) = c_Orderings_Obot__class_Obot(tc_fun(_1236413, tc_HOL_Obool)))], (24571 ^ _780086) ^ [_1236544, _1236546, _1236548, _1236550, _1236552] : [class_Orderings_Olinorder(_1236544), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1236544, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1236544, _1236546, _1236548)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1236544, _1236550, _1236552)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1236544, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1236544), _1236546), _1236550), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1236544), _1236548), _1236552)))], (24577 ^ _780086) ^ [_1236703, _1236705] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1236703, _1236705)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1236705), hAPP(c_Nat_OSuc, _1236703)))], (24579 ^ _780086) ^ [_1236744, _1236746] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1236744), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1236746) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1236744, _1236746))], (24627 ^ _780086) ^ [_1237763, _1237765, _1237767] : [-(hBOOL(hAPP(_1237763, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1237765), _1237767)))), 24630 ^ _780086 : [(24631 ^ _780086) ^ [] : [-(_1237767 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (24633 ^ _780086) ^ [] : [hBOOL(hAPP(_1237763, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], 24636 ^ _780086 : [(24637 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1237767)))], (24641 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 24639 ^ [_1237763, _1237765, _1237767])))], (24643 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 24639 ^ [_1237763, _1237765, _1237767]), _1237767)))], (24645 ^ _780086) ^ [] : [-(_1237765 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1237767), 24638 ^ [_1237763, _1237765, _1237767])), 24639 ^ [_1237763, _1237765, _1237767]))], (24647 ^ _780086) ^ [] : [hBOOL(hAPP(_1237763, 24638 ^ [_1237763, _1237765, _1237767]))]], 24648 ^ _780086 : [(24649 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1237767), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24653 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1237767), 24651 ^ [_1237763, _1237765, _1237767])))], (24655 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 24651 ^ [_1237763, _1237765, _1237767]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24657 ^ _780086) ^ [] : [-(_1237765 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1237767), 24650 ^ [_1237763, _1237765, _1237767])), 24651 ^ [_1237763, _1237765, _1237767]))], (24659 ^ _780086) ^ [] : [hBOOL(hAPP(_1237763, 24650 ^ [_1237763, _1237765, _1237767]))]]], (24581 ^ _780086) ^ [_1236803, _1236805, _1236807] : [hBOOL(hAPP(_1236803, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1236805), _1236807))), 24584 ^ _780086 : [(24585 ^ _780086) ^ [] : [_1236807 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1236803, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24591 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1236807)), 24594 ^ _780086 : [(24595 ^ _780086) ^ [_1237137] : [-(hBOOL(hAPP(_1236803, _1237137))), 24596 ^ _780086 : [(24597 ^ _780086) ^ [_1237208] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1237208)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1237208), _1236807)), _1236805 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1236807), _1237137)), _1237208)]]]]], (24609 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1236807), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 24612 ^ _780086 : [(24613 ^ _780086) ^ [_1237467] : [-(hBOOL(hAPP(_1236803, _1237467))), 24614 ^ _780086 : [(24615 ^ _780086) ^ [_1237541] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1236807), _1237541)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1237541), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1236805 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1236807), _1237467)), _1237541)]]]]]]], (24663 ^ _780086) ^ [_1238477, _1238479, _1238481, _1238483] : [_1238477 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1238479), _1238481)), _1238483), -(_1238479 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1238477), _1238479) = _1238481), 24670 ^ _780086 : [(24671 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1238479)))], (24673 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1238483)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1238483), _1238479))]], 24678 ^ _780086 : [(24679 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1238479))], (24681 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1238479), _1238483)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1238483), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (24693 ^ _780086) ^ [_1238946, _1238948] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1238946)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1238948)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Nat__Transfer_Otsub(_1238946, _1238948))))], (24703 ^ _780086) ^ [_1239093, _1239095] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1239093), _1239095)), -(c_Nat__Transfer_Otsub(_1239095, _1239093) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1239095), _1239093))], (24709 ^ _780086) ^ [_1239198, _1239200] : [-(c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1239198), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1239200)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1239198), _1239200)))], (24711 ^ _780086) ^ [_1239241, _1239243, _1239245, _1239247] : [class_Orderings_Olinorder(_1239241), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1239241), _1239243), _1239245)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1239241), _1239245), _1239247)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1239241, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1239241, _1239243, _1239245)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1239241, _1239245), _1239247)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1239241, _1239243, _1239247))], (24725 ^ _780086) ^ [_1239510, _1239512] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(_1239510, _1239512)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_1239512)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (24727 ^ _780086) ^ [_1239557, _1239559] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1239557)), -(c_SMT_Oz3div(_1239559, _1239557) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1239559), _1239557))], (24733 ^ _780086) ^ [_1239650, _1239652] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1239650))), -(c_SMT_Oz3div(_1239652, _1239650) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1239652), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1239650))))], (24739 ^ _780086) ^ [_1239705, _1239707, _1239709] : [class_Orderings_Olinorder(_1239705), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1239705), _1239707), _1239709)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1239705, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1239705, _1239707, _1239709)), hAPP(hAPP(c_Set_Oinsert(_1239705), _1239709), c_Orderings_Obot__class_Obot(tc_fun(_1239705, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1239705, _1239707, _1239709))], (24749 ^ _780086) ^ [_1239914, _1239916, _1239918] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1239914, tc_HOL_Obool)), _1239916), _1239918)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1239914, tc_HOL_Obool), tc_HOL_Obool)), c_Predicate_OPowp(_1239914, _1239916)), c_Predicate_OPowp(_1239914, _1239918))))], (24765 ^ _780086) ^ [_1240271, _1240273, _1240275, _1240277] : [24766 ^ _780086 : [(24767 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1240271), _1240273)))], (24769 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1240275), _1240277)))]], -(hAPP(c_Finite__Set_Ocard(tc_sum(_1240271, _1240275)), c_Sum__Type_OPlus(_1240271, _1240275, _1240273, _1240277)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24755 ^ _780086) ^ [_1240066, _1240068, _1240070, _1240072] : [-(hAPP(c_Finite__Set_Ocard(tc_sum(_1240066, _1240070)), c_Sum__Type_OPlus(_1240066, _1240070, _1240068, _1240072)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1240066), _1240068)), hAPP(c_Finite__Set_Ocard(_1240070), _1240072))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1240066), _1240068)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1240070), _1240072))], (24773 ^ _780086) ^ [_1240371, _1240373] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OSemi(_1240371, _1240373)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1240371)), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1240373))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (24775 ^ _780086) ^ [_1240420, _1240422] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1240420, _1240422))))], (24777 ^ _780086) ^ [_1240451, _1240453] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1240451, _1240453))))], (24779 ^ _780086) ^ [_1240482, _1240484, _1240486] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1240482), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1240484), _1240486)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1240482), _1240484)), _1240486))], (24781 ^ _780086) ^ [_1240533, _1240535] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1240533), _1240535)), _1240533)))], (24783 ^ _780086) ^ [_1240569, _1240571, _1240573] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1240569), _1240571)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1240569), _1240573)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1240571), _1240573))))], (24789 ^ _780086) ^ [_1240692] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1240692), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = _1240692)], (24791 ^ _780086) ^ [_1240721, _1240723] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1240721), _1240723)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1240721), _1240723) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24797 ^ _780086) ^ [_1240832, _1240834, _1240836] : [_1240832 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1240832), _1240834)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1240832), _1240836)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24803 ^ _780086) ^ [_1240941, _1240943, _1240945] : [-(_1240941 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1240941), _1240943)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1240941), _1240945)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1240943), _1240945))], (24809 ^ _780086) ^ [_1241005, _1241007] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1241005), _1241007)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1241005)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1241007)))], (24811 ^ _780086) ^ [_1241051, _1241053] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1241051)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1241053)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1241051), _1241053)))], (24813 ^ _780086) ^ [_1241097, _1241099, _1241101] : [class_Orderings_Oorder(_1241097), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1241097), _1241099), _1241101)), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1241097, _1241101, _1241099) = c_Orderings_Obot__class_Obot(tc_fun(_1241097, tc_HOL_Obool)))], (24823 ^ _780086) ^ [_1241260, _1241262, _1241264] : [class_Orderings_Oorder(_1241260), 24826 ^ _780086 : [(24827 ^ _780086) ^ [] : [c_SetInterval_Oord__class_OgreaterThanAtMost(_1241260, _1241262, _1241264) = c_Orderings_Obot__class_Obot(tc_fun(_1241260, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1241260), _1241262), _1241264))], (24833 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1241260), _1241262), _1241264))), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1241260, _1241262, _1241264) = c_Orderings_Obot__class_Obot(tc_fun(_1241260, tc_HOL_Obool)))]]], (24839 ^ _780086) ^ [_1241479, _1241481, _1241483] : [class_Orderings_Oorder(_1241479), 24842 ^ _780086 : [(24843 ^ _780086) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1241479, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1241479, _1241481, _1241483), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1241479), _1241481), _1241483))], (24849 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1241479), _1241481), _1241483))), -(c_Orderings_Obot__class_Obot(tc_fun(_1241479, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1241479, _1241481, _1241483))]]], (24855 ^ _780086) ^ [_1241698, _1241700, _1241702, _1241704] : [class_Orderings_Olinorder(_1241698), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1241698), _1241700), _1241702)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1241698), _1241702), _1241704)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1241698, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1241698, _1241700, _1241702)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1241698, _1241702, _1241704)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1241698, _1241700, _1241704))], (24869 ^ _780086) ^ [_1241963, _1241965, _1241967, _1241969] : [class_Orderings_Oorder(_1241963), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1241963, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1241963, _1241965, _1241967)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1241963, _1241967, _1241969)) = c_Orderings_Obot__class_Obot(tc_fun(_1241963, tc_HOL_Obool)))], (24875 ^ _780086) ^ [_1242090, _1242092, _1242094] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1242090)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1242090), _1242092)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1242094), _1242092)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1242094), _1242090))))], (24885 ^ _780086) ^ [_1242271, _1242273, _1242275] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1242271)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1242271), _1242273)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1242271), _1242275)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1242273), _1242275))], (24891 ^ _780086) ^ [_1242402, _1242404] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1242402)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1242402), _1242404)), _1242402) = _1242404)], (24897 ^ _780086) ^ [_1242507, _1242509] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1242507)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1242509), _1242507)), _1242507) = _1242509)], (24903 ^ _780086) ^ [_1242612, _1242614] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1242612)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1242614)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1242614), _1242612)), _1242614)))], (24913 ^ _780086) ^ [_1242771, _1242773] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1242771, _1242773)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1242773), _1242771))], (24915 ^ _780086) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24917 ^ _780086) ^ [_1242827, _1242829] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1242827)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1242829), _1242827))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1242829), _1242827) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1242829), _1242827)), _1242827)))], (24927 ^ _780086) ^ [_1242975, _1242977] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1242975)), 24930 ^ _780086 : [(24931 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1242977), _1242975)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1242977), _1242975) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24937 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1242977), _1242975))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1242977), _1242975) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1242977), _1242975)), _1242975)))]]], (24967 ^ _780086) ^ [_1243684, _1243686, _1243688] : [-(hBOOL(hAPP(_1243684, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1243686), _1243688)))), 24970 ^ _780086 : [(24971 ^ _780086) ^ [] : [-(_1243688 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24973 ^ _780086) ^ [] : [hBOOL(hAPP(_1243684, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 24974 ^ _780086 : [(24975 ^ _780086) ^ [] : [_1243688 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (24979 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 24977 ^ [_1243684, _1243686, _1243688]), _1243688)))], (24981 ^ _780086) ^ [] : [-(_1243686 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1243688), 24976 ^ [_1243684, _1243686, _1243688])), 24977 ^ [_1243684, _1243686, _1243688]))], (24983 ^ _780086) ^ [] : [hBOOL(hAPP(_1243684, 24976 ^ [_1243684, _1243686, _1243688]))]]], (24943 ^ _780086) ^ [_1243247, _1243249, _1243251] : [hBOOL(hAPP(_1243247, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1243249), _1243251))), 24946 ^ _780086 : [(24947 ^ _780086) ^ [] : [_1243251 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1243247, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (24953 ^ _780086) ^ [] : [-(_1243251 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 24956 ^ _780086 : [(24957 ^ _780086) ^ [_1243499, _1243501] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1243499), _1243251)), _1243249 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1243251), _1243501)), _1243499), -(hBOOL(hAPP(_1243247, _1243501)))]]]]], (24987 ^ _780086) ^ [_1244106, _1244108, _1244110, _1244112, _1244114] : [class_Orderings_Olinorder(_1244106), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1244106, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1244106, _1244108, _1244110)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1244106, _1244112, _1244114)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1244106, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1244106), _1244108), _1244112), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1244106), _1244110), _1244114)))], (24993 ^ _780086) ^ [_1244265, _1244267, _1244269] : [class_Groups_Oordered__ab__group__add(_1244265), -(hAPP(c_Set_Oimage(_1244265, _1244265, c_Groups_Ouminus__class_Ouminus(_1244265)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1244265, _1244267), _1244269)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1244265, hAPP(c_Groups_Ouminus__class_Ouminus(_1244265), _1244269), hAPP(c_Groups_Ouminus__class_Ouminus(_1244265), _1244267)))], (24999 ^ _780086) ^ [_1244400, _1244402, _1244404] : [class_Groups_Oordered__ab__group__add(_1244400), -(hAPP(c_Set_Oimage(_1244400, _1244400, c_Groups_Ouminus__class_Ouminus(_1244400)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1244400, _1244402, _1244404)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1244400, hAPP(c_Groups_Ouminus__class_Ouminus(_1244400), _1244404)), hAPP(c_Groups_Ouminus__class_Ouminus(_1244400), _1244402)))], (25005 ^ _780086) ^ [_1244535, _1244537, _1244539, _1244541] : [class_Orderings_Oorder(_1244535), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1244535, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1244535, _1244537, _1244539)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1244535, _1244539, _1244541)) = c_Orderings_Obot__class_Obot(tc_fun(_1244535, tc_HOL_Obool)))], (25011 ^ _780086) ^ [_1244683, _1244685, _1244687, _1244689] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1244683, _1244685)), c_Sum__Type_OPlus(_1244683, _1244685, _1244687, _1244689))), 25014 ^ _780086 : [(25015 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1244683), _1244687)))], (25017 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1244685), _1244689)))]]], (25019 ^ _780086) ^ [_1244826, _1244828, _1244830, _1244832] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1244826, _1244828)), c_Sum__Type_OPlus(_1244826, _1244828, _1244830, _1244832)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1244826), _1244830)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1244828), _1244832))], (25029 ^ _780086) ^ [_1245005, _1245007, _1245009, _1245011] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1245005), _1245007)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1245009), _1245011)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1245005, _1245009)), c_Sum__Type_OPlus(_1245005, _1245009, _1245007, _1245011))))], (25039 ^ _780086) ^ [_1245182, _1245184, _1245186, _1245188] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1245182, _1245184)), c_Sum__Type_OPlus(_1245182, _1245184, _1245186, _1245188))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1245182), _1245186)))], (25045 ^ _780086) ^ [_1245295, _1245297, _1245299, _1245301] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1245295, _1245297)), c_Sum__Type_OPlus(_1245295, _1245297, _1245299, _1245301))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1245297), _1245301)))], (25051 ^ _780086) ^ [_1245408, _1245410] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1245408)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1245408), _1245410)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1245410), _1245408) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1245410), _1245408)), _1245408)))], (25061 ^ _780086) ^ [_1245611, _1245613, _1245615] : [hBOOL(hAPP(_1245611, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1245613), _1245615))), 25066 ^ _780086 : [(25067 ^ _780086) ^ [] : [-(_1245615 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25069 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1245611, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]], 25071 ^ _780086 : [(25072 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1245615), 25070 ^ [_1245611, _1245613, _1245615])), _1245613)))], (25074 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1245613), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1245615), hAPP(c_Nat_OSuc, 25070 ^ [_1245611, _1245613, _1245615])))))], (25076 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1245611, 25070 ^ [_1245611, _1245613, _1245615])))]]], (25078 ^ _780086) ^ [_1245915, _1245917, _1245919] : [-(hBOOL(hAPP(_1245915, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1245917), _1245919)))), 25079 ^ _780086 : [(25080 ^ _780086) ^ [] : [_1245919 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hBOOL(hAPP(_1245915, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (25086 ^ _780086) ^ [_1246083] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1245919), _1246083)), _1245917)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1245917), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1245919), hAPP(c_Nat_OSuc, _1246083)))), hBOOL(hAPP(_1245915, _1246083))]]], (25098 ^ _780086) ^ [_1246313, _1246315, _1246317] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1246313)), 25101 ^ _780086 : [(25112 ^ _780086) ^ [] : [_1246315 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1246317), _1246313), 25115 ^ _780086 : [(25116 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1246313), _1246315)), _1246317)))], (25118 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1246317), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1246313), hAPP(c_Nat_OSuc, _1246315)))))]]], (25102 ^ _780086) ^ [] : [-(_1246315 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1246317), _1246313)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1246313), _1246315)), _1246317)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1246317), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1246313), hAPP(c_Nat_OSuc, _1246315))))]]], (25120 ^ _780086) ^ [_1246697, _1246699, _1246701, _1246703] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1246697), _1246699)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1246701), _1246703)), -(hAPP(c_Finite__Set_Ocard(tc_sum(_1246697, _1246701)), c_Sum__Type_OPlus(_1246697, _1246701, _1246699, _1246703)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1246697), _1246699)), hAPP(c_Finite__Set_Ocard(_1246701), _1246703)))], (25130 ^ _780086) ^ [_1246908, _1246910, _1246912, _1246914] : [class_Orderings_Olinorder(_1246908), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1246908), _1246910), _1246912)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1246908), _1246912), _1246914)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1246908, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1246908, _1246910, _1246912)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1246908, _1246912, _1246914)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1246908, _1246910, _1246914))], (25144 ^ _780086) ^ [_1247173, _1247175] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OWhile(_1247173, _1247175)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1247175)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (25146 ^ _780086) ^ [_1247213, _1247215] : [-(c_Sum__Type_OPlus(_1247213, _1247215, c_Orderings_Otop__class_Otop(tc_fun(_1247213, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1247215, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1247213, _1247215), tc_HOL_Obool)))], (25148 ^ _780086) ^ [_1247282, _1247284, _1247286, _1247288] : [c_Sum__Type_OPlus(_1247282, _1247284, _1247286, _1247288) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1247282, _1247284), tc_HOL_Obool)), 25151 ^ _780086 : [(25152 ^ _780086) ^ [] : [-(_1247286 = c_Orderings_Obot__class_Obot(tc_fun(_1247282, tc_HOL_Obool)))], (25154 ^ _780086) ^ [] : [-(_1247288 = c_Orderings_Obot__class_Obot(tc_fun(_1247284, tc_HOL_Obool)))]]], (25156 ^ _780086) ^ [_1247431, _1247433, _1247435, _1247437] : [-(c_Sum__Type_OPlus(_1247431, _1247433, _1247435, _1247437) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1247431, _1247433), tc_HOL_Obool))), _1247435 = c_Orderings_Obot__class_Obot(tc_fun(_1247431, tc_HOL_Obool)), _1247437 = c_Orderings_Obot__class_Obot(tc_fun(_1247433, tc_HOL_Obool))], (25166 ^ _780086) ^ [_1247616, _1247618, _1247620, _1247622, _1247624] : [class_Fields_Ofield(_1247616), hBOOL(hAPP(c_Finite__Set_Ofinite(_1247618), _1247620)), -(hAPP(_1247622, _1247624) = c_Groups_Ozero__class_Ozero(_1247616)), 25177 ^ _780086 : [(25178 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1247618), _1247624), _1247620)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1247618, _1247616), _1247622), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1247618, tc_HOL_Obool)), _1247620), hAPP(hAPP(c_Set_Oinsert(_1247618), _1247624), c_Orderings_Obot__class_Obot(tc_fun(_1247618, tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1247616), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1247618, _1247616), _1247622), _1247620)), hAPP(_1247622, _1247624)))], (25184 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1247618), _1247624), _1247620))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1247618, _1247616), _1247622), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1247618, tc_HOL_Obool)), _1247620), hAPP(hAPP(c_Set_Oinsert(_1247618), _1247624), c_Orderings_Obot__class_Obot(tc_fun(_1247618, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1247618, _1247616), _1247622), _1247620))]]], (25190 ^ _780086) ^ [_1248157] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1248157)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1248157) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Int_Onat, _1248157))))], (25196 ^ _780086) ^ [_1248260, _1248262, _1248264, _1248266, _1248268] : [class_Groups_Oordered__ab__group__add(_1248260), hBOOL(hAPP(c_Finite__Set_Ofinite(_1248262), _1248264)), 25206 ^ _780086 : [(25207 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1248262), 25205 ^ [_1248260, _1248262, _1248264, _1248266, _1248268]), _1248264)))], (25209 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1248260), c_Groups_Ozero__class_Ozero(_1248260)), hAPP(_1248266, 25205 ^ [_1248260, _1248262, _1248264, _1248266, _1248268])))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1248262, _1248260), _1248266), _1248264) = c_Groups_Ozero__class_Ozero(_1248260), hBOOL(hAPP(hAPP(c_member(_1248262), _1248268), _1248264)), -(hAPP(_1248266, _1248268) = c_Groups_Ozero__class_Ozero(_1248260))], (25221 ^ _780086) ^ [_1248758, _1248760, _1248762, _1248764] : [class_Fields_Ofield__inverse__zero(_1248758), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1248758), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1248758), _1248760), _1248762)), _1248764) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1248758), hAPP(hAPP(c_Power_Opower__class_Opower(_1248758), _1248760), _1248764)), hAPP(hAPP(c_Power_Opower__class_Opower(_1248758), _1248762), _1248764)))], (25227 ^ _780086) ^ [_1248917] : [-(hAPP(c_Int_Onat, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1248917)) = _1248917)], (25229 ^ _780086) ^ [_1248946, _1248948] : [class_Rings_Odivision__ring(_1248946), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1248946), c_Groups_Ozero__class_Ozero(_1248946)), _1248948) = c_Groups_Ozero__class_Ozero(_1248946))], (25235 ^ _780086) ^ [_1249045, _1249047] : [class_Rings_Odivision__ring__inverse__zero(_1249045), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1249045), _1249047), c_Groups_Ozero__class_Ozero(_1249045)) = c_Groups_Ozero__class_Ozero(_1249045))], (25241 ^ _780086) ^ [_1249144, _1249146, _1249148] : [class_Rings_Odivision__ring(_1249144), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1249144), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1249144), _1249146), _1249148)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1249144), hAPP(c_Groups_Ouminus__class_Ouminus(_1249144), _1249146)), _1249148))], (25247 ^ _780086) ^ [_1249273, _1249275] : [class_Rings_Odivision__ring(_1249273), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1249273), _1249275), c_Groups_Oone__class_Oone(_1249273)) = _1249275)], (25253 ^ _780086) ^ [_1249368, _1249370, _1249372, _1249374] : [class_Rings_Odivision__ring(_1249368), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1249368), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1249368), _1249370), _1249372)), _1249374) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1249368), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1249368), _1249370), _1249374)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1249368), _1249372), _1249374)))], (25259 ^ _780086) ^ [_1249527, _1249529, _1249531, _1249533] : [class_Rings_Odivision__ring(_1249527), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1249527), _1249529), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1249527), _1249531), _1249533)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1249527), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1249527), _1249529), _1249531)), _1249533))], (25265 ^ _780086) ^ [_1249670, _1249672, _1249674, _1249676] : [class_Rings_Odivision__ring(_1249670), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1249670), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1249670), _1249672), _1249674)), _1249676) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1249670), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1249670), _1249672), _1249676)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1249670), _1249674), _1249676)))], (25271 ^ _780086) ^ [_1249829, _1249831, _1249833, _1249835, _1249837] : [class_Fields_Ofield(_1249829), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1249829), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1249831, _1249829), _1249833), _1249835)), _1249837) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1249831, _1249829), hAPP(hAPP(c_COMBC(_1249831, _1249829, _1249829), hAPP(hAPP(c_COMBB(_1249829, tc_fun(_1249829, _1249829), _1249831), c_Rings_Oinverse__class_Odivide(_1249829)), _1249833)), _1249837)), _1249835))], (25277 ^ _780086) ^ [_1250012, _1250014, _1250016, _1250018] : [class_Rings_Odivision__ring(_1250012), -(_1250014 = c_Groups_Ozero__class_Ozero(_1250012)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1250012), _1250016), _1250014) = _1250018, -(_1250016 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1250012), _1250018), _1250014))], (25291 ^ _780086) ^ [_1250242, _1250244, _1250246, _1250248] : [class_Rings_Odivision__ring(_1250242), -(_1250244 = c_Groups_Ozero__class_Ozero(_1250242)), _1250246 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1250242), _1250248), _1250244), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1250242), _1250246), _1250244) = _1250248)], (25305 ^ _780086) ^ [_1250472, _1250474, _1250476, _1250478] : [class_Rings_Odivision__ring(_1250472), -(_1250474 = c_Groups_Ozero__class_Ozero(_1250472)), 25312 ^ _780086 : [(25313 ^ _780086) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1250472), _1250476), _1250474) = _1250478, -(_1250476 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1250472), _1250478), _1250474))], (25319 ^ _780086) ^ [] : [_1250476 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1250472), _1250478), _1250474), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1250472), _1250476), _1250474) = _1250478)]]], (25325 ^ _780086) ^ [_1250800, _1250802, _1250804, _1250806] : [class_Rings_Odivision__ring(_1250800), -(_1250802 = c_Groups_Ozero__class_Ozero(_1250800)), 25332 ^ _780086 : [(25333 ^ _780086) ^ [] : [_1250804 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1250800), _1250806), _1250802), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1250800), _1250804), _1250802) = _1250806)], (25339 ^ _780086) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1250800), _1250804), _1250802) = _1250806, -(_1250804 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1250800), _1250806), _1250802))]]], (25345 ^ _780086) ^ [_1251128, _1251130, _1251132] : [class_Rings_Odivision__ring(_1251128), -(_1251130 = c_Groups_Ozero__class_Ozero(_1251128)), 25352 ^ _780086 : [(25353 ^ _780086) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1251128), _1251132), _1251130) = c_Groups_Oone__class_Oone(_1251128), -(_1251132 = _1251130)], (25359 ^ _780086) ^ [] : [_1251132 = _1251130, -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1251128), _1251132), _1251130) = c_Groups_Oone__class_Oone(_1251128))]]], (25365 ^ _780086) ^ [_1251430, _1251432] : [class_Rings_Odivision__ring(_1251430), -(_1251432 = c_Groups_Ozero__class_Ozero(_1251430)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1251430), _1251432), _1251432) = c_Groups_Oone__class_Oone(_1251430))], (25375 ^ _780086) ^ [_1251544, _1251546] : [class_Rings_Odivision__ring__inverse__zero(_1251544), 25378 ^ _780086 : [(25379 ^ _780086) ^ [] : [_1251546 = c_Groups_Ozero__class_Ozero(_1251544), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1251544), _1251546), _1251546) = c_Groups_Ozero__class_Ozero(_1251544))], (25385 ^ _780086) ^ [] : [-(_1251546 = c_Groups_Ozero__class_Ozero(_1251544)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1251544), _1251546), _1251546) = c_Groups_Oone__class_Oone(_1251544))]]], (25391 ^ _780086) ^ [_1251766, _1251768, _1251770] : [class_Rings_Odivision__ring(_1251766), -(_1251768 = c_Groups_Ozero__class_Ozero(_1251766)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1251766), hAPP(c_Groups_Ouminus__class_Ouminus(_1251766), _1251770)), hAPP(c_Groups_Ouminus__class_Ouminus(_1251766), _1251768)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1251766), _1251770), _1251768))], (25401 ^ _780086) ^ [_1251914, _1251916, _1251918] : [class_Rings_Odivision__ring(_1251914), -(_1251916 = c_Groups_Ozero__class_Ozero(_1251914)), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1251914), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1251914), _1251918), _1251916)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1251914), _1251918), hAPP(c_Groups_Ouminus__class_Ouminus(_1251914), _1251916)))], (25411 ^ _780086) ^ [_1252062, _1252064, _1252066, _1252068] : [class_Fields_Ofield(_1252062), -(_1252064 = c_Groups_Ozero__class_Ozero(_1252062)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1252062), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1252062), _1252066), _1252064)), _1252068) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1252062), hAPP(hAPP(c_Power_Opower__class_Opower(_1252062), _1252066), _1252068)), hAPP(hAPP(c_Power_Opower__class_Opower(_1252062), _1252064), _1252068)))], (25421 ^ _780086) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25423 ^ _780086) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (25425 ^ _780086) ^ [_1252276, _1252278] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1252276)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1252278)), 25432 ^ _780086 : [(25433 ^ _780086) ^ [] : [hAPP(c_Int_Onat, _1252276) = hAPP(c_Int_Onat, _1252278), -(_1252276 = _1252278)], (25439 ^ _780086) ^ [] : [_1252276 = _1252278, -(hAPP(c_Int_Onat, _1252276) = hAPP(c_Int_Onat, _1252278))]]], (25445 ^ _780086) ^ [_1252561, _1252563] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1252561)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1252563)), 25452 ^ _780086 : [(25453 ^ _780086) ^ [] : [hAPP(c_Int_Onat, _1252561) = hAPP(c_Int_Onat, _1252563), -(_1252561 = _1252563)], (25459 ^ _780086) ^ [] : [_1252561 = _1252563, -(hAPP(c_Int_Onat, _1252561) = hAPP(c_Int_Onat, _1252563))]]], (25476 ^ _780086) ^ [_1253043] : [25478 ^ _780086 : [(25479 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 25477 ^ [_1253043])))], (25481 ^ _780086) ^ [] : [hBOOL(hAPP(_1253043, hAPP(c_Int_Onat, 25477 ^ [_1253043])))]], 25482 ^ _780086 : [(25483 ^ _780086) ^ [_1253176] : [-(hBOOL(hAPP(_1253043, _1253176)))]]], (25465 ^ _780086) ^ [_1252858] : [hBOOL(hAPP(_1252858, 25466 ^ [_1252858])), 25469 ^ _780086 : [(25470 ^ _780086) ^ [_1252952] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1252952)), -(hBOOL(hAPP(_1252858, hAPP(c_Int_Onat, _1252952))))]]], (25485 ^ _780086) ^ [_1253221] : [25486 ^ _780086 : [(25487 ^ _780086) ^ [_1253278] : [hBOOL(hAPP(_1253221, _1253278))]], 25489 ^ _780086 : [(25490 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 25488 ^ [_1253221])))], (25492 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1253221, hAPP(c_Int_Onat, 25488 ^ [_1253221]))))]]], (25494 ^ _780086) ^ [_1253364] : [-(hBOOL(hAPP(_1253364, 25501 ^ [_1253364]))), 25495 ^ _780086 : [(25496 ^ _780086) ^ [_1253416] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1253416)), hBOOL(hAPP(_1253364, hAPP(c_Int_Onat, _1253416)))]]], (25505 ^ _780086) ^ [_1253543, _1253545, _1253547] : [class_Fields_Ofield__inverse__zero(_1253543), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1253543), c_Groups_Oone__class_Oone(_1253543)), hAPP(hAPP(c_Power_Opower__class_Opower(_1253543), _1253545), _1253547)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1253543), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1253543), c_Groups_Oone__class_Oone(_1253543)), _1253545)), _1253547))], (25511 ^ _780086) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (25513 ^ _780086) ^ [_1253710, _1253712] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1253710), _1253712) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1253710)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1253712))))], (25515 ^ _780086) ^ [_1253756] : [-(hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1253756)) = _1253756)], (25517 ^ _780086) ^ [_1253785, _1253787, _1253789, _1253791, _1253793] : [class_Fields_Ofield__inverse__zero(_1253785), hBOOL(hAPP(c_Finite__Set_Ofinite(_1253787), _1253789)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1253787, _1253785), hAPP(hAPP(c_COMBS(_1253787, _1253785, _1253785), hAPP(hAPP(c_COMBB(_1253785, tc_fun(_1253785, _1253785), _1253787), c_Rings_Oinverse__class_Odivide(_1253785)), _1253791)), _1253793)), _1253789) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1253785), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1253787, _1253785), _1253791), _1253789)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1253787, _1253785), _1253793), _1253789)))], (25527 ^ _780086) ^ [_1254052, _1254054] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1254052, _1254054)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1254054), _1254052)))], (25529 ^ _780086) ^ [_1254093, _1254095, _1254097] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1254093), _1254095), _1254097) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1254093), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1254093, tc_Int_Oint), _1254095), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1254097))), class_Groups_Ocomm__monoid__add(_1254093), class_Groups_Ocomm__monoid__mult(_1254093)], (25539 ^ _780086) ^ [] : [-(c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (25541 ^ _780086) ^ [_1254314] : [hAPP(c_Int_Onat, _1254314) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1254314), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (25547 ^ _780086) ^ [_1254401] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1254401), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1254401) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25553 ^ _780086) ^ [_1254494] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1254494), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1254494) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25559 ^ _780086) ^ [_1254600, _1254602] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1254600)), hAPP(c_Int_Onat, _1254602))), 25562 ^ _780086 : [(25563 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1254602)))], (25565 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1254600), _1254602)))]]], (25567 ^ _780086) ^ [_1254735, _1254737] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1254735)), hAPP(c_Int_Onat, _1254737)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1254737)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1254735), _1254737))], (25577 ^ _780086) ^ [_1254902, _1254904] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1254902)), 25580 ^ _780086 : [(25581 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1254904)), hAPP(c_Int_Onat, _1254902))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1254904), _1254902)))], (25587 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1254904), _1254902)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1254904)), hAPP(c_Int_Onat, _1254902))))]]], (25593 ^ _780086) ^ [_1255161, _1255163] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1255161)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1255163)), 25600 ^ _780086 : [(25601 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1255161)), hAPP(c_Int_Onat, _1255163))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1255161), _1255163)))], (25607 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1255161), _1255163)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1255161)), hAPP(c_Int_Onat, _1255163))))]]], (25613 ^ _780086) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (25615 ^ _780086) ^ [_1255500] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1255500)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1255500)) = _1255500)], (25621 ^ _780086) ^ [_1255585] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1255585))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1255585)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (25627 ^ _780086) ^ [_1255644, _1255646] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1255644) = _1255646, 25630 ^ _780086 : [(25631 ^ _780086) ^ [] : [-(_1255644 = hAPP(c_Int_Onat, _1255646))], (25633 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1255646)))]]], (25635 ^ _780086) ^ [_1255759, _1255761] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1255759) = _1255761), _1255759 = hAPP(c_Int_Onat, _1255761), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1255761))], (25645 ^ _780086) ^ [_1255906] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1255906)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1255906)) = _1255906)], (25651 ^ _780086) ^ [_1256012, _1256014] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1256012), hAPP(c_Int_Onat, _1256014))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1256012)), _1256014)))], (25657 ^ _780086) ^ [_1256117, _1256119] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1256117)), _1256119)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1256117), hAPP(c_Int_Onat, _1256119))))], (25663 ^ _780086) ^ [_1256228, _1256230] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1256228)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1256230)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1256228)), hAPP(c_Int_Onat, _1256230)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1256228), _1256230)))], (25673 ^ _780086) ^ [_1256407, _1256409] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1256407)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1256407), _1256409)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1256407)), hAPP(c_Int_Onat, _1256409)))], (25679 ^ _780086) ^ [_1256530] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1256530))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25681 ^ _780086) ^ [_1256562, _1256564, _1256566] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1256562), _1256564), _1256566) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1256562), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1256562, tc_Int_Oint), _1256564), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1256566))), class_Groups_Ocomm__monoid__add(_1256562), class_Groups_Ocomm__monoid__mult(_1256562)], (25691 ^ _780086) ^ [_1256753] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1256753)) = hAPP(c_Int_Onat, _1256753))], (25693 ^ _780086) ^ [_1256785, _1256787] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1256785), _1256787)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1256787), _1256785)))], (25695 ^ _780086) ^ [_1256840] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1256840))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1256840)))], (25701 ^ _780086) ^ [_1256925] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1256925)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1256925))))], (25707 ^ _780086) ^ [_1257016, _1257018, _1257020, _1257022] : [class_Fields_Ofield(_1257016), -(_1257018 = c_Groups_Ozero__class_Ozero(_1257016)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1257020), _1257022)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1257016), _1257018), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1257022), _1257020)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1257016), hAPP(hAPP(c_Power_Opower__class_Opower(_1257016), _1257018), _1257022)), hAPP(hAPP(c_Power_Opower__class_Opower(_1257016), _1257018), _1257020)))], (25721 ^ _780086) ^ [_1257300, _1257302] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1257300)), 25724 ^ _780086 : [(25725 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1257300)), hAPP(c_Int_Onat, _1257302))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1257300), _1257302)))], (25731 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1257300), _1257302)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1257300)), hAPP(c_Int_Onat, _1257302))))]]], (25737 ^ _780086) ^ [_1257559, _1257561] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1257559)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1257561)), 25744 ^ _780086 : [(25745 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1257559)), hAPP(c_Int_Onat, _1257561))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1257559), _1257561)))], (25751 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1257559), _1257561)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1257559)), hAPP(c_Int_Onat, _1257561))))]]], (25773 ^ _780086) ^ [_1258081, _1258083] : [-(hAPP(c_Int_Onat, _1258081) = _1258083), 25776 ^ _780086 : [(25777 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1258081)))], (25779 ^ _780086) ^ [] : [_1258081 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1258083)]], 25780 ^ _780086 : [(25781 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1258081))], (25783 ^ _780086) ^ [] : [_1258083 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (25757 ^ _780086) ^ [_1257889, _1257891] : [hAPP(c_Int_Onat, _1257889) = _1257891, 25760 ^ _780086 : [(25761 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1257889)), -(_1257889 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1257891))], (25767 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1257889))), -(_1257891 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (25803 ^ _780086) ^ [_1258512, _1258514] : [-(_1258512 = hAPP(c_Int_Onat, _1258514)), 25806 ^ _780086 : [(25807 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1258514)))], (25809 ^ _780086) ^ [] : [_1258514 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1258512)]], 25810 ^ _780086 : [(25811 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1258514))], (25813 ^ _780086) ^ [] : [_1258512 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (25787 ^ _780086) ^ [_1258320, _1258322] : [_1258320 = hAPP(c_Int_Onat, _1258322), 25790 ^ _780086 : [(25791 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1258322)), -(_1258322 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1258320))], (25797 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1258322))), -(_1258320 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (25817 ^ _780086) ^ [_1258736, _1258738] : [25818 ^ _780086 : [(25819 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1258736))], (25821 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1258738))]], 25822 ^ _780086 : [(25823 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1258736)), hAPP(c_Int_Onat, _1258738))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1258736), _1258738)))], (25829 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1258736), _1258738)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1258736)), hAPP(c_Int_Onat, _1258738))))]]], (25851 ^ _780086) ^ [_1259315, _1259317] : [-(hBOOL(hAPP(_1259315, hAPP(c_Int_Onat, _1259317)))), 25855 ^ _780086 : [(25856 ^ _780086) ^ [] : [-(_1259317 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 25854 ^ [_1259315, _1259317]))], (25858 ^ _780086) ^ [] : [hBOOL(hAPP(_1259315, 25854 ^ [_1259315, _1259317]))]], 25859 ^ _780086 : [(25860 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1259317), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (25862 ^ _780086) ^ [] : [hBOOL(hAPP(_1259315, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (25835 ^ _780086) ^ [_1259052, _1259054] : [hBOOL(hAPP(_1259052, hAPP(c_Int_Onat, _1259054))), 25838 ^ _780086 : [(25839 ^ _780086) ^ [_1259152] : [_1259054 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1259152), -(hBOOL(hAPP(_1259052, _1259152)))], (25845 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1259054), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(_1259052, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (25866 ^ _780086) ^ [_1259578, _1259580] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1259578)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1259580)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1259578), _1259580)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1259578)), hAPP(c_Int_Onat, _1259580)))], (25876 ^ _780086) ^ [_1259757, _1259759] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1259757)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1259759)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1259757)), hAPP(c_Int_Onat, _1259759)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1259757), _1259759)))], (25886 ^ _780086) ^ [_1259936, _1259938] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1259936)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1259936), _1259938)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1259936)), hAPP(c_Int_Onat, _1259938)))], (25892 ^ _780086) ^ [_1260059, _1260061] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1260059)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1260061)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1260059)), hAPP(c_Int_Onat, _1260061)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1260059), _1260061)))], (25902 ^ _780086) ^ [_1260238, _1260240] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1260238), _1260240) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1260238)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1260240))))], (25904 ^ _780086) ^ [_1260284, _1260286] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1260284)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1260284), _1260286)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1260286), _1260284)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1260286)), hAPP(c_Int_Onat, _1260284)))], (25914 ^ _780086) ^ [_1260469, _1260471, _1260473] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1260469, tc_Nat_Onat), _1260471), _1260473) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1260469, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1260469), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1260471)), _1260473)))], (25916 ^ _780086) ^ [_1260527, _1260529] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1260527)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1260527)), _1260529) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1260527), _1260529)))], (25922 ^ _780086) ^ [_1260644, _1260646] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1260644)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1260644), _1260646)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1260644)), _1260646))], (25928 ^ _780086) ^ [_1260761, _1260763, _1260765] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1260761, tc_Nat_Onat), _1260763), _1260765) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1260761, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1260761), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1260763)), _1260765)))], (25930 ^ _780086) ^ [_1260819, _1260821] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1260819)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1260821)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1260819)), hAPP(c_Int_Onat, _1260821)) = hAPP(c_Int_Onat, c_Nat__Transfer_Otsub(_1260819, _1260821)))], (25940 ^ _780086) ^ [_1261004] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), hAPP(c_Int_Onat, _1261004))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1261004)))], (25946 ^ _780086) ^ [_1261089] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1261089)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), hAPP(c_Int_Onat, _1261089))))], (25952 ^ _780086) ^ [_1261180, _1261182] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1261180)), 25955 ^ _780086 : [(25956 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1261180)), _1261182)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1261180), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1261182))))], (25962 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1261180), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1261182))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1261180)), _1261182)))]]], (25968 ^ _780086) ^ [_1261439] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1261439)), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onat, _1261439)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1261439)))], (25974 ^ _780086) ^ [_1261542, _1261544] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1261542), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1261542), _1261544)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1261542))), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1261544))))], (25980 ^ _780086) ^ [_1261683, _1261685] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1261683, _1261685)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1261685), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1261683), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (25982 ^ _780086) ^ [_1261730, _1261732, _1261734] : [class_Fields_Ofield(_1261730), -(_1261732 = c_Groups_Oone__class_Oone(_1261730)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1261730), hAPP(c_Power_Opower__class_Opower(_1261730), _1261732)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1261734)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1261730), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1261730), hAPP(hAPP(c_Power_Opower__class_Opower(_1261730), _1261732), _1261734)), c_Groups_Oone__class_Oone(_1261730))), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1261730), _1261732), c_Groups_Oone__class_Oone(_1261730))))], (25992 ^ _780086) ^ [_1261932, _1261934, _1261936, _1261938] : [class_Fields_Olinordered__field__inverse__zero(_1261932), 25995 ^ _780086 : [(26022 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1261932), _1261934), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1261932), _1261936), _1261938)))), 26025 ^ _780086 : [(26026 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1261932), c_Groups_Ozero__class_Ozero(_1261932)), _1261938)))], (26028 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1261932), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1261932), _1261934), _1261938)), _1261936))]], 26029 ^ _780086 : [(26030 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1261932), c_Groups_Ozero__class_Ozero(_1261932)), _1261938))], (26032 ^ _780086) ^ [] : [26033 ^ _780086 : [(26034 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1261932), _1261938), c_Groups_Ozero__class_Ozero(_1261932))))], (26036 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1261932), _1261936), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1261932), _1261934), _1261938)))]], 26037 ^ _780086 : [(26038 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1261932), _1261938), c_Groups_Ozero__class_Ozero(_1261932)))], (26040 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1261932), _1261934), c_Groups_Ozero__class_Ozero(_1261932)))]]]]], (25996 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1261932), _1261934), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1261932), _1261936), _1261938))), 25999 ^ _780086 : [(26000 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1261932), c_Groups_Ozero__class_Ozero(_1261932)), _1261938)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1261932), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1261932), _1261934), _1261938)), _1261936)))], (26006 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1261932), c_Groups_Ozero__class_Ozero(_1261932)), _1261938))), 26009 ^ _780086 : [(26010 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1261932), _1261938), c_Groups_Ozero__class_Ozero(_1261932))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1261932), _1261936), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1261932), _1261934), _1261938))))], (26016 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1261932), _1261938), c_Groups_Ozero__class_Ozero(_1261932)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1261932), _1261934), c_Groups_Ozero__class_Ozero(_1261932))))]]]]]]], (26044 ^ _780086) ^ [_1262885, _1262887, _1262889, _1262891] : [class_Fields_Olinordered__field__inverse__zero(_1262885), 26047 ^ _780086 : [(26074 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262885), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1262885), _1262887), _1262889)), _1262891))), 26077 ^ _780086 : [(26078 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1262885), c_Groups_Ozero__class_Ozero(_1262885)), _1262889)))], (26080 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262885), _1262887), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1262885), _1262891), _1262889)))]], 26081 ^ _780086 : [(26082 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1262885), c_Groups_Ozero__class_Ozero(_1262885)), _1262889))], (26084 ^ _780086) ^ [] : [26085 ^ _780086 : [(26086 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1262885), _1262889), c_Groups_Ozero__class_Ozero(_1262885))))], (26088 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262885), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1262885), _1262891), _1262889)), _1262887))]], 26089 ^ _780086 : [(26090 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1262885), _1262889), c_Groups_Ozero__class_Ozero(_1262885)))], (26092 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262885), c_Groups_Ozero__class_Ozero(_1262885)), _1262891))]]]]], (26048 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262885), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1262885), _1262887), _1262889)), _1262891)), 26051 ^ _780086 : [(26052 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1262885), c_Groups_Ozero__class_Ozero(_1262885)), _1262889)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262885), _1262887), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1262885), _1262891), _1262889))))], (26058 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1262885), c_Groups_Ozero__class_Ozero(_1262885)), _1262889))), 26061 ^ _780086 : [(26062 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1262885), _1262889), c_Groups_Ozero__class_Ozero(_1262885))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262885), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1262885), _1262891), _1262889)), _1262887)))], (26068 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1262885), _1262889), c_Groups_Ozero__class_Ozero(_1262885)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262885), c_Groups_Ozero__class_Ozero(_1262885)), _1262891)))]]]]]]], (26096 ^ _780086) ^ [_1263838, _1263840, _1263842, _1263844] : [class_Fields_Olinordered__field(_1263838), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1263838), c_Groups_Ozero__class_Ozero(_1263838)), _1263840)), 26103 ^ _780086 : [(26104 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263838), _1263842), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1263838), _1263844), _1263840))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263838), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1263838), _1263842), _1263840)), _1263844)))], (26110 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263838), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1263838), _1263842), _1263840)), _1263844)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263838), _1263842), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1263838), _1263844), _1263840))))]]], (26116 ^ _780086) ^ [_1264219, _1264221, _1264223, _1264225] : [class_Fields_Olinordered__field(_1264219), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1264219), c_Groups_Ozero__class_Ozero(_1264219)), _1264221)), 26123 ^ _780086 : [(26124 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264219), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1264219), _1264223), _1264221)), _1264225)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264219), _1264223), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1264219), _1264225), _1264221))))], (26130 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264219), _1264223), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1264219), _1264225), _1264221))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264219), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1264219), _1264223), _1264221)), _1264225)))]]], (26136 ^ _780086) ^ [_1264600, _1264602, _1264604, _1264606] : [class_Fields_Olinordered__field(_1264600), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1264600), c_Groups_Ozero__class_Ozero(_1264600)), _1264602)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264600), _1264604), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1264600), _1264606), _1264602))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264600), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1264600), _1264604), _1264602)), _1264606)))], (26150 ^ _780086) ^ [_1264869, _1264871, _1264873, _1264875, _1264877] : [class_Fields_Ofield__inverse__zero(_1264869), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1264869), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1264869), _1264871), _1264873)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1264869), _1264875), _1264877)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1264869), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1264869), _1264871), _1264875)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1264869), _1264873), _1264877)))], (26156 ^ _780086) ^ [_1265046, _1265048, _1265050] : [class_Fields_Ofield__inverse__zero(_1265046), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1265046), hAPP(c_Groups_Ouminus__class_Ouminus(_1265046), _1265048)), hAPP(c_Groups_Ouminus__class_Ouminus(_1265046), _1265050)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1265046), _1265048), _1265050))], (26162 ^ _780086) ^ [_1265175, _1265177, _1265179] : [class_Fields_Ofield__inverse__zero(_1265175), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1265175), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1265175), _1265177), _1265179)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1265175), _1265177), hAPP(c_Groups_Ouminus__class_Ouminus(_1265175), _1265179)))], (26168 ^ _780086) ^ [_1265304, _1265306, _1265308] : [class_Fields_Olinordered__field__inverse__zero(_1265304), 26171 ^ _780086 : [(26172 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265304), c_Groups_Ozero__class_Ozero(_1265304)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1265304), _1265306), _1265308))), 26177 ^ _780086 : [(26178 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265304), c_Groups_Ozero__class_Ozero(_1265304)), _1265306)))], (26180 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265304), c_Groups_Ozero__class_Ozero(_1265304)), _1265308)))]], 26181 ^ _780086 : [(26182 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265304), _1265306), c_Groups_Ozero__class_Ozero(_1265304))))], (26184 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265304), _1265308), c_Groups_Ozero__class_Ozero(_1265304))))]]], (26186 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265304), c_Groups_Ozero__class_Ozero(_1265304)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1265304), _1265306), _1265308)))), 26187 ^ _780086 : [(26188 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265304), c_Groups_Ozero__class_Ozero(_1265304)), _1265306)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265304), c_Groups_Ozero__class_Ozero(_1265304)), _1265308))], (26194 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265304), _1265306), c_Groups_Ozero__class_Ozero(_1265304))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265304), _1265308), c_Groups_Ozero__class_Ozero(_1265304)))]]]]], (26202 ^ _780086) ^ [_1265894, _1265896, _1265898] : [class_Fields_Olinordered__field__inverse__zero(_1265894), 26205 ^ _780086 : [(26206 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265894), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1265894), _1265896), _1265898)), c_Groups_Ozero__class_Ozero(_1265894))), 26211 ^ _780086 : [(26212 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265894), c_Groups_Ozero__class_Ozero(_1265894)), _1265896)))], (26214 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265894), _1265898), c_Groups_Ozero__class_Ozero(_1265894))))]], 26215 ^ _780086 : [(26216 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265894), _1265896), c_Groups_Ozero__class_Ozero(_1265894))))], (26218 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265894), c_Groups_Ozero__class_Ozero(_1265894)), _1265898)))]]], (26220 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265894), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1265894), _1265896), _1265898)), c_Groups_Ozero__class_Ozero(_1265894)))), 26221 ^ _780086 : [(26222 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265894), c_Groups_Ozero__class_Ozero(_1265894)), _1265896)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265894), _1265898), c_Groups_Ozero__class_Ozero(_1265894)))], (26228 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265894), _1265896), c_Groups_Ozero__class_Ozero(_1265894))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265894), c_Groups_Ozero__class_Ozero(_1265894)), _1265898))]]]]], (26236 ^ _780086) ^ [_1266484, _1266486, _1266488, _1266490] : [class_Fields_Olinordered__field__inverse__zero(_1266484), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1266484), _1266486), _1266488)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1266484), c_Groups_Ozero__class_Ozero(_1266484)), _1266490)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1266484), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1266484), _1266486), _1266490)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1266484), _1266488), _1266490))))], (26250 ^ _780086) ^ [_1266753, _1266755, _1266757, _1266759] : [class_Fields_Olinordered__field__inverse__zero(_1266753), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1266753), _1266755), _1266757)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1266753), _1266759), c_Groups_Ozero__class_Ozero(_1266753))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1266753), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1266753), _1266757), _1266759)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1266753), _1266755), _1266759))))], (26264 ^ _780086) ^ [_1267022, _1267024, _1267026] : [class_Fields_Olinordered__field__inverse__zero(_1267022), 26267 ^ _780086 : [(26268 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267022), c_Groups_Ozero__class_Ozero(_1267022)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1267022), _1267024), _1267026))), 26273 ^ _780086 : [(26274 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267022), c_Groups_Ozero__class_Ozero(_1267022)), _1267024)))], (26276 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267022), c_Groups_Ozero__class_Ozero(_1267022)), _1267026)))]], 26277 ^ _780086 : [(26278 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267022), _1267024), c_Groups_Ozero__class_Ozero(_1267022))))], (26280 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267022), _1267026), c_Groups_Ozero__class_Ozero(_1267022))))]]], (26282 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267022), c_Groups_Ozero__class_Ozero(_1267022)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1267022), _1267024), _1267026)))), 26283 ^ _780086 : [(26284 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267022), c_Groups_Ozero__class_Ozero(_1267022)), _1267024)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267022), c_Groups_Ozero__class_Ozero(_1267022)), _1267026))], (26290 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267022), _1267024), c_Groups_Ozero__class_Ozero(_1267022))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267022), _1267026), c_Groups_Ozero__class_Ozero(_1267022)))]]]]], (26298 ^ _780086) ^ [_1267612, _1267614, _1267616] : [class_Fields_Olinordered__field__inverse__zero(_1267612), 26301 ^ _780086 : [(26302 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267612), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1267612), _1267614), _1267616)), c_Groups_Ozero__class_Ozero(_1267612))), 26307 ^ _780086 : [(26308 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267612), c_Groups_Ozero__class_Ozero(_1267612)), _1267614)))], (26310 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267612), _1267616), c_Groups_Ozero__class_Ozero(_1267612))))]], 26311 ^ _780086 : [(26312 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267612), _1267614), c_Groups_Ozero__class_Ozero(_1267612))))], (26314 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267612), c_Groups_Ozero__class_Ozero(_1267612)), _1267616)))]]], (26316 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267612), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1267612), _1267614), _1267616)), c_Groups_Ozero__class_Ozero(_1267612)))), 26317 ^ _780086 : [(26318 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267612), c_Groups_Ozero__class_Ozero(_1267612)), _1267614)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267612), _1267616), c_Groups_Ozero__class_Ozero(_1267612)))], (26324 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267612), _1267614), c_Groups_Ozero__class_Ozero(_1267612))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267612), c_Groups_Ozero__class_Ozero(_1267612)), _1267616))]]]]], (26332 ^ _780086) ^ [_1268202, _1268204, _1268206] : [class_Fields_Olinordered__field(_1268202), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1268202), c_Groups_Ozero__class_Ozero(_1268202)), _1268204)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1268202), c_Groups_Ozero__class_Ozero(_1268202)), _1268206)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1268202), c_Groups_Ozero__class_Ozero(_1268202)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1268202), _1268204), _1268206))))], (26346 ^ _780086) ^ [_1268457, _1268459, _1268461] : [class_Fields_Olinordered__field(_1268457), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1268457), c_Groups_Ozero__class_Ozero(_1268457)), _1268459)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1268457), _1268461), c_Groups_Ozero__class_Ozero(_1268457))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1268457), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1268457), _1268459), _1268461)), c_Groups_Ozero__class_Ozero(_1268457))))], (26360 ^ _780086) ^ [_1268712, _1268714, _1268716] : [class_Fields_Olinordered__field(_1268712), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1268712), _1268714), c_Groups_Ozero__class_Ozero(_1268712))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1268712), c_Groups_Ozero__class_Ozero(_1268712)), _1268716)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1268712), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1268712), _1268714), _1268716)), c_Groups_Ozero__class_Ozero(_1268712))))], (26374 ^ _780086) ^ [_1268967, _1268969, _1268971] : [class_Fields_Olinordered__field(_1268967), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1268967), _1268969), c_Groups_Ozero__class_Ozero(_1268967))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1268967), _1268971), c_Groups_Ozero__class_Ozero(_1268967))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1268967), c_Groups_Ozero__class_Ozero(_1268967)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1268967), _1268969), _1268971))))], (26388 ^ _780086) ^ [_1269222, _1269224, _1269226, _1269228] : [class_Fields_Olinordered__field(_1269222), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1269222), _1269224), _1269226)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1269222), c_Groups_Ozero__class_Ozero(_1269222)), _1269228)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1269222), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1269222), _1269224), _1269228)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1269222), _1269226), _1269228))))], (26402 ^ _780086) ^ [_1269491, _1269493, _1269495, _1269497] : [class_Fields_Olinordered__field(_1269491), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1269491), _1269493), _1269495)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1269491), _1269497), c_Groups_Ozero__class_Ozero(_1269491))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1269491), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1269491), _1269495), _1269497)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1269491), _1269493), _1269497))))], (26416 ^ _780086) ^ [_1269760, _1269762, _1269764, _1269766, _1269768] : [class_Fields_Ofield(_1269760), -(_1269762 = c_Groups_Ozero__class_Ozero(_1269760)), -(_1269764 = c_Groups_Ozero__class_Ozero(_1269760)), 26427 ^ _780086 : [(26428 ^ _780086) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1269760), _1269766), _1269762) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1269760), _1269768), _1269764), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1269760), _1269766), _1269764) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1269760), _1269768), _1269762))], (26434 ^ _780086) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1269760), _1269766), _1269764) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1269760), _1269768), _1269762), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1269760), _1269766), _1269762) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1269760), _1269768), _1269764))]]], (26440 ^ _780086) ^ [_1270209, _1270211, _1270213, _1270215] : [class_Fields_Ofield__inverse__zero(_1270209), -(_1270211 = c_Groups_Ozero__class_Ozero(_1270209)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1270209), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1270209), _1270211), _1270213)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1270209), _1270211), _1270215)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1270209), _1270213), _1270215))], (26450 ^ _780086) ^ [_1270371, _1270373, _1270375, _1270377] : [class_Fields_Ofield__inverse__zero(_1270371), -(_1270373 = c_Groups_Ozero__class_Ozero(_1270371)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1270371), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1270371), _1270375), _1270373)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1270371), _1270377), _1270373)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1270371), _1270375), _1270377))], (26460 ^ _780086) ^ [_1270533, _1270535, _1270537, _1270539] : [class_Fields_Ofield__inverse__zero(_1270533), 26463 ^ _780086 : [(26480 ^ _780086) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1270533), _1270535), _1270537) = _1270539), 26483 ^ _780086 : [(26484 ^ _780086) ^ [] : [_1270537 = c_Groups_Ozero__class_Ozero(_1270533)], (26486 ^ _780086) ^ [] : [_1270535 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1270533), _1270539), _1270537)]], 26487 ^ _780086 : [(26488 ^ _780086) ^ [] : [-(_1270537 = c_Groups_Ozero__class_Ozero(_1270533))], (26490 ^ _780086) ^ [] : [_1270539 = c_Groups_Ozero__class_Ozero(_1270533)]]], (26464 ^ _780086) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1270533), _1270535), _1270537) = _1270539, 26467 ^ _780086 : [(26468 ^ _780086) ^ [] : [-(_1270537 = c_Groups_Ozero__class_Ozero(_1270533)), -(_1270535 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1270533), _1270539), _1270537))], (26474 ^ _780086) ^ [] : [_1270537 = c_Groups_Ozero__class_Ozero(_1270533), -(_1270539 = c_Groups_Ozero__class_Ozero(_1270533))]]]]], (26494 ^ _780086) ^ [_1271027, _1271029, _1271031, _1271033] : [class_Fields_Ofield__inverse__zero(_1271027), 26497 ^ _780086 : [(26514 ^ _780086) ^ [] : [-(_1271029 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1271027), _1271031), _1271033)), 26517 ^ _780086 : [(26518 ^ _780086) ^ [] : [_1271033 = c_Groups_Ozero__class_Ozero(_1271027)], (26520 ^ _780086) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1271027), _1271029), _1271033) = _1271031]], 26521 ^ _780086 : [(26522 ^ _780086) ^ [] : [-(_1271033 = c_Groups_Ozero__class_Ozero(_1271027))], (26524 ^ _780086) ^ [] : [_1271029 = c_Groups_Ozero__class_Ozero(_1271027)]]], (26498 ^ _780086) ^ [] : [_1271029 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1271027), _1271031), _1271033), 26501 ^ _780086 : [(26502 ^ _780086) ^ [] : [-(_1271033 = c_Groups_Ozero__class_Ozero(_1271027)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1271027), _1271029), _1271033) = _1271031)], (26508 ^ _780086) ^ [] : [_1271033 = c_Groups_Ozero__class_Ozero(_1271027), -(_1271029 = c_Groups_Ozero__class_Ozero(_1271027))]]]]], (26528 ^ _780086) ^ [_1271521, _1271523, _1271525] : [class_Fields_Olinordered__field(_1271521), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271521), c_Groups_Ozero__class_Ozero(_1271521)), _1271523)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1271521), c_Groups_Ozero__class_Ozero(_1271521)), _1271525)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271521), c_Groups_Ozero__class_Ozero(_1271521)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1271521), _1271523), _1271525))))], (26542 ^ _780086) ^ [_1271776, _1271778, _1271780] : [class_Fields_Olinordered__field(_1271776), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271776), c_Groups_Ozero__class_Ozero(_1271776)), _1271778)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1271776), _1271780), c_Groups_Ozero__class_Ozero(_1271776))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271776), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1271776), _1271778), _1271780)), c_Groups_Ozero__class_Ozero(_1271776))))], (26556 ^ _780086) ^ [_1272031, _1272033, _1272035, _1272037, _1272039] : [class_Fields_Olinordered__field(_1272031), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1272031), c_Groups_Ozero__class_Ozero(_1272031)), _1272033)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272031), _1272033), _1272035)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1272031), c_Groups_Ozero__class_Ozero(_1272031)), _1272037)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1272031), _1272037), _1272039)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1272031), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1272031), _1272033), _1272039)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1272031), _1272035), _1272037))))], (26578 ^ _780086) ^ [_1272454, _1272456, _1272458, _1272460, _1272462] : [class_Fields_Olinordered__field(_1272454), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272454), c_Groups_Ozero__class_Ozero(_1272454)), _1272456)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1272454), _1272456), _1272458)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1272454), c_Groups_Ozero__class_Ozero(_1272454)), _1272460)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272454), _1272460), _1272462)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1272454), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1272454), _1272456), _1272462)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1272454), _1272458), _1272460))))], (26600 ^ _780086) ^ [_1272877, _1272879, _1272881, _1272883, _1272885] : [class_Fields_Olinordered__field(_1272877), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272877), c_Groups_Ozero__class_Ozero(_1272877)), _1272879)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272877), _1272879), _1272881)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1272877), c_Groups_Ozero__class_Ozero(_1272877)), _1272883)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272877), _1272883), _1272885)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272877), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1272877), _1272879), _1272885)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1272877), _1272881), _1272883))))], (26622 ^ _780086) ^ [_1273300, _1273302, _1273304] : [class_Fields_Olinordered__field(_1273300), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273300), _1273302), c_Groups_Ozero__class_Ozero(_1273300))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1273300), c_Groups_Ozero__class_Ozero(_1273300)), _1273304)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273300), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1273300), _1273302), _1273304)), c_Groups_Ozero__class_Ozero(_1273300))))], (26636 ^ _780086) ^ [_1273555, _1273557, _1273559] : [class_Fields_Olinordered__field(_1273555), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273555), _1273557), c_Groups_Ozero__class_Ozero(_1273555))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1273555), _1273559), c_Groups_Ozero__class_Ozero(_1273555))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273555), c_Groups_Ozero__class_Ozero(_1273555)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1273555), _1273557), _1273559))))], (26650 ^ _780086) ^ [_1273810, _1273812, _1273814, _1273816] : [class_Fields_Olinordered__field__inverse__zero(_1273810), 26653 ^ _780086 : [(26680 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1273810), _1273812), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1273810), _1273814), _1273816)))), 26683 ^ _780086 : [(26684 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1273810), c_Groups_Ozero__class_Ozero(_1273810)), _1273816)))], (26686 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1273810), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1273810), _1273812), _1273816)), _1273814))]], 26687 ^ _780086 : [(26688 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1273810), c_Groups_Ozero__class_Ozero(_1273810)), _1273816))], (26690 ^ _780086) ^ [] : [26691 ^ _780086 : [(26692 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1273810), _1273816), c_Groups_Ozero__class_Ozero(_1273810))))], (26694 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1273810), _1273814), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1273810), _1273812), _1273816)))]], 26695 ^ _780086 : [(26696 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1273810), _1273816), c_Groups_Ozero__class_Ozero(_1273810)))], (26698 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1273810), _1273812), c_Groups_Ozero__class_Ozero(_1273810)))]]]]], (26654 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1273810), _1273812), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1273810), _1273814), _1273816))), 26657 ^ _780086 : [(26658 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1273810), c_Groups_Ozero__class_Ozero(_1273810)), _1273816)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1273810), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1273810), _1273812), _1273816)), _1273814)))], (26664 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1273810), c_Groups_Ozero__class_Ozero(_1273810)), _1273816))), 26667 ^ _780086 : [(26668 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1273810), _1273816), c_Groups_Ozero__class_Ozero(_1273810))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1273810), _1273814), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1273810), _1273812), _1273816))))], (26674 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1273810), _1273816), c_Groups_Ozero__class_Ozero(_1273810)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1273810), _1273812), c_Groups_Ozero__class_Ozero(_1273810))))]]]]]]], (26702 ^ _780086) ^ [_1274763, _1274765, _1274767, _1274769] : [class_Fields_Olinordered__field__inverse__zero(_1274763), 26705 ^ _780086 : [(26732 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274763), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1274763), _1274765), _1274767)), _1274769))), 26735 ^ _780086 : [(26736 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274763), c_Groups_Ozero__class_Ozero(_1274763)), _1274767)))], (26738 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274763), _1274765), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1274763), _1274769), _1274767)))]], 26739 ^ _780086 : [(26740 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274763), c_Groups_Ozero__class_Ozero(_1274763)), _1274767))], (26742 ^ _780086) ^ [] : [26743 ^ _780086 : [(26744 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274763), _1274767), c_Groups_Ozero__class_Ozero(_1274763))))], (26746 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274763), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1274763), _1274769), _1274767)), _1274765))]], 26747 ^ _780086 : [(26748 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274763), _1274767), c_Groups_Ozero__class_Ozero(_1274763)))], (26750 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274763), c_Groups_Ozero__class_Ozero(_1274763)), _1274769))]]]]], (26706 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274763), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1274763), _1274765), _1274767)), _1274769)), 26709 ^ _780086 : [(26710 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274763), c_Groups_Ozero__class_Ozero(_1274763)), _1274767)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274763), _1274765), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1274763), _1274769), _1274767))))], (26716 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274763), c_Groups_Ozero__class_Ozero(_1274763)), _1274767))), 26719 ^ _780086 : [(26720 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274763), _1274767), c_Groups_Ozero__class_Ozero(_1274763))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274763), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1274763), _1274769), _1274767)), _1274765)))], (26726 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274763), _1274767), c_Groups_Ozero__class_Ozero(_1274763)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274763), c_Groups_Ozero__class_Ozero(_1274763)), _1274769)))]]]]]]], (26754 ^ _780086) ^ [_1275716, _1275718, _1275720, _1275722] : [class_Fields_Olinordered__field(_1275716), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275716), c_Groups_Ozero__class_Ozero(_1275716)), _1275718)), 26761 ^ _780086 : [(26762 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275716), _1275720), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1275716), _1275722), _1275718))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275716), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1275716), _1275720), _1275718)), _1275722)))], (26768 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275716), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1275716), _1275720), _1275718)), _1275722)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275716), _1275720), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1275716), _1275722), _1275718))))]]], (26774 ^ _780086) ^ [_1276097, _1276099, _1276101, _1276103] : [class_Fields_Olinordered__field(_1276097), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1276097), c_Groups_Ozero__class_Ozero(_1276097)), _1276099)), 26781 ^ _780086 : [(26782 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1276097), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1276097), _1276101), _1276099)), _1276103)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1276097), _1276101), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1276097), _1276103), _1276099))))], (26788 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1276097), _1276101), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1276097), _1276103), _1276099))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1276097), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1276097), _1276101), _1276099)), _1276103)))]]], (26794 ^ _780086) ^ [_1276478, _1276480, _1276482, _1276484] : [class_Fields_Olinordered__field(_1276478), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1276478), c_Groups_Ozero__class_Ozero(_1276478)), _1276480)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1276478), _1276482), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1276478), _1276484), _1276480))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1276478), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1276478), _1276482), _1276480)), _1276484)))], (26808 ^ _780086) ^ [_1276747, _1276749, _1276751, _1276753] : [class_Fields_Olinordered__field(_1276747), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1276747), c_Groups_Ozero__class_Ozero(_1276747)), _1276749)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1276747), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1276747), _1276751), _1276749)), _1276753)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1276747), _1276751), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1276747), _1276753), _1276749))))], (26822 ^ _780086) ^ [_1277016, _1277018, _1277020, _1277022] : [class_Fields_Olinordered__field(_1277016), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1277016), _1277018), c_Groups_Ozero__class_Ozero(_1277016))), 26829 ^ _780086 : [(26830 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1277016), _1277020), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1277016), _1277022), _1277018))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1277016), _1277022), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1277016), _1277020), _1277018))))], (26836 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1277016), _1277022), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1277016), _1277020), _1277018))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1277016), _1277020), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1277016), _1277022), _1277018))))]]], (26842 ^ _780086) ^ [_1277397, _1277399, _1277401, _1277403] : [class_Fields_Olinordered__field(_1277397), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1277397), _1277399), c_Groups_Ozero__class_Ozero(_1277397))), 26849 ^ _780086 : [(26850 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1277397), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1277397), _1277401), _1277399)), _1277403)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1277397), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1277397), _1277403), _1277399)), _1277401)))], (26856 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1277397), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1277397), _1277403), _1277399)), _1277401)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1277397), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1277397), _1277401), _1277399)), _1277403)))]]], (26862 ^ _780086) ^ [_1277778, _1277780, _1277782, _1277784] : [class_Fields_Olinordered__field(_1277778), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1277778), _1277780), _1277782)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1277778), c_Groups_Ozero__class_Ozero(_1277778)), _1277784)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1277778), c_Groups_Ozero__class_Ozero(_1277778)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1277778), _1277782), _1277780))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1277778), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1277778), _1277784), _1277782)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1277778), _1277784), _1277780))))], (26880 ^ _780086) ^ [_1278137, _1278139, _1278141, _1278143] : [class_Fields_Olinordered__field(_1278137), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1278137), _1278139), _1278141)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1278137), _1278143), c_Groups_Ozero__class_Ozero(_1278137))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1278137), c_Groups_Ozero__class_Ozero(_1278137)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1278137), _1278139), _1278141))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1278137), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1278137), _1278143), _1278139)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1278137), _1278143), _1278141))))], (26898 ^ _780086) ^ [_1278496, _1278498, _1278500, _1278502, _1278504] : [class_Fields_Ofield(_1278496), -(_1278498 = c_Groups_Ozero__class_Ozero(_1278496)), -(_1278500 = c_Groups_Ozero__class_Ozero(_1278496)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1278496), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1278496), _1278502), _1278498)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1278496), _1278504), _1278500)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1278496), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1278496), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1278496), _1278502), _1278500)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1278496), _1278504), _1278498))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1278496), _1278498), _1278500)))], (26912 ^ _780086) ^ [_1278743, _1278745, _1278747, _1278749] : [class_Fields_Ofield(_1278743), -(_1278745 = c_Groups_Ozero__class_Ozero(_1278743)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1278743), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1278743), _1278747), _1278745)), _1278749) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1278743), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1278743), _1278747), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1278743), _1278745), _1278749))), _1278745))], (26922 ^ _780086) ^ [_1278921, _1278923, _1278925, _1278927] : [class_Fields_Ofield__inverse__zero(_1278921), -(_1278923 = c_Groups_Ozero__class_Ozero(_1278921)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1278921), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1278921), _1278925), _1278923)), _1278927) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1278921), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1278921), _1278925), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1278921), _1278927), _1278923))), _1278923))], (26932 ^ _780086) ^ [_1279099, _1279101, _1279103, _1279105] : [class_Fields_Ofield(_1279099), -(_1279101 = c_Groups_Ozero__class_Ozero(_1279099)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1279099), _1279103), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1279099), _1279105), _1279101)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1279099), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1279099), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1279099), _1279101), _1279103)), _1279105)), _1279101))], (26942 ^ _780086) ^ [_1279277, _1279279, _1279281, _1279283] : [class_Fields_Ofield__inverse__zero(_1279277), -(_1279279 = c_Groups_Ozero__class_Ozero(_1279277)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1279277), _1279281), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1279277), _1279283), _1279279)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1279277), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1279277), _1279283), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1279277), _1279281), _1279279))), _1279279))], (26952 ^ _780086) ^ [_1279455, _1279457, _1279459, _1279461, _1279463] : [class_Fields_Ofield(_1279455), -(_1279457 = c_Groups_Ozero__class_Ozero(_1279455)), -(_1279459 = c_Groups_Ozero__class_Ozero(_1279455)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1279455), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1279455), _1279461), _1279457)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1279455), _1279463), _1279459)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1279455), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1279455), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1279455), _1279461), _1279459)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1279455), _1279463), _1279457))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1279455), _1279457), _1279459)))], (26966 ^ _780086) ^ [_1279702, _1279704, _1279706, 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c_Nat__Transfer_Onat__set(_1284919), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1284917), _1284921), _1284919) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1284917), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1284917, tc_Nat_Onat), _1284921), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1284919)))], (27289 ^ _780086) ^ [_1285162, _1285164, _1285166, _1285168, _1285170] : [class_Fields_Ofield(_1285162), hBOOL(hAPP(c_Finite__Set_Ofinite(_1285164), _1285166)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1285164), _1285168)), 27303 ^ _780086 : [(27304 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1285164), 27302 ^ [_1285162, _1285164, _1285166, _1285168, _1285170]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1285164, tc_HOL_Obool)), _1285166), _1285168))))], (27306 ^ _780086) ^ [] : [-(hAPP(_1285170, 27302 ^ [_1285162, _1285164, _1285166, _1285168, _1285170]) = 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-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1285658)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1285660))))], (27324 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1285658)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1285660))), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1285658), _1285660)))]]], (27330 ^ _780086) ^ [_1285961, _1285963] : [class_Rings_Oring__1(_1285961), 27333 ^ _780086 : [(27334 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1285963), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1285961), _1285963) = hAPP(c_Groups_Ouminus__class_Ouminus(_1285961), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1285961), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1285963)))))], (27340 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1285963), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1285961), _1285963) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1285961), hAPP(c_Int_Onat, _1285963)))]]], (27346 ^ _780086) ^ [_1286223, _1286225, _1286227, _1286229, _1286231, _1286233] : [class_Groups_Oordered__ab__group__add(_1286223), hBOOL(hAPP(c_Finite__Set_Ofinite(_1286225), _1286227)), 27356 ^ _780086 : [(27357 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1286225), 27355 ^ [_1286223, _1286225, _1286227, _1286229, _1286231, _1286233]), _1286227)))], (27359 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1286223), c_Groups_Ozero__class_Ozero(_1286223)), hAPP(_1286229, 27355 ^ [_1286223, _1286225, _1286227, _1286229, _1286231, _1286233])))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1286225, _1286223), _1286229), _1286227) = _1286231, hBOOL(hAPP(hAPP(c_member(_1286225), _1286233), _1286227)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1286223), hAPP(_1286229, _1286233)), _1286231)))], (27371 ^ _780086) ^ [] : [-(hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (27373 ^ _780086) ^ [_1286761, _1286763, _1286765] : [class_Orderings_Olinorder(_1286761), 27376 ^ _780086 : [(27377 ^ _780086) ^ [] : [hAPP(c_SetInterval_Oord__class_OgreaterThan(_1286761), _1286763) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1286761), _1286765), -(_1286763 = _1286765)], (27383 ^ _780086) ^ [] : [_1286763 = _1286765, -(hAPP(c_SetInterval_Oord__class_OgreaterThan(_1286761), _1286763) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1286761), _1286765))]]], (27389 ^ _780086) ^ [_1287002, _1287004, _1287006] : [class_Int_Oring__char__0(_1287002), 27392 ^ _780086 : [(27393 ^ _780086) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_1287002), _1287004) = hAPP(c_Int_Oring__1__class_Oof__int(_1287002), _1287006), -(_1287004 = _1287006)], (27399 ^ _780086) ^ [] : [_1287004 = _1287006, -(hAPP(c_Int_Oring__1__class_Oof__int(_1287002), _1287004) = hAPP(c_Int_Oring__1__class_Oof__int(_1287002), _1287006))]]], (27405 ^ _780086) ^ [_1287243] : [-(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1287243)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1287243))], (27407 ^ _780086) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (27409 ^ _780086) ^ [_1287293, _1287295] : [c_Nat__Transfer_Ois__nat(_1287293), c_Nat__Transfer_Ois__nat(_1287295), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1287293), _1287295)))], (27419 ^ _780086) ^ [_1287428] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1287428)))], (27421 ^ _780086) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)))], (27423 ^ _780086) ^ [_1287471, _1287473] : [c_Nat__Transfer_Ois__nat(_1287471), c_Nat__Transfer_Ois__nat(_1287473), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1287471), _1287473)))], (27433 ^ _780086) ^ [_1287606, _1287608] : [c_Nat__Transfer_Ois__nat(_1287606), c_Nat__Transfer_Ois__nat(_1287608), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1287606), _1287608)))], (27443 ^ _780086) ^ [_1287741, _1287743] : [c_Nat__Transfer_Ois__nat(_1287741), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1287741), _1287743)))], (27449 ^ _780086) ^ [_1287826, _1287828] : [c_Nat__Transfer_Ois__nat(_1287826), c_Nat__Transfer_Ois__nat(_1287828), -(c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(_1287826, _1287828)))], (27459 ^ _780086) ^ [_1287955] : [class_Rings_Oring__1(_1287955), -(hAPP(c_Int_Oring__1__class_Oof__int(_1287955), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(_1287955))], (27465 ^ _780086) ^ [_1288042, _1288044] : [class_Int_Oring__char__0(_1288042), 27468 ^ _780086 : [(27469 ^ _780086) ^ [] : [c_Groups_Ozero__class_Ozero(_1288042) = hAPP(c_Int_Oring__1__class_Oof__int(_1288042), _1288044), -(_1288044 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (27475 ^ _780086) ^ [] : [_1288044 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Ozero__class_Ozero(_1288042) = hAPP(c_Int_Oring__1__class_Oof__int(_1288042), _1288044))]]], (27481 ^ _780086) ^ [_1288268, _1288270] : [class_Int_Oring__char__0(_1288268), 27484 ^ _780086 : [(27485 ^ _780086) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_1288268), _1288270) = c_Groups_Ozero__class_Ozero(_1288268), -(_1288270 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (27491 ^ _780086) ^ [] : [_1288270 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1288268), _1288270) = c_Groups_Ozero__class_Ozero(_1288268))]]], (27497 ^ _780086) ^ [_1288494, _1288496, _1288498] : [class_Rings_Olinordered__idom(_1288494), 27500 ^ _780086 : [(27501 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288494), hAPP(c_Int_Oring__1__class_Oof__int(_1288494), _1288496)), hAPP(c_Int_Oring__1__class_Oof__int(_1288494), _1288498))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1288496), _1288498)))], (27507 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1288496), _1288498)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288494), hAPP(c_Int_Oring__1__class_Oof__int(_1288494), _1288496)), hAPP(c_Int_Oring__1__class_Oof__int(_1288494), _1288498))))]]], (27513 ^ _780086) ^ [_1288771, _1288773, _1288775] : [class_Rings_Olinordered__idom(_1288771), 27516 ^ _780086 : [(27517 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1288771), hAPP(c_Int_Oring__1__class_Oof__int(_1288771), _1288773)), hAPP(c_Int_Oring__1__class_Oof__int(_1288771), _1288775))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1288773), _1288775)))], (27523 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1288773), _1288775)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1288771), hAPP(c_Int_Oring__1__class_Oof__int(_1288771), _1288773)), hAPP(c_Int_Oring__1__class_Oof__int(_1288771), _1288775))))]]], (27529 ^ _780086) ^ [_1289048, _1289050, _1289052] : [class_Rings_Oring__1(_1289048), -(hAPP(c_Int_Oring__1__class_Oof__int(_1289048), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1289050), _1289052)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1289048), hAPP(c_Int_Oring__1__class_Oof__int(_1289048), _1289050)), hAPP(c_Int_Oring__1__class_Oof__int(_1289048), _1289052)))], (27535 ^ _780086) ^ [_1289183, _1289185, _1289187] : [class_Rings_Oring__1(_1289183), -(hAPP(c_Int_Oring__1__class_Oof__int(_1289183), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1289185), _1289187)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1289183), hAPP(c_Int_Oring__1__class_Oof__int(_1289183), _1289185)), hAPP(c_Int_Oring__1__class_Oof__int(_1289183), _1289187)))], (27541 ^ _780086) ^ [_1289318] : [class_Rings_Oring__1(_1289318), -(hAPP(c_Int_Oring__1__class_Oof__int(_1289318), c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(_1289318))], (27547 ^ _780086) ^ [_1289405, _1289407, _1289409] : [class_Rings_Oring__1(_1289405), -(hAPP(c_Int_Oring__1__class_Oof__int(_1289405), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1289407), _1289409)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1289405), hAPP(c_Int_Oring__1__class_Oof__int(_1289405), _1289407)), hAPP(c_Int_Oring__1__class_Oof__int(_1289405), _1289409)))], (27553 ^ _780086) ^ [_1289540, _1289542] : [class_Rings_Oring__1(_1289540), -(hAPP(c_Int_Oring__1__class_Oof__int(_1289540), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1289542)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1289540), _1289542))], (27559 ^ _780086) ^ [_1289641, _1289643] : [class_Rings_Oring__1(_1289641), -(hAPP(c_Int_Oring__1__class_Oof__int(_1289641), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1289643)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1289641), hAPP(c_Int_Oring__1__class_Oof__int(_1289641), _1289643)))], (27565 ^ _780086) ^ [_1289752, _1289754] : [class_Rings_Oring__1(_1289752), -(hBOOL(hAPP(hAPP(c_member(_1289752), hAPP(c_Int_Oring__1__class_Oof__int(_1289752), _1289754)), c_Int_Oring__1__class_OInts(_1289752))))], (27571 ^ _780086) ^ [_1289855, _1289857, _1289859] : [class_Rings_Oring__1(_1289855), -(hAPP(c_Int_Oring__1__class_Oof__int(_1289855), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1289857), _1289859)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1289855), hAPP(c_Int_Oring__1__class_Oof__int(_1289855), _1289857)), _1289859))], (27577 ^ _780086) ^ [_1289992] : [c_Nat__Transfer_Ois__nat(_1289992), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1289992)))], (27583 ^ _780086) ^ [_1290065] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1290065)), -(c_Nat__Transfer_Ois__nat(_1290065))], (27589 ^ _780086) ^ [_1290144, _1290146, _1290148] : [class_Orderings_Oord(_1290144), 27592 ^ _780086 : [(27593 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1290144), _1290146), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1290144), _1290148))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1290144), _1290148), _1290146)))], (27599 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1290144), _1290148), _1290146)), -(hBOOL(hAPP(hAPP(c_member(_1290144), _1290146), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1290144), _1290148))))]]], (27605 ^ _780086) ^ [_1290412, _1290414, _1290416] : [class_Orderings_Olinorder(_1290412), 27608 ^ _780086 : [(27609 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1290412, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1290412), _1290414)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1290412), _1290416))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290412), _1290416), _1290414)))], (27615 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290412), _1290416), _1290414)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1290412, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1290412), _1290414)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1290412), _1290416))))]]], (27621 ^ _780086) ^ [_1290704, _1290706, _1290708, _1290710] : [class_Rings_Oring__1(_1290704), -(hAPP(c_Int_Oring__1__class_Oof__int(_1290704), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1290706, tc_Int_Oint), _1290708), _1290710)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1290706, _1290704), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1290704, _1290706), c_Int_Oring__1__class_Oof__int(_1290704)), _1290708)), _1290710))], (27627 ^ _780086) ^ [_1290853, _1290855] : [c_Nat__Transfer_Onat__set(_1290853), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1290855), _1290853)), -(c_Nat__Transfer_Ois__nat(_1290855))], (27637 ^ _780086) ^ [_1290988, _1290990, _1290992, _1290994] : [-(hAPP(c_Int_Oring__1__class_Oof__int(_1290988), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1290990, tc_Int_Oint), _1290992), _1290994)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1290990, _1290988), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1290988, _1290990), c_Int_Oring__1__class_Oof__int(_1290988)), _1290992)), _1290994)), class_Groups_Ocomm__monoid__mult(_1290988), class_Rings_Oring__1(_1290988)], (27647 ^ _780086) ^ [] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (27649 ^ _780086) ^ [_1291209, _1291211] : [class_Rings_Olinordered__idom(_1291209), 27652 ^ _780086 : [(27653 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291209), c_Groups_Ozero__class_Ozero(_1291209)), hAPP(c_Int_Oring__1__class_Oof__int(_1291209), _1291211))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1291211)))], (27659 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1291211)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291209), c_Groups_Ozero__class_Ozero(_1291209)), hAPP(c_Int_Oring__1__class_Oof__int(_1291209), _1291211))))]]], (27665 ^ _780086) ^ [_1291462, _1291464] : [class_Rings_Olinordered__idom(_1291462), 27668 ^ _780086 : [(27669 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291462), hAPP(c_Int_Oring__1__class_Oof__int(_1291462), _1291464)), c_Groups_Ozero__class_Ozero(_1291462))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1291464), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (27675 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1291464), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291462), hAPP(c_Int_Oring__1__class_Oof__int(_1291462), _1291464)), c_Groups_Ozero__class_Ozero(_1291462))))]]], (27681 ^ _780086) ^ [_1291724, _1291726] : [class_Rings_Olinordered__idom(_1291724), 27684 ^ _780086 : [(27685 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1291724), c_Groups_Ozero__class_Ozero(_1291724)), hAPP(c_Int_Oring__1__class_Oof__int(_1291724), _1291726))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1291726)))], (27691 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1291726)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1291724), c_Groups_Ozero__class_Ozero(_1291724)), hAPP(c_Int_Oring__1__class_Oof__int(_1291724), _1291726))))]]], (27697 ^ _780086) ^ [_1291977, _1291979] : [class_Rings_Olinordered__idom(_1291977), 27700 ^ _780086 : [(27701 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1291977), hAPP(c_Int_Oring__1__class_Oof__int(_1291977), _1291979)), c_Groups_Ozero__class_Ozero(_1291977))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1291979), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (27707 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1291979), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1291977), hAPP(c_Int_Oring__1__class_Oof__int(_1291977), _1291979)), c_Groups_Ozero__class_Ozero(_1291977))))]]], (27713 ^ _780086) ^ [_1292239, _1292241] : [class_Rings_Oring__1(_1292239), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1292241)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1292239), hAPP(c_Int_Onat, _1292241)) = hAPP(c_Int_Oring__1__class_Oof__int(_1292239), _1292241))], (27723 ^ _780086) ^ [_1292396, _1292398, _1292400] : [class_Orderings_Olinorder(_1292396), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1292396), _1292398), _1292400)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1292396, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1292396, _1292398, _1292400)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1292396), _1292400)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1292396), _1292398))], (27733 ^ _780086) ^ [_1292591, _1292593] : [class_Groups_Oordered__ab__group__add(_1292591), -(hAPP(c_Set_Oimage(_1292591, _1292591, c_Groups_Ouminus__class_Ouminus(_1292591)), hAPP(c_SetInterval_Oord__class_OlessThan(_1292591), _1292593)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1292591), hAPP(c_Groups_Ouminus__class_Ouminus(_1292591), _1292593)))], (27739 ^ _780086) ^ [_1292714, _1292716] : [class_Groups_Oordered__ab__group__add(_1292714), -(hAPP(c_Set_Oimage(_1292714, _1292714, c_Groups_Ouminus__class_Ouminus(_1292714)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1292714), _1292716)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1292714), hAPP(c_Groups_Ouminus__class_Ouminus(_1292714), _1292716)))], (27745 ^ _780086) ^ [_1292837, _1292839, _1292841] : [class_Orderings_Oorder(_1292837), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1292837, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1292837, _1292839, _1292841)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1292837), _1292841)) = c_Orderings_Obot__class_Obot(tc_fun(_1292837, tc_HOL_Obool)))], (27751 ^ _780086) ^ [_1292964] : [-(hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1292964)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1292964)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1292964)), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (27753 ^ _780086) ^ [_1293011, _1293013, _1293015] : [27755 ^ _780086 : [(27756 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1293011), 27754 ^ [_1293011, _1293013, _1293015]), _1293013)))], (27758 ^ _780086) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1293015, 27754 ^ [_1293011, _1293013, _1293015]))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1293011, tc_Int_Oint), _1293015), _1293013) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1293011, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1293011), c_Int_Onat), _1293015)), _1293013)))], (27762 ^ _780086) ^ [_1293241, _1293243, _1293245] : [27764 ^ _780086 : [(27765 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1293241), 27763 ^ [_1293241, _1293243, _1293245]), _1293243)))], (27767 ^ _780086) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1293245, 27763 ^ [_1293241, _1293243, _1293245]))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1293241, tc_Int_Oint), _1293245), _1293243) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1293241, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1293241), c_Int_Onat), _1293245)), _1293243)))], (27771 ^ _780086) ^ [_1293471, _1293473, _1293475] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1293471, 27772 ^ [_1293471, _1293473, _1293475])), hAPP(_1293473, 27772 ^ [_1293471, _1293473, _1293475]))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1293473), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1293475))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1293471), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1293475))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat)), _1293473)), _1293471)), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1293475)))], (27778 ^ _780086) ^ [_1293704, _1293706, _1293708, _1293710] : [class_Groups_Oab__group__add(_1293704), 27781 ^ _780086 : [(27782 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1293706), _1293708)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1293704), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1293704, _1293704), hAPP(hAPP(c_COMBB(_1293704, tc_fun(_1293704, _1293704), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1293704)), _1293710)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1293704, tc_Nat_Onat), _1293710), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1293706, _1293708)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1293704), hAPP(_1293710, _1293706)), hAPP(_1293710, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1293708), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (27788 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1293706), _1293708))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1293704), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1293704, _1293704), hAPP(hAPP(c_COMBB(_1293704, tc_fun(_1293704, _1293704), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1293704)), _1293710)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1293704, tc_Nat_Onat), _1293710), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1293706, _1293708)) = c_Groups_Ozero__class_Ozero(_1293704))]]], (27794 ^ _780086) ^ [_1294142, _1294144] : [class_Rings_Ocomm__semiring__1(_1294142), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1294142), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1294142), c_Groups_Oone__class_Oone(_1294142)), c_Groups_Oone__class_Oone(_1294142))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1294142), c_Nat_Osemiring__1__class_Oof__nat(_1294142)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1294144))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1294142), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1294142), _1294144)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1294142), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1294142), _1294144)), c_Groups_Oone__class_Oone(_1294142))))], (27800 ^ _780086) ^ [_1294343, _1294345] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1294343, _1294345))))], (27802 ^ _780086) ^ [_1294389, _1294391] : [27804 ^ _780086 : [(27805 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 27803 ^ [_1294389, _1294391]), _1294389)))], (27807 ^ _780086) ^ [] : [hBOOL(hAPP(_1294391, 27803 ^ [_1294389, _1294391]))]], 27808 ^ _780086 : [(27809 ^ _780086) ^ [_1294540] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1294540), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1294389))), -(hBOOL(hAPP(_1294391, _1294540)))]]], (27815 ^ _780086) ^ [_1294643, _1294645] : [27817 ^ _780086 : [(27818 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 27816 ^ [_1294643, _1294645]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1294643))))], (27820 ^ _780086) ^ [] : [hBOOL(hAPP(_1294645, 27816 ^ [_1294643, _1294645]))]], 27821 ^ _780086 : [(27822 ^ _780086) ^ [_1294798] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1294798), _1294643)), -(hBOOL(hAPP(_1294645, _1294798)))]]], (27828 ^ _780086) ^ [_1294914, _1294916] : [27836 ^ _780086 : [(27837 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 27835 ^ [_1294914, _1294916]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1294914))))], (27839 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1294916, 27835 ^ [_1294914, _1294916])))]], 27829 ^ _780086 : [(27830 ^ _780086) ^ [_1294983] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1294983), _1294914)), hBOOL(hAPP(_1294916, _1294983))]]], (27841 ^ _780086) ^ [_1295144, _1295146] : [27849 ^ _780086 : [(27850 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 27848 ^ [_1295144, _1295146]), _1295144)))], (27852 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1295146, 27848 ^ [_1295144, _1295146])))]], 27842 ^ _780086 : [(27843 ^ _780086) ^ [_1295213] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1295213), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1295144))), hBOOL(hAPP(_1295146, _1295213))]]], (27854 ^ _780086) ^ [_1295384, _1295386] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1295384), hAPP(c_Nat_OSuc, _1295386)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1295384, _1295386))], (27856 ^ _780086) ^ [_1295422, _1295424, _1295426] : [class_Orderings_Oorder(_1295422), 27859 ^ _780086 : [(27860 ^ _780086) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1295422, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1295422, _1295424, _1295426), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1295422), _1295424), _1295426))], (27866 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1295422), _1295424), _1295426))), -(c_Orderings_Obot__class_Obot(tc_fun(_1295422, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1295422, _1295424, _1295426))]]], (27872 ^ _780086) ^ [_1295641, _1295643, _1295645] : [class_Orderings_Oorder(_1295641), 27875 ^ _780086 : [(27876 ^ _780086) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1295641, _1295643, _1295645) = c_Orderings_Obot__class_Obot(tc_fun(_1295641, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1295641), _1295643), _1295645))], (27882 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1295641), _1295643), _1295645))), -(c_SetInterval_Oord__class_OatLeastAtMost(_1295641, _1295643, _1295645) = c_Orderings_Obot__class_Obot(tc_fun(_1295641, tc_HOL_Obool)))]]], (27888 ^ _780086) ^ [_1295860, _1295862, _1295864] : [class_Orderings_Oorder(_1295860), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295860), _1295862), _1295864)), -(c_SetInterval_Oord__class_OatLeastAtMost(_1295860, _1295864, _1295862) = c_Orderings_Obot__class_Obot(tc_fun(_1295860, tc_HOL_Obool)))], (27898 ^ _780086) ^ [_1296023, _1296025, _1296027, _1296029, _1296031] : [class_Orderings_Oorder(_1296023), 27901 ^ _780086 : [(27902 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1296023, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1296023, _1296025, _1296027)), c_SetInterval_Oord__class_OatLeastAtMost(_1296023, _1296029, _1296031))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1296023), _1296025), _1296027)), 27909 ^ _780086 : [(27910 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1296023), _1296029), _1296025)))], (27912 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1296023), _1296027), _1296031)))]]], (27914 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1296023, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1296023, _1296025, _1296027)), c_SetInterval_Oord__class_OatLeastAtMost(_1296023, _1296029, _1296031)))), 27915 ^ _780086 : [(27916 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1296023), _1296025), _1296027)))], (27918 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1296023), _1296029), _1296025)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1296023), _1296027), _1296031))]]]]], (27926 ^ _780086) ^ [_1296526, _1296528, _1296530] : [class_Orderings_Oorder(_1296526), _1296528 = _1296530, -(c_SetInterval_Oord__class_OatLeastAtMost(_1296526, _1296528, _1296530) = hAPP(hAPP(c_Set_Oinsert(_1296526), _1296528), c_Orderings_Obot__class_Obot(tc_fun(_1296526, tc_HOL_Obool))))], (27936 ^ _780086) ^ [_1296691, _1296693, _1296695, _1296697] : [class_Orderings_Oorder(_1296691), 27939 ^ _780086 : [(27940 ^ _780086) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1296691, _1296693, _1296695) = hAPP(hAPP(c_Set_Oinsert(_1296691), _1296697), c_Orderings_Obot__class_Obot(tc_fun(_1296691, tc_HOL_Obool))), 27943 ^ _780086 : [(27944 ^ _780086) ^ [] : [-(_1296693 = _1296695)], (27946 ^ _780086) ^ [] : [-(_1296695 = _1296697)]]], (27948 ^ _780086) ^ [] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_1296691, _1296693, _1296695) = hAPP(hAPP(c_Set_Oinsert(_1296691), _1296697), c_Orderings_Obot__class_Obot(tc_fun(_1296691, tc_HOL_Obool)))), _1296693 = _1296695, _1296695 = _1296697]]], (27958 ^ _780086) ^ [_1297035, _1297037] : [class_Orderings_Oorder(_1297035), -(c_SetInterval_Oord__class_OatLeastAtMost(_1297035, _1297037, _1297037) = hAPP(hAPP(c_Set_Oinsert(_1297035), _1297037), c_Orderings_Obot__class_Obot(tc_fun(_1297035, tc_HOL_Obool))))], (27964 ^ _780086) ^ [_1297144, _1297146, _1297148] : [class_Groups_Oordered__ab__group__add(_1297144), -(hAPP(c_Set_Oimage(_1297144, _1297144, c_Groups_Ouminus__class_Ouminus(_1297144)), c_SetInterval_Oord__class_OatLeastAtMost(_1297144, _1297146, _1297148)) = c_SetInterval_Oord__class_OatLeastAtMost(_1297144, hAPP(c_Groups_Ouminus__class_Ouminus(_1297144), _1297148), hAPP(c_Groups_Ouminus__class_Ouminus(_1297144), _1297146)))], (27970 ^ _780086) ^ [_1297275, _1297277] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1297275, _1297277)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1297275), hAPP(c_Nat_OSuc, _1297277)))], (27972 ^ _780086) ^ [_1297317, _1297319, _1297321, _1297323] : [class_Groups_Ocomm__monoid__add(_1297317), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1297317), _1297319), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1297321), hAPP(c_Nat_OSuc, _1297323))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1297317), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1297317, tc_Nat_Onat), _1297319), c_Nat_OSuc)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1297321, _1297323)))], (27978 ^ _780086) ^ [_1297480, _1297482, _1297484, _1297486, _1297488] : [class_Groups_Ocomm__monoid__add(_1297480), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1297480), _1297482), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1297484), _1297486), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1297488), _1297486))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1297480), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1297480, tc_Nat_Onat), _1297482), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1297486))), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1297484, _1297488)))], (27984 ^ _780086) ^ [_1297663, _1297665] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1297663), _1297665) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1297663, _1297665))], (27986 ^ _780086) ^ [_1297699, _1297701, _1297703] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1297699)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1297701, _1297703)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1297701), _1297699), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1297703), _1297699)))], (27988 ^ _780086) ^ [_1297756, _1297758] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1297756, _1297758)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1297758)), _1297756))], (27990 ^ _780086) ^ [_1297797, _1297799] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1297797), hAPP(c_Nat_OSuc, _1297799))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1297797, hAPP(c_Nat_OSuc, _1297799)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1297799)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1297797, _1297799)))], (27996 ^ _780086) ^ [_1297930, _1297932] : [hAPP(_1297930, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1297930), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1297932)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1297930), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1297932)))], (28002 ^ _780086) ^ [_1298053, _1298055, _1298057, _1298059] : [class_Orderings_Olinorder(_1298053), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1298053), _1298055), _1298057)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1298053), _1298057), _1298059)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1298053, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1298053, _1298055), _1298057)), c_SetInterval_Oord__class_OatLeastAtMost(_1298053, _1298057, _1298059)) = c_SetInterval_Oord__class_OatLeastAtMost(_1298053, _1298055, _1298059))], (28016 ^ _780086) ^ [_1298322, _1298324, _1298326, _1298328] : [class_Orderings_Oorder(_1298322), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1298322, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1298322, _1298324), _1298326)), c_SetInterval_Oord__class_OatLeastAtMost(_1298322, _1298326, _1298328)) = c_Orderings_Obot__class_Obot(tc_fun(_1298322, tc_HOL_Obool)))], (28022 ^ _780086) ^ [_1298453, _1298455, _1298457, _1298459, _1298461] : [class_Orderings_Olinorder(_1298453), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1298453, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1298453, _1298455, _1298457)), c_SetInterval_Oord__class_OatLeastAtMost(_1298453, _1298459, _1298461)) = c_SetInterval_Oord__class_OatLeastAtMost(_1298453, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1298453), _1298455), _1298459), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1298453), _1298457), _1298461)))], (28028 ^ _780086) ^ [_1298612, _1298614, _1298616, _1298618, _1298620] : [class_Orderings_Oorder(_1298612), 28031 ^ _780086 : [(28032 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1298612, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1298612, _1298614, _1298616)), c_SetInterval_Oord__class_OatLeastAtMost(_1298612, _1298618, _1298620))), 28035 ^ _780086 : [(28050 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1298612), _1298618), _1298620)))], (28036 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1298612), _1298614), _1298616)), 28039 ^ _780086 : [(28040 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1298612), _1298618), _1298614)))], (28042 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1298612), _1298616), _1298620)))], (28044 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1298612), _1298618), _1298614))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1298612), _1298616), _1298620)))]]]]], (28052 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1298612, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1298612, _1298614, _1298616)), c_SetInterval_Oord__class_OatLeastAtMost(_1298612, _1298618, _1298620)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1298612), _1298618), _1298620)), 28055 ^ _780086 : [(28056 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1298612), _1298614), _1298616)))], (28058 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1298612), _1298618), _1298614)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1298612), _1298616), _1298620)), 28065 ^ _780086 : [(28066 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1298612), _1298618), _1298614))], (28068 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1298612), _1298616), _1298620))]]]]]]], (28074 ^ _780086) ^ [_1299383, _1299385, _1299387, _1299389] : [class_Orderings_Olinorder(_1299383), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1299383), _1299385), _1299387)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1299383), _1299387), _1299389)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1299383, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1299383, _1299385, _1299387)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1299383, _1299387, _1299389)) = c_SetInterval_Oord__class_OatLeastAtMost(_1299383, _1299385, _1299389))], (28088 ^ _780086) ^ [_1299648, _1299650, _1299652] : [class_Orderings_Oorder(_1299648), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1299648, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1299648), _1299650)), c_SetInterval_Oord__class_OatLeastAtMost(_1299648, _1299650, _1299652)) = c_Orderings_Obot__class_Obot(tc_fun(_1299648, tc_HOL_Obool)))], (28094 ^ _780086) ^ [_1299775, _1299777, _1299779, _1299781] : [class_Orderings_Oorder(_1299775), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1299775, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1299775, _1299777, _1299779)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1299775, _1299779, _1299781)) = c_Orderings_Obot__class_Obot(tc_fun(_1299775, tc_HOL_Obool)))], (28100 ^ _780086) ^ [_1299902, _1299904, _1299906, _1299908] : [class_Orderings_Oorder(_1299902), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1299902, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1299902, _1299904, _1299906)), c_SetInterval_Oord__class_OatLeastAtMost(_1299902, _1299906, _1299908)) = c_Orderings_Obot__class_Obot(tc_fun(_1299902, tc_HOL_Obool)))], (28106 ^ _780086) ^ [_1300029, _1300031, _1300033, _1300035] : [class_Orderings_Oorder(_1300029), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1300029, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1300029, _1300031, _1300033)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1300029, _1300033, _1300035)) = c_Orderings_Obot__class_Obot(tc_fun(_1300029, tc_HOL_Obool)))], (28112 ^ _780086) ^ [_1300156, _1300158, _1300160] : [class_Orderings_Oorder(_1300156), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1300156, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1300156, _1300158, _1300160)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1300156), _1300160)) = c_Orderings_Obot__class_Obot(tc_fun(_1300156, tc_HOL_Obool)))], (28118 ^ _780086) ^ [_1300283, _1300285, _1300287, _1300289] : [class_Groups_Ocomm__monoid__add(_1300283), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1300285), _1300287)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1300283), _1300289), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1300285, _1300287)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1300283), hAPP(_1300289, _1300285)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1300283), _1300289), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1300285), _1300287))))], (28128 ^ _780086) ^ [_1300508, _1300510, _1300512, _1300514] : [class_Groups_Ocomm__monoid__add(_1300508), 28131 ^ _780086 : [(28132 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1300510)), _1300512)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1300508), _1300514), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1300512, hAPP(c_Nat_OSuc, _1300510))) = c_Groups_Ozero__class_Ozero(_1300508))], (28138 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1300510)), _1300512))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1300508), _1300514), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1300512, hAPP(c_Nat_OSuc, _1300510))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1300508), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1300508), _1300514), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1300512, _1300510))), hAPP(_1300514, hAPP(c_Nat_OSuc, _1300510))))]]], (28144 ^ _780086) ^ [_1300844, _1300846, _1300848, _1300850] : [class_Groups_Ocomm__monoid__add(_1300844), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1300846), _1300848)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1300844), _1300850), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1300846, _1300848)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1300844), hAPP(_1300850, _1300846)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1300844), _1300850), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1300846, _1300848))))], (28154 ^ _780086) ^ [_1301063, _1301065, _1301067, _1301069, _1301071] : [class_Groups_Ocomm__monoid__add(_1301063), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1301065), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1301067), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1301063), _1301069), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1301065, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1301067), _1301071))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1301063), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1301063), _1301069), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1301065, _1301067))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1301063), _1301069), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1301067), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1301067), _1301071)))))], (28164 ^ _780086) ^ [_1301354, _1301356, _1301358] : [class_Orderings_Olinorder(_1301354), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1301354), _1301356), _1301358)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1301354, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1301354, _1301356), _1301358)), hAPP(hAPP(c_Set_Oinsert(_1301354), _1301358), c_Orderings_Obot__class_Obot(tc_fun(_1301354, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(_1301354, _1301356, _1301358))], (28174 ^ _780086) ^ [_1301567, _1301569, _1301571] : [class_Orderings_Olinorder(_1301567), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1301567), _1301569), _1301571)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1301567, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1301567), _1301569), c_Orderings_Obot__class_Obot(tc_fun(_1301567, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanAtMost(_1301567, _1301569, _1301571)) = c_SetInterval_Oord__class_OatLeastAtMost(_1301567, _1301569, _1301571))], (28184 ^ _780086) ^ [_1301776, _1301778, _1301780, _1301782] : [class_Orderings_Olinorder(_1301776), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1301776), _1301778), _1301780)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1301776), _1301780), _1301782)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1301776, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1301776, _1301778, _1301780)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1301776, _1301780, _1301782)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1301776, _1301778), _1301782))], (28198 ^ _780086) ^ [_1302045, _1302047, _1302049, _1302051] : [class_Orderings_Olinorder(_1302045), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1302045), _1302047), _1302049)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1302045), _1302049), _1302051)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1302045, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1302045, _1302047, _1302049)), c_SetInterval_Oord__class_OatLeastAtMost(_1302045, _1302049, _1302051)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1302045, _1302047, _1302051))], (28212 ^ _780086) ^ [_1302310] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1302310)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), _1302310)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1302310), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (28214 ^ _780086) ^ [_1302354, _1302356, _1302358] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1302354, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1302356)), _1302358) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1302354, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1302354, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1302356)), _1302358)), hAPP(_1302358, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (28216 ^ _780086) ^ [_1302426, _1302428, _1302430] : [class_Orderings_Olinorder(_1302426), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1302426), _1302428), _1302430)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1302426, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1302426, _1302428, _1302430)), hAPP(c_SetInterval_Oord__class_OatLeast(_1302426), _1302430)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1302426), _1302428))], (28226 ^ _780086) ^ [_1302621, _1302623, _1302625] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1302621)), 28232 ^ _780086 : [(28233 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1302623, 28231 ^ [_1302621, _1302623, _1302625])))], (28235 ^ _780086) ^ [] : [hBOOL(hAPP(_1302623, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 28231 ^ [_1302621, _1302623, _1302625]), _1302621)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1302625)), 28240 ^ _780086 : [(28241 ^ _780086) ^ [_1302910] : [hBOOL(hAPP(_1302623, _1302910)), -(hBOOL(hAPP(_1302623, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1302910), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1302625), _1302621)))))]]], (28247 ^ _780086) ^ [_1303033] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1303033), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1303033 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 28250 ^ [_1303033]))))], (28254 ^ _780086) ^ [_1303146, _1303148] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1303146, _1303148))))], (28256 ^ _780086) ^ [_1303177] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1303177))))], (28258 ^ _780086) ^ [_1303205, _1303207, _1303209] : [class_Orderings_Olinorder(_1303205), 28261 ^ _780086 : [(28262 ^ _780086) ^ [] : [hAPP(c_SetInterval_Oord__class_OatMost(_1303205), _1303207) = hAPP(c_SetInterval_Oord__class_OatMost(_1303205), _1303209), -(_1303207 = _1303209)], (28268 ^ _780086) ^ [] : [_1303207 = _1303209, -(hAPP(c_SetInterval_Oord__class_OatMost(_1303205), _1303207) = hAPP(c_SetInterval_Oord__class_OatMost(_1303205), _1303209))]]], (28274 ^ _780086) ^ [_1303446, _1303448, _1303450] : [class_Orderings_Olinorder(_1303446), 28277 ^ _780086 : [(28278 ^ _780086) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeast(_1303446), _1303448) = hAPP(c_SetInterval_Oord__class_OatLeast(_1303446), _1303450), -(_1303448 = _1303450)], (28284 ^ _780086) ^ [] : [_1303448 = _1303450, -(hAPP(c_SetInterval_Oord__class_OatLeast(_1303446), _1303448) = hAPP(c_SetInterval_Oord__class_OatLeast(_1303446), _1303450))]]], (28290 ^ _780086) ^ [_1303687, _1303689] : [class_Groups_Oordered__ab__group__add(_1303687), -(hAPP(c_Set_Oimage(_1303687, _1303687, c_Groups_Ouminus__class_Ouminus(_1303687)), hAPP(c_SetInterval_Oord__class_OatMost(_1303687), _1303689)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1303687), hAPP(c_Groups_Ouminus__class_Ouminus(_1303687), _1303689)))], (28296 ^ _780086) ^ [_1303810, _1303812] : [class_Groups_Oordered__ab__group__add(_1303810), -(hAPP(c_Set_Oimage(_1303810, _1303810, c_Groups_Ouminus__class_Ouminus(_1303810)), hAPP(c_SetInterval_Oord__class_OatLeast(_1303810), _1303812)) = hAPP(c_SetInterval_Oord__class_OatMost(_1303810), hAPP(c_Groups_Ouminus__class_Ouminus(_1303810), _1303812)))], (28302 ^ _780086) ^ [_1303933, _1303935] : [class_Orderings_Oorder(_1303933), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1303933, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1303933), _1303935)), hAPP(c_SetInterval_Oord__class_OatLeast(_1303933), _1303935)) = hAPP(hAPP(c_Set_Oinsert(_1303933), _1303935), c_Orderings_Obot__class_Obot(tc_fun(_1303933, tc_HOL_Obool))))], (28308 ^ _780086) ^ [_1304076] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1304076) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1304076))))], (28310 ^ _780086) ^ [_1304112, _1304114] : [c_Nat__Transfer_Ois__nat(_1304112), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1304112, _1304114)))], (28316 ^ _780086) ^ [_1304193] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1304193) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1304193))], (28318 ^ _780086) ^ [_1304223] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1304223)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1304223))], (28320 ^ _780086) ^ [_1304255] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1304255)) = hAPP(c_Nat_OSuc, _1304255))], (28322 ^ _780086) ^ [_1304287] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1304287)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1304287)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1304287)))], (28324 ^ _780086) ^ [_1304328, _1304330, _1304332] : [class_Orderings_Oord(_1304328), 28327 ^ _780086 : [(28328 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1304328), _1304330), hAPP(c_SetInterval_Oord__class_OatMost(_1304328), _1304332))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1304328), _1304330), _1304332)))], (28334 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1304328), _1304330), _1304332)), -(hBOOL(hAPP(hAPP(c_member(_1304328), _1304330), hAPP(c_SetInterval_Oord__class_OatMost(_1304328), _1304332))))]]], (28340 ^ _780086) ^ [_1304596, _1304598, _1304600] : [class_Orderings_Oord(_1304596), 28343 ^ _780086 : [(28344 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1304596), _1304598), hAPP(c_SetInterval_Oord__class_OatLeast(_1304596), _1304600))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1304596), _1304600), _1304598)))], (28350 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1304596), _1304600), _1304598)), -(hBOOL(hAPP(hAPP(c_member(_1304596), _1304598), hAPP(c_SetInterval_Oord__class_OatLeast(_1304596), _1304600))))]]], (28356 ^ _780086) ^ [_1304864, _1304866, _1304868] : [class_Orderings_Oorder(_1304864), 28359 ^ _780086 : [(28360 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1304864, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1304864), _1304866)), hAPP(c_SetInterval_Oord__class_OatLeast(_1304864), _1304868))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1304864), _1304868), _1304866)))], (28366 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1304864), _1304868), _1304866)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1304864, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1304864), _1304866)), hAPP(c_SetInterval_Oord__class_OatLeast(_1304864), _1304868))))]]], (28372 ^ _780086) ^ [_1305156, _1305158, _1305160] : [class_Orderings_Oorder(_1305156), 28375 ^ _780086 : [(28376 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1305156, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1305156), _1305158)), hAPP(c_SetInterval_Oord__class_OatMost(_1305156), _1305160))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1305156), _1305158), _1305160)))], (28382 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1305156), _1305158), _1305160)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1305156, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1305156), _1305158)), hAPP(c_SetInterval_Oord__class_OatMost(_1305156), _1305160))))]]], (28388 ^ _780086) ^ [] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (28390 ^ _780086) ^ [_1305466, _1305468] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1305466)), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1305466, _1305468)))], (28396 ^ _780086) ^ [_1305553, _1305555] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1305553), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1305555), c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1305553, _1305555))], (28398 ^ _780086) ^ [_1305594, _1305596] : [class_Orderings_Olinorder(_1305594), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1305594, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1305594), _1305596)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1305594), _1305596))], (28404 ^ _780086) ^ [_1305705, _1305707] : [class_Orderings_Olinorder(_1305705), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1305705, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1305705), _1305707)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1305705), _1305707))], (28410 ^ _780086) ^ [_1305816, _1305818] : [class_Orderings_Olinorder(_1305816), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1305816, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1305816), _1305818)) = hAPP(c_SetInterval_Oord__class_OatMost(_1305816), _1305818))], (28416 ^ _780086) ^ [_1305927, _1305929] : [class_Orderings_Olinorder(_1305927), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1305927, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1305927), _1305929)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1305927), _1305929))], (28422 ^ _780086) ^ [_1306038, _1306040] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1306038), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1306040) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1306038, _1306040))], (28424 ^ _780086) ^ [_1306077] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1306077)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1306077))], (28426 ^ _780086) ^ [] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), c_SetInterval_Oord__class_OatMost(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (28428 ^ _780086) ^ [_1306127, _1306129] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1306127, _1306129) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1306127), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1306129))))], (28430 ^ _780086) ^ [_1306169, _1306171, _1306173] : [class_Groups_Ocomm__monoid__add(_1306169), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1306169), _1306171), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1306173))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1306169), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1306169), _1306171), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1306173))), hAPP(_1306171, hAPP(c_Nat_OSuc, _1306173))))], (28436 ^ _780086) ^ [] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (28438 ^ _780086) ^ [_1306346, _1306348, _1306350] : [class_Orderings_Olinorder(_1306346), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1306346), _1306348), _1306350)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1306346, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1306346, _1306348), _1306350)), hAPP(c_SetInterval_Oord__class_OatLeast(_1306346), _1306350)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1306346), _1306348))], (28448 ^ _780086) ^ [_1306554, _1306556] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1306554), _1306556)), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1306556, _1306554) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool)))], (28454 ^ _780086) ^ [_1306643, _1306645] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1306643), _1306645))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1306645, _1306643) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint), _1306645), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1306645), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1306643)))], (28460 ^ _780086) ^ [_1306706, _1306708, _1306710] : [class_Orderings_Oorder(_1306706), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1306706, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1306706, _1306708), _1306710)), hAPP(c_SetInterval_Oord__class_OatLeast(_1306706), _1306710)) = c_Orderings_Obot__class_Obot(tc_fun(_1306706, tc_HOL_Obool)))], (28466 ^ _780086) ^ [_1306837, _1306839, _1306841, _1306843] : [class_Orderings_Olinorder(_1306837), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1306837, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1306837), _1306839)), c_SetInterval_Oord__class_OatLeastAtMost(_1306837, _1306841, _1306843)) = c_SetInterval_Oord__class_OatLeastAtMost(_1306837, _1306841, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1306837), _1306839), _1306843)))], (28472 ^ _780086) ^ [_1306980, _1306982, _1306984, _1306986] : [class_Orderings_Olinorder(_1306980), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1306980, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1306980, _1306982, _1306984)), hAPP(c_SetInterval_Oord__class_OatMost(_1306980), _1306986)) = c_SetInterval_Oord__class_OatLeastAtMost(_1306980, _1306982, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1306980), _1306984), _1306986)))], (28478 ^ _780086) ^ [_1307123, _1307125, _1307127, _1307129] : [class_Orderings_Olinorder(_1307123), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1307123, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1307123), _1307125)), c_SetInterval_Oord__class_OatLeastAtMost(_1307123, _1307127, _1307129)) = c_SetInterval_Oord__class_OatLeastAtMost(_1307123, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1307123), _1307125), _1307127), _1307129))], (28484 ^ _780086) ^ [_1307266, _1307268, _1307270, _1307272] : [class_Orderings_Olinorder(_1307266), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1307266, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1307266, _1307268, _1307270)), hAPP(c_SetInterval_Oord__class_OatLeast(_1307266), _1307272)) = c_SetInterval_Oord__class_OatLeastAtMost(_1307266, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1307266), _1307268), _1307272), _1307270))], (28490 ^ _780086) ^ [] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (28492 ^ _780086) ^ [_1307427, _1307429, _1307431] : [class_Orderings_Olinorder(_1307427), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1307427), _1307429), _1307431)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1307427, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1307427), _1307429)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1307427, _1307429, _1307431)) = hAPP(c_SetInterval_Oord__class_OatMost(_1307427), _1307431))], (28502 ^ _780086) ^ [_1307622, _1307624, _1307626, _1307628] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1307622, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1307624)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1307622, tc_HOL_Obool), tc_Nat_Onat), _1307626), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1307628))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1307622, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1307628, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1307624), _1307628))), _1307626))], (28504 ^ _780086) ^ [_1307704, _1307706, _1307708] : [class_Orderings_Oorder(_1307704), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1307704, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1307704), _1307706)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1307704, _1307706, _1307708)) = c_Orderings_Obot__class_Obot(tc_fun(_1307704, tc_HOL_Obool)))], (28510 ^ _780086) ^ [_1307831, _1307833, _1307835] : [class_Orderings_Oorder(_1307831), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1307831, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1307831), _1307833)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1307831, _1307833, _1307835)) = c_Orderings_Obot__class_Obot(tc_fun(_1307831, tc_HOL_Obool)))], (28516 ^ _780086) ^ [_1307958, _1307960, _1307962] : [class_Orderings_Oorder(_1307958), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1307958, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1307958, _1307960, _1307962)), hAPP(c_SetInterval_Oord__class_OatLeast(_1307958), _1307962)) = c_Orderings_Obot__class_Obot(tc_fun(_1307958, tc_HOL_Obool)))], (28522 ^ _780086) ^ [_1308085, _1308087] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1308085, _1308087)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1308087), _1308085)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (28524 ^ _780086) ^ [_1308132, _1308134] : [c_Nat__Transfer_Ois__nat(_1308132), c_Nat__Transfer_Ois__nat(_1308134), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1308132, _1308134) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Int_Onat, _1308132), hAPP(c_Int_Onat, _1308134))))], (28534 ^ _780086) ^ [_1308291, _1308293] : [class_Orderings_Olinorder(_1308291), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1308291, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1308291), _1308293)), hAPP(hAPP(c_Set_Oinsert(_1308291), _1308293), c_Orderings_Obot__class_Obot(tc_fun(_1308291, tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(_1308291), _1308293))], (28540 ^ _780086) ^ [_1308434, _1308436, _1308438] : [class_Orderings_Olinorder(_1308434), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1308434), _1308436), _1308438)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1308434, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1308434), _1308436)), c_SetInterval_Oord__class_OatLeastAtMost(_1308434, _1308436, _1308438)) = hAPP(c_SetInterval_Oord__class_OatMost(_1308434), _1308438))], (28550 ^ _780086) ^ [_1308629, _1308631] : [class_Orderings_Olinorder(_1308629), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1308629, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1308629), _1308631), c_Orderings_Obot__class_Obot(tc_fun(_1308629, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1308629), _1308631)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1308629), _1308631))], (28556 ^ _780086) ^ [_1308772, _1308774, _1308776] : [class_Orderings_Olinorder(_1308772), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1308772), _1308774), _1308776)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1308772, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1308772, _1308774, _1308776)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1308772), _1308776)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1308772), _1308774))], (28566 ^ _780086) ^ [_1308967, _1308969, _1308971] : [class_Orderings_Olinorder(_1308967), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1308967), _1308969), _1308971)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1308967, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1308967), _1308969)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1308967, _1308969, _1308971)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1308967), _1308971))], (28576 ^ _780086) ^ [_1309162, _1309164, _1309166] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1309162)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1309164), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1309166)), 28583 ^ _780086 : [(28584 ^ _780086) ^ [_1309370] : [28586 ^ _780086 : [(28587 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28585 ^ [_1309162, _1309164, _1309166, _1309370]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1309162))))], (28590 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28588 ^ [_1309162, _1309164, _1309166, _1309370]), _1309166)))], (28592 ^ _780086) ^ [] : [-(_1309370 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 28588 ^ [_1309162, _1309164, _1309166, _1309370]), 28585 ^ [_1309162, _1309164, _1309166, _1309370]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1309370), _1309164)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1309370), _1309162)), _1309164)))]]], (28600 ^ _780086) ^ [_1309646, _1309648, _1309650] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1309646)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1309648), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1309650)), 28607 ^ _780086 : [(28608 ^ _780086) ^ [_1309854] : [28610 ^ _780086 : [(28611 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28609 ^ [_1309646, _1309648, _1309650, _1309854]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1309646))))], (28614 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28612 ^ [_1309646, _1309648, _1309650, _1309854]), _1309650)))], (28616 ^ _780086) ^ [] : [-(_1309854 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 28612 ^ [_1309646, _1309648, _1309650, _1309854]), 28609 ^ [_1309646, _1309648, _1309650, _1309854]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1309648), _1309854)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1309648), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1309854), _1309646))))]]], (28624 ^ _780086) ^ [_1310130, _1310132, _1310134] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1310130)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1310132), _1310134)), 28631 ^ _780086 : [(28632 ^ _780086) ^ [_1310320] : [28634 ^ _780086 : [(28635 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28633 ^ [_1310130, _1310132, _1310134, _1310320]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1310130))))], (28638 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28636 ^ [_1310130, _1310132, _1310134, _1310320]), _1310134)))], (28640 ^ _780086) ^ [] : [-(_1310320 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 28636 ^ [_1310130, _1310132, _1310134, _1310320]), 28633 ^ [_1310130, _1310132, _1310134, _1310320]))]], -(_1310320 = _1310132), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1310320), _1310130) = _1310132]]], (28648 ^ _780086) ^ [_1310580, _1310582, _1310584] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1310580)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1310582), _1310584)), 28655 ^ _780086 : [(28656 ^ _780086) ^ [_1310770] : [28658 ^ _780086 : [(28659 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28657 ^ [_1310580, _1310582, _1310584, _1310770]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1310580))))], (28662 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28660 ^ [_1310580, _1310582, _1310584, _1310770]), _1310584)))], (28664 ^ _780086) ^ [] : [-(_1310770 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 28660 ^ [_1310580, _1310582, _1310584, _1310770]), 28657 ^ [_1310580, _1310582, _1310584, _1310770]))]], -(_1310770 = _1310582), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1310770), _1310580) = _1310582]]], (28672 ^ _780086) ^ [_1311030, _1311032, _1311034] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1311030)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1311032), _1311034)), 28679 ^ _780086 : [(28680 ^ _780086) ^ [_1311226] : [28682 ^ _780086 : [(28683 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28681 ^ [_1311030, _1311032, _1311034, _1311226]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1311030))))], (28686 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28684 ^ [_1311030, _1311032, _1311034, _1311226]), _1311034)))], (28688 ^ _780086) ^ [] : [-(_1311226 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 28684 ^ [_1311030, _1311032, _1311034, _1311226]), 28681 ^ [_1311030, _1311032, _1311034, _1311226]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1311032), _1311226)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1311032), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1311226), _1311030))))]]], (28696 ^ _780086) ^ [_1311502, _1311504, _1311506] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1311502)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1311504), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1311506)), 28706 ^ _780086 : [(28707 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28705 ^ [_1311502, _1311504, _1311506]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1311502))))], (28710 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28708 ^ [_1311502, _1311504, _1311506]), _1311506)))], (28712 ^ _780086) ^ [] : [-(_1311504 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 28708 ^ [_1311502, _1311504, _1311506]), 28705 ^ [_1311502, _1311504, _1311506]))]], -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1311504), _1311502) = _1311504)], (28716 ^ _780086) ^ [_1311841, _1311843, _1311845] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1311841)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1311843), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1311845)), 28726 ^ _780086 : [(28727 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28725 ^ [_1311841, _1311843, _1311845]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1311841))))], (28730 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28728 ^ [_1311841, _1311843, _1311845]), _1311845)))], (28732 ^ _780086) ^ [] : [-(_1311843 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 28728 ^ [_1311841, _1311843, _1311845]), 28725 ^ [_1311841, _1311843, _1311845]))]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1311843), _1311841) = _1311843)], (28736 ^ _780086) ^ [_1312180, _1312182, _1312184] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1312180)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1312182), _1312184)), 28743 ^ _780086 : [(28744 ^ _780086) ^ [_1312376] : [28746 ^ _780086 : [(28747 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28745 ^ [_1312180, _1312182, _1312184, _1312376]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1312180))))], (28750 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28748 ^ [_1312180, _1312182, _1312184, _1312376]), _1312184)))], (28752 ^ _780086) ^ [] : [-(_1312376 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 28748 ^ [_1312180, _1312182, _1312184, _1312376]), 28745 ^ [_1312180, _1312182, _1312184, _1312376]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1312376), _1312182)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1312376), _1312180)), _1312182)))]]], (28760 ^ _780086) ^ [_1312652, _1312654, _1312656] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1312652)), 28763 ^ _780086 : [(28764 ^ _780086) ^ [_1312786] : [28766 ^ _780086 : [(28767 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28765 ^ [_1312652, _1312654, _1312656, _1312786]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1312652))))], (28770 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28768 ^ [_1312652, _1312654, _1312656, _1312786]), _1312654)))], (28772 ^ _780086) ^ [] : [-(_1312786 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 28768 ^ [_1312652, _1312654, _1312656, _1312786]), 28765 ^ [_1312652, _1312654, _1312656, _1312786]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1312786), _1312656)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1312786), _1312652)), _1312656)))]]], (28780 ^ _780086) ^ [_1313060, _1313062, _1313064] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1313060)), 28783 ^ _780086 : [(28784 ^ _780086) ^ [_1313194] : [28786 ^ _780086 : [(28787 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28785 ^ [_1313060, _1313062, _1313064, _1313194]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1313060))))], (28790 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28788 ^ [_1313060, _1313062, _1313064, _1313194]), _1313062)))], (28792 ^ _780086) ^ [] : [-(_1313194 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 28788 ^ [_1313060, _1313062, _1313064, _1313194]), 28785 ^ [_1313060, _1313062, _1313064, _1313194]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1313064), _1313194)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1313064), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1313194), _1313060))))]]], (28800 ^ _780086) ^ [_1313468, _1313470] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1313468)), 28809 ^ _780086 : [(28810 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1313470, 28805 ^ [_1313468, _1313470])))], (28812 ^ _780086) ^ [] : [hBOOL(hAPP(_1313470, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 28805 ^ [_1313468, _1313470]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 28806 ^ [_1313468, _1313470]), _1313468))))]], 28813 ^ _780086 : [(28814 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1313470, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 28805 ^ [_1313468, _1313470]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 28806 ^ [_1313468, _1313470]), _1313468)))))], (28816 ^ _780086) ^ [] : [hBOOL(hAPP(_1313470, 28805 ^ [_1313468, _1313470]))]], 28817 ^ _780086 : [(28818 ^ _780086) ^ [] : [28819 ^ _780086 : [(28820 ^ _780086) ^ [_1313900] : [hBOOL(hAPP(_1313470, _1313900))]], 28822 ^ _780086 : [(28823 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28821 ^ [_1313468, _1313470]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1313468))))], (28825 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1313470, 28821 ^ [_1313468, _1313470])))]]], (28827 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1313470, 28834 ^ [_1313468, _1313470]))), 28828 ^ _780086 : [(28829 ^ _780086) ^ [_1314015] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1314015), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1313468))), hBOOL(hAPP(_1313470, _1314015))]]]]], (28838 ^ _780086) ^ [_1314162, _1314164, _1314166] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1314162)), 28841 ^ _780086 : [(28842 ^ _780086) ^ [_1314296] : [28844 ^ _780086 : [(28845 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28843 ^ [_1314162, _1314164, _1314166, _1314296]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1314162))))], (28848 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28846 ^ [_1314162, _1314164, _1314166, _1314296]), _1314164)))], (28850 ^ _780086) ^ [] : [-(_1314296 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 28846 ^ [_1314162, _1314164, _1314166, _1314296]), 28843 ^ [_1314162, _1314164, _1314166, _1314296]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1314296), _1314166)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1314296), _1314162)), _1314166)))]]], (28858 ^ _780086) ^ [_1314570, _1314572, _1314574] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1314570)), 28861 ^ _780086 : [(28862 ^ _780086) ^ [_1314704] : [28864 ^ _780086 : [(28865 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28863 ^ [_1314570, _1314572, _1314574, _1314704]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1314570))))], (28868 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28866 ^ [_1314570, _1314572, _1314574, _1314704]), _1314572)))], (28870 ^ _780086) ^ [] : [-(_1314704 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 28866 ^ [_1314570, _1314572, _1314574, _1314704]), 28863 ^ [_1314570, _1314572, _1314574, _1314704]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1314574), _1314704)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1314574), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1314704), _1314570))))]]], (28878 ^ _780086) ^ [_1314978, _1314980, _1314982] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1314978)), 28884 ^ _780086 : [(28885 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1314980, 28883 ^ [_1314978, _1314980, _1314982])))], (28887 ^ _780086) ^ [] : [hBOOL(hAPP(_1314980, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 28883 ^ [_1314978, _1314980, _1314982]), _1314978)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1314982)), 28892 ^ _780086 : [(28893 ^ _780086) ^ [_1315267] : [hBOOL(hAPP(_1314980, _1315267)), -(hBOOL(hAPP(_1314980, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1315267), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1314982), _1314978)))))]]], (28899 ^ _780086) ^ [_1315389, _1315391] : [-(hBOOL(hAPP(_1315389, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_1315389, _1315391)), 28907 ^ _780086 : [(28908 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 28906 ^ [_1315389, _1315391]), _1315391)))], (28916 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1315389, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 28906 ^ [_1315389, _1315391]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (28910 ^ _780086) ^ [_1315627] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1315627), 28906 ^ [_1315389, _1315391])), hBOOL(hAPP(_1315389, _1315627))]]], (28918 ^ _780086) ^ [_1315779] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1315779)), 28922 ^ _780086 : [(28923 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 28921 ^ [_1315779])))], (28925 ^ _780086) ^ [] : [-(_1315779 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 28921 ^ [_1315779]))]]], (28927 ^ _780086) ^ [_1315909, _1315911, _1315913, _1315915, _1315917] : [class_Groups_Ocomm__monoid__add(_1315909), hBOOL(hAPP(c_Finite__Set_Ofinite(_1315911), _1315913)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1315911, tc_HOL_Obool)), _1315915), _1315913)), 28941 ^ _780086 : [(28942 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1315911), 28940 ^ [_1315909, _1315911, _1315913, _1315915, _1315917]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1315911, tc_HOL_Obool)), _1315913), _1315915))))], (28944 ^ _780086) ^ [] : [hAPP(_1315917, 28940 ^ [_1315909, _1315911, _1315913, _1315915, _1315917]) = c_Groups_Ozero__class_Ozero(_1315909)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1315911, _1315909), _1315917), _1315913) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1315911, _1315909), _1315917), _1315915))], (28948 ^ _780086) ^ [_1316360, _1316362, _1316364, _1316366, _1316368] : [class_Groups_Ocomm__monoid__add(_1316360), hBOOL(hAPP(c_Finite__Set_Ofinite(_1316362), _1316364)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1316362, tc_HOL_Obool)), _1316366), _1316364)), 28962 ^ _780086 : [(28963 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1316362), 28961 ^ [_1316360, _1316362, _1316364, _1316366, _1316368]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1316362, tc_HOL_Obool)), _1316364), _1316366))))], (28965 ^ _780086) ^ [] : [hAPP(_1316368, 28961 ^ [_1316360, _1316362, _1316364, _1316366, _1316368]) = c_Groups_Ozero__class_Ozero(_1316360)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1316362, _1316360), _1316368), _1316366) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1316362, _1316360), _1316368), _1316364))], (28969 ^ _780086) ^ [_1316811, _1316813] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1316811), _1316813)), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1316811, tc_HOL_Obool)), hAPP(c_Set_OPow(_1316811), _1316813)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_Finite__Set_Ocard(_1316811), _1316813)))], (28975 ^ _780086) ^ [_1316938, _1316940] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1316938), hAPP(c_Nat_OSuc, _1316940)) = c_Nat_Onat_Onat__case(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Orderings_Oord__class_Omin(tc_Nat_Onat)), _1316940)), _1316938))], (28977 ^ _780086) ^ [_1316983, _1316985] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1316983)), _1316985) = c_Nat_Onat_Onat__case(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1316983)), _1316985))], (28979 ^ _780086) ^ [_1317028, _1317030, _1317032] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1317028, tc_HOL_Obool)), _1317030), _1317032)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1317028, tc_HOL_Obool)), _1317030), hAPP(c_Set_OPow(_1317028), _1317032))))], (28985 ^ _780086) ^ [_1317172, _1317174] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1317172, tc_HOL_Obool)), hAPP(c_Set_OPow(_1317172), _1317174))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1317172), _1317174)))], (28991 ^ _780086) ^ [_1317277, _1317279] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1317277), _1317279)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1317277, tc_HOL_Obool)), hAPP(c_Set_OPow(_1317277), _1317279))))], (28997 ^ _780086) ^ [_1317388, _1317390, _1317392, _1317394, _1317396] : [hAPP(c_Set_Oimage(_1317388, _1317390, _1317392), _1317394) = _1317396, -(hAPP(c_Set_Oimage(tc_fun(_1317388, tc_HOL_Obool), tc_fun(_1317390, tc_HOL_Obool), c_Set_Oimage(_1317388, _1317390, _1317392)), hAPP(c_Set_OPow(_1317388), _1317394)) = hAPP(c_Set_OPow(_1317390), _1317396))], (29003 ^ _780086) ^ [_1317539, _1317541] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1317539, tc_HOL_Obool)), _1317541), hAPP(c_Set_OPow(_1317539), _1317541))))], (29005 ^ _780086) ^ [_1317595, _1317597, _1317599] : [hAPP(c_Set_Oimage(_1317597, tc_fun(_1317597, tc_HOL_Obool), _1317595), _1317599) = hAPP(c_Set_OPow(_1317597), _1317599)], (29007 ^ _780086) ^ [_1317649, _1317651] : [hAPP(c_Set_OPow(_1317649), _1317651) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1317649, tc_HOL_Obool), tc_HOL_Obool))], (29009 ^ _780086) ^ [_1317687, _1317689, _1317691, _1317693] : [-(hAPP(c_Set_OPow(_1317687), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1317689, tc_fun(_1317687, tc_HOL_Obool)), _1317691), _1317693)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1317689, tc_fun(tc_fun(_1317687, tc_HOL_Obool), tc_HOL_Obool)), _1317691), hAPP(hAPP(c_COMBB(tc_fun(_1317687, tc_HOL_Obool), tc_fun(tc_fun(_1317687, tc_HOL_Obool), tc_HOL_Obool), _1317689), c_Set_OPow(_1317687)), _1317693)))], (29011 ^ _780086) ^ [_1317769, _1317771] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1317769, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1317769, tc_HOL_Obool))), hAPP(c_Set_OPow(_1317769), _1317771))))], (29013 ^ _780086) ^ [_1317814, _1317816, _1317818] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1317814, tc_HOL_Obool)), _1317816), hAPP(c_Set_OPow(_1317814), _1317818))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1317814, tc_HOL_Obool)), _1317816), _1317818)))], (29019 ^ _780086) ^ [_1317961, _1317963, _1317965] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1317961, tc_HOL_Obool)), _1317963), hAPP(c_Set_OPow(_1317961), _1317965))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1317961, tc_HOL_Obool)), _1317963), _1317965)))], (29025 ^ _780086) ^ [_1318086, _1318088, _1318090] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1318086, tc_HOL_Obool)), _1318088), _1318090)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1318086, tc_HOL_Obool)), _1318088), hAPP(c_Set_OPow(_1318086), _1318090))))], (29031 ^ _780086) ^ [_1318217, _1318219, _1318221] : [-(c_Nat_Onat_Onat__case(_1318217, _1318219, _1318221, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1318219)], (29033 ^ _780086) ^ [_1318249, _1318251, _1318253, _1318255] : [-(c_Nat_Onat_Onat__case(_1318249, _1318251, _1318253, hAPP(c_Nat_OSuc, _1318255)) = hAPP(_1318253, _1318255))], (29035 ^ _780086) ^ [_1318289, _1318291, _1318293] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1318289, tc_HOL_Obool)), _1318291), _1318293)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1318289, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1318289), _1318291)), hAPP(c_Set_OPow(_1318289), _1318293))))], (29041 ^ _780086) ^ [_1318434, _1318436, _1318438] : [-(hAPP(c_Set_OPow(_1318434), hAPP(hAPP(c_Set_Oinsert(_1318434), _1318436), _1318438)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1318434, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1318434), _1318438)), hAPP(c_Set_Oimage(tc_fun(_1318434, tc_HOL_Obool), tc_fun(_1318434, tc_HOL_Obool), hAPP(c_Set_Oinsert(_1318434), _1318436)), hAPP(c_Set_OPow(_1318434), _1318438))))], (29043 ^ _780086) ^ [_1318516] : [-(hAPP(c_Set_OPow(_1318516), c_Orderings_Otop__class_Otop(tc_fun(_1318516, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1318516, tc_HOL_Obool), tc_HOL_Obool)))], (29045 ^ _780086) ^ [_1318557, _1318559, _1318561, _1318563] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1318557, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1318559, tc_fun(tc_fun(_1318557, tc_HOL_Obool), tc_HOL_Obool)), _1318561), hAPP(hAPP(c_COMBB(tc_fun(_1318557, tc_HOL_Obool), tc_fun(tc_fun(_1318557, tc_HOL_Obool), tc_HOL_Obool), _1318559), c_Set_OPow(_1318557)), _1318563))), hAPP(c_Set_OPow(_1318557), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1318559, tc_fun(_1318557, tc_HOL_Obool)), _1318561), _1318563)))))], (29047 ^ _780086) ^ [_1318652, _1318654, _1318656] : [-(hAPP(c_Set_OPow(_1318652), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1318652, tc_HOL_Obool)), _1318654), _1318656)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1318652, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1318652), _1318654)), hAPP(c_Set_OPow(_1318652), _1318656)))], (29049 ^ _780086) ^ [_1318719, _1318721, _1318723, _1318725, _1318727] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1318719, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1318721, _1318719, _1318723), _1318725)), _1318727)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1318719, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_fun(_1318721, tc_HOL_Obool), tc_fun(_1318719, tc_HOL_Obool), c_Set_Oimage(_1318721, _1318719, _1318723)), hAPP(c_Set_OPow(_1318721), _1318725))), hAPP(c_Set_OPow(_1318719), _1318727))))], (29055 ^ _780086) ^ [_1318916] : [-(hAPP(c_Set_OPow(_1318916), c_Orderings_Obot__class_Obot(tc_fun(_1318916, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1318916, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1318916, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1318916, tc_HOL_Obool), tc_HOL_Obool))))], (29057 ^ _780086) ^ [_1318973, _1318975] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1318973), hAPP(c_Nat_OSuc, _1318975)) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1318975), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), _1318975)), _1318973))], (29059 ^ _780086) ^ [_1319021, _1319023] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1319021)), _1319023) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1319021), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1319021)), _1319023))], (29061 ^ _780086) ^ [_1319069, _1319071, _1319073] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1319069, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1319069, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1319069), _1319071)), hAPP(c_Set_OPow(_1319069), _1319073))), hAPP(c_Set_OPow(_1319069), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1319069, tc_HOL_Obool)), _1319071), _1319073)))))], (29063 ^ _780086) ^ [_1319167, _1319169, _1319171] : [hBOOL(hAPP(c_Predicate_OPowp(_1319167, hAPP(hAPP(c_COMBC(_1319167, tc_fun(_1319167, tc_HOL_Obool), tc_HOL_Obool), c_member(_1319167)), _1319169)), _1319171)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1319167, tc_HOL_Obool)), _1319171), hAPP(c_Set_OPow(_1319167), _1319169))))], (29069 ^ _780086) ^ [_1319312, _1319314, _1319316] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1319312, tc_HOL_Obool)), _1319316), hAPP(c_Set_OPow(_1319312), _1319314))), -(hBOOL(hAPP(c_Predicate_OPowp(_1319312, hAPP(hAPP(c_COMBC(_1319312, tc_fun(_1319312, tc_HOL_Obool), tc_HOL_Obool), c_member(_1319312)), _1319314)), _1319316)))], (29075 ^ _780086) ^ [_1319463, _1319465] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1319463), hAPP(c_Nat_OSuc, _1319465)) = c_Nat_Onat_Onat__case(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_COMBI(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1319463), _1319465)))], (29077 ^ _780086) ^ [_1319508, _1319510, _1319512] : [class_Fields_Olinordered__field__inverse__zero(_1319508), 29083 ^ _780086 : [(29084 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319508), c_Groups_Ozero__class_Ozero(_1319508)), 29082 ^ [_1319508, _1319510, _1319512])))], (29086 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319508), 29082 ^ [_1319508, _1319510, _1319512]), c_Groups_Oone__class_Oone(_1319508))))], (29088 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319508), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1319508), 29082 ^ [_1319508, _1319510, _1319512]), _1319510)), _1319512))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319508), _1319510), _1319512)))], (29092 ^ _780086) ^ [_1319857, _1319859, _1319861, _1319863, _1319865] : [class_Groups_Ocomm__monoid__add(_1319857), class_Groups_Ocomm__monoid__mult(_1319857), _1319859 = _1319861, c_Nat__Transfer_Onat__set(_1319861), 29110 ^ _780086 : [(29111 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 29109 ^ [_1319857, _1319859, _1319861, _1319863, _1319865])))], (29113 ^ _780086) ^ [] : [hAPP(_1319863, 29109 ^ [_1319857, _1319859, _1319861, _1319863, _1319865]) = hAPP(_1319865, 29109 ^ [_1319857, _1319859, _1319861, _1319863, _1319865])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1319857), _1319863), _1319859) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1319857), _1319865), _1319861))], (29117 ^ _780086) ^ [_1320320, _1320322, _1320324] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1320320)), 29120 ^ _780086 : [(29139 ^ _780086) ^ [] : [29142 ^ _780086 : [(29143 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 29141 ^ [_1320320, _1320322, _1320324])))], (29145 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 29141 ^ [_1320320, _1320322, _1320324]), _1320320)))], (29147 ^ _780086) ^ [] : [-(_1320324 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1320320), 29140 ^ [_1320320, _1320322, _1320324])), 29141 ^ [_1320320, _1320322, _1320324]))], (29149 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(_1320322, 29140 ^ [_1320320, _1320322, _1320324]), 29141 ^ [_1320320, _1320322, _1320324]))]], -(hBOOL(hAPP(hAPP(_1320322, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1320324), _1320320)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1320324, _1320320))))], (29121 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(_1320322, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1320324), _1320320)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1320324, _1320320))), 29124 ^ _780086 : [(29125 ^ _780086) ^ [_1320521, _1320523] : [-(hBOOL(hAPP(hAPP(_1320322, _1320523), _1320521))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1320521)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1320521), _1320320)), _1320324 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1320320), _1320523)), _1320521)]]]]], (29153 ^ _780086) ^ [_1321035, _1321037, _1321039] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1321035), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 29156 ^ _780086 : [(29175 ^ _780086) ^ [] : [29178 ^ _780086 : [(29179 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1321035), 29177 ^ [_1321035, _1321037, _1321039])))], (29181 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 29177 ^ [_1321035, _1321037, _1321039]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (29183 ^ _780086) ^ [] : [-(_1321039 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1321035), 29176 ^ [_1321035, _1321037, _1321039])), 29177 ^ [_1321035, _1321037, _1321039]))], (29185 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(_1321037, 29176 ^ [_1321035, _1321037, _1321039]), 29177 ^ [_1321035, _1321037, _1321039]))]], -(hBOOL(hAPP(hAPP(_1321037, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1321039), _1321035)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1321039, _1321035))))], (29157 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(_1321037, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1321039), _1321035)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1321039, _1321035))), 29160 ^ _780086 : [(29161 ^ _780086) ^ [_1321245, _1321247] : [-(hBOOL(hAPP(hAPP(_1321037, _1321247), _1321245))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1321035), _1321245)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1321245), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1321039 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1321035), _1321247)), _1321245)]]]]], (29189 ^ _780086) ^ [_1321768, _1321770, _1321772] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1321768, _1321770)), _1321772), _1321770) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1321768), _1321772), _1321770))], (29191 ^ _780086) ^ [_1321819, _1321821, _1321823] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1321819, _1321821)), _1321823), _1321821) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1321819), _1321823), _1321821))], (29193 ^ _780086) ^ [_1321870, _1321872, _1321874] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1321870), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1321872, _1321874)), _1321874) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1321870), _1321872), _1321874))], (29195 ^ _780086) ^ [_1321921, _1321923, _1321925, _1321927, _1321929, _1321931] : [class_Divides_Oring__div(_1321921), c_Divides_Odiv__class_Omod(_1321921, _1321923, _1321925) = c_Divides_Odiv__class_Omod(_1321921, _1321927, _1321925), c_Divides_Odiv__class_Omod(_1321921, _1321929, _1321925) = c_Divides_Odiv__class_Omod(_1321921, _1321931, _1321925), -(c_Divides_Odiv__class_Omod(_1321921, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1321921), _1321923), _1321929), _1321925) = c_Divides_Odiv__class_Omod(_1321921, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1321921), _1321927), _1321931), _1321925))], (29209 ^ _780086) ^ [_1322204, _1322206, _1322208, _1322210] : [class_Divides_Oring__div(_1322204), -(c_Divides_Odiv__class_Omod(_1322204, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1322204), _1322206), _1322208), _1322210) = c_Divides_Odiv__class_Omod(_1322204, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1322204), c_Divides_Odiv__class_Omod(_1322204, _1322206, _1322210)), c_Divides_Odiv__class_Omod(_1322204, _1322208, _1322210)), _1322210))], (29215 ^ _780086) ^ [_1322347, _1322349, _1322351, _1322353] : [class_Divides_Oring__div(_1322347), -(c_Divides_Odiv__class_Omod(_1322347, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1322347), _1322349), _1322351), _1322353) = c_Divides_Odiv__class_Omod(_1322347, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1322347), c_Divides_Odiv__class_Omod(_1322347, _1322349, _1322353)), _1322351), _1322353))], (29221 ^ _780086) ^ [_1322482, _1322484, _1322486, _1322488] : [class_Divides_Oring__div(_1322482), -(c_Divides_Odiv__class_Omod(_1322482, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1322482), _1322484), _1322486), _1322488) = c_Divides_Odiv__class_Omod(_1322482, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1322482), _1322484), c_Divides_Odiv__class_Omod(_1322482, _1322486, _1322488)), _1322488))], (29227 ^ _780086) ^ [_1322617, _1322619, _1322621] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1322617), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1322619, _1322621)), _1322621) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1322617), _1322619), _1322621))], (29229 ^ _780086) ^ [_1322668, _1322670, _1322672] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1322668), _1322670), _1322672) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1322668), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1322670, _1322672)), _1322672))], (29231 ^ _780086) ^ [_1322719] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1322719, _1322719) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (29233 ^ _780086) ^ [_1322746] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1322746) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (29235 ^ _780086) ^ [_1322773, _1322775, _1322777, _1322779, _1322781, _1322783] : [class_Divides_Osemiring__div(_1322773), c_Divides_Odiv__class_Omod(_1322773, _1322775, _1322777) = c_Divides_Odiv__class_Omod(_1322773, _1322779, _1322777), c_Divides_Odiv__class_Omod(_1322773, _1322781, _1322777) = c_Divides_Odiv__class_Omod(_1322773, _1322783, _1322777), -(c_Divides_Odiv__class_Omod(_1322773, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1322773), _1322775), _1322781), _1322777) = c_Divides_Odiv__class_Omod(_1322773, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1322773), _1322779), _1322783), _1322777))], (29249 ^ _780086) ^ [_1323056, _1323058, _1323060, _1323062] : [class_Divides_Osemiring__div(_1323056), -(c_Divides_Odiv__class_Omod(_1323056, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1323056), c_Divides_Odiv__class_Omod(_1323056, _1323058, _1323060)), _1323062), _1323060) = c_Divides_Odiv__class_Omod(_1323056, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1323056), _1323058), _1323062), _1323060))], (29255 ^ _780086) ^ [_1323191, _1323193, _1323195, _1323197] : [class_Divides_Osemiring__div(_1323191), -(c_Divides_Odiv__class_Omod(_1323191, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1323191), _1323193), c_Divides_Odiv__class_Omod(_1323191, _1323195, _1323197)), _1323197) = c_Divides_Odiv__class_Omod(_1323191, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1323191), _1323193), _1323195), _1323197))], (29261 ^ _780086) ^ [_1323326, _1323328, _1323330, _1323332] : [class_Divides_Osemiring__div(_1323326), -(c_Divides_Odiv__class_Omod(_1323326, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1323326), _1323328), _1323330), _1323332) = c_Divides_Odiv__class_Omod(_1323326, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1323326), c_Divides_Odiv__class_Omod(_1323326, _1323328, _1323332)), c_Divides_Odiv__class_Omod(_1323326, _1323330, _1323332)), _1323332))], (29267 ^ _780086) ^ [_1323469, _1323471, _1323473, _1323475] : [class_Divides_Osemiring__div(_1323469), -(c_Divides_Odiv__class_Omod(_1323469, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1323469), _1323471), _1323473), _1323475) = c_Divides_Odiv__class_Omod(_1323469, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1323469), c_Divides_Odiv__class_Omod(_1323469, _1323471, _1323475)), _1323473), _1323475))], (29273 ^ _780086) ^ [_1323604, _1323606, _1323608, _1323610] : [class_Divides_Osemiring__div(_1323604), -(c_Divides_Odiv__class_Omod(_1323604, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1323604), _1323606), _1323608), _1323610) = c_Divides_Odiv__class_Omod(_1323604, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1323604), _1323606), c_Divides_Odiv__class_Omod(_1323604, _1323608, _1323610)), _1323610))], (29279 ^ _780086) ^ [_1323739, _1323741, _1323743] : [class_Divides_Osemiring__div(_1323739), -(c_Divides_Odiv__class_Omod(_1323739, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1323739), _1323741), _1323743), _1323741) = c_Divides_Odiv__class_Omod(_1323739, _1323743, _1323741))], (29285 ^ _780086) ^ [_1323848, _1323850, _1323852] : [class_Divides_Osemiring__div(_1323848), -(c_Divides_Odiv__class_Omod(_1323848, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1323848), _1323850), _1323852), _1323852) = c_Divides_Odiv__class_Omod(_1323848, _1323850, _1323852))], (29291 ^ _780086) ^ [_1323957, _1323959, _1323961] : [class_Divides_Oring__div(_1323957), -(c_Divides_Odiv__class_Omod(_1323957, hAPP(c_Groups_Ouminus__class_Ouminus(_1323957), _1323959), _1323961) = c_Divides_Odiv__class_Omod(_1323957, hAPP(c_Groups_Ouminus__class_Ouminus(_1323957), c_Divides_Odiv__class_Omod(_1323957, _1323959, _1323961)), _1323961))], (29297 ^ _780086) ^ [_1324078, _1324080, _1324082, _1324084] : [class_Divides_Oring__div(_1324078), c_Divides_Odiv__class_Omod(_1324078, _1324080, _1324082) = c_Divides_Odiv__class_Omod(_1324078, _1324084, _1324082), -(c_Divides_Odiv__class_Omod(_1324078, hAPP(c_Groups_Ouminus__class_Ouminus(_1324078), _1324080), _1324082) = c_Divides_Odiv__class_Omod(_1324078, hAPP(c_Groups_Ouminus__class_Ouminus(_1324078), _1324084), _1324082))], (29307 ^ _780086) ^ [_1324265, _1324267] : [class_Divides_Osemiring__div(_1324265), -(c_Divides_Odiv__class_Omod(_1324265, _1324267, _1324267) = c_Groups_Ozero__class_Ozero(_1324265))], (29313 ^ _780086) ^ [_1324352, _1324354] : [class_Divides_Osemiring__div(_1324352), -(c_Divides_Odiv__class_Omod(_1324352, _1324354, c_Groups_Ozero__class_Ozero(_1324352)) = _1324354)], (29319 ^ _780086) ^ [_1324439, _1324441] : [class_Divides_Osemiring__div(_1324439), -(c_Divides_Odiv__class_Omod(_1324439, c_Groups_Ozero__class_Ozero(_1324439), _1324441) = c_Groups_Ozero__class_Ozero(_1324439))], (29325 ^ _780086) ^ [_1324530, _1324532, _1324534] : [class_Divides_Osemiring__div(_1324530), -(c_Divides_Odiv__class_Omod(_1324530, c_Divides_Odiv__class_Omod(_1324530, _1324532, _1324534), _1324534) = c_Divides_Odiv__class_Omod(_1324530, _1324532, _1324534))], (29331 ^ _780086) ^ [_1324631, _1324633, _1324635, _1324637, _1324639, _1324641] : [class_Divides_Osemiring__div(_1324631), c_Divides_Odiv__class_Omod(_1324631, _1324633, _1324635) = c_Divides_Odiv__class_Omod(_1324631, _1324637, _1324635), c_Divides_Odiv__class_Omod(_1324631, _1324639, _1324635) = c_Divides_Odiv__class_Omod(_1324631, _1324641, _1324635), -(c_Divides_Odiv__class_Omod(_1324631, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1324631), _1324633), _1324639), _1324635) = c_Divides_Odiv__class_Omod(_1324631, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1324631), _1324637), _1324641), _1324635))], (29345 ^ _780086) ^ [_1324914, _1324916, _1324918, _1324920] : [class_Divides_Osemiring__div(_1324914), -(c_Divides_Odiv__class_Omod(_1324914, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1324914), c_Divides_Odiv__class_Omod(_1324914, _1324916, _1324918)), _1324920), _1324918) = c_Divides_Odiv__class_Omod(_1324914, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1324914), _1324916), _1324920), _1324918))], (29351 ^ _780086) ^ [_1325049, _1325051, _1325053, _1325055] : [class_Divides_Osemiring__div(_1325049), -(c_Divides_Odiv__class_Omod(_1325049, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1325049), _1325051), _1325053), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1325049), _1325055), _1325053)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1325049), c_Divides_Odiv__class_Omod(_1325049, _1325051, _1325055)), _1325053))], (29357 ^ _780086) ^ [_1325192, _1325194, _1325196, _1325198] : [class_Divides_Osemiring__div(_1325192), -(c_Divides_Odiv__class_Omod(_1325192, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1325192), _1325194), _1325196), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1325192), _1325194), _1325198)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1325192), _1325194), c_Divides_Odiv__class_Omod(_1325192, _1325196, _1325198)))], (29363 ^ _780086) ^ [_1325335, _1325337, _1325339, _1325341] : [class_Divides_Osemiring__div(_1325335), -(c_Divides_Odiv__class_Omod(_1325335, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1325335), _1325337), _1325339), _1325341) = c_Divides_Odiv__class_Omod(_1325335, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1325335), c_Divides_Odiv__class_Omod(_1325335, _1325337, _1325341)), c_Divides_Odiv__class_Omod(_1325335, _1325339, _1325341)), _1325341))], (29369 ^ _780086) ^ [_1325478, _1325480, _1325482, _1325484] : [class_Divides_Osemiring__div(_1325478), -(c_Divides_Odiv__class_Omod(_1325478, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1325478), _1325480), _1325482), _1325484) = c_Divides_Odiv__class_Omod(_1325478, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1325478), c_Divides_Odiv__class_Omod(_1325478, _1325480, _1325484)), _1325482), _1325484))], (29375 ^ _780086) ^ [_1325613, _1325615, _1325617, _1325619] : [class_Divides_Osemiring__div(_1325613), -(c_Divides_Odiv__class_Omod(_1325613, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1325613), _1325615), _1325617), _1325619) = c_Divides_Odiv__class_Omod(_1325613, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1325613), _1325615), c_Divides_Odiv__class_Omod(_1325613, _1325617, _1325619)), _1325619))], (29381 ^ _780086) ^ [_1325748, _1325750] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1325748, _1325750)), _1325750) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1325748), _1325750))], (29383 ^ _780086) ^ [_1325791, _1325793] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1325791), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1325793)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1325791, _1325793)))], (29385 ^ _780086) ^ [_1325833, _1325835] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1325833, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1325835)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1325833), _1325835)))], (29387 ^ _780086) ^ [_1325875, _1325877] : [c_Nat__Transfer_Ois__nat(_1325875), c_Nat__Transfer_Ois__nat(_1325877), -(c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1325875, _1325877)))], (29397 ^ _780086) ^ [_1326006, _1326008, _1326010] : [class_Divides_Osemiring__div(_1326006), -(c_Divides_Odiv__class_Omod(_1326006, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1326006), _1326008), _1326010), _1326008) = c_Groups_Ozero__class_Ozero(_1326006))], (29403 ^ _780086) ^ [_1326111, _1326113, _1326115] : [class_Divides_Osemiring__div(_1326111), -(c_Divides_Odiv__class_Omod(_1326111, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1326111), _1326113), _1326115), _1326115) = c_Groups_Ozero__class_Ozero(_1326111))], (29409 ^ _780086) ^ [_1326216, _1326218, _1326220, _1326222] : [class_Divides_Osemiring__div(_1326216), -(c_Divides_Odiv__class_Omod(_1326216, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1326216), _1326218), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1326216), _1326220), _1326222)), _1326220) = c_Divides_Odiv__class_Omod(_1326216, _1326218, _1326220))], (29415 ^ _780086) ^ [_1326343, _1326345, _1326347, _1326349] : [class_Divides_Osemiring__div(_1326343), -(c_Divides_Odiv__class_Omod(_1326343, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1326343), _1326345), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1326343), _1326347), _1326349)), _1326349) = c_Divides_Odiv__class_Omod(_1326343, _1326345, _1326349))], (29421 ^ _780086) ^ [_1326470, _1326472] : [class_Divides_Osemiring__div(_1326470), -(c_Divides_Odiv__class_Omod(_1326470, _1326472, c_Groups_Oone__class_Oone(_1326470)) = c_Groups_Ozero__class_Ozero(_1326470))], (29427 ^ _780086) ^ [_1326561, _1326563, _1326565] : [class_Divides_Osemiring__div(_1326561), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1326561), c_Divides_Odiv__class_Omod(_1326561, _1326563, _1326565)), _1326565) = c_Groups_Ozero__class_Ozero(_1326561))], (29433 ^ _780086) ^ [_1326666, _1326668] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1326666)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1326666, _1326668)), _1326666)))], (29439 ^ _780086) ^ [_1326765, _1326767] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1326765)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1326767)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1326765, _1326767))))], (29449 ^ _780086) ^ [_1326914, _1326916] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1326914)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1326916, _1326914)), _1326914)))], (29455 ^ _780086) ^ [_1327013, _1327015] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1327013), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1327013), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1327015, _1327013))))], (29461 ^ _780086) ^ [_1327133, _1327135] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1327133, _1327135) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1327133 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1327135), 29464 ^ [_1327133, _1327135]))], (29468 ^ _780086) ^ [_1327238, _1327240] : [29469 ^ _780086 : [(29470 ^ _780086) ^ [_1327287] : [_1327238 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1327240), _1327287)]], -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1327238, _1327240) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (29474 ^ _780086) ^ [_1327349, _1327351] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1327349), _1327351) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1327349, _1327351) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (29480 ^ _780086) ^ [_1327439, _1327441] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1327439, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1327441)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1327439, _1327441) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (29486 ^ _780086) ^ [_1327530, _1327532] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1327530, _1327532)), _1327532) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (29488 ^ _780086) ^ [_1327563] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1327563), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (29490 ^ _780086) ^ [_1327589] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1327589, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1327589)], (29492 ^ _780086) ^ [_1327618, _1327620, _1327622] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1327618), _1327620)), _1327622) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1327618), _1327622)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1327620), _1327622))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1327618, _1327622)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1327620, _1327622))), _1327622)))], (29494 ^ _780086) ^ [_1327701, _1327703, _1327705] : [class_Divides_Osemiring__div(_1327701), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1327701), c_Divides_Odiv__class_Omod(_1327701, _1327703, _1327705)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1327701), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1327701), _1327703), _1327705)), _1327705)) = _1327703)], (29500 ^ _780086) ^ [_1327834, _1327836, _1327838] : [class_Divides_Osemiring__div(_1327834), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1327834), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1327834), _1327836), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1327834), _1327838), _1327836))), c_Divides_Odiv__class_Omod(_1327834, _1327838, _1327836)) = _1327838)], (29506 ^ _780086) ^ [_1327967, _1327969, _1327971] : [class_Divides_Osemiring__div(_1327967), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1327967), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1327967), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1327967), _1327969), _1327971)), _1327971)), c_Divides_Odiv__class_Omod(_1327967, _1327969, _1327971)) = _1327969)], (29512 ^ _780086) ^ [_1328100, _1328102, _1328104, _1328106] : [class_Divides_Osemiring__div(_1328100), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1328100), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1328100), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1328100), _1328102), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1328100), _1328104), _1328102))), c_Divides_Odiv__class_Omod(_1328100, _1328104, _1328102))), _1328106) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1328100), _1328104), _1328106))], (29518 ^ _780086) ^ [_1328267, _1328269, _1328271, _1328273] : [class_Divides_Osemiring__div(_1328267), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1328267), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1328267), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1328267), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1328267), _1328269), _1328271)), _1328271)), c_Divides_Odiv__class_Omod(_1328267, _1328269, _1328271))), _1328273) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1328267), _1328269), _1328273))], (29524 ^ _780086) ^ [_1328434, _1328436] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1328434), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1328436), _1328434)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1328434, _1328436) = _1328434)], (29534 ^ _780086) ^ [_1328591, _1328593] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1328591), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 29537 ^ _780086 : [(29538 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1328593, _1328591)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (29540 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1328591), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1328593, _1328591))))]]], (29542 ^ _780086) ^ [_1328740, _1328742] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1328740), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1328742, _1328740)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (29548 ^ _780086) ^ [_1328845, _1328847] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1328845)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1328845), _1328847)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1328845, _1328847) = _1328845)], (29558 ^ _780086) ^ [_1328996, _1328998] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1328996)), 29561 ^ _780086 : [(29562 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1328998, _1328996))))], (29564 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1328998, _1328996)), _1328996)))]]], (29566 ^ _780086) ^ [_1329133, _1329135] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1329133)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1329135, _1329133))))], (29572 ^ _780086) ^ [_1329235, _1329237] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1329235, _1329237) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1329235, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1329237)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (29578 ^ _780086) ^ [_1329328, _1329330] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1329328, _1329330) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1329328, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1329330)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1329328, _1329330)), _1329330))], (29584 ^ _780086) ^ [_1329396, _1329398] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1329396, _1329398) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1329396), _1329398) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (29590 ^ _780086) ^ [_1329489, _1329491] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1329489, _1329491) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1329489), _1329491) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1329491), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1329489, _1329491)))], (29596 ^ _780086) ^ [_1329548, _1329550] : [-(_1329548 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1329550), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1329548), _1329550))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1329548, _1329550)))], (29598 ^ _780086) ^ [_1329595, _1329597, _1329599] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1329595), _1329597)), _1329599) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1329595), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1329597), _1329599))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1329595), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1329597, _1329599))), _1329599)))], (29600 ^ _780086) ^ [_1329668, _1329670, _1329672] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1329668), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1329670), _1329668))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1329670, _1329668))), _1329672) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1329670), _1329672))], (29602 ^ _780086) ^ [_1329729, _1329731, _1329733] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1329729), _1329731)), _1329731)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1329729, _1329731))), _1329733) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1329729), _1329733))], (29604 ^ _780086) ^ [_1329790, _1329792] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1329790), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1329792), _1329790)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1329792), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1329792, _1329790)))], (29606 ^ _780086) ^ [_1329837, _1329839] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1329837, _1329839) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1329837), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1329837), _1329839)), _1329839)))], (29608 ^ _780086) ^ [_1329884, _1329886] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1329884)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1329884), _1329886)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1329884, _1329886) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1329884), _1329886))], (29618 ^ _780086) ^ [_1330059, _1330061, _1330063, _1330065] : [_1330059 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1330061), _1330063)), _1330065), -(_1330061 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1330059, _1330061) = _1330065), 29625 ^ _780086 : [(29626 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1330061)))], (29628 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1330065)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1330065), _1330061))]], 29633 ^ _780086 : [(29634 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1330061))], (29636 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1330061), _1330065)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1330065), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (29648 ^ _780086) ^ [_1330524, _1330526, _1330528, _1330530] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1330524)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1330526), _1330528)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1330528), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(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), _1330526), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1330530, _1330524))), _1330528)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (29662 ^ _780086) ^ [_1330783, _1330785, _1330787, _1330789] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1330783)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1330785), _1330787)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1330787), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1330785), _1330783)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1330785), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1330789, _1330783))), _1330787))))], (29676 ^ _780086) ^ [_1331054, _1331056, _1331058, _1331060] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1331054)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1331056)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1331056), _1331058)), -(hBOOL(hAPP(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), _1331058), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1331060, _1331054))), _1331056)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1331058), _1331054))))], (29690 ^ _780086) ^ [_1331319, _1331321, _1331323, _1331325] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1331319)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1331321)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1331321), _1331323)), -(hBOOL(hAPP(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), _1331323), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1331325, _1331319))), _1331321))))], (29750 ^ _780086) ^ [_1332461, _1332463, _1332465] : [-(hBOOL(hAPP(_1332461, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1332463, _1332465)))), 29753 ^ _780086 : [(29754 ^ _780086) ^ [] : [-(_1332465 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (29756 ^ _780086) ^ [] : [hBOOL(hAPP(_1332461, _1332463))]], 29759 ^ _780086 : [(29760 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1332465)))], (29764 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 29762 ^ [_1332461, _1332463, _1332465])))], (29766 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 29762 ^ [_1332461, _1332463, _1332465]), _1332465)))], (29768 ^ _780086) ^ [] : [-(_1332463 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1332465), 29761 ^ [_1332461, _1332463, _1332465])), 29762 ^ [_1332461, _1332463, _1332465]))], (29770 ^ _780086) ^ [] : [hBOOL(hAPP(_1332461, 29762 ^ [_1332461, _1332463, _1332465]))]], 29771 ^ _780086 : [(29772 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1332465), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (29776 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1332465), 29774 ^ [_1332461, _1332463, _1332465])))], (29778 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 29774 ^ [_1332461, _1332463, _1332465]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (29780 ^ _780086) ^ [] : [-(_1332463 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1332465), 29773 ^ [_1332461, _1332463, _1332465])), 29774 ^ [_1332461, _1332463, _1332465]))], (29782 ^ _780086) ^ [] : [hBOOL(hAPP(_1332461, 29774 ^ [_1332461, _1332463, _1332465]))]]], (29704 ^ _780086) ^ [_1331584, _1331586, _1331588] : [hBOOL(hAPP(_1331584, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1331586, _1331588))), 29707 ^ _780086 : [(29708 ^ _780086) ^ [] : [_1331588 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1331584, _1331586)))], (29714 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1331588)), 29717 ^ _780086 : [(29718 ^ _780086) ^ [_1331914, _1331916] : [-(hBOOL(hAPP(_1331584, _1331914))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1331914)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1331914), _1331588)), _1331586 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1331588), _1331916)), _1331914)]]], (29732 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1331588), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 29735 ^ _780086 : [(29736 ^ _780086) ^ [_1332206, _1332208] : [-(hBOOL(hAPP(_1331584, _1332206))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1331588), _1332206)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1332206), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1331586 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1331588), _1332208)), _1332206)]]]]], (29786 ^ _780086) ^ [_1333173, _1333175, _1333177] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1333173)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1333175, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1333177), _1333173)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1333177), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1333175), _1333177), _1333173))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1333175, _1333177)))], (29792 ^ _780086) ^ [_1333327, _1333329] : [-(_1333327 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 29795 ^ _780086 : [(29796 ^ _780086) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1333329, _1333327) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1333329), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1333327)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1333329), _1333327)))], (29802 ^ _780086) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1333329, _1333327) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1333329), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1333327)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1333329), _1333327))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]]], (29808 ^ _780086) ^ [_1333600, _1333602] : [-(_1333600 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 29811 ^ _780086 : [(29812 ^ _780086) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1333602, _1333600) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1333602)), _1333600) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1333602), _1333600)))], (29818 ^ _780086) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1333602, _1333600) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1333602)), _1333600) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1333602), _1333600))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]]], (29824 ^ _780086) ^ [_1333889, _1333891] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1333889)), _1333891)), -(hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1333889), _1333891)))], (29830 ^ _780086) ^ [_1333992, _1333994] : [hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1333992), _1333994)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1333992)), _1333994)))], (29836 ^ _780086) ^ [_1334110, _1334112] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1334110)), -(c_SMT_Oz3mod(_1334112, _1334110) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1334112, _1334110))], (29842 ^ _780086) ^ [_1334199, _1334201] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1334199))), -(c_SMT_Oz3mod(_1334201, _1334199) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1334201, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1334199)))], (29848 ^ _780086) ^ [_1334249, _1334251] : [class_Rings_Olinordered__idom(_1334249), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1334249), _1334251), c_Groups_Ozero__class_Ozero(_1334249))), -(c_Groups_Osgn__class_Osgn(_1334249, _1334251) = hAPP(c_Groups_Ouminus__class_Ouminus(_1334249), c_Groups_Oone__class_Oone(_1334249)))], (29858 ^ _780086) ^ [_1334414, _1334416] : [class_Rings_Olinordered__idom(_1334414), 29861 ^ _780086 : [(29862 ^ _780086) ^ [] : [c_Groups_Osgn__class_Osgn(_1334414, _1334416) = hAPP(c_Groups_Ouminus__class_Ouminus(_1334414), c_Groups_Oone__class_Oone(_1334414)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1334414), _1334416), c_Groups_Ozero__class_Ozero(_1334414))))], (29868 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1334414), _1334416), c_Groups_Ozero__class_Ozero(_1334414))), -(c_Groups_Osgn__class_Osgn(_1334414, _1334416) = hAPP(c_Groups_Ouminus__class_Ouminus(_1334414), c_Groups_Oone__class_Oone(_1334414)))]]], (29874 ^ _780086) ^ [_1334676, _1334678] : [class_Groups_Osgn__if(_1334676), 29877 ^ _780086 : [(29878 ^ _780086) ^ [] : [_1334678 = c_Groups_Ozero__class_Ozero(_1334676), -(c_Groups_Osgn__class_Osgn(_1334676, _1334678) = c_Groups_Ozero__class_Ozero(_1334676))], (29884 ^ _780086) ^ [] : [-(_1334678 = c_Groups_Ozero__class_Ozero(_1334676)), 29887 ^ _780086 : [(29888 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1334676), c_Groups_Ozero__class_Ozero(_1334676)), _1334678)), -(c_Groups_Osgn__class_Osgn(_1334676, _1334678) = c_Groups_Oone__class_Oone(_1334676))], (29894 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1334676), c_Groups_Ozero__class_Ozero(_1334676)), _1334678))), -(c_Groups_Osgn__class_Osgn(_1334676, _1334678) = hAPP(c_Groups_Ouminus__class_Ouminus(_1334676), c_Groups_Oone__class_Oone(_1334676)))]]]]], (29900 ^ _780086) ^ [_1335073, _1335075] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1335073), _1335075)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1335073, _1335075) = _1335073)], (29906 ^ _780086) ^ [_1335168, _1335170] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1335168), _1335170) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1335168, _1335170)), _1335170))], (29908 ^ _780086) ^ [_1335211, _1335213, _1335215] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1335211, _1335213)), _1335215) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1335211), _1335215), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1335213), _1335215)))], (29910 ^ _780086) ^ [_1335264, _1335266, _1335268] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1335264), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1335266, _1335268)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1335264), _1335266), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1335264), _1335268)))], (29912 ^ _780086) ^ [_1335317, _1335319] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1335317, _1335319)), _1335317)))], (29914 ^ _780086) ^ [_1335351, _1335353] : [class_Rings_Olinordered__idom(_1335351), -(c_Groups_Osgn__class_Osgn(_1335351, c_Groups_Osgn__class_Osgn(_1335351, _1335353)) = c_Groups_Osgn__class_Osgn(_1335351, _1335353))], (29920 ^ _780086) ^ [_1335444, _1335446] : [class_Rings_Olinordered__idom(_1335444), 29923 ^ _780086 : [(29924 ^ _780086) ^ [] : [c_Groups_Osgn__class_Osgn(_1335444, _1335446) = c_Groups_Ozero__class_Ozero(_1335444), -(_1335446 = c_Groups_Ozero__class_Ozero(_1335444))], (29930 ^ _780086) ^ [] : [_1335446 = c_Groups_Ozero__class_Ozero(_1335444), -(c_Groups_Osgn__class_Osgn(_1335444, _1335446) = c_Groups_Ozero__class_Ozero(_1335444))]]], (29936 ^ _780086) ^ [_1335670] : [class_Groups_Osgn__if(_1335670), -(c_Groups_Osgn__class_Osgn(_1335670, c_Groups_Ozero__class_Ozero(_1335670)) = c_Groups_Ozero__class_Ozero(_1335670))], (29942 ^ _780086) ^ [_1335757, _1335759, _1335761] : [class_Rings_Olinordered__idom(_1335757), -(c_Groups_Osgn__class_Osgn(_1335757, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1335757), _1335759), _1335761)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1335757), c_Groups_Osgn__class_Osgn(_1335757, _1335759)), c_Groups_Osgn__class_Osgn(_1335757, _1335761)))], (29948 ^ _780086) ^ [_1335893, _1335895] : [hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1335893, _1335895)) = _1335895, -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1335893), _1335895) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29954 ^ _780086) ^ [_1335992, _1335994] : [-(hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1335992, _1335994)) = _1335994), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1335992), _1335994) = hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1335992, _1335994)))], (29960 ^ _780086) ^ [_1336051] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1336051, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29962 ^ _780086) ^ [_1336078, _1336080] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1336078)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1336080, _1336078)), _1336078)))], (29968 ^ _780086) ^ [_1336192, _1336194] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1336192, _1336194) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1336192 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1336194), 29971 ^ [_1336192, _1336194]))], (29975 ^ _780086) ^ [_1336297, _1336299] : [29976 ^ _780086 : [(29977 ^ _780086) ^ [_1336346] : [_1336297 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1336299), _1336346)]], -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1336297, _1336299) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29981 ^ _780086) ^ [_1336418, _1336420] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1336418), _1336420)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1336418, _1336420) = _1336418)], (29987 ^ _780086) ^ [_1336507, _1336509] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1336507), _1336509))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1336507, _1336509) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1336507), _1336509), _1336509))], (29993 ^ _780086) ^ [_1336560, _1336562] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1336560), _1336562))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1336560, _1336562) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1336560), _1336562), _1336562))], (29999 ^ _780086) ^ [_1336615, _1336617, _1336619] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1336615), _1336617)), _1336619), _1336617) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1336619, _1336617))], (30001 ^ _780086) ^ [_1336662, _1336664] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1336662), _1336664)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1336664, _1336662) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1336664), _1336662), _1336662))], (30007 ^ _780086) ^ [_1336777, _1336779] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1336777), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1336779)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1336777, _1336779)))], (30009 ^ _780086) ^ [_1336819, _1336821] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1336819, _1336821)) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1336819), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1336821)))], (30011 ^ _780086) ^ [_1336861, _1336863, _1336865] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1336861), _1336863)), _1336865) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1336861), _1336865)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1336863), _1336865))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1336861, _1336865)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1336863, _1336865))), _1336865)))], (30013 ^ _780086) ^ [_1336944, _1336946] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1336944)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1336946, _1336944)), _1336944)))], (30019 ^ _780086) ^ [_1337043, _1337045, _1337047] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1337043), _1337045)), _1337047)), _1337045) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1337047), _1337045))], (30021 ^ _780086) ^ [_1337096, _1337098] : [class_Rings_Olinordered__idom(_1337096), 30024 ^ _780086 : [(30025 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1337096), c_Groups_Ozero__class_Ozero(_1337096)), c_Groups_Osgn__class_Osgn(_1337096, _1337098))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1337096), c_Groups_Ozero__class_Ozero(_1337096)), _1337098)))], (30031 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1337096), c_Groups_Ozero__class_Ozero(_1337096)), _1337098)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1337096), c_Groups_Ozero__class_Ozero(_1337096)), c_Groups_Osgn__class_Osgn(_1337096, _1337098))))]]], (30037 ^ _780086) ^ [_1337364, _1337366] : [class_Rings_Olinordered__idom(_1337364), 30040 ^ _780086 : [(30041 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1337364), c_Groups_Osgn__class_Osgn(_1337364, _1337366)), c_Groups_Ozero__class_Ozero(_1337364))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1337364), _1337366), c_Groups_Ozero__class_Ozero(_1337364))))], (30047 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1337364), _1337366), c_Groups_Ozero__class_Ozero(_1337364))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1337364), c_Groups_Osgn__class_Osgn(_1337364, _1337366)), c_Groups_Ozero__class_Ozero(_1337364))))]]], (30053 ^ _780086) ^ [_1337632, _1337634, _1337636] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1337632, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1337634), _1337636)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1337634), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1337632), _1337634), _1337636))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1337632, _1337634)))], (30055 ^ _780086) ^ [_1337695, _1337697, _1337699] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1337695), _1337697)), _1337699) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1337695), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1337697), _1337699))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1337695), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1337697, _1337699))), _1337699)))], (30057 ^ _780086) ^ [_1337768, _1337770] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1337768), _1337770)), _1337770) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1337768), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1337768, _1337770)))], (30059 ^ _780086) ^ [_1337815, _1337817] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1337815), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1337817), _1337815)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1337817), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1337817, _1337815)))], (30061 ^ _780086) ^ [_1337862, _1337864] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1337862, _1337864) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1337862), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1337862), _1337864)), _1337864)))], (30087 ^ _780086) ^ [_1338360, _1338362, _1338364] : [-(hBOOL(hAPP(_1338360, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1338362, _1338364)))), 30090 ^ _780086 : [(30091 ^ _780086) ^ [] : [-(_1338364 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30093 ^ _780086) ^ [] : [hBOOL(hAPP(_1338360, _1338362))]], 30094 ^ _780086 : [(30095 ^ _780086) ^ [] : [_1338364 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (30099 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 30097 ^ [_1338360, _1338362, _1338364]), _1338364)))], (30101 ^ _780086) ^ [] : [-(_1338362 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1338364), 30096 ^ [_1338360, _1338362, _1338364])), 30097 ^ [_1338360, _1338362, _1338364]))], (30103 ^ _780086) ^ [] : [hBOOL(hAPP(_1338360, 30097 ^ [_1338360, _1338362, _1338364]))]]], (30063 ^ _780086) ^ [_1337927, _1337929, _1337931] : [hBOOL(hAPP(_1337927, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1337929, _1337931))), 30066 ^ _780086 : [(30067 ^ _780086) ^ [] : [_1337931 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1337927, _1337929)))], (30073 ^ _780086) ^ [] : [-(_1337931 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 30076 ^ _780086 : [(30077 ^ _780086) ^ [_1338175, _1338177] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1338175), _1337931)), _1337929 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1337931), _1338177)), _1338175), -(hBOOL(hAPP(_1337927, _1338175)))]]]]], (30107 ^ _780086) ^ [_1338769, _1338771, _1338773, _1338775] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1338769)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1338771), _1338773)), -(hBOOL(hAPP(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), _1338773), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1338775, _1338769))), _1338771)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1338773), _1338769))))], (30117 ^ _780086) ^ [_1338974, _1338976] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1338974)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1338974), _1338976)), _1338974) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (30123 ^ _780086) ^ [_1339081, _1339083] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1339081)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1339083)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1339081), hAPP(c_Int_Onat, _1339083)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1339081, _1339083)))], (30133 ^ _780086) ^ [_1339252, _1339254] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1339252)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1339254)), -(hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1339252, _1339254)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1339252), hAPP(c_Int_Onat, _1339254)))], (30143 ^ _780086) ^ [_1339423, _1339425] : [class_Rings_Olinordered__idom(_1339423), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1339423), c_Groups_Ozero__class_Ozero(_1339423)), _1339425)), -(c_Groups_Osgn__class_Osgn(_1339423, _1339425) = c_Groups_Oone__class_Oone(_1339423))], (30153 ^ _780086) ^ [_1339578, _1339580] : [class_Rings_Olinordered__idom(_1339578), 30156 ^ _780086 : [(30157 ^ _780086) ^ [] : [c_Groups_Osgn__class_Osgn(_1339578, _1339580) = c_Groups_Oone__class_Oone(_1339578), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1339578), c_Groups_Ozero__class_Ozero(_1339578)), _1339580)))], (30163 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1339578), c_Groups_Ozero__class_Ozero(_1339578)), _1339580)), -(c_Groups_Osgn__class_Osgn(_1339578, _1339580) = c_Groups_Oone__class_Oone(_1339578))]]], (30169 ^ _780086) ^ [_1339831] : [_1339831 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1339831) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (30175 ^ _780086) ^ [_1339907] : [-(_1339907 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 30178 ^ _780086 : [(30179 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1339907)), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1339907) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (30185 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1339907))), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1339907) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))]]], (30191 ^ _780086) ^ [_1340099, _1340101, _1340103] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1340099)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1340101), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1340101), _1340103))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1340099))), _1340103)))], (30197 ^ _780086) ^ [_1340246, _1340248, _1340250] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1340246)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1340248), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1340250), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1340250), _1340248))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1340246)))))], (30203 ^ _780086) ^ [_1340393, _1340395, _1340397, _1340399, _1340401] : [class_Groups_Ocomm__monoid__add(_1340393), class_Groups_Ocomm__monoid__mult(_1340393), _1340395 = _1340397, c_Nat__Transfer_Onat__set(_1340397), 30221 ^ _780086 : [(30222 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 30220 ^ [_1340393, _1340395, _1340397, _1340399, _1340401])))], (30224 ^ _780086) ^ [] : [hAPP(_1340399, 30220 ^ [_1340393, _1340395, _1340397, _1340399, _1340401]) = hAPP(_1340401, 30220 ^ [_1340393, _1340395, _1340397, _1340399, _1340401])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1340393), _1340399), _1340395) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1340393), _1340401), _1340397))], (30228 ^ _780086) ^ [_1340856, _1340858] : [class_Complete__Lattice_Ocomplete__lattice(_1340856), hBOOL(hAPP(c_Finite__Set_Ofinite(_1340856), _1340858)), -(c_Complete__Lattice_OSup__class_OSup(_1340856, _1340858) = hAPP(hAPP(c_Finite__Set_Ofold(_1340856, _1340856, c_Lattices_Osemilattice__sup__class_Osup(_1340856)), c_Orderings_Obot__class_Obot(_1340856)), _1340858))], (30238 ^ _780086) ^ [_1341025, _1341027, _1341029, _1341031] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1341025, tc_HOL_Obool)), _1341027), _1341029)), hBOOL(hAPP(hAPP(c_member(_1341025), _1341031), _1341027)), -(hBOOL(hAPP(hAPP(c_member(_1341025), _1341031), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1341025, tc_HOL_Obool), _1341029))))], (30248 ^ _780086) ^ [_1341222, _1341224, _1341226, _1341228] : [class_Groups_Oordered__ab__group__add__abs(_1341222), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1341222), hAPP(c_Groups_Oabs__class_Oabs(_1341222), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1341224, _1341222), _1341226), _1341228))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1341224, _1341222), hAPP(hAPP(c_COMBB(_1341222, _1341222, _1341224), c_Groups_Oabs__class_Oabs(_1341222)), _1341226)), _1341228))))], (30254 ^ _780086) ^ [_1341385, _1341387, _1341389, _1341391] : [class_Groups_Oordered__ab__group__add__abs(_1341385), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1341385), c_Groups_Ozero__class_Ozero(_1341385)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1341387, _1341385), hAPP(hAPP(c_COMBB(_1341385, _1341385, _1341387), c_Groups_Oabs__class_Oabs(_1341385)), _1341389)), _1341391))))], (30260 ^ _780086) ^ [_1341524, _1341526] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1341524, tc_HOL_Obool), hAPP(c_Set_OPow(_1341524), _1341526)) = _1341526)], (30262 ^ _780086) ^ [_1341560, _1341562, _1341564] : [class_Groups_Oordered__ab__group__add__abs(_1341560), -(hAPP(c_Groups_Oabs__class_Oabs(_1341560), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1341560), _1341562), _1341564)) = hAPP(c_Groups_Oabs__class_Oabs(_1341560), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1341560), _1341564), _1341562)))], (30268 ^ _780086) ^ [_1341689, _1341691, _1341693] : [class_Groups_Oordered__ab__group__add__abs(_1341689), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1341689), hAPP(c_Groups_Oabs__class_Oabs(_1341689), _1341691)), _1341693)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1341689), _1341691), _1341693)))], (30278 ^ _780086) ^ [_1341858, _1341860] : [class_Groups_Oordered__ab__group__add__abs(_1341858), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1341858), _1341860), hAPP(c_Groups_Oabs__class_Oabs(_1341858), _1341860))))], (30284 ^ _780086) ^ [_1341957] : [class_Rings_Olinordered__idom(_1341957), -(hAPP(c_Groups_Oabs__class_Oabs(_1341957), c_Groups_Oone__class_Oone(_1341957)) = c_Groups_Oone__class_Oone(_1341957))], (30290 ^ _780086) ^ [_1342048, _1342050] : [class_Groups_Oordered__ab__group__add__abs(_1342048), -(hAPP(c_Groups_Oabs__class_Oabs(_1342048), hAPP(c_Groups_Ouminus__class_Ouminus(_1342048), _1342050)) = hAPP(c_Groups_Oabs__class_Oabs(_1342048), _1342050))], (30296 ^ _780086) ^ [_1342153, _1342155] : [class_Rings_Olinordered__idom(_1342153), -(hAPP(c_Groups_Oabs__class_Oabs(_1342153), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1342153), _1342155)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1342153), _1342155))], (30302 ^ _780086) ^ [_1342258, _1342260, _1342262] : [class_Rings_Olinordered__idom(_1342258), -(hAPP(c_Groups_Oabs__class_Oabs(_1342258), hAPP(hAPP(c_Power_Opower__class_Opower(_1342258), _1342260), _1342262)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1342258), hAPP(c_Groups_Oabs__class_Oabs(_1342258), _1342260)), _1342262))], (30308 ^ _780086) ^ [_1342387, _1342389] : [class_Groups_Oordered__ab__group__add__abs(_1342387), -(hAPP(c_Groups_Oabs__class_Oabs(_1342387), hAPP(c_Groups_Oabs__class_Oabs(_1342387), _1342389)) = hAPP(c_Groups_Oabs__class_Oabs(_1342387), _1342389))], (30314 ^ _780086) ^ [_1342492, _1342494, _1342496] : [class_Rings_Olinordered__idom(_1342492), -(hAPP(c_Groups_Oabs__class_Oabs(_1342492), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1342492), _1342494), _1342496)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1342492), hAPP(c_Groups_Oabs__class_Oabs(_1342492), _1342494)), hAPP(c_Groups_Oabs__class_Oabs(_1342492), _1342496)))], (30320 ^ _780086) ^ [_1342631, _1342633] : [class_Rings_Olinordered__idom(_1342631), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1342631), hAPP(c_Groups_Oabs__class_Oabs(_1342631), _1342633)), hAPP(c_Groups_Oabs__class_Oabs(_1342631), _1342633)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1342631), _1342633), _1342633))], (30326 ^ _780086) ^ [_1342758, _1342760, _1342762] : [class_Groups_Oordered__ab__group__add__abs(_1342758), -(hAPP(c_Groups_Oabs__class_Oabs(_1342758), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1342758), hAPP(c_Groups_Oabs__class_Oabs(_1342758), _1342760)), hAPP(c_Groups_Oabs__class_Oabs(_1342758), _1342762))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1342758), hAPP(c_Groups_Oabs__class_Oabs(_1342758), _1342760)), hAPP(c_Groups_Oabs__class_Oabs(_1342758), _1342762)))], (30332 ^ _780086) ^ [_1342917, _1342919] : [class_Groups_Oordered__ab__group__add__abs(_1342917), 30335 ^ _780086 : [(30336 ^ _780086) ^ [] : [hAPP(c_Groups_Oabs__class_Oabs(_1342917), _1342919) = c_Groups_Ozero__class_Ozero(_1342917), -(_1342919 = c_Groups_Ozero__class_Ozero(_1342917))], (30342 ^ _780086) ^ [] : [_1342919 = c_Groups_Ozero__class_Ozero(_1342917), -(hAPP(c_Groups_Oabs__class_Oabs(_1342917), _1342919) = c_Groups_Ozero__class_Ozero(_1342917))]]], (30348 ^ _780086) ^ [_1343149] : [class_Groups_Oordered__ab__group__add__abs(_1343149), -(hAPP(c_Groups_Oabs__class_Oabs(_1343149), c_Groups_Ozero__class_Ozero(_1343149)) = c_Groups_Ozero__class_Ozero(_1343149))], (30354 ^ _780086) ^ [_1343240] : [-(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1343240)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1343240))], (30356 ^ _780086) ^ [_1343272, _1343274, _1343276] : [class_Fields_Olinordered__field__inverse__zero(_1343272), -(hAPP(c_Groups_Oabs__class_Oabs(_1343272), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1343272), _1343274), _1343276)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1343272), hAPP(c_Groups_Oabs__class_Oabs(_1343272), _1343274)), hAPP(c_Groups_Oabs__class_Oabs(_1343272), _1343276)))], (30362 ^ _780086) ^ [_1343411, _1343413, _1343415, _1343417] : [class_Groups_Oordered__ab__group__add__abs(_1343411), -(hAPP(c_Groups_Oabs__class_Oabs(_1343411), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1343413, _1343411), hAPP(hAPP(c_COMBB(_1343411, _1343411, _1343413), c_Groups_Oabs__class_Oabs(_1343411)), _1343415)), _1343417)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1343413, _1343411), hAPP(hAPP(c_COMBB(_1343411, _1343411, _1343413), c_Groups_Oabs__class_Oabs(_1343411)), _1343415)), _1343417))], (30368 ^ _780086) ^ [_1343584, _1343586, _1343588, _1343590] : [class_Fields_Olinordered__field(_1343584), -(hAPP(c_Groups_Oabs__class_Oabs(_1343584), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1343586, _1343584), _1343588), _1343590)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1343586, _1343584), hAPP(hAPP(c_COMBB(_1343584, _1343584, _1343586), c_Groups_Oabs__class_Oabs(_1343584)), _1343588)), _1343590))], (30374 ^ _780086) ^ [_1343733, _1343735, _1343737, _1343739] : [-(hAPP(c_Set_Oimage(_1343733, _1343735, _1343737), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1343733, tc_HOL_Obool), _1343739)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1343733, tc_HOL_Obool), tc_fun(_1343735, tc_HOL_Obool)), _1343739), c_Set_Oimage(_1343733, _1343735, _1343737)))], (30376 ^ _780086) ^ [_1343794, _1343796, _1343798] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1343794, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1343794, tc_HOL_Obool), _1343796)), _1343798) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1343794, tc_HOL_Obool), tc_fun(_1343794, tc_HOL_Obool)), _1343796), hAPP(hAPP(c_COMBC(tc_fun(_1343794, tc_HOL_Obool), tc_fun(_1343794, tc_HOL_Obool), tc_fun(_1343794, tc_HOL_Obool)), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1343794, tc_HOL_Obool))), _1343798)))], (30378 ^ _780086) ^ [_1343877, _1343879, _1343881] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1343877, tc_HOL_Obool)), _1343879), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1343877, tc_HOL_Obool), _1343881)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1343877, tc_HOL_Obool), tc_fun(_1343877, tc_HOL_Obool)), _1343881), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1343877, tc_HOL_Obool)), _1343879)))], (30380 ^ _780086) ^ [_1343944, _1343946, _1343948, _1343950] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1343944, tc_HOL_Obool), tc_fun(_1343946, tc_HOL_Obool)), _1343948), hAPP(hAPP(c_COMBC(tc_fun(_1343944, tc_HOL_Obool), tc_fun(_1343944, tc_fun(_1343946, tc_HOL_Obool)), tc_fun(_1343946, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1343944, tc_fun(_1343946, tc_HOL_Obool))), _1343950)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1343944, tc_fun(_1343946, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1343944, tc_HOL_Obool), _1343948)), _1343950))], (30382 ^ _780086) ^ [_1344034, _1344036, _1344038, _1344040] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1344034, tc_fun(_1344036, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1344034, tc_HOL_Obool), _1344038)), _1344040) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1344034, tc_HOL_Obool), tc_fun(_1344036, tc_HOL_Obool)), _1344038), hAPP(hAPP(c_COMBC(tc_fun(_1344034, tc_HOL_Obool), tc_fun(_1344034, tc_fun(_1344036, tc_HOL_Obool)), tc_fun(_1344036, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1344034, tc_fun(_1344036, tc_HOL_Obool))), _1344040)))], (30384 ^ _780086) ^ [_1344124, _1344126, _1344128] : [class_Complete__Lattice_Ocomplete__lattice(_1344124), 30387 ^ _780086 : [(30398 ^ _780086) ^ [] : [30400 ^ _780086 : [(30401 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1344124), 30399 ^ [_1344124, _1344126, _1344128]), _1344126)))], (30403 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1344124), 30399 ^ [_1344124, _1344126, _1344128]), _1344128))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1344124), c_Complete__Lattice_OSup__class_OSup(_1344124, _1344126)), _1344128)))], (30388 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1344124), c_Complete__Lattice_OSup__class_OSup(_1344124, _1344126)), _1344128)), 30391 ^ _780086 : [(30392 ^ _780086) ^ [_1344282] : [hBOOL(hAPP(hAPP(c_member(_1344124), _1344282), _1344126)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1344124), _1344282), _1344128)))]]]]], (30407 ^ _780086) ^ [_1344558, _1344560, _1344562] : [class_Complete__Lattice_Ocomplete__lattice(_1344558), class_Orderings_Olinorder(_1344558), 30414 ^ _780086 : [(30415 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1344558), _1344560), c_Complete__Lattice_OSup__class_OSup(_1344558, _1344562))), 30419 ^ _780086 : [(30420 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1344558), 30418 ^ [_1344558, _1344560, _1344562]), _1344562)))], (30422 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1344558), _1344560), 30418 ^ [_1344558, _1344560, _1344562])))]]], (30424 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1344558), _1344560), c_Complete__Lattice_OSup__class_OSup(_1344558, _1344562)))), 30425 ^ _780086 : [(30426 ^ _780086) ^ [_1344864] : [hBOOL(hAPP(hAPP(c_member(_1344558), _1344864), _1344562)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1344558), _1344560), _1344864))]]]]], (30434 ^ _780086) ^ [_1345018, _1345020, _1345022, _1345024] : [-(hAPP(c_Set_Ovimage(_1345018, _1345020, _1345022), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1345020, tc_HOL_Obool), _1345024)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1345020, tc_HOL_Obool), tc_fun(_1345018, tc_HOL_Obool)), _1345024), c_Set_Ovimage(_1345018, _1345020, _1345022)))], (30436 ^ _780086) ^ [_1345079, _1345081] : [class_Groups_Oordered__ab__group__add__abs(_1345079), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345079), c_Groups_Ozero__class_Ozero(_1345079)), hAPP(c_Groups_Oabs__class_Oabs(_1345079), _1345081))))], (30442 ^ _780086) ^ [_1345182, _1345184] : [class_Groups_Oordered__ab__group__add__abs(_1345182), 30445 ^ _780086 : [(30446 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345182), hAPP(c_Groups_Oabs__class_Oabs(_1345182), _1345184)), c_Groups_Ozero__class_Ozero(_1345182))), -(_1345184 = c_Groups_Ozero__class_Ozero(_1345182))], (30452 ^ _780086) ^ [] : [_1345184 = c_Groups_Ozero__class_Ozero(_1345182), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345182), hAPP(c_Groups_Oabs__class_Oabs(_1345182), _1345184)), c_Groups_Ozero__class_Ozero(_1345182))))]]], (30458 ^ _780086) ^ [_1345435, _1345437] : [class_Groups_Oordered__ab__group__add__abs(_1345435), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345435), c_Groups_Ozero__class_Ozero(_1345435)), _1345437)), -(hAPP(c_Groups_Oabs__class_Oabs(_1345435), _1345437) = _1345437)], (30468 ^ _780086) ^ [_1345590, _1345592] : [class_Groups_Oordered__ab__group__add__abs(_1345590), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1345590), c_Groups_Ozero__class_Ozero(_1345590)), _1345592)), -(hAPP(c_Groups_Oabs__class_Oabs(_1345590), _1345592) = _1345592)], (30478 ^ _780086) ^ [_1345745, _1345747] : [class_Groups_Oordered__ab__group__add__abs(_1345745), 30481 ^ _780086 : [(30482 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1345745), c_Groups_Ozero__class_Ozero(_1345745)), hAPP(c_Groups_Oabs__class_Oabs(_1345745), _1345747))), _1345747 = c_Groups_Ozero__class_Ozero(_1345745)], (30488 ^ _780086) ^ [] : [-(_1345747 = c_Groups_Ozero__class_Ozero(_1345745)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1345745), c_Groups_Ozero__class_Ozero(_1345745)), hAPP(c_Groups_Oabs__class_Oabs(_1345745), _1345747))))]]], (30494 ^ _780086) ^ [_1345960, _1345962] : [class_Groups_Oordered__ab__group__add__abs(_1345960), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1345960), hAPP(c_Groups_Oabs__class_Oabs(_1345960), _1345962)), c_Groups_Ozero__class_Ozero(_1345960)))], (30500 ^ _780086) ^ [_1346064, _1346066, _1346068] : [class_Groups_Oordered__ab__group__add__abs(_1346064), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1346064), hAPP(c_Groups_Oabs__class_Oabs(_1346064), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1346064), _1346066), _1346068))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1346064), hAPP(c_Groups_Oabs__class_Oabs(_1346064), _1346066)), hAPP(c_Groups_Oabs__class_Oabs(_1346064), _1346068)))))], (30506 ^ _780086) ^ [_1346217, _1346219, _1346221, _1346223, _1346225] : [class_Rings_Olinordered__idom(_1346217), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1346217), hAPP(c_Groups_Oabs__class_Oabs(_1346217), _1346219)), _1346221)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1346217), hAPP(c_Groups_Oabs__class_Oabs(_1346217), _1346223)), _1346225)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1346217), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1346217), hAPP(c_Groups_Oabs__class_Oabs(_1346217), _1346219)), hAPP(c_Groups_Oabs__class_Oabs(_1346217), _1346223))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1346217), _1346221), _1346225))))], (30520 ^ _780086) ^ [_1346528, _1346530, _1346532] : [class_Groups_Oordered__ab__group__add__abs(_1346528), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1346528), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1346528), hAPP(c_Groups_Oabs__class_Oabs(_1346528), _1346530)), hAPP(c_Groups_Oabs__class_Oabs(_1346528), _1346532))), hAPP(c_Groups_Oabs__class_Oabs(_1346528), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1346528), _1346532), _1346530)))))], (30526 ^ _780086) ^ [_1346681, _1346683, _1346685] : [class_Groups_Oordered__ab__group__add__abs(_1346681), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1346681), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1346681), hAPP(c_Groups_Oabs__class_Oabs(_1346681), _1346683)), hAPP(c_Groups_Oabs__class_Oabs(_1346681), _1346685))), hAPP(c_Groups_Oabs__class_Oabs(_1346681), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1346681), _1346683), _1346685)))))], (30532 ^ _780086) ^ [_1346834, _1346836, _1346838] : [class_Groups_Oordered__ab__group__add__abs(_1346834), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1346834), hAPP(c_Groups_Oabs__class_Oabs(_1346834), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1346834), hAPP(c_Groups_Oabs__class_Oabs(_1346834), _1346836)), hAPP(c_Groups_Oabs__class_Oabs(_1346834), _1346838)))), hAPP(c_Groups_Oabs__class_Oabs(_1346834), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1346834), _1346836), _1346838)))))], (30538 ^ _780086) ^ [_1346997, _1346999, _1347001] : [class_Groups_Oordered__ab__group__add__abs(_1346997), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1346997), hAPP(c_Groups_Oabs__class_Oabs(_1346997), _1346999)), _1347001)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1346997), hAPP(c_Groups_Ouminus__class_Ouminus(_1346997), _1346999)), _1347001)))], (30548 ^ _780086) ^ [_1347176, _1347178, _1347180] : [class_Groups_Oordered__ab__group__add__abs(_1347176), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347176), _1347178), _1347180)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347176), hAPP(c_Groups_Ouminus__class_Ouminus(_1347176), _1347178)), _1347180)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347176), hAPP(c_Groups_Oabs__class_Oabs(_1347176), _1347178)), _1347180)))], (30562 ^ _780086) ^ [_1347423, _1347425, _1347427] : [class_Groups_Oordered__ab__group__add__abs(_1347423), 30565 ^ _780086 : [(30566 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347423), hAPP(c_Groups_Oabs__class_Oabs(_1347423), _1347425)), _1347427)), 30569 ^ _780086 : [(30570 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347423), _1347425), _1347427)))], (30572 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347423), hAPP(c_Groups_Ouminus__class_Ouminus(_1347423), _1347425)), _1347427)))]]], (30574 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347423), hAPP(c_Groups_Oabs__class_Oabs(_1347423), _1347425)), _1347427))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347423), _1347425), _1347427)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347423), hAPP(c_Groups_Ouminus__class_Ouminus(_1347423), _1347425)), _1347427))]]], (30584 ^ _780086) ^ [_1347801, _1347803] : [class_Groups_Oordered__ab__group__add__abs(_1347801), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347801), hAPP(c_Groups_Ouminus__class_Ouminus(_1347801), _1347803)), hAPP(c_Groups_Oabs__class_Oabs(_1347801), _1347803))))], (30590 ^ _780086) ^ [_1347910, _1347912, _1347914] : [class_Rings_Olinordered__idom(_1347910), 30593 ^ _780086 : [(30594 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1347910), hAPP(c_Groups_Oabs__class_Oabs(_1347910), _1347912)), _1347914)), 30597 ^ _780086 : [(30598 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1347910), _1347912), _1347914)))], (30600 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1347910), hAPP(c_Groups_Ouminus__class_Ouminus(_1347910), _1347912)), _1347914)))]]], (30602 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1347910), hAPP(c_Groups_Oabs__class_Oabs(_1347910), _1347912)), _1347914))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1347910), _1347912), _1347914)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1347910), hAPP(c_Groups_Ouminus__class_Ouminus(_1347910), _1347912)), _1347914))]]], (30612 ^ _780086) ^ [_1348288, _1348290, _1348292] : [class_Fields_Olinordered__field(_1348288), -(_1348290 = c_Groups_Ozero__class_Ozero(_1348288)), -(hAPP(c_Groups_Oabs__class_Oabs(_1348288), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348288), _1348292), _1348290)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348288), hAPP(c_Groups_Oabs__class_Oabs(_1348288), _1348292)), hAPP(c_Groups_Oabs__class_Oabs(_1348288), _1348290)))], (30622 ^ _780086) ^ [_1348446, _1348448, _1348450] : [class_Rings_Olinordered__idom(_1348446), -(hAPP(c_Groups_Oabs__class_Oabs(_1348446), hAPP(hAPP(c_Power_Opower__class_Opower(_1348446), hAPP(c_Groups_Ouminus__class_Ouminus(_1348446), _1348448)), _1348450)) = hAPP(c_Groups_Oabs__class_Oabs(_1348446), hAPP(hAPP(c_Power_Opower__class_Opower(_1348446), _1348448), _1348450)))], (30628 ^ _780086) ^ [_1348585, _1348587] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1348585), _1348587)) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1348585) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (30644 ^ _780086) ^ [_1348972, _1348974, _1348976] : [30646 ^ _780086 : [(30647 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1348972, tc_HOL_Obool)), 30645 ^ [_1348972, _1348974, _1348976]), _1348974)))], (30649 ^ _780086) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1348972, tc_HOL_Obool)), 30645 ^ [_1348972, _1348974, _1348976]), _1348976) = c_Orderings_Obot__class_Obot(tc_fun(_1348972, tc_HOL_Obool))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1348972, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1348972, tc_HOL_Obool), _1348974)), _1348976) = c_Orderings_Obot__class_Obot(tc_fun(_1348972, tc_HOL_Obool)))], (30634 ^ _780086) ^ [_1348704, _1348706, _1348708] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1348704, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1348704, tc_HOL_Obool), _1348706)), _1348708) = c_Orderings_Obot__class_Obot(tc_fun(_1348704, tc_HOL_Obool)), 30637 ^ _780086 : [(30638 ^ _780086) ^ [_1348839] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1348704, tc_HOL_Obool)), _1348839), _1348706)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1348704, tc_HOL_Obool)), _1348839), _1348708) = c_Orderings_Obot__class_Obot(tc_fun(_1348704, tc_HOL_Obool)))]]], (30653 ^ _780086) ^ [_1349235, _1349237, _1349239] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1349235, tc_HOL_Obool)), _1349237), _1349239)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1349235, tc_HOL_Obool)), _1349237), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1349235, tc_HOL_Obool), _1349239))))], (30659 ^ _780086) ^ [_1349366, _1349368] : [class_Rings_Olinordered__idom(_1349366), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1349366), c_Groups_Osgn__class_Osgn(_1349366, _1349368)), hAPP(c_Groups_Oabs__class_Oabs(_1349366), _1349368)) = _1349368)], (30665 ^ _780086) ^ [_1349473, _1349475] : [class_Rings_Olinordered__idom(_1349473), -(hAPP(c_Groups_Oabs__class_Oabs(_1349473), _1349475) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1349473), _1349475), c_Groups_Osgn__class_Osgn(_1349473, _1349475)))], (30671 ^ _780086) ^ [_1349580] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1349580, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1349580, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1349580, tc_HOL_Obool)))], (30673 ^ _780086) ^ [_1349622, _1349624, _1349626] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1349622, tc_HOL_Obool), tc_HOL_Obool)), _1349624), _1349626)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1349622, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1349622, tc_HOL_Obool), _1349624)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1349622, tc_HOL_Obool), _1349626))))], (30679 ^ _780086) ^ [_1349771, _1349773, _1349775] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1349771, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1349771, tc_HOL_Obool)), _1349773), _1349775)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1349771, tc_HOL_Obool)), _1349773), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1349771, tc_HOL_Obool), _1349775)))], (30681 ^ _780086) ^ [_1349832, _1349834] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1349832), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1349832, tc_HOL_Obool), _1349834))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1349832, tc_HOL_Obool)), _1349834)))], (30687 ^ _780086) ^ [_1349943, _1349945] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1349943, tc_HOL_Obool), tc_HOL_Obool)), _1349945), hAPP(c_Set_OPow(_1349943), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1349943, tc_HOL_Obool), _1349945)))))], (30689 ^ _780086) ^ [_1349992] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1349992, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1349992, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1349992, tc_HOL_Obool)))], (30691 ^ _780086) ^ [_1350034, _1350036, _1350038] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1350034, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1350034, tc_HOL_Obool), tc_HOL_Obool)), _1350036), _1350038)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1350034, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1350034, tc_HOL_Obool), _1350036)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1350034, tc_HOL_Obool), _1350038)))], (30693 ^ _780086) ^ [_1350104, _1350106, _1350108] : [class_Rings_Oordered__ring__abs(_1350104), -(hAPP(c_Groups_Oabs__class_Oabs(_1350104), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1350104), _1350106), _1350108)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1350104), hAPP(c_Groups_Oabs__class_Oabs(_1350104), _1350106)), hAPP(c_Groups_Oabs__class_Oabs(_1350104), _1350108))), 30700 ^ _780086 : [(30701 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1350104), c_Groups_Ozero__class_Ozero(_1350104)), _1350106))], (30703 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1350104), _1350106), c_Groups_Ozero__class_Ozero(_1350104)))]], 30704 ^ _780086 : [(30705 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1350104), c_Groups_Ozero__class_Ozero(_1350104)), _1350108))], (30707 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1350104), _1350108), c_Groups_Ozero__class_Ozero(_1350104)))]]], (30711 ^ _780086) ^ [_1350499, _1350501, _1350503] : [class_Rings_Olinordered__idom(_1350499), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1350499), c_Groups_Ozero__class_Ozero(_1350499)), _1350501)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1350499), hAPP(c_Groups_Oabs__class_Oabs(_1350499), _1350503)), _1350501) = hAPP(c_Groups_Oabs__class_Oabs(_1350499), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1350499), _1350503), _1350501)))], (30721 ^ _780086) ^ [_1350700, _1350702, _1350704, _1350706] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1350700, tc_fun(_1350702, tc_HOL_Obool)), _1350704), _1350706) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1350702, tc_HOL_Obool), hAPP(c_Set_Oimage(_1350700, tc_fun(_1350702, tc_HOL_Obool), _1350706), _1350704)))], (30723 ^ _780086) ^ [_1350757, _1350759, _1350761, _1350763] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1350757, tc_HOL_Obool), hAPP(c_Set_Oimage(_1350759, tc_fun(_1350757, tc_HOL_Obool), _1350761), _1350763)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1350759, tc_fun(_1350757, tc_HOL_Obool)), _1350763), _1350761))], (30725 ^ _780086) ^ [_1350814, _1350816, _1350818, _1350820, _1350822] : [class_Groups_Oordered__ab__group__add__abs(_1350814), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1350814), hAPP(c_Groups_Oabs__class_Oabs(_1350814), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1350814), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1350814), _1350816), _1350818)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1350814), _1350820), _1350822)))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1350814), hAPP(c_Groups_Oabs__class_Oabs(_1350814), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1350814), _1350816), _1350820))), hAPP(c_Groups_Oabs__class_Oabs(_1350814), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1350814), _1350818), _1350822))))))], (30731 ^ _780086) ^ [_1351035, _1351037, _1351039] : [class_Groups_Oordered__ab__group__add__abs(_1351035), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1351035), hAPP(c_Groups_Oabs__class_Oabs(_1351035), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1351035), _1351037), _1351039))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1351035), hAPP(c_Groups_Oabs__class_Oabs(_1351035), _1351037)), hAPP(c_Groups_Oabs__class_Oabs(_1351035), _1351039)))))], (30737 ^ _780086) ^ [_1351188, _1351190] : [class_Groups_Oordered__ab__group__add__abs(_1351188), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1351188), _1351190), c_Groups_Ozero__class_Ozero(_1351188))), -(hAPP(c_Groups_Oabs__class_Oabs(_1351188), _1351190) = hAPP(c_Groups_Ouminus__class_Ouminus(_1351188), _1351190))], (30747 ^ _780086) ^ [_1351353, _1351355] : [class_Groups_Oordered__ab__group__add__abs(_1351353), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1351353), hAPP(c_Groups_Ouminus__class_Ouminus(_1351353), hAPP(c_Groups_Oabs__class_Oabs(_1351353), _1351355))), c_Groups_Ozero__class_Ozero(_1351353))))], (30753 ^ _780086) ^ [_1351466, _1351468] : [class_Groups_Oabs__if(_1351466), 30756 ^ _780086 : [(30757 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351466), _1351468), c_Groups_Ozero__class_Ozero(_1351466))), -(hAPP(c_Groups_Oabs__class_Oabs(_1351466), _1351468) = hAPP(c_Groups_Ouminus__class_Ouminus(_1351466), _1351468))], (30763 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351466), _1351468), c_Groups_Ozero__class_Ozero(_1351466)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1351466), _1351468) = _1351468)]]], (30769 ^ _780086) ^ [_1351706, _1351708] : [class_Groups_Oordered__ab__group__add__abs(_1351706), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351706), _1351708), c_Groups_Ozero__class_Ozero(_1351706))), -(hAPP(c_Groups_Oabs__class_Oabs(_1351706), _1351708) = hAPP(c_Groups_Ouminus__class_Ouminus(_1351706), _1351708))], (30779 ^ _780086) ^ [_1351871, _1351873, _1351875] : [class_Rings_Olinordered__idom(_1351871), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1351871), c_Groups_Ozero__class_Ozero(_1351871)), hAPP(hAPP(c_Power_Opower__class_Opower(_1351871), hAPP(c_Groups_Oabs__class_Oabs(_1351871), _1351873)), _1351875))))], (30785 ^ _780086) ^ [_1351992, _1351994, _1351996] : [class_Fields_Olinordered__field__inverse__zero(_1351992), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351992), c_Groups_Ozero__class_Ozero(_1351992)), _1351994)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1351992), hAPP(c_Groups_Oabs__class_Oabs(_1351992), _1351996)), _1351994) = hAPP(c_Groups_Oabs__class_Oabs(_1351992), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1351992), _1351996), _1351994)))], (30795 ^ _780086) ^ [_1352193, _1352195, _1352197] : [class_Complete__Lattice_Ocomplete__lattice(_1352193), hBOOL(hAPP(hAPP(c_member(_1352193), _1352195), _1352197)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1352193), _1352195), c_Complete__Lattice_OSup__class_OSup(_1352193, _1352197))))], (30805 ^ _780086) ^ [_1352358] : [class_Complete__Lattice_Ocomplete__lattice(_1352358), -(c_Complete__Lattice_OSup__class_OSup(_1352358, c_Orderings_Obot__class_Obot(tc_fun(_1352358, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1352358))], (30811 ^ _780086) ^ [_1352451, _1352453] : [class_Complete__Lattice_Ocomplete__lattice(_1352451), -(c_Complete__Lattice_OSup__class_OSup(_1352451, hAPP(hAPP(c_Set_Oinsert(_1352451), _1352453), c_Orderings_Obot__class_Obot(tc_fun(_1352451, tc_HOL_Obool)))) = _1352453)], (30817 ^ _780086) ^ [_1352570] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1352570)), c_Groups_Oone__class_Oone(tc_Int_Oint))), -(_1352570 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (30823 ^ _780086) ^ [_1352657] : [_1352657 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1352657)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (30829 ^ _780086) ^ [_1352750, _1352752, _1352754] : [class_Complete__Lattice_Ocomplete__lattice(_1352750), -(c_Complete__Lattice_OSup__class_OSup(_1352750, hAPP(hAPP(c_Set_Oinsert(_1352750), _1352752), _1352754)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1352750), _1352752), c_Complete__Lattice_OSup__class_OSup(_1352750, _1352754)))], (30835 ^ _780086) ^ [_1352877] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1352877), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1352877) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1352877))], (30841 ^ _780086) ^ [_1352968] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1352968), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1352968) = _1352968)], (30847 ^ _780086) ^ [_1353012] : [class_Complete__Lattice_Ocomplete__lattice(_1353012), -(c_Complete__Lattice_OSup__class_OSup(_1353012, c_Orderings_Otop__class_Otop(tc_fun(_1353012, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1353012))], (30853 ^ _780086) ^ [_1353105, _1353107] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1353105), _1353107))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1353105))), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1353107))))], (30855 ^ _780086) ^ [_1353160, _1353162] : [-(hBOOL(hAPP(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), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1353160)), _1353162))))], (30857 ^ _780086) ^ [_1353196, _1353198, _1353200, _1353202] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1353196, tc_fun(_1353198, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1353196, tc_HOL_Obool), _1353200)), _1353202) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1353196, tc_HOL_Obool), tc_fun(_1353198, tc_HOL_Obool)), _1353200), hAPP(hAPP(c_COMBC(tc_fun(_1353196, tc_HOL_Obool), tc_fun(_1353196, tc_fun(_1353198, tc_HOL_Obool)), tc_fun(_1353198, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1353196, tc_fun(_1353198, tc_HOL_Obool))), _1353202)))], (30859 ^ _780086) ^ [_1353286, _1353288, _1353290, _1353292] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1353286, tc_HOL_Obool), tc_fun(_1353288, tc_HOL_Obool)), _1353290), hAPP(hAPP(c_COMBC(tc_fun(_1353286, tc_HOL_Obool), tc_fun(_1353286, tc_fun(_1353288, tc_HOL_Obool)), tc_fun(_1353288, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1353286, tc_fun(_1353288, tc_HOL_Obool))), _1353292)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1353286, tc_fun(_1353288, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1353286, tc_HOL_Obool), _1353290)), _1353292))], (30861 ^ _780086) ^ [_1353376, _1353378, _1353380] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1353376, tc_HOL_Obool)), _1353378), _1353380) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1353376, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1353376, tc_HOL_Obool)), _1353378), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1353376, tc_HOL_Obool)), _1353380), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1353376, tc_HOL_Obool), tc_HOL_Obool))))))], (30863 ^ _780086) ^ [_1353450, _1353452, _1353454, _1353456, _1353458] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1353450, tc_fun(_1353452, tc_HOL_Obool)), _1353454), hAPP(hAPP(c_COMBS(_1353450, tc_fun(_1353452, tc_HOL_Obool), tc_fun(_1353452, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1353452, tc_HOL_Obool), tc_fun(tc_fun(_1353452, tc_HOL_Obool), tc_fun(_1353452, tc_HOL_Obool)), _1353450), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1353452, tc_HOL_Obool))), _1353456)), _1353458)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1353452, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1353452, tc_HOL_Obool), hAPP(c_Set_Oimage(_1353450, tc_fun(_1353452, tc_HOL_Obool), _1353456), _1353454))), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1353452, tc_HOL_Obool), hAPP(c_Set_Oimage(_1353450, tc_fun(_1353452, tc_HOL_Obool), _1353458), _1353454))))], (30865 ^ _780086) ^ [_1353579, _1353581, _1353583] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1353579, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1353579, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1353579, tc_HOL_Obool), tc_HOL_Obool)), _1353581), _1353583))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1353579, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1353579, tc_HOL_Obool), _1353581)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1353579, tc_HOL_Obool), _1353583)))))], (30877 ^ _780086) ^ [_1353823, _1353825] : [30878 ^ _780086 : [(30879 ^ _780086) ^ [] : [-(_1353823 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (30881 ^ _780086) ^ [] : [_1353825 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hBOOL(hAPP(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), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1353823)), _1353825))))], (30867 ^ _780086) ^ [_1353674, _1353676] : [hBOOL(hAPP(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), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1353674)), _1353676))), _1353674 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1353676 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30885 ^ _780086) ^ [_1353959, _1353961, _1353963] : [class_Complete__Lattice_Ocomplete__lattice(_1353959), -(c_Complete__Lattice_OSup__class_OSup(_1353959, hAPP(hAPP(c_Set_Oinsert(_1353959), _1353961), hAPP(hAPP(c_Set_Oinsert(_1353959), _1353963), c_Orderings_Obot__class_Obot(tc_fun(_1353959, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1353959), _1353961), _1353963))], (30891 ^ _780086) ^ [_1354100, _1354102, _1354104] : [class_Complete__Lattice_Ocomplete__lattice(_1354100), hBOOL(hAPP(c_Finite__Set_Ofinite(_1354100), _1354102)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1354100), _1354104), c_Complete__Lattice_OSup__class_OSup(_1354100, _1354102)) = hAPP(hAPP(c_Finite__Set_Ofold(_1354100, _1354100, c_Lattices_Osemilattice__sup__class_Osup(_1354100)), _1354104), _1354102))], (30901 ^ _780086) ^ [_1354285, _1354287] : [class_Complete__Lattice_Ocomplete__lattice(_1354285), hBOOL(hAPP(c_Finite__Set_Ofinite(_1354285), _1354287)), -(_1354287 = c_Orderings_Obot__class_Obot(tc_fun(_1354285, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1354285, _1354287) = c_Complete__Lattice_OSup__class_OSup(_1354285, _1354287))], (30915 ^ _780086) ^ [_1354457, _1354459] : [-(c_Nitpick_Oint__lcm(_1354457, _1354459) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Nitpick_Onat__lcm(hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1354457)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1354459)))))], (30917 ^ _780086) ^ [_1354502, _1354504, _1354506, _1354508] : [-(_1354502 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1354504, tc_HOL_Obool), tc_HOL_Obool))), 30923 ^ _780086 : [(30924 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1354504, tc_HOL_Obool)), 30922 ^ [_1354502, _1354504, _1354506, _1354508]), _1354502)))], (30926 ^ _780086) ^ [] : [c_Fun_Oinj__on(_1354504, _1354506, _1354508, 30922 ^ [_1354502, _1354504, _1354506, _1354508])]], -(c_Fun_Oinj__on(_1354504, _1354506, _1354508, c_Complete__Lattice_OInf__class_OInf(tc_fun(_1354504, tc_HOL_Obool), _1354502)))], (30930 ^ _780086) ^ [_1354763, _1354765, _1354767] : [30932 ^ _780086 : [(30933 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1354763, tc_HOL_Obool)), 30931 ^ [_1354763, _1354765, _1354767]), _1354765)))], (30935 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1354763, tc_HOL_Obool)), 30931 ^ [_1354763, _1354765, _1354767]), _1354767))]], -(_1354765 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1354763, tc_HOL_Obool), tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1354763, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1354763, tc_HOL_Obool), _1354765)), _1354767)))], (30943 ^ _780086) ^ [_1355025, _1355027, _1355029] : [30945 ^ _780086 : [(30946 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 30944 ^ [_1355025, _1355027, _1355029]), _1355025)))], (30948 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(_1355027, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 30944 ^ [_1355025, _1355027, _1355029]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1355027, 30944 ^ [_1355025, _1355027, _1355029])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1355027, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1355029)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1355029), hAPP(_1355027, _1355025))), 30958 ^ _780086 : [(30959 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 30957 ^ [_1355025, _1355027, _1355029]), _1355025)))], (30961 ^ _780086) ^ [] : [-(hAPP(_1355027, 30957 ^ [_1355025, _1355027, _1355029]) = _1355029)]]], (30963 ^ _780086) ^ [_1355475, _1355477] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1355475, tc_HOL_Obool), _1355477) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1355475, tc_HOL_Obool), tc_fun(_1355475, tc_HOL_Obool)), _1355477), c_COMBI(tc_fun(_1355475, tc_HOL_Obool))))], (30965 ^ _780086) ^ [_1355526, _1355528] : [-(c_Nitpick_Onat__lcm(_1355526, _1355528) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1355526), _1355528)), c_Nitpick_Onat__gcd(_1355526, _1355528)))], (30967 ^ _780086) ^ [_1355569, _1355571] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1355569, tc_HOL_Obool)), _1355571)), 30973 ^ _780086 : [(30974 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1355569, tc_HOL_Obool)), 30972 ^ [_1355569, _1355571]), _1355571)))], (30976 ^ _780086) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1355569), 30972 ^ [_1355569, _1355571]))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1355569), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1355569, tc_HOL_Obool), _1355571))))], (30980 ^ _780086) ^ [_1355827, _1355829, _1355831] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1355827, tc_HOL_Obool)), _1355829), _1355831))), 30986 ^ _780086 : [(30987 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1355827, tc_HOL_Obool)), 30985 ^ [_1355827, _1355829, _1355831]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1355827, tc_HOL_Obool)), _1355829), _1355831))))], (30990 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1355827, tc_HOL_Obool)), 30988 ^ [_1355827, _1355829, _1355831]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1355827, tc_HOL_Obool)), _1355829), _1355831))))], (30992 ^ _780086) ^ [] : [30985 ^ [_1355827, _1355829, _1355831] = 30988 ^ [_1355827, _1355829, _1355831]], (30994 ^ _780086) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1355827, tc_HOL_Obool)), 30985 ^ [_1355827, _1355829, _1355831]), 30988 ^ [_1355827, _1355829, _1355831]) = c_Orderings_Obot__class_Obot(tc_fun(_1355827, tc_HOL_Obool))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1355827, tc_HOL_Obool)), _1355829), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1355827, tc_HOL_Obool), _1355831)) = c_Orderings_Obot__class_Obot(tc_fun(_1355827, tc_HOL_Obool)))], (30998 ^ _780086) ^ [_1356421, _1356423, _1356425] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1356421, tc_HOL_Obool)), _1356423)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1356421), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1356421, tc_HOL_Obool), _1356423))), 31008 ^ _780086 : [(31009 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1356421, tc_HOL_Obool)), 31007 ^ [_1356421, _1356423, _1356425]), _1356423)))], (31011 ^ _780086) ^ [] : [hAPP(c_Finite__Set_Ocard(_1356421), 31007 ^ [_1356421, _1356423, _1356425]) = _1356425]], 31015 ^ _780086 : [(31016 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1356421, tc_HOL_Obool)), 31014 ^ [_1356421, _1356423, _1356425]), _1356423)))], (31019 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1356421, tc_HOL_Obool)), 31017 ^ [_1356421, _1356423, _1356425]), _1356423)))], (31021 ^ _780086) ^ [] : [31014 ^ [_1356421, _1356423, _1356425] = 31017 ^ [_1356421, _1356423, _1356425]], (31023 ^ _780086) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1356421, tc_HOL_Obool)), 31014 ^ [_1356421, _1356423, _1356425]), 31017 ^ [_1356421, _1356423, _1356425]) = c_Orderings_Obot__class_Obot(tc_fun(_1356421, tc_HOL_Obool))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1356425), hAPP(c_Finite__Set_Ocard(tc_fun(_1356421, tc_HOL_Obool)), _1356423)) = hAPP(c_Finite__Set_Ocard(_1356421), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1356421, tc_HOL_Obool), _1356423)))], (31027 ^ _780086) ^ [_1357212, _1357214] : [_1357212 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1357214, _1357212) = _1357214)], (31033 ^ _780086) ^ [_1357289, _1357291] : [-(_1357289 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1357291, _1357289) = c_Nitpick_Onat__gcd(_1357289, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1357291, _1357289)))], (31039 ^ _780086) ^ [_1357337, _1357339] : [-(hAPP(hAPP(c_Nitpick_Oint__gcd, _1357337), _1357339) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Nitpick_Onat__gcd(hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1357337)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1357339)))))], (31041 ^ _780086) ^ [_1357386, _1357388, _1357390] : [31043 ^ _780086 : [(31044 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 31042 ^ [_1357386, _1357388, _1357390]), _1357386)))], (31046 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(_1357388, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 31042 ^ [_1357386, _1357388, _1357390]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1357388, 31042 ^ [_1357386, _1357388, _1357390])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1357388, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1357390)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1357390), hAPP(_1357388, _1357386))), 31056 ^ _780086 : [(31057 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 31055 ^ [_1357386, _1357388, _1357390]), _1357386)))], (31059 ^ _780086) ^ [] : [-(hAPP(_1357388, 31055 ^ [_1357386, _1357388, _1357390]) = _1357390)]]], (31061 ^ _780086) ^ [_1357836, _1357838, _1357840] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1357836), _1357838)), 31067 ^ _780086 : [(31068 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1357836), 31066 ^ [_1357836, _1357838, _1357840]), _1357838)))], (31070 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1357840, 31066 ^ [_1357836, _1357838, _1357840])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1357836, tc_Nat_Onat), _1357840), _1357838))))], (31074 ^ _780086) ^ [_1358096, _1358098, _1358100, _1358102, _1358104, _1358106] : [-(_1358096 = c_Orderings_Obot__class_Obot(tc_fun(_1358098, tc_HOL_Obool))), 31080 ^ _780086 : [(31081 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1358098), 31079 ^ [_1358096, _1358098, _1358100, _1358102, _1358104, _1358106]), _1358096)))], (31083 ^ _780086) ^ [] : [c_Fun_Oinj__on(_1358100, _1358102, _1358104, hAPP(_1358106, 31079 ^ [_1358096, _1358098, _1358100, _1358102, _1358104, _1358106]))]], -(c_Fun_Oinj__on(_1358100, _1358102, _1358104, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1358098, tc_fun(_1358100, tc_HOL_Obool)), _1358096), _1358106)))], (31087 ^ _780086) ^ [_1358388, _1358390, _1358392, _1358394, _1358396, _1358398, _1358400, _1358402] : [c_Finite__Set_Ofolding__image__simple(_1358388, _1358390, _1358392, _1358394, _1358396, _1358398), hBOOL(hAPP(c_Finite__Set_Ofinite(_1358390), _1358400)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1358390), _1358402)), 31101 ^ _780086 : [(31102 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1358390), 31100 ^ [_1358388, _1358390, _1358392, _1358394, _1358396, _1358398, _1358400, _1358402]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1358390, tc_HOL_Obool)), _1358400), _1358402))))], (31104 ^ _780086) ^ [] : [hAPP(_1358396, 31100 ^ [_1358388, _1358390, _1358392, _1358394, _1358396, _1358398, _1358400, _1358402]) = _1358394]], -(hAPP(_1358398, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1358390, tc_HOL_Obool)), _1358400), _1358402)) = hAPP(hAPP(_1358392, hAPP(_1358398, _1358400)), hAPP(_1358398, _1358402)))], (31108 ^ _780086) ^ [_1358885, _1358887] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1358885))), -(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_Set_OCollect(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), tc_Nat_Onat), c_member(tc_Nat_Onat)), c_Nat_OSuc)), _1358885))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1358887)))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_Set_OCollect(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1358885))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), hAPP(c_Nat_OSuc, _1358887))))))], (31114 ^ _780086) ^ [_1358968, _1358970] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1358968)), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_Set_OCollect(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1358968))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), hAPP(c_Nat_OSuc, _1358970))))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (31120 ^ _780086) ^ [_1359098, _1359100] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1359098)), -(hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_Set_OCollect(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), tc_Nat_Onat), c_member(tc_Nat_Onat)), c_Nat_OSuc)), _1359098))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1359100))))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_Set_OCollect(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1359098))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), hAPP(c_Nat_OSuc, _1359100))))))], (31126 ^ _780086) ^ [_1359275, _1359277, _1359279] : [hBOOL(hAPP(_1359275, _1359277)), -(hBOOL(hAPP(hAPP(c_member(_1359279), _1359277), hAPP(c_Set_OCollect(_1359279), _1359275))))], (31132 ^ _780086) ^ [_1359382, _1359384, _1359386] : [31133 ^ _780086 : [(31134 ^ _780086) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1359382), hAPP(c_Set_OCollect(_1359382), _1359384)))], (31136 ^ _780086) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1359382), hAPP(c_Set_OCollect(_1359382), _1359386)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1359382), hAPP(c_Set_OCollect(_1359382), hAPP(hAPP(c_COMBS(_1359382, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1359382), c_fconj), _1359384)), _1359386)))))], (31140 ^ _780086) ^ [_1359593] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_OCollect(tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1359593)))))], (31142 ^ _780086) ^ [_1359624] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_OCollect(tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)), _1359624)))))], (31144 ^ _780086) ^ [_1359655, _1359657, _1359659] : [-(hAPP(c_Set_OCollect(_1359655), hAPP(hAPP(c_COMBS(_1359655, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1359655), c_fdisj), _1359657)), _1359659)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1359655, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1359655), _1359657)), hAPP(c_Set_OCollect(_1359655), _1359659)))], (31146 ^ _780086) ^ [_1359728, _1359730, _1359732] : [-(hAPP(c_Set_OCollect(_1359728), hAPP(hAPP(c_COMBS(_1359728, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1359728), c_fconj), _1359730)), _1359732)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1359728, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1359728), _1359730)), hAPP(c_Set_OCollect(_1359728), _1359732)))], (31148 ^ _780086) ^ [_1359801, _1359803, _1359805] : [hBOOL(hAPP(hAPP(c_member(_1359801), _1359803), hAPP(c_Set_OCollect(_1359801), _1359805))), -(hBOOL(hAPP(_1359805, _1359803)))], (31154 ^ _780086) ^ [_1359908, _1359910, _1359912] : [hBOOL(hAPP(hAPP(c_member(_1359908), _1359910), hAPP(c_Set_OCollect(_1359908), _1359912))), -(hBOOL(hAPP(_1359912, _1359910)))], (31160 ^ _780086) ^ [_1360033, _1360035, _1360037] : [hBOOL(hAPP(hAPP(c_member(_1360033), _1360035), hAPP(c_Set_OCollect(_1360033), _1360037))), -(hBOOL(hAPP(_1360037, _1360035)))], (31166 ^ _780086) ^ [_1360136, _1360138, _1360140] : [hBOOL(hAPP(_1360140, _1360138)), -(hBOOL(hAPP(hAPP(c_member(_1360136), _1360138), hAPP(c_Set_OCollect(_1360136), _1360140))))], (31172 ^ _780086) ^ [_1360245, _1360247] : [-(hAPP(c_Set_OCollect(_1360245), hAPP(hAPP(c_COMBC(_1360245, tc_fun(_1360245, tc_HOL_Obool), tc_HOL_Obool), c_member(_1360245)), _1360247)) = _1360247)], (31174 ^ _780086) ^ [_1360290] : [-(c_Orderings_Obot__class_Obot(tc_fun(_1360290, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1360290), hAPP(c_COMBK(tc_HOL_Obool, _1360290), c_fFalse)))], (31176 ^ _780086) ^ [_1360344, _1360346] : [c_Orderings_Obot__class_Obot(tc_fun(_1360344, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1360344), _1360346), 31179 ^ _780086 : [(31180 ^ _780086) ^ [_1360429] : [hBOOL(hAPP(_1360346, _1360429))]]], (31182 ^ _780086) ^ [_1360452, _1360454] : [-(hBOOL(hAPP(_1360454, 31183 ^ [_1360452, _1360454]))), -(c_Orderings_Obot__class_Obot(tc_fun(_1360452, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1360452), _1360454))], (31189 ^ _780086) ^ [_1360524, _1360526] : [hAPP(c_Set_OCollect(_1360524), _1360526) = c_Orderings_Obot__class_Obot(tc_fun(_1360524, tc_HOL_Obool)), 31192 ^ _780086 : [(31193 ^ _780086) ^ [_1360609] : [hBOOL(hAPP(_1360526, _1360609))]]], (31195 ^ _780086) ^ [_1360632, _1360634] : [-(hBOOL(hAPP(_1360634, 31196 ^ [_1360632, _1360634]))), -(hAPP(c_Set_OCollect(_1360632), _1360634) = c_Orderings_Obot__class_Obot(tc_fun(_1360632, tc_HOL_Obool)))], (31202 ^ _780086) ^ [_1360689, _1360691] : [-(hAPP(c_Set_OCollect(_1360689), _1360691) = _1360691)], (31204 ^ _780086) ^ [_1360719] : [-(c_Orderings_Otop__class_Otop(tc_fun(_1360719, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1360719), hAPP(c_COMBK(tc_HOL_Obool, _1360719), c_fTrue)))], (31206 ^ _780086) ^ [_1360758, _1360760, _1360762] : [-(hAPP(hAPP(c_Set_Oinsert(_1360758), _1360760), hAPP(c_Set_OCollect(_1360758), _1360762)) = hAPP(c_Set_OCollect(_1360758), hAPP(hAPP(c_COMBS(_1360758, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1360758), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1360758), c_fNot), hAPP(hAPP(c_COMBC(_1360758, _1360758, tc_HOL_Obool), c_fequal), _1360760)))), _1360762)))], (31208 ^ _780086) ^ [_1360861, _1360863, _1360865] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1360861), hAPP(c_Set_OCollect(_1360861), hAPP(hAPP(c_COMBS(_1360861, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1360861), c_fdisj), _1360863)), _1360865)))), 31211 ^ _780086 : [(31212 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1360861), hAPP(c_Set_OCollect(_1360861), _1360863))))], (31214 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1360861), hAPP(c_Set_OCollect(_1360861), _1360865))))]]], (31216 ^ _780086) ^ [_1361056, _1361058, _1361060] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1361056), hAPP(c_Set_OCollect(_1361056), hAPP(hAPP(c_COMBS(_1361056, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1361056), c_fdisj), _1361058)), _1361060))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1361056), hAPP(c_Set_OCollect(_1361056), _1361058))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1361056), hAPP(c_Set_OCollect(_1361056), _1361060)))], (31226 ^ _780086) ^ [_1361285, _1361287] : [-(hAPP(c_Set_OCollect(_1361285), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1361285), c_fNot), _1361287)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1361285, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1361285), _1361287)))], (31228 ^ _780086) ^ [_1361338, _1361340, _1361342, _1361344] : [-(hAPP(c_Set_Ovimage(_1361338, _1361340, _1361342), hAPP(c_Set_OCollect(_1361340), _1361344)) = hAPP(c_Set_OCollect(_1361338), hAPP(hAPP(c_COMBB(_1361340, tc_HOL_Obool, _1361338), _1361344), _1361342)))], (31230 ^ _780086) ^ [_1361394, _1361396, _1361398] : [-(hAPP(hAPP(c_Set_Oinsert(_1361394), _1361396), _1361398) = hAPP(c_Set_OCollect(_1361394), hAPP(hAPP(c_COMBS(_1361394, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1361394), c_fdisj), hAPP(hAPP(c_COMBC(_1361394, _1361394, tc_HOL_Obool), c_fequal), _1361396))), hAPP(hAPP(c_COMBC(_1361394, tc_fun(_1361394, tc_HOL_Obool), tc_HOL_Obool), c_member(_1361394)), _1361398))))], (31232 ^ _780086) ^ [_1361479, _1361481, _1361483] : [-(hAPP(hAPP(c_Set_Oinsert(_1361479), _1361481), _1361483) = hAPP(c_Set_OCollect(_1361479), hAPP(hAPP(c_COMBS(_1361479, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1361479), c_fdisj), hAPP(hAPP(c_COMBC(_1361479, _1361479, tc_HOL_Obool), c_fequal), _1361481))), hAPP(hAPP(c_COMBC(_1361479, tc_fun(_1361479, tc_HOL_Obool), tc_HOL_Obool), c_member(_1361479)), _1361483))))], (31234 ^ _780086) ^ [_1361564, _1361566, _1361568] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1361564, tc_HOL_Obool)), _1361566), _1361568) = hAPP(c_Set_OCollect(_1361564), hAPP(hAPP(c_COMBS(_1361564, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1361564), c_fdisj), hAPP(hAPP(c_COMBC(_1361564, tc_fun(_1361564, tc_HOL_Obool), tc_HOL_Obool), c_member(_1361564)), _1361566))), hAPP(hAPP(c_COMBC(_1361564, tc_fun(_1361564, tc_HOL_Obool), tc_HOL_Obool), c_member(_1361564)), _1361568))))], (31236 ^ _780086) ^ [_1361657, _1361659, _1361661] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1361657, tc_HOL_Obool)), _1361659), _1361661) = hAPP(c_Set_OCollect(_1361657), hAPP(hAPP(c_COMBS(_1361657, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1361657), c_fconj), hAPP(hAPP(c_COMBC(_1361657, tc_fun(_1361657, tc_HOL_Obool), tc_HOL_Obool), c_member(_1361657)), _1361659))), hAPP(hAPP(c_COMBC(_1361657, tc_fun(_1361657, tc_HOL_Obool), tc_HOL_Obool), c_member(_1361657)), _1361661))))], (31238 ^ _780086) ^ [_1361771, _1361773, _1361775, _1361777] : [hBOOL(hAPP(hAPP(c_member(_1361771), _1361773), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1361771, tc_HOL_Obool)), _1361775), hAPP(c_Set_OCollect(_1361771), _1361777)))), 31241 ^ _780086 : [(31242 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1361771), _1361773), _1361775)))], (31244 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1361777, _1361773)))]]], (31246 ^ _780086) ^ [_1361938, _1361940, _1361942, _1361944] : [-(hBOOL(hAPP(hAPP(c_member(_1361938), _1361940), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1361938, tc_HOL_Obool)), _1361942), hAPP(c_Set_OCollect(_1361938), _1361944))))), hBOOL(hAPP(hAPP(c_member(_1361938), _1361940), _1361942)), hBOOL(hAPP(_1361944, _1361940))], (31256 ^ _780086) ^ [_1362141, _1362143] : [-(hAPP(c_Set_OCollect(_1362141), hAPP(c_fequal, _1362143)) = hAPP(hAPP(c_Set_Oinsert(_1362141), _1362143), c_Orderings_Obot__class_Obot(tc_fun(_1362141, tc_HOL_Obool))))], (31258 ^ _780086) ^ [_1362187, _1362189] : [-(hAPP(c_Set_OCollect(_1362187), hAPP(hAPP(c_COMBC(_1362187, _1362187, tc_HOL_Obool), c_fequal), _1362189)) = hAPP(hAPP(c_Set_Oinsert(_1362187), _1362189), c_Orderings_Obot__class_Obot(tc_fun(_1362187, tc_HOL_Obool))))], (31260 ^ _780086) ^ [_1362252, _1362254, _1362256] : [hBOOL(hAPP(_1362252, _1362254)), -(hAPP(c_Set_OCollect(_1362256), hAPP(hAPP(c_COMBS(_1362256, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1362256), c_fconj), hAPP(c_fequal, _1362254))), _1362252)) = hAPP(hAPP(c_Set_Oinsert(_1362256), _1362254), c_Orderings_Obot__class_Obot(tc_fun(_1362256, tc_HOL_Obool))))], (31266 ^ _780086) ^ [_1362411, _1362413, _1362415] : [-(hBOOL(hAPP(_1362411, _1362413))), -(hAPP(c_Set_OCollect(_1362415), hAPP(hAPP(c_COMBS(_1362415, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1362415), c_fconj), hAPP(c_fequal, _1362413))), _1362411)) = c_Orderings_Obot__class_Obot(tc_fun(_1362415, tc_HOL_Obool)))], (31272 ^ _780086) ^ [_1362498, _1362500, _1362502] : [hBOOL(hAPP(_1362498, _1362500)), -(hAPP(c_Set_OCollect(_1362502), hAPP(hAPP(c_COMBS(_1362502, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1362502), c_fconj), hAPP(hAPP(c_COMBC(_1362502, _1362502, tc_HOL_Obool), c_fequal), _1362500))), _1362498)) = hAPP(hAPP(c_Set_Oinsert(_1362502), _1362500), c_Orderings_Obot__class_Obot(tc_fun(_1362502, tc_HOL_Obool))))], (31278 ^ _780086) ^ [_1362671, _1362673, _1362675] : [-(hBOOL(hAPP(_1362671, _1362673))), -(hAPP(c_Set_OCollect(_1362675), hAPP(hAPP(c_COMBS(_1362675, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1362675), c_fconj), hAPP(hAPP(c_COMBC(_1362675, _1362675, tc_HOL_Obool), c_fequal), _1362673))), _1362671)) = c_Orderings_Obot__class_Obot(tc_fun(_1362675, tc_HOL_Obool)))], (31284 ^ _780086) ^ [_1362753, _1362755, _1362757] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1362753, tc_HOL_Obool)), _1362755), _1362757) = hAPP(c_Set_OCollect(_1362753), hAPP(hAPP(c_COMBS(_1362753, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1362753), c_fconj), hAPP(hAPP(c_COMBC(_1362753, tc_fun(_1362753, tc_HOL_Obool), tc_HOL_Obool), c_member(_1362753)), _1362755))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1362753), c_fNot), hAPP(hAPP(c_COMBC(_1362753, tc_fun(_1362753, tc_HOL_Obool), tc_HOL_Obool), c_member(_1362753)), _1362757)))))], (31286 ^ _780086) ^ [_1362856, _1362858] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1362856), hAPP(c_Set_OCollect(_1362856), _1362858))), 31289 ^ _780086 : [(31290 ^ _780086) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1362856), hAPP(c_Set_OCollect(_1362856), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1362856), c_fNot), _1362858)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1362856), c_Orderings_Otop__class_Otop(tc_fun(_1362856, tc_HOL_Obool)))))], (31296 ^ _780086) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1362856), c_Orderings_Otop__class_Otop(tc_fun(_1362856, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1362856), hAPP(c_Set_OCollect(_1362856), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1362856), c_fNot), _1362858)))))]]], (31302 ^ _780086) ^ [_1363165, _1363167, _1363169] : [-(hAPP(hAPP(c_Set_Oinsert(_1363165), _1363167), _1363169) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363165, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1363165), hAPP(hAPP(c_COMBC(_1363165, _1363165, tc_HOL_Obool), c_fequal), _1363167))), _1363169))], (31304 ^ _780086) ^ [_1363226, _1363228] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1363226, tc_HOL_Obool)), _1363228) = hAPP(c_Set_OCollect(_1363226), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1363226), c_fNot), hAPP(hAPP(c_COMBC(_1363226, tc_fun(_1363226, tc_HOL_Obool), tc_HOL_Obool), c_member(_1363226)), _1363228))))], (31306 ^ _780086) ^ [_1363289, _1363291, _1363293, _1363295] : [-(hAPP(c_Set_Ovimage(_1363289, _1363291, _1363293), _1363295) = hAPP(c_Set_OCollect(_1363289), hAPP(hAPP(c_COMBC(_1363289, tc_fun(_1363291, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1363291, tc_fun(tc_fun(_1363291, tc_HOL_Obool), tc_HOL_Obool), _1363289), c_member(_1363291)), _1363293)), _1363295)))], (31308 ^ _780086) ^ [_1363361, _1363363, _1363365] : [-(hAPP(c_Set_OCollect(_1363361), hAPP(hAPP(c_COMBS(_1363361, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1363361), c_fimplies), _1363363)), _1363365)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363361, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1363361, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1363361), _1363363))), hAPP(c_Set_OCollect(_1363361), _1363365)))], (31310 ^ _780086) ^ [_1363442, _1363444] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_OCollect(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj), _1363442)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1363444))))))], (31312 ^ _780086) ^ [_1363484, _1363486, _1363488, _1363490, _1363492, _1363494, _1363496] : [class_Groups_Ocomm__monoid__add(_1363484), hBOOL(hAPP(c_Finite__Set_Ofinite(_1363486), _1363488)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1363490), _1363492)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1363486, _1363484), hAPP(hAPP(c_COMBS(_1363486, tc_fun(_1363490, tc_HOL_Obool), _1363484), hAPP(hAPP(c_COMBB(tc_fun(_1363490, _1363484), tc_fun(tc_fun(_1363490, tc_HOL_Obool), _1363484), _1363486), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1363490, _1363484)), _1363494)), hAPP(hAPP(c_COMBB(tc_fun(_1363490, tc_HOL_Obool), tc_fun(_1363490, tc_HOL_Obool), _1363486), c_Set_OCollect(_1363490)), hAPP(hAPP(c_COMBB(tc_fun(_1363490, tc_HOL_Obool), tc_fun(_1363490, tc_HOL_Obool), _1363486), hAPP(c_COMBS(_1363490, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1363490), c_fconj), hAPP(hAPP(c_COMBC(_1363490, tc_fun(_1363490, tc_HOL_Obool), tc_HOL_Obool), c_member(_1363490)), _1363492)))), _1363496)))), _1363488) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1363490, _1363484), hAPP(hAPP(c_COMBS(_1363490, tc_fun(_1363486, tc_HOL_Obool), _1363484), hAPP(hAPP(c_COMBB(tc_fun(_1363486, _1363484), tc_fun(tc_fun(_1363486, tc_HOL_Obool), _1363484), _1363490), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1363486, _1363484)), hAPP(c_COMBC(_1363486, _1363490, _1363484), _1363494))), hAPP(hAPP(c_COMBB(tc_fun(_1363486, tc_HOL_Obool), tc_fun(_1363486, tc_HOL_Obool), _1363490), c_Set_OCollect(_1363486)), hAPP(hAPP(c_COMBB(tc_fun(_1363486, tc_HOL_Obool), tc_fun(_1363486, tc_HOL_Obool), _1363490), hAPP(c_COMBS(_1363486, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1363486), c_fconj), hAPP(hAPP(c_COMBC(_1363486, tc_fun(_1363486, tc_HOL_Obool), tc_HOL_Obool), c_member(_1363486)), _1363488)))), hAPP(c_COMBC(_1363486, _1363490, tc_HOL_Obool), _1363496))))), _1363492))], (31326 ^ _780086) ^ [_1364177, _1364179, _1364181, _1364183, _1364185, _1364187] : [-(hAPP(c_Set_Oimage(_1364177, _1364179, hAPP(hAPP(c_COMBS(_1364177, _1364179, _1364179), hAPP(hAPP(c_COMBS(_1364177, _1364179, tc_fun(_1364179, _1364179)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1364179, tc_fun(_1364179, _1364179)), _1364177), c_If(_1364179)), _1364181)), _1364183)), _1364185)), _1364187) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1364179, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1364177, _1364179, _1364183), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1364177, tc_HOL_Obool)), _1364187), hAPP(c_Set_OCollect(_1364177), _1364181)))), hAPP(c_Set_Oimage(_1364177, _1364179, _1364185), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1364177, tc_HOL_Obool)), _1364187), hAPP(c_Set_OCollect(_1364177), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1364177), c_fNot), _1364181))))))], (31328 ^ _780086) ^ [_1364325, _1364327, _1364329, _1364331] : [_1364325 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1364327, _1364329), hAPP(c_Set_OCollect(tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1364331))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1364327), _1364325)))], (31334 ^ _780086) ^ [_1364440, _1364442, _1364444, _1364446, _1364448] : [class_Groups_Ocomm__monoid__add(_1364440), hBOOL(hAPP(c_Finite__Set_Ofinite(_1364442), _1364444)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1364442, _1364440), _1364446), hAPP(c_Set_OCollect(_1364442), hAPP(hAPP(c_COMBS(_1364442, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1364442), c_fconj), hAPP(hAPP(c_COMBC(_1364442, tc_fun(_1364442, tc_HOL_Obool), tc_HOL_Obool), c_member(_1364442)), _1364444))), hAPP(hAPP(c_COMBC(_1364442, tc_fun(_1364442, tc_HOL_Obool), tc_HOL_Obool), c_member(_1364442)), _1364448)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1364442, _1364440), hAPP(hAPP(c_COMBC(_1364442, _1364440, _1364440), hAPP(hAPP(c_COMBS(_1364442, _1364440, tc_fun(_1364440, _1364440)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1364440, tc_fun(_1364440, _1364440)), _1364442), c_If(_1364440)), hAPP(hAPP(c_COMBC(_1364442, tc_fun(_1364442, tc_HOL_Obool), tc_HOL_Obool), c_member(_1364442)), _1364448))), _1364446)), c_Groups_Ozero__class_Ozero(_1364440))), _1364444))], (31344 ^ _780086) ^ [_1364849, _1364851, _1364853, _1364855, _1364857, _1364859] : [class_Groups_Ocomm__monoid__add(_1364849), hBOOL(hAPP(c_Finite__Set_Ofinite(_1364851), _1364853)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1364851, _1364849), _1364855), _1364853) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1364857, _1364849), hAPP(hAPP(c_COMBB(tc_fun(_1364851, tc_HOL_Obool), _1364849, _1364857), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1364851, _1364849), _1364855)), hAPP(hAPP(c_COMBB(tc_fun(_1364851, tc_HOL_Obool), tc_fun(_1364851, tc_HOL_Obool), _1364857), c_Set_OCollect(_1364851)), hAPP(hAPP(c_COMBB(tc_fun(_1364851, tc_HOL_Obool), tc_fun(_1364851, tc_HOL_Obool), _1364857), hAPP(c_COMBS(_1364851, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1364851), c_fconj), hAPP(hAPP(c_COMBC(_1364851, tc_fun(_1364851, tc_HOL_Obool), tc_HOL_Obool), c_member(_1364851)), _1364853)))), hAPP(c_COMBC(_1364851, _1364857, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1364857, tc_fun(_1364857, tc_HOL_Obool), _1364851), c_fequal), _1364859)))))), hAPP(c_Set_Oimage(_1364851, _1364857, _1364859), _1364853)))], (31354 ^ _780086) ^ [_1365260, _1365262, _1365264, _1365266, _1365268, _1365270] : [class_Groups_Ocomm__monoid__add(_1365260), hBOOL(hAPP(c_Finite__Set_Ofinite(_1365262), _1365264)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1365262, _1365260), hAPP(hAPP(c_COMBS(_1365262, _1365260, _1365260), hAPP(hAPP(c_COMBS(_1365262, _1365260, tc_fun(_1365260, _1365260)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1365260, tc_fun(_1365260, _1365260)), _1365262), c_If(_1365260)), _1365266)), _1365268)), _1365270)), _1365264) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1365260), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1365262, _1365260), _1365268), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1365262, tc_HOL_Obool)), _1365264), hAPP(c_Set_OCollect(_1365262), _1365266)))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1365262, _1365260), _1365270), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1365262, tc_HOL_Obool)), _1365264), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1365262, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1365262), _1365266))))))], (31364 ^ _780086) ^ [_1365643, _1365645, _1365647, _1365649, _1365651, _1365653] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1365643), _1365645)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1365647), _1365649)), 31374 ^ _780086 : [(31375 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1365647), 31373 ^ [_1365643, _1365645, _1365647, _1365649, _1365651, _1365653]), _1365649)))], (31377 ^ _780086) ^ [] : [hAPP(c_Finite__Set_Ocard(_1365643), hAPP(c_Set_OCollect(_1365643), hAPP(hAPP(c_COMBS(_1365643, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1365643), c_fconj), hAPP(hAPP(c_COMBC(_1365643, tc_fun(_1365643, tc_HOL_Obool), tc_HOL_Obool), c_member(_1365643)), _1365645))), hAPP(hAPP(c_COMBC(_1365643, _1365647, tc_HOL_Obool), _1365651), 31373 ^ [_1365643, _1365645, _1365647, _1365649, _1365651, _1365653])))) = _1365653]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1365643, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1365647, tc_HOL_Obool), tc_Nat_Onat, _1365643), c_Finite__Set_Ocard(_1365647)), hAPP(hAPP(c_COMBB(tc_fun(_1365647, tc_HOL_Obool), tc_fun(_1365647, tc_HOL_Obool), _1365643), c_Set_OCollect(_1365647)), hAPP(hAPP(c_COMBB(tc_fun(_1365647, tc_HOL_Obool), tc_fun(_1365647, tc_HOL_Obool), _1365643), hAPP(c_COMBS(_1365647, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1365647), c_fconj), hAPP(hAPP(c_COMBC(_1365647, tc_fun(_1365647, tc_HOL_Obool), tc_HOL_Obool), c_member(_1365647)), _1365649)))), _1365651)))), _1365645) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1365653), hAPP(c_Finite__Set_Ocard(_1365647), _1365649)))], (31381 ^ _780086) ^ [_1366333, _1366335, _1366337] : [class_Orderings_Olinorder(_1366333), hBOOL(hAPP(c_Finite__Set_Ofinite(_1366333), _1366335)), -(_1366335 = c_Orderings_Obot__class_Obot(tc_fun(_1366333, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1366333), _1366337), c_Big__Operators_Olattice_OInf__fin(_1366333, c_Orderings_Oord__class_Omin(_1366333), _1366335)) = c_Big__Operators_Olattice_OInf__fin(_1366333, c_Orderings_Oord__class_Omin(_1366333), hAPP(c_Set_OCollect(_1366333), hAPP(hAPP(c_COMBB(tc_fun(_1366333, tc_HOL_Obool), tc_HOL_Obool, _1366333), c_HOL_OEx(_1366333)), hAPP(hAPP(c_COMBC(_1366333, tc_fun(_1366333, tc_HOL_Obool), tc_fun(_1366333, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1366333, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1366333, tc_HOL_Obool), tc_fun(_1366333, tc_HOL_Obool)), _1366333), c_COMBS(_1366333, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1366333, tc_HOL_Obool), tc_fun(_1366333, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1366333), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1366333), c_fconj)), hAPP(hAPP(c_COMBC(_1366333, tc_fun(_1366333, _1366333), tc_fun(_1366333, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1366333, tc_HOL_Obool), tc_fun(tc_fun(_1366333, _1366333), tc_fun(_1366333, tc_HOL_Obool)), _1366333), c_COMBB(_1366333, tc_HOL_Obool, _1366333)), c_fequal)), hAPP(c_Orderings_Oord__class_Omax(_1366333), _1366337))))), hAPP(hAPP(c_COMBC(_1366333, tc_fun(_1366333, tc_HOL_Obool), tc_HOL_Obool), c_member(_1366333)), _1366335))))))], (31395 ^ _780086) ^ [_1366831, _1366833, _1366835] : [class_Orderings_Olinorder(_1366831), hBOOL(hAPP(c_Finite__Set_Ofinite(_1366831), _1366833)), -(_1366833 = c_Orderings_Obot__class_Obot(tc_fun(_1366831, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1366831), _1366835), c_Big__Operators_Olattice_OSup__fin(_1366831, c_Orderings_Oord__class_Omax(_1366831), _1366833)) = c_Big__Operators_Olattice_OSup__fin(_1366831, c_Orderings_Oord__class_Omax(_1366831), hAPP(c_Set_OCollect(_1366831), hAPP(hAPP(c_COMBB(tc_fun(_1366831, tc_HOL_Obool), tc_HOL_Obool, _1366831), c_HOL_OEx(_1366831)), hAPP(hAPP(c_COMBC(_1366831, tc_fun(_1366831, tc_HOL_Obool), tc_fun(_1366831, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1366831, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1366831, tc_HOL_Obool), tc_fun(_1366831, tc_HOL_Obool)), _1366831), c_COMBS(_1366831, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1366831, tc_HOL_Obool), tc_fun(_1366831, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1366831), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1366831), c_fconj)), hAPP(hAPP(c_COMBC(_1366831, tc_fun(_1366831, _1366831), tc_fun(_1366831, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1366831, tc_HOL_Obool), tc_fun(tc_fun(_1366831, _1366831), tc_fun(_1366831, tc_HOL_Obool)), _1366831), c_COMBB(_1366831, tc_HOL_Obool, _1366831)), c_fequal)), hAPP(c_Orderings_Oord__class_Omin(_1366831), _1366835))))), hAPP(hAPP(c_COMBC(_1366831, tc_fun(_1366831, tc_HOL_Obool), tc_HOL_Obool), c_member(_1366831)), _1366833))))))], (31409 ^ _780086) ^ [_1367329, _1367331, _1367333] : [class_Orderings_Olinorder(_1367329), hBOOL(hAPP(c_Finite__Set_Ofinite(_1367329), _1367331)), -(_1367331 = c_Orderings_Obot__class_Obot(tc_fun(_1367329, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1367329), _1367333)), -(_1367333 = c_Orderings_Obot__class_Obot(tc_fun(_1367329, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1367329), c_Big__Operators_Olattice_OInf__fin(_1367329, c_Orderings_Oord__class_Omin(_1367329), _1367331)), c_Big__Operators_Olattice_OInf__fin(_1367329, c_Orderings_Oord__class_Omin(_1367329), _1367333)) = c_Big__Operators_Olattice_OInf__fin(_1367329, c_Orderings_Oord__class_Omin(_1367329), hAPP(c_Set_OCollect(_1367329), hAPP(hAPP(c_COMBB(tc_fun(_1367329, tc_HOL_Obool), tc_HOL_Obool, _1367329), c_HOL_OEx(_1367329)), hAPP(hAPP(c_COMBB(tc_fun(_1367329, tc_fun(_1367329, tc_HOL_Obool)), tc_fun(_1367329, tc_HOL_Obool), _1367329), hAPP(c_COMBB(tc_fun(_1367329, tc_HOL_Obool), tc_HOL_Obool, _1367329), c_HOL_OEx(_1367329))), hAPP(hAPP(c_COMBC(_1367329, tc_fun(_1367329, tc_fun(_1367329, tc_HOL_Obool)), tc_fun(_1367329, tc_fun(_1367329, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1367329, tc_fun(tc_fun(_1367329, tc_HOL_Obool), tc_fun(_1367329, tc_HOL_Obool))), tc_fun(tc_fun(_1367329, tc_fun(_1367329, tc_HOL_Obool)), tc_fun(_1367329, tc_fun(_1367329, tc_HOL_Obool))), _1367329), c_COMBS(_1367329, tc_fun(_1367329, tc_HOL_Obool), tc_fun(_1367329, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1367329, tc_fun(_1367329, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1367329, tc_fun(tc_fun(_1367329, tc_HOL_Obool), tc_fun(_1367329, tc_HOL_Obool))), _1367329), hAPP(c_COMBB(tc_fun(_1367329, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1367329, tc_HOL_Obool), tc_fun(_1367329, tc_HOL_Obool)), _1367329), c_COMBS(_1367329, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1367329, tc_fun(_1367329, tc_HOL_Obool)), tc_fun(_1367329, tc_fun(_1367329, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1367329), hAPP(c_COMBB(tc_fun(_1367329, tc_HOL_Obool), tc_fun(_1367329, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1367329), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1367329), c_fconj))), hAPP(hAPP(c_COMBC(_1367329, tc_fun(_1367329, tc_fun(_1367329, _1367329)), tc_fun(_1367329, tc_fun(_1367329, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1367329, _1367329), tc_fun(_1367329, tc_HOL_Obool)), tc_fun(tc_fun(_1367329, tc_fun(_1367329, _1367329)), tc_fun(_1367329, tc_fun(_1367329, tc_HOL_Obool))), _1367329), c_COMBB(tc_fun(_1367329, _1367329), tc_fun(_1367329, tc_HOL_Obool), _1367329)), hAPP(hAPP(c_COMBB(tc_fun(_1367329, tc_HOL_Obool), tc_fun(tc_fun(_1367329, _1367329), tc_fun(_1367329, tc_HOL_Obool)), _1367329), c_COMBB(_1367329, tc_HOL_Obool, _1367329)), c_fequal))), c_Orderings_Oord__class_Omax(_1367329)))))), hAPP(hAPP(c_COMBC(_1367329, tc_fun(_1367329, tc_HOL_Obool), tc_fun(_1367329, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1367329, tc_HOL_Obool), tc_fun(_1367329, tc_HOL_Obool)), _1367329), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1367329)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1367329), c_fconj), hAPP(hAPP(c_COMBC(_1367329, tc_fun(_1367329, tc_HOL_Obool), tc_HOL_Obool), c_member(_1367329)), _1367331)))), hAPP(hAPP(c_COMBC(_1367329, tc_fun(_1367329, tc_HOL_Obool), tc_HOL_Obool), c_member(_1367329)), _1367333))))))))], (31431 ^ _780086) ^ [_1368446, _1368448] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1368446), _1368448)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1368446, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_fun(_1368446, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1368446, tc_HOL_Obool), tc_fun(_1368446, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1368446, tc_HOL_Obool))), _1368448)))))], (31437 ^ _780086) ^ [_1368603, _1368605] : [-(hAPP(c_Set_OPow(_1368603), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1368603, tc_HOL_Obool)), _1368605)) = hAPP(c_Set_OCollect(tc_fun(_1368603, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1368603, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1368603, tc_HOL_Obool)), c_HOL_OEx(tc_fun(_1368603, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1368603, tc_HOL_Obool), tc_fun(tc_fun(_1368603, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1368603, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1368603, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1368603, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1368603, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1368603, tc_HOL_Obool)), c_COMBS(tc_fun(_1368603, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1368603, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1368603, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1368603, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1368603, tc_HOL_Obool)), c_fconj)), hAPP(hAPP(c_COMBC(tc_fun(_1368603, tc_HOL_Obool), tc_fun(tc_fun(_1368603, tc_HOL_Obool), tc_fun(_1368603, tc_HOL_Obool)), tc_fun(tc_fun(_1368603, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1368603, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1368603, tc_HOL_Obool), tc_fun(_1368603, tc_HOL_Obool)), tc_fun(tc_fun(_1368603, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1368603, tc_HOL_Obool)), c_COMBB(tc_fun(_1368603, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1368603, tc_HOL_Obool))), c_fequal)), c_Groups_Ouminus__class_Ouminus(tc_fun(_1368603, tc_HOL_Obool)))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1368603, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1368603, tc_HOL_Obool)), hAPP(c_member(tc_fun(_1368603, tc_HOL_Obool)), _1368605)), c_Set_OPow(_1368603))))))], (31439 ^ _780086) ^ [_1368883, _1368885] : [-(hAPP(c_Set_OPow(_1368883), _1368885) = hAPP(c_Set_OCollect(tc_fun(_1368883, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1368883, tc_HOL_Obool), tc_fun(_1368883, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1368883, tc_HOL_Obool))), _1368885)))], (31441 ^ _780086) ^ [_1368942, _1368944, _1368946, _1368948] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1368942), hAPP(c_Set_OCollect(_1368942), _1368944))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1368946), hAPP(c_Set_OCollect(_1368946), hAPP(hAPP(c_COMBB(tc_fun(_1368942, tc_HOL_Obool), tc_HOL_Obool, _1368946), c_HOL_OEx(_1368942)), hAPP(hAPP(c_COMBC(_1368946, tc_fun(_1368942, tc_HOL_Obool), tc_fun(_1368942, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1368942, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1368942, tc_HOL_Obool), tc_fun(_1368942, tc_HOL_Obool)), _1368946), c_COMBS(_1368942, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1368942, tc_HOL_Obool), tc_fun(_1368942, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1368946), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1368942), c_fconj)), hAPP(hAPP(c_COMBC(_1368946, tc_fun(_1368942, _1368946), tc_fun(_1368942, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1368946, tc_HOL_Obool), tc_fun(tc_fun(_1368942, _1368946), tc_fun(_1368942, tc_HOL_Obool)), _1368946), c_COMBB(_1368946, tc_HOL_Obool, _1368942)), c_fequal)), _1368948)))), _1368944))))))], (31447 ^ _780086) ^ [_1369303, _1369305, _1369307, _1369309] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1369303), hAPP(c_Set_OCollect(_1369303), _1369305))), 31450 ^ _780086 : [(31461 ^ _780086) ^ [] : [31463 ^ _780086 : [(31464 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1369305, 31462 ^ [_1369303, _1369305, _1369307, _1369309])))], (31466 ^ _780086) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1369307), hAPP(c_Set_OCollect(_1369307), hAPP(hAPP(c_COMBC(_1369307, _1369303, tc_HOL_Obool), _1369309), 31462 ^ [_1369303, _1369305, _1369307, _1369309]))))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1369307), hAPP(c_Set_OCollect(_1369307), hAPP(hAPP(c_COMBB(tc_fun(_1369303, tc_HOL_Obool), tc_HOL_Obool, _1369307), c_HOL_OEx(_1369303)), hAPP(hAPP(c_COMBB(tc_fun(_1369303, tc_HOL_Obool), tc_fun(_1369303, tc_HOL_Obool), _1369307), hAPP(c_COMBS(_1369303, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1369303), c_fconj), _1369305))), _1369309))))))], (31451 ^ _780086) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1369307), hAPP(c_Set_OCollect(_1369307), hAPP(hAPP(c_COMBB(tc_fun(_1369303, tc_HOL_Obool), tc_HOL_Obool, _1369307), c_HOL_OEx(_1369303)), hAPP(hAPP(c_COMBB(tc_fun(_1369303, tc_HOL_Obool), tc_fun(_1369303, tc_HOL_Obool), _1369307), hAPP(c_COMBS(_1369303, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1369303), c_fconj), _1369305))), _1369309))))), 31454 ^ _780086 : [(31455 ^ _780086) ^ [_1369586] : [hBOOL(hAPP(_1369305, _1369586)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1369307), hAPP(c_Set_OCollect(_1369307), hAPP(hAPP(c_COMBC(_1369307, _1369303, tc_HOL_Obool), _1369309), _1369586)))))]]]]], (31470 ^ _780086) ^ [_1369951] : [-(c_Nat__Transfer_Onat__set(hAPP(c_Set_OCollect(tc_Int_Oint), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fconj), hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), _1369951))))], (31472 ^ _780086) ^ [_1369979] : [-(hAPP(c_Set_OCollect(tc_Int_Oint), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fconj), hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), _1369979)) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), hAPP(c_Set_OCollect(tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_HOL_Obool, tc_Nat_Onat), _1369979), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))))], (31474 ^ _780086) ^ [_1370020] : [-(hAPP(c_Set_OCollect(tc_Nat_Onat), _1370020) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), hAPP(c_Set_OCollect(tc_Int_Oint), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fconj), hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_Int_Oint), _1370020), c_Int_Onat)))))], (31476 ^ _780086) ^ [_1370061, _1370063, _1370065] : [class_Groups_Olinordered__ab__semigroup__add(_1370061), hBOOL(hAPP(c_Finite__Set_Ofinite(_1370061), _1370063)), -(_1370063 = c_Orderings_Obot__class_Obot(tc_fun(_1370061, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1370061), _1370065), c_Big__Operators_Olinorder__class_OMin(_1370061, _1370063)) = c_Big__Operators_Olinorder__class_OMin(_1370061, hAPP(c_Set_OCollect(_1370061), hAPP(hAPP(c_COMBB(tc_fun(_1370061, tc_HOL_Obool), tc_HOL_Obool, _1370061), c_HOL_OEx(_1370061)), hAPP(hAPP(c_COMBC(_1370061, tc_fun(_1370061, tc_HOL_Obool), tc_fun(_1370061, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1370061, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1370061, tc_HOL_Obool), tc_fun(_1370061, tc_HOL_Obool)), _1370061), c_COMBS(_1370061, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1370061, tc_HOL_Obool), tc_fun(_1370061, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1370061), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1370061), c_fconj)), hAPP(hAPP(c_COMBC(_1370061, tc_fun(_1370061, _1370061), tc_fun(_1370061, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1370061, tc_HOL_Obool), tc_fun(tc_fun(_1370061, _1370061), tc_fun(_1370061, tc_HOL_Obool)), _1370061), c_COMBB(_1370061, tc_HOL_Obool, _1370061)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1370061), _1370065))))), hAPP(hAPP(c_COMBC(_1370061, tc_fun(_1370061, tc_HOL_Obool), tc_HOL_Obool), c_member(_1370061)), _1370063))))))], (31490 ^ _780086) ^ [_1370547, _1370549, _1370551] : [class_Groups_Olinordered__ab__semigroup__add(_1370547), hBOOL(hAPP(c_Finite__Set_Ofinite(_1370547), _1370549)), -(_1370549 = c_Orderings_Obot__class_Obot(tc_fun(_1370547, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1370547), _1370551), c_Big__Operators_Olinorder__class_OMax(_1370547, _1370549)) = c_Big__Operators_Olinorder__class_OMax(_1370547, hAPP(c_Set_OCollect(_1370547), hAPP(hAPP(c_COMBB(tc_fun(_1370547, tc_HOL_Obool), tc_HOL_Obool, _1370547), c_HOL_OEx(_1370547)), hAPP(hAPP(c_COMBC(_1370547, tc_fun(_1370547, tc_HOL_Obool), tc_fun(_1370547, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1370547, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1370547, tc_HOL_Obool), tc_fun(_1370547, tc_HOL_Obool)), _1370547), c_COMBS(_1370547, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1370547, tc_HOL_Obool), tc_fun(_1370547, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1370547), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1370547), c_fconj)), hAPP(hAPP(c_COMBC(_1370547, tc_fun(_1370547, _1370547), tc_fun(_1370547, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1370547, tc_HOL_Obool), tc_fun(tc_fun(_1370547, _1370547), tc_fun(_1370547, tc_HOL_Obool)), _1370547), c_COMBB(_1370547, tc_HOL_Obool, _1370547)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1370547), _1370551))))), hAPP(hAPP(c_COMBC(_1370547, tc_fun(_1370547, tc_HOL_Obool), tc_HOL_Obool), c_member(_1370547)), _1370549))))))], (31504 ^ _780086) ^ [_1371033, _1371035, _1371037] : [class_Lattices_Odistrib__lattice(_1371033), hBOOL(hAPP(c_Finite__Set_Ofinite(_1371033), _1371035)), -(_1371035 = c_Orderings_Obot__class_Obot(tc_fun(_1371033, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1371033), _1371037)), -(_1371037 = c_Orderings_Obot__class_Obot(tc_fun(_1371033, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1371033), c_Big__Operators_Olattice__class_OInf__fin(_1371033, _1371035)), c_Big__Operators_Olattice__class_OInf__fin(_1371033, _1371037)) = c_Big__Operators_Olattice__class_OInf__fin(_1371033, hAPP(c_Set_OCollect(_1371033), hAPP(hAPP(c_COMBB(tc_fun(_1371033, tc_HOL_Obool), tc_HOL_Obool, _1371033), c_HOL_OEx(_1371033)), hAPP(hAPP(c_COMBB(tc_fun(_1371033, tc_fun(_1371033, tc_HOL_Obool)), tc_fun(_1371033, tc_HOL_Obool), _1371033), hAPP(c_COMBB(tc_fun(_1371033, tc_HOL_Obool), tc_HOL_Obool, _1371033), c_HOL_OEx(_1371033))), hAPP(hAPP(c_COMBC(_1371033, tc_fun(_1371033, tc_fun(_1371033, tc_HOL_Obool)), tc_fun(_1371033, tc_fun(_1371033, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1371033, tc_fun(tc_fun(_1371033, tc_HOL_Obool), tc_fun(_1371033, tc_HOL_Obool))), tc_fun(tc_fun(_1371033, tc_fun(_1371033, tc_HOL_Obool)), tc_fun(_1371033, tc_fun(_1371033, tc_HOL_Obool))), _1371033), c_COMBS(_1371033, tc_fun(_1371033, tc_HOL_Obool), tc_fun(_1371033, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1371033, tc_fun(_1371033, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1371033, tc_fun(tc_fun(_1371033, tc_HOL_Obool), tc_fun(_1371033, tc_HOL_Obool))), _1371033), hAPP(c_COMBB(tc_fun(_1371033, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1371033, tc_HOL_Obool), tc_fun(_1371033, tc_HOL_Obool)), _1371033), c_COMBS(_1371033, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1371033, tc_fun(_1371033, tc_HOL_Obool)), tc_fun(_1371033, tc_fun(_1371033, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1371033), hAPP(c_COMBB(tc_fun(_1371033, tc_HOL_Obool), tc_fun(_1371033, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1371033), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1371033), c_fconj))), hAPP(hAPP(c_COMBC(_1371033, tc_fun(_1371033, tc_fun(_1371033, _1371033)), tc_fun(_1371033, tc_fun(_1371033, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1371033, _1371033), tc_fun(_1371033, tc_HOL_Obool)), tc_fun(tc_fun(_1371033, tc_fun(_1371033, _1371033)), tc_fun(_1371033, tc_fun(_1371033, tc_HOL_Obool))), _1371033), c_COMBB(tc_fun(_1371033, _1371033), tc_fun(_1371033, tc_HOL_Obool), _1371033)), hAPP(hAPP(c_COMBB(tc_fun(_1371033, tc_HOL_Obool), tc_fun(tc_fun(_1371033, _1371033), tc_fun(_1371033, tc_HOL_Obool)), _1371033), c_COMBB(_1371033, tc_HOL_Obool, _1371033)), c_fequal))), c_Lattices_Osemilattice__sup__class_Osup(_1371033)))))), hAPP(hAPP(c_COMBC(_1371033, tc_fun(_1371033, tc_HOL_Obool), tc_fun(_1371033, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1371033, tc_HOL_Obool), tc_fun(_1371033, tc_HOL_Obool)), _1371033), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1371033)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1371033), c_fconj), hAPP(hAPP(c_COMBC(_1371033, tc_fun(_1371033, tc_HOL_Obool), tc_HOL_Obool), c_member(_1371033)), _1371035)))), hAPP(hAPP(c_COMBC(_1371033, tc_fun(_1371033, tc_HOL_Obool), tc_HOL_Obool), c_member(_1371033)), _1371037))))))))], (31526 ^ _780086) ^ [_1372132, _1372134, _1372136] : [class_Lattices_Odistrib__lattice(_1372132), hBOOL(hAPP(c_Finite__Set_Ofinite(_1372132), _1372134)), -(_1372134 = c_Orderings_Obot__class_Obot(tc_fun(_1372132, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1372132), _1372136), c_Big__Operators_Olattice__class_OInf__fin(_1372132, _1372134)) = c_Big__Operators_Olattice__class_OInf__fin(_1372132, hAPP(c_Set_OCollect(_1372132), hAPP(hAPP(c_COMBB(tc_fun(_1372132, tc_HOL_Obool), tc_HOL_Obool, _1372132), c_HOL_OEx(_1372132)), hAPP(hAPP(c_COMBC(_1372132, tc_fun(_1372132, tc_HOL_Obool), tc_fun(_1372132, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1372132, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1372132, tc_HOL_Obool), tc_fun(_1372132, tc_HOL_Obool)), _1372132), c_COMBS(_1372132, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1372132, tc_HOL_Obool), tc_fun(_1372132, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1372132), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1372132), c_fconj)), hAPP(hAPP(c_COMBC(_1372132, tc_fun(_1372132, _1372132), tc_fun(_1372132, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1372132, tc_HOL_Obool), tc_fun(tc_fun(_1372132, _1372132), tc_fun(_1372132, tc_HOL_Obool)), _1372132), c_COMBB(_1372132, tc_HOL_Obool, _1372132)), c_fequal)), hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1372132), _1372136))))), hAPP(hAPP(c_COMBC(_1372132, tc_fun(_1372132, tc_HOL_Obool), tc_HOL_Obool), c_member(_1372132)), _1372134))))))], (31540 ^ _780086) ^ [_1372618, _1372620, _1372622] : [class_Lattices_Odistrib__lattice(_1372618), hBOOL(hAPP(c_Finite__Set_Ofinite(_1372618), _1372620)), -(_1372620 = c_Orderings_Obot__class_Obot(tc_fun(_1372618, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1372618), _1372622)), -(_1372622 = c_Orderings_Obot__class_Obot(tc_fun(_1372618, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1372618), c_Big__Operators_Olattice__class_OSup__fin(_1372618, _1372620)), c_Big__Operators_Olattice__class_OSup__fin(_1372618, _1372622)) = c_Big__Operators_Olattice__class_OSup__fin(_1372618, hAPP(c_Set_OCollect(_1372618), hAPP(hAPP(c_COMBB(tc_fun(_1372618, tc_HOL_Obool), tc_HOL_Obool, _1372618), c_HOL_OEx(_1372618)), hAPP(hAPP(c_COMBB(tc_fun(_1372618, tc_fun(_1372618, tc_HOL_Obool)), tc_fun(_1372618, tc_HOL_Obool), _1372618), hAPP(c_COMBB(tc_fun(_1372618, tc_HOL_Obool), tc_HOL_Obool, _1372618), c_HOL_OEx(_1372618))), hAPP(hAPP(c_COMBC(_1372618, tc_fun(_1372618, tc_fun(_1372618, tc_HOL_Obool)), tc_fun(_1372618, tc_fun(_1372618, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1372618, tc_fun(tc_fun(_1372618, tc_HOL_Obool), tc_fun(_1372618, tc_HOL_Obool))), tc_fun(tc_fun(_1372618, tc_fun(_1372618, tc_HOL_Obool)), tc_fun(_1372618, tc_fun(_1372618, tc_HOL_Obool))), _1372618), c_COMBS(_1372618, tc_fun(_1372618, tc_HOL_Obool), tc_fun(_1372618, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1372618, tc_fun(_1372618, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1372618, tc_fun(tc_fun(_1372618, tc_HOL_Obool), tc_fun(_1372618, tc_HOL_Obool))), _1372618), hAPP(c_COMBB(tc_fun(_1372618, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1372618, tc_HOL_Obool), tc_fun(_1372618, tc_HOL_Obool)), _1372618), c_COMBS(_1372618, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1372618, tc_fun(_1372618, tc_HOL_Obool)), tc_fun(_1372618, tc_fun(_1372618, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1372618), hAPP(c_COMBB(tc_fun(_1372618, tc_HOL_Obool), tc_fun(_1372618, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1372618), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1372618), c_fconj))), hAPP(hAPP(c_COMBC(_1372618, tc_fun(_1372618, tc_fun(_1372618, _1372618)), tc_fun(_1372618, tc_fun(_1372618, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1372618, _1372618), tc_fun(_1372618, tc_HOL_Obool)), tc_fun(tc_fun(_1372618, tc_fun(_1372618, _1372618)), tc_fun(_1372618, tc_fun(_1372618, tc_HOL_Obool))), _1372618), c_COMBB(tc_fun(_1372618, _1372618), tc_fun(_1372618, tc_HOL_Obool), _1372618)), hAPP(hAPP(c_COMBB(tc_fun(_1372618, tc_HOL_Obool), tc_fun(tc_fun(_1372618, _1372618), tc_fun(_1372618, tc_HOL_Obool)), _1372618), c_COMBB(_1372618, tc_HOL_Obool, _1372618)), c_fequal))), c_Lattices_Osemilattice__inf__class_Oinf(_1372618)))))), hAPP(hAPP(c_COMBC(_1372618, tc_fun(_1372618, tc_HOL_Obool), tc_fun(_1372618, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1372618, tc_HOL_Obool), tc_fun(_1372618, tc_HOL_Obool)), _1372618), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1372618)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1372618), c_fconj), hAPP(hAPP(c_COMBC(_1372618, tc_fun(_1372618, tc_HOL_Obool), tc_HOL_Obool), c_member(_1372618)), _1372620)))), hAPP(hAPP(c_COMBC(_1372618, tc_fun(_1372618, tc_HOL_Obool), tc_HOL_Obool), c_member(_1372618)), _1372622))))))))], (31562 ^ _780086) ^ [_1373717, _1373719, _1373721] : [class_Lattices_Odistrib__lattice(_1373717), hBOOL(hAPP(c_Finite__Set_Ofinite(_1373717), _1373719)), -(_1373719 = c_Orderings_Obot__class_Obot(tc_fun(_1373717, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1373717), _1373721), c_Big__Operators_Olattice__class_OSup__fin(_1373717, _1373719)) = c_Big__Operators_Olattice__class_OSup__fin(_1373717, hAPP(c_Set_OCollect(_1373717), hAPP(hAPP(c_COMBB(tc_fun(_1373717, tc_HOL_Obool), tc_HOL_Obool, _1373717), c_HOL_OEx(_1373717)), hAPP(hAPP(c_COMBC(_1373717, tc_fun(_1373717, tc_HOL_Obool), tc_fun(_1373717, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1373717, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1373717, tc_HOL_Obool), tc_fun(_1373717, tc_HOL_Obool)), _1373717), c_COMBS(_1373717, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1373717, tc_HOL_Obool), tc_fun(_1373717, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1373717), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1373717), c_fconj)), hAPP(hAPP(c_COMBC(_1373717, tc_fun(_1373717, _1373717), tc_fun(_1373717, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1373717, tc_HOL_Obool), tc_fun(tc_fun(_1373717, _1373717), tc_fun(_1373717, tc_HOL_Obool)), _1373717), c_COMBB(_1373717, tc_HOL_Obool, _1373717)), c_fequal)), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1373717), _1373721))))), hAPP(hAPP(c_COMBC(_1373717, tc_fun(_1373717, tc_HOL_Obool), tc_HOL_Obool), c_member(_1373717)), _1373719))))))], (31576 ^ _780086) ^ [_1374203, _1374205, _1374207] : [class_Orderings_Olinorder(_1374203), hBOOL(hAPP(c_Finite__Set_Ofinite(_1374203), _1374205)), -(_1374205 = c_Orderings_Obot__class_Obot(tc_fun(_1374203, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1374203), _1374207)), -(_1374207 = c_Orderings_Obot__class_Obot(tc_fun(_1374203, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1374203), c_Big__Operators_Olattice_OSup__fin(_1374203, c_Orderings_Oord__class_Omax(_1374203), _1374205)), c_Big__Operators_Olattice_OSup__fin(_1374203, c_Orderings_Oord__class_Omax(_1374203), _1374207)) = c_Big__Operators_Olattice_OSup__fin(_1374203, c_Orderings_Oord__class_Omax(_1374203), hAPP(c_Set_OCollect(_1374203), hAPP(hAPP(c_COMBB(tc_fun(_1374203, tc_HOL_Obool), tc_HOL_Obool, _1374203), c_HOL_OEx(_1374203)), hAPP(hAPP(c_COMBB(tc_fun(_1374203, tc_fun(_1374203, tc_HOL_Obool)), tc_fun(_1374203, tc_HOL_Obool), _1374203), hAPP(c_COMBB(tc_fun(_1374203, tc_HOL_Obool), tc_HOL_Obool, _1374203), c_HOL_OEx(_1374203))), hAPP(hAPP(c_COMBC(_1374203, tc_fun(_1374203, tc_fun(_1374203, tc_HOL_Obool)), tc_fun(_1374203, tc_fun(_1374203, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1374203, tc_fun(tc_fun(_1374203, tc_HOL_Obool), tc_fun(_1374203, tc_HOL_Obool))), tc_fun(tc_fun(_1374203, tc_fun(_1374203, tc_HOL_Obool)), tc_fun(_1374203, tc_fun(_1374203, tc_HOL_Obool))), _1374203), c_COMBS(_1374203, tc_fun(_1374203, tc_HOL_Obool), tc_fun(_1374203, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1374203, tc_fun(_1374203, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1374203, tc_fun(tc_fun(_1374203, tc_HOL_Obool), tc_fun(_1374203, tc_HOL_Obool))), _1374203), hAPP(c_COMBB(tc_fun(_1374203, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1374203, tc_HOL_Obool), tc_fun(_1374203, tc_HOL_Obool)), _1374203), c_COMBS(_1374203, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1374203, tc_fun(_1374203, tc_HOL_Obool)), tc_fun(_1374203, tc_fun(_1374203, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1374203), hAPP(c_COMBB(tc_fun(_1374203, tc_HOL_Obool), tc_fun(_1374203, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1374203), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1374203), c_fconj))), hAPP(hAPP(c_COMBC(_1374203, tc_fun(_1374203, tc_fun(_1374203, _1374203)), tc_fun(_1374203, tc_fun(_1374203, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1374203, _1374203), tc_fun(_1374203, tc_HOL_Obool)), tc_fun(tc_fun(_1374203, tc_fun(_1374203, _1374203)), tc_fun(_1374203, tc_fun(_1374203, tc_HOL_Obool))), _1374203), c_COMBB(tc_fun(_1374203, _1374203), tc_fun(_1374203, tc_HOL_Obool), _1374203)), hAPP(hAPP(c_COMBB(tc_fun(_1374203, tc_HOL_Obool), tc_fun(tc_fun(_1374203, _1374203), tc_fun(_1374203, tc_HOL_Obool)), _1374203), c_COMBB(_1374203, tc_HOL_Obool, _1374203)), c_fequal))), c_Orderings_Oord__class_Omin(_1374203)))))), hAPP(hAPP(c_COMBC(_1374203, tc_fun(_1374203, tc_HOL_Obool), tc_fun(_1374203, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1374203, tc_HOL_Obool), tc_fun(_1374203, tc_HOL_Obool)), _1374203), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1374203)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1374203), c_fconj), hAPP(hAPP(c_COMBC(_1374203, tc_fun(_1374203, tc_HOL_Obool), tc_HOL_Obool), c_member(_1374203)), _1374205)))), hAPP(hAPP(c_COMBC(_1374203, tc_fun(_1374203, tc_HOL_Obool), tc_HOL_Obool), c_member(_1374203)), _1374207))))))))], (31598 ^ _780086) ^ [_1375320, _1375322, _1375324, _1375326, _1375328, _1375330] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1375320), _1375322)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1375324), _1375326)), 31608 ^ _780086 : [(31609 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1375324), 31607 ^ [_1375320, _1375322, _1375324, _1375326, _1375328, _1375330]), _1375326)))], (31611 ^ _780086) ^ [] : [hAPP(c_Finite__Set_Ocard(_1375320), hAPP(c_Set_OCollect(_1375320), hAPP(hAPP(c_COMBS(_1375320, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1375320), c_fconj), hAPP(hAPP(c_COMBC(_1375320, tc_fun(_1375320, tc_HOL_Obool), tc_HOL_Obool), c_member(_1375320)), _1375322))), hAPP(hAPP(c_COMBC(_1375320, _1375324, tc_HOL_Obool), _1375328), 31607 ^ [_1375320, _1375322, _1375324, _1375326, _1375328, _1375330])))) = hAPP(_1375330, 31607 ^ [_1375320, _1375322, _1375324, _1375326, _1375328, _1375330])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1375320, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1375324, tc_HOL_Obool), tc_Nat_Onat, _1375320), c_Finite__Set_Ocard(_1375324)), hAPP(hAPP(c_COMBB(tc_fun(_1375324, tc_HOL_Obool), tc_fun(_1375324, tc_HOL_Obool), _1375320), c_Set_OCollect(_1375324)), hAPP(hAPP(c_COMBB(tc_fun(_1375324, tc_HOL_Obool), tc_fun(_1375324, tc_HOL_Obool), _1375320), hAPP(c_COMBS(_1375324, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1375324), c_fconj), hAPP(hAPP(c_COMBC(_1375324, tc_fun(_1375324, tc_HOL_Obool), tc_HOL_Obool), c_member(_1375324)), _1375326)))), _1375328)))), _1375322) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1375324, tc_Nat_Onat), _1375330), _1375326))], (31615 ^ _780086) ^ [_1376045, _1376047] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1376045), _1376047)), -(_1376047 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1376045, 31619 ^ [_1376045, _1376047]), hAPP(c_Set_OCollect(tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), 31618 ^ [_1376045, _1376047]))))], (31623 ^ _780086) ^ [_1376176, _1376178] : [31624 ^ _780086 : [(31625 ^ _780086) ^ [_1376240, _1376242] : [_1376178 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1376176, _1376240), hAPP(c_Set_OCollect(tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1376242)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1376176), _1376178)))], (31629 ^ _780086) ^ [_1376311, _1376313, _1376315, _1376317] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1376311), _1376313))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1376315), hAPP(c_Set_Oimage(_1376311, _1376315, _1376317), _1376313))), 31637 ^ _780086 : [(31638 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1376311), 31636 ^ [_1376311, _1376313, _1376315, _1376317]), _1376313)))], (31640 ^ _780086) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1376311), hAPP(c_Set_OCollect(_1376311), hAPP(hAPP(c_COMBS(_1376311, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1376311), c_fconj), hAPP(hAPP(c_COMBC(_1376311, tc_fun(_1376311, tc_HOL_Obool), tc_HOL_Obool), c_member(_1376311)), _1376313))), hAPP(hAPP(c_COMBC(_1376311, _1376315, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1376315, tc_fun(_1376315, tc_HOL_Obool), _1376311), c_fequal), _1376317)), hAPP(_1376317, 31636 ^ [_1376311, _1376313, _1376315, _1376317]))))))]]], (31642 ^ _780086) ^ [_1376776, _1376778, _1376780] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1376776), _1376778)), c_Fun_Oinj__on(_1376776, tc_fun(tc_fun(_1376776, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1376776, tc_fun(tc_prod(_1376776, _1376776), tc_HOL_Obool), tc_fun(tc_fun(_1376776, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1376776, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1376776, _1376776), tc_HOL_Obool), tc_fun(tc_fun(_1376776, tc_HOL_Obool), tc_HOL_Obool)), _1376776), c_Equiv__Relations_Oquotient(_1376776)), hAPP(hAPP(c_COMBC(_1376776, tc_fun(_1376776, tc_HOL_Obool), tc_fun(_1376776, tc_HOL_Obool)), c_Set_Oinsert(_1376776)), c_Orderings_Obot__class_Obot(tc_fun(_1376776, tc_HOL_Obool))))), _1376780), _1376778), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1376776, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1376776), _1376778), _1376780)) = hAPP(c_Finite__Set_Ocard(_1376776), _1376778))], (31652 ^ _780086) ^ [_1377143, _1377145, _1377147] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1377143), _1377145), _1377147) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1377143, tc_HOL_Obool), tc_HOL_Obool)), -(_1377145 = c_Orderings_Obot__class_Obot(tc_fun(_1377143, tc_HOL_Obool)))], (31658 ^ _780086) ^ [_1377260, _1377262, _1377264] : [_1377262 = c_Orderings_Obot__class_Obot(tc_fun(_1377260, tc_HOL_Obool)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1377260), _1377262), _1377264) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1377260, tc_HOL_Obool), tc_HOL_Obool)))], (31664 ^ _780086) ^ [_1377401, _1377403, _1377405] : [c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1377401, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1377401), _1377403), _1377405), -(_1377403 = c_Orderings_Obot__class_Obot(tc_fun(_1377401, tc_HOL_Obool)))], (31670 ^ _780086) ^ [_1377518, _1377520, _1377522] : [_1377520 = c_Orderings_Obot__class_Obot(tc_fun(_1377518, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1377518, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1377518), _1377520), _1377522))], (31676 ^ _780086) ^ [_1377641, _1377643] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1377641), c_Orderings_Obot__class_Obot(tc_fun(_1377641, tc_HOL_Obool))), _1377643) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1377641, tc_HOL_Obool), tc_HOL_Obool)))], (31678 ^ _780086) ^ [_1377687, _1377689, _1377691, _1377693] : [c_Fun_Oinj__on(_1377687, tc_fun(tc_fun(_1377687, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1377687, tc_fun(tc_prod(_1377687, _1377687), tc_HOL_Obool), tc_fun(tc_fun(_1377687, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1377687, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1377687, _1377687), tc_HOL_Obool), tc_fun(tc_fun(_1377687, tc_HOL_Obool), tc_HOL_Obool)), _1377687), c_Equiv__Relations_Oquotient(_1377687)), hAPP(hAPP(c_COMBC(_1377687, tc_fun(_1377687, tc_HOL_Obool), tc_fun(_1377687, tc_HOL_Obool)), c_Set_Oinsert(_1377687)), c_Orderings_Obot__class_Obot(tc_fun(_1377687, tc_HOL_Obool))))), _1377689), _1377691), hBOOL(hAPP(hAPP(c_member(_1377687), _1377693), _1377691)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1377687), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1377687, tc_HOL_Obool)), _1377691), hAPP(hAPP(c_Set_Oinsert(_1377687), _1377693), c_Orderings_Obot__class_Obot(tc_fun(_1377687, tc_HOL_Obool))))), _1377689) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(_1377687, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1377687), _1377691), _1377689)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1377687), hAPP(hAPP(c_Set_Oinsert(_1377687), _1377693), c_Orderings_Obot__class_Obot(tc_fun(_1377687, tc_HOL_Obool)))), _1377689)))], (31688 ^ _780086) ^ [_1378154, _1378156, _1378158] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1378154), _1378156), _1378158) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1378154, tc_fun(tc_fun(_1378154, tc_HOL_Obool), tc_HOL_Obool)), _1378156), hAPP(hAPP(c_COMBC(_1378154, tc_fun(tc_fun(_1378154, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1378154, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1378154, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1378154, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1378154, tc_HOL_Obool), tc_HOL_Obool)), _1378154), c_Set_Oinsert(tc_fun(_1378154, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1378154, tc_HOL_Obool), tc_fun(_1378154, tc_HOL_Obool), _1378154), c_Relation_OImage(_1378154, _1378154, _1378158)), hAPP(hAPP(c_COMBC(_1378154, tc_fun(_1378154, tc_HOL_Obool), tc_fun(_1378154, tc_HOL_Obool)), c_Set_Oinsert(_1378154)), c_Orderings_Obot__class_Obot(tc_fun(_1378154, tc_HOL_Obool)))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1378154, tc_HOL_Obool), tc_HOL_Obool)))))], (31690 ^ _780086) ^ [_1378310, _1378312, _1378314] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1378310), hAPP(hAPP(c_Set_Oinsert(_1378310), _1378312), c_Orderings_Obot__class_Obot(tc_fun(_1378310, tc_HOL_Obool)))), _1378314) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1378310, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1378310, _1378310, _1378314), hAPP(hAPP(c_Set_Oinsert(_1378310), _1378312), c_Orderings_Obot__class_Obot(tc_fun(_1378310, tc_HOL_Obool))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1378310, tc_HOL_Obool), tc_HOL_Obool))))], (31692 ^ _780086) ^ [_1378397, _1378399, _1378401, _1378403] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1378397), _1378399)), 31698 ^ _780086 : [(31699 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1378397), 31697 ^ [_1378397, _1378399, _1378401, _1378403]), _1378399)))], (31701 ^ _780086) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1378401), hAPP(_1378403, 31697 ^ [_1378397, _1378399, _1378401, _1378403])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1378401), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1378397, tc_fun(_1378401, tc_HOL_Obool)), _1378399), _1378403))))], (31705 ^ _780086) ^ [_1378684, _1378686] : [31707 ^ _780086 : [(31708 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 31706 ^ [_1378684, _1378686]), _1378684)))], (31710 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1378686), 31706 ^ [_1378684, _1378686]))]], -(c_Fun_Oinj__on(tc_Nat_Onat, tc_Nat_Onat, hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat)), _1378686), _1378684))], (31714 ^ _780086) ^ [_1378859, _1378861, _1378863, _1378865] : [hBOOL(hAPP(hAPP(c_member(_1378859), _1378861), _1378863)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1378859, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1378859, _1378859, _1378865), hAPP(hAPP(c_Set_Oinsert(_1378859), _1378861), c_Orderings_Obot__class_Obot(tc_fun(_1378859, tc_HOL_Obool))))), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1378859), _1378863), _1378865))))], (31720 ^ _780086) ^ [_1379030, _1379032, _1379034, _1379036] : [-(hAPP(c_Relation_OImage(_1379030, _1379032, _1379034), _1379036) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1379030, tc_fun(_1379032, tc_HOL_Obool)), _1379036), hAPP(hAPP(c_COMBB(tc_fun(_1379030, tc_HOL_Obool), tc_fun(_1379032, tc_HOL_Obool), _1379030), c_Relation_OImage(_1379030, _1379032, _1379034)), hAPP(hAPP(c_COMBC(_1379030, tc_fun(_1379030, tc_HOL_Obool), tc_fun(_1379030, tc_HOL_Obool)), c_Set_Oinsert(_1379030)), c_Orderings_Obot__class_Obot(tc_fun(_1379030, tc_HOL_Obool))))))], (31722 ^ _780086) ^ [_1379121, _1379123, _1379125, _1379127, _1379129, _1379131] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1379121, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1379123, _1379121, _1379125), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1379127, tc_fun(_1379123, tc_HOL_Obool)), _1379129), _1379131))), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1379127, tc_fun(_1379121, tc_HOL_Obool)), _1379129), hAPP(hAPP(c_COMBB(tc_fun(_1379123, tc_HOL_Obool), tc_fun(_1379121, tc_HOL_Obool), _1379127), c_Relation_OImage(_1379123, _1379121, _1379125)), _1379131)))))], (31724 ^ _780086) ^ [_1379215, _1379217, _1379219, _1379221, _1379223] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1379215, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1379217, _1379215, _1379219), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1379217, tc_HOL_Obool)), _1379221), _1379223))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1379215, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1379217, _1379215, _1379219), _1379221)), hAPP(c_Relation_OImage(_1379217, _1379215, _1379219), _1379223)))))], (31726 ^ _780086) ^ [_1379299, _1379301, _1379303, _1379305, _1379307, _1379309] : [-(hAPP(c_Relation_OImage(_1379299, _1379301, _1379303), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1379305, tc_fun(_1379299, tc_HOL_Obool)), _1379307), _1379309)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1379305, tc_fun(_1379301, tc_HOL_Obool)), _1379307), hAPP(hAPP(c_COMBB(tc_fun(_1379299, tc_HOL_Obool), tc_fun(_1379301, tc_HOL_Obool), _1379305), c_Relation_OImage(_1379299, _1379301, _1379303)), _1379309)))], (31728 ^ _780086) ^ [_1379383, _1379385, _1379387] : [-(hAPP(c_Relation_OImage(_1379383, _1379385, _1379387), c_Orderings_Obot__class_Obot(tc_fun(_1379383, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1379385, tc_HOL_Obool)))], (31730 ^ _780086) ^ [_1379427, _1379429, _1379431, _1379433, _1379435, _1379437] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1379427, _1379429), tc_HOL_Obool)), _1379431), _1379433)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1379427, tc_HOL_Obool)), _1379435), _1379437)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1379429, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1379427, _1379429, _1379431), _1379435)), hAPP(c_Relation_OImage(_1379427, _1379429, _1379433), _1379437))))], (31740 ^ _780086) ^ [_1379666, _1379668, _1379670, _1379672, _1379674] : [-(hAPP(c_Relation_OImage(_1379666, _1379668, _1379670), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1379666, tc_HOL_Obool)), _1379672), _1379674)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1379668, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1379666, _1379668, _1379670), _1379672)), hAPP(c_Relation_OImage(_1379666, _1379668, _1379670), _1379674)))], (31742 ^ _780086) ^ [_1379740, _1379742, _1379744, _1379746, _1379748] : [-(hAPP(c_Relation_OImage(_1379740, _1379742, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1379740, _1379742), tc_HOL_Obool)), _1379744), _1379746)), _1379748) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1379742, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1379740, _1379742, _1379744), _1379748)), hAPP(c_Relation_OImage(_1379740, _1379742, _1379746), _1379748)))], (31744 ^ _780086) ^ [_1379817, _1379819, _1379821, _1379823] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1379817, tc_HOL_Obool)), _1379819), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1379817), _1379821), _1379823))), 31748 ^ _780086 : [(31749 ^ _780086) ^ [] : [-(_1379819 = hAPP(c_Relation_OImage(_1379817, _1379817, _1379823), hAPP(hAPP(c_Set_Oinsert(_1379817), 31747 ^ [_1379817, _1379819, _1379821, _1379823]), c_Orderings_Obot__class_Obot(tc_fun(_1379817, tc_HOL_Obool)))))], (31751 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1379817), 31747 ^ [_1379817, _1379819, _1379821, _1379823]), _1379821)))]]], (31753 ^ _780086) ^ [_1380054, _1380056] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1380054)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1380056)), hAPP(c_Int_Onat, _1380054)) = hAPP(c_Int_Onat, _1380056))], (31759 ^ _780086) ^ [_1380159, _1380161] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1380159))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1380161)), hAPP(c_Int_Onat, _1380159)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1380161), _1380159)), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat)), tc_Int_Oint), c_If(tc_Nat_Onat)), c_Nat__Numeral_Oneg)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), c_Int_Onat)))], (31765 ^ _780086) ^ [_1380223, _1380225, _1380227, _1380229] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1380223, tc_Nat_Onat), _1380225), _1380227) = hAPP(c_Nat_OSuc, _1380229), 31769 ^ _780086 : [(31770 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1380223), 31768 ^ [_1380223, _1380225, _1380227, _1380229]), _1380227)))], (31772 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1380225, 31768 ^ [_1380223, _1380225, _1380227, _1380229]))))]]], (31774 ^ _780086) ^ [_1380405, _1380407, _1380409] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1380405, _1380407) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1380409, _1380407), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1380409), _1380405)), -(_1380405 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1380409), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1380407), 31781 ^ [_1380405, _1380407, _1380409])))], (31785 ^ _780086) ^ [_1380611] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1380611)))], (31787 ^ _780086) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (31789 ^ _780086) ^ [_1380663, _1380665, _1380667] : [_1380663 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1380665, _1380665), tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1380665, _1380665), tc_HOL_Obool)), _1380663), _1380667)))], (31795 ^ _780086) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (31797 ^ _780086) ^ [_1380814] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1380814))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1380814)))], (31803 ^ _780086) ^ [_1380848] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1380848)), hBOOL(hAPP(c_Nat__Numeral_Oneg, _1380848))], (31809 ^ _780086) ^ [_1380946] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1380946)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1380946), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (31815 ^ _780086) ^ [_1381031] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1381031), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1381031)))], (31821 ^ _780086) ^ [_1381122] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1381122)), -(hAPP(c_Int_Onat, _1381122) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31827 ^ _780086) ^ [_1381203] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1381203))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1381203)) = _1381203)], (31833 ^ _780086) ^ [_1381245] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1381245))))))], (31835 ^ _780086) ^ [_1381279, _1381281, _1381283] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(_1381279, _1381281, _1381283)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_1381281)), c_Com_Ocom_Ocom__size(_1381283))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (31837 ^ _780086) ^ [_1381328, _1381330, _1381332] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OCond(_1381328, _1381330, _1381332)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1381330)), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1381332))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (31839 ^ _780086) ^ [_1381380, _1381382, _1381384, _1381386] : [class_Groups_Ocomm__monoid__mult(_1381380), hBOOL(hAPP(c_Finite__Set_Ofinite(_1381382), _1381384)), 31849 ^ _780086 : [(31850 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1381382), 31848 ^ [_1381380, _1381382, _1381384, _1381386]), _1381384)))], (31852 ^ _780086) ^ [] : [hAPP(_1381386, 31848 ^ [_1381380, _1381382, _1381384, _1381386]) = c_Groups_Oone__class_Oone(_1381380)]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1381380, _1381382, c_Groups_Otimes__class_Otimes(_1381380)), _1381386), c_Groups_Oone__class_Oone(_1381380)), _1381384) = c_Groups_Oone__class_Oone(_1381380))], (31856 ^ _780086) ^ [_1381721, _1381723] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1381721), _1381723)), 31862 ^ _780086 : [(31863 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1381721), 31861 ^ [_1381721, _1381723]), _1381723)))], (31865 ^ _780086) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(c_Finite__Set_Ocard(_1381721), _1381723) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31869 ^ _780086) ^ [_1381948, _1381950, _1381952, _1381954, _1381956, _1381958] : [c_Com_Ocom_OCond(_1381948, _1381950, _1381952) = c_Com_Ocom_OCond(_1381954, _1381956, _1381958), 31872 ^ _780086 : [(31873 ^ _780086) ^ [] : [-(_1381948 = _1381954)], (31875 ^ _780086) ^ [] : [-(_1381950 = _1381956)], (31877 ^ _780086) ^ [] : [-(_1381952 = _1381958)]]], (31879 ^ _780086) ^ [_1382095, _1382097, _1382099, _1382101, _1382103, _1382105] : [-(c_Com_Ocom_OCond(_1382095, _1382097, _1382099) = c_Com_Ocom_OCond(_1382101, _1382103, _1382105)), _1382095 = _1382101, _1382097 = _1382103, _1382099 = _1382105], (31893 ^ _780086) ^ [_1382339, _1382341, _1382343, _1382345, _1382347] : [c_Com_Ocom_OCond(_1382339, _1382341, _1382343) = c_Com_Ocom_OWhile(_1382345, _1382347)], (31895 ^ _780086) ^ [_1382398, _1382400, _1382402, _1382404, _1382406] : [c_Com_Ocom_OWhile(_1382398, _1382400) = c_Com_Ocom_OCond(_1382402, _1382404, _1382406)], (31897 ^ _780086) ^ [_1382457, _1382459, _1382461, _1382463, _1382465] : [c_Com_Ocom_OCond(_1382457, _1382459, _1382461) = c_Com_Ocom_OSemi(_1382463, _1382465)], (31899 ^ _780086) ^ [_1382516, _1382518, _1382520, _1382522, _1382524] : [c_Com_Ocom_OSemi(_1382516, _1382518) = c_Com_Ocom_OCond(_1382520, _1382522, _1382524)], (31901 ^ _780086) ^ [_1382569, _1382571, _1382573] : [c_Com_Ocom_OCond(_1382569, _1382571, _1382573) = c_Com_Ocom_OSKIP], (31903 ^ _780086) ^ [_1382615, _1382617, _1382619] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OCond(_1382615, _1382617, _1382619)], (31905 ^ _780086) ^ [_1382646, _1382648, _1382650] : [31907 ^ _780086 : [(31908 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 31906 ^ [_1382646, _1382648, _1382650]), _1382646)))], (31910 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1382648, 31906 ^ [_1382646, _1382648, _1382650])))], (31912 ^ _780086) ^ [] : [hBOOL(hAPP(_1382648, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, 31906 ^ [_1382646, _1382648, _1382650]), _1382646)))]], hBOOL(hAPP(_1382648, _1382650)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1382650), _1382646)), -(hBOOL(hAPP(_1382648, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (31924 ^ _780086) ^ [_1383008, _1383010, _1383012] : [31926 ^ _780086 : [(31927 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1383008, tc_HOL_Obool)), 31925 ^ [_1383008, _1383010, _1383012]), _1383010)))], (31929 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1383008), _1383012), 31925 ^ [_1383008, _1383010, _1383012]))]], -(hBOOL(hAPP(hAPP(c_member(_1383008), _1383012), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1383008, tc_HOL_Obool), _1383010))))], (31933 ^ _780086) ^ [_1383224, _1383226, _1383228, _1383230, _1383232, _1383234] : [class_Groups_Oab__semigroup__mult(_1383224), hBOOL(hAPP(c_Finite__Set_Ofinite(_1383226), _1383228)), 31943 ^ _780086 : [(31944 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1383226), 31942 ^ [_1383224, _1383226, _1383228, _1383230, _1383232, _1383234]), _1383228)))], (31946 ^ _780086) ^ [] : [hAPP(_1383230, 31942 ^ [_1383224, _1383226, _1383228, _1383230, _1383232, _1383234]) = hAPP(_1383232, 31942 ^ [_1383224, _1383226, _1383228, _1383230, _1383232, _1383234])]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1383224, _1383226, c_Groups_Otimes__class_Otimes(_1383224)), _1383230), _1383234), _1383228) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1383224, _1383226, c_Groups_Otimes__class_Otimes(_1383224)), _1383232), _1383234), _1383228))], (31950 ^ _780086) ^ [_1383629, _1383631, _1383633, _1383635] : [class_Lattices_Osemilattice__inf(_1383629), hBOOL(hAPP(c_Finite__Set_Ofinite(_1383629), _1383631)), 31960 ^ _780086 : [(31961 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1383629), 31959 ^ [_1383629, _1383631, _1383633, _1383635]), _1383631)))], (31963 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1383629), _1383633), 31959 ^ [_1383629, _1383631, _1383633, _1383635]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1383629), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1383629), _1383633), _1383635)), hAPP(hAPP(c_Finite__Set_Ofold(_1383629, _1383629, c_Lattices_Osemilattice__inf__class_Oinf(_1383629)), _1383635), _1383631))))], (31967 ^ _780086) ^ [_1383993, _1383995, _1383997, _1383999] : [class_Lattices_Osemilattice__sup(_1383993), hBOOL(hAPP(c_Finite__Set_Ofinite(_1383993), _1383995)), 31977 ^ _780086 : [(31978 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1383993), 31976 ^ [_1383993, _1383995, _1383997, _1383999]), _1383995)))], (31980 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1383993), 31976 ^ [_1383993, _1383995, _1383997, _1383999]), _1383997))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1383993), hAPP(hAPP(c_Finite__Set_Ofold(_1383993, _1383993, c_Lattices_Osemilattice__sup__class_Osup(_1383993)), _1383999), _1383995)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1383993), _1383997), _1383999))))], (31984 ^ _780086) ^ [_1384357] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1384357))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1384357) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1384357)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (31990 ^ _780086) ^ [_1384472, _1384474, _1384476, _1384478, _1384480] : [c_Equiv__Relations_Oequiv(_1384472, _1384474, _1384476), hBOOL(hAPP(hAPP(c_member(tc_fun(_1384472, tc_HOL_Obool)), _1384478), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1384472), _1384474), _1384476))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1384472, tc_HOL_Obool)), _1384480), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1384472), _1384474), _1384476))), -(_1384478 = _1384480), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1384472, tc_HOL_Obool)), _1384478), _1384480) = c_Orderings_Obot__class_Obot(tc_fun(_1384472, tc_HOL_Obool)))], (32008 ^ _780086) ^ [_1384790, _1384792, _1384794] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(_1384790, _1384792, _1384794)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_1384794)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (32010 ^ _780086) ^ [_1384831, _1384833] : [class_Int_Onumber__ring(_1384831), 32013 ^ _780086 : [(32014 ^ _780086) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1384833))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1384831), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1384833)) = c_Groups_Ozero__class_Ozero(_1384831))], (32020 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1384833)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1384831), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1384833)) = hAPP(c_Int_Onumber__class_Onumber__of(_1384831), _1384833))]]], (32026 ^ _780086) ^ [_1385071, _1385073] : [class_Int_Onumber__ring(_1385071), 32029 ^ _780086 : [(32030 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1385073))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1385071), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1385073)) = hAPP(c_Int_Onumber__class_Onumber__of(_1385071), _1385073))], (32036 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1385073)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1385071), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1385073)) = c_Groups_Ozero__class_Ozero(_1385071))]]], (32042 ^ _780086) ^ [_1385311, _1385313] : [class_Int_Onumber__ring(_1385311), -(hAPP(c_Int_Onumber__class_Onumber__of(_1385311), _1385313) = hAPP(c_Int_Oring__1__class_Oof__int(_1385311), _1385313))], (32048 ^ _780086) ^ [_1385406, _1385408] : [class_Int_Onumber__ring(_1385406), -(hAPP(c_Int_Oring__1__class_Oof__int(_1385406), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1385408)) = hAPP(c_Int_Onumber__class_Onumber__of(_1385406), _1385408))], (32054 ^ _780086) ^ [_1385534, _1385536, _1385538, _1385540, _1385542, _1385544] : [c_Com_Ocom_OLocal(_1385534, _1385536, _1385538) = c_Com_Ocom_OLocal(_1385540, _1385542, _1385544), 32057 ^ _780086 : [(32058 ^ _780086) ^ [] : [-(_1385534 = _1385540)], (32060 ^ _780086) ^ [] : [-(_1385536 = _1385542)], (32062 ^ _780086) ^ [] : [-(_1385538 = _1385544)]]], (32064 ^ _780086) ^ [_1385681, _1385683, _1385685, _1385687, _1385689, _1385691] : [-(c_Com_Ocom_OLocal(_1385681, _1385683, _1385685) = c_Com_Ocom_OLocal(_1385687, _1385689, _1385691)), _1385681 = _1385687, _1385683 = _1385689, _1385685 = _1385691], (32078 ^ _780086) ^ [_1385904, _1385906, _1385908] : [class_Int_Onumber(_1385904), 32081 ^ _780086 : [(32082 ^ _780086) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1385904), _1385906) = _1385908, -(_1385908 = hAPP(c_Int_Onumber__class_Onumber__of(_1385904), _1385906))], (32088 ^ _780086) ^ [] : [_1385908 = hAPP(c_Int_Onumber__class_Onumber__of(_1385904), _1385906), -(hAPP(c_Int_Onumber__class_Onumber__of(_1385904), _1385906) = _1385908)]]], (32094 ^ _780086) ^ [_1386145, _1386147, _1386149] : [class_Int_Onumber__ring(_1386145), class_Int_Oring__char__0(_1386145), 32101 ^ _780086 : [(32102 ^ _780086) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1386145), _1386147) = hAPP(c_Int_Onumber__class_Onumber__of(_1386145), _1386149), -(_1386147 = _1386149)], (32108 ^ _780086) ^ [] : [_1386147 = _1386149, -(hAPP(c_Int_Onumber__class_Onumber__of(_1386145), _1386147) = hAPP(c_Int_Onumber__class_Onumber__of(_1386145), _1386149))]]], (32114 ^ _780086) ^ [_1386461, _1386463, _1386465, _1386467, _1386469] : [c_Com_Ocom_OWhile(_1386461, _1386463) = c_Com_Ocom_OLocal(_1386465, _1386467, _1386469)], (32116 ^ _780086) ^ [_1386520, _1386522, _1386524, _1386526, _1386528] : [c_Com_Ocom_OLocal(_1386520, _1386522, _1386524) = c_Com_Ocom_OWhile(_1386526, _1386528)], (32118 ^ _780086) ^ [_1386582, _1386584, _1386586, _1386588, _1386590, _1386592] : [c_Com_Ocom_OCond(_1386582, _1386584, _1386586) = c_Com_Ocom_OLocal(_1386588, _1386590, _1386592)], (32120 ^ _780086) ^ [_1386647, _1386649, _1386651, _1386653, _1386655, _1386657] : [c_Com_Ocom_OLocal(_1386647, _1386649, _1386651) = c_Com_Ocom_OCond(_1386653, _1386655, _1386657)], (32122 ^ _780086) ^ [_1386709, _1386711, _1386713, _1386715, _1386717] : [c_Com_Ocom_OLocal(_1386709, _1386711, _1386713) = c_Com_Ocom_OSemi(_1386715, _1386717)], (32124 ^ _780086) ^ [_1386768, _1386770, _1386772, _1386774, _1386776] : [c_Com_Ocom_OSemi(_1386768, _1386770) = c_Com_Ocom_OLocal(_1386772, _1386774, _1386776)], (32126 ^ _780086) ^ [_1386821, _1386823, _1386825] : [c_Com_Ocom_OLocal(_1386821, _1386823, _1386825) = c_Com_Ocom_OSKIP], (32128 ^ _780086) ^ [_1386867, _1386869, _1386871] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OLocal(_1386867, _1386869, _1386871)], (32130 ^ _780086) ^ [_1386898, _1386900, _1386902] : [class_Int_Onumber(_1386898), class_Orderings_Olinorder(_1386898), 32137 ^ _780086 : [(32138 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1386898), hAPP(c_Int_Onumber__class_Onumber__of(_1386898), _1386900)), hAPP(c_Int_Onumber__class_Onumber__of(_1386898), _1386902))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1386898), hAPP(c_Int_Onumber__class_Onumber__of(_1386898), _1386902)), hAPP(c_Int_Onumber__class_Onumber__of(_1386898), _1386900)))], (32144 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1386898), hAPP(c_Int_Onumber__class_Onumber__of(_1386898), _1386902)), hAPP(c_Int_Onumber__class_Onumber__of(_1386898), _1386900)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1386898), hAPP(c_Int_Onumber__class_Onumber__of(_1386898), _1386900)), hAPP(c_Int_Onumber__class_Onumber__of(_1386898), _1386902))))]]], (32150 ^ _780086) ^ [_1387225, _1387227, _1387229, _1387231] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387225), hAPP(c_Int_Onumber__class_Onumber__of(_1387225), _1387227)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1387225), _1387229), _1387231)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1387225), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387225), hAPP(c_Int_Onumber__class_Onumber__of(_1387225), _1387227)), _1387229)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387225), hAPP(c_Int_Onumber__class_Onumber__of(_1387225), _1387227)), _1387231))), class_Int_Onumber(_1387225), class_Rings_Osemiring(_1387225)], (32160 ^ _780086) ^ [_1387468, _1387470, _1387472, _1387474] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387468), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1387468), _1387470), _1387472)), hAPP(c_Int_Onumber__class_Onumber__of(_1387468), _1387474)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1387468), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387468), _1387470), hAPP(c_Int_Onumber__class_Onumber__of(_1387468), _1387474))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387468), _1387472), hAPP(c_Int_Onumber__class_Onumber__of(_1387468), _1387474)))), class_Int_Onumber(_1387468), class_Rings_Osemiring(_1387468)], (32170 ^ _780086) ^ [_1387711, _1387713, _1387715, _1387717] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387711), hAPP(c_Int_Onumber__class_Onumber__of(_1387711), _1387713)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1387711), _1387715), _1387717)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1387711), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387711), hAPP(c_Int_Onumber__class_Onumber__of(_1387711), _1387713)), _1387715)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387711), hAPP(c_Int_Onumber__class_Onumber__of(_1387711), _1387713)), _1387717))), class_Int_Onumber(_1387711), class_Rings_Oring(_1387711)], (32180 ^ _780086) ^ [_1387954, _1387956, _1387958, _1387960] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387954), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1387954), _1387956), _1387958)), hAPP(c_Int_Onumber__class_Onumber__of(_1387954), _1387960)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1387954), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387954), _1387956), hAPP(c_Int_Onumber__class_Onumber__of(_1387954), _1387960))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387954), _1387958), hAPP(c_Int_Onumber__class_Onumber__of(_1387954), _1387960)))), class_Int_Onumber(_1387954), class_Rings_Oring(_1387954)], (32190 ^ _780086) ^ [_1388197, _1388199, _1388201] : [class_Int_Onumber__ring(_1388197), class_Rings_Olinordered__idom(_1388197), 32197 ^ _780086 : [(32198 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1388197), hAPP(c_Int_Onumber__class_Onumber__of(_1388197), _1388199)), hAPP(c_Int_Onumber__class_Onumber__of(_1388197), _1388201))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1388199), _1388201)))], (32204 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1388199), _1388201)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1388197), hAPP(c_Int_Onumber__class_Onumber__of(_1388197), _1388199)), hAPP(c_Int_Onumber__class_Onumber__of(_1388197), _1388201))))]]], (32210 ^ _780086) ^ [_1388528, _1388530, _1388532] : [class_Int_Onumber__ring(_1388528), class_Rings_Olinordered__idom(_1388528), 32217 ^ _780086 : [(32218 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388528), hAPP(c_Int_Onumber__class_Onumber__of(_1388528), _1388530)), hAPP(c_Int_Onumber__class_Onumber__of(_1388528), _1388532))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1388530), _1388532)))], (32224 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1388530), _1388532)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388528), hAPP(c_Int_Onumber__class_Onumber__of(_1388528), _1388530)), hAPP(c_Int_Onumber__class_Onumber__of(_1388528), _1388532))))]]], (32230 ^ _780086) ^ [_1388859, _1388861, _1388863] : [class_Int_Onumber(_1388859), class_Orderings_Oord(_1388859), 32237 ^ _780086 : [(32238 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1388859), hAPP(c_Int_Onumber__class_Onumber__of(_1388859), _1388861)), hAPP(c_Int_Onumber__class_Onumber__of(_1388859), _1388863))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1388859), hAPP(c_Int_Onumber__class_Onumber__of(_1388859), _1388861)), hAPP(c_Int_Onumber__class_Onumber__of(_1388859), _1388863)) = hAPP(c_Int_Onumber__class_Onumber__of(_1388859), _1388861))], (32244 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1388859), hAPP(c_Int_Onumber__class_Onumber__of(_1388859), _1388861)), hAPP(c_Int_Onumber__class_Onumber__of(_1388859), _1388863)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1388859), hAPP(c_Int_Onumber__class_Onumber__of(_1388859), _1388861)), hAPP(c_Int_Onumber__class_Onumber__of(_1388859), _1388863)) = hAPP(c_Int_Onumber__class_Onumber__of(_1388859), _1388863))]]], (32250 ^ _780086) ^ [_1389251, _1389253, _1389255] : [class_Int_Onumber(_1389251), class_Orderings_Oord(_1389251), 32257 ^ _780086 : [(32258 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1389251), hAPP(c_Int_Onumber__class_Onumber__of(_1389251), _1389253)), hAPP(c_Int_Onumber__class_Onumber__of(_1389251), _1389255))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1389251), hAPP(c_Int_Onumber__class_Onumber__of(_1389251), _1389253)), hAPP(c_Int_Onumber__class_Onumber__of(_1389251), _1389255)) = hAPP(c_Int_Onumber__class_Onumber__of(_1389251), _1389255))], (32264 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1389251), hAPP(c_Int_Onumber__class_Onumber__of(_1389251), _1389253)), hAPP(c_Int_Onumber__class_Onumber__of(_1389251), _1389255)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1389251), hAPP(c_Int_Onumber__class_Onumber__of(_1389251), _1389253)), hAPP(c_Int_Onumber__class_Onumber__of(_1389251), _1389255)) = hAPP(c_Int_Onumber__class_Onumber__of(_1389251), _1389253))]]], (32270 ^ _780086) ^ [_1389643, _1389645, _1389647, _1389649] : [class_Int_Onumber__ring(_1389643), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1389643), hAPP(c_Int_Onumber__class_Onumber__of(_1389643), _1389645)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1389643), hAPP(c_Int_Onumber__class_Onumber__of(_1389643), _1389647)), _1389649)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1389643), hAPP(c_Int_Onumber__class_Onumber__of(_1389643), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1389645), _1389647))), _1389649))], (32276 ^ _780086) ^ [_1389812, _1389814, _1389816] : [class_Int_Onumber__ring(_1389812), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1389812), hAPP(c_Int_Onumber__class_Onumber__of(_1389812), _1389814)), hAPP(c_Int_Onumber__class_Onumber__of(_1389812), _1389816)) = hAPP(c_Int_Onumber__class_Onumber__of(_1389812), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1389814), _1389816)))], (32282 ^ _780086) ^ [_1389947, _1389949, _1389951] : [class_Int_Onumber__ring(_1389947), -(hAPP(c_Int_Onumber__class_Onumber__of(_1389947), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1389949), _1389951)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1389947), hAPP(c_Int_Onumber__class_Onumber__of(_1389947), _1389949)), hAPP(c_Int_Onumber__class_Onumber__of(_1389947), _1389951)))], (32288 ^ _780086) ^ [_1390082, _1390084, _1390086, _1390088] : [class_Int_Onumber__ring(_1390082), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1390082), hAPP(c_Int_Onumber__class_Onumber__of(_1390082), _1390084)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1390082), hAPP(c_Int_Onumber__class_Onumber__of(_1390082), _1390086)), _1390088)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1390082), hAPP(c_Int_Onumber__class_Onumber__of(_1390082), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1390084), _1390086))), _1390088))], (32294 ^ _780086) ^ [_1390251, _1390253, _1390255] : [class_Int_Onumber__ring(_1390251), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1390251), hAPP(c_Int_Onumber__class_Onumber__of(_1390251), _1390253)), hAPP(c_Int_Onumber__class_Onumber__of(_1390251), _1390255)) = hAPP(c_Int_Onumber__class_Onumber__of(_1390251), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1390253), _1390255)))], (32300 ^ _780086) ^ [_1390386, _1390388, _1390390] : [class_Int_Onumber__ring(_1390386), -(hAPP(c_Int_Onumber__class_Onumber__of(_1390386), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1390388), _1390390)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1390386), hAPP(c_Int_Onumber__class_Onumber__of(_1390386), _1390388)), hAPP(c_Int_Onumber__class_Onumber__of(_1390386), _1390390)))], (32306 ^ _780086) ^ [_1390521, _1390523, _1390525] : [class_Int_Onumber__ring(_1390521), -(hAPP(c_Int_Onumber__class_Onumber__of(_1390521), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1390523), _1390525)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1390521), hAPP(c_Int_Onumber__class_Onumber__of(_1390521), _1390523)), hAPP(c_Int_Onumber__class_Onumber__of(_1390521), _1390525)))], (32312 ^ _780086) ^ [_1390656, _1390658] : [class_Int_Onumber__ring(_1390656), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1390656), hAPP(c_Int_Onumber__class_Onumber__of(_1390656), _1390658)) = hAPP(c_Int_Onumber__class_Onumber__of(_1390656), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1390658)))], (32318 ^ _780086) ^ [_1390767, _1390769] : [class_Int_Onumber__ring(_1390767), -(hAPP(c_Int_Onumber__class_Onumber__of(_1390767), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1390769)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1390767), hAPP(c_Int_Onumber__class_Onumber__of(_1390767), _1390769)))], (32324 ^ _780086) ^ [_1390878, _1390880] : [class_Int_Onumber__ring(_1390878), -(hBOOL(hAPP(hAPP(c_member(_1390878), hAPP(c_Int_Onumber__class_Onumber__of(_1390878), _1390880)), c_Int_Oring__1__class_OInts(_1390878))))], (32330 ^ _780086) ^ [_1390981, _1390983, _1390985] : [c_Equiv__Relations_Oequiv(_1390981, _1390983, _1390985), -(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1390981, tc_HOL_Obool), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1390981), _1390983), _1390985)) = _1390983)], (32336 ^ _780086) ^ [_1391090, _1391092, _1391094, _1391096] : [class_Fields_Ofield__inverse__zero(_1391090), class_Int_Onumber(_1391090), 32343 ^ _780086 : [(32360 ^ _780086) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1391090), _1391092), hAPP(c_Int_Onumber__class_Onumber__of(_1391090), _1391094)) = _1391096), 32363 ^ _780086 : [(32364 ^ _780086) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1391090), _1391094) = c_Groups_Ozero__class_Ozero(_1391090)], (32366 ^ _780086) ^ [] : [_1391092 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1391090), _1391096), hAPP(c_Int_Onumber__class_Onumber__of(_1391090), _1391094))]], 32367 ^ _780086 : [(32368 ^ _780086) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1391090), _1391094) = c_Groups_Ozero__class_Ozero(_1391090))], (32370 ^ _780086) ^ [] : [_1391096 = c_Groups_Ozero__class_Ozero(_1391090)]]], (32344 ^ _780086) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1391090), _1391092), hAPP(c_Int_Onumber__class_Onumber__of(_1391090), _1391094)) = _1391096, 32347 ^ _780086 : [(32348 ^ _780086) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1391090), _1391094) = c_Groups_Ozero__class_Ozero(_1391090)), -(_1391092 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1391090), _1391096), hAPP(c_Int_Onumber__class_Onumber__of(_1391090), _1391094)))], (32354 ^ _780086) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1391090), _1391094) = c_Groups_Ozero__class_Ozero(_1391090), -(_1391096 = c_Groups_Ozero__class_Ozero(_1391090))]]]]], (32374 ^ _780086) ^ [_1391700, _1391702, _1391704, _1391706] : [class_Fields_Ofield__inverse__zero(_1391700), class_Int_Onumber(_1391700), 32381 ^ _780086 : [(32398 ^ _780086) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1391700), _1391702), _1391704) = hAPP(c_Int_Onumber__class_Onumber__of(_1391700), _1391706)), 32401 ^ _780086 : [(32402 ^ _780086) ^ [] : [_1391704 = c_Groups_Ozero__class_Ozero(_1391700)], (32404 ^ _780086) ^ [] : [_1391702 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1391700), hAPP(c_Int_Onumber__class_Onumber__of(_1391700), _1391706)), _1391704)]], 32405 ^ _780086 : [(32406 ^ _780086) ^ [] : [-(_1391704 = c_Groups_Ozero__class_Ozero(_1391700))], (32408 ^ _780086) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1391700), _1391706) = c_Groups_Ozero__class_Ozero(_1391700)]]], (32382 ^ _780086) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1391700), _1391702), _1391704) = hAPP(c_Int_Onumber__class_Onumber__of(_1391700), _1391706), 32385 ^ _780086 : [(32386 ^ _780086) ^ [] : [-(_1391704 = c_Groups_Ozero__class_Ozero(_1391700)), -(_1391702 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1391700), hAPP(c_Int_Onumber__class_Onumber__of(_1391700), _1391706)), _1391704))], (32392 ^ _780086) ^ [] : [_1391704 = c_Groups_Ozero__class_Ozero(_1391700), -(hAPP(c_Int_Onumber__class_Onumber__of(_1391700), _1391706) = c_Groups_Ozero__class_Ozero(_1391700))]]]]], (32412 ^ _780086) ^ [_1392295, _1392297, _1392299, _1392301] : [class_Fields_Ofield__inverse__zero(_1392295), class_Int_Onumber(_1392295), 32419 ^ _780086 : [(32436 ^ _780086) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1392295), _1392297) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1392295), _1392299), _1392301)), 32439 ^ _780086 : [(32440 ^ _780086) ^ [] : [_1392301 = c_Groups_Ozero__class_Ozero(_1392295)], (32442 ^ _780086) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1392295), hAPP(c_Int_Onumber__class_Onumber__of(_1392295), _1392297)), _1392301) = _1392299]], 32443 ^ _780086 : [(32444 ^ _780086) ^ [] : [-(_1392301 = c_Groups_Ozero__class_Ozero(_1392295))], (32446 ^ _780086) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1392295), _1392297) = c_Groups_Ozero__class_Ozero(_1392295)]]], (32420 ^ _780086) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1392295), _1392297) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1392295), _1392299), _1392301), 32423 ^ _780086 : [(32424 ^ _780086) ^ [] : [-(_1392301 = c_Groups_Ozero__class_Ozero(_1392295)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1392295), hAPP(c_Int_Onumber__class_Onumber__of(_1392295), _1392297)), _1392301) = _1392299)], (32430 ^ _780086) ^ [] : [_1392301 = c_Groups_Ozero__class_Ozero(_1392295), -(hAPP(c_Int_Onumber__class_Onumber__of(_1392295), _1392297) = c_Groups_Ozero__class_Ozero(_1392295))]]]]], (32450 ^ _780086) ^ [_1392890, _1392892, _1392894, _1392896] : [class_Fields_Ofield__inverse__zero(_1392890), class_Int_Onumber(_1392890), 32457 ^ _780086 : [(32474 ^ _780086) ^ [] : [-(_1392892 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1392890), _1392894), hAPP(c_Int_Onumber__class_Onumber__of(_1392890), _1392896))), 32477 ^ _780086 : [(32478 ^ _780086) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1392890), _1392896) = c_Groups_Ozero__class_Ozero(_1392890)], (32480 ^ _780086) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1392890), _1392892), hAPP(c_Int_Onumber__class_Onumber__of(_1392890), _1392896)) = _1392894]], 32481 ^ _780086 : [(32482 ^ _780086) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1392890), _1392896) = c_Groups_Ozero__class_Ozero(_1392890))], (32484 ^ _780086) ^ [] : [_1392892 = c_Groups_Ozero__class_Ozero(_1392890)]]], (32458 ^ _780086) ^ [] : [_1392892 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1392890), _1392894), hAPP(c_Int_Onumber__class_Onumber__of(_1392890), _1392896)), 32461 ^ _780086 : [(32462 ^ _780086) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1392890), _1392896) = c_Groups_Ozero__class_Ozero(_1392890)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1392890), _1392892), hAPP(c_Int_Onumber__class_Onumber__of(_1392890), _1392896)) = _1392894)], (32468 ^ _780086) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1392890), _1392896) = c_Groups_Ozero__class_Ozero(_1392890), -(_1392892 = c_Groups_Ozero__class_Ozero(_1392890))]]]]], (32488 ^ _780086) ^ [_1393500, _1393502, _1393504, _1393506] : [class_Int_Onumber__ring(_1393500), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1393500), hAPP(c_Int_Onumber__class_Onumber__of(_1393500), _1393502)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1393500), hAPP(c_Int_Onumber__class_Onumber__of(_1393500), _1393504)), _1393506)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1393500), hAPP(c_Int_Onumber__class_Onumber__of(_1393500), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1393502), _1393504))), _1393506))], (32494 ^ _780086) ^ [_1393669, _1393671, _1393673] : [class_Int_Onumber__ring(_1393669), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1393669), hAPP(c_Groups_Ouminus__class_Ouminus(_1393669), hAPP(c_Int_Onumber__class_Onumber__of(_1393669), _1393671))), _1393673) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1393669), hAPP(c_Int_Onumber__class_Onumber__of(_1393669), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1393671))), _1393673))], (32500 ^ _780086) ^ [_1393814, _1393816, _1393818] : [class_Int_Onumber__ring(_1393814), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1393814), hAPP(c_Int_Onumber__class_Onumber__of(_1393814), _1393816)), hAPP(c_Int_Onumber__class_Onumber__of(_1393814), _1393818)) = hAPP(c_Int_Onumber__class_Onumber__of(_1393814), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1393816), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1393818))))], (32506 ^ _780086) ^ [_1393955, _1393957, _1393959, _1393961] : [class_Fields_Olinordered__field__inverse__zero(_1393955), class_Int_Onumber(_1393955), 32513 ^ _780086 : [(32540 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1393955), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1393955), _1393957), hAPP(c_Int_Onumber__class_Onumber__of(_1393955), _1393959))), _1393961))), 32543 ^ _780086 : [(32544 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1393955), c_Groups_Ozero__class_Ozero(_1393955)), hAPP(c_Int_Onumber__class_Onumber__of(_1393955), _1393959))))], (32546 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1393955), _1393957), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1393955), _1393961), hAPP(c_Int_Onumber__class_Onumber__of(_1393955), _1393959))))]], 32547 ^ _780086 : [(32548 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1393955), c_Groups_Ozero__class_Ozero(_1393955)), hAPP(c_Int_Onumber__class_Onumber__of(_1393955), _1393959)))], (32550 ^ _780086) ^ [] : [32551 ^ _780086 : [(32552 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1393955), hAPP(c_Int_Onumber__class_Onumber__of(_1393955), _1393959)), c_Groups_Ozero__class_Ozero(_1393955))))], (32554 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1393955), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1393955), _1393961), hAPP(c_Int_Onumber__class_Onumber__of(_1393955), _1393959))), _1393957))]], 32555 ^ _780086 : [(32556 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1393955), hAPP(c_Int_Onumber__class_Onumber__of(_1393955), _1393959)), c_Groups_Ozero__class_Ozero(_1393955)))], (32558 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1393955), c_Groups_Ozero__class_Ozero(_1393955)), _1393961))]]]]], (32514 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1393955), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1393955), _1393957), hAPP(c_Int_Onumber__class_Onumber__of(_1393955), _1393959))), _1393961)), 32517 ^ _780086 : [(32518 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1393955), c_Groups_Ozero__class_Ozero(_1393955)), hAPP(c_Int_Onumber__class_Onumber__of(_1393955), _1393959))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1393955), _1393957), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1393955), _1393961), hAPP(c_Int_Onumber__class_Onumber__of(_1393955), _1393959)))))], (32524 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1393955), c_Groups_Ozero__class_Ozero(_1393955)), hAPP(c_Int_Onumber__class_Onumber__of(_1393955), _1393959)))), 32527 ^ _780086 : [(32528 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1393955), hAPP(c_Int_Onumber__class_Onumber__of(_1393955), _1393959)), c_Groups_Ozero__class_Ozero(_1393955))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1393955), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1393955), _1393961), hAPP(c_Int_Onumber__class_Onumber__of(_1393955), _1393959))), _1393957)))], (32534 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1393955), hAPP(c_Int_Onumber__class_Onumber__of(_1393955), _1393959)), c_Groups_Ozero__class_Ozero(_1393955)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1393955), c_Groups_Ozero__class_Ozero(_1393955)), _1393961)))]]]]]]], (32562 ^ _780086) ^ [_1395069, _1395071, _1395073, _1395075] : [class_Fields_Olinordered__field__inverse__zero(_1395069), class_Int_Onumber(_1395069), 32569 ^ _780086 : [(32596 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395069), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1395069), _1395071), _1395073)), hAPP(c_Int_Onumber__class_Onumber__of(_1395069), _1395075)))), 32599 ^ _780086 : [(32600 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395069), c_Groups_Ozero__class_Ozero(_1395069)), _1395073)))], (32602 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395069), _1395071), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1395069), hAPP(c_Int_Onumber__class_Onumber__of(_1395069), _1395075)), _1395073)))]], 32603 ^ _780086 : [(32604 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395069), c_Groups_Ozero__class_Ozero(_1395069)), _1395073))], (32606 ^ _780086) ^ [] : [32607 ^ _780086 : [(32608 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395069), _1395073), c_Groups_Ozero__class_Ozero(_1395069))))], (32610 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395069), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1395069), hAPP(c_Int_Onumber__class_Onumber__of(_1395069), _1395075)), _1395073)), _1395071))]], 32611 ^ _780086 : [(32612 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395069), _1395073), c_Groups_Ozero__class_Ozero(_1395069)))], (32614 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395069), c_Groups_Ozero__class_Ozero(_1395069)), hAPP(c_Int_Onumber__class_Onumber__of(_1395069), _1395075)))]]]]], (32570 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395069), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1395069), _1395071), _1395073)), hAPP(c_Int_Onumber__class_Onumber__of(_1395069), _1395075))), 32573 ^ _780086 : [(32574 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395069), c_Groups_Ozero__class_Ozero(_1395069)), _1395073)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395069), _1395071), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1395069), hAPP(c_Int_Onumber__class_Onumber__of(_1395069), _1395075)), _1395073))))], (32580 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395069), c_Groups_Ozero__class_Ozero(_1395069)), _1395073))), 32583 ^ _780086 : [(32584 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395069), _1395073), c_Groups_Ozero__class_Ozero(_1395069))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395069), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1395069), hAPP(c_Int_Onumber__class_Onumber__of(_1395069), _1395075)), _1395073)), _1395071)))], (32590 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395069), _1395073), c_Groups_Ozero__class_Ozero(_1395069)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395069), c_Groups_Ozero__class_Ozero(_1395069)), hAPP(c_Int_Onumber__class_Onumber__of(_1395069), _1395075))))]]]]]]], (32618 ^ _780086) ^ [_1396138, _1396140, _1396142, _1396144] : [class_Fields_Olinordered__field__inverse__zero(_1396138), class_Int_Onumber(_1396138), 32625 ^ _780086 : [(32652 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396138), hAPP(c_Int_Onumber__class_Onumber__of(_1396138), _1396140)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1396138), _1396142), _1396144)))), 32655 ^ _780086 : [(32656 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396138), c_Groups_Ozero__class_Ozero(_1396138)), _1396144)))], (32658 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396138), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1396138), hAPP(c_Int_Onumber__class_Onumber__of(_1396138), _1396140)), _1396144)), _1396142))]], 32659 ^ _780086 : [(32660 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396138), c_Groups_Ozero__class_Ozero(_1396138)), _1396144))], (32662 ^ _780086) ^ [] : [32663 ^ _780086 : [(32664 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396138), _1396144), c_Groups_Ozero__class_Ozero(_1396138))))], (32666 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396138), _1396142), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1396138), hAPP(c_Int_Onumber__class_Onumber__of(_1396138), _1396140)), _1396144)))]], 32667 ^ _780086 : [(32668 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396138), _1396144), c_Groups_Ozero__class_Ozero(_1396138)))], (32670 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396138), hAPP(c_Int_Onumber__class_Onumber__of(_1396138), _1396140)), c_Groups_Ozero__class_Ozero(_1396138)))]]]]], (32626 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396138), hAPP(c_Int_Onumber__class_Onumber__of(_1396138), _1396140)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1396138), _1396142), _1396144))), 32629 ^ _780086 : [(32630 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396138), c_Groups_Ozero__class_Ozero(_1396138)), _1396144)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396138), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1396138), hAPP(c_Int_Onumber__class_Onumber__of(_1396138), _1396140)), _1396144)), _1396142)))], (32636 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396138), c_Groups_Ozero__class_Ozero(_1396138)), _1396144))), 32639 ^ _780086 : [(32640 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396138), _1396144), c_Groups_Ozero__class_Ozero(_1396138))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396138), _1396142), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1396138), hAPP(c_Int_Onumber__class_Onumber__of(_1396138), _1396140)), _1396144))))], (32646 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396138), _1396144), c_Groups_Ozero__class_Ozero(_1396138)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396138), hAPP(c_Int_Onumber__class_Onumber__of(_1396138), _1396140)), c_Groups_Ozero__class_Ozero(_1396138))))]]]]]]], (32674 ^ _780086) ^ [_1397207, _1397209, _1397211, _1397213] : [class_Fields_Olinordered__field__inverse__zero(_1397207), class_Int_Onumber(_1397207), 32681 ^ _780086 : [(32708 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1397207), _1397209), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1397207), _1397211), hAPP(c_Int_Onumber__class_Onumber__of(_1397207), _1397213))))), 32711 ^ _780086 : [(32712 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1397207), c_Groups_Ozero__class_Ozero(_1397207)), hAPP(c_Int_Onumber__class_Onumber__of(_1397207), _1397213))))], (32714 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1397207), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1397207), _1397209), hAPP(c_Int_Onumber__class_Onumber__of(_1397207), _1397213))), _1397211))]], 32715 ^ _780086 : [(32716 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1397207), c_Groups_Ozero__class_Ozero(_1397207)), hAPP(c_Int_Onumber__class_Onumber__of(_1397207), _1397213)))], (32718 ^ _780086) ^ [] : [32719 ^ _780086 : [(32720 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1397207), hAPP(c_Int_Onumber__class_Onumber__of(_1397207), _1397213)), c_Groups_Ozero__class_Ozero(_1397207))))], (32722 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1397207), _1397211), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1397207), _1397209), hAPP(c_Int_Onumber__class_Onumber__of(_1397207), _1397213))))]], 32723 ^ _780086 : [(32724 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1397207), hAPP(c_Int_Onumber__class_Onumber__of(_1397207), _1397213)), c_Groups_Ozero__class_Ozero(_1397207)))], (32726 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1397207), _1397209), c_Groups_Ozero__class_Ozero(_1397207)))]]]]], (32682 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1397207), _1397209), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1397207), _1397211), hAPP(c_Int_Onumber__class_Onumber__of(_1397207), _1397213)))), 32685 ^ _780086 : [(32686 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1397207), c_Groups_Ozero__class_Ozero(_1397207)), hAPP(c_Int_Onumber__class_Onumber__of(_1397207), _1397213))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1397207), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1397207), _1397209), hAPP(c_Int_Onumber__class_Onumber__of(_1397207), _1397213))), _1397211)))], (32692 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1397207), c_Groups_Ozero__class_Ozero(_1397207)), hAPP(c_Int_Onumber__class_Onumber__of(_1397207), _1397213)))), 32695 ^ _780086 : [(32696 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1397207), hAPP(c_Int_Onumber__class_Onumber__of(_1397207), _1397213)), c_Groups_Ozero__class_Ozero(_1397207))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1397207), _1397211), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1397207), _1397209), hAPP(c_Int_Onumber__class_Onumber__of(_1397207), _1397213)))))], (32702 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1397207), hAPP(c_Int_Onumber__class_Onumber__of(_1397207), _1397213)), c_Groups_Ozero__class_Ozero(_1397207)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1397207), _1397209), c_Groups_Ozero__class_Ozero(_1397207))))]]]]]]], (32730 ^ _780086) ^ [_1398321, _1398323] : [class_Int_Onumber__ring(_1398321), class_Rings_Olinordered__idom(_1398321), 32737 ^ _780086 : [(32738 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1398321), hAPP(c_Int_Onumber__class_Onumber__of(_1398321), _1398323)), c_Groups_Ozero__class_Ozero(_1398321))), -(hAPP(c_Groups_Oabs__class_Oabs(_1398321), hAPP(c_Int_Onumber__class_Onumber__of(_1398321), _1398323)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1398321), hAPP(c_Int_Onumber__class_Onumber__of(_1398321), _1398323)))], (32744 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1398321), hAPP(c_Int_Onumber__class_Onumber__of(_1398321), _1398323)), c_Groups_Ozero__class_Ozero(_1398321)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1398321), hAPP(c_Int_Onumber__class_Onumber__of(_1398321), _1398323)) = hAPP(c_Int_Onumber__class_Onumber__of(_1398321), _1398323))]]], (32750 ^ _780086) ^ [_1398673, _1398675, _1398677, _1398679] : [class_Int_Onumber__ring(_1398673), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1398673), hAPP(c_Int_Onumber__class_Onumber__of(_1398673), _1398675)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1398673), _1398677), hAPP(c_Int_Onumber__class_Onumber__of(_1398673), _1398679))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1398673), hAPP(c_Int_Onumber__class_Onumber__of(_1398673), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1398675), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1398679)))), _1398677))], (32756 ^ _780086) ^ [_1398848, _1398850, _1398852, _1398854] : [class_Fields_Olinordered__field__inverse__zero(_1398848), class_Int_Onumber(_1398848), 32763 ^ _780086 : [(32790 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1398848), _1398850), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1398848), _1398852), hAPP(c_Int_Onumber__class_Onumber__of(_1398848), _1398854))))), 32793 ^ _780086 : [(32794 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1398848), c_Groups_Ozero__class_Ozero(_1398848)), hAPP(c_Int_Onumber__class_Onumber__of(_1398848), _1398854))))], (32796 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1398848), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1398848), _1398850), hAPP(c_Int_Onumber__class_Onumber__of(_1398848), _1398854))), _1398852))]], 32797 ^ _780086 : [(32798 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1398848), c_Groups_Ozero__class_Ozero(_1398848)), hAPP(c_Int_Onumber__class_Onumber__of(_1398848), _1398854)))], (32800 ^ _780086) ^ [] : [32801 ^ _780086 : [(32802 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1398848), hAPP(c_Int_Onumber__class_Onumber__of(_1398848), _1398854)), c_Groups_Ozero__class_Ozero(_1398848))))], (32804 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1398848), _1398852), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1398848), _1398850), hAPP(c_Int_Onumber__class_Onumber__of(_1398848), _1398854))))]], 32805 ^ _780086 : [(32806 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1398848), hAPP(c_Int_Onumber__class_Onumber__of(_1398848), _1398854)), c_Groups_Ozero__class_Ozero(_1398848)))], (32808 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1398848), _1398850), c_Groups_Ozero__class_Ozero(_1398848)))]]]]], (32764 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1398848), _1398850), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1398848), _1398852), hAPP(c_Int_Onumber__class_Onumber__of(_1398848), _1398854)))), 32767 ^ _780086 : [(32768 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1398848), c_Groups_Ozero__class_Ozero(_1398848)), hAPP(c_Int_Onumber__class_Onumber__of(_1398848), _1398854))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1398848), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1398848), _1398850), hAPP(c_Int_Onumber__class_Onumber__of(_1398848), _1398854))), _1398852)))], (32774 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1398848), c_Groups_Ozero__class_Ozero(_1398848)), hAPP(c_Int_Onumber__class_Onumber__of(_1398848), _1398854)))), 32777 ^ _780086 : [(32778 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1398848), hAPP(c_Int_Onumber__class_Onumber__of(_1398848), _1398854)), c_Groups_Ozero__class_Ozero(_1398848))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1398848), _1398852), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1398848), _1398850), hAPP(c_Int_Onumber__class_Onumber__of(_1398848), _1398854)))))], (32784 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1398848), hAPP(c_Int_Onumber__class_Onumber__of(_1398848), _1398854)), c_Groups_Ozero__class_Ozero(_1398848)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1398848), _1398850), c_Groups_Ozero__class_Ozero(_1398848))))]]]]]]], (32812 ^ _780086) ^ [_1399962, _1399964, _1399966, _1399968] : [class_Fields_Olinordered__field__inverse__zero(_1399962), class_Int_Onumber(_1399962), 32819 ^ _780086 : [(32846 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1399962), hAPP(c_Int_Onumber__class_Onumber__of(_1399962), _1399964)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1399962), _1399966), _1399968)))), 32849 ^ _780086 : [(32850 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1399962), c_Groups_Ozero__class_Ozero(_1399962)), _1399968)))], (32852 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1399962), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1399962), hAPP(c_Int_Onumber__class_Onumber__of(_1399962), _1399964)), _1399968)), _1399966))]], 32853 ^ _780086 : [(32854 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1399962), c_Groups_Ozero__class_Ozero(_1399962)), _1399968))], (32856 ^ _780086) ^ [] : [32857 ^ _780086 : [(32858 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1399962), _1399968), c_Groups_Ozero__class_Ozero(_1399962))))], (32860 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1399962), _1399966), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1399962), hAPP(c_Int_Onumber__class_Onumber__of(_1399962), _1399964)), _1399968)))]], 32861 ^ _780086 : [(32862 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1399962), _1399968), c_Groups_Ozero__class_Ozero(_1399962)))], (32864 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1399962), hAPP(c_Int_Onumber__class_Onumber__of(_1399962), _1399964)), c_Groups_Ozero__class_Ozero(_1399962)))]]]]], (32820 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1399962), hAPP(c_Int_Onumber__class_Onumber__of(_1399962), _1399964)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1399962), _1399966), _1399968))), 32823 ^ _780086 : [(32824 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1399962), c_Groups_Ozero__class_Ozero(_1399962)), _1399968)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1399962), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1399962), hAPP(c_Int_Onumber__class_Onumber__of(_1399962), _1399964)), _1399968)), _1399966)))], (32830 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1399962), c_Groups_Ozero__class_Ozero(_1399962)), _1399968))), 32833 ^ _780086 : [(32834 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1399962), _1399968), c_Groups_Ozero__class_Ozero(_1399962))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1399962), _1399966), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1399962), hAPP(c_Int_Onumber__class_Onumber__of(_1399962), _1399964)), _1399968))))], (32840 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1399962), _1399968), c_Groups_Ozero__class_Ozero(_1399962)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1399962), hAPP(c_Int_Onumber__class_Onumber__of(_1399962), _1399964)), c_Groups_Ozero__class_Ozero(_1399962))))]]]]]]], (32868 ^ _780086) ^ [_1401031, _1401033, _1401035, _1401037] : [class_Fields_Olinordered__field__inverse__zero(_1401031), class_Int_Onumber(_1401031), 32875 ^ _780086 : [(32902 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1401031), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1401031), _1401033), _1401035)), hAPP(c_Int_Onumber__class_Onumber__of(_1401031), _1401037)))), 32905 ^ _780086 : [(32906 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1401031), c_Groups_Ozero__class_Ozero(_1401031)), _1401035)))], (32908 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1401031), _1401033), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1401031), hAPP(c_Int_Onumber__class_Onumber__of(_1401031), _1401037)), _1401035)))]], 32909 ^ _780086 : [(32910 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1401031), c_Groups_Ozero__class_Ozero(_1401031)), _1401035))], (32912 ^ _780086) ^ [] : [32913 ^ _780086 : [(32914 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1401031), _1401035), c_Groups_Ozero__class_Ozero(_1401031))))], (32916 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1401031), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1401031), hAPP(c_Int_Onumber__class_Onumber__of(_1401031), _1401037)), _1401035)), _1401033))]], 32917 ^ _780086 : [(32918 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1401031), _1401035), c_Groups_Ozero__class_Ozero(_1401031)))], (32920 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1401031), c_Groups_Ozero__class_Ozero(_1401031)), hAPP(c_Int_Onumber__class_Onumber__of(_1401031), _1401037)))]]]]], (32876 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1401031), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1401031), _1401033), _1401035)), hAPP(c_Int_Onumber__class_Onumber__of(_1401031), _1401037))), 32879 ^ _780086 : [(32880 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1401031), c_Groups_Ozero__class_Ozero(_1401031)), _1401035)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1401031), _1401033), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1401031), hAPP(c_Int_Onumber__class_Onumber__of(_1401031), _1401037)), _1401035))))], (32886 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1401031), c_Groups_Ozero__class_Ozero(_1401031)), _1401035))), 32889 ^ _780086 : [(32890 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1401031), _1401035), c_Groups_Ozero__class_Ozero(_1401031))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1401031), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1401031), hAPP(c_Int_Onumber__class_Onumber__of(_1401031), _1401037)), _1401035)), _1401033)))], (32896 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1401031), _1401035), c_Groups_Ozero__class_Ozero(_1401031)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1401031), c_Groups_Ozero__class_Ozero(_1401031)), hAPP(c_Int_Onumber__class_Onumber__of(_1401031), _1401037))))]]]]]]], (32924 ^ _780086) ^ [_1402100, _1402102, _1402104, _1402106] : [class_Fields_Olinordered__field__inverse__zero(_1402100), class_Int_Onumber(_1402100), 32931 ^ _780086 : [(32958 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1402100), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1402100), _1402102), hAPP(c_Int_Onumber__class_Onumber__of(_1402100), _1402104))), _1402106))), 32961 ^ _780086 : [(32962 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1402100), c_Groups_Ozero__class_Ozero(_1402100)), hAPP(c_Int_Onumber__class_Onumber__of(_1402100), _1402104))))], (32964 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1402100), _1402102), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1402100), _1402106), hAPP(c_Int_Onumber__class_Onumber__of(_1402100), _1402104))))]], 32965 ^ _780086 : [(32966 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1402100), c_Groups_Ozero__class_Ozero(_1402100)), hAPP(c_Int_Onumber__class_Onumber__of(_1402100), _1402104)))], (32968 ^ _780086) ^ [] : [32969 ^ _780086 : [(32970 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1402100), hAPP(c_Int_Onumber__class_Onumber__of(_1402100), _1402104)), c_Groups_Ozero__class_Ozero(_1402100))))], (32972 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1402100), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1402100), _1402106), hAPP(c_Int_Onumber__class_Onumber__of(_1402100), _1402104))), _1402102))]], 32973 ^ _780086 : [(32974 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1402100), hAPP(c_Int_Onumber__class_Onumber__of(_1402100), _1402104)), c_Groups_Ozero__class_Ozero(_1402100)))], (32976 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1402100), c_Groups_Ozero__class_Ozero(_1402100)), _1402106))]]]]], (32932 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1402100), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1402100), _1402102), hAPP(c_Int_Onumber__class_Onumber__of(_1402100), _1402104))), _1402106)), 32935 ^ _780086 : [(32936 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1402100), c_Groups_Ozero__class_Ozero(_1402100)), hAPP(c_Int_Onumber__class_Onumber__of(_1402100), _1402104))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1402100), _1402102), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1402100), _1402106), hAPP(c_Int_Onumber__class_Onumber__of(_1402100), _1402104)))))], (32942 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1402100), c_Groups_Ozero__class_Ozero(_1402100)), hAPP(c_Int_Onumber__class_Onumber__of(_1402100), _1402104)))), 32945 ^ _780086 : [(32946 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1402100), hAPP(c_Int_Onumber__class_Onumber__of(_1402100), _1402104)), c_Groups_Ozero__class_Ozero(_1402100))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1402100), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1402100), _1402106), hAPP(c_Int_Onumber__class_Onumber__of(_1402100), _1402104))), _1402102)))], (32952 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1402100), hAPP(c_Int_Onumber__class_Onumber__of(_1402100), _1402104)), c_Groups_Ozero__class_Ozero(_1402100)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1402100), c_Groups_Ozero__class_Ozero(_1402100)), _1402106)))]]]]]]], (32980 ^ _780086) ^ [_1403214, _1403216, _1403218, _1403220] : [c_Equiv__Relations_Oequiv(_1403214, _1403216, _1403218), hBOOL(hAPP(hAPP(c_member(_1403214), _1403220), _1403216)), -(hBOOL(hAPP(hAPP(c_member(_1403214), _1403220), hAPP(c_Relation_OImage(_1403214, _1403214, _1403218), hAPP(hAPP(c_Set_Oinsert(_1403214), _1403220), c_Orderings_Obot__class_Obot(tc_fun(_1403214, tc_HOL_Obool)))))))], (32990 ^ _780086) ^ [_1403421, _1403423, _1403425] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OLocal(_1403421, _1403423, _1403425)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1403425)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (32992 ^ _780086) ^ [_1403464, _1403466, _1403468, _1403470, _1403472, _1403474] : [c_Equiv__Relations_Oequiv(_1403464, _1403466, _1403468), c_Equiv__Relations_Ocongruent(_1403464, tc_fun(_1403470, tc_HOL_Obool), _1403468, _1403472), hBOOL(hAPP(hAPP(c_member(_1403464), _1403474), _1403466)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1403464, tc_fun(_1403470, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1403464, _1403464, _1403468), hAPP(hAPP(c_Set_Oinsert(_1403464), _1403474), c_Orderings_Obot__class_Obot(tc_fun(_1403464, tc_HOL_Obool))))), _1403472) = hAPP(_1403472, _1403474))], (33006 ^ _780086) ^ [_1403765, _1403767, _1403769, _1403771, _1403773, _1403775, _1403777, _1403779, _1403781, _1403783] : [c_Equiv__Relations_Oequiv(_1403765, _1403767, _1403769), c_Equiv__Relations_Oequiv(_1403771, _1403773, _1403775), c_Equiv__Relations_Ocongruent2(_1403765, _1403771, tc_fun(_1403777, tc_HOL_Obool), _1403769, _1403775, _1403779), hBOOL(hAPP(hAPP(c_member(_1403765), _1403781), _1403767)), hBOOL(hAPP(hAPP(c_member(_1403771), _1403783), _1403773)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1403765, tc_fun(_1403777, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1403765, _1403765, _1403769), hAPP(hAPP(c_Set_Oinsert(_1403765), _1403781), c_Orderings_Obot__class_Obot(tc_fun(_1403765, tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(_1403771, tc_fun(_1403777, tc_HOL_Obool)), tc_fun(_1403777, tc_HOL_Obool), _1403765), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1403771, tc_fun(_1403777, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1403771, _1403771, _1403775), hAPP(hAPP(c_Set_Oinsert(_1403771), _1403783), c_Orderings_Obot__class_Obot(tc_fun(_1403771, tc_HOL_Obool)))))), _1403779)) = hAPP(hAPP(_1403779, _1403781), _1403783))], (33028 ^ _780086) ^ [_1404354] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1404354))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1404354)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (33034 ^ _780086) ^ [_1404447] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1404447)))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1404447)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1404447))))], (33040 ^ _780086) ^ [_1404505] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1404505)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1404505))))], (33042 ^ _780086) ^ [_1404558, _1404560] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1404558)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1404560))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1404558), _1404560)))], (33048 ^ _780086) ^ [_1404663, _1404665] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1404663), _1404665)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1404663)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1404665))))], (33054 ^ _780086) ^ [_1404774] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1404774)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1404774)))], (33056 ^ _780086) ^ [_1404809] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1404809) = _1404809)], (33058 ^ _780086) ^ [_1404835, _1404837] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1404835)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1404837)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1404835), _1404837)))], (33060 ^ _780086) ^ [_1404881, _1404883] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1404881)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1404883)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1404881), _1404883)))], (33062 ^ _780086) ^ [_1404942, _1404944] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1404942)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1404944))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1404942), _1404944)))], (33068 ^ _780086) ^ [_1405047, _1405049] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1405047), _1405049)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1405047)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1405049))))], (33074 ^ _780086) ^ [_1405158] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1405158) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), _1405158))], (33076 ^ _780086) ^ [_1405187] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1405187) = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1405187)))], (33078 ^ _780086) ^ [_1405219] : [-(hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1405219)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1405219))], (33080 ^ _780086) ^ [_1405251, _1405253, _1405255, _1405257, _1405259, _1405261, _1405263, _1405265] : [c_Equiv__Relations_Oequiv(_1405251, _1405253, _1405255), c_Equiv__Relations_Ocongruent2(_1405251, _1405257, _1405259, _1405255, _1405261, _1405263), hBOOL(hAPP(hAPP(c_member(_1405251), _1405265), _1405253)), -(c_Equiv__Relations_Ocongruent(_1405257, _1405259, _1405261, hAPP(_1405263, _1405265)))], (33094 ^ _780086) ^ [_1405502, _1405504] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1405502)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1405504)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1405502), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1405504))))], (33096 ^ _780086) ^ [_1405551] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1405551))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1405551) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33102 ^ _780086) ^ [_1405657, _1405659] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1405657) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1405659), 33105 ^ _780086 : [(33106 ^ _780086) ^ [] : [-(_1405657 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1405659)))], (33108 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1405659))))]]], (33110 ^ _780086) ^ [_1405790, _1405792] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1405790) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1405792)), _1405790 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1405792)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1405792)))], (33146 ^ _780086) ^ [_1406355, _1406357] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1406355) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1406357)), 33149 ^ _780086 : [(33150 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1406355))))], (33152 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1406357)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], 33153 ^ _780086 : [(33154 ^ _780086) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1406355)))], (33156 ^ _780086) ^ [] : [33157 ^ _780086 : [(33158 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1406357))))], (33160 ^ _780086) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1406355) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], 33161 ^ _780086 : [(33162 ^ _780086) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1406357)))], (33164 ^ _780086) ^ [] : [_1406355 = _1406357]]]]], (33120 ^ _780086) ^ [_1405970, _1405972] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1405970) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1405972), 33123 ^ _780086 : [(33124 ^ _780086) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1405970))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1405972)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (33130 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1405970)))), 33133 ^ _780086 : [(33134 ^ _780086) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1405972))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1405970) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (33140 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1405972)))), -(_1405970 = _1405972)]]]]], (33168 ^ _780086) ^ [_1406768, _1406770, _1406772] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1406768))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1406768)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1406770)), _1406772)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1406770)), _1406772))], (33174 ^ _780086) ^ [_1406906, _1406908, _1406910] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1406906)))), 33177 ^ _780086 : [(33178 ^ _780086) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1406908))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1406906)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1406908)), _1406910)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1406906)), _1406910))], (33184 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1406908)))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1406906)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1406908)), _1406910)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1406906), _1406908))), _1406910))]]], (33190 ^ _780086) ^ [_1407237] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1407237))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407237)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (33196 ^ _780086) ^ [_1407328] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1407328)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407328)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1407328))], (33202 ^ _780086) ^ [_1407387, _1407389] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1407387))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407387), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407389)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33208 ^ _780086) ^ [_1407489, _1407491] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1407489)))), 33211 ^ _780086 : [(33212 ^ _780086) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1407491))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407489), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407491)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407489))], (33218 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1407491)))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407489), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407491)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1407489), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1407491))))]]], (33224 ^ _780086) ^ [_1407762, _1407764, _1407766, _1407768, _1407770, _1407772, _1407774, _1407776, _1407778] : [c_Equiv__Relations_Oequiv(_1407762, _1407764, _1407766), c_Equiv__Relations_Oequiv(_1407768, _1407770, _1407772), c_Equiv__Relations_Ocongruent2(_1407762, _1407768, tc_fun(_1407774, tc_HOL_Obool), _1407766, _1407772, _1407776), hBOOL(hAPP(hAPP(c_member(_1407768), _1407778), _1407770)), -(c_Equiv__Relations_Ocongruent(_1407762, tc_fun(_1407774, tc_HOL_Obool), _1407766, hAPP(hAPP(c_COMBB(tc_fun(_1407768, tc_fun(_1407774, tc_HOL_Obool)), tc_fun(_1407774, tc_HOL_Obool), _1407762), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1407768, tc_fun(_1407774, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1407768, _1407768, _1407772), hAPP(hAPP(c_Set_Oinsert(_1407768), _1407778), c_Orderings_Obot__class_Obot(tc_fun(_1407768, tc_HOL_Obool)))))), _1407776)))], (33242 ^ _780086) ^ [_1408198, _1408200] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1408198))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408198)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408200)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33248 ^ _780086) ^ [_1408303, _1408305] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1408303)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408303)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408305)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1408303)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1408305))))], (33254 ^ _780086) ^ [_1408382, _1408384] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1408382))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408382)), _1408384) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1408384))], (33260 ^ _780086) ^ [_1408487, _1408489] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1408487)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408487)), _1408489) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1408487)), _1408489)))], (33266 ^ _780086) ^ [_1408560, _1408562] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1408560))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408560)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408562)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408562)))], (33272 ^ _780086) ^ [_1408677, _1408679] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1408677)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408677)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408679)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1408677)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408679))))], (33278 ^ _780086) ^ [_1408756, _1408758] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1408756))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408756)), _1408758)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1408758))], (33284 ^ _780086) ^ [_1408867, _1408869] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1408867)))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408867)), _1408869)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1408867))), _1408869))], (33290 ^ _780086) ^ [_1408942, _1408944] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1408942), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408944)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408942)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408944))], (33296 ^ _780086) ^ [_1409053, _1409055] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1409053), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1409055)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1409053)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1409055), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1409053)))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat)), tc_Int_Oint), c_If(tc_Nat_Onat)), c_Nat__Numeral_Oneg)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), c_Int_Onat)))], (33302 ^ _780086) ^ [_1409126, _1409128] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1409126)), hAPP(c_Nat_OSuc, _1409128)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1409126))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat)), tc_Int_Oint), c_If(tc_Nat_Onat)), c_Nat__Numeral_Oneg)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Int_Oint), c_Nat_OSuc), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_Int_Oint), c_Orderings_Oord__class_Omin(tc_Nat_Onat)), c_Int_Onat)), _1409128)))))], (33304 ^ _780086) ^ [_1409183, _1409185] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1409183)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1409185)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1409185))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat)), tc_Int_Oint), c_If(tc_Nat_Onat)), c_Nat__Numeral_Oneg)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Int_Oint), c_Nat_OSuc), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Int_Oint), hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1409183)), c_Int_Onat)))))], (33306 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OPls)))], (33308 ^ _780086) ^ [_1409264] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1409264), c_Int_OPls) = _1409264)], (33310 ^ _780086) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls) = c_Int_OPls)], (33312 ^ _780086) ^ [_1409311] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1409311), c_Int_OPls) = _1409311)], (33314 ^ _780086) ^ [_1409340] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), _1409340) = _1409340)], (33316 ^ _780086) ^ [_1409366] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OPls), _1409366) = c_Int_OPls)], (33318 ^ _780086) ^ [_1409392] : [-(c_Int_Osucc(c_Int_Opred(_1409392)) = _1409392)], (33320 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OPls))], (33322 ^ _780086) ^ [] : [-(c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (33324 ^ _780086) ^ [_1409461] : [class_Int_Onumber__ring(_1409461), -(c_Groups_Ozero__class_Ozero(_1409461) = hAPP(c_Int_Onumber__class_Onumber__of(_1409461), c_Int_OPls))], (33330 ^ _780086) ^ [_1409548] : [class_Int_Onumber__ring(_1409548), -(hAPP(c_Int_Onumber__class_Onumber__of(_1409548), c_Int_OPls) = c_Groups_Ozero__class_Ozero(_1409548))], (33336 ^ _780086) ^ [_1409635, _1409637] : [class_Int_Onumber__ring(_1409635), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1409635), hAPP(c_Int_Onumber__class_Onumber__of(_1409635), c_Int_OPls)), _1409637) = _1409637)], (33342 ^ _780086) ^ [_1409736, _1409738] : [class_Int_Onumber__ring(_1409736), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1409736), _1409738), hAPP(c_Int_Onumber__class_Onumber__of(_1409736), c_Int_OPls)) = _1409738)], (33348 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (33350 ^ _780086) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls))], (33352 ^ _780086) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33354 ^ _780086) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls))], (33356 ^ _780086) ^ [_1409915, _1409917] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1409915)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1409917)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1409915)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1409917), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1409915))))], (33362 ^ _780086) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls)))], (33364 ^ _780086) ^ [_1410072] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1410072), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1410072)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (33370 ^ _780086) ^ [_1410169] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1410169), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1410169)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1410169)))], (33376 ^ _780086) ^ [_1410230] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1410230), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1410230)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (33382 ^ _780086) ^ [_1410321] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1410321), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1410321)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1410321)))], (33388 ^ _780086) ^ [_1410388, _1410390] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1410388), _1410390)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1410388)), _1410390)))], (33394 ^ _780086) ^ [_1410485, _1410487] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1410485)), _1410487)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1410485), _1410487)))], (33400 ^ _780086) ^ [_1410588] : [-(c_Int_Opred(_1410588) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1410588), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (33402 ^ _780086) ^ [_1410625] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1410625), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1410625)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33408 ^ _780086) ^ [_1410722] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1410722), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1410722)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1410722)))], (33414 ^ _780086) ^ [_1410777, _1410779] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1410777), _1410779), hAPP(c_Int_Onumber__class_Onumber__of(_1410777), c_Int_OPls)) = c_Groups_Ozero__class_Ozero(_1410777)), class_Fields_Ofield__inverse__zero(_1410777), class_Int_Onumber__ring(_1410777)], (33424 ^ _780086) ^ [_1410944] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1410944) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1410944), c_Int_OPls)))], (33430 ^ _780086) ^ [_1411031] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1411031), c_Int_OPls)), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1411031) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33436 ^ _780086) ^ [_1411136] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1411136), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1411136), c_Int_OPls)))], (33442 ^ _780086) ^ [_1411223] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1411223), c_Int_OPls)), -(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1411223))], (33448 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls))))], (33450 ^ _780086) ^ [_1411349, _1411351] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1411349)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1411351))), 33453 ^ _780086 : [(33460 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1411349), _1411351)))], (33454 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1411349), _1411351)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1411351)))]]], (33462 ^ _780086) ^ [_1411552, _1411554] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1411552)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1411554)))), 33465 ^ _780086 : [(33466 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1411552), _1411554)))], (33468 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1411554))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1411552), _1411554))], (33484 ^ _780086) ^ [_1411907, _1411909] : [33485 ^ _780086 : [(33486 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1411907), _1411909))], (33488 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1411907), c_Int_OPls))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1411907)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1411909))))], (33474 ^ _780086) ^ [_1411777, _1411779] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1411777)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1411779))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1411777), _1411779))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1411777), c_Int_OPls)))], (33492 ^ _780086) ^ [_1412068] : [-(c_Int_Osucc(_1412068) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1412068), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (33494 ^ _780086) ^ [_1412099, _1412101] : [class_Int_Onumber__ring(_1412099), class_Rings_Olinordered__idom(_1412099), 33501 ^ _780086 : [(33502 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1412099), c_Groups_Ozero__class_Ozero(_1412099)), hAPP(c_Int_Onumber__class_Onumber__of(_1412099), _1412101))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1412101)))], (33508 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1412101)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1412099), c_Groups_Ozero__class_Ozero(_1412099)), hAPP(c_Int_Onumber__class_Onumber__of(_1412099), _1412101))))]]], (33514 ^ _780086) ^ [_1412404, _1412406] : [class_Int_Onumber__ring(_1412404), class_Rings_Olinordered__idom(_1412404), 33521 ^ _780086 : [(33522 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1412404), hAPP(c_Int_Onumber__class_Onumber__of(_1412404), _1412406)), c_Groups_Ozero__class_Ozero(_1412404))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1412406), c_Int_OPls)))], (33528 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1412406), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1412404), hAPP(c_Int_Onumber__class_Onumber__of(_1412404), _1412406)), c_Groups_Ozero__class_Ozero(_1412404))))]]], (33534 ^ _780086) ^ [_1412718, _1412720] : [class_Int_Onumber__ring(_1412718), class_Rings_Olinordered__idom(_1412718), 33541 ^ _780086 : [(33542 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1412718), hAPP(c_Int_Onumber__class_Onumber__of(_1412718), _1412720)), c_Groups_Ozero__class_Ozero(_1412718))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1412720), c_Int_OPls)))], (33548 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1412720), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1412718), hAPP(c_Int_Onumber__class_Onumber__of(_1412718), _1412720)), c_Groups_Ozero__class_Ozero(_1412718))))]]], (33554 ^ _780086) ^ [_1413032, _1413034] : [class_Int_Onumber__ring(_1413032), class_Rings_Olinordered__idom(_1413032), 33561 ^ _780086 : [(33562 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1413032), c_Groups_Ozero__class_Ozero(_1413032)), hAPP(c_Int_Onumber__class_Onumber__of(_1413032), _1413034))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1413034)))], (33568 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1413034)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1413032), c_Groups_Ozero__class_Ozero(_1413032)), hAPP(c_Int_Onumber__class_Onumber__of(_1413032), _1413034))))]]], (33574 ^ _780086) ^ [_1413349] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1413349))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1413349)))], (33580 ^ _780086) ^ [_1413434] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1413434)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1413434))))], (33586 ^ _780086) ^ [_1413534, _1413536] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1413534), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1413534)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1413536)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1413536))], (33592 ^ _780086) ^ [_1413646, _1413648] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1413646), c_Int_OPls))), 33595 ^ _780086 : [(33596 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1413648), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1413646)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1413648)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1413646))], (33602 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1413648), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1413646)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1413648)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1413646), _1413648)))]]], (33608 ^ _780086) ^ [_1413919, _1413921] : [class_Int_Onumber__ring(_1413919), -(hAPP(c_Int_Onumber__class_Onumber__of(_1413919), c_Int_Osucc(_1413921)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1413919), c_Groups_Oone__class_Oone(_1413919)), hAPP(c_Int_Onumber__class_Onumber__of(_1413919), _1413921)))], (33614 ^ _780086) ^ [_1414038, _1414040] : [class_Int_Onumber__ring(_1414038), -(hAPP(c_Int_Onumber__class_Onumber__of(_1414038), c_Int_Opred(_1414040)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1414038), hAPP(c_Groups_Ouminus__class_Ouminus(_1414038), c_Groups_Oone__class_Oone(_1414038))), hAPP(c_Int_Onumber__class_Onumber__of(_1414038), _1414040)))], (33620 ^ _780086) ^ [_1414176, _1414178] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1414176), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1414176)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1414178)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33626 ^ _780086) ^ [_1414281, _1414283] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1414281), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1414281)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1414283)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1414281), _1414283)))], (33632 ^ _780086) ^ [_1414357, _1414359, _1414361] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1414357), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1414357)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1414359)), _1414361)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33638 ^ _780086) ^ [_1414476, _1414478, _1414480] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1414476), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1414476)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1414478)), _1414480)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1414476), _1414478))), _1414480))], (33644 ^ _780086) ^ [_1414566] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1414566)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1414566) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33650 ^ _780086) ^ [_1414657] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1414657) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1414657)))))], (33656 ^ _780086) ^ [_1414769, _1414771] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1414769) = hAPP(c_Nat_OSuc, _1414771), -(hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_HOL_Obool), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1414769))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fconj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint), c_fNot), c_Nat__Numeral_Oneg))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint), c_fNot), c_Nat__Numeral_Oneg))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Int_Oint), c_fequal), c_Int_Onat)), _1414771))))))], (33662 ^ _780086) ^ [_1414892, _1414894] : [hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_HOL_Obool), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1414892))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fconj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint), c_fNot), c_Nat__Numeral_Oneg))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint), c_fNot), c_Nat__Numeral_Oneg))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Int_Oint), c_fequal), c_Int_Onat)), _1414894))))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1414892) = hAPP(c_Nat_OSuc, _1414894))], (33668 ^ _780086) ^ [_1415036, _1415038] : [hAPP(c_Nat_OSuc, _1415036) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1415038), -(hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_HOL_Obool), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1415038))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fconj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint), c_fNot), c_Nat__Numeral_Oneg))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint), c_fNot), c_Nat__Numeral_Oneg))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Int_Oint), c_fequal), c_Int_Onat)), _1415036))))))], (33674 ^ _780086) ^ [_1415159, _1415161] : [hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_HOL_Obool), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1415161))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fconj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint), c_fNot), c_Nat__Numeral_Oneg))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint), c_fNot), c_Nat__Numeral_Oneg))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Int_Oint), c_fequal), c_Int_Onat)), _1415159))))), -(hAPP(c_Nat_OSuc, _1415159) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1415161))], (33680 ^ _780086) ^ [_1415288, _1415290, _1415292, _1415294] : [-(c_Nat_Onat_Onat__case(_1415288, _1415290, _1415292, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1415294)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1415288), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1415294))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1415288, _1415288), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1415288, tc_fun(_1415288, _1415288)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1415288, tc_fun(_1415288, _1415288)), tc_Int_Oint), c_If(_1415288)), c_Nat__Numeral_Oneg)), _1415290)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1415288, tc_Int_Oint), _1415292), c_Int_Onat))))], (33682 ^ _780086) ^ [_1415405, _1415407] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1415405)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1415407))), -(hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_HOL_Obool), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1415407))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fconj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint), c_fNot), c_Nat__Numeral_Oneg))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint), c_fNot), c_Nat__Numeral_Oneg))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_Int_Oint), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1415405)), c_Int_Onat))))))], (33688 ^ _780086) ^ [_1415550, _1415552] : [hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_HOL_Obool), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1415552))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fconj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint), c_fNot), c_Nat__Numeral_Oneg))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint), c_fNot), c_Nat__Numeral_Oneg))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_Int_Oint), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1415550)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1415550)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1415552))))], (33694 ^ _780086) ^ [_1415716, _1415718] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1415716)), hAPP(c_Nat_OSuc, _1415718))), -(hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_HOL_Obool), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1415716))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint), c_fNot), c_Nat__Numeral_Oneg))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Int_Oint), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), c_Int_Onat)), _1415718)))))], (33700 ^ _780086) ^ [_1415843, _1415845] : [hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_HOL_Obool), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1415843))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint), c_fNot), c_Nat__Numeral_Oneg))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Int_Oint), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), c_Int_Onat)), _1415845)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1415843)), hAPP(c_Nat_OSuc, _1415845))))], (33706 ^ _780086) ^ [_1415991, _1415993] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1415991)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1415993))), -(hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_HOL_Obool), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1415993))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fconj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint), c_fNot), c_Nat__Numeral_Oneg))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint), c_fNot), c_Nat__Numeral_Oneg))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_Int_Oint), hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1415991)), c_Int_Onat))))))], (33712 ^ _780086) ^ [_1416136, _1416138] : [hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_HOL_Obool), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1416138))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fconj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint), c_fNot), c_Nat__Numeral_Oneg))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint), c_fNot), c_Nat__Numeral_Oneg))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_Int_Oint), hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1416136)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1416136)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1416138))))], (33718 ^ _780086) ^ [_1416302, _1416304] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1416302)), hAPP(c_Nat_OSuc, _1416304))), -(hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_HOL_Obool), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1416302))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint), c_fNot), c_Nat__Numeral_Oneg))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Int_Oint), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)), c_Int_Onat)), _1416304)))))], (33724 ^ _780086) ^ [_1416429, _1416431] : [hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_HOL_Obool), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1416429))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint), c_fNot), c_Nat__Numeral_Oneg))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Int_Oint), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)), c_Int_Onat)), _1416431)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1416429)), hAPP(c_Nat_OSuc, _1416431))))], (33730 ^ _780086) ^ [_1416568] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1416568))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1416568)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (33736 ^ _780086) ^ [_1416659] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1416659)))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1416659)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1416659)))], (33742 ^ _780086) ^ [_1416711, _1416713] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1416711)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1416713)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1416713))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat)), tc_Int_Oint), c_If(tc_Nat_Onat)), c_Nat__Numeral_Oneg)), hAPP(c_Nat_OSuc, _1416711))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Int_Oint), c_Nat_OSuc), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Int_Oint), hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1416711)), c_Int_Onat)))))], (33744 ^ _780086) ^ [_1416783, _1416785] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1416783)), hAPP(c_Nat_OSuc, _1416785)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1416783))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat)), tc_Int_Oint), c_If(tc_Nat_Onat)), c_Nat__Numeral_Oneg)), hAPP(c_Nat_OSuc, _1416785))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Int_Oint), c_Nat_OSuc), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_Int_Oint), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Int_Onat)), _1416785)))))], (33746 ^ _780086) ^ [_1416849, _1416851, _1416853, _1416855, _1416857] : [-(c_Nat_Onat_Onat__case(_1416849, _1416851, _1416853, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1416855)), _1416857)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1416849), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1416855))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1416849, _1416849), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1416849, tc_fun(_1416849, _1416849)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1416849, tc_fun(_1416849, _1416849)), tc_Int_Oint), c_If(_1416849)), c_Nat__Numeral_Oneg)), c_Nat_Onat_Onat__case(_1416849, _1416851, _1416853, _1416857))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1416849, tc_Int_Oint), _1416853), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Int_Onat)), _1416857)))))], (33748 ^ _780086) ^ [_1416967, _1416969, _1416971, _1416973, _1416975] : [-(hAPP(c_Nat_Onat_Onat__rec(_1416967, _1416969, _1416971), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1416973)), _1416975)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1416967), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1416973))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1416967, _1416967), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1416967, tc_fun(_1416967, _1416967)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1416967, tc_fun(_1416967, _1416967)), tc_Int_Oint), c_If(_1416967)), c_Nat__Numeral_Oneg)), hAPP(c_Nat_Onat_Onat__rec(_1416967, _1416969, _1416971), _1416975))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1416967, _1416967), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1416967, _1416967), tc_Int_Oint), _1416971), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Int_Onat)), _1416975))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1416967, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1416967, _1416969, _1416971)), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Int_Onat)), _1416975))))))], (33750 ^ _780086) ^ [_1417119, _1417121, _1417123, _1417125] : [-(hAPP(c_Nat_Onat_Onat__rec(_1417119, _1417121, _1417123), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1417125)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1417119), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1417125))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1417119, _1417119), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1417119, tc_fun(_1417119, _1417119)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1417119, tc_fun(_1417119, _1417119)), tc_Int_Oint), c_If(_1417119)), c_Nat__Numeral_Oneg)), _1417121)), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1417119, _1417119), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1417119, _1417119), tc_Int_Oint), _1417123), c_Int_Onat)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1417119, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1417119, _1417121, _1417123)), c_Int_Onat)))))], (33752 ^ _780086) ^ [_1417250, _1417252, _1417254, _1417256, _1417258, _1417260, _1417262, _1417264, _1417266, _1417268, _1417270] : [c_Equiv__Relations_Oequiv(_1417250, _1417252, _1417254), c_Equiv__Relations_Oequiv(_1417256, _1417258, _1417260), c_Equiv__Relations_Ocongruent2(_1417250, _1417256, tc_fun(_1417262, tc_HOL_Obool), _1417254, _1417260, _1417264), hBOOL(hAPP(hAPP(c_member(tc_fun(_1417250, tc_HOL_Obool)), _1417266), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1417250), _1417252), _1417254))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1417256, tc_HOL_Obool)), _1417268), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1417256), _1417258), _1417260))), 33774 ^ _780086 : [(33775 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1417250), 33773 ^ [_1417250, _1417252, _1417254, _1417256, _1417258, _1417260, _1417262, _1417264, _1417266, _1417268, _1417270]), _1417252)))], (33778 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1417256), 33776 ^ [_1417250, _1417252, _1417254, _1417256, _1417258, _1417260, _1417262, _1417264, _1417266, _1417268, _1417270]), _1417258)))], (33780 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1417262, tc_HOL_Obool)), hAPP(hAPP(_1417264, 33773 ^ [_1417250, _1417252, _1417254, _1417256, _1417258, _1417260, _1417262, _1417264, _1417266, _1417268, _1417270]), 33776 ^ [_1417250, _1417252, _1417254, _1417256, _1417258, _1417260, _1417262, _1417264, _1417266, _1417268, _1417270])), _1417270))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1417262, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1417250, tc_fun(_1417262, tc_HOL_Obool)), _1417266), hAPP(hAPP(c_COMBB(tc_fun(_1417256, tc_fun(_1417262, tc_HOL_Obool)), tc_fun(_1417262, tc_HOL_Obool), _1417250), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1417256, tc_fun(_1417262, tc_HOL_Obool)), _1417268)), _1417264))), _1417270)))], (33784 ^ _780086) ^ [_1418252, _1418254, _1418256, _1418258, _1418260, _1418262, _1418264] : [c_Equiv__Relations_Oequiv(_1418252, _1418254, _1418256), c_Equiv__Relations_Ocongruent(_1418252, tc_fun(_1418258, tc_HOL_Obool), _1418256, _1418260), hBOOL(hAPP(hAPP(c_member(tc_fun(_1418252, tc_HOL_Obool)), _1418262), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1418252), _1418254), _1418256))), 33798 ^ _780086 : [(33799 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1418252), 33797 ^ [_1418252, _1418254, _1418256, _1418258, _1418260, _1418262, _1418264]), _1418254)))], (33801 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1418258, tc_HOL_Obool)), hAPP(_1418260, 33797 ^ [_1418252, _1418254, _1418256, _1418258, _1418260, _1418262, _1418264])), _1418264))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1418258, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1418252, tc_fun(_1418258, tc_HOL_Obool)), _1418262), _1418260)), _1418264)))], (33805 ^ _780086) ^ [_1418763, _1418765, _1418767] : [-(hAPP(c_Nat_Onat_Onat__rec(_1418763, _1418765, _1418767), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1418765)], (33807 ^ _780086) ^ [_1418797, _1418799, _1418801, _1418803] : [-(hAPP(c_Nat_Onat_Onat__rec(_1418797, _1418799, _1418801), hAPP(c_Nat_OSuc, _1418803)) = hAPP(hAPP(_1418801, _1418803), hAPP(c_Nat_Onat_Onat__rec(_1418797, _1418799, _1418801), _1418803)))], (33809 ^ _780086) ^ [_1418849, _1418851] : [class_Int_Onumber__ring(_1418849), 33812 ^ _780086 : [(33813 ^ _780086) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1418849), _1418851) = c_Groups_Ozero__class_Ozero(_1418849), -(c_Int_Oiszero(_1418849, hAPP(c_Int_Onumber__class_Onumber__of(_1418849), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1418851), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))))], (33819 ^ _780086) ^ [] : [c_Int_Oiszero(_1418849, hAPP(c_Int_Onumber__class_Onumber__of(_1418849), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1418851), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1418849), _1418851) = c_Groups_Ozero__class_Ozero(_1418849))]]], (33825 ^ _780086) ^ [_1419108, _1419110] : [class_Int_Onumber__ring(_1419108), 33828 ^ _780086 : [(33829 ^ _780086) ^ [] : [c_Groups_Ozero__class_Ozero(_1419108) = hAPP(c_Int_Onumber__class_Onumber__of(_1419108), _1419110), -(c_Int_Oiszero(_1419108, hAPP(c_Int_Onumber__class_Onumber__of(_1419108), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1419110)))))], (33835 ^ _780086) ^ [] : [c_Int_Oiszero(_1419108, hAPP(c_Int_Onumber__class_Onumber__of(_1419108), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1419110)))), -(c_Groups_Ozero__class_Ozero(_1419108) = hAPP(c_Int_Onumber__class_Onumber__of(_1419108), _1419110))]]], (33841 ^ _780086) ^ [_1419367, _1419369, _1419371] : [class_Int_Onumber__ring(_1419367), 33844 ^ _780086 : [(33845 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1419369))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1419367), hAPP(c_Int_Onumber__class_Onumber__of(_1419367), _1419371)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1419369))) = hAPP(hAPP(c_HOL_OLet(_1419367, _1419367), hAPP(hAPP(c_Power_Opower__class_Opower(_1419367), hAPP(c_Int_Onumber__class_Onumber__of(_1419367), _1419371)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1419369))), hAPP(hAPP(c_COMBS(_1419367, _1419367, _1419367), hAPP(hAPP(c_COMBB(_1419367, tc_fun(_1419367, _1419367), _1419367), c_Groups_Otimes__class_Otimes(_1419367)), hAPP(c_Groups_Otimes__class_Otimes(_1419367), hAPP(c_Int_Onumber__class_Onumber__of(_1419367), _1419371)))), c_COMBI(_1419367))))], (33851 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1419369)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1419367), hAPP(c_Int_Onumber__class_Onumber__of(_1419367), _1419371)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1419369))) = c_Groups_Oone__class_Oone(_1419367))]]], (33857 ^ _780086) ^ [_1419774, _1419776] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1419774))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1419776), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1419774))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1419776), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1419774))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint), c_Groups_Otimes__class_Otimes(tc_Int_Oint)), hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1419776))), c_COMBI(tc_Int_Oint))))], (33863 ^ _780086) ^ [_1419931, _1419933] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1419931)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1419933), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1419931))) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (33869 ^ _780086) ^ [_1419985, _1419987] : [c_Int_Oiszero(_1419985, hAPP(c_Int_Onumber__class_Onumber__of(_1419985), c_Int_OBit1(_1419987))), class_Int_Onumber__ring(_1419985), class_Int_Oring__char__0(_1419985)], (33879 ^ _780086) ^ [_1420140, _1420142] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1420140)), c_Int_OBit1(_1420142))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1420140), _1420142)))], (33885 ^ _780086) ^ [_1420241, _1420243] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1420241), _1420243)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1420241)), c_Int_OBit1(_1420243))))], (33891 ^ _780086) ^ [_1420363, _1420365] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1420363)), c_Int_OBit1(_1420365))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1420363), _1420365)))], (33897 ^ _780086) ^ [_1420464, _1420466] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1420464), _1420466)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1420464)), c_Int_OBit1(_1420466))))], (33903 ^ _780086) ^ [_1420586, _1420588] : [c_Int_OBit1(_1420586) = c_Int_OBit1(_1420588), -(_1420586 = _1420588)], (33909 ^ _780086) ^ [_1420667, _1420669] : [_1420667 = _1420669, -(c_Int_OBit1(_1420667) = c_Int_OBit1(_1420669))], (33915 ^ _780086) ^ [_1420769, _1420771] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1420769)), c_Int_OBit1(_1420771))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1420769), _1420771)))], (33921 ^ _780086) ^ [_1420870, _1420872] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1420870), _1420872)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1420870)), c_Int_OBit1(_1420872))))], (33927 ^ _780086) ^ [_1420992, _1420994] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1420992)), c_Int_OBit1(_1420994))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1420992), _1420994)))], (33933 ^ _780086) ^ [_1421093, _1421095] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1421093), _1421095)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1421093)), c_Int_OBit1(_1421095))))], (33939 ^ _780086) ^ [_1421209] : [c_Int_OBit1(_1421209) = c_Int_OPls], (33941 ^ _780086) ^ [_1421243] : [c_Int_OPls = c_Int_OBit1(_1421243)], (33943 ^ _780086) ^ [_1421268] : [class_Int_Onumber__ring(_1421268), c_Int_Oiszero(_1421268, hAPP(c_Int_Onumber__class_Onumber__of(_1421268), c_Int_OBit1(c_Int_OPls)))], (33949 ^ _780086) ^ [_1421352] : [class_Rings_Osemiring__1(_1421352), -(c_Int_Oiszero(_1421352, c_Groups_Ozero__class_Ozero(_1421352)))], (33955 ^ _780086) ^ [_1421429, _1421431] : [class_Rings_Osemiring__1(_1421429), 33958 ^ _780086 : [(33959 ^ _780086) ^ [] : [c_Int_Oiszero(_1421429, _1421431), -(_1421431 = c_Groups_Ozero__class_Ozero(_1421429))], (33965 ^ _780086) ^ [] : [_1421431 = c_Groups_Ozero__class_Ozero(_1421429), -(c_Int_Oiszero(_1421429, _1421431))]]], (33971 ^ _780086) ^ [_1421640] : [class_Rings_Osemiring__1(_1421640), c_Int_Oiszero(_1421640, c_Groups_Oone__class_Oone(_1421640))], (33977 ^ _780086) ^ [_1421730] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1421730)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1421730), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (33983 ^ _780086) ^ [_1421825] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1421825), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1421825)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (33989 ^ _780086) ^ [_1421938] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1421938))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1421938)))], (33995 ^ _780086) ^ [_1422021] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1422021)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1422021))))], (34001 ^ _780086) ^ [_1422122] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1422122)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1422122), c_Int_OPls)))], (34007 ^ _780086) ^ [_1422217] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1422217), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1422217)), c_Int_OPls)))], (34013 ^ _780086) ^ [_1422318] : [-(c_Int_OBit1(_1422318) = 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)), _1422318)), _1422318))], (34015 ^ _780086) ^ [_1422364] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1422364)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1422364))))], (34021 ^ _780086) ^ [_1422459] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1422459))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1422459)))))], (34027 ^ _780086) ^ [_1422560] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(_1422560)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1422560))))], (34029 ^ _780086) ^ [] : [-(c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls))], (34031 ^ _780086) ^ [_1422613, _1422615] : [class_Int_Onumber__ring(_1422613), -(hAPP(c_Int_Onumber__class_Onumber__of(_1422613), c_Int_OBit1(_1422615)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1422613), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1422613), c_Groups_Oone__class_Oone(_1422613)), hAPP(c_Int_Onumber__class_Onumber__of(_1422613), _1422615))), hAPP(c_Int_Onumber__class_Onumber__of(_1422613), _1422615)))], (34037 ^ _780086) ^ [_1422758, _1422760] : [class_Int_Onumber__ring(_1422758), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1422758), hAPP(c_Int_Onumber__class_Onumber__of(_1422758), c_Int_OBit1(c_Int_OPls))), _1422760) = _1422760)], (34043 ^ _780086) ^ [_1422859, _1422861] : [class_Int_Onumber__ring(_1422859), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1422859), _1422861), hAPP(c_Int_Onumber__class_Onumber__of(_1422859), c_Int_OBit1(c_Int_OPls))) = _1422861)], (34049 ^ _780086) ^ [_1422960] : [class_Int_Onumber__ring(_1422960), -(hAPP(c_Int_Onumber__class_Onumber__of(_1422960), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(_1422960))], (34055 ^ _780086) ^ [_1423047] : [class_Int_Onumber__ring(_1423047), -(c_Groups_Oone__class_Oone(_1423047) = hAPP(c_Int_Onumber__class_Onumber__of(_1423047), c_Int_OBit1(c_Int_OPls)))], (34061 ^ _780086) ^ [_1423146] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1423146))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1423146)))], (34067 ^ _780086) ^ [_1423229] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1423229)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1423229))))], (34073 ^ _780086) ^ [_1423330] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1423330)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1423330), c_Int_OPls)))], (34079 ^ _780086) ^ [_1423425] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1423425), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1423425)), c_Int_OPls)))], (34085 ^ _780086) ^ [_1423526, _1423528] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1423526), _1423528), hAPP(c_Int_Onumber__class_Onumber__of(_1423526), c_Int_OBit1(c_Int_OPls))) = _1423528), class_Fields_Ofield(_1423526), class_Int_Onumber__ring(_1423526)], (34095 ^ _780086) ^ [_1423677, _1423679] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1423677), _1423679), hAPP(c_Int_Onumber__class_Onumber__of(_1423677), c_Int_OBit1(c_Int_OPls))) = _1423679), class_Fields_Ofield(_1423677), class_Int_Onumber__ring(_1423677)], (34105 ^ _780086) ^ [_1423828, _1423830] : [class_Int_Onumber__ring(_1423828), 34108 ^ _780086 : [(34109 ^ _780086) ^ [] : [c_Groups_Oone__class_Oone(_1423828) = hAPP(c_Int_Onumber__class_Onumber__of(_1423828), _1423830), -(c_Int_Oiszero(_1423828, hAPP(c_Int_Onumber__class_Onumber__of(_1423828), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1423830)))))], (34115 ^ _780086) ^ [] : [c_Int_Oiszero(_1423828, hAPP(c_Int_Onumber__class_Onumber__of(_1423828), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1423830)))), -(c_Groups_Oone__class_Oone(_1423828) = hAPP(c_Int_Onumber__class_Onumber__of(_1423828), _1423830))]]], (34121 ^ _780086) ^ [_1424087, _1424089] : [class_Int_Onumber__ring(_1424087), 34124 ^ _780086 : [(34125 ^ _780086) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1424087), _1424089) = c_Groups_Oone__class_Oone(_1424087), -(c_Int_Oiszero(_1424087, hAPP(c_Int_Onumber__class_Onumber__of(_1424087), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1424089), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))))], (34131 ^ _780086) ^ [] : [c_Int_Oiszero(_1424087, hAPP(c_Int_Onumber__class_Onumber__of(_1424087), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1424089), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1424087), _1424089) = c_Groups_Oone__class_Oone(_1424087))]]], (34137 ^ _780086) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))], (34139 ^ _780086) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (34141 ^ _780086) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))], (34143 ^ _780086) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))], (34145 ^ _780086) ^ [_1424418] : [class_Int_Onumber__ring(_1424418), -(c_Int_Oiszero(_1424418, hAPP(c_Int_Onumber__class_Onumber__of(_1424418), c_Int_OPls)))], (34151 ^ _780086) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (34153 ^ _780086) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (34155 ^ _780086) ^ [_1424537, _1424539] : [class_Groups_Omonoid__mult(_1424537), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1424537), _1424539), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1424537), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1424537), _1424539), _1424539)), _1424539))], (34161 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))))], (34163 ^ _780086) ^ [_1424678] : [-(hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1424678))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))), _1424678))], (34165 ^ _780086) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))], (34167 ^ _780086) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))], (34169 ^ _780086) ^ [_1424749, _1424751] : [class_Int_Onumber__ring(_1424749), class_Rings_Olinordered__idom(_1424749), 34176 ^ _780086 : [(34177 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1424749), c_Groups_Oone__class_Oone(_1424749)), hAPP(c_Int_Onumber__class_Onumber__of(_1424749), _1424751))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1424751)))], (34183 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1424751)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1424749), c_Groups_Oone__class_Oone(_1424749)), hAPP(c_Int_Onumber__class_Onumber__of(_1424749), _1424751))))]]], (34189 ^ _780086) ^ [_1425054, _1425056] : [class_Int_Onumber__ring(_1425054), class_Rings_Olinordered__idom(_1425054), 34196 ^ _780086 : [(34197 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1425054), hAPP(c_Int_Onumber__class_Onumber__of(_1425054), _1425056)), c_Groups_Oone__class_Oone(_1425054))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1425056), c_Int_OBit1(c_Int_OPls))))], (34203 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1425056), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1425054), hAPP(c_Int_Onumber__class_Onumber__of(_1425054), _1425056)), c_Groups_Oone__class_Oone(_1425054))))]]], (34209 ^ _780086) ^ [_1425368, _1425370] : [class_Int_Onumber__ring(_1425368), class_Rings_Olinordered__idom(_1425368), 34216 ^ _780086 : [(34217 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1425368), hAPP(c_Int_Onumber__class_Onumber__of(_1425368), _1425370)), c_Groups_Oone__class_Oone(_1425368))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1425370), c_Int_OBit1(c_Int_OPls))))], (34223 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1425370), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1425368), hAPP(c_Int_Onumber__class_Onumber__of(_1425368), _1425370)), c_Groups_Oone__class_Oone(_1425368))))]]], (34229 ^ _780086) ^ [_1425682, _1425684] : [class_Int_Onumber__ring(_1425682), class_Rings_Olinordered__idom(_1425682), 34236 ^ _780086 : [(34237 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1425682), c_Groups_Oone__class_Oone(_1425682)), hAPP(c_Int_Onumber__class_Onumber__of(_1425682), _1425684))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1425684)))], (34243 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1425684)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1425682), c_Groups_Oone__class_Oone(_1425682)), hAPP(c_Int_Onumber__class_Onumber__of(_1425682), _1425684))))]]], (34249 ^ _780086) ^ [_1425987, _1425989] : [class_Int_Onumber__ring(_1425987), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1425987), c_Groups_Oone__class_Oone(_1425987)), hAPP(c_Int_Onumber__class_Onumber__of(_1425987), _1425989)) = hAPP(c_Int_Onumber__class_Onumber__of(_1425987), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1425989)))], (34255 ^ _780086) ^ [_1426108, _1426110] : [class_Int_Onumber__ring(_1426108), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1426108), hAPP(c_Int_Onumber__class_Onumber__of(_1426108), _1426110)), c_Groups_Oone__class_Oone(_1426108)) = hAPP(c_Int_Onumber__class_Onumber__of(_1426108), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1426110), c_Int_OBit1(c_Int_OPls))))], (34261 ^ _780086) ^ [_1426235, _1426237] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls)), _1426235)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1426237)), _1426235) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1426237), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1426235), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))))], (34267 ^ _780086) ^ [_1426358, _1426360] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1426358))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1426360)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))), _1426358), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1426360)))], (34269 ^ _780086) ^ [_1426409, _1426411] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1426409))), _1426411) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))), _1426409), _1426411))], (34271 ^ _780086) ^ [_1426454, _1426456] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1426454, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1426456)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1426454, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))), _1426456)))], (34273 ^ _780086) ^ [_1426499, _1426501] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1426499)))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1426501)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))), _1426499)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1426501)))], (34275 ^ _780086) ^ [_1426554, _1426556] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1426554)))), _1426556) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))), _1426554)), _1426556))], (34277 ^ _780086) ^ [_1426603, _1426605] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1426603), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1426605)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1426603), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))), _1426605)))], (34279 ^ _780086) ^ [_1426652, _1426654, _1426656] : [class_Int_Onumber__ring(_1426652), 34282 ^ _780086 : [(34283 ^ _780086) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1426652), _1426654) = hAPP(c_Int_Onumber__class_Onumber__of(_1426652), _1426656), -(c_Int_Oiszero(_1426652, hAPP(c_Int_Onumber__class_Onumber__of(_1426652), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1426654), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1426656)))))], (34289 ^ _780086) ^ [] : [c_Int_Oiszero(_1426652, hAPP(c_Int_Onumber__class_Onumber__of(_1426652), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1426654), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1426656)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1426652), _1426654) = hAPP(c_Int_Onumber__class_Onumber__of(_1426652), _1426656))]]], (34295 ^ _780086) ^ [_1426935, _1426937] : [class_Int_Onumber__ring(_1426935), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1426935), c_Groups_Oone__class_Oone(_1426935)), hAPP(c_Int_Onumber__class_Onumber__of(_1426935), _1426937)) = hAPP(c_Int_Onumber__class_Onumber__of(_1426935), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1426937))))], (34301 ^ _780086) ^ [_1427062, _1427064] : [class_Int_Onumber__ring(_1427062), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1427062), hAPP(c_Int_Onumber__class_Onumber__of(_1427062), _1427064)), c_Groups_Oone__class_Oone(_1427062)) = hAPP(c_Int_Onumber__class_Onumber__of(_1427062), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1427064), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))))], (34307 ^ _780086) ^ [_1427195] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1427195))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1427195)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34313 ^ _780086) ^ [_1427284] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1427284)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1427284)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1427284)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_COMBI(tc_Nat_Onat)))))], (34319 ^ _780086) ^ [_1427339, _1427341, _1427343] : [class_Int_Onumber__ring(_1427339), 34322 ^ _780086 : [(34323 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1427341))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1427339), _1427343), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1427341))) = hAPP(hAPP(c_HOL_OLet(_1427339, _1427339), hAPP(hAPP(c_Power_Opower__class_Opower(_1427339), _1427343), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1427341))), hAPP(hAPP(c_COMBS(_1427339, _1427339, _1427339), hAPP(hAPP(c_COMBB(_1427339, tc_fun(_1427339, _1427339), _1427339), c_Groups_Otimes__class_Otimes(_1427339)), hAPP(c_Groups_Otimes__class_Otimes(_1427339), _1427343))), c_COMBI(_1427339))))], (34329 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1427341)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1427339), _1427343), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1427341))) = c_Groups_Oone__class_Oone(_1427339))]]], (34335 ^ _780086) ^ [_1427706, _1427708] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1427706))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1427708)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1427706))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1427708), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1427706)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (34341 ^ _780086) ^ [_1427853, _1427855] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1427853)))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1427855)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1427853))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1427855)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1427853)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (34347 ^ _780086) ^ [_1427935, _1427937] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1427935), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1427937)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1427935)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1427937), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1427935))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (34353 ^ _780086) ^ [_1428086, _1428088, _1428090] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Int_Oint, tc_Nat_Onat), hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1428086)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_Int_Oint), tc_Nat_Onat), c_Groups_Otimes__class_Otimes(tc_Int_Oint)), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), _1428088))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1428090))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1428090)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1428086), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1428086), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1428090), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1428088)))))], (34355 ^ _780086) ^ [_1428173, _1428175] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1428173)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1428175))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1428173)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1428175), _1428173))], (34361 ^ _780086) ^ [_1428308, _1428310] : [c_Int_OBit0(_1428308) = c_Int_OBit1(_1428310)], (34363 ^ _780086) ^ [_1428349, _1428351] : [c_Int_OBit1(_1428349) = c_Int_OBit0(_1428351)], (34365 ^ _780086) ^ [] : [-(c_Int_OBit0(c_Int_OPls) = c_Int_OPls)], (34367 ^ _780086) ^ [_1428408] : [c_Int_OPls = c_Int_OBit0(_1428408), -(c_Int_OPls = _1428408)], (34373 ^ _780086) ^ [_1428483] : [c_Int_OPls = _1428483, -(c_Int_OPls = c_Int_OBit0(_1428483))], (34379 ^ _780086) ^ [_1428576] : [c_Int_OBit0(_1428576) = c_Int_OPls, -(_1428576 = c_Int_OPls)], (34385 ^ _780086) ^ [_1428651] : [_1428651 = c_Int_OPls, -(c_Int_OBit0(_1428651) = c_Int_OPls)], (34391 ^ _780086) ^ [_1428732] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit0(_1428732)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1428732)))], (34393 ^ _780086) ^ [_1428780, _1428782] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1428780)), c_Int_OBit0(_1428782))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1428780), _1428782)))], (34399 ^ _780086) ^ [_1428881, _1428883] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1428881), _1428883)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1428881)), c_Int_OBit0(_1428883))))], (34405 ^ _780086) ^ [_1429003, _1429005] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1429003)), c_Int_OBit0(_1429005))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1429003), _1429005)))], (34411 ^ _780086) ^ [_1429104, _1429106] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1429104), _1429106)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1429104)), c_Int_OBit0(_1429106))))], (34417 ^ _780086) ^ [_1429211] : [-(c_Int_OBit0(_1429211) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1429211), _1429211))], (34419 ^ _780086) ^ [_1429242, _1429244] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1429242)), c_Int_OBit0(_1429244)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1429242), _1429244)))], (34421 ^ _780086) ^ [_1429300, _1429302] : [c_Int_OBit0(_1429300) = c_Int_OBit0(_1429302), -(_1429300 = _1429302)], (34427 ^ _780086) ^ [_1429381, _1429383] : [_1429381 = _1429383, -(c_Int_OBit0(_1429381) = c_Int_OBit0(_1429383))], (34433 ^ _780086) ^ [_1429468, _1429470] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit0(_1429468)), _1429470) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1429468), _1429470)))], (34435 ^ _780086) ^ [_1429509, _1429511] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1429509)), c_Int_OBit0(_1429511)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1429509), _1429511)))], (34437 ^ _780086) ^ [_1429567, _1429569] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1429567)), c_Int_OBit0(_1429569))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1429567), _1429569)))], (34443 ^ _780086) ^ [_1429668, _1429670] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1429668), _1429670)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1429668)), c_Int_OBit0(_1429670))))], (34449 ^ _780086) ^ [_1429790, _1429792] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1429790)), c_Int_OBit0(_1429792))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1429790), _1429792)))], (34455 ^ _780086) ^ [_1429891, _1429893] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1429891), _1429893)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1429891)), c_Int_OBit0(_1429893))))], (34461 ^ _780086) ^ [_1430010] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1430010)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1430010), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (34467 ^ _780086) ^ [_1430105] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1430105), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1430105)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (34473 ^ _780086) ^ [_1430218] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1430218))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1430218)))], (34479 ^ _780086) ^ [_1430301] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1430301)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1430301))))], (34485 ^ _780086) ^ [_1430402] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1430402)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1430402), c_Int_OPls)))], (34491 ^ _780086) ^ [_1430497] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1430497), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1430497)), c_Int_OPls)))], (34497 ^ _780086) ^ [_1430613, _1430615] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1430613)), c_Int_OBit1(_1430615))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1430613), _1430615)))], (34503 ^ _780086) ^ [_1430714, _1430716] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1430714), _1430716)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1430714)), c_Int_OBit1(_1430716))))], (34509 ^ _780086) ^ [_1430836, _1430838] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1430836)), c_Int_OBit1(_1430838))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1430836), _1430838)))], (34515 ^ _780086) ^ [_1430937, _1430939] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1430937), _1430939)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1430937)), c_Int_OBit1(_1430939))))], (34521 ^ _780086) ^ [_1431056] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1431056))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1431056)))], (34527 ^ _780086) ^ [_1431139] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1431139)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1431139))))], (34533 ^ _780086) ^ [_1431240] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1431240)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1431240), c_Int_OPls)))], (34539 ^ _780086) ^ [_1431335] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1431335), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1431335)), c_Int_OPls)))], (34545 ^ _780086) ^ [_1431451, _1431453] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1431451)), c_Int_OBit0(_1431453))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1431451), _1431453)))], (34551 ^ _780086) ^ [_1431552, _1431554] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1431552), _1431554)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1431552)), c_Int_OBit0(_1431554))))], (34557 ^ _780086) ^ [_1431674, _1431676] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1431674)), c_Int_OBit0(_1431676))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1431674), _1431676)))], (34563 ^ _780086) ^ [_1431775, _1431777] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1431775), _1431777)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1431775)), c_Int_OBit0(_1431777))))], (34569 ^ _780086) ^ [_1431882, _1431884] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1431882)), c_Int_OBit1(_1431884)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1431882), _1431884)))], (34571 ^ _780086) ^ [_1431925, _1431927] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1431925)), c_Int_OBit0(_1431927)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1431925), _1431927)))], (34573 ^ _780086) ^ [_1431968] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1431968)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), _1431968)))], (34575 ^ _780086) ^ [_1432001, _1432003] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1432001)), c_Int_OBit1(_1432003)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1432001), _1432003)))], (34577 ^ _780086) ^ [_1432044, _1432046] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1432044)), c_Int_OBit0(_1432046)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1432044), _1432046)))], (34579 ^ _780086) ^ [_1432087, _1432089] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1432087))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1432089))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1432087)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1432089)))], (34581 ^ _780086) ^ [_1432152] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1432152)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1432152))))], (34587 ^ _780086) ^ [_1432247] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1432247))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1432247)))))], (34593 ^ _780086) ^ [_1432348] : [-(c_Int_Opred(c_Int_OBit1(_1432348)) = c_Int_OBit0(_1432348))], (34595 ^ _780086) ^ [_1432377] : [-(c_Int_Opred(c_Int_OBit0(_1432377)) = c_Int_OBit1(c_Int_Opred(_1432377)))], (34597 ^ _780086) ^ [_1432408, _1432410] : [class_Int_Onumber__ring(_1432408), class_Int_Oring__char__0(_1432408), 34604 ^ _780086 : [(34605 ^ _780086) ^ [] : [c_Int_Oiszero(_1432408, hAPP(c_Int_Onumber__class_Onumber__of(_1432408), c_Int_OBit0(_1432410))), -(c_Int_Oiszero(_1432408, hAPP(c_Int_Onumber__class_Onumber__of(_1432408), _1432410)))], (34611 ^ _780086) ^ [] : [c_Int_Oiszero(_1432408, hAPP(c_Int_Onumber__class_Onumber__of(_1432408), _1432410)), -(c_Int_Oiszero(_1432408, hAPP(c_Int_Onumber__class_Onumber__of(_1432408), c_Int_OBit0(_1432410))))]]], (34617 ^ _780086) ^ [_1432701] : [-(c_Int_Osucc(c_Int_OBit0(_1432701)) = c_Int_OBit1(_1432701))], (34619 ^ _780086) ^ [_1432730] : [-(c_Int_Osucc(c_Int_OBit1(_1432730)) = c_Int_OBit0(c_Int_Osucc(_1432730)))], (34621 ^ _780086) ^ [_1432761] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1432761)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1432761)), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_COMBI(tc_Nat_Onat))))], (34623 ^ _780086) ^ [_1432798, _1432800] : [class_Int_Onumber__ring(_1432798), -(hAPP(c_Int_Onumber__class_Onumber__of(_1432798), c_Int_OBit0(_1432800)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1432798), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1432798), c_Groups_Ozero__class_Ozero(_1432798)), hAPP(c_Int_Onumber__class_Onumber__of(_1432798), _1432800))), hAPP(c_Int_Onumber__class_Onumber__of(_1432798), _1432800)))], (34629 ^ _780086) ^ [_1432958, _1432960] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1432958)), c_Int_OBit0(_1432960))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1432958), _1432960)))], (34635 ^ _780086) ^ [_1433059, _1433061] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1433059), _1433061)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1433059)), c_Int_OBit0(_1433061))))], (34641 ^ _780086) ^ [_1433181, _1433183] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1433181)), c_Int_OBit0(_1433183))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1433181), _1433183)))], (34647 ^ _780086) ^ [_1433282, _1433284] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1433282), _1433284)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1433282)), c_Int_OBit0(_1433284))))], (34653 ^ _780086) ^ [_1433404, _1433406] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1433404)), c_Int_OBit1(_1433406))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1433404), _1433406)))], (34659 ^ _780086) ^ [_1433505, _1433507] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1433505), _1433507)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1433505)), c_Int_OBit1(_1433507))))], (34665 ^ _780086) ^ [_1433627, _1433629] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1433627)), c_Int_OBit1(_1433629))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1433627), _1433629)))], (34671 ^ _780086) ^ [_1433728, _1433730] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1433728), _1433730)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1433728)), c_Int_OBit1(_1433730))))], (34677 ^ _780086) ^ [] : [-(hAPP(c_Finite__Set_Ocard(tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool, tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))], (34679 ^ _780086) ^ [_1433853, _1433855] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit1(_1433853)), _1433855) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1433853), _1433855))), _1433855))], (34681 ^ _780086) ^ [_1433900, _1433902] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1433900)), c_Int_OBit1(_1433902)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_Opred(_1433900)), _1433902)))], (34683 ^ _780086) ^ [_1433945, _1433947] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1433945)), c_Int_OBit1(_1433947)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1433945), c_Int_Osucc(_1433947))))], (34685 ^ _780086) ^ [_1433990, _1433992, _1433994] : [class_Int_Onumber__ring(_1433990), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1433990), _1433992), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1433994))) = hAPP(hAPP(c_HOL_OLet(_1433990, _1433990), hAPP(hAPP(c_Power_Opower__class_Opower(_1433990), _1433992), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1433994))), hAPP(hAPP(c_COMBS(_1433990, _1433990, _1433990), c_Groups_Otimes__class_Otimes(_1433990)), c_COMBI(_1433990))))], (34691 ^ _780086) ^ [_1434161, _1434163] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1434161), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1434163))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1434161), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1434163))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint), c_Groups_Otimes__class_Otimes(tc_Int_Oint)), c_COMBI(tc_Int_Oint))))], (34693 ^ _780086) ^ [_1434212, _1434214] : [class_Int_Onumber__ring(_1434212), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1434212), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1434212), c_Groups_Oone__class_Oone(_1434212)), c_Groups_Oone__class_Oone(_1434212))), hAPP(c_Int_Onumber__class_Onumber__of(_1434212), _1434214)) = hAPP(c_Int_Onumber__class_Onumber__of(_1434212), c_Int_OBit0(_1434214)))], (34699 ^ _780086) ^ [_1434351] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1434351))), 34702 ^ _780086 : [(34703 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1434351)))))], (34705 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1434351)))))]]], (34707 ^ _780086) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (34709 ^ _780086) ^ [_1434508, _1434510, _1434512] : [class_Int_Onumber__ring(_1434508), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1434508), hAPP(c_Int_Onumber__class_Onumber__of(_1434508), _1434510)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1434512))) = hAPP(hAPP(c_HOL_OLet(_1434508, _1434508), hAPP(hAPP(c_Power_Opower__class_Opower(_1434508), hAPP(c_Int_Onumber__class_Onumber__of(_1434508), _1434510)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1434512))), hAPP(hAPP(c_COMBS(_1434508, _1434508, _1434508), c_Groups_Otimes__class_Otimes(_1434508)), c_COMBI(_1434508))))], (34715 ^ _780086) ^ [_1434699, _1434701] : [class_Int_Onumber__ring(_1434699), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1434699), hAPP(c_Int_Onumber__class_Onumber__of(_1434699), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1434701) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1434699), _1434701), _1434701))], (34721 ^ _780086) ^ [_1434816, _1434818] : [class_Int_Onumber__ring(_1434816), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1434816), _1434818), hAPP(c_Int_Onumber__class_Onumber__of(_1434816), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1434816), _1434818), _1434818))], (34727 ^ _780086) ^ [_1434933] : [class_Int_Onumber__ring(_1434933), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1434933), c_Groups_Oone__class_Oone(_1434933)), c_Groups_Oone__class_Oone(_1434933)) = hAPP(c_Int_Onumber__class_Onumber__of(_1434933), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))], (34733 ^ _780086) ^ [_1435040, _1435042] : [class_Rings_Oring__1__no__zero__divisors(_1435040), 34736 ^ _780086 : [(34737 ^ _780086) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1435040), _1435042), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1435040), -(_1435042 = c_Groups_Ozero__class_Ozero(_1435040))], (34743 ^ _780086) ^ [] : [_1435042 = c_Groups_Ozero__class_Ozero(_1435040), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1435040), _1435042), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1435040))]]], (34749 ^ _780086) ^ [_1435281] : [class_Rings_Osemiring__1(_1435281), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1435281), c_Groups_Ozero__class_Ozero(_1435281)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1435281))], (34755 ^ _780086) ^ [] : [-(hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))], (34757 ^ _780086) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (34759 ^ _780086) ^ [_1435414, _1435416] : [class_Rings_Ocomm__semiring__1(_1435414), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1435414), _1435416), _1435416) = hAPP(hAPP(c_Power_Opower__class_Opower(_1435414), _1435416), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (34765 ^ _780086) ^ [_1435521, _1435523] : [class_Groups_Omonoid__mult(_1435521), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1435521), _1435523), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1435521), _1435523), _1435523))], (34771 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (34773 ^ _780086) ^ [_1435646] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1435646) = hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1435646)))], (34775 ^ _780086) ^ [_1435678] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1435678), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1435678)))], (34777 ^ _780086) ^ [_1435713] : [class_Rings_Osemiring__1(_1435713), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1435713), c_Groups_Oone__class_Oone(_1435713)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1435713))], (34783 ^ _780086) ^ [_1435810, _1435812] : [class_Rings_Oring__1(_1435810), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1435810), hAPP(c_Groups_Ouminus__class_Ouminus(_1435810), _1435812)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(_1435810), _1435812), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (34789 ^ _780086) ^ [_1435927] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1435927) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1435927), _1435927))], (34791 ^ _780086) ^ [_1435959] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1435959), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1435959), _1435959))], (34793 ^ _780086) ^ [_1435994, _1435996, _1435998] : [class_Groups_Omonoid__mult(_1435994), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1435994), _1435996), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1435998)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1435994), hAPP(hAPP(c_Power_Opower__class_Opower(_1435994), _1435996), _1435998)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (34799 ^ _780086) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (34801 ^ _780086) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (34803 ^ _780086) ^ [_1436161, _1436163] : [class_Rings_Olinordered__idom(_1436161), -(hAPP(c_Groups_Oabs__class_Oabs(_1436161), hAPP(hAPP(c_Power_Opower__class_Opower(_1436161), _1436163), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = hAPP(hAPP(c_Power_Opower__class_Opower(_1436161), _1436163), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (34809 ^ _780086) ^ [_1436278, _1436280] : [class_Rings_Olinordered__idom(_1436278), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1436278), hAPP(c_Groups_Oabs__class_Oabs(_1436278), _1436280)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(_1436278), _1436280), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (34815 ^ _780086) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))], (34817 ^ _780086) ^ [_1436413] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1436413)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1436413, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (34819 ^ _780086) ^ [_1436450] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1436450))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1436450), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (34821 ^ _780086) ^ [_1436494, _1436496] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1436494)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1436496))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1436494), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1436496))))], (34823 ^ _780086) ^ [_1436546] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1436546), _1436546)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = _1436546)], (34825 ^ _780086) ^ [_1436581, _1436583] : [class_Fields_Olinordered__field__inverse__zero(_1436581), class_Int_Onumber__ring(_1436581), 34832 ^ _780086 : [(34833 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1436581), c_Groups_Ozero__class_Ozero(_1436581)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1436581), _1436583), hAPP(c_Int_Onumber__class_Onumber__of(_1436581), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1436581), c_Groups_Ozero__class_Ozero(_1436581)), _1436583)))], (34839 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1436581), c_Groups_Ozero__class_Ozero(_1436581)), _1436583)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1436581), c_Groups_Ozero__class_Ozero(_1436581)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1436581), _1436583), hAPP(c_Int_Onumber__class_Onumber__of(_1436581), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))]]], (34845 ^ _780086) ^ [_1436931, _1436933] : [class_Fields_Olinordered__field__inverse__zero(_1436931), class_Int_Onumber__ring(_1436931), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1436931), c_Groups_Ozero__class_Ozero(_1436931)), _1436933)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1436931), c_Groups_Ozero__class_Ozero(_1436931)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1436931), _1436933), hAPP(c_Int_Onumber__class_Onumber__of(_1436931), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (34859 ^ _780086) ^ [_1437172, _1437174] : [class_Rings_Olinordered__idom(_1437172), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1437172), c_Groups_Ozero__class_Ozero(_1437172)), hAPP(hAPP(c_Power_Opower__class_Opower(_1437172), _1437174), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (34865 ^ _780086) ^ [_1437281, _1437283, _1437285] : [class_Rings_Olinordered__semidom(_1437281), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1437281), hAPP(hAPP(c_Power_Opower__class_Opower(_1437281), _1437283), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), hAPP(hAPP(c_Power_Opower__class_Opower(_1437281), _1437285), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1437281), c_Groups_Ozero__class_Ozero(_1437281)), _1437285)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1437281), _1437283), _1437285)))], (34879 ^ _780086) ^ [_1437544, _1437546, _1437548] : [class_Rings_Olinordered__semidom(_1437544), hAPP(hAPP(c_Power_Opower__class_Opower(_1437544), _1437546), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(_1437544), _1437548), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1437544), c_Groups_Ozero__class_Ozero(_1437544)), _1437546)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1437544), c_Groups_Ozero__class_Ozero(_1437544)), _1437548)), -(_1437546 = _1437548)], (34897 ^ _780086) ^ [_1437851, _1437853] : [class_Rings_Olinordered__idom(_1437851), 34900 ^ _780086 : [(34901 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1437851), c_Groups_Ozero__class_Ozero(_1437851)), hAPP(hAPP(c_Power_Opower__class_Opower(_1437851), _1437853), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), _1437853 = c_Groups_Ozero__class_Ozero(_1437851)], (34907 ^ _780086) ^ [] : [-(_1437853 = c_Groups_Ozero__class_Ozero(_1437851)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1437851), c_Groups_Ozero__class_Ozero(_1437851)), hAPP(hAPP(c_Power_Opower__class_Opower(_1437851), _1437853), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))]]], (34913 ^ _780086) ^ [_1438075, _1438077] : [class_Rings_Olinordered__idom(_1438075), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1438075), hAPP(hAPP(c_Power_Opower__class_Opower(_1438075), _1438077), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), c_Groups_Ozero__class_Ozero(_1438075)))], (34919 ^ _780086) ^ [_1438185, _1438187, _1438189] : [class_Rings_Olinordered__idom(_1438185), 34922 ^ _780086 : [(34923 ^ _780086) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1438185), hAPP(hAPP(c_Power_Opower__class_Opower(_1438185), _1438187), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), hAPP(hAPP(c_Power_Opower__class_Opower(_1438185), _1438189), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1438185), 34926 ^ _780086 : [(34927 ^ _780086) ^ [] : [-(_1438187 = c_Groups_Ozero__class_Ozero(_1438185))], (34929 ^ _780086) ^ [] : [-(_1438189 = c_Groups_Ozero__class_Ozero(_1438185))]]], (34931 ^ _780086) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1438185), hAPP(hAPP(c_Power_Opower__class_Opower(_1438185), _1438187), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), hAPP(hAPP(c_Power_Opower__class_Opower(_1438185), _1438189), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1438185)), _1438187 = c_Groups_Ozero__class_Ozero(_1438185), _1438189 = c_Groups_Ozero__class_Ozero(_1438185)]]], (34941 ^ _780086) ^ [_1438560, _1438562] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1438560), hAPP(c_Int_Onumber__class_Onumber__of(_1438560), _1438562)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1438560), hAPP(c_Int_Onumber__class_Onumber__of(_1438560), _1438562)), hAPP(c_Int_Onumber__class_Onumber__of(_1438560), _1438562))), class_Groups_Omonoid__mult(_1438560), class_Int_Onumber(_1438560)], (34951 ^ _780086) ^ [_1438747] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1438747), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), -(_1438747 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1438747 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (34961 ^ _780086) ^ [] : [-(hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (34963 ^ _780086) ^ [_1438863, _1438865] : [class_Rings_Oring__1__no__zero__divisors(_1438863), 34966 ^ _780086 : [(34977 ^ _780086) ^ [] : [34978 ^ _780086 : [(34979 ^ _780086) ^ [] : [_1438865 = c_Groups_Oone__class_Oone(_1438863)], (34981 ^ _780086) ^ [] : [_1438865 = hAPP(c_Groups_Ouminus__class_Ouminus(_1438863), c_Groups_Oone__class_Oone(_1438863))]], -(hAPP(hAPP(c_Power_Opower__class_Opower(_1438863), _1438865), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1438863))], (34967 ^ _780086) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1438863), _1438865), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1438863), -(_1438865 = c_Groups_Oone__class_Oone(_1438863)), -(_1438865 = hAPP(c_Groups_Ouminus__class_Ouminus(_1438863), c_Groups_Oone__class_Oone(_1438863)))]]], (34985 ^ _780086) ^ [_1439170, _1439172, _1439174] : [class_Rings_Ocomm__semiring__1(_1439170), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1439170), _1439172), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1439174)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1439170), hAPP(hAPP(c_Power_Opower__class_Opower(_1439170), _1439172), _1439174)), hAPP(hAPP(c_Power_Opower__class_Opower(_1439170), _1439172), _1439174)))], (34991 ^ _780086) ^ [_1439317, _1439319, _1439321] : [class_Rings_Oring__1(_1439317), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1439317), hAPP(c_Groups_Ouminus__class_Ouminus(_1439317), _1439319)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1439321)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1439317), _1439319), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1439321)))], (34997 ^ _780086) ^ [_1439448, _1439450, _1439452] : [class_Rings_Olinordered__semidom(_1439448), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1439448), hAPP(hAPP(c_Power_Opower__class_Opower(_1439448), _1439450), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), hAPP(hAPP(c_Power_Opower__class_Opower(_1439448), _1439452), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1439448), c_Groups_Ozero__class_Ozero(_1439448)), _1439452)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1439448), _1439450), _1439452)))], (35011 ^ _780086) ^ [_1439711, _1439713, _1439715] : [class_Rings_Olinordered__idom(_1439711), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1439711), c_Groups_Ozero__class_Ozero(_1439711)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1439711), hAPP(hAPP(c_Power_Opower__class_Opower(_1439711), _1439713), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), hAPP(hAPP(c_Power_Opower__class_Opower(_1439711), _1439715), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))], (35017 ^ _780086) ^ [_1439854, _1439856, _1439858] : [class_Rings_Olinordered__idom(_1439854), 35020 ^ _780086 : [(35021 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1439854), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1439854), hAPP(hAPP(c_Power_Opower__class_Opower(_1439854), _1439856), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), hAPP(hAPP(c_Power_Opower__class_Opower(_1439854), _1439858), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1439854))), 35024 ^ _780086 : [(35025 ^ _780086) ^ [] : [-(_1439856 = c_Groups_Ozero__class_Ozero(_1439854))], (35027 ^ _780086) ^ [] : [-(_1439858 = c_Groups_Ozero__class_Ozero(_1439854))]]], (35029 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1439854), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1439854), hAPP(hAPP(c_Power_Opower__class_Opower(_1439854), _1439856), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), hAPP(hAPP(c_Power_Opower__class_Opower(_1439854), _1439858), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1439854)))), _1439856 = c_Groups_Ozero__class_Ozero(_1439854), _1439858 = c_Groups_Ozero__class_Ozero(_1439854)]]], (35039 ^ _780086) ^ [_1440250, _1440252, _1440254] : [class_Rings_Olinordered__idom(_1440250), 35042 ^ _780086 : [(35053 ^ _780086) ^ [] : [35054 ^ _780086 : [(35055 ^ _780086) ^ [] : [-(_1440252 = c_Groups_Ozero__class_Ozero(_1440250))], (35057 ^ _780086) ^ [] : [-(_1440254 = c_Groups_Ozero__class_Ozero(_1440250))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1440250), c_Groups_Ozero__class_Ozero(_1440250)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1440250), hAPP(hAPP(c_Power_Opower__class_Opower(_1440250), _1440252), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), hAPP(hAPP(c_Power_Opower__class_Opower(_1440250), _1440254), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))], (35043 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1440250), c_Groups_Ozero__class_Ozero(_1440250)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1440250), hAPP(hAPP(c_Power_Opower__class_Opower(_1440250), _1440252), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), hAPP(hAPP(c_Power_Opower__class_Opower(_1440250), _1440254), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))), _1440252 = c_Groups_Ozero__class_Ozero(_1440250), _1440254 = c_Groups_Ozero__class_Ozero(_1440250)]]], (35061 ^ _780086) ^ [_1440625, _1440627, _1440629] : [class_Rings_Olinordered__idom(_1440625), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1440625), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1440625), hAPP(hAPP(c_Power_Opower__class_Opower(_1440625), _1440627), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), hAPP(hAPP(c_Power_Opower__class_Opower(_1440625), _1440629), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1440625)))], (35067 ^ _780086) ^ [_1440769, _1440771, _1440773] : [class_Int_Onumber__ring(_1440769), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1440769), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1440769), _1440771), _1440773)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1440769), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1440769), hAPP(hAPP(c_Power_Opower__class_Opower(_1440769), _1440771), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), hAPP(hAPP(c_Power_Opower__class_Opower(_1440769), _1440773), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1440769), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1440769), hAPP(c_Int_Onumber__class_Onumber__of(_1440769), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1440771)), _1440773)))], (35073 ^ _780086) ^ [_1440984, _1440986, _1440988] : [class_Rings_Olinordered__idom(_1440984), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1440984), c_Groups_Ozero__class_Ozero(_1440984)), hAPP(hAPP(c_Power_Opower__class_Opower(_1440984), _1440986), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1440988)))))], (35079 ^ _780086) ^ [_1441101, _1441103, _1441105] : [class_Groups_Omonoid__mult(_1441101), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1441101), _1441103), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1441105))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1441101), _1441103), hAPP(hAPP(c_Power_Opower__class_Opower(_1441101), hAPP(hAPP(c_Power_Opower__class_Opower(_1441101), _1441103), _1441105)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (35085 ^ _780086) ^ [_1441254, _1441256, _1441258] : [class_Rings_Ocomm__semiring__1(_1441254), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1441254), _1441256), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1441258))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1441254), _1441256), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1441254), hAPP(hAPP(c_Power_Opower__class_Opower(_1441254), _1441256), _1441258)), hAPP(hAPP(c_Power_Opower__class_Opower(_1441254), _1441256), _1441258))))], (35091 ^ _780086) ^ [_1441423, _1441425] : [class_Rings_Oring__1(_1441423), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1441423), hAPP(c_Groups_Ouminus__class_Ouminus(_1441423), c_Groups_Oone__class_Oone(_1441423))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1441425)) = c_Groups_Oone__class_Oone(_1441423))], (35097 ^ _780086) ^ [_1441547, _1441549] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1441547))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1441549))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1441547))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1441549)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1441547)))], (35103 ^ _780086) ^ [_1441684, _1441686] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1441684)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1441686))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1441684))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1441686)), c_Groups_Oone__class_Oone(tc_Int_Oint))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1441684)))], (35109 ^ _780086) ^ [_1441773] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1441773, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1441773, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (35115 ^ _780086) ^ [_1441864] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1441864, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1441864, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (35121 ^ _780086) ^ [_1441961] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1441961)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1441961), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (35127 ^ _780086) ^ [_1442056, _1442058, _1442060] : [class_Int_Onumber__ring(_1442056), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1442056), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1442056), _1442058), _1442060)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1442056), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1442056), hAPP(hAPP(c_Power_Opower__class_Opower(_1442056), _1442058), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), hAPP(hAPP(c_Power_Opower__class_Opower(_1442056), _1442060), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1442056), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1442056), hAPP(c_Int_Onumber__class_Onumber__of(_1442056), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1442058)), _1442060)))], (35133 ^ _780086) ^ [_1442271, _1442273, _1442275] : [class_Rings_Olinordered__idom(_1442271), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1442271), c_Groups_Ozero__class_Ozero(_1442271)), hAPP(hAPP(c_Power_Opower__class_Opower(_1442271), _1442273), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1442275))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1442271), c_Groups_Ozero__class_Ozero(_1442271)), _1442273)))], (35143 ^ _780086) ^ [_1442466, _1442468, _1442470] : [class_Rings_Olinordered__idom(_1442466), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1442466), _1442468), c_Groups_Ozero__class_Ozero(_1442466))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1442466), hAPP(hAPP(c_Power_Opower__class_Opower(_1442466), _1442468), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1442470)))), c_Groups_Ozero__class_Ozero(_1442466))))], (35153 ^ _780086) ^ [_1442661, _1442663] : [class_Rings_Oring__1(_1442661), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1442661), hAPP(c_Groups_Ouminus__class_Ouminus(_1442661), c_Groups_Oone__class_Oone(_1442661))), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1442663))) = hAPP(c_Groups_Ouminus__class_Ouminus(_1442661), c_Groups_Oone__class_Oone(_1442661)))], (35159 ^ _780086) ^ [_1442792] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1442792)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1442792), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (35165 ^ _780086) ^ [_1442899, _1442901] : [class_Rings_Osemiring__1(_1442899), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1442901)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1442899), hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1442901))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1442899), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1442899), hAPP(c_Int_Onat, _1442901))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1442899), hAPP(c_Int_Onat, _1442901))))], (35175 ^ _780086) ^ [_1443100, _1443102] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1443100)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1443102)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1443100)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1443102, _1443100))))], (35181 ^ _780086) ^ [_1443227, _1443229] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1443227), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1443229))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1443227)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1443229), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1443227))], (35187 ^ _780086) ^ [_1443374] : [_1443374 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Code__Numeral_Oint__of, _1443374) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (35193 ^ _780086) ^ [_1443450] : [-(_1443450 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), 35196 ^ _780086 : [(35197 ^ _780086) ^ [] : [c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1443450, hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Code__Numeral_Oint__of, _1443450) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), hAPP(c_Code__Numeral_Oint__of, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1443450), hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (35203 ^ _780086) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1443450, hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_Code__Numeral_Oint__of, _1443450) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), hAPP(c_Code__Numeral_Oint__of, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1443450), hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]]], (35209 ^ _780086) ^ [_1443710, _1443712] : [class_Rings_Oring__1(_1443710), 35212 ^ _780086 : [(35213 ^ _780086) ^ [] : [_1443712 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1443710), _1443712) = c_Groups_Ozero__class_Ozero(_1443710))], (35219 ^ _780086) ^ [] : [-(_1443712 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 35222 ^ _780086 : [(35223 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1443712), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1443710), _1443712) = hAPP(c_Groups_Ouminus__class_Ouminus(_1443710), hAPP(c_Int_Oring__1__class_Oof__int(_1443710), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1443712))))], (35229 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1443712), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1443710), _1443712) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, _1443710), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_fun(_1443710, _1443710)), tc_fun(tc_Int_Oint, _1443710)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1443710, _1443710), _1443710), tc_fun(tc_fun(tc_Int_Oint, tc_fun(_1443710, _1443710)), tc_fun(tc_Int_Oint, _1443710)), tc_Int_Oint), c_COMBB(tc_fun(_1443710, _1443710), _1443710, tc_Int_Oint)), hAPP(hAPP(c_COMBB(_1443710, tc_fun(tc_fun(_1443710, _1443710), _1443710), tc_Int_Oint), c_HOL_OLet(_1443710, _1443710)), c_Int_Oring__1__class_Oof__int(_1443710)))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1443710, _1443710), tc_fun(_1443710, _1443710)), hAPP(hAPP(c_COMBB(tc_fun(_1443710, tc_fun(_1443710, _1443710)), tc_fun(tc_fun(_1443710, _1443710), tc_fun(_1443710, _1443710)), tc_Int_Oint), c_COMBS(_1443710, _1443710, _1443710)), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1443710, _1443710), tc_fun(_1443710, tc_fun(_1443710, _1443710))), hAPP(hAPP(c_COMBB(tc_fun(_1443710, tc_fun(_1443710, _1443710)), tc_fun(tc_fun(_1443710, _1443710), tc_fun(_1443710, tc_fun(_1443710, _1443710))), tc_Int_Oint), c_COMBB(_1443710, tc_fun(_1443710, _1443710), _1443710)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1443710, tc_fun(_1443710, _1443710)), tc_Int_Oint), c_If(_1443710)), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Int_Oint, tc_HOL_Obool), c_fequal), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), hAPP(hAPP(c_COMBS(_1443710, _1443710, _1443710), c_Groups_Oplus__class_Oplus(_1443710)), c_COMBI(_1443710))))), hAPP(hAPP(c_COMBC(_1443710, _1443710, _1443710), hAPP(hAPP(c_COMBB(_1443710, tc_fun(_1443710, _1443710), _1443710), c_Groups_Oplus__class_Oplus(_1443710)), hAPP(hAPP(c_COMBS(_1443710, _1443710, _1443710), c_Groups_Oplus__class_Oplus(_1443710)), c_COMBI(_1443710)))), c_Groups_Oone__class_Oone(_1443710))))), c_Divides_Odivmod__int(_1443712, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))]]]]], (35235 ^ _780086) ^ [_1444623, _1444625] : [class_Int_Onumber__ring(_1444623), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1444623), hAPP(c_Int_Onumber__class_Onumber__of(_1444623), c_Int_OMin)), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1444625))) = hAPP(c_Int_Onumber__class_Onumber__of(_1444623), c_Int_OMin))], (35241 ^ _780086) ^ [_1444755] : [c_Int_OBit0(_1444755) = c_Int_OMin], (35243 ^ _780086) ^ [_1444789] : [c_Int_OMin = c_Int_OBit0(_1444789)], (35245 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OMin)))], (35247 ^ _780086) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (35249 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OMin))], (35251 ^ _780086) ^ [] : [c_Int_OPls = c_Int_OMin], (35253 ^ _780086) ^ [] : [c_Int_OMin = c_Int_OPls], (35255 ^ _780086) ^ [_1444934] : [c_Int_OBit1(_1444934) = c_Int_OMin, -(_1444934 = c_Int_OMin)], (35261 ^ _780086) ^ [_1445009] : [_1445009 = c_Int_OMin, -(c_Int_OBit1(_1445009) = c_Int_OMin)], (35267 ^ _780086) ^ [_1445102] : [c_Int_OMin = c_Int_OBit1(_1445102), -(c_Int_OMin = _1445102)], (35273 ^ _780086) ^ [_1445177] : [c_Int_OMin = _1445177, -(c_Int_OMin = c_Int_OBit1(_1445177))], (35279 ^ _780086) ^ [] : [-(c_Int_OBit1(c_Int_OMin) = c_Int_OMin)], (35281 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (35283 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (35285 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (35287 ^ _780086) ^ [_1445348] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1445348)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1445348), c_Int_OMin)))], (35293 ^ _780086) ^ [_1445443] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1445443), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1445443)), c_Int_OMin)))], (35299 ^ _780086) ^ [_1445556] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1445556))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1445556)))], (35305 ^ _780086) ^ [_1445639] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1445639)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1445639))))], (35311 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (35313 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (35315 ^ _780086) ^ [_1445782] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1445782)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1445782), c_Int_OMin)))], (35321 ^ _780086) ^ [_1445877] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1445877), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1445877)), c_Int_OMin)))], (35327 ^ _780086) ^ [_1445990] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1445990))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1445990)))], (35333 ^ _780086) ^ [_1446073] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1446073)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1446073))))], (35339 ^ _780086) ^ [_1446174] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1446174)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1446174), c_Int_OMin)))], (35345 ^ _780086) ^ [_1446269] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1446269), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1446269)), c_Int_OMin)))], (35351 ^ _780086) ^ [_1446382] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1446382))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1446382)))], (35357 ^ _780086) ^ [_1446465] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1446465)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1446465))))], (35363 ^ _780086) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)], (35365 ^ _780086) ^ [] : [-(c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (35367 ^ _780086) ^ [_1446596] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OMin), _1446596) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1446596))], (35369 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))))], (35371 ^ _780086) ^ [] : [-(c_Int_Opred(c_Int_OPls) = c_Int_OMin)], (35373 ^ _780086) ^ [_1446661] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1446661), c_Int_OMin) = c_Int_Opred(_1446661))], (35375 ^ _780086) ^ [_1446692] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OMin), _1446692) = c_Int_Opred(_1446692))], (35377 ^ _780086) ^ [] : [-(c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin))], (35379 ^ _780086) ^ [_1446738] : [class_Int_Onumber__ring(_1446738), c_Int_Oiszero(_1446738, hAPP(c_Int_Onumber__class_Onumber__of(_1446738), c_Int_OMin))], (35385 ^ _780086) ^ [] : [-(c_Int_Osucc(c_Int_OMin) = c_Int_OPls)], (35387 ^ _780086) ^ [_1446840] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1446840), c_Int_OMin) = c_Int_Osucc(_1446840))], (35389 ^ _780086) ^ [_1446871, _1446873] : [class_Int_Onumber__ring(_1446871), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1446871), _1446873), hAPP(c_Int_Onumber__class_Onumber__of(_1446871), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1446871), _1446873))], (35395 ^ _780086) ^ [_1446982, _1446984] : [class_Int_Onumber__ring(_1446982), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1446982), hAPP(c_Int_Onumber__class_Onumber__of(_1446982), c_Int_OMin)), _1446984) = hAPP(c_Groups_Ouminus__class_Ouminus(_1446982), _1446984))], (35401 ^ _780086) ^ [_1447093] : [class_Int_Onumber__ring(_1447093), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1447093), c_Groups_Oone__class_Oone(_1447093)) = hAPP(c_Int_Onumber__class_Onumber__of(_1447093), c_Int_OMin))], (35407 ^ _780086) ^ [_1447190] : [class_Int_Onumber__ring(_1447190), -(hAPP(c_Int_Onumber__class_Onumber__of(_1447190), c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(_1447190), c_Groups_Oone__class_Oone(_1447190)))], (35413 ^ _780086) ^ [_1447287] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1447287), hAPP(c_Int_Onumber__class_Onumber__of(_1447287), c_Int_OMin)) = c_Groups_Oone__class_Oone(_1447287)), class_Int_Onumber__ring(_1447287), class_Rings_Olinordered__idom(_1447287)], (35423 ^ _780086) ^ [_1447432, _1447434] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1447432), _1447434), hAPP(c_Int_Onumber__class_Onumber__of(_1447432), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1447432), _1447434)), class_Fields_Ofield__inverse__zero(_1447432), class_Int_Onumber__ring(_1447432)], (35433 ^ _780086) ^ [_1447605] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1447605))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1447605)))], (35439 ^ _780086) ^ [_1447688] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1447688)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1447688))))], (35445 ^ _780086) ^ [_1447789] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1447789)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1447789), c_Int_OMin)))], (35451 ^ _780086) ^ [_1447884] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1447884), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1447884)), c_Int_OMin)))], (35457 ^ _780086) ^ [_1447985] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1447985, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (35459 ^ _780086) ^ [_1448012] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1448012)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1448012)))], (35461 ^ _780086) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OMin) = c_Int_OBit1(c_Int_OPls))], (35463 ^ _780086) ^ [_1448078, _1448080] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1448078), _1448080) = c_Groups_Oone__class_Oone(tc_Int_Oint), 35468 ^ _780086 : [(35469 ^ _780086) ^ [] : [-(_1448078 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (35471 ^ _780086) ^ [] : [-(_1448080 = c_Groups_Oone__class_Oone(tc_Int_Oint))]], 35472 ^ _780086 : [(35473 ^ _780086) ^ [] : [-(_1448078 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (35475 ^ _780086) ^ [] : [-(_1448080 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))]]], (35477 ^ _780086) ^ [_1448262, _1448264] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1448262), _1448264) = c_Groups_Oone__class_Oone(tc_Int_Oint)), 35478 ^ _780086 : [(35479 ^ _780086) ^ [] : [_1448262 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1448264 = c_Groups_Oone__class_Oone(tc_Int_Oint)], (35485 ^ _780086) ^ [] : [_1448262 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1448264 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)]]], (35493 ^ _780086) ^ [_1448488, _1448490] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1448488), _1448490) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(_1448488 = c_Groups_Oone__class_Oone(tc_Int_Oint)), -(_1448488 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (35503 ^ _780086) ^ [_1448590] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1448590)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1448590)))], (35505 ^ _780086) ^ [_1448623] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1448623)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1448623)))], (35507 ^ _780086) ^ [_1448656] : [class_Int_Onumber__ring(_1448656), -(hAPP(c_Int_Oring__1__class_Oof__int(_1448656), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(_1448656), c_Int_OMin))], (35513 ^ _780086) ^ [_1448749] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1448749), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1448749))], (35515 ^ _780086) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), c_Int_OPls))], (35517 ^ _780086) ^ [_1448799, _1448801] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1448799), hAPP(c_Int_Onumber__class_Onumber__of(_1448799), c_Int_OMin)), _1448801) = hAPP(c_Groups_Ouminus__class_Ouminus(_1448799), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1448799), c_Groups_Oone__class_Oone(_1448799)), _1448801))), class_Fields_Ofield__inverse__zero(_1448799), class_Int_Onumber__ring(_1448799)], (35527 ^ _780086) ^ [_1448980, _1448982] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1448980), hAPP(hAPP(c_Power_Opower__class_Opower(_1448980), hAPP(c_Int_Onumber__class_Onumber__of(_1448980), c_Int_OMin)), _1448982)) = c_Groups_Oone__class_Oone(_1448980)), class_Int_Onumber__ring(_1448980), class_Rings_Olinordered__idom(_1448980)], (35537 ^ _780086) ^ [_1449145] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1449145)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)), _1449145) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (35543 ^ _780086) ^ [_1449230, _1449232] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1449230)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1449230), _1449232)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1449230), _1449232) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (35553 ^ _780086) ^ [_1449397] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1449397)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1449397) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1449397), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (35559 ^ _780086) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), c_Int_OBit1(c_Int_OPls)))], (35561 ^ _780086) ^ [_1449514, _1449516] : [class_Int_Onumber__ring(_1449514), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1449514), hAPP(c_Int_Onumber__class_Onumber__of(_1449514), c_Int_OMin)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1449516)) = c_Groups_Oone__class_Oone(_1449514))], (35567 ^ _780086) ^ [] : [-(c_Nitpick_OFrac = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint, tc_HOL_Obool), tc_fun(tc_Int_Oint, tc_HOL_Obool), tc_Int_Oint), hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fconj), hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Int_Oint, tc_fun(tc_Int_Oint, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_HOL_Obool)), tc_fun(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_HOL_Obool)), tc_Int_Oint), c_COMBC(tc_Int_Oint, tc_Int_Oint, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint, tc_Int_Oint), tc_fun(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_HOL_Obool)), tc_Int_Oint), hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_HOL_Obool), tc_Int_Oint), c_fequal)), c_Nitpick_Oint__gcd))), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (35569 ^ _780086) ^ [_1449643] : [-(c_Int_Oint__ge__less__than(_1449643) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, tc_HOL_Obool), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_HOL_Obool), tc_fun(tc_Int_Oint, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_Int_Oint, tc_HOL_Obool), tc_fun(tc_Int_Oint, tc_HOL_Obool)), tc_Int_Oint), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fconj), hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1449643)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (35571 ^ _780086) ^ [_1449689] : [-(c_Int_Oint__ge__less__than2(_1449689) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint, tc_HOL_Obool), tc_fun(tc_Int_Oint, tc_HOL_Obool), tc_Int_Oint), hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fconj), hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1449689)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (35573 ^ _780086) ^ [_1449735, _1449737] : [-(c_Fun_Oinj__on(tc_fun(_1449735, _1449737), tc_fun(tc_prod(_1449735, _1449737), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1449735, _1449737), tc_HOL_Obool), tc_fun(tc_prod(_1449735, _1449737), tc_HOL_Obool), tc_fun(_1449735, _1449737)), c_Set_OCollect(tc_prod(_1449735, _1449737))), hAPP(hAPP(c_COMBB(tc_fun(_1449735, tc_fun(_1449737, tc_HOL_Obool)), tc_fun(tc_prod(_1449735, _1449737), tc_HOL_Obool), tc_fun(_1449735, _1449737)), c_Product__Type_Oprod_Oprod__case(_1449735, _1449737, tc_HOL_Obool)), hAPP(c_COMBB(_1449737, tc_fun(_1449737, tc_HOL_Obool), _1449735), hAPP(c_COMBC(_1449737, _1449737, tc_HOL_Obool), c_fequal)))), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1449735, _1449737), tc_HOL_Obool))))], (35575 ^ _780086) ^ [_1449855, _1449857, _1449859, _1449861] : [-(c_Nitpick_Oprod(_1449855, _1449857, _1449859, _1449861) = hAPP(c_Set_OCollect(tc_prod(_1449855, _1449857)), hAPP(c_Product__Type_Oprod_Oprod__case(_1449855, _1449857, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1449855, tc_fun(_1449857, tc_HOL_Obool), tc_fun(_1449857, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1449857, tc_HOL_Obool), tc_fun(_1449857, tc_HOL_Obool)), _1449855), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1449857)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1449855), c_fconj), hAPP(hAPP(c_COMBC(_1449855, tc_fun(_1449855, tc_HOL_Obool), tc_HOL_Obool), c_member(_1449855)), _1449859)))), hAPP(hAPP(c_COMBC(_1449857, tc_fun(_1449857, tc_HOL_Obool), tc_HOL_Obool), c_member(_1449857)), _1449861)))))], (35577 ^ _780086) ^ [_1449992, _1449994] : [_1449992 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(c_Code__Numeral_Onat__of__aux(_1449992, _1449994) = _1449994)], (35583 ^ _780086) ^ [_1450069, _1450071] : [-(_1450069 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(c_Code__Numeral_Onat__of__aux(_1450069, _1450071) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1450069), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), hAPP(c_Nat_OSuc, _1450071)))], (35589 ^ _780086) ^ [_1450122, _1450124] : [-(c_Divides_Odivmod__int__rel(_1450122, _1450124) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_HOL_Obool), tc_fun(tc_Int_Oint, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Int_Oint, tc_HOL_Obool), tc_fun(tc_Int_Oint, tc_HOL_Obool)), tc_Int_Oint), c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint, tc_HOL_Obool), tc_fun(tc_Int_Oint, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Int_Oint), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fconj)), hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint, tc_Int_Oint), tc_fun(tc_Int_Oint, tc_HOL_Obool), tc_Int_Oint), hAPP(c_COMBB(tc_Int_Oint, tc_HOL_Obool, tc_Int_Oint), hAPP(c_fequal, _1450122))), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint)), hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1450124)))))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fconj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint), hAPP(c_fimplies, hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1450124))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fconj), hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Int_Oint, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Int_Oint)), _1450124))))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint), hAPP(c_fimplies, hAPP(c_fNot, hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1450124)))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fconj), hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1450124))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Int_Oint, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))))], (35591 ^ _780086) ^ [_1450233, _1450235] : [-(_1450233 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1450235, _1450233), c_Divides_Odivmod__int(_1450235, _1450233))))], (35597 ^ _780086) ^ [_1450277, _1450279, _1450281, _1450283, _1450285] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1450277, _1450279), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1450281), _1450283))), -(_1450279 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1450285)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1450277, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1450279), _1450285)), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1450281), _1450285)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1450279), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1450281, _1450285))), _1450283)))))], (35611 ^ _780086) ^ [] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (35613 ^ _780086) ^ [_1450601, _1450603] : [class_Int_Onumber__ring(_1450601), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1450603)), -(hBOOL(hAPP(hAPP(c_member(_1450601), hAPP(c_Int_Onumber__class_Onumber__of(_1450601), _1450603)), c_Nat_Osemiring__1__class_ONats(_1450601))))], (35623 ^ _780086) ^ [_1450787, _1450789, _1450791, _1450793, _1450795, _1450797] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1450787, tc_fun(_1450789, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1450787, tc_fun(tc_prod(_1450787, _1450789), tc_HOL_Obool), tc_fun(_1450789, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1450789, tc_fun(tc_fun(tc_prod(_1450787, _1450789), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1450787, _1450789), tc_HOL_Obool), tc_fun(_1450789, tc_HOL_Obool)), _1450787), c_COMBC(_1450789, tc_fun(tc_prod(_1450787, _1450789), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1450789, tc_prod(_1450787, _1450789)), tc_fun(_1450789, tc_fun(tc_fun(tc_prod(_1450787, _1450789), tc_HOL_Obool), tc_HOL_Obool)), _1450787), hAPP(c_COMBB(tc_prod(_1450787, _1450789), tc_fun(tc_fun(tc_prod(_1450787, _1450789), tc_HOL_Obool), tc_HOL_Obool), _1450789), c_member(tc_prod(_1450787, _1450789)))), c_Product__Type_OPair(_1450787, _1450789)))), _1450791)), hAPP(hAPP(c_COMBC(_1450787, tc_fun(tc_prod(_1450787, _1450789), tc_HOL_Obool), tc_fun(_1450789, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1450789, tc_fun(tc_fun(tc_prod(_1450787, _1450789), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1450787, _1450789), tc_HOL_Obool), tc_fun(_1450789, tc_HOL_Obool)), _1450787), c_COMBC(_1450789, tc_fun(tc_prod(_1450787, _1450789), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1450789, tc_prod(_1450787, _1450789)), tc_fun(_1450789, tc_fun(tc_fun(tc_prod(_1450787, _1450789), tc_HOL_Obool), tc_HOL_Obool)), _1450787), hAPP(c_COMBB(tc_prod(_1450787, _1450789), tc_fun(tc_fun(tc_prod(_1450787, _1450789), tc_HOL_Obool), tc_HOL_Obool), _1450789), c_member(tc_prod(_1450787, _1450789)))), c_Product__Type_OPair(_1450787, _1450789)))), _1450793)), _1450795), _1450797)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1450787, _1450789)), hAPP(hAPP(c_Product__Type_OPair(_1450787, _1450789), _1450795), _1450797)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1450787, _1450789), tc_HOL_Obool)), _1450791), _1450793))))], (35629 ^ _780086) ^ [_1451444, _1451446, _1451448, _1451450, _1451452, _1451454] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1451444, _1451446)), hAPP(hAPP(c_Product__Type_OPair(_1451444, _1451446), _1451452), _1451454)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1451444, _1451446), tc_HOL_Obool)), _1451448), _1451450))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1451444, tc_fun(_1451446, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1451444, tc_fun(tc_prod(_1451444, _1451446), tc_HOL_Obool), tc_fun(_1451446, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1451446, tc_fun(tc_fun(tc_prod(_1451444, _1451446), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1451444, _1451446), tc_HOL_Obool), tc_fun(_1451446, tc_HOL_Obool)), _1451444), c_COMBC(_1451446, tc_fun(tc_prod(_1451444, _1451446), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1451446, tc_prod(_1451444, _1451446)), tc_fun(_1451446, tc_fun(tc_fun(tc_prod(_1451444, _1451446), tc_HOL_Obool), tc_HOL_Obool)), _1451444), hAPP(c_COMBB(tc_prod(_1451444, _1451446), tc_fun(tc_fun(tc_prod(_1451444, _1451446), tc_HOL_Obool), tc_HOL_Obool), _1451446), c_member(tc_prod(_1451444, _1451446)))), c_Product__Type_OPair(_1451444, _1451446)))), _1451448)), hAPP(hAPP(c_COMBC(_1451444, tc_fun(tc_prod(_1451444, _1451446), tc_HOL_Obool), tc_fun(_1451446, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1451446, tc_fun(tc_fun(tc_prod(_1451444, _1451446), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1451444, _1451446), tc_HOL_Obool), tc_fun(_1451446, tc_HOL_Obool)), _1451444), c_COMBC(_1451446, tc_fun(tc_prod(_1451444, _1451446), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1451446, tc_prod(_1451444, _1451446)), tc_fun(_1451446, tc_fun(tc_fun(tc_prod(_1451444, _1451446), tc_HOL_Obool), tc_HOL_Obool)), _1451444), hAPP(c_COMBB(tc_prod(_1451444, _1451446), tc_fun(tc_fun(tc_prod(_1451444, _1451446), tc_HOL_Obool), tc_HOL_Obool), _1451446), c_member(tc_prod(_1451444, _1451446)))), c_Product__Type_OPair(_1451444, _1451446)))), _1451450)), _1451452), _1451454)))], (35635 ^ _780086) ^ [_1452128, _1452130, _1452132, _1452134] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1452128, tc_fun(_1452130, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1452128, tc_fun(tc_prod(_1452128, _1452130), tc_HOL_Obool), tc_fun(_1452130, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1452130, tc_fun(tc_fun(tc_prod(_1452128, _1452130), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1452128, _1452130), tc_HOL_Obool), tc_fun(_1452130, tc_HOL_Obool)), _1452128), c_COMBC(_1452130, tc_fun(tc_prod(_1452128, _1452130), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1452130, tc_prod(_1452128, _1452130)), tc_fun(_1452130, tc_fun(tc_fun(tc_prod(_1452128, _1452130), tc_HOL_Obool), tc_HOL_Obool)), _1452128), hAPP(c_COMBB(tc_prod(_1452128, _1452130), tc_fun(tc_fun(tc_prod(_1452128, _1452130), tc_HOL_Obool), tc_HOL_Obool), _1452130), c_member(tc_prod(_1452128, _1452130)))), c_Product__Type_OPair(_1452128, _1452130)))), _1452132)), hAPP(hAPP(c_COMBC(_1452128, tc_fun(tc_prod(_1452128, _1452130), tc_HOL_Obool), tc_fun(_1452130, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1452130, tc_fun(tc_fun(tc_prod(_1452128, _1452130), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1452128, _1452130), tc_HOL_Obool), tc_fun(_1452130, tc_HOL_Obool)), _1452128), c_COMBC(_1452130, tc_fun(tc_prod(_1452128, _1452130), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1452130, tc_prod(_1452128, _1452130)), tc_fun(_1452130, tc_fun(tc_fun(tc_prod(_1452128, _1452130), tc_HOL_Obool), tc_HOL_Obool)), _1452128), hAPP(c_COMBB(tc_prod(_1452128, _1452130), tc_fun(tc_fun(tc_prod(_1452128, _1452130), tc_HOL_Obool), tc_HOL_Obool), _1452130), c_member(tc_prod(_1452128, _1452130)))), c_Product__Type_OPair(_1452128, _1452130)))), _1452134))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1452128, _1452130), tc_HOL_Obool)), _1452132), _1452134)))], (35641 ^ _780086) ^ [_1452729, _1452731, _1452733, _1452735] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1452729, _1452731), tc_HOL_Obool)), _1452733), _1452735)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1452729, tc_fun(_1452731, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1452729, tc_fun(tc_prod(_1452729, _1452731), tc_HOL_Obool), tc_fun(_1452731, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1452731, tc_fun(tc_fun(tc_prod(_1452729, _1452731), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1452729, _1452731), tc_HOL_Obool), tc_fun(_1452731, tc_HOL_Obool)), _1452729), c_COMBC(_1452731, tc_fun(tc_prod(_1452729, _1452731), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1452731, tc_prod(_1452729, _1452731)), tc_fun(_1452731, tc_fun(tc_fun(tc_prod(_1452729, _1452731), tc_HOL_Obool), tc_HOL_Obool)), _1452729), hAPP(c_COMBB(tc_prod(_1452729, _1452731), tc_fun(tc_fun(tc_prod(_1452729, _1452731), tc_HOL_Obool), tc_HOL_Obool), _1452731), c_member(tc_prod(_1452729, _1452731)))), c_Product__Type_OPair(_1452729, _1452731)))), _1452733)), hAPP(hAPP(c_COMBC(_1452729, tc_fun(tc_prod(_1452729, _1452731), tc_HOL_Obool), tc_fun(_1452731, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1452731, tc_fun(tc_fun(tc_prod(_1452729, _1452731), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1452729, _1452731), tc_HOL_Obool), tc_fun(_1452731, tc_HOL_Obool)), _1452729), c_COMBC(_1452731, tc_fun(tc_prod(_1452729, _1452731), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1452731, tc_prod(_1452729, _1452731)), tc_fun(_1452731, tc_fun(tc_fun(tc_prod(_1452729, _1452731), tc_HOL_Obool), tc_HOL_Obool)), _1452729), hAPP(c_COMBB(tc_prod(_1452729, _1452731), tc_fun(tc_fun(tc_prod(_1452729, _1452731), tc_HOL_Obool), tc_HOL_Obool), _1452731), c_member(tc_prod(_1452729, _1452731)))), c_Product__Type_OPair(_1452729, _1452731)))), _1452735))))], (35647 ^ _780086) ^ [_1453357, _1453359, _1453361, _1453363] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1453357, tc_fun(_1453359, tc_HOL_Obool))), _1453361), _1453363)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1453357, _1453359)), hAPP(hAPP(c_Product__Type_OPair(_1453357, _1453359), _1453361), _1453363)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1453357, _1453359), tc_HOL_Obool)))))], (35653 ^ _780086) ^ [_1453514, _1453516, _1453518, _1453520] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1453514, _1453516)), hAPP(hAPP(c_Product__Type_OPair(_1453514, _1453516), _1453518), _1453520)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1453514, _1453516), tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1453514, tc_fun(_1453516, tc_HOL_Obool))), _1453518), _1453520)))], (35659 ^ _780086) ^ [_1453698, _1453700, _1453702, _1453704] : [hAPP(hAPP(c_COMBC(_1453698, tc_fun(tc_prod(_1453698, _1453700), tc_HOL_Obool), tc_fun(_1453700, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1453700, tc_fun(tc_fun(tc_prod(_1453698, _1453700), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1453698, _1453700), tc_HOL_Obool), tc_fun(_1453700, tc_HOL_Obool)), _1453698), c_COMBC(_1453700, tc_fun(tc_prod(_1453698, _1453700), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1453700, tc_prod(_1453698, _1453700)), tc_fun(_1453700, tc_fun(tc_fun(tc_prod(_1453698, _1453700), tc_HOL_Obool), tc_HOL_Obool)), _1453698), hAPP(c_COMBB(tc_prod(_1453698, _1453700), tc_fun(tc_fun(tc_prod(_1453698, _1453700), tc_HOL_Obool), tc_HOL_Obool), _1453700), c_member(tc_prod(_1453698, _1453700)))), c_Product__Type_OPair(_1453698, _1453700)))), _1453702) = hAPP(hAPP(c_COMBC(_1453698, tc_fun(tc_prod(_1453698, _1453700), tc_HOL_Obool), tc_fun(_1453700, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1453700, tc_fun(tc_fun(tc_prod(_1453698, _1453700), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1453698, _1453700), tc_HOL_Obool), tc_fun(_1453700, tc_HOL_Obool)), _1453698), c_COMBC(_1453700, tc_fun(tc_prod(_1453698, _1453700), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1453700, tc_prod(_1453698, _1453700)), tc_fun(_1453700, tc_fun(tc_fun(tc_prod(_1453698, _1453700), tc_HOL_Obool), tc_HOL_Obool)), _1453698), hAPP(c_COMBB(tc_prod(_1453698, _1453700), tc_fun(tc_fun(tc_prod(_1453698, _1453700), tc_HOL_Obool), tc_HOL_Obool), _1453700), c_member(tc_prod(_1453698, _1453700)))), c_Product__Type_OPair(_1453698, _1453700)))), _1453704), -(_1453702 = _1453704)], (35665 ^ _780086) ^ [_1454247, _1454249, _1454251, _1454253] : [_1454251 = _1454253, -(hAPP(hAPP(c_COMBC(_1454247, tc_fun(tc_prod(_1454247, _1454249), tc_HOL_Obool), tc_fun(_1454249, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1454249, tc_fun(tc_fun(tc_prod(_1454247, _1454249), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1454247, _1454249), tc_HOL_Obool), tc_fun(_1454249, tc_HOL_Obool)), _1454247), c_COMBC(_1454249, tc_fun(tc_prod(_1454247, _1454249), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1454249, tc_prod(_1454247, _1454249)), tc_fun(_1454249, tc_fun(tc_fun(tc_prod(_1454247, _1454249), tc_HOL_Obool), tc_HOL_Obool)), _1454247), hAPP(c_COMBB(tc_prod(_1454247, _1454249), tc_fun(tc_fun(tc_prod(_1454247, _1454249), tc_HOL_Obool), tc_HOL_Obool), _1454249), c_member(tc_prod(_1454247, _1454249)))), c_Product__Type_OPair(_1454247, _1454249)))), _1454251) = hAPP(hAPP(c_COMBC(_1454247, tc_fun(tc_prod(_1454247, _1454249), tc_HOL_Obool), tc_fun(_1454249, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1454249, tc_fun(tc_fun(tc_prod(_1454247, _1454249), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1454247, _1454249), tc_HOL_Obool), tc_fun(_1454249, tc_HOL_Obool)), _1454247), c_COMBC(_1454249, tc_fun(tc_prod(_1454247, _1454249), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1454249, tc_prod(_1454247, _1454249)), tc_fun(_1454249, tc_fun(tc_fun(tc_prod(_1454247, _1454249), tc_HOL_Obool), tc_HOL_Obool)), _1454247), hAPP(c_COMBB(tc_prod(_1454247, _1454249), tc_fun(tc_fun(tc_prod(_1454247, _1454249), tc_HOL_Obool), tc_HOL_Obool), _1454249), c_member(tc_prod(_1454247, _1454249)))), c_Product__Type_OPair(_1454247, _1454249)))), _1454253))], (35671 ^ _780086) ^ [_1454829, _1454831, _1454833, _1454835, _1454837, _1454839] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1454829, tc_fun(_1454831, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1454829, tc_fun(tc_prod(_1454829, _1454831), tc_HOL_Obool), tc_fun(_1454831, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1454831, tc_fun(tc_fun(tc_prod(_1454829, _1454831), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1454829, _1454831), tc_HOL_Obool), tc_fun(_1454831, tc_HOL_Obool)), _1454829), c_COMBC(_1454831, tc_fun(tc_prod(_1454829, _1454831), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1454831, tc_prod(_1454829, _1454831)), tc_fun(_1454831, tc_fun(tc_fun(tc_prod(_1454829, _1454831), tc_HOL_Obool), tc_HOL_Obool)), _1454829), hAPP(c_COMBB(tc_prod(_1454829, _1454831), tc_fun(tc_fun(tc_prod(_1454829, _1454831), tc_HOL_Obool), tc_HOL_Obool), _1454831), c_member(tc_prod(_1454829, _1454831)))), c_Product__Type_OPair(_1454829, _1454831)))), _1454833)), hAPP(hAPP(c_COMBC(_1454829, tc_fun(tc_prod(_1454829, _1454831), tc_HOL_Obool), tc_fun(_1454831, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1454831, tc_fun(tc_fun(tc_prod(_1454829, _1454831), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1454829, _1454831), tc_HOL_Obool), tc_fun(_1454831, tc_HOL_Obool)), _1454829), c_COMBC(_1454831, tc_fun(tc_prod(_1454829, _1454831), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1454831, tc_prod(_1454829, _1454831)), tc_fun(_1454831, tc_fun(tc_fun(tc_prod(_1454829, _1454831), tc_HOL_Obool), tc_HOL_Obool)), _1454829), hAPP(c_COMBB(tc_prod(_1454829, _1454831), tc_fun(tc_fun(tc_prod(_1454829, _1454831), tc_HOL_Obool), tc_HOL_Obool), _1454831), c_member(tc_prod(_1454829, _1454831)))), c_Product__Type_OPair(_1454829, _1454831)))), _1454835)), _1454837), _1454839)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1454829, _1454831)), hAPP(hAPP(c_Product__Type_OPair(_1454829, _1454831), _1454837), _1454839)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1454829, _1454831), tc_HOL_Obool)), _1454833), _1454835))))], (35677 ^ _780086) ^ [_1455486, _1455488, _1455490, _1455492, _1455494, _1455496] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1455486, _1455488)), hAPP(hAPP(c_Product__Type_OPair(_1455486, _1455488), _1455494), _1455496)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1455486, _1455488), tc_HOL_Obool)), _1455490), _1455492))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1455486, tc_fun(_1455488, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1455486, tc_fun(tc_prod(_1455486, _1455488), tc_HOL_Obool), tc_fun(_1455488, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1455488, tc_fun(tc_fun(tc_prod(_1455486, _1455488), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1455486, _1455488), tc_HOL_Obool), tc_fun(_1455488, tc_HOL_Obool)), _1455486), c_COMBC(_1455488, tc_fun(tc_prod(_1455486, _1455488), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1455488, tc_prod(_1455486, _1455488)), tc_fun(_1455488, tc_fun(tc_fun(tc_prod(_1455486, _1455488), tc_HOL_Obool), tc_HOL_Obool)), _1455486), hAPP(c_COMBB(tc_prod(_1455486, _1455488), tc_fun(tc_fun(tc_prod(_1455486, _1455488), tc_HOL_Obool), tc_HOL_Obool), _1455488), c_member(tc_prod(_1455486, _1455488)))), c_Product__Type_OPair(_1455486, _1455488)))), _1455490)), hAPP(hAPP(c_COMBC(_1455486, tc_fun(tc_prod(_1455486, _1455488), tc_HOL_Obool), tc_fun(_1455488, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1455488, tc_fun(tc_fun(tc_prod(_1455486, _1455488), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1455486, _1455488), tc_HOL_Obool), tc_fun(_1455488, tc_HOL_Obool)), _1455486), c_COMBC(_1455488, tc_fun(tc_prod(_1455486, _1455488), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1455488, tc_prod(_1455486, _1455488)), tc_fun(_1455488, tc_fun(tc_fun(tc_prod(_1455486, _1455488), tc_HOL_Obool), tc_HOL_Obool)), _1455486), hAPP(c_COMBB(tc_prod(_1455486, _1455488), tc_fun(tc_fun(tc_prod(_1455486, _1455488), tc_HOL_Obool), tc_HOL_Obool), _1455488), c_member(tc_prod(_1455486, _1455488)))), c_Product__Type_OPair(_1455486, _1455488)))), _1455492)), _1455494), _1455496)))], (35683 ^ _780086) ^ [_1456149, _1456151, _1456153, _1456155, _1456157, _1456159] : [c_Equiv__Relations_Ocongruent(_1456149, _1456151, _1456153, _1456155), hBOOL(hAPP(hAPP(c_member(tc_prod(_1456149, _1456149)), hAPP(hAPP(c_Product__Type_OPair(_1456149, _1456149), _1456157), _1456159)), _1456153)), -(hAPP(_1456155, _1456157) = hAPP(_1456155, _1456159))], (35693 ^ _780086) ^ [_1456348, _1456350, _1456352, _1456354, _1456356, _1456358, _1456360, _1456362, _1456364, _1456366] : [c_Equiv__Relations_Ocongruent2(_1456348, _1456350, _1456352, _1456354, _1456356, _1456358), hBOOL(hAPP(hAPP(c_member(tc_prod(_1456348, _1456348)), hAPP(hAPP(c_Product__Type_OPair(_1456348, _1456348), _1456360), _1456362)), _1456354)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1456350, _1456350)), hAPP(hAPP(c_Product__Type_OPair(_1456350, _1456350), _1456364), _1456366)), _1456356)), -(hAPP(hAPP(_1456358, _1456360), _1456364) = hAPP(hAPP(_1456358, _1456362), _1456366))], (35707 ^ _780086) ^ [_1456709, _1456711, _1456713, _1456715, _1456717] : [hBOOL(hAPP(hAPP(c_member(_1456709), _1456711), hAPP(c_Relation_OImage(_1456713, _1456709, _1456715), _1456717))), 35711 ^ _780086 : [(35712 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1456713), 35710 ^ [_1456709, _1456711, _1456713, _1456715, _1456717]), _1456717)))], (35714 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1456713, _1456709)), hAPP(hAPP(c_Product__Type_OPair(_1456713, _1456709), 35710 ^ [_1456709, _1456711, _1456713, _1456715, _1456717]), _1456711)), _1456715)))]]], (35716 ^ _780086) ^ [_1456925, _1456927, _1456929, _1456931, _1456933] : [-(hBOOL(hAPP(hAPP(c_member(_1456925), _1456927), hAPP(c_Relation_OImage(_1456929, _1456925, _1456931), _1456933)))), 35717 ^ _780086 : [(35718 ^ _780086) ^ [_1457011] : [hBOOL(hAPP(hAPP(c_member(_1456929), _1457011), _1456933)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1456929, _1456925)), hAPP(hAPP(c_Product__Type_OPair(_1456929, _1456925), _1457011), _1456927)), _1456931))]]], (35726 ^ _780086) ^ [_1457191, _1457193, _1457195, _1457197, _1457199, _1457201] : [hBOOL(hAPP(hAPP(c_member(_1457191), _1457193), _1457195)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1457191, _1457197)), hAPP(hAPP(c_Product__Type_OPair(_1457191, _1457197), _1457193), _1457199)), _1457201)), -(hBOOL(hAPP(hAPP(c_member(_1457197), _1457199), hAPP(c_Relation_OImage(_1457191, _1457197, _1457201), _1457195))))], (35736 ^ _780086) ^ [_1457416, _1457418, _1457420, _1457422, _1457424, _1457426] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1457416, _1457418), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1457420), _1457422))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1457416, _1457418), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1457424), _1457426))), -(_1457418 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1457422 = _1457426)], (35750 ^ _780086) ^ [_1457620, _1457622, _1457624, _1457626, _1457628, _1457630] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1457620, _1457622), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1457624), _1457626))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1457620, _1457622), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1457628), _1457630))), -(_1457622 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1457624 = _1457628)], (35764 ^ _780086) ^ [_1457824, _1457826, _1457828] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1457824, _1457824), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1457826), _1457828))), -(_1457824 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1457828 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (35774 ^ _780086) ^ [_1457936] : [-(_1457936 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1457936), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))], (35780 ^ _780086) ^ [_1458002, _1458004, _1458006, _1458008, _1458010, _1458012] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1458002, tc_fun(_1458004, tc_fun(_1458006, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1458002, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1458004, _1458006), tc_HOL_Obool), tc_fun(_1458004, tc_fun(_1458006, tc_HOL_Obool)), _1458002), hAPP(c_COMBC(_1458004, tc_fun(tc_prod(_1458004, _1458006), tc_HOL_Obool), tc_fun(_1458006, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1458006, tc_fun(tc_fun(tc_prod(_1458004, _1458006), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1458004, _1458006), tc_HOL_Obool), tc_fun(_1458006, tc_HOL_Obool)), _1458004), c_COMBC(_1458006, tc_fun(tc_prod(_1458004, _1458006), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1458006, tc_prod(_1458004, _1458006)), tc_fun(_1458006, tc_fun(tc_fun(tc_prod(_1458004, _1458006), tc_HOL_Obool), tc_HOL_Obool)), _1458004), hAPP(c_COMBB(tc_prod(_1458004, _1458006), tc_fun(tc_fun(tc_prod(_1458004, _1458006), tc_HOL_Obool), tc_HOL_Obool), _1458006), c_member(tc_prod(_1458004, _1458006)))), c_Product__Type_OPair(_1458004, _1458006))))), _1458008)), _1458010), _1458012)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1458004, _1458006)), hAPP(hAPP(c_Product__Type_OPair(_1458004, _1458006), _1458010), _1458012)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1458002, tc_fun(tc_prod(_1458004, _1458006), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1458002, tc_HOL_Obool))), _1458008))))], (35786 ^ _780086) ^ [_1458485, _1458487, _1458489, _1458491, _1458493, _1458495] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1458487, _1458489)), hAPP(hAPP(c_Product__Type_OPair(_1458487, _1458489), _1458493), _1458495)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1458485, tc_fun(tc_prod(_1458487, _1458489), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1458485, tc_HOL_Obool))), _1458491))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1458485, tc_fun(_1458487, tc_fun(_1458489, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1458485, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1458487, _1458489), tc_HOL_Obool), tc_fun(_1458487, tc_fun(_1458489, tc_HOL_Obool)), _1458485), hAPP(c_COMBC(_1458487, tc_fun(tc_prod(_1458487, _1458489), tc_HOL_Obool), tc_fun(_1458489, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1458489, tc_fun(tc_fun(tc_prod(_1458487, _1458489), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1458487, _1458489), tc_HOL_Obool), tc_fun(_1458489, tc_HOL_Obool)), _1458487), c_COMBC(_1458489, tc_fun(tc_prod(_1458487, _1458489), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1458489, tc_prod(_1458487, _1458489)), tc_fun(_1458489, tc_fun(tc_fun(tc_prod(_1458487, _1458489), tc_HOL_Obool), tc_HOL_Obool)), _1458487), hAPP(c_COMBB(tc_prod(_1458487, _1458489), tc_fun(tc_fun(tc_prod(_1458487, _1458489), tc_HOL_Obool), tc_HOL_Obool), _1458489), c_member(tc_prod(_1458487, _1458489)))), c_Product__Type_OPair(_1458487, _1458489))))), _1458491)), _1458493), _1458495)))], (35792 ^ _780086) ^ [_1459001, _1459003, _1459005, _1459007, _1459009, _1459011] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1459001, tc_fun(_1459003, tc_fun(_1459005, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1459001, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1459003, _1459005), tc_HOL_Obool), tc_fun(_1459003, tc_fun(_1459005, tc_HOL_Obool)), _1459001), hAPP(c_COMBC(_1459003, tc_fun(tc_prod(_1459003, _1459005), tc_HOL_Obool), tc_fun(_1459005, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1459005, tc_fun(tc_fun(tc_prod(_1459003, _1459005), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1459003, _1459005), tc_HOL_Obool), tc_fun(_1459005, tc_HOL_Obool)), _1459003), c_COMBC(_1459005, tc_fun(tc_prod(_1459003, _1459005), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1459005, tc_prod(_1459003, _1459005)), tc_fun(_1459005, tc_fun(tc_fun(tc_prod(_1459003, _1459005), tc_HOL_Obool), tc_HOL_Obool)), _1459003), hAPP(c_COMBB(tc_prod(_1459003, _1459005), tc_fun(tc_fun(tc_prod(_1459003, _1459005), tc_HOL_Obool), tc_HOL_Obool), _1459005), c_member(tc_prod(_1459003, _1459005)))), c_Product__Type_OPair(_1459003, _1459005))))), _1459007)), _1459009), _1459011)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1459003, _1459005)), hAPP(hAPP(c_Product__Type_OPair(_1459003, _1459005), _1459009), _1459011)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1459001, tc_fun(tc_prod(_1459003, _1459005), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1459001, tc_HOL_Obool))), _1459007))))], (35798 ^ _780086) ^ [_1459484, _1459486, _1459488, _1459490, _1459492, _1459494] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1459486, _1459488)), hAPP(hAPP(c_Product__Type_OPair(_1459486, _1459488), _1459492), _1459494)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1459484, tc_fun(tc_prod(_1459486, _1459488), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1459484, tc_HOL_Obool))), _1459490))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1459484, tc_fun(_1459486, tc_fun(_1459488, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1459484, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1459486, _1459488), tc_HOL_Obool), tc_fun(_1459486, tc_fun(_1459488, tc_HOL_Obool)), _1459484), hAPP(c_COMBC(_1459486, tc_fun(tc_prod(_1459486, _1459488), tc_HOL_Obool), tc_fun(_1459488, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1459488, tc_fun(tc_fun(tc_prod(_1459486, _1459488), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1459486, _1459488), tc_HOL_Obool), tc_fun(_1459488, tc_HOL_Obool)), _1459486), c_COMBC(_1459488, tc_fun(tc_prod(_1459486, _1459488), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1459488, tc_prod(_1459486, _1459488)), tc_fun(_1459488, tc_fun(tc_fun(tc_prod(_1459486, _1459488), tc_HOL_Obool), tc_HOL_Obool)), _1459486), hAPP(c_COMBB(tc_prod(_1459486, _1459488), tc_fun(tc_fun(tc_prod(_1459486, _1459488), tc_HOL_Obool), tc_HOL_Obool), _1459488), c_member(tc_prod(_1459486, _1459488)))), c_Product__Type_OPair(_1459486, _1459488))))), _1459490)), _1459492), _1459494)))], (35804 ^ _780086) ^ [_1459973, _1459975, _1459977] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1459973, _1459973), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1459975), _1459977))), -(_1459973 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1459975 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (35814 ^ _780086) ^ [_1460089, _1460091, _1460093, _1460095] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1460089, _1460091), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1460093), _1460095))), -(_1460091 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1460089, _1460091) = _1460095)], (35824 ^ _780086) ^ [_1460215, _1460217, _1460219, _1460221] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1460215, _1460217), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1460219), _1460221))), -(_1460217 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1460215), _1460217) = _1460219)], (35834 ^ _780086) ^ [_1460345] : [class_Rings_Osemiring__1(_1460345), -(hBOOL(hAPP(hAPP(c_member(_1460345), c_Groups_Ozero__class_Ozero(_1460345)), c_Nat_Osemiring__1__class_ONats(_1460345))))], (35840 ^ _780086) ^ [_1460440, _1460442] : [-(c_Divides_Odivmod__int(_1460440, _1460442) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1460440), _1460442)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1460440, _1460442)))], (35842 ^ _780086) ^ [_1460484, _1460486, _1460488] : [class_Rings_Osemiring__1(_1460484), hBOOL(hAPP(hAPP(c_member(_1460484), _1460486), c_Nat_Osemiring__1__class_ONats(_1460484))), hBOOL(hAPP(hAPP(c_member(_1460484), _1460488), c_Nat_Osemiring__1__class_ONats(_1460484))), -(hBOOL(hAPP(hAPP(c_member(_1460484), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1460484), _1460486), _1460488)), c_Nat_Osemiring__1__class_ONats(_1460484))))], (35856 ^ _780086) ^ [_1460739, _1460741, _1460743] : [class_Rings_Osemiring__1(_1460739), hBOOL(hAPP(hAPP(c_member(_1460739), _1460741), c_Nat_Osemiring__1__class_ONats(_1460739))), hBOOL(hAPP(hAPP(c_member(_1460739), _1460743), c_Nat_Osemiring__1__class_ONats(_1460739))), -(hBOOL(hAPP(hAPP(c_member(_1460739), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1460739), _1460741), _1460743)), c_Nat_Osemiring__1__class_ONats(_1460739))))], (35870 ^ _780086) ^ [_1460994] : [class_Rings_Osemiring__1(_1460994), -(hBOOL(hAPP(hAPP(c_member(_1460994), c_Groups_Oone__class_Oone(_1460994)), c_Nat_Osemiring__1__class_ONats(_1460994))))], (35876 ^ _780086) ^ [_1461089, _1461091] : [class_Rings_Osemiring__1(_1461089), -(hBOOL(hAPP(hAPP(c_member(_1461089), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1461089), _1461091)), c_Nat_Osemiring__1__class_ONats(_1461089))))], (35882 ^ _780086) ^ [_1461216, _1461218, _1461220, _1461222, _1461224] : [hBOOL(hAPP(hAPP(c_member(_1461216), _1461218), hAPP(c_Relation_OImage(_1461220, _1461216, _1461222), hAPP(hAPP(c_Set_Oinsert(_1461220), _1461224), c_Orderings_Obot__class_Obot(tc_fun(_1461220, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1461220, _1461216)), hAPP(hAPP(c_Product__Type_OPair(_1461220, _1461216), _1461224), _1461218)), _1461222)))], (35888 ^ _780086) ^ [_1461387, _1461389, _1461391, _1461393, _1461395] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1461391, _1461387)), hAPP(hAPP(c_Product__Type_OPair(_1461391, _1461387), _1461395), _1461389)), _1461393)), -(hBOOL(hAPP(hAPP(c_member(_1461387), _1461389), hAPP(c_Relation_OImage(_1461391, _1461387, _1461393), hAPP(hAPP(c_Set_Oinsert(_1461391), _1461395), c_Orderings_Obot__class_Obot(tc_fun(_1461391, tc_HOL_Obool)))))))], (35894 ^ _780086) ^ [_1461564, _1461566, _1461568, _1461570, _1461572] : [c_Equiv__Relations_Oequiv(_1461564, _1461566, _1461568), hBOOL(hAPP(hAPP(c_member(tc_prod(_1461564, _1461564)), hAPP(hAPP(c_Product__Type_OPair(_1461564, _1461564), _1461570), _1461572)), _1461568)), -(hAPP(c_Relation_OImage(_1461564, _1461564, _1461568), hAPP(hAPP(c_Set_Oinsert(_1461564), _1461570), c_Orderings_Obot__class_Obot(tc_fun(_1461564, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1461564, _1461564, _1461568), hAPP(hAPP(c_Set_Oinsert(_1461564), _1461572), c_Orderings_Obot__class_Obot(tc_fun(_1461564, tc_HOL_Obool)))))], (35904 ^ _780086) ^ [_1461825, _1461827, _1461829, _1461831, _1461833, _1461835, _1461837] : [c_Equiv__Relations_Oequiv(_1461825, _1461827, _1461829), hBOOL(hAPP(hAPP(c_member(tc_fun(_1461825, tc_HOL_Obool)), _1461831), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1461825), _1461827), _1461829))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1461825, tc_HOL_Obool)), _1461833), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1461825), _1461827), _1461829))), hBOOL(hAPP(hAPP(c_member(_1461825), _1461835), _1461831)), hBOOL(hAPP(hAPP(c_member(_1461825), _1461837), _1461833)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1461825, _1461825)), hAPP(hAPP(c_Product__Type_OPair(_1461825, _1461825), _1461835), _1461837)), _1461829)), -(_1461831 = _1461833)], (35930 ^ _780086) ^ [_1462362, _1462364, _1462366, _1462368, _1462370, _1462372, _1462374] : [c_Equiv__Relations_Oequiv(_1462362, _1462364, _1462366), hBOOL(hAPP(hAPP(c_member(tc_fun(_1462362, tc_HOL_Obool)), _1462368), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1462362), _1462364), _1462366))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1462362, tc_HOL_Obool)), _1462370), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1462362), _1462364), _1462366))), hBOOL(hAPP(hAPP(c_member(_1462362), _1462372), _1462368)), hBOOL(hAPP(hAPP(c_member(_1462362), _1462374), _1462370)), 35949 ^ _780086 : [(35950 ^ _780086) ^ [] : [_1462368 = _1462370, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1462362, _1462362)), hAPP(hAPP(c_Product__Type_OPair(_1462362, _1462362), _1462372), _1462374)), _1462366)))], (35956 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1462362, _1462362)), hAPP(hAPP(c_Product__Type_OPair(_1462362, _1462362), _1462372), _1462374)), _1462366)), -(_1462368 = _1462370)]]], (35962 ^ _780086) ^ [_1463002, _1463004] : [-(_1463002 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1463004, _1463002), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1463004), _1463002)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1463004, _1463002)))))], (35968 ^ _780086) ^ [_1463059, _1463061, _1463063, _1463065] : [-(hAPP(c_Relation_OImage(_1463059, _1463061, _1463063), hAPP(hAPP(c_Set_Oinsert(_1463059), _1463065), c_Orderings_Obot__class_Obot(tc_fun(_1463059, tc_HOL_Obool)))) = hAPP(c_Set_OCollect(_1463061), hAPP(hAPP(c_COMBC(_1463061, tc_fun(tc_prod(_1463059, _1463061), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1463059, _1463061), tc_fun(tc_fun(tc_prod(_1463059, _1463061), tc_HOL_Obool), tc_HOL_Obool), _1463061), c_member(tc_prod(_1463059, _1463061))), hAPP(c_Product__Type_OPair(_1463059, _1463061), _1463065))), _1463063)))], (35970 ^ _780086) ^ [_1463162, _1463164, _1463166, _1463168, _1463170] : [hAPP(c_Relation_OImage(_1463162, _1463162, _1463164), hAPP(hAPP(c_Set_Oinsert(_1463162), _1463166), c_Orderings_Obot__class_Obot(tc_fun(_1463162, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1463162, _1463162, _1463164), hAPP(hAPP(c_Set_Oinsert(_1463162), _1463168), c_Orderings_Obot__class_Obot(tc_fun(_1463162, tc_HOL_Obool)))), c_Equiv__Relations_Oequiv(_1463162, _1463170, _1463164), hBOOL(hAPP(hAPP(c_member(_1463162), _1463168), _1463170)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1463162, _1463162)), hAPP(hAPP(c_Product__Type_OPair(_1463162, _1463162), _1463166), _1463168)), _1463164)))], (35984 ^ _780086) ^ [_1463495, _1463497, _1463499, _1463501, _1463503] : [c_Equiv__Relations_Oequiv(_1463495, _1463497, _1463499), hBOOL(hAPP(hAPP(c_member(_1463495), _1463501), _1463497)), hBOOL(hAPP(hAPP(c_member(_1463495), _1463503), _1463497)), 35995 ^ _780086 : [(35996 ^ _780086) ^ [] : [hAPP(c_Relation_OImage(_1463495, _1463495, _1463499), hAPP(hAPP(c_Set_Oinsert(_1463495), _1463501), c_Orderings_Obot__class_Obot(tc_fun(_1463495, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1463495, _1463495, _1463499), hAPP(hAPP(c_Set_Oinsert(_1463495), _1463503), c_Orderings_Obot__class_Obot(tc_fun(_1463495, tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1463495, _1463495)), hAPP(hAPP(c_Product__Type_OPair(_1463495, _1463495), _1463501), _1463503)), _1463499)))], (36002 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1463495, _1463495)), hAPP(hAPP(c_Product__Type_OPair(_1463495, _1463495), _1463501), _1463503)), _1463499)), -(hAPP(c_Relation_OImage(_1463495, _1463495, _1463499), hAPP(hAPP(c_Set_Oinsert(_1463495), _1463501), c_Orderings_Obot__class_Obot(tc_fun(_1463495, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1463495, _1463495, _1463499), hAPP(hAPP(c_Set_Oinsert(_1463495), _1463503), c_Orderings_Obot__class_Obot(tc_fun(_1463495, tc_HOL_Obool)))))]]], (36008 ^ _780086) ^ [_1464043, _1464045, _1464047, _1464049, _1464051] : [c_Equiv__Relations_Oequiv(_1464043, _1464045, _1464047), 36011 ^ _780086 : [(36012 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1464043, _1464043)), hAPP(hAPP(c_Product__Type_OPair(_1464043, _1464043), _1464049), _1464051)), _1464047)), 36015 ^ _780086 : [(36016 ^ _780086) ^ [] : [-(hAPP(c_Relation_OImage(_1464043, _1464043, _1464047), hAPP(hAPP(c_Set_Oinsert(_1464043), _1464049), c_Orderings_Obot__class_Obot(tc_fun(_1464043, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1464043, _1464043, _1464047), hAPP(hAPP(c_Set_Oinsert(_1464043), _1464051), c_Orderings_Obot__class_Obot(tc_fun(_1464043, tc_HOL_Obool)))))], (36018 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1464043), _1464049), _1464045)))], (36020 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1464043), _1464051), _1464045)))]]], (36022 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1464043, _1464043)), hAPP(hAPP(c_Product__Type_OPair(_1464043, _1464043), _1464049), _1464051)), _1464047))), hAPP(c_Relation_OImage(_1464043, _1464043, _1464047), hAPP(hAPP(c_Set_Oinsert(_1464043), _1464049), c_Orderings_Obot__class_Obot(tc_fun(_1464043, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1464043, _1464043, _1464047), hAPP(hAPP(c_Set_Oinsert(_1464043), _1464051), c_Orderings_Obot__class_Obot(tc_fun(_1464043, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(_1464043), _1464049), _1464045)), hBOOL(hAPP(hAPP(c_member(_1464043), _1464051), _1464045))]]], (36036 ^ _780086) ^ [_1464643, _1464645, _1464647, _1464649, _1464651] : [c_Equiv__Relations_Oequiv(_1464643, _1464645, _1464647), hBOOL(hAPP(hAPP(c_member(tc_prod(_1464643, _1464643)), hAPP(hAPP(c_Product__Type_OPair(_1464643, _1464643), _1464649), _1464651)), _1464647)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1464643, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1464643, _1464643, _1464647), hAPP(hAPP(c_Set_Oinsert(_1464643), _1464649), c_Orderings_Obot__class_Obot(tc_fun(_1464643, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1464643, _1464643, _1464647), hAPP(hAPP(c_Set_Oinsert(_1464643), _1464651), c_Orderings_Obot__class_Obot(tc_fun(_1464643, tc_HOL_Obool)))))))], (36046 ^ _780086) ^ [_1464924, _1464926, _1464928, _1464930, _1464932] : [c_Equiv__Relations_Oequiv(_1464924, _1464926, _1464928), hBOOL(hAPP(hAPP(c_member(_1464924), _1464930), _1464926)), hBOOL(hAPP(hAPP(c_member(_1464924), _1464932), _1464926)), 36057 ^ _780086 : [(36058 ^ _780086) ^ [] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1464924), hAPP(hAPP(c_Set_Oinsert(_1464924), _1464930), c_Orderings_Obot__class_Obot(tc_fun(_1464924, tc_HOL_Obool)))), _1464928) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1464924), hAPP(hAPP(c_Set_Oinsert(_1464924), _1464932), c_Orderings_Obot__class_Obot(tc_fun(_1464924, tc_HOL_Obool)))), _1464928), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1464924, _1464924)), hAPP(hAPP(c_Product__Type_OPair(_1464924, _1464924), _1464930), _1464932)), _1464928)))], (36064 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1464924, _1464924)), hAPP(hAPP(c_Product__Type_OPair(_1464924, _1464924), _1464930), _1464932)), _1464928)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1464924), hAPP(hAPP(c_Set_Oinsert(_1464924), _1464930), c_Orderings_Obot__class_Obot(tc_fun(_1464924, tc_HOL_Obool)))), _1464928) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1464924), hAPP(hAPP(c_Set_Oinsert(_1464924), _1464932), c_Orderings_Obot__class_Obot(tc_fun(_1464924, tc_HOL_Obool)))), _1464928))]]], (36070 ^ _780086) ^ [_1465478, _1465480, _1465482, _1465484, _1465486, _1465488, _1465490] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1465478, _1465480), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1465482), _1465484))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1465486, _1465480), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1465488), _1465490))), -(_1465480 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1465478), _1465486), _1465480), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1465482), _1465488)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1465484), _1465490)), _1465480))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1465484), _1465490), _1465480)))))], (36084 ^ _780086) ^ [_1465788, _1465790, _1465792, _1465794] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1465788, _1465790), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1465792), _1465794))), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1465788), _1465790), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1465794), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1465792)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1465792)), c_Groups_Oone__class_Oone(tc_Int_Oint)))), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1465794), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1465790), _1465794))))))], (36090 ^ _780086) ^ [_1466015, _1466017, _1466019, _1466021, _1466023] : [c_Equiv__Relations_Oequiv(_1466015, _1466017, _1466019), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1466015, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1466015, _1466015, _1466019), hAPP(hAPP(c_Set_Oinsert(_1466015), _1466021), c_Orderings_Obot__class_Obot(tc_fun(_1466015, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1466015, _1466015, _1466019), hAPP(hAPP(c_Set_Oinsert(_1466015), _1466023), c_Orderings_Obot__class_Obot(tc_fun(_1466015, tc_HOL_Obool)))))), hBOOL(hAPP(hAPP(c_member(_1466015), _1466021), _1466017)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1466015, _1466015)), hAPP(hAPP(c_Product__Type_OPair(_1466015, _1466015), _1466023), _1466021)), _1466019)))], (36104 ^ _780086) ^ [_1466368, _1466370, _1466372, _1466374, _1466376, _1466378] : [c_Equiv__Relations_Oequiv(_1466368, _1466370, _1466372), hBOOL(hAPP(hAPP(c_member(_1466368), _1466374), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1466368, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1466368, _1466368, _1466372), hAPP(hAPP(c_Set_Oinsert(_1466368), _1466376), c_Orderings_Obot__class_Obot(tc_fun(_1466368, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1466368, _1466368, _1466372), hAPP(hAPP(c_Set_Oinsert(_1466368), _1466378), c_Orderings_Obot__class_Obot(tc_fun(_1466368, tc_HOL_Obool))))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1466368, _1466368)), hAPP(hAPP(c_Product__Type_OPair(_1466368, _1466368), _1466376), _1466378)), _1466372)))], (36114 ^ _780086) ^ [_1466669, _1466671, _1466673, _1466675] : [_1466669 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1466671), _1466673)), _1466675), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1466669, _1466671), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1466673), _1466675)))), 36121 ^ _780086 : [(36122 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1466671)))], (36124 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1466675)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1466675), _1466671))]], 36129 ^ _780086 : [(36130 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1466671))], (36132 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1466671), _1466675)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1466675), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (36140 ^ _780086) ^ [_1467131, _1467133, _1467135, _1467137, _1467139] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1467131, _1467133), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1467135), _1467137))), -(_1467133 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1467139), _1467131), _1467133), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1467139), _1467135)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1467139), _1467137)), _1467133))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1467139), _1467137), _1467133)))))], (36150 ^ _780086) ^ [_1467353, _1467355, _1467357, _1467359, _1467361, _1467363, _1467365] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1467353, _1467355)), hAPP(hAPP(c_Product__Type_OPair(_1467353, _1467355), _1467357), _1467359)), _1467361)), -(hBOOL(hAPP(hAPP(c_member(_1467363), hAPP(hAPP(_1467365, _1467357), _1467359)), hAPP(c_Set_Oimage(tc_prod(_1467353, _1467355), _1467363, hAPP(c_Product__Type_Oprod_Oprod__case(_1467353, _1467355, _1467363), _1467365)), _1467361))))], (36156 ^ _780086) ^ [_1467547, _1467549] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1467547), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1467549, _1467547) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1467549), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1467547)))], (36162 ^ _780086) ^ [_1467653, _1467655] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1467653), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 36165 ^ _780086 : [(36166 ^ _780086) ^ [] : [36167 ^ _780086 : [(36168 ^ _780086) ^ [] : [_1467655 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (36170 ^ _780086) ^ [] : [_1467653 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1467655, _1467653) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (36174 ^ _780086) ^ [] : [-(c_Nitpick_Onorm__frac(_1467655, _1467653) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1467655), _1467653)), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), tc_Int_Oint), c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint)), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1467655))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1467653)))), -(_1467655 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1467653 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (36184 ^ _780086) ^ [_1467951, _1467953, _1467955] : [-(hAPP(c_Divides_Oadjust(_1467951), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1467953), _1467955)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1467955), _1467951)), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint), tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint), tc_fun(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_prod(tc_Int_Oint, tc_Int_Oint))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_fun(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_prod(tc_Int_Oint, tc_Int_Oint))), tc_Int_Oint), c_If(tc_prod(tc_Int_Oint, tc_Int_Oint))), hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1467953)), c_Groups_Oone__class_Oone(tc_Int_Oint))))), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1467953)), _1467955))))], (36186 ^ _780086) ^ [_1468031, _1468033, _1468035, _1468037, _1468039, _1468041] : [36187 ^ _780086 : [(36188 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(_1468031, _1468033), _1468035))], (36190 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(_1468037, _1468033), _1468035))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1468039, tc_fun(_1468041, tc_HOL_Obool))), _1468037), _1468031), _1468033), _1468035)))], (36194 ^ _780086) ^ [_1468214, _1468216, _1468218, _1468220, _1468222, _1468224] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1468214, tc_fun(_1468216, tc_HOL_Obool))), _1468218), _1468220), _1468222), _1468224)), -(hBOOL(hAPP(hAPP(_1468218, _1468222), _1468224))), -(hBOOL(hAPP(hAPP(_1468220, _1468222), _1468224)))], (36204 ^ _780086) ^ [_1468372, _1468374, _1468376, _1468378, _1468380, _1468382] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1468372, tc_fun(_1468374, tc_HOL_Obool))), _1468376), _1468378), _1468380), _1468382)), 36207 ^ _780086 : [(36208 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(_1468376, _1468380), _1468382)))], (36210 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(_1468378, _1468380), _1468382)))]]], (36212 ^ _780086) ^ [_1468545, _1468547, _1468549, _1468551, _1468553, _1468555] : [hBOOL(hAPP(hAPP(_1468545, _1468547), _1468549)), hBOOL(hAPP(hAPP(_1468551, _1468547), _1468549)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1468553, tc_fun(_1468555, tc_HOL_Obool))), _1468545), _1468551), _1468547), _1468549)))], (36222 ^ _780086) ^ [_1468748, _1468750, _1468752, _1468754, _1468756, _1468758, _1468760] : [hBOOL(hAPP(hAPP(c_member(_1468748), _1468750), hAPP(hAPP(_1468752, _1468754), _1468756))), -(hBOOL(hAPP(hAPP(c_member(_1468748), _1468750), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1468758, _1468760, tc_fun(_1468748, tc_HOL_Obool)), _1468752), hAPP(hAPP(c_Product__Type_OPair(_1468758, _1468760), _1468754), _1468756)))))], (36228 ^ _780086) ^ [_1468919, _1468921, _1468923, _1468925, _1468927] : [hBOOL(hAPP(hAPP(_1468919, _1468921), _1468923)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1468925, _1468927, tc_HOL_Obool), _1468919), hAPP(hAPP(c_Product__Type_OPair(_1468925, _1468927), _1468921), _1468923))))], (36234 ^ _780086) ^ [_1469048, _1469050, _1469052, _1469054, _1469056] : [hBOOL(hAPP(hAPP(_1469048, _1469050), _1469052)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1469054, _1469056, tc_HOL_Obool), _1469048), hAPP(hAPP(c_Product__Type_OPair(_1469054, _1469056), _1469050), _1469052))))], (36240 ^ _780086) ^ [_1469195, _1469197, _1469199, _1469201] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1469195, tc_fun(_1469197, tc_HOL_Obool))), _1469199), _1469201))], (36242 ^ _780086) ^ [_1469237, _1469239, _1469241, _1469243, _1469245, _1469247, _1469249] : [hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1469237, _1469239, tc_fun(_1469241, tc_HOL_Obool)), _1469243), hAPP(hAPP(c_Product__Type_OPair(_1469237, _1469239), _1469245), _1469247)), _1469249)), -(hBOOL(hAPP(hAPP(hAPP(_1469243, _1469245), _1469247), _1469249)))], (36248 ^ _780086) ^ [_1469388, _1469390, _1469392] : [-(c_Fun_Oinj__on(tc_prod(_1469388, _1469390), tc_prod(_1469390, _1469388), hAPP(c_Product__Type_Oprod_Oprod__case(_1469388, _1469390, tc_prod(_1469390, _1469388)), hAPP(c_COMBC(_1469390, _1469388, tc_prod(_1469390, _1469388)), c_Product__Type_OPair(_1469390, _1469388))), _1469392))], (36250 ^ _780086) ^ [_1469446, _1469448, _1469450, _1469452, _1469454, _1469456] : [hBOOL(hAPP(hAPP(_1469446, _1469448), _1469450)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1469452, tc_fun(_1469454, tc_HOL_Obool))), _1469456), _1469446), _1469448), _1469450)))], (36256 ^ _780086) ^ [_1469579, _1469581, _1469583, _1469585, _1469587, _1469589] : [hBOOL(hAPP(hAPP(_1469579, _1469581), _1469583)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1469585, tc_fun(_1469587, tc_HOL_Obool))), _1469579), _1469589), _1469581), _1469583)))], (36262 ^ _780086) ^ [_1469712, _1469714, _1469716, _1469718, _1469720, _1469722] : [hBOOL(hAPP(hAPP(_1469712, _1469714), _1469716)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1469718, tc_fun(_1469720, tc_HOL_Obool))), _1469712), _1469722)), -(hBOOL(hAPP(hAPP(_1469722, _1469714), _1469716)))], (36272 ^ _780086) ^ [_1469903, _1469905, _1469907, _1469909, _1469911, _1469913] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1469903, tc_fun(_1469905, tc_HOL_Obool))), _1469907), _1469909)), hBOOL(hAPP(hAPP(_1469907, _1469911), _1469913)), -(hBOOL(hAPP(hAPP(_1469909, _1469911), _1469913)))], (36282 ^ _780086) ^ [_1470094, _1470096, _1470098, _1470100, _1470102, _1470104] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1470094, tc_fun(_1470096, tc_HOL_Obool))), _1470098), _1470100), _1470102), _1470104)), -(hBOOL(hAPP(hAPP(_1470100, _1470102), _1470104)))], (36288 ^ _780086) ^ [_1470227, _1470229, _1470231, _1470233, _1470235, _1470237] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1470227, tc_fun(_1470229, tc_HOL_Obool))), _1470231), _1470233), _1470235), _1470237)), -(hBOOL(hAPP(hAPP(_1470231, _1470235), _1470237)))], (36294 ^ _780086) ^ [_1470360, _1470362, _1470364, _1470366, _1470368, _1470370] : [hAPP(hAPP(c_Product__Type_OPair(_1470360, _1470362), _1470364), _1470366) = hAPP(hAPP(c_Product__Type_OPair(_1470360, _1470362), _1470368), _1470370), 36297 ^ _780086 : [(36298 ^ _780086) ^ [] : [-(_1470364 = _1470368)], (36300 ^ _780086) ^ [] : [-(_1470366 = _1470370)]]], (36302 ^ _780086) ^ [_1470538, _1470540, _1470542, _1470544, _1470546, _1470548] : [hAPP(hAPP(c_Product__Type_OPair(_1470538, _1470540), _1470542), _1470544) = hAPP(hAPP(c_Product__Type_OPair(_1470538, _1470540), _1470546), _1470548), 36305 ^ _780086 : [(36306 ^ _780086) ^ [] : [-(_1470542 = _1470546)], (36308 ^ _780086) ^ [] : [-(_1470544 = _1470548)]]], (36310 ^ _780086) ^ [_1470681, _1470683, _1470685, _1470687, _1470689, _1470691] : [-(hAPP(hAPP(c_Product__Type_OPair(_1470681, _1470683), _1470685), _1470687) = hAPP(hAPP(c_Product__Type_OPair(_1470681, _1470683), _1470689), _1470691)), _1470685 = _1470689, _1470687 = _1470691], (36320 ^ _780086) ^ [_1470882, _1470884, _1470886] : [hBOOL(hAPP(_1470882, 36321 ^ [_1470882, _1470884, _1470886])), 36324 ^ _780086 : [(36325 ^ _780086) ^ [_1470993, _1470995] : [-(hBOOL(hAPP(_1470882, hAPP(hAPP(c_Product__Type_OPair(_1470884, _1470886), _1470995), _1470993))))]]], (36327 ^ _780086) ^ [_1471029, _1471031, _1471033] : [hBOOL(hAPP(_1471029, hAPP(hAPP(c_Product__Type_OPair(_1471031, _1471033), 36328 ^ [_1471029, _1471031, _1471033]), 36329 ^ [_1471029, _1471031, _1471033]))), 36332 ^ _780086 : [(36333 ^ _780086) ^ [_1471176] : [-(hBOOL(hAPP(_1471029, _1471176)))]]], (36335 ^ _780086) ^ [_1471207, _1471209, _1471211, _1471213, _1471215, _1471217] : [_1471207 = _1471209, -(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1471211, _1471213, _1471215), _1471217), _1471207) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1471211, _1471213, _1471215), _1471217), _1471209))], (36341 ^ _780086) ^ [_1471332, _1471334, _1471336, _1471338, _1471340, _1471342, _1471344, _1471346] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1471332, _1471334, _1471336), _1471338), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1471340, _1471342, tc_prod(_1471332, _1471334)), _1471344), _1471346)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1471340, _1471342, _1471336), hAPP(hAPP(c_COMBB(tc_fun(_1471342, tc_prod(_1471332, _1471334)), tc_fun(_1471342, _1471336), _1471340), hAPP(c_COMBB(tc_prod(_1471332, _1471334), _1471336, _1471342), hAPP(c_Product__Type_Oprod_Oprod__case(_1471332, _1471334, _1471336), _1471338))), _1471344)), _1471346))], (36343 ^ _780086) ^ [_1471438, _1471440, _1471442, _1471444, _1471446, _1471448] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1471438, _1471440, _1471442), _1471444), hAPP(hAPP(c_Product__Type_OPair(_1471438, _1471440), _1471446), _1471448)) = hAPP(hAPP(_1471444, _1471446), _1471448))], (36345 ^ _780086) ^ [_1471496, _1471498, _1471500, _1471502, _1471504, _1471506] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1471496, _1471498, _1471500), _1471502), hAPP(hAPP(c_Product__Type_OPair(_1471496, _1471498), _1471504), _1471506)) = hAPP(hAPP(_1471502, _1471504), _1471506))], (36347 ^ _780086) ^ [_1471554, _1471556, _1471558, _1471560, _1471562] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1471554, _1471556, tc_HOL_Obool), _1471558), hAPP(hAPP(c_Product__Type_OPair(_1471554, _1471556), _1471560), _1471562))), -(hBOOL(hAPP(hAPP(_1471558, _1471560), _1471562)))], (36353 ^ _780086) ^ [_1471683, _1471685, _1471687, _1471689] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1471683, _1471685, _1471687), hAPP(hAPP(c_COMBB(tc_fun(_1471685, tc_prod(_1471683, _1471685)), tc_fun(_1471685, _1471687), _1471683), hAPP(c_COMBB(tc_prod(_1471683, _1471685), _1471687, _1471685), _1471689)), c_Product__Type_OPair(_1471683, _1471685))) = _1471689)], (36355 ^ _780086) ^ [_1471751, _1471753, _1471755, _1471757] : [-(c_HOL_OThe(tc_prod(_1471751, _1471753), hAPP(c_Product__Type_Oprod_Oprod__case(_1471751, _1471753, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1471751, tc_fun(_1471753, tc_HOL_Obool), tc_fun(_1471753, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1471753, tc_HOL_Obool), tc_fun(_1471753, tc_HOL_Obool)), _1471751), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1471753)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1471751), c_fconj), hAPP(c_fequal, _1471755)))), hAPP(c_fequal, _1471757)))) = hAPP(hAPP(c_Product__Type_OPair(_1471751, _1471753), _1471755), _1471757))], (36357 ^ _780086) ^ [_1471857, _1471859, _1471861] : [-(c_HOL_OThe(tc_prod(_1471857, _1471859), _1471861) = c_HOL_OThe(tc_prod(_1471857, _1471859), hAPP(c_Product__Type_Oprod_Oprod__case(_1471857, _1471859, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1471859, tc_prod(_1471857, _1471859)), tc_fun(_1471859, tc_HOL_Obool), _1471857), hAPP(c_COMBB(tc_prod(_1471857, _1471859), tc_HOL_Obool, _1471859), _1471861)), c_Product__Type_OPair(_1471857, _1471859)))))], (36359 ^ _780086) ^ [_1471935] : [-(c_Divides_Oadjust(_1471935) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint))), hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint, tc_fun(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_prod(tc_Int_Oint, tc_Int_Oint))), tc_fun(tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint))), tc_Int_Oint), c_COMBS(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint), tc_prod(tc_Int_Oint, tc_Int_Oint))), hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), tc_fun(tc_Int_Oint, tc_fun(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_prod(tc_Int_Oint, tc_Int_Oint))), tc_Int_Oint), hAPP(c_COMBS(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint), tc_fun(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_prod(tc_Int_Oint, tc_Int_Oint))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_fun(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_prod(tc_Int_Oint, tc_Int_Oint))), tc_Int_Oint), c_If(tc_prod(tc_Int_Oint, tc_Int_Oint))), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_HOL_Obool, tc_Int_Oint), hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint), c_Groups_Ominus__class_Ominus(tc_Int_Oint)), _1471935))))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_Int_Oint), tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint))), hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), tc_fun(tc_fun(tc_Int_Oint, tc_Int_Oint), tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint))), tc_Int_Oint), c_COMBB(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint)), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), tc_Int_Oint), c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint)), hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Oone__class_Oone(tc_Int_Oint))))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint), c_Groups_Ominus__class_Ominus(tc_Int_Oint)), _1471935))))), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), tc_Int_Oint), c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint)), hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))], (36361 ^ _780086) ^ [_1472020, _1472022, _1472024, _1472026, _1472028] : [hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1472020, _1472022, _1472024), _1472026), _1472028)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1472020, _1472022)), hAPP(hAPP(c_Product__Type_OPair(_1472020, _1472022), _1472026), _1472028)), _1472024)))], (36367 ^ _780086) ^ [_1472155, _1472157, _1472159, _1472161, _1472163] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1472155, _1472157)), hAPP(hAPP(c_Product__Type_OPair(_1472155, _1472157), _1472161), _1472163)), _1472159)), -(hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1472155, _1472157, _1472159), _1472161), _1472163)))], (36373 ^ _780086) ^ [_1472296, _1472298] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_1472296, _1472298) = hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1472296), _1472298)), c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1472296, _1472298)))], (36375 ^ _780086) ^ [_1472340] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1472340))), 36378 ^ _780086 : [(36379 ^ _780086) ^ [] : [hBOOL(hAPP(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), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1472340)))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1472340)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1472340))))], (36385 ^ _780086) ^ [] : [-(hBOOL(hAPP(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), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1472340))))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1472340)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1472340)), c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1472340)))))]]], (36391 ^ _780086) ^ [_1472630, _1472632] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1472630), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1472632)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1472630, _1472632), c_Divides_OnegDivAlg(_1472630, _1472632))))], (36401 ^ _780086) ^ [_1472789, _1472791] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1472789), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1472791)), -(c_Divides_OnegDivAlg(_1472789, _1472791) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1472789), _1472791)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1472789, _1472791)))], (36411 ^ _780086) ^ [_1472970] : [-(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1472970) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1472970), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (36413 ^ _780086) ^ [_1473014, _1473016] : [36414 ^ _780086 : [(36415 ^ _780086) ^ [] : [hBOOL(hAPP(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), _1473014), _1473016)))], (36417 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1473016), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], -(c_Divides_OnegDivAlg(_1473014, _1473016) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1473014), _1473016)))], (36421 ^ _780086) ^ [_1473173, _1473175] : [-(c_Divides_OnegDivAlg(_1473173, _1473175) = hAPP(c_Divides_Oadjust(_1473175), c_Divides_OnegDivAlg(_1473173, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1473175)))), -(hBOOL(hAPP(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), _1473173), _1473175)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1473175), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (36431 ^ _780086) ^ [_1473245, _1473247] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1473245)), 36434 ^ _780086 : [(36435 ^ _780086) ^ [] : [hBOOL(hAPP(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), _1473247), _1473245))), -(c_Divides_OnegDivAlg(_1473247, _1473245) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1473247), _1473245)))], (36441 ^ _780086) ^ [] : [-(hBOOL(hAPP(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), _1473247), _1473245)))), -(c_Divides_OnegDivAlg(_1473247, _1473245) = hAPP(c_Divides_Oadjust(_1473245), c_Divides_OnegDivAlg(_1473247, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1473245))))]]], (36447 ^ _780086) ^ [_1473509, _1473511] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1473509))), 36450 ^ _780086 : [(36451 ^ _780086) ^ [] : [hBOOL(hAPP(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(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1473511)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1473509)))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1473511), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1473509)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1473511)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1473509))))], (36457 ^ _780086) ^ [] : [-(hBOOL(hAPP(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(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1473511)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1473509))))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1473511), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1473509)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1473509)), c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1473511), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1473509)))))]]], (36463 ^ _780086) ^ [_1473872, _1473874] : [c_Nitpick_Orefl_H(_1473872, _1473874), 36466 ^ _780086 : [(36467 ^ _780086) ^ [_1473950] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1473872, _1473872)), hAPP(hAPP(c_Product__Type_OPair(_1473872, _1473872), _1473950), _1473950)), _1473874)))]]], (36469 ^ _780086) ^ [_1473992, _1473994] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1473992, _1473992)), hAPP(hAPP(c_Product__Type_OPair(_1473992, _1473992), 36470 ^ [_1473992, _1473994]), 36470 ^ [_1473992, _1473994])), _1473994)), -(c_Nitpick_Orefl_H(_1473992, _1473994))], (36476 ^ _780086) ^ [_1474159] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1474159))), 36479 ^ _780086 : [(36480 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1474159))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1474159)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (36486 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1474159)))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1474159)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1474159)), c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1474159)))))]]], (36492 ^ _780086) ^ [_1474428, _1474430] : [36493 ^ _780086 : [(36494 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1474428), _1474430))], (36496 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1474430), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], -(c_Divides_OposDivAlg(_1474428, _1474430) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1474428))], (36500 ^ _780086) ^ [_1474569, _1474571] : [-(c_Divides_OposDivAlg(_1474569, _1474571) = hAPP(c_Divides_Oadjust(_1474571), c_Divides_OposDivAlg(_1474569, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1474571)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1474569), _1474571))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1474571), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (36510 ^ _780086) ^ [_1474638] : [-(c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1474638) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (36512 ^ _780086) ^ [_1474664, _1474666] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1474664)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1474666)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1474664, _1474666), c_Divides_OposDivAlg(_1474664, _1474666))))], (36522 ^ _780086) ^ [_1474817, _1474819] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1474817)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1474819)), -(c_Divides_OposDivAlg(_1474817, _1474819) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1474817), _1474819)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1474817, _1474819)))], (36532 ^ _780086) ^ [_1474992, _1474994] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1474992))), 36535 ^ _780086 : [(36536 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1474994)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1474992))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1474994), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1474992)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1474994)))], (36542 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1474994)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1474992)))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1474994), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1474992)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1474992)), c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1474994), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1474992)))))]]], (36548 ^ _780086) ^ [_1475310, _1475312] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1475310)), 36551 ^ _780086 : [(36552 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1475312), _1475310)), -(c_Divides_OposDivAlg(_1475312, _1475310) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1475312))], (36558 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1475312), _1475310))), -(c_Divides_OposDivAlg(_1475312, _1475310) = hAPP(c_Divides_Oadjust(_1475310), c_Divides_OposDivAlg(_1475312, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1475310))))]]], (36590 ^ _780086) ^ [_1475929, _1475931] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1475929))), 36593 ^ _780086 : [(36594 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1475931)), -(c_Divides_Odivmod__int(_1475929, _1475931) = c_Divides_OnegDivAlg(_1475929, _1475931))], (36600 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1475931))), -(c_Divides_Odivmod__int(_1475929, _1475931) = hAPP(c_Divides_OnegateSnd, c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1475929), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1475931))))]]], (36564 ^ _780086) ^ [_1475559, _1475561] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1475559)), 36567 ^ _780086 : [(36568 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1475561)), -(c_Divides_Odivmod__int(_1475559, _1475561) = c_Divides_OposDivAlg(_1475559, _1475561))], (36574 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1475561))), 36577 ^ _780086 : [(36578 ^ _780086) ^ [] : [_1475559 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1475559, _1475561) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (36584 ^ _780086) ^ [] : [-(_1475559 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1475559, _1475561) = hAPP(c_Divides_OnegateSnd, c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1475559), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1475561))))]]]]], (36606 ^ _780086) ^ [_1476157, _1476159] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1476157)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1476157), _1476159)), -(c_Divides_Odivmod__nat(_1476159, _1476157) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1476159), _1476157)), _1476157))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1476159), _1476157), _1476157)))], (36616 ^ _780086) ^ [_1476377, _1476379] : [_1476377 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1476377, _1476379) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (36622 ^ _780086) ^ [_1476455, _1476457] : [-(_1476455 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 36625 ^ _780086 : [(36626 ^ _780086) ^ [] : [_1476457 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1476455, _1476457) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1476455))], (36632 ^ _780086) ^ [] : [-(_1476457 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1476455, _1476457) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint, hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1476457))), hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_fdisj, hAPP(hAPP(c_fconj, hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1476457)), hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1476455))), hAPP(hAPP(c_fconj, hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1476457), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1476455), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), c_Divides_Opdivmod(_1476455, _1476457)), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint))), hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint, tc_fun(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_prod(tc_Int_Oint, tc_Int_Oint))), tc_fun(tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint))), tc_Int_Oint), c_COMBS(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint), tc_prod(tc_Int_Oint, tc_Int_Oint))), hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_fun(tc_Int_Oint, tc_fun(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_prod(tc_Int_Oint, tc_Int_Oint))), tc_Int_Oint), hAPP(c_COMBC(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint), tc_fun(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_prod(tc_Int_Oint, tc_Int_Oint))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_fun(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_prod(tc_Int_Oint, tc_Int_Oint))), tc_Int_Oint), c_If(tc_prod(tc_Int_Oint, tc_Int_Oint))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Int_Oint, tc_HOL_Obool), c_fequal), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), tc_Int_Oint), c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint)), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_Int_Oint), tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint))), hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), tc_fun(tc_fun(tc_Int_Oint, tc_Int_Oint), tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint))), tc_Int_Oint), c_COMBB(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint)), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), tc_Int_Oint), c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint), c_Groups_Ominus__class_Ominus(tc_Int_Oint)), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))), c_Groups_Oone__class_Oone(tc_Int_Oint))))), hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1476457))))), c_Divides_Opdivmod(_1476455, _1476457)))))]]], (36638 ^ _780086) ^ [] : [-(c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)))], (36640 ^ _780086) ^ [_1476833, _1476835, _1476837, _1476839, _1476841, _1476843] : [-(hAPP(c_Product__Type_Oapsnd(_1476833, _1476835, _1476837, _1476839), hAPP(hAPP(c_Product__Type_OPair(_1476837, _1476833), _1476841), _1476843)) = hAPP(hAPP(c_Product__Type_OPair(_1476837, _1476835), _1476841), hAPP(_1476839, _1476843)))], (36642 ^ _780086) ^ [_1476895] : [-(c_Divides_Odivmod__nat(_1476895, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1476895))], (36644 ^ _780086) ^ [_1476924, _1476926] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1476924), _1476926)), -(c_Divides_Odivmod__nat(_1476924, _1476926) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1476924))], (36650 ^ _780086) ^ [_1477023, _1477025] : [-(hAPP(c_Divides_OnegateSnd, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1477023), _1477025)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1477023), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1477025)))], (36652 ^ _780086) ^ [_1477066, _1477068] : [-(c_Divides_Odivmod__nat(_1477066, _1477068) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1477066), _1477068)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1477066, _1477068)))], (36654 ^ _780086) ^ [_1477110, _1477112, _1477114] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1477110), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1477112)), _1477114)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1477110, _1477112), hAPP(c_Divides_OnegateSnd, _1477114))))], (36660 ^ _780086) ^ [_1477236, _1477238] : [36661 ^ _780086 : [(36662 ^ _780086) ^ [] : [_1477236 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (36664 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1477238), _1477236))]], -(c_Divides_Odivmod__nat(_1477238, _1477236) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1477238))], (36668 ^ _780086) ^ [_1477367, _1477369] : [-(c_Divides_Odivmod__nat(_1477369, _1477367) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat, tc_Nat_Onat, tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_prod(tc_Nat_Onat, tc_Nat_Onat)), tc_Nat_Onat), c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat)), c_Nat_OSuc)), c_Divides_Odivmod__nat(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1477369), _1477367), _1477367))), -(_1477367 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1477369), _1477367)))], (36678 ^ _780086) ^ [_1477432, _1477434] : [-(c_Divides_Opdivmod(_1477432, _1477434) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1477432)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1477434))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1477432), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1477434))))], (36680 ^ _780086) ^ [_1477497, _1477499] : [_1477497 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Opdivmod(_1477499, _1477497) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1477499)))], (36686 ^ _780086) ^ [_1477586, _1477588] : [-(_1477586 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Opdivmod(_1477588, _1477586) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1477588), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1477586)))], (36692 ^ _780086) ^ [_1477645, _1477647] : [_1477645 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1477645, _1477647) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (36698 ^ _780086) ^ [_1477723, _1477725] : [-(_1477723 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 36701 ^ _780086 : [(36702 ^ _780086) ^ [] : [_1477725 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1477723, _1477725) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1477723))], (36708 ^ _780086) ^ [] : [-(_1477725 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1477723, _1477725) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint, hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1477725))), hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_fequal, c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1477723)), c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1477725))), c_Divides_Opdivmod(_1477723, _1477725)), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint))), hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint, tc_fun(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_prod(tc_Int_Oint, tc_Int_Oint))), tc_fun(tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint))), tc_Int_Oint), c_COMBS(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint), tc_prod(tc_Int_Oint, tc_Int_Oint))), hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_fun(tc_Int_Oint, tc_fun(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_prod(tc_Int_Oint, tc_Int_Oint))), tc_Int_Oint), hAPP(c_COMBC(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint), tc_fun(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_prod(tc_Int_Oint, tc_Int_Oint))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_fun(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_prod(tc_Int_Oint, tc_Int_Oint))), tc_Int_Oint), c_If(tc_prod(tc_Int_Oint, tc_Int_Oint))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Int_Oint, tc_HOL_Obool), c_fequal), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), tc_Int_Oint), c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint)), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_Int_Oint), tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint))), hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), tc_fun(tc_fun(tc_Int_Oint, tc_Int_Oint), tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint))), tc_Int_Oint), c_COMBB(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint)), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), tc_Int_Oint), c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint), c_Groups_Ominus__class_Ominus(tc_Int_Oint)), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))), c_Groups_Oone__class_Oone(tc_Int_Oint))))), hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1477725))))), c_Divides_Opdivmod(_1477723, _1477725)))))]]], (36714 ^ _780086) ^ [_1478035, _1478037, _1478039, _1478041, _1478043, _1478045, _1478047] : [c_Equiv__Relations_Oequiv(_1478035, _1478037, _1478039), c_Equiv__Relations_Ocongruent(_1478035, tc_fun(_1478041, tc_HOL_Obool), _1478039, _1478043), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1478035, tc_fun(_1478041, tc_HOL_Obool)), _1478045), _1478043) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1478035, tc_fun(_1478041, tc_HOL_Obool)), _1478047), _1478043), hBOOL(hAPP(hAPP(c_member(tc_fun(_1478035, tc_HOL_Obool)), _1478045), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1478035), _1478037), _1478039))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1478035, tc_HOL_Obool)), _1478047), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1478035), _1478037), _1478039))), 36736 ^ _780086 : [(36737 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1478035), 36735 ^ [_1478035, _1478037, _1478039, _1478041, _1478043, _1478045, _1478047]), _1478037)))], (36740 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1478035), 36738 ^ [_1478035, _1478037, _1478039, _1478041, _1478043, _1478045, _1478047]), _1478037)))], (36742 ^ _780086) ^ [] : [-(hAPP(_1478043, 36735 ^ [_1478035, _1478037, _1478039, _1478041, _1478043, _1478045, _1478047]) = hAPP(_1478043, 36738 ^ [_1478035, _1478037, _1478039, _1478041, _1478043, _1478045, _1478047]))], (36744 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1478035, _1478035)), hAPP(hAPP(c_Product__Type_OPair(_1478035, _1478035), 36735 ^ [_1478035, _1478037, _1478039, _1478041, _1478043, _1478045, _1478047]), 36738 ^ [_1478035, _1478037, _1478039, _1478041, _1478043, _1478045, _1478047])), _1478039))]], -(_1478045 = _1478047)], (36748 ^ _780086) ^ [_1479005, _1479007, _1479009, _1479011, _1479013] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1479005, _1479007), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1479009), _1479011))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1479007)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1479013), _1479005), _1479007), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1479013), _1479009)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1479013), _1479011)), _1479007))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1479013), _1479011), _1479007)))))], (36758 ^ _780086) ^ [_1479274, _1479276, _1479278, _1479280, _1479282] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1479274, _1479276), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1479278), _1479280))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1479276)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1479282)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1479274, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1479276), _1479282)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1479278), _1479282)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1479276), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1479278, _1479282))), _1479280)))))], (36772 ^ _780086) ^ [_1479581, _1479583, _1479585, _1479587] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1479581, _1479583), _1479585)), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1479581, _1479583), _1479587)), -(_1479585 = _1479587)], (36782 ^ _780086) ^ [_1479738, _1479740] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1479738, _1479740), c_Divides_Odivmod__nat(_1479738, _1479740))))], (36784 ^ _780086) ^ [_1479771, _1479773, _1479775] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1479771, _1479773), _1479775)), -(c_Divides_Odivmod__nat(_1479771, _1479773) = _1479775)], (36790 ^ _780086) ^ [_1479866, _1479868] : [-(c_Divides_Odivmod__nat(_1479866, _1479868) = c_HOL_OThe(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat__rel(_1479866, _1479868)))], (36792 ^ _780086) ^ [_1479900, _1479902, _1479904, _1479906] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1479900, _1479902), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1479904), _1479906))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1479900, _1479902) = _1479906)], (36798 ^ _780086) ^ [_1480011, _1480013, _1480015, _1480017] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1480011, _1480013), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1480015), _1480017))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1480011), _1480013) = _1480015)], (36804 ^ _780086) ^ [_1480126, _1480128] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1480126, _1480128), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1480126), _1480128)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1480126, _1480128)))))], (36806 ^ _780086) ^ [_1480172, _1480174, _1480176, _1480178, _1480180, _1480182, _1480184] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1480172, _1480174), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1480176), _1480178))), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1480180, _1480174), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1480182), _1480184))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1480174)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1480172), _1480180), _1480174), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1480176), _1480182)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1480178), _1480184)), _1480174))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1480178), _1480184), _1480174)))))], (36820 ^ _780086) ^ [_1480533, _1480535] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1480533), _1480535))), 36823 ^ _780086 : [(36824 ^ _780086) ^ [] : [36825 ^ _780086 : [(36826 ^ _780086) ^ [] : [hBOOL(hAPP(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), _1480533), _1480535)))], (36828 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1480535), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], -(c_Divides_OnegDivAlg(_1480533, _1480535) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1480533), _1480535)))], (36832 ^ _780086) ^ [] : [-(c_Divides_OnegDivAlg(_1480533, _1480535) = hAPP(c_Divides_Oadjust(_1480535), c_Divides_OnegDivAlg(_1480533, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1480535)))), -(hBOOL(hAPP(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), _1480533), _1480535)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1480535), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (36842 ^ _780086) ^ [_1480880, _1480882] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1480880), _1480882))), 36845 ^ _780086 : [(36846 ^ _780086) ^ [] : [36847 ^ _780086 : [(36848 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1480880), _1480882))], (36850 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1480882), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], -(c_Divides_OposDivAlg(_1480880, _1480882) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1480880))], (36854 ^ _780086) ^ [] : [-(c_Divides_OposDivAlg(_1480880, _1480882) = hAPP(c_Divides_Oadjust(_1480882), c_Divides_OposDivAlg(_1480880, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1480882)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1480880), _1480882))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1480882), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (36864 ^ _780086) ^ [_1481203] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1481203)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1481203)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), hAPP(c_Divides_OnegateSnd, c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1481203))))))], (36870 ^ _780086) ^ [_1481365, _1481367, _1481369, _1481371, _1481373, _1481375] : [hAPP(c_Product__Type_Oapsnd(_1481365, _1481367, _1481369, _1481371), _1481373) = hAPP(c_Product__Type_Oapsnd(_1481365, _1481367, _1481369, _1481375), _1481373), -(hAPP(_1481371, hAPP(c_Product__Type_Osnd(_1481369, _1481365), _1481373)) = hAPP(_1481375, hAPP(c_Product__Type_Osnd(_1481369, _1481365), _1481373)))], (36876 ^ _780086) ^ [_1481514, _1481516, _1481518, _1481520, _1481522, _1481524] : [hAPP(_1481520, hAPP(c_Product__Type_Osnd(_1481518, _1481514), _1481522)) = hAPP(_1481524, hAPP(c_Product__Type_Osnd(_1481518, _1481514), _1481522)), -(hAPP(c_Product__Type_Oapsnd(_1481514, _1481516, _1481518, _1481520), _1481522) = hAPP(c_Product__Type_Oapsnd(_1481514, _1481516, _1481518, _1481524), _1481522))], (36882 ^ _780086) ^ [_1481669, _1481671, _1481673, _1481675, _1481677] : [-(hAPP(c_Product__Type_Osnd(_1481669, _1481671), hAPP(c_Product__Type_Oapsnd(_1481673, _1481671, _1481669, _1481675), _1481677)) = hAPP(_1481675, hAPP(c_Product__Type_Osnd(_1481669, _1481673), _1481677)))], (36884 ^ _780086) ^ [_1481723, _1481725, _1481727] : [-(hAPP(c_Product__Type_Osnd(_1481723, _1481725), _1481727) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1481723, _1481725, _1481725), hAPP(c_COMBK(tc_fun(_1481725, _1481725), _1481723), c_COMBI(_1481725))), _1481727))], (36886 ^ _780086) ^ [_1481777, _1481779, _1481781, _1481783] : [-(hAPP(c_Product__Type_Osnd(_1481777, _1481779), hAPP(hAPP(c_Product__Type_OPair(_1481777, _1481779), _1481781), _1481783)) = _1481783)], (36888 ^ _780086) ^ [_1481821, _1481823, _1481825, _1481827, _1481829] : [hAPP(c_Product__Type_Osnd(_1481821, _1481823), hAPP(hAPP(c_Product__Type_OPair(_1481821, _1481823), _1481825), _1481827)) = _1481829, -(_1481827 = _1481829)], (36894 ^ _780086) ^ [_1481934, _1481936] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1481934, _1481936) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1481934, _1481936)))], (36896 ^ _780086) ^ [_1481969, _1481971] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1481969), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1481971)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1481969, _1481971) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1481969, _1481971)))], (36906 ^ _780086) ^ [_1482132, _1482134] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1482132)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1482134)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1482132, _1482134) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1482132, _1482134)))], (36916 ^ _780086) ^ [_1482289] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1482289))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1482289)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1482289))))], (36922 ^ _780086) ^ [_1482406, _1482408] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1482406)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1482408), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1482406, _1482408) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), hAPP(c_Divides_OnegateSnd, c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1482406), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1482408)))))], (36932 ^ _780086) ^ [_1482587, _1482589] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1482587), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1482589), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1482587, _1482589) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), hAPP(c_Divides_OnegateSnd, c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1482587), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1482589)))))], (36942 ^ _780086) ^ [_1482774, _1482776] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_Nitpick_Onorm__frac__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1482774), _1482776))), 36945 ^ _780086 : [(36946 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1482776), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1482774, _1482776) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1482774), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1482776)))], (36952 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1482776), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 36955 ^ _780086 : [(36956 ^ _780086) ^ [] : [36957 ^ _780086 : [(36958 ^ _780086) ^ [] : [_1482774 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (36960 ^ _780086) ^ [] : [_1482776 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1482774, _1482776) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (36964 ^ _780086) ^ [] : [-(c_Nitpick_Onorm__frac(_1482774, _1482776) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1482774), _1482776)), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), tc_Int_Oint), c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint)), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1482774))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1482776)))), -(_1482774 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1482776 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]]]], (36974 ^ _780086) ^ [_1483266, _1483268, _1483270] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1483266), _1483268))), -(hBOOL(hAPP(hAPP(_1483270, _1483266), _1483268))), 36981 ^ _780086 : [(36982 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), 36979 ^ [_1483266, _1483268, _1483270]), 36980 ^ [_1483266, _1483268, _1483270]))))], (36994 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(_1483270, 36979 ^ [_1483266, _1483268, _1483270]), 36980 ^ [_1483266, _1483268, _1483270]))], (36984 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(_1483270, 36979 ^ [_1483266, _1483268, _1483270]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), 36980 ^ [_1483266, _1483268, _1483270])))), -(hBOOL(hAPP(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), 36979 ^ [_1483266, _1483268, _1483270]), 36980 ^ [_1483266, _1483268, _1483270])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 36980 ^ [_1483266, _1483268, _1483270]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (36998 ^ _780086) ^ [_1483761, _1483763, _1483765] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1483761), _1483763))), -(hBOOL(hAPP(hAPP(_1483765, _1483761), _1483763))), 37005 ^ _780086 : [(37006 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), 37003 ^ [_1483761, _1483763, _1483765]), 37004 ^ [_1483761, _1483763, _1483765]))))], (37018 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(_1483765, 37003 ^ [_1483761, _1483763, _1483765]), 37004 ^ [_1483761, _1483763, _1483765]))], (37008 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(_1483765, 37003 ^ [_1483761, _1483763, _1483765]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), 37004 ^ [_1483761, _1483763, _1483765])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 37003 ^ [_1483761, _1483763, _1483765]), 37004 ^ [_1483761, _1483763, _1483765]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 37004 ^ [_1483761, _1483763, _1483765]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (37022 ^ _780086) ^ [_1484247, _1484249] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1484247, _1484249) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1484247, _1484249)))], (37024 ^ _780086) ^ [_1484282, _1484284, _1484286] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1484282, tc_fun(_1484282, tc_HOL_Obool))), _1484284), _1484286)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1484282, tc_HOL_Obool)), c_Wellfounded_Oaccp(_1484282, _1484286)), c_Wellfounded_Oaccp(_1484282, _1484284))))], (37030 ^ _780086) ^ [_1484434, _1484436] : [c_Relation_Oirrefl(_1484434, _1484436), 37033 ^ _780086 : [(37034 ^ _780086) ^ [_1484516] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1484434, _1484434)), hAPP(hAPP(c_Product__Type_OPair(_1484434, _1484434), _1484516), _1484516)), _1484436))]]], (37036 ^ _780086) ^ [_1484556, _1484558] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1484556, _1484556)), hAPP(hAPP(c_Product__Type_OPair(_1484556, _1484556), 37037 ^ [_1484556, _1484558]), 37037 ^ [_1484556, _1484558])), _1484558))), -(c_Relation_Oirrefl(_1484556, _1484558))], (37043 ^ _780086) ^ [_1484627, _1484629, _1484631] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_Nitpick_Onorm__frac__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1484627), _1484629))), -(hBOOL(hAPP(hAPP(_1484631, _1484627), _1484629))), 37050 ^ _780086 : [(37051 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_Nitpick_Onorm__frac__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), 37048 ^ [_1484627, _1484629, _1484631]), 37049 ^ [_1484627, _1484629, _1484631]))))], (37059 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(_1484631, 37048 ^ [_1484627, _1484629, _1484631]), 37049 ^ [_1484627, _1484629, _1484631]))], (37053 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 37049 ^ [_1484627, _1484629, _1484631]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(_1484631, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 37048 ^ [_1484627, _1484629, _1484631])), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 37049 ^ [_1484627, _1484629, _1484631]))))]]], (37073 ^ _780086) ^ [_1485304, _1485306, _1485308] : [37075 ^ _780086 : [(37076 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(_1485306, 37074 ^ [_1485304, _1485306, _1485308]), _1485308)))], (37078 ^ _780086) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1485304, _1485306), 37074 ^ [_1485304, _1485306, _1485308]))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1485304, _1485306), _1485308)))], (37063 ^ _780086) ^ [_1485118, _1485120, _1485122] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1485118, _1485120), _1485122)), 37066 ^ _780086 : [(37067 ^ _780086) ^ [_1485203] : [hBOOL(hAPP(hAPP(_1485120, _1485203), _1485122)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1485118, _1485120), _1485203)))]]], (37092 ^ _780086) ^ [_1485694, _1485696, _1485698] : [37094 ^ _780086 : [(37095 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(_1485696, 37093 ^ [_1485694, _1485696, _1485698]), _1485698)))], (37097 ^ _780086) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1485694, _1485696), 37093 ^ [_1485694, _1485696, _1485698]))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1485694, _1485696), _1485698)))], (37082 ^ _780086) ^ [_1485508, _1485510, _1485512] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1485508, _1485510), _1485512)), 37085 ^ _780086 : [(37086 ^ _780086) ^ [_1485593] : [hBOOL(hAPP(hAPP(_1485510, _1485593), _1485512)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1485508, _1485510), _1485593)))]]], (37101 ^ _780086) ^ [_1485880, _1485882, _1485884, _1485886] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1485880, _1485882), _1485884)), hBOOL(hAPP(hAPP(_1485882, _1485886), _1485884)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1485880, _1485882), _1485886)))], (37111 ^ _780086) ^ [_1486047, _1486049] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Nitpick_Onat__gcd__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1486047), _1486049))), 37114 ^ _780086 : [(37115 ^ _780086) ^ [] : [_1486049 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1486047, _1486049) = _1486047)], (37121 ^ _780086) ^ [] : [-(_1486049 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1486047, _1486049) = c_Nitpick_Onat__gcd(_1486049, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1486047, _1486049)))]]], (37127 ^ _780086) ^ [_1486265] : [-(c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc, _1486265)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Nat_Onat_Onat__size(_1486265)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (37129 ^ _780086) ^ [_1486322, _1486324, _1486326, _1486328] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1486322, _1486322)), hAPP(hAPP(c_Product__Type_OPair(_1486322, _1486322), _1486324), _1486326)), hAPP(c_Wellfounded_Omeasure(_1486322), _1486328))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1486328, _1486324)), hAPP(_1486328, _1486326))))], (37135 ^ _780086) ^ [_1486469, _1486471, _1486473, _1486475] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1486475, _1486471)), hAPP(_1486475, _1486473))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1486469, _1486469)), hAPP(hAPP(c_Product__Type_OPair(_1486469, _1486469), _1486471), _1486473)), hAPP(c_Wellfounded_Omeasure(_1486469), _1486475))))], (37141 ^ _780086) ^ [] : [-(c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37143 ^ _780086) ^ [_1486640] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1486640)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1486640)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), hAPP(c_Divides_OnegateSnd, c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1486640))))))], (37149 ^ _780086) ^ [_1486773] : [-(hAPP(c_Int_Onat, _1486773) = c_Set_Othe__elem(tc_Nat_Onat, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_Int_ORep__Integ, _1486773)), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat, tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool))), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool))), tc_Nat_Onat), c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_fun(tc_Nat_Onat, tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool))), tc_Nat_Onat), hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_Set_Oinsert(tc_Nat_Onat))), c_Groups_Ominus__class_Ominus(tc_Nat_Onat)))), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))))], (37151 ^ _780086) ^ [_1486811, _1486813, _1486815] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Nitpick_Onat__gcd__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1486811), _1486813))), -(hBOOL(hAPP(hAPP(_1486815, _1486811), _1486813))), 37158 ^ _780086 : [(37159 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Nitpick_Onat__gcd__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), 37156 ^ [_1486811, _1486813, _1486815]), 37157 ^ [_1486811, _1486813, _1486815]))))], (37167 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(_1486815, 37156 ^ [_1486811, _1486813, _1486815]), 37157 ^ [_1486811, _1486813, _1486815]))], (37161 ^ _780086) ^ [] : [-(37157 ^ [_1486811, _1486813, _1486815] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(_1486815, 37157 ^ [_1486811, _1486813, _1486815]), c_Divides_Odiv__class_Omod(tc_Nat_Onat, 37156 ^ [_1486811, _1486813, _1486815], 37157 ^ [_1486811, _1486813, _1486815]))))]]], (37171 ^ _780086) ^ [_1487233, _1487235, _1487237, _1487239, _1487241] : [-(hAPP(c_Product__Type_Ofst(_1487233, _1487235), hAPP(c_Product__Type_Oapsnd(_1487237, _1487235, _1487233, _1487239), _1487241)) = hAPP(c_Product__Type_Ofst(_1487233, _1487237), _1487241))], (37173 ^ _780086) ^ [_1487284, _1487286, _1487288] : [-(hAPP(c_Product__Type_Ofst(_1487284, _1487286), _1487288) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1487284, _1487286, _1487284), c_COMBK(_1487284, _1487286)), _1487288))], (37175 ^ _780086) ^ [_1487345, _1487347] : [hAPP(c_Int_ORep__Integ, _1487345) = hAPP(c_Int_ORep__Integ, _1487347), -(_1487345 = _1487347)], (37181 ^ _780086) ^ [_1487430, _1487432] : [_1487430 = _1487432, -(hAPP(c_Int_ORep__Integ, _1487430) = hAPP(c_Int_ORep__Integ, _1487432))], (37187 ^ _780086) ^ [_1487521, _1487523, _1487525, _1487527] : [-(hAPP(c_Product__Type_Ofst(_1487521, _1487523), hAPP(hAPP(c_Product__Type_OPair(_1487521, _1487523), _1487525), _1487527)) = _1487525)], (37189 ^ _780086) ^ [_1487565, _1487567, _1487569, _1487571, _1487573] : [hAPP(c_Product__Type_Ofst(_1487565, _1487567), hAPP(hAPP(c_Product__Type_OPair(_1487565, _1487567), _1487569), _1487571)) = _1487573, -(_1487569 = _1487573)], (37195 ^ _780086) ^ [_1487699, _1487701, _1487703, _1487705] : [_1487699 = _1487701, 37198 ^ _780086 : [(37199 ^ _780086) ^ [] : [-(hAPP(c_Product__Type_Ofst(_1487703, _1487705), _1487699) = hAPP(c_Product__Type_Ofst(_1487703, _1487705), _1487701))], (37201 ^ _780086) ^ [] : [-(hAPP(c_Product__Type_Osnd(_1487703, _1487705), _1487699) = hAPP(c_Product__Type_Osnd(_1487703, _1487705), _1487701))]]], (37203 ^ _780086) ^ [_1487850, _1487852, _1487854, _1487856] : [-(_1487850 = _1487852), hAPP(c_Product__Type_Ofst(_1487854, _1487856), _1487850) = hAPP(c_Product__Type_Ofst(_1487854, _1487856), _1487852), hAPP(c_Product__Type_Osnd(_1487854, _1487856), _1487850) = hAPP(c_Product__Type_Osnd(_1487854, _1487856), _1487852)], (37213 ^ _780086) ^ [_1488037, _1488039, _1488041, _1488043] : [hAPP(c_Product__Type_Ofst(_1488037, _1488039), _1488041) = hAPP(c_Product__Type_Ofst(_1488037, _1488039), _1488043), hAPP(c_Product__Type_Osnd(_1488037, _1488039), _1488041) = hAPP(c_Product__Type_Osnd(_1488037, _1488039), _1488043), -(_1488041 = _1488043)], (37223 ^ _780086) ^ [_1488222, _1488224, _1488226] : [-(_1488222 = hAPP(hAPP(c_Product__Type_OPair(_1488224, _1488226), hAPP(c_Product__Type_Ofst(_1488224, _1488226), _1488222)), hAPP(c_Product__Type_Osnd(_1488224, _1488226), _1488222)))], (37225 ^ _780086) ^ [_1488270, _1488272, _1488274] : [-(hAPP(hAPP(c_Product__Type_OPair(_1488270, _1488272), hAPP(c_Product__Type_Ofst(_1488270, _1488272), _1488274)), hAPP(c_Product__Type_Osnd(_1488270, _1488272), _1488274)) = _1488274)], (37227 ^ _780086) ^ [_1488318, _1488320, _1488322, _1488324, _1488326] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1488318, _1488320, _1488322), _1488324), _1488326) = hAPP(hAPP(_1488324, hAPP(c_Product__Type_Ofst(_1488318, _1488320), _1488326)), hAPP(c_Product__Type_Osnd(_1488318, _1488320), _1488326)))], (37229 ^ _780086) ^ [_1488377, _1488379] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1488377), _1488379) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1488377, _1488379)))], (37231 ^ _780086) ^ [_1488414, _1488416, _1488418, _1488420, _1488422, _1488424] : [-(hAPP(hAPP(c_COMBS(tc_prod(_1488414, _1488416), _1488416, _1488418), hAPP(hAPP(c_COMBB(_1488420, tc_fun(_1488416, _1488418), tc_prod(_1488414, _1488416)), _1488422), hAPP(hAPP(c_COMBB(_1488414, _1488420, tc_prod(_1488414, _1488416)), _1488424), c_Product__Type_Ofst(_1488414, _1488416)))), c_Product__Type_Osnd(_1488414, _1488416)) = hAPP(c_Product__Type_Oprod_Oprod__case(_1488414, _1488416, _1488418), hAPP(hAPP(c_COMBB(_1488420, tc_fun(_1488416, _1488418), _1488414), _1488422), _1488424)))], (37233 ^ _780086) ^ [_1488515, _1488517, _1488519, _1488521, _1488523] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1488515, _1488517, _1488519), _1488521), _1488523) = hAPP(hAPP(_1488521, hAPP(c_Product__Type_Ofst(_1488515, _1488517), _1488523)), hAPP(c_Product__Type_Osnd(_1488515, _1488517), _1488523)))], (37235 ^ _780086) ^ [_1488574, _1488576, _1488578, _1488580, _1488582] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1488574, _1488576, _1488578), _1488580), _1488582) = hAPP(hAPP(_1488580, hAPP(c_Product__Type_Ofst(_1488574, _1488576), _1488582)), hAPP(c_Product__Type_Osnd(_1488574, _1488576), _1488582)))], (37237 ^ _780086) ^ [_1488633, _1488635, _1488637] : [-(c_HOL_OThe(tc_prod(_1488633, _1488635), hAPP(c_Product__Type_Oprod_Oprod__case(_1488633, _1488635, tc_HOL_Obool), _1488637)) = c_HOL_OThe(tc_prod(_1488633, _1488635), hAPP(hAPP(c_COMBS(tc_prod(_1488633, _1488635), _1488635, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1488633, tc_fun(_1488635, tc_HOL_Obool), tc_prod(_1488633, _1488635)), _1488637), c_Product__Type_Ofst(_1488633, _1488635))), c_Product__Type_Osnd(_1488633, _1488635))))], (37239 ^ _780086) ^ [_1488714, _1488716] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1488714), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1488716)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1488714), _1488716) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1488714, _1488716)))], (37249 ^ _780086) ^ [_1488881, _1488883] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1488881)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1488883)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1488881), _1488883) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1488881, _1488883)))], (37259 ^ _780086) ^ [_1489042] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1489042))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1489042)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1489042))))], (37265 ^ _780086) ^ [_1489157, _1489159] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1489157)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1489159), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1489157), _1489159) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), hAPP(c_Divides_OnegateSnd, c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1489157), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1489159)))))], (37275 ^ _780086) ^ [_1489342, _1489344] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1489342), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1489344), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1489342), _1489344) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), hAPP(c_Divides_OnegateSnd, c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1489342), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1489344)))))], (37285 ^ _780086) ^ [_1489533, _1489535, _1489537, _1489539, _1489541] : [-(c_Product__Type_Oprod_Oprod__size(_1489533, _1489535, _1489537, _1489539, _1489541) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1489537, hAPP(c_Product__Type_Ofst(_1489533, _1489535), _1489541))), hAPP(_1489539, hAPP(c_Product__Type_Osnd(_1489533, _1489535), _1489541)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (37287 ^ _780086) ^ [_1489600, _1489602, _1489604, _1489606, _1489608] : [hBOOL(hAPP(hAPP(_1489600, _1489602), _1489604)), -(hBOOL(hAPP(hAPP(_1489600, hAPP(c_Product__Type_Osnd(_1489606, _1489608), hAPP(hAPP(c_Product__Type_OPair(_1489606, _1489608), _1489604), _1489602))), hAPP(c_Product__Type_Ofst(_1489606, _1489608), hAPP(hAPP(c_Product__Type_OPair(_1489606, _1489608), _1489604), _1489602)))))], (37293 ^ _780086) ^ [_1489763, _1489765, _1489767, _1489769, _1489771, _1489773] : [hBOOL(hAPP(_1489763, _1489765)), hBOOL(hAPP(_1489767, _1489769)), 37300 ^ _780086 : [(37301 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1489763, hAPP(c_Product__Type_Ofst(_1489771, _1489773), hAPP(hAPP(c_Product__Type_OPair(_1489771, _1489773), _1489765), _1489769)))))], (37303 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1489767, hAPP(c_Product__Type_Osnd(_1489771, _1489773), hAPP(hAPP(c_Product__Type_OPair(_1489771, _1489773), _1489765), _1489769)))))]]], (37305 ^ _780086) ^ [_1490010, _1490012] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1490010), _1490012) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1490010, _1490012)))], (37339 ^ _780086) ^ [_1490601, _1490603, _1490605] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1490601, _1490603), _1490605))), _1490601 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1490605)), _1490603)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1490605)), 37346 ^ _780086 : [(37347 ^ _780086) ^ [] : [-(_1490603 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37349 ^ _780086) ^ [] : [hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1490605) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], 37350 ^ _780086 : [(37351 ^ _780086) ^ [] : [_1490603 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (37353 ^ _780086) ^ [] : [37354 ^ _780086 : [(37355 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1490603)))], (37357 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1490605))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1490605)), _1490603))]], 37362 ^ _780086 : [(37363 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1490603))], (37365 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1490603), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1490605))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1490605)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]]]], (37307 ^ _780086) ^ [_1490065, _1490067, _1490069] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1490065, _1490067), _1490069)), 37310 ^ _780086 : [(37311 ^ _780086) ^ [] : [-(_1490065 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1490069)), _1490067)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1490069)))], (37313 ^ _780086) ^ [] : [_1490067 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1490069) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37319 ^ _780086) ^ [] : [-(_1490067 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 37322 ^ _780086 : [(37323 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1490067)), 37326 ^ _780086 : [(37327 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1490069))))], (37329 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1490069)), _1490067)))]]], (37331 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1490067))), 37334 ^ _780086 : [(37335 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1490067), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1490069))))], (37337 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1490069)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]]]]]], (37373 ^ _780086) ^ [_1491210, _1491212, _1491214, _1491216] : [-(hAPP(hAPP(c_Relation_Oinv__image(_1491210, _1491212), _1491214), _1491216) = hAPP(c_Set_OCollect(tc_prod(_1491212, _1491212)), hAPP(c_Product__Type_Oprod_Oprod__case(_1491212, _1491212, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1491212, tc_fun(tc_prod(_1491210, _1491210), tc_HOL_Obool), tc_fun(_1491212, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1491212, tc_fun(tc_fun(tc_prod(_1491210, _1491210), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1491210, _1491210), tc_HOL_Obool), tc_fun(_1491212, tc_HOL_Obool)), _1491212), c_COMBC(_1491212, tc_fun(tc_prod(_1491210, _1491210), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1491212, tc_prod(_1491210, _1491210)), tc_fun(_1491212, tc_fun(tc_fun(tc_prod(_1491210, _1491210), tc_HOL_Obool), tc_HOL_Obool)), _1491212), hAPP(c_COMBB(tc_prod(_1491210, _1491210), tc_fun(tc_fun(tc_prod(_1491210, _1491210), tc_HOL_Obool), tc_HOL_Obool), _1491212), c_member(tc_prod(_1491210, _1491210)))), hAPP(hAPP(c_COMBC(_1491212, tc_fun(_1491212, _1491210), tc_fun(_1491212, tc_prod(_1491210, _1491210))), hAPP(hAPP(c_COMBB(tc_fun(_1491210, tc_prod(_1491210, _1491210)), tc_fun(tc_fun(_1491212, _1491210), tc_fun(_1491212, tc_prod(_1491210, _1491210))), _1491212), c_COMBB(_1491210, tc_prod(_1491210, _1491210), _1491212)), hAPP(hAPP(c_COMBB(_1491210, tc_fun(_1491210, tc_prod(_1491210, _1491210)), _1491212), c_Product__Type_OPair(_1491210, _1491210)), _1491216))), _1491216)))), _1491214))))], (37375 ^ _780086) ^ [_1491451, _1491453, _1491455, _1491457, _1491459] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1491451, _1491453)), hAPP(_1491451, _1491455))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1491457, _1491457)), hAPP(hAPP(c_Product__Type_OPair(_1491457, _1491457), _1491453), _1491455)), _1491459)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1491457, _1491457)), hAPP(hAPP(c_Product__Type_OPair(_1491457, _1491457), _1491453), _1491455)), c_Wellfounded_Omlex__prod(_1491457, _1491451, _1491459))))], (37385 ^ _780086) ^ [_1491698] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(_1491698)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_1491698)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (37387 ^ _780086) ^ [_1491748, _1491750] : [c_Code__Numeral_OSuc__code__numeral(_1491748) = c_Code__Numeral_OSuc__code__numeral(_1491750), -(_1491748 = _1491750)], (37393 ^ _780086) ^ [_1491829, _1491831] : [_1491829 = _1491831, -(c_Code__Numeral_OSuc__code__numeral(_1491829) = c_Code__Numeral_OSuc__code__numeral(_1491831))], (37399 ^ _780086) ^ [_1491925] : [c_Code__Numeral_OSuc__code__numeral(_1491925) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)], (37401 ^ _780086) ^ [_1491959] : [c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_OSuc__code__numeral(_1491959)], (37403 ^ _780086) ^ [_1492011, _1492013, _1492015, _1492017, _1492019, _1492021] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1492011, _1492011)), hAPP(hAPP(c_Product__Type_OPair(_1492011, _1492011), _1492013), _1492015)), hAPP(hAPP(c_Relation_Oinv__image(_1492017, _1492011), _1492019), _1492021))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1492017, _1492017)), hAPP(hAPP(c_Product__Type_OPair(_1492017, _1492017), hAPP(_1492021, _1492013)), hAPP(_1492021, _1492015))), _1492019)))], (37409 ^ _780086) ^ [_1492198, _1492200, _1492202, _1492204, _1492206, _1492208] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1492204, _1492204)), hAPP(hAPP(c_Product__Type_OPair(_1492204, _1492204), hAPP(_1492208, _1492200)), hAPP(_1492208, _1492202))), _1492206)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1492198, _1492198)), hAPP(hAPP(c_Product__Type_OPair(_1492198, _1492198), _1492200), _1492202)), hAPP(hAPP(c_Relation_Oinv__image(_1492204, _1492198), _1492206), _1492208))))], (37415 ^ _780086) ^ [_1492391] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1492391)), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = _1492391)], (37417 ^ _780086) ^ [_1492422, _1492424, _1492426, _1492428, _1492430] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1492422, _1492424)), hAPP(_1492422, _1492426))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1492428, _1492428)), hAPP(hAPP(c_Product__Type_OPair(_1492428, _1492428), _1492424), _1492426)), c_Wellfounded_Omlex__prod(_1492428, _1492422, _1492430))))], (37423 ^ _780086) ^ [_1492573] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1492573)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), _1492573)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (37425 ^ _780086) ^ [_1492610, _1492612] : [-(c_FunDef_Orp__inv__image(_1492610, _1492612) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(_1492610, _1492610), tc_HOL_Obool), tc_fun(tc_prod(_1492610, _1492610), tc_HOL_Obool), tc_fun(tc_fun(_1492612, _1492610), tc_prod(tc_fun(tc_prod(_1492612, _1492612), tc_HOL_Obool), tc_fun(tc_prod(_1492612, _1492612), tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(tc_fun(tc_prod(_1492610, _1492610), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1492610, _1492610), tc_HOL_Obool), tc_fun(tc_fun(_1492612, _1492610), tc_fun(tc_prod(_1492612, _1492612), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1492610, _1492610), tc_HOL_Obool), tc_fun(tc_fun(_1492612, _1492610), tc_prod(tc_fun(tc_prod(_1492612, _1492612), tc_HOL_Obool), tc_fun(tc_prod(_1492612, _1492612), tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(_1492612, _1492610), tc_fun(tc_prod(_1492612, _1492612), tc_HOL_Obool)), tc_fun(tc_fun(_1492612, _1492610), tc_prod(tc_fun(tc_prod(_1492612, _1492612), tc_HOL_Obool), tc_fun(tc_prod(_1492612, _1492612), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(tc_prod(_1492610, _1492610), tc_HOL_Obool), tc_fun(tc_fun(_1492612, _1492610), tc_fun(tc_prod(_1492612, _1492612), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1492610, _1492610), tc_HOL_Obool), tc_fun(tc_fun(_1492612, _1492610), tc_prod(tc_fun(tc_prod(_1492612, _1492612), tc_HOL_Obool), tc_fun(tc_prod(_1492612, _1492612), tc_HOL_Obool))))), tc_fun(tc_prod(_1492610, _1492610), tc_HOL_Obool)), c_COMBB(tc_fun(tc_fun(_1492612, _1492610), tc_fun(tc_prod(_1492612, _1492612), tc_HOL_Obool)), tc_fun(tc_fun(_1492612, _1492610), tc_prod(tc_fun(tc_prod(_1492612, _1492612), tc_HOL_Obool), tc_fun(tc_prod(_1492612, _1492612), tc_HOL_Obool))), tc_fun(tc_prod(_1492610, _1492610), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1492612, _1492610), tc_fun(tc_fun(tc_prod(_1492612, _1492612), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1492612, _1492612), tc_HOL_Obool), tc_fun(tc_prod(_1492612, _1492612), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(_1492612, _1492610), tc_fun(tc_prod(_1492612, _1492612), tc_HOL_Obool)), tc_fun(tc_fun(_1492612, _1492610), tc_prod(tc_fun(tc_prod(_1492612, _1492612), tc_HOL_Obool), tc_fun(tc_prod(_1492612, _1492612), tc_HOL_Obool)))), tc_fun(tc_prod(_1492610, _1492610), tc_HOL_Obool)), c_COMBS(tc_fun(_1492612, _1492610), tc_fun(tc_prod(_1492612, _1492612), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1492612, _1492612), tc_HOL_Obool), tc_fun(tc_prod(_1492612, _1492612), tc_HOL_Obool)))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1492612, _1492610), tc_fun(tc_prod(_1492612, _1492612), tc_HOL_Obool)), tc_fun(tc_fun(_1492612, _1492610), tc_fun(tc_fun(tc_prod(_1492612, _1492612), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1492612, _1492612), tc_HOL_Obool), tc_fun(tc_prod(_1492612, _1492612), tc_HOL_Obool)))), tc_fun(tc_prod(_1492610, _1492610), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(tc_prod(_1492612, _1492612), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1492612, _1492612), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1492612, _1492612), tc_HOL_Obool), tc_fun(tc_prod(_1492612, _1492612), tc_HOL_Obool))), tc_fun(_1492612, _1492610)), c_Product__Type_OPair(tc_fun(tc_prod(_1492612, _1492612), tc_HOL_Obool), tc_fun(tc_prod(_1492612, _1492612), tc_HOL_Obool)))), c_Relation_Oinv__image(_1492610, _1492612))))), c_Relation_Oinv__image(_1492610, _1492612))))], (37427 ^ _780086) ^ [_1493123] : [-(c_Wellfounded_Ofinite__psubset(_1493123) = hAPP(c_Set_OCollect(tc_prod(tc_fun(_1493123, tc_HOL_Obool), tc_fun(_1493123, tc_HOL_Obool))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(_1493123, tc_HOL_Obool), tc_fun(_1493123, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1493123, tc_HOL_Obool), tc_fun(tc_fun(_1493123, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1493123, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1493123, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1493123, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1493123, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1493123, tc_HOL_Obool)), c_COMBS(tc_fun(_1493123, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1493123, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1493123, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1493123, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1493123, tc_HOL_Obool)), c_fconj)), c_Orderings_Oord__class_Oless(tc_fun(_1493123, tc_HOL_Obool))))), c_Finite__Set_Ofinite(_1493123)))))], (37429 ^ _780086) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37431 ^ _780086) ^ [_1493319, _1493321, _1493323] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1493319, tc_HOL_Obool), tc_fun(_1493319, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1493319, tc_HOL_Obool), tc_fun(_1493319, tc_HOL_Obool)), _1493321), _1493323)), c_Wellfounded_Ofinite__psubset(_1493319))), 37434 ^ _780086 : [(37435 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1493319, tc_HOL_Obool)), _1493321), _1493323)))], (37437 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1493319), _1493323)))]]], (37439 ^ _780086) ^ [_1493514, _1493516, _1493518] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1493514, tc_HOL_Obool), tc_fun(_1493514, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1493514, tc_HOL_Obool), tc_fun(_1493514, tc_HOL_Obool)), _1493516), _1493518)), c_Wellfounded_Ofinite__psubset(_1493514)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1493514, tc_HOL_Obool)), _1493516), _1493518)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1493514), _1493518))], (37449 ^ _780086) ^ [_1493743] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1493743)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1493743)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (37451 ^ _780086) ^ [_1493781, _1493783, _1493785, _1493787, _1493789, _1493791] : [-(c_Product__Type_Oprod_Oprod__rec(_1493781, _1493783, _1493785, _1493787, hAPP(hAPP(c_Product__Type_OPair(_1493781, _1493783), _1493789), _1493791)) = hAPP(hAPP(_1493787, _1493789), _1493791))], (37453 ^ _780086) ^ [_1493868, _1493870, _1493872, _1493874, _1493876, _1493878, _1493880, _1493882] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1493868, _1493870), tc_prod(_1493868, _1493870))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1493868, _1493870), tc_prod(_1493868, _1493870)), hAPP(hAPP(c_Product__Type_OPair(_1493868, _1493870), _1493872), _1493874)), hAPP(hAPP(c_Product__Type_OPair(_1493868, _1493870), _1493876), _1493878))), c_Wellfounded_Olex__prod(_1493868, _1493870, _1493880, _1493882))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1493868, _1493868)), hAPP(hAPP(c_Product__Type_OPair(_1493868, _1493868), _1493872), _1493876)), _1493880))), 37460 ^ _780086 : [(37461 ^ _780086) ^ [] : [-(_1493872 = _1493876)], (37463 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1493870, _1493870)), hAPP(hAPP(c_Product__Type_OPair(_1493870, _1493870), _1493874), _1493878)), _1493882)))]]], (37465 ^ _780086) ^ [_1494193, _1494195, _1494197, _1494199, _1494201, _1494203, _1494205, _1494207] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1494193, _1494195), tc_prod(_1494193, _1494195))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1494193, _1494195), tc_prod(_1494193, _1494195)), hAPP(hAPP(c_Product__Type_OPair(_1494193, _1494195), _1494197), _1494199)), hAPP(hAPP(c_Product__Type_OPair(_1494193, _1494195), _1494201), _1494203))), c_Wellfounded_Olex__prod(_1494193, _1494195, _1494205, _1494207)))), 37466 ^ _780086 : [(37467 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1494193, _1494193)), hAPP(hAPP(c_Product__Type_OPair(_1494193, _1494193), _1494197), _1494201)), _1494205))], (37469 ^ _780086) ^ [] : [_1494197 = _1494201, hBOOL(hAPP(hAPP(c_member(tc_prod(_1494195, _1494195)), hAPP(hAPP(c_Product__Type_OPair(_1494195, _1494195), _1494199), _1494203)), _1494207))]]], (37477 ^ _780086) ^ [_1494568] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1494568) = _1494568)], (37479 ^ _780086) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37481 ^ _780086) ^ [_1494612, _1494614, _1494616, _1494618, _1494620, _1494622, _1494624] : [hBOOL(hAPP(_1494612, _1494614)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1494616, _1494616)), hAPP(hAPP(c_Product__Type_OPair(_1494616, _1494616), _1494618), _1494620)), hAPP(_1494622, _1494614))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1494624, _1494616), tc_prod(_1494624, _1494616))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1494624, _1494616), tc_prod(_1494624, _1494616)), hAPP(hAPP(c_Product__Type_OPair(_1494624, _1494616), _1494614), _1494618)), hAPP(hAPP(c_Product__Type_OPair(_1494624, _1494616), _1494614), _1494620))), c_Recdef_Osame__fst(_1494624, _1494616, _1494612, _1494622))))], (37491 ^ _780086) ^ [_1494932, _1494934] : [c_Equiv__Relations_Oequiv(_1494932, c_Orderings_Otop__class_Otop(tc_fun(_1494932, tc_HOL_Obool)), _1494934), -(c_Equiv__Relations_Oequivp(_1494932, hAPP(hAPP(c_COMBC(_1494932, tc_fun(tc_prod(_1494932, _1494932), tc_HOL_Obool), tc_fun(_1494932, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1494932, tc_fun(tc_fun(tc_prod(_1494932, _1494932), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1494932, _1494932), tc_HOL_Obool), tc_fun(_1494932, tc_HOL_Obool)), _1494932), c_COMBC(_1494932, tc_fun(tc_prod(_1494932, _1494932), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1494932, tc_prod(_1494932, _1494932)), tc_fun(_1494932, tc_fun(tc_fun(tc_prod(_1494932, _1494932), tc_HOL_Obool), tc_HOL_Obool)), _1494932), hAPP(c_COMBB(tc_prod(_1494932, _1494932), tc_fun(tc_fun(tc_prod(_1494932, _1494932), tc_HOL_Obool), tc_HOL_Obool), _1494932), c_member(tc_prod(_1494932, _1494932)))), c_Product__Type_OPair(_1494932, _1494932)))), _1494934)))], (37497 ^ _780086) ^ [_1495253, _1495255] : [c_Equiv__Relations_Oequivp(_1495253, hAPP(hAPP(c_COMBC(_1495253, tc_fun(tc_prod(_1495253, _1495253), tc_HOL_Obool), tc_fun(_1495253, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1495253, tc_fun(tc_fun(tc_prod(_1495253, _1495253), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1495253, _1495253), tc_HOL_Obool), tc_fun(_1495253, tc_HOL_Obool)), _1495253), c_COMBC(_1495253, tc_fun(tc_prod(_1495253, _1495253), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1495253, tc_prod(_1495253, _1495253)), tc_fun(_1495253, tc_fun(tc_fun(tc_prod(_1495253, _1495253), tc_HOL_Obool), tc_HOL_Obool)), _1495253), hAPP(c_COMBB(tc_prod(_1495253, _1495253), tc_fun(tc_fun(tc_prod(_1495253, _1495253), tc_HOL_Obool), tc_HOL_Obool), _1495253), c_member(tc_prod(_1495253, _1495253)))), c_Product__Type_OPair(_1495253, _1495253)))), _1495255)), -(c_Equiv__Relations_Oequiv(_1495253, c_Orderings_Otop__class_Otop(tc_fun(_1495253, tc_HOL_Obool)), _1495255))], (37503 ^ _780086) ^ [_1495580, _1495582, _1495584, _1495586, _1495588, _1495590, _1495592] : [-(hAPP(c_Product__Type_Oapsnd(_1495580, _1495582, _1495584, _1495586), hAPP(c_Product__Type_Oapfst(_1495588, _1495584, _1495580, _1495590), _1495592)) = hAPP(hAPP(c_Product__Type_OPair(_1495584, _1495582), hAPP(_1495590, hAPP(c_Product__Type_Ofst(_1495588, _1495580), _1495592))), hAPP(_1495586, hAPP(c_Product__Type_Osnd(_1495588, _1495580), _1495592))))], (37505 ^ _780086) ^ [_1495658, _1495660, _1495662, _1495664, _1495666, _1495668] : [-(hAPP(c_Product__Type_Oapfst(_1495658, _1495660, _1495662, _1495664), hAPP(hAPP(c_Product__Type_OPair(_1495658, _1495662), _1495666), _1495668)) = hAPP(hAPP(c_Product__Type_OPair(_1495660, _1495662), hAPP(_1495664, _1495666)), _1495668))], (37507 ^ _780086) ^ [_1495747, _1495749, _1495751, _1495753, _1495755, _1495757] : [hAPP(c_Product__Type_Oapfst(_1495747, _1495749, _1495751, _1495753), _1495755) = hAPP(c_Product__Type_Oapfst(_1495747, _1495749, _1495751, _1495757), _1495755), -(hAPP(_1495753, hAPP(c_Product__Type_Ofst(_1495747, _1495751), _1495755)) = hAPP(_1495757, hAPP(c_Product__Type_Ofst(_1495747, _1495751), _1495755)))], (37513 ^ _780086) ^ [_1495896, _1495898, _1495900, _1495902, _1495904, _1495906] : [hAPP(_1495902, hAPP(c_Product__Type_Ofst(_1495896, _1495900), _1495904)) = hAPP(_1495906, hAPP(c_Product__Type_Ofst(_1495896, _1495900), _1495904)), -(hAPP(c_Product__Type_Oapfst(_1495896, _1495898, _1495900, _1495902), _1495904) = hAPP(c_Product__Type_Oapfst(_1495896, _1495898, _1495900, _1495906), _1495904))], (37519 ^ _780086) ^ [_1496051, _1496053, _1496055, _1496057, _1496059] : [-(hAPP(c_Product__Type_Ofst(_1496051, _1496053), hAPP(c_Product__Type_Oapfst(_1496055, _1496051, _1496053, _1496057), _1496059)) = hAPP(_1496057, hAPP(c_Product__Type_Ofst(_1496055, _1496053), _1496059)))], (37521 ^ _780086) ^ [_1496105, _1496107, _1496109, _1496111, _1496113] : [-(hAPP(c_Product__Type_Osnd(_1496105, _1496107), hAPP(c_Product__Type_Oapfst(_1496109, _1496105, _1496107, _1496111), _1496113)) = hAPP(c_Product__Type_Osnd(_1496109, _1496107), _1496113))], (37523 ^ _780086) ^ [_1496156] : [-(c_Equiv__Relations_Oequivp(_1496156, c_fequal))], (37541 ^ _780086) ^ [_1496492, _1496494] : [-(c_Equiv__Relations_Oequivp(_1496492, _1496494)), 37546 ^ _780086 : [(37547 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(_1496494, 37542 ^ [_1496492, _1496494]), 37543 ^ [_1496492, _1496494])))], (37549 ^ _780086) ^ [] : [hAPP(_1496494, 37542 ^ [_1496492, _1496494]) = hAPP(_1496494, 37543 ^ [_1496492, _1496494])]], 37550 ^ _780086 : [(37551 ^ _780086) ^ [] : [-(hAPP(_1496494, 37542 ^ [_1496492, _1496494]) = hAPP(_1496494, 37543 ^ [_1496492, _1496494]))], (37553 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(_1496494, 37542 ^ [_1496492, _1496494]), 37543 ^ [_1496492, _1496494]))]]], (37525 ^ _780086) ^ [_1496194, _1496196] : [c_Equiv__Relations_Oequivp(_1496194, _1496196), 37528 ^ _780086 : [(37529 ^ _780086) ^ [_1496288, _1496290] : [hBOOL(hAPP(hAPP(_1496196, _1496290), _1496288)), -(hAPP(_1496196, _1496290) = hAPP(_1496196, _1496288))], (37535 ^ _780086) ^ [_1496387, _1496389] : [hAPP(_1496196, _1496389) = hAPP(_1496196, _1496387), -(hBOOL(hAPP(hAPP(_1496196, _1496389), _1496387)))]]], (37557 ^ _780086) ^ [_1496821, _1496823, _1496825] : [c_Equiv__Relations_Oequivp(_1496821, _1496823), -(hBOOL(hAPP(hAPP(_1496823, _1496825), _1496825)))], (37563 ^ _780086) ^ [_1496910, _1496912, _1496914, _1496916] : [c_Equiv__Relations_Oequivp(_1496910, _1496912), hBOOL(hAPP(hAPP(_1496912, _1496914), _1496916)), -(hBOOL(hAPP(hAPP(_1496912, _1496916), _1496914)))], (37573 ^ _780086) ^ [_1497067, _1497069, _1497071, _1497073, _1497075] : [c_Equiv__Relations_Oequivp(_1497067, _1497069), hBOOL(hAPP(hAPP(_1497069, _1497071), _1497073)), hBOOL(hAPP(hAPP(_1497069, _1497073), _1497075)), -(hBOOL(hAPP(hAPP(_1497069, _1497071), _1497075)))], (37587 ^ _780086) ^ [_1497296, _1497298, _1497300, _1497302, _1497304, _1497306, _1497308] : [-(hAPP(c_Product__Type_Oapsnd(_1497296, _1497298, _1497300, _1497302), hAPP(c_Product__Type_Oapfst(_1497304, _1497300, _1497296, _1497306), _1497308)) = hAPP(c_Product__Type_Oapfst(_1497304, _1497300, _1497298, _1497306), hAPP(c_Product__Type_Oapsnd(_1497296, _1497298, _1497304, _1497302), _1497308)))], (37589 ^ _780086) ^ [_1497363, _1497365, _1497367, _1497369, _1497371, _1497373, _1497375] : [-(hAPP(c_Product__Type_Oapfst(_1497363, _1497365, _1497367, _1497369), hAPP(c_Product__Type_Oapsnd(_1497371, _1497367, _1497363, _1497373), _1497375)) = hAPP(hAPP(c_Product__Type_OPair(_1497365, _1497367), hAPP(_1497369, hAPP(c_Product__Type_Ofst(_1497363, _1497371), _1497375))), hAPP(_1497373, hAPP(c_Product__Type_Osnd(_1497363, _1497371), _1497375))))], (37591 ^ _780086) ^ [_1497441, _1497443, _1497445, _1497447] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1497441), _1497443)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1497445), _1497447)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1497441), _1497445)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1497443), _1497447))), c_FunDef_Opair__less)))], (37601 ^ _780086) ^ [_1497644, _1497646, _1497648, _1497650, _1497652] : [hBOOL(hAPP(hAPP(c_member(_1497644), _1497646), hAPP(c_Relation_OImage(_1497648, _1497644, _1497650), _1497652))), 37605 ^ _780086 : [(37606 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1497648, _1497644)), hAPP(hAPP(c_Product__Type_OPair(_1497648, _1497644), 37604 ^ [_1497644, _1497646, _1497648, _1497650, _1497652]), _1497646)), _1497650)))], (37608 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1497648), 37604 ^ [_1497644, _1497646, _1497648, _1497650, _1497652]), _1497652)))]]], (37610 ^ _780086) ^ [_1497868, _1497870, _1497872] : [-(c_Wellfounded_Omlex__prod(_1497868, _1497870, _1497872) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, _1497868), _1497868), c_Wellfounded_Olex__prod(tc_Nat_Onat, _1497868, c_Wellfounded_Oless__than, _1497872)), hAPP(hAPP(c_COMBS(_1497868, _1497868, tc_prod(tc_Nat_Onat, _1497868)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1497868, tc_prod(tc_Nat_Onat, _1497868)), _1497868), c_Product__Type_OPair(tc_Nat_Onat, _1497868)), _1497870)), c_COMBI(_1497868))))], (37612 ^ _780086) ^ [] : [-(c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_Nat_Onat, c_Wellfounded_Oless__than, c_Wellfounded_Oless__than))], (37614 ^ _780086) ^ [_1497968] : [-(c_Wellfounded_Omeasure(_1497968) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat, _1497968), c_Wellfounded_Oless__than))], (37616 ^ _780086) ^ [_1498014, _1498016] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1498014), _1498016)), c_Wellfounded_Oless__than)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1498014), _1498016)))], (37622 ^ _780086) ^ [_1498119, _1498121] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1498119), _1498121)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1498119), _1498121)), c_Wellfounded_Oless__than)))], (37628 ^ _780086) ^ [_1498230, _1498232, _1498234, _1498236] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1498230), _1498232)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1498230), _1498234)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1498232), _1498236))), c_FunDef_Opair__less)))], (37634 ^ _780086) ^ [_1498367, _1498369, _1498371, _1498373] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1498367), _1498369)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1498371), _1498373)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1498367), _1498371)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1498369), _1498373))), c_FunDef_Opair__leq)))], (37644 ^ _780086) ^ [_1498570, _1498572, _1498574, _1498576] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1498570), _1498572)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1498570), _1498574)), c_FunDef_Opair__less)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1498572), _1498576)), c_FunDef_Omin__strict)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1498572), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1498574), _1498576))), c_FunDef_Omin__strict)))], (37658 ^ _780086) ^ [_1498851, _1498853, _1498855, _1498857] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1498851), _1498853)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1498855), _1498851)), c_FunDef_Opair__less)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1498857), _1498853)), c_FunDef_Omax__strict)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1498855), _1498857)), _1498853)), c_FunDef_Omax__strict)))], (37672 ^ _780086) ^ [_1499128] : [-(_1499128 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1499128), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__strict)))], (37678 ^ _780086) ^ [_1499173] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1499173)), -(_1499173 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), _1499173)), c_FunDef_Omax__strict)))], (37688 ^ _780086) ^ [_1499283, _1499285, _1499287, _1499289] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1499283), _1499285)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1499283), _1499287)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1499285), _1499289))), c_FunDef_Opair__leq)))], (37694 ^ _780086) ^ [_1499420, _1499422, _1499424, _1499426] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1499420), _1499422)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1499424), _1499420)), c_FunDef_Opair__leq)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1499426), _1499422)), c_FunDef_Omax__weak)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1499424), _1499426)), _1499422)), c_FunDef_Omax__weak)))], (37708 ^ _780086) ^ [_1499701, _1499703, _1499705, _1499707] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1499701), _1499703)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1499701), _1499705)), c_FunDef_Opair__leq)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1499703), _1499707)), c_FunDef_Omin__weak)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1499703), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1499705), _1499707))), c_FunDef_Omin__weak)))], (37722 ^ _780086) ^ [_1499982, _1499984, _1499986, _1499988] : [-(hAPP(c_Relation_OField(_1499982), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1499982, _1499982)), hAPP(hAPP(c_Product__Type_OPair(_1499982, _1499982), _1499984), _1499986)), _1499988)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1499982, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1499982), _1499984), hAPP(hAPP(c_Set_Oinsert(_1499982), _1499986), c_Orderings_Obot__class_Obot(tc_fun(_1499982, tc_HOL_Obool))))), hAPP(c_Relation_OField(_1499982), _1499988)))], (37724 ^ _780086) ^ [_1500073, _1500075] : [-(hAPP(c_Relation_OField(_1500073), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1500073, _1500073), tc_HOL_Obool), _1500075)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1500073, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_fun(tc_prod(_1500073, _1500073), tc_HOL_Obool), tc_fun(_1500073, tc_HOL_Obool), c_Relation_OField(_1500073)), _1500075)))], (37726 ^ _780086) ^ [_1500136] : [-(hAPP(c_Relation_OField(_1500136), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1500136, _1500136), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1500136, tc_HOL_Obool)))], (37728 ^ _780086) ^ [_1500177, _1500179, _1500181] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1500177, _1500177), tc_HOL_Obool)), _1500179), _1500181)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1500177, tc_HOL_Obool)), hAPP(c_Relation_OField(_1500177), _1500179)), hAPP(c_Relation_OField(_1500177), _1500181))))], (37734 ^ _780086) ^ [_1500322, _1500324, _1500326] : [-(hAPP(c_Relation_OField(_1500322), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1500322, _1500322), tc_HOL_Obool)), _1500324), _1500326)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1500322, tc_HOL_Obool)), hAPP(c_Relation_OField(_1500322), _1500324)), hAPP(c_Relation_OField(_1500322), _1500326)))], (37736 ^ _780086) ^ [_1500389, _1500391] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1500389, _1500389)), _1500391)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1500389), hAPP(c_Relation_OField(_1500389), _1500391))))], (37742 ^ _780086) ^ [_1500498] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1500498)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), _1500498)), c_FunDef_Omax__weak)))], (37748 ^ _780086) ^ [_1500593] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1500593), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__weak)))], (37750 ^ _780086) ^ [] : [-(c_FunDef_Omin__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__leq)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), tc_HOL_Obool)))))], (37752 ^ _780086) ^ [] : [-(c_FunDef_Omax__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__leq)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), tc_HOL_Obool)))))], (37754 ^ _780086) ^ [_1500663, _1500665] : [-(c_Relation_OId__on(_1500663, _1500665) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1500663, tc_fun(tc_prod(_1500663, _1500663), tc_HOL_Obool)), _1500665), hAPP(hAPP(c_COMBC(_1500663, tc_fun(tc_prod(_1500663, _1500663), tc_HOL_Obool), tc_fun(tc_prod(_1500663, _1500663), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_prod(_1500663, _1500663), tc_fun(tc_fun(tc_prod(_1500663, _1500663), tc_HOL_Obool), tc_fun(tc_prod(_1500663, _1500663), tc_HOL_Obool)), _1500663), c_Set_Oinsert(tc_prod(_1500663, _1500663))), hAPP(hAPP(c_COMBS(_1500663, _1500663, tc_prod(_1500663, _1500663)), c_Product__Type_OPair(_1500663, _1500663)), c_COMBI(_1500663)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1500663, _1500663), tc_HOL_Obool)))))], (37756 ^ _780086) ^ [_1500787, _1500789] : [-(c_Relation_OId__on(_1500787, _1500789) = hAPP(c_Product__Type_Oprod_Oprod__case(_1500787, _1500787, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1500787, tc_HOL_Obool, tc_fun(_1500787, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1500787, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_HOL_Obool, tc_fun(_1500787, tc_HOL_Obool)), _1500787), c_COMBC(_1500787, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1500787, tc_HOL_Obool), tc_fun(_1500787, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1500787), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1500787), c_fconj)), c_fequal))), _1500789)))], (37758 ^ _780086) ^ [_1500881] : [-(c_Relation_OId__on(_1500881, c_Orderings_Obot__class_Obot(tc_fun(_1500881, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1500881, _1500881), tc_HOL_Obool)))], (37760 ^ _780086) ^ [_1500920, _1500922, _1500924] : [-(hAPP(c_Relation_OImage(_1500920, _1500920, c_Relation_OId__on(_1500920, _1500922)), _1500924) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1500920, tc_HOL_Obool)), _1500922), _1500924))], (37762 ^ _780086) ^ [_1500968, _1500970, _1500972, _1500974] : [_1500968 = _1500970, hBOOL(hAPP(hAPP(c_member(_1500972), _1500968), _1500974)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1500972, _1500972)), hAPP(hAPP(c_Product__Type_OPair(_1500972, _1500972), _1500968), _1500970)), c_Relation_OId__on(_1500972, _1500974))))], (37772 ^ _780086) ^ [_1501184, _1501186, _1501188, _1501190] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1501184, _1501184)), hAPP(hAPP(c_Product__Type_OPair(_1501184, _1501184), _1501186), _1501188)), c_Relation_OId__on(_1501184, _1501190))), 37775 ^ _780086 : [(37776 ^ _780086) ^ [] : [-(_1501186 = _1501188)], (37778 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1501184), _1501186), _1501190)))]]], (37780 ^ _780086) ^ [_1501345, _1501347, _1501349, _1501351] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1501345, _1501345)), hAPP(hAPP(c_Product__Type_OPair(_1501345, _1501345), _1501347), _1501349)), c_Relation_OId__on(_1501345, _1501351)))), _1501347 = _1501349, hBOOL(hAPP(hAPP(c_member(_1501345), _1501347), _1501351))], (37790 ^ _780086) ^ [] : [-(c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (37792 ^ _780086) ^ [_1501560, _1501562, _1501564, _1501566, _1501568, _1501570] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1501560, tc_HOL_Obool), tc_fun(_1501560, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1501560, tc_HOL_Obool), tc_fun(_1501560, tc_HOL_Obool)), _1501562), _1501564)), c_Wellfounded_Omax__ext(_1501560, _1501566))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1501560, tc_HOL_Obool), tc_fun(_1501560, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1501560, tc_HOL_Obool), tc_fun(_1501560, tc_HOL_Obool)), _1501568), _1501570)), c_Wellfounded_Omax__ext(_1501560, _1501566))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1501560, tc_HOL_Obool), tc_fun(_1501560, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1501560, tc_HOL_Obool), tc_fun(_1501560, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1501560, tc_HOL_Obool)), _1501562), _1501568)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1501560, tc_HOL_Obool)), _1501564), _1501570))), c_Wellfounded_Omax__ext(_1501560, _1501566))))], (37802 ^ _780086) ^ [] : [-(c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (37804 ^ _780086) ^ [_1501992, _1501994, _1501996, _1501998] : [c_Wellfounded_Omax__extp(_1501992, hAPP(hAPP(c_COMBC(_1501992, tc_fun(tc_prod(_1501992, _1501992), tc_HOL_Obool), tc_fun(_1501992, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1501992, tc_fun(tc_fun(tc_prod(_1501992, _1501992), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1501992, _1501992), tc_HOL_Obool), tc_fun(_1501992, tc_HOL_Obool)), _1501992), c_COMBC(_1501992, tc_fun(tc_prod(_1501992, _1501992), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1501992, tc_prod(_1501992, _1501992)), tc_fun(_1501992, tc_fun(tc_fun(tc_prod(_1501992, _1501992), tc_HOL_Obool), tc_HOL_Obool)), _1501992), hAPP(c_COMBB(tc_prod(_1501992, _1501992), tc_fun(tc_fun(tc_prod(_1501992, _1501992), tc_HOL_Obool), tc_HOL_Obool), _1501992), c_member(tc_prod(_1501992, _1501992)))), c_Product__Type_OPair(_1501992, _1501992)))), _1501994), _1501996, _1501998), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1501992, tc_HOL_Obool), tc_fun(_1501992, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1501992, tc_HOL_Obool), tc_fun(_1501992, tc_HOL_Obool)), _1501996), _1501998)), c_Wellfounded_Omax__ext(_1501992, _1501994))))], (37810 ^ _780086) ^ [_1502377, _1502379, _1502381, _1502383] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1502377, tc_HOL_Obool), tc_fun(_1502377, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1502377, tc_HOL_Obool), tc_fun(_1502377, tc_HOL_Obool)), _1502381), _1502383)), c_Wellfounded_Omax__ext(_1502377, _1502379))), -(c_Wellfounded_Omax__extp(_1502377, hAPP(hAPP(c_COMBC(_1502377, tc_fun(tc_prod(_1502377, _1502377), tc_HOL_Obool), tc_fun(_1502377, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1502377, tc_fun(tc_fun(tc_prod(_1502377, _1502377), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1502377, _1502377), tc_HOL_Obool), tc_fun(_1502377, tc_HOL_Obool)), _1502377), c_COMBC(_1502377, tc_fun(tc_prod(_1502377, _1502377), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1502377, tc_prod(_1502377, _1502377)), tc_fun(_1502377, tc_fun(tc_fun(tc_prod(_1502377, _1502377), tc_HOL_Obool), tc_HOL_Obool)), _1502377), hAPP(c_COMBB(tc_prod(_1502377, _1502377), tc_fun(tc_fun(tc_prod(_1502377, _1502377), tc_HOL_Obool), tc_HOL_Obool), _1502377), c_member(tc_prod(_1502377, _1502377)))), c_Product__Type_OPair(_1502377, _1502377)))), _1502379), _1502381, _1502383))], (37816 ^ _780086) ^ [] : [-(c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), tc_HOL_Obool), tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), tc_HOL_Obool)), c_FunDef_Omin__strict), c_FunDef_Omin__weak)))], (37818 ^ _780086) ^ [] : [-(c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), tc_HOL_Obool), tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), tc_HOL_Obool)), c_FunDef_Omax__strict), c_FunDef_Omax__weak)))], (37820 ^ _780086) ^ [_1502804, _1502806, _1502808, _1502810] : [c_FunDef_Oreduction__pair(_1502804, _1502806), -(c_FunDef_Oreduction__pair(_1502808, hAPP(hAPP(c_FunDef_Orp__inv__image(_1502804, _1502808), _1502806), _1502810)))], (37826 ^ _780086) ^ [_1502918, _1502920] : [hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1502918), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))) = hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1502920), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1502918), _1502920)), c_Int_Ointrel)))], (37832 ^ _780086) ^ [_1503049, _1503051] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1503049), _1503051)), c_Int_Ointrel)), -(hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1503049), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))) = hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1503051), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))], (37838 ^ _780086) ^ [_1503207, _1503209, _1503211, _1503213] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1503207), _1503209)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1503211), _1503213))), c_Int_Ointrel)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1503207), _1503213) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1503211), _1503209))], (37844 ^ _780086) ^ [_1503354, _1503356, _1503358, _1503360] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1503354), _1503360) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1503358), _1503356), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1503354), _1503356)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1503358), _1503360))), c_Int_Ointrel)))], (37850 ^ _780086) ^ [_1503507, _1503509, _1503511] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1503507, _1503507)), _1503509), c_Relation_OId__on(_1503507, _1503511))), 37854 ^ _780086 : [(37855 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1503507), 37853 ^ [_1503507, _1503509, _1503511]), _1503511)))], (37857 ^ _780086) ^ [] : [-(_1503509 = hAPP(hAPP(c_Product__Type_OPair(_1503507, _1503507), 37853 ^ [_1503507, _1503509, _1503511]), 37853 ^ [_1503507, _1503509, _1503511]))]]], (37859 ^ _780086) ^ [] : [-(c_Equiv__Relations_Oequiv(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), c_Int_Ointrel))], (37861 ^ _780086) ^ [_1503724, _1503726, _1503728] : [class_Rings_Oring__1(_1503724), -(hAPP(c_Int_Oring__1__class_Oof__int(_1503724), hAPP(c_Int_OAbs__Integ, hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1503726), _1503728)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1503724), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1503724), _1503726)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1503724), _1503728)))], (37867 ^ _780086) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ, hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (37869 ^ _780086) ^ [_1503901, _1503903, _1503905, _1503907] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_OAbs__Integ, hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1503901), _1503903)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))), hAPP(c_Int_OAbs__Integ, hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1503905), _1503907)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ, hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1503901), _1503905)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1503903), _1503907))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1503901), _1503907)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1503903), _1503905)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (37871 ^ _780086) ^ [_1504026] : [-(hAPP(c_Int_OAbs__Integ, hAPP(c_Int_ORep__Integ, _1504026)) = _1504026)], (37873 ^ _780086) ^ [_1504055, _1504057] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Int_OAbs__Integ, hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1504055), _1504057)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ, hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1504057), _1504055)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (37875 ^ _780086) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ, hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (37877 ^ _780086) ^ [_1504137] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1504137) = hAPP(c_Int_OAbs__Integ, hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1504137), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (37879 ^ _780086) ^ [_1504181, _1504183, _1504185, _1504187] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_OAbs__Integ, hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1504181), _1504183)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))), hAPP(c_Int_OAbs__Integ, hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1504185), _1504187)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ, hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1504181), _1504185)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1504183), _1504187))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (37881 ^ _780086) ^ [_1504282, _1504284] : [-(hAPP(c_Int_Onat, hAPP(c_Int_OAbs__Integ, hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1504282), _1504284)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1504282), _1504284))], (37883 ^ _780086) ^ [_1504334] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1504334) = hAPP(c_Int_OAbs__Integ, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), hAPP(c_Int_ORep__Integ, _1504334)), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat, tc_Nat_Onat, tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), tc_fun(tc_Nat_Onat, tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_Nat_Onat), c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), tc_Nat_Onat), c_COMBC(tc_Nat_Onat, tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_prod(tc_Nat_Onat, tc_Nat_Onat)), tc_fun(tc_Nat_Onat, tc_fun(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), tc_Nat_Onat), hAPP(c_COMBB(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_fun(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), tc_Nat_Onat), c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)))), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_prod(tc_Nat_Onat, tc_Nat_Onat)), c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat))))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (37885 ^ _780086) ^ [_1504393, _1504395, _1504397, _1504399] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_OAbs__Integ, hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1504393), _1504395)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))), hAPP(c_Int_OAbs__Integ, hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1504397), _1504399)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1504393), _1504399)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1504397), _1504395))))], (37891 ^ _780086) ^ [_1504586, _1504588, _1504590, _1504592] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1504586), _1504592)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1504590), _1504588))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_OAbs__Integ, hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1504586), _1504588)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))), hAPP(c_Int_OAbs__Integ, hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1504590), _1504592)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (37897 ^ _780086) ^ [_1504806, _1504808, _1504810, _1504812] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_OAbs__Integ, hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1504806), _1504808)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))), hAPP(c_Int_OAbs__Integ, hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1504810), _1504812)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1504806), _1504812)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1504810), _1504808))))], (37903 ^ _780086) ^ [_1504999, _1505001, _1505003, _1505005] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1504999), _1505005)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1505003), _1505001))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_OAbs__Integ, hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1504999), _1505001)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))), hAPP(c_Int_OAbs__Integ, hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1505003), _1505005)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (37911 ^ _780086) ^ [_1505198] : [-(_1505198 = hAPP(c_Int_OAbs__Integ, hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), 37908 ^ [_1505198]), 37909 ^ [_1505198])), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (37913 ^ _780086) ^ [] : [-(c_Int_OInteg = hAPP(hAPP(c_Equiv__Relations_Oquotient(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), c_Int_Ointrel))], (37915 ^ _780086) ^ [_1505267, _1505269, _1505271, _1505273] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1505267, _1505269, _1505271, c_Code__Numeral_OSuc__code__numeral(_1505273)) = hAPP(_1505271, _1505273))], (37917 ^ _780086) ^ [_1505306] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), hAPP(c_Int_ORep__Integ, _1505306)), c_Int_OInteg)))], (37919 ^ _780086) ^ [_1505337, _1505339, _1505341] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1505337, _1505339, _1505341, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1505339)], (37921 ^ _780086) ^ [] : [-(c_Typedef_Otype__definition(tc_Int_Oint, tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), c_Int_ORep__Integ, c_Int_OAbs__Integ, c_Int_OInteg))], (37923 ^ _780086) ^ [_1505405, _1505407, _1505409] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1505405, hAPP(hAPP(c_COMBC(_1505405, tc_fun(tc_prod(_1505405, _1505405), tc_HOL_Obool), tc_fun(_1505405, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1505405, tc_fun(tc_fun(tc_prod(_1505405, _1505405), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1505405, _1505405), tc_HOL_Obool), tc_fun(_1505405, tc_HOL_Obool)), _1505405), c_COMBC(_1505405, tc_fun(tc_prod(_1505405, _1505405), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1505405, tc_prod(_1505405, _1505405)), tc_fun(_1505405, tc_fun(tc_fun(tc_prod(_1505405, _1505405), tc_HOL_Obool), tc_HOL_Obool)), _1505405), hAPP(c_COMBB(tc_prod(_1505405, _1505405), tc_fun(tc_fun(tc_prod(_1505405, _1505405), tc_HOL_Obool), tc_HOL_Obool), _1505405), c_member(tc_prod(_1505405, _1505405)))), c_Product__Type_OPair(_1505405, _1505405)))), _1505407)), _1505409)), -(hBOOL(hAPP(hAPP(c_member(_1505405), _1505409), c_Wellfounded_Oacc(_1505405, _1505407))))], (37929 ^ _780086) ^ [_1505746, _1505748, _1505750] : [hBOOL(hAPP(hAPP(c_member(_1505746), _1505750), c_Wellfounded_Oacc(_1505746, _1505748))), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1505746, hAPP(hAPP(c_COMBC(_1505746, tc_fun(tc_prod(_1505746, _1505746), tc_HOL_Obool), tc_fun(_1505746, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1505746, tc_fun(tc_fun(tc_prod(_1505746, _1505746), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1505746, _1505746), tc_HOL_Obool), tc_fun(_1505746, tc_HOL_Obool)), _1505746), c_COMBC(_1505746, tc_fun(tc_prod(_1505746, _1505746), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1505746, tc_prod(_1505746, _1505746)), tc_fun(_1505746, tc_fun(tc_fun(tc_prod(_1505746, _1505746), tc_HOL_Obool), tc_HOL_Obool)), _1505746), hAPP(c_COMBB(tc_prod(_1505746, _1505746), tc_fun(tc_fun(tc_prod(_1505746, _1505746), tc_HOL_Obool), tc_HOL_Obool), _1505746), c_member(tc_prod(_1505746, _1505746)))), c_Product__Type_OPair(_1505746, _1505746)))), _1505748)), _1505750)))], (37935 ^ _780086) ^ [_1506093, _1506095, _1506097, _1506099, _1506101] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1506093, _1506095, _1506097), _1506099), _1506101) = hAPP(c_Set_OCollect(tc_prod(_1506093, _1506097)), hAPP(c_Product__Type_Oprod_Oprod__case(_1506093, _1506097, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1506097, tc_fun(_1506095, tc_HOL_Obool)), tc_fun(_1506097, tc_HOL_Obool), _1506093), hAPP(c_COMBB(tc_fun(_1506095, tc_HOL_Obool), tc_HOL_Obool, _1506097), c_HOL_OEx(_1506095))), hAPP(hAPP(c_COMBC(_1506093, tc_fun(_1506097, tc_fun(_1506095, tc_HOL_Obool)), tc_fun(_1506097, tc_fun(_1506095, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1506095, tc_HOL_Obool), tc_fun(_1506095, tc_HOL_Obool)), tc_fun(tc_fun(_1506097, tc_fun(_1506095, tc_HOL_Obool)), tc_fun(_1506097, tc_fun(_1506095, tc_HOL_Obool))), _1506093), c_COMBB(tc_fun(_1506095, tc_HOL_Obool), tc_fun(_1506095, tc_HOL_Obool), _1506097)), hAPP(hAPP(c_COMBB(tc_fun(_1506095, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1506095, tc_HOL_Obool), tc_fun(_1506095, tc_HOL_Obool)), _1506093), c_COMBS(_1506095, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1506095, tc_HOL_Obool), tc_fun(_1506095, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1506093), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1506095), c_fconj)), hAPP(hAPP(c_COMBC(_1506093, tc_fun(tc_prod(_1506093, _1506095), tc_HOL_Obool), tc_fun(_1506095, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1506095, tc_fun(tc_fun(tc_prod(_1506093, _1506095), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1506093, _1506095), tc_HOL_Obool), tc_fun(_1506095, tc_HOL_Obool)), _1506093), c_COMBC(_1506095, tc_fun(tc_prod(_1506093, _1506095), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1506095, tc_prod(_1506093, _1506095)), tc_fun(_1506095, tc_fun(tc_fun(tc_prod(_1506093, _1506095), tc_HOL_Obool), tc_HOL_Obool)), _1506093), hAPP(c_COMBB(tc_prod(_1506093, _1506095), tc_fun(tc_fun(tc_prod(_1506093, _1506095), tc_HOL_Obool), tc_HOL_Obool), _1506095), c_member(tc_prod(_1506093, _1506095)))), c_Product__Type_OPair(_1506093, _1506095)))), _1506099))))), hAPP(hAPP(c_COMBC(_1506097, tc_fun(tc_prod(_1506095, _1506097), tc_HOL_Obool), tc_fun(_1506095, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1506095, tc_fun(tc_fun(tc_prod(_1506095, _1506097), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1506095, _1506097), tc_HOL_Obool), tc_fun(_1506095, tc_HOL_Obool)), _1506097), c_COMBC(_1506095, tc_fun(tc_prod(_1506095, _1506097), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1506095, tc_prod(_1506095, _1506097)), tc_fun(_1506095, tc_fun(tc_fun(tc_prod(_1506095, _1506097), tc_HOL_Obool), tc_HOL_Obool)), _1506097), hAPP(c_COMBB(tc_prod(_1506095, _1506097), tc_fun(tc_fun(tc_prod(_1506095, _1506097), tc_HOL_Obool), tc_HOL_Obool), _1506095), c_member(tc_prod(_1506095, _1506097)))), hAPP(c_COMBC(_1506095, _1506097, tc_prod(_1506095, _1506097)), c_Product__Type_OPair(_1506095, _1506097))))), _1506101))))))], (37937 ^ _780086) ^ [_1506541, _1506543, _1506545, _1506547, _1506549, _1506551, _1506553, _1506555] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1506541, _1506543)), hAPP(hAPP(c_Product__Type_OPair(_1506541, _1506543), _1506545), _1506547)), _1506549)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1506543, _1506551)), hAPP(hAPP(c_Product__Type_OPair(_1506543, _1506551), _1506547), _1506553)), _1506555)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1506541, _1506551)), hAPP(hAPP(c_Product__Type_OPair(_1506541, _1506551), _1506545), _1506553)), hAPP(hAPP(c_Relation_Orel__comp(_1506541, _1506543, _1506551), _1506549), _1506555))))], (37947 ^ _780086) ^ [_1506828, _1506830, _1506832, _1506834, _1506836, _1506838, _1506840] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1506828, _1506830, _1506832), _1506834), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1506836, tc_fun(tc_prod(_1506830, _1506832), tc_HOL_Obool)), _1506838), _1506840)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1506836, tc_fun(tc_prod(_1506828, _1506832), tc_HOL_Obool)), _1506838), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1506830, _1506832), tc_HOL_Obool), tc_fun(tc_prod(_1506828, _1506832), tc_HOL_Obool), _1506836), hAPP(c_Relation_Orel__comp(_1506828, _1506830, _1506832), _1506834)), _1506840)))], (37949 ^ _780086) ^ [_1506932, _1506934, _1506936, _1506938, _1506940, _1506942, _1506944] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1506932, _1506934, _1506936), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1506938, tc_fun(tc_prod(_1506932, _1506934), tc_HOL_Obool)), _1506940), _1506942)), _1506944) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1506938, tc_fun(tc_prod(_1506932, _1506936), tc_HOL_Obool)), _1506940), hAPP(hAPP(c_COMBC(_1506938, tc_fun(tc_prod(_1506934, _1506936), tc_HOL_Obool), tc_fun(tc_prod(_1506932, _1506936), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1506932, _1506934), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1506934, _1506936), tc_HOL_Obool), tc_fun(tc_prod(_1506932, _1506936), tc_HOL_Obool)), _1506938), c_Relation_Orel__comp(_1506932, _1506934, _1506936)), _1506942)), _1506944)))], (37951 ^ _780086) ^ [_1507064, _1507066, _1507068, _1507070] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1507064, _1507066, _1507068), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1507064, _1507066), tc_HOL_Obool))), _1507070) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1507064, _1507068), tc_HOL_Obool)))], (37953 ^ _780086) ^ [_1507119, _1507121, _1507123, _1507125] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1507119, _1507121, _1507123), _1507125), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1507121, _1507123), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1507119, _1507123), tc_HOL_Obool)))], (37955 ^ _780086) ^ [_1507174, _1507176, _1507178, _1507180, _1507182, _1507184] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1507174, _1507176, _1507178), _1507180), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1507176, _1507178), tc_HOL_Obool)), _1507182), _1507184)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1507174, _1507178), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1507174, _1507176, _1507178), _1507180), _1507182)), hAPP(hAPP(c_Relation_Orel__comp(_1507174, _1507176, _1507178), _1507180), _1507184)))], (37957 ^ _780086) ^ [_1507265, _1507267, _1507269, _1507271, _1507273, _1507275] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1507265, _1507267, _1507269), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1507265, _1507267), tc_HOL_Obool)), _1507271), _1507273)), _1507275) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1507265, _1507269), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1507265, _1507267, _1507269), _1507271), _1507275)), hAPP(hAPP(c_Relation_Orel__comp(_1507265, _1507267, _1507269), _1507273), _1507275)))], (37959 ^ _780086) ^ [_1507356, _1507358, _1507360, _1507362, _1507364, _1507366, _1507368] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1507356, _1507358), tc_HOL_Obool)), _1507360), _1507362)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1507358, _1507364), tc_HOL_Obool)), _1507366), _1507368)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1507356, _1507364), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1507356, _1507358, _1507364), _1507360), _1507366)), hAPP(hAPP(c_Relation_Orel__comp(_1507356, _1507358, _1507364), _1507362), _1507368))))], (37969 ^ _780086) ^ [_1507623, _1507625, _1507627, _1507629, _1507631, _1507633, _1507635] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1507623, _1507625, _1507627), hAPP(hAPP(c_Relation_Orel__comp(_1507623, _1507629, _1507625), _1507631), _1507633)), _1507635) = hAPP(hAPP(c_Relation_Orel__comp(_1507623, _1507629, _1507627), _1507631), hAPP(hAPP(c_Relation_Orel__comp(_1507629, _1507625, _1507627), _1507633), _1507635)))], (37971 ^ _780086) ^ [_1507698, _1507700, _1507702, _1507704] : [hAPP(hAPP(c_Relation_Orel__comp(_1507698, _1507698, _1507698), _1507700), _1507702) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1507698, _1507698), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1507698, _1507698, _1507698), _1507704), _1507702) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1507698, _1507698), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1507698, _1507698, _1507698), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1507698, _1507698), tc_HOL_Obool)), _1507700), _1507704)), _1507702) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1507698, _1507698), tc_HOL_Obool)))], (37981 ^ _780086) ^ [_1507971, _1507973, _1507975, _1507977] : [hAPP(hAPP(c_Relation_Orel__comp(_1507971, _1507971, _1507971), _1507973), _1507975) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1507971, _1507971), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1507971, _1507971, _1507971), _1507973), _1507977) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1507971, _1507971), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1507971, _1507971, _1507971), _1507973), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1507971, _1507971), tc_HOL_Obool)), _1507975), _1507977)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1507971, _1507971), tc_HOL_Obool)))], (37991 ^ _780086) ^ [_1508244, _1508246, _1508248] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1508244, _1508244), tc_HOL_Obool)), _1508246), _1508248)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1508244, tc_HOL_Obool)), c_Wellfounded_Oacc(_1508244, _1508248)), c_Wellfounded_Oacc(_1508244, _1508246))))], (38007 ^ _780086) ^ [_1508652, _1508654, _1508656] : [38009 ^ _780086 : [(38010 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1508652, _1508652)), hAPP(hAPP(c_Product__Type_OPair(_1508652, _1508652), 38008 ^ [_1508652, _1508654, _1508656]), _1508654)), _1508656)))], (38012 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1508652), 38008 ^ [_1508652, _1508654, _1508656]), c_Wellfounded_Oacc(_1508652, _1508656)))]], -(hBOOL(hAPP(hAPP(c_member(_1508652), _1508654), c_Wellfounded_Oacc(_1508652, _1508656))))], (37997 ^ _780086) ^ [_1508399, _1508401, _1508403] : [hBOOL(hAPP(hAPP(c_member(_1508399), _1508401), c_Wellfounded_Oacc(_1508399, _1508403))), 38000 ^ _780086 : [(38001 ^ _780086) ^ [_1508513] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1508399, _1508399)), hAPP(hAPP(c_Product__Type_OPair(_1508399, _1508399), _1508513), _1508401)), _1508403)), -(hBOOL(hAPP(hAPP(c_member(_1508399), _1508513), c_Wellfounded_Oacc(_1508399, _1508403))))]]], (38016 ^ _780086) ^ [_1508892, _1508894, _1508896, _1508898] : [hBOOL(hAPP(hAPP(c_member(_1508892), _1508894), c_Wellfounded_Oacc(_1508892, _1508896))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1508892, _1508892)), hAPP(hAPP(c_Product__Type_OPair(_1508892, _1508892), _1508898), _1508894)), _1508896)), -(hBOOL(hAPP(hAPP(c_member(_1508892), _1508898), c_Wellfounded_Oacc(_1508892, _1508896))))], (38026 ^ _780086) ^ [_1509107, _1509109, _1509111] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1509107, _1509107), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1509107, _1509107, _1509107), _1509109), _1509111)), _1509109)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1509107, tc_HOL_Obool), tc_fun(_1509107, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1509107, tc_HOL_Obool), tc_fun(_1509107, tc_HOL_Obool), tc_fun(_1509107, tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1509107, _1509109)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1509107, tc_HOL_Obool), tc_fun(_1509107, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1509107, _1509111)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1509107, tc_HOL_Obool), tc_fun(_1509107, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1509107, tc_HOL_Obool), tc_fun(_1509107, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1509107, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1509107, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1509107, tc_HOL_Obool), tc_fun(_1509107, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omax__ext(_1509107, _1509109))))], (38032 ^ _780086) ^ [_1509478, _1509480, _1509482] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1509478, _1509478), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1509478, _1509478, _1509478), _1509480), _1509482)), _1509480)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1509478, tc_HOL_Obool), tc_fun(_1509478, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1509478, tc_HOL_Obool), tc_fun(_1509478, tc_HOL_Obool), tc_fun(_1509478, tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1509478, _1509480)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1509478, tc_HOL_Obool), tc_fun(_1509478, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1509478, _1509482)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1509478, tc_HOL_Obool), tc_fun(_1509478, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1509478, tc_HOL_Obool), tc_fun(_1509478, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1509478, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1509478, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1509478, tc_HOL_Obool), tc_fun(_1509478, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omin__ext(_1509478, _1509480))))], (38038 ^ _780086) ^ [_1509849, _1509851, _1509853, _1509855, _1509857] : [c_Typedef_Otype__definition(_1509849, _1509851, _1509853, _1509855, _1509857), -(hAPP(c_Set_Oimage(_1509851, _1509849, _1509855), _1509857) = c_Orderings_Otop__class_Otop(tc_fun(_1509849, tc_HOL_Obool)))], (38044 ^ _780086) ^ [_1509962, _1509964, _1509966, _1509968, _1509970] : [c_Typedef_Otype__definition(_1509962, _1509964, _1509966, _1509968, _1509970), -(hAPP(c_Set_Oimage(_1509962, _1509964, _1509966), c_Orderings_Otop__class_Otop(tc_fun(_1509962, tc_HOL_Obool))) = _1509970)], (38050 ^ _780086) ^ [_1510075, _1510077, _1510079, _1510081, _1510083, _1510085, _1510087] : [c_Typedef_Otype__definition(_1510075, _1510077, _1510079, _1510081, _1510083), hBOOL(hAPP(hAPP(c_member(_1510077), _1510085), _1510083)), hBOOL(hAPP(hAPP(c_member(_1510077), _1510087), _1510083)), 38061 ^ _780086 : [(38062 ^ _780086) ^ [] : [hAPP(_1510081, _1510085) = hAPP(_1510081, _1510087), -(_1510085 = _1510087)], (38068 ^ _780086) ^ [] : [_1510085 = _1510087, -(hAPP(_1510081, _1510085) = hAPP(_1510081, _1510087))]]], (38074 ^ _780086) ^ [_1510488, _1510490, _1510492, _1510494, _1510496, _1510498, _1510500] : [c_Typedef_Otype__definition(_1510488, _1510490, _1510492, _1510494, _1510496), 38077 ^ _780086 : [(38078 ^ _780086) ^ [] : [hAPP(_1510492, _1510498) = hAPP(_1510492, _1510500), -(_1510498 = _1510500)], (38084 ^ _780086) ^ [] : [_1510498 = _1510500, -(hAPP(_1510492, _1510498) = hAPP(_1510492, _1510500))]]], (38090 ^ _780086) ^ [_1510749, _1510751, _1510753, _1510755, _1510757, _1510759] : [c_Typedef_Otype__definition(_1510749, _1510751, _1510753, _1510755, _1510757), -(hAPP(_1510755, hAPP(_1510753, _1510759)) = _1510759)], (38096 ^ _780086) ^ [_1510852, _1510854, _1510856, _1510858, _1510860, _1510862] : [c_Typedef_Otype__definition(_1510852, _1510854, _1510856, _1510858, _1510860), -(hBOOL(hAPP(hAPP(c_member(_1510854), hAPP(_1510856, _1510862)), _1510860)))], (38102 ^ _780086) ^ [_1510963, _1510965, _1510967, _1510969, _1510971, _1510973] : [c_Typedef_Otype__definition(_1510963, _1510965, _1510967, _1510969, _1510971), hBOOL(hAPP(hAPP(c_member(_1510965), _1510973), _1510971)), -(hAPP(_1510967, hAPP(_1510969, _1510973)) = _1510973)], (38112 ^ _780086) ^ [_1511170, _1511172, _1511174, _1511176, _1511178, _1511180, _1511182] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1511170, _1511172, _1511174, hAPP(hAPP(c_COMBC(_1511170, tc_fun(tc_prod(_1511170, _1511172), tc_HOL_Obool), tc_fun(_1511172, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511172, tc_fun(tc_fun(tc_prod(_1511170, _1511172), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1511170, _1511172), tc_HOL_Obool), tc_fun(_1511172, tc_HOL_Obool)), _1511170), c_COMBC(_1511172, tc_fun(tc_prod(_1511170, _1511172), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511172, tc_prod(_1511170, _1511172)), tc_fun(_1511172, tc_fun(tc_fun(tc_prod(_1511170, _1511172), tc_HOL_Obool), tc_HOL_Obool)), _1511170), hAPP(c_COMBB(tc_prod(_1511170, _1511172), tc_fun(tc_fun(tc_prod(_1511170, _1511172), tc_HOL_Obool), tc_HOL_Obool), _1511172), c_member(tc_prod(_1511170, _1511172)))), c_Product__Type_OPair(_1511170, _1511172)))), _1511176), hAPP(hAPP(c_COMBC(_1511172, tc_fun(tc_prod(_1511172, _1511174), tc_HOL_Obool), tc_fun(_1511174, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511174, tc_fun(tc_fun(tc_prod(_1511172, _1511174), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1511172, _1511174), tc_HOL_Obool), tc_fun(_1511174, tc_HOL_Obool)), _1511172), c_COMBC(_1511174, tc_fun(tc_prod(_1511172, _1511174), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511174, tc_prod(_1511172, _1511174)), tc_fun(_1511174, tc_fun(tc_fun(tc_prod(_1511172, _1511174), tc_HOL_Obool), tc_HOL_Obool)), _1511172), hAPP(c_COMBB(tc_prod(_1511172, _1511174), tc_fun(tc_fun(tc_prod(_1511172, _1511174), tc_HOL_Obool), tc_HOL_Obool), _1511174), c_member(tc_prod(_1511172, _1511174)))), c_Product__Type_OPair(_1511172, _1511174)))), _1511178)), _1511180), _1511182)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1511170, _1511174)), hAPP(hAPP(c_Product__Type_OPair(_1511170, _1511174), _1511180), _1511182)), hAPP(hAPP(c_Relation_Orel__comp(_1511170, _1511172, _1511174), _1511176), _1511178))))], (38118 ^ _780086) ^ [_1511805, _1511807, _1511809, _1511811, _1511813, _1511815, _1511817] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1511805, _1511809)), hAPP(hAPP(c_Product__Type_OPair(_1511805, _1511809), _1511815), _1511817)), hAPP(hAPP(c_Relation_Orel__comp(_1511805, _1511807, _1511809), _1511811), _1511813))), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1511805, _1511807, _1511809, hAPP(hAPP(c_COMBC(_1511805, tc_fun(tc_prod(_1511805, _1511807), tc_HOL_Obool), tc_fun(_1511807, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511807, tc_fun(tc_fun(tc_prod(_1511805, _1511807), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1511805, _1511807), tc_HOL_Obool), tc_fun(_1511807, tc_HOL_Obool)), _1511805), c_COMBC(_1511807, tc_fun(tc_prod(_1511805, _1511807), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511807, tc_prod(_1511805, _1511807)), tc_fun(_1511807, tc_fun(tc_fun(tc_prod(_1511805, _1511807), tc_HOL_Obool), tc_HOL_Obool)), _1511805), hAPP(c_COMBB(tc_prod(_1511805, _1511807), tc_fun(tc_fun(tc_prod(_1511805, _1511807), tc_HOL_Obool), tc_HOL_Obool), _1511807), c_member(tc_prod(_1511805, _1511807)))), c_Product__Type_OPair(_1511805, _1511807)))), _1511811), hAPP(hAPP(c_COMBC(_1511807, tc_fun(tc_prod(_1511807, _1511809), tc_HOL_Obool), tc_fun(_1511809, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511809, tc_fun(tc_fun(tc_prod(_1511807, _1511809), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1511807, _1511809), tc_HOL_Obool), tc_fun(_1511809, tc_HOL_Obool)), _1511807), c_COMBC(_1511809, tc_fun(tc_prod(_1511807, _1511809), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511809, tc_prod(_1511807, _1511809)), tc_fun(_1511809, tc_fun(tc_fun(tc_prod(_1511807, _1511809), tc_HOL_Obool), tc_HOL_Obool)), _1511807), hAPP(c_COMBB(tc_prod(_1511807, _1511809), tc_fun(tc_fun(tc_prod(_1511807, _1511809), tc_HOL_Obool), tc_HOL_Obool), _1511809), c_member(tc_prod(_1511807, _1511809)))), c_Product__Type_OPair(_1511807, _1511809)))), _1511813)), _1511815), _1511817)))], (38124 ^ _780086) ^ [_1512446, _1512448, _1512450] : [c_Wellfounded_Owf(_1512446, _1512448), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1512446, _1512446), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1512446, _1512446, _1512446), _1512448), _1512450)), _1512448)), -(c_FunDef_Oreduction__pair(_1512446, hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(_1512446, _1512446), tc_HOL_Obool), tc_fun(tc_prod(_1512446, _1512446), tc_HOL_Obool)), _1512448), _1512450)))], (38134 ^ _780086) ^ [_1512688, _1512690, _1512692, _1512694] : [c_Wellfounded_Omax__extp(_1512688, _1512690, _1512692, _1512694), 38137 ^ _780086 : [(38138 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1512688), _1512692)))], (38140 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1512688), _1512694)))], (38142 ^ _780086) ^ [] : [_1512694 = c_Orderings_Obot__class_Obot(tc_fun(_1512688, tc_HOL_Obool))], (38144 ^ _780086) ^ [_1512904] : [hBOOL(hAPP(hAPP(c_member(_1512688), _1512904), _1512692)), 38148 ^ _780086 : [(38149 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1512688), 38147 ^ [_1512688, _1512690, _1512692, _1512694, _1512904]), _1512694)))], (38151 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(_1512690, _1512904), 38147 ^ [_1512688, _1512690, _1512692, _1512694, _1512904])))]]]]], (38153 ^ _780086) ^ [_1513088, _1513090, _1513092, _1513094] : [-(c_Wellfounded_Omax__extp(_1513088, _1513090, _1513092, _1513094)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1513088), _1513092)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1513088), _1513094)), -(_1513094 = c_Orderings_Obot__class_Obot(tc_fun(_1513088, tc_HOL_Obool))), 38167 ^ _780086 : [(38168 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1513088), 38166 ^ [_1513088, _1513090, _1513092, _1513094]), _1513092)))], (38170 ^ _780086) ^ [_1513433] : [hBOOL(hAPP(hAPP(c_member(_1513088), _1513433), _1513094)), hBOOL(hAPP(hAPP(_1513090, 38166 ^ [_1513088, _1513090, _1513092, _1513094]), _1513433))]]], (38178 ^ _780086) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Oless__than))], (38180 ^ _780086) ^ [_1513619, _1513621, _1513623, _1513625, _1513627, _1513629, _1513631, _1513633] : [hBOOL(hAPP(hAPP(_1513619, _1513621), _1513623)), hBOOL(hAPP(hAPP(_1513625, _1513623), _1513627)), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1513629, _1513631, _1513633, _1513619, _1513625), _1513621), _1513627)))], (38190 ^ _780086) ^ [_1513814] : [-(c_Wellfounded_Owf(_1513814, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1513814, _1513814), tc_HOL_Obool))))], (38192 ^ _780086) ^ [_1513845, _1513847, _1513849, _1513851] : [c_Wellfounded_Owf(_1513845, _1513847), -(c_Wellfounded_Owf(_1513849, hAPP(hAPP(c_Relation_Oinv__image(_1513845, _1513849), _1513847), _1513851)))], (38198 ^ _780086) ^ [_1513944, _1513946, _1513948, _1513950] : [c_Wellfounded_Owf(_1513944, _1513946), c_Wellfounded_Owf(_1513948, _1513950), -(c_Wellfounded_Owf(tc_prod(_1513944, _1513948), c_Wellfounded_Olex__prod(_1513944, _1513948, _1513946, _1513950)))], (38208 ^ _780086) ^ [_1514097, _1514099] : [-(c_Wellfounded_Owf(_1514097, hAPP(c_Wellfounded_Omeasure(_1514097), _1514099)))], (38210 ^ _780086) ^ [_1514142, _1514144] : [c_Wellfounded_Owf(_1514142, _1514144), -(c_Wellfounded_Owf(_1514142, hAPP(hAPP(c_Relation_Orel__comp(_1514142, _1514142, _1514142), _1514144), _1514144)))], (38216 ^ _780086) ^ [_1514235, _1514237] : [c_Wellfounded_Owf(_1514235, hAPP(hAPP(c_Relation_Orel__comp(_1514235, _1514235, _1514235), _1514237), _1514237)), -(c_Wellfounded_Owf(_1514235, _1514237))], (38222 ^ _780086) ^ [_1514334, _1514336, _1514338] : [c_Wellfounded_Owf(_1514334, _1514336), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1514334, _1514334), tc_HOL_Obool)), _1514338), _1514336)), -(c_Wellfounded_Owf(_1514334, _1514338))], (38232 ^ _780086) ^ [_1514493, _1514495] : [c_Wellfounded_Owf(_1514493, _1514495), -(c_Wellfounded_Owf(tc_fun(_1514493, tc_HOL_Obool), c_Wellfounded_Omin__ext(_1514493, _1514495)))], (38238 ^ _780086) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)))))], (38240 ^ _780086) ^ [_1514600] : [-(c_Wellfounded_Owf(tc_fun(_1514600, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1514600)))], (38242 ^ _780086) ^ [_1514658, _1514660, _1514662, _1514664, _1514666, _1514668, _1514670] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1514658, _1514660, _1514662, _1514664, _1514666), _1514668), _1514670)), 38246 ^ _780086 : [(38247 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(_1514664, _1514668), 38245 ^ [_1514658, _1514660, _1514662, _1514664, _1514666, _1514668, _1514670])))], (38249 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(_1514666, 38245 ^ [_1514658, _1514660, _1514662, _1514664, _1514666, _1514668, _1514670]), _1514670)))]]], (38251 ^ _780086) ^ [_1514848, _1514850, _1514852, _1514854, _1514856, _1514858, _1514860] : [-(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1514848, _1514850, _1514852, _1514854, _1514856), _1514858), _1514860))), 38252 ^ _780086 : [(38253 ^ _780086) ^ [_1514919] : [hBOOL(hAPP(hAPP(_1514854, _1514858), _1514919)), hBOOL(hAPP(hAPP(_1514856, _1514919), _1514860))]]], (38261 ^ _780086) ^ [_1515068, _1515070, _1515072] : [c_Wellfounded_Owf(_1515068, _1515070), -(c_Wellfounded_Owf(_1515068, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1515068, _1515068), tc_HOL_Obool)), _1515072), _1515070)))], (38267 ^ _780086) ^ [_1515175, _1515177, _1515179] : [c_Wellfounded_Owf(_1515175, _1515177), -(c_Wellfounded_Owf(_1515175, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1515175, _1515175), tc_HOL_Obool)), _1515177), _1515179)))], (38273 ^ _780086) ^ [_1515282, _1515284, _1515286] : [c_Wellfounded_Owf(_1515282, _1515284), -(c_Wellfounded_Owf(_1515282, c_Wellfounded_Omlex__prod(_1515282, _1515286, _1515284)))], (38279 ^ _780086) ^ [] : [-(c_Wellfounded_Owf(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (38281 ^ _780086) ^ [_1515387, _1515389] : [c_Wellfounded_Owf(_1515387, _1515389), -(c_Wellfounded_Owf(tc_fun(_1515387, tc_HOL_Obool), c_Wellfounded_Omax__ext(_1515387, _1515389)))], (38287 ^ _780086) ^ [_1515476, _1515478, _1515480] : [c_Wellfounded_Owf(_1515476, _1515478), hBOOL(hAPP(hAPP(c_member(tc_prod(_1515476, _1515476)), hAPP(hAPP(c_Product__Type_OPair(_1515476, _1515476), _1515480), _1515480)), _1515478))], (38293 ^ _780086) ^ [_1515594, _1515596, _1515598, _1515600] : [c_Wellfounded_Owf(_1515594, _1515596), hBOOL(hAPP(hAPP(c_member(tc_prod(_1515594, _1515594)), hAPP(hAPP(c_Product__Type_OPair(_1515594, _1515594), _1515598), _1515600)), _1515596)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1515594, _1515594)), hAPP(hAPP(c_Product__Type_OPair(_1515594, _1515594), _1515600), _1515598)), _1515596))], (38303 ^ _780086) ^ [_1515808, _1515810, _1515812, _1515814] : [c_Wellfounded_Owf(_1515808, _1515810), hBOOL(hAPP(hAPP(c_member(tc_prod(_1515808, _1515808)), hAPP(hAPP(c_Product__Type_OPair(_1515808, _1515808), _1515812), _1515814)), _1515810)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1515808, _1515808)), hAPP(hAPP(c_Product__Type_OPair(_1515808, _1515808), _1515814), _1515812)), _1515810))], (38313 ^ _780086) ^ [_1516022, _1516024, _1516026] : [c_Wellfounded_Owf(_1516022, _1516024), hBOOL(hAPP(hAPP(c_member(tc_prod(_1516022, _1516022)), hAPP(hAPP(c_Product__Type_OPair(_1516022, _1516022), _1516026), _1516026)), _1516024))], (38319 ^ _780086) ^ [_1516140] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than2(_1516140)))], (38321 ^ _780086) ^ [_1516165] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than(_1516165)))], (38323 ^ _780086) ^ [_1516205, _1516207] : [c_Wellfounded_Owf(_1516205, _1516207), 38326 ^ _780086 : [(38327 ^ _780086) ^ [_1516274] : [-(hBOOL(hAPP(hAPP(c_member(_1516205), _1516274), c_Wellfounded_Oacc(_1516205, _1516207))))]]], (38329 ^ _780086) ^ [_1516307, _1516309] : [hBOOL(hAPP(hAPP(c_member(_1516307), 38330 ^ [_1516307, _1516309]), c_Wellfounded_Oacc(_1516307, _1516309))), -(c_Wellfounded_Owf(_1516307, _1516309))], (38336 ^ _780086) ^ [_1516440, _1516442, _1516444] : [c_Wellfounded_Owf(_1516440, _1516442), -(hBOOL(hAPP(hAPP(c_member(_1516440), _1516444), c_Wellfounded_Oacc(_1516440, _1516442))))], (38342 ^ _780086) ^ [_1516539, _1516541] : [hAPP(hAPP(c_Relation_Orel__comp(_1516539, _1516539, _1516539), _1516541), _1516541) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1516539, _1516539), tc_HOL_Obool)), -(c_Wellfounded_Owf(_1516539, _1516541))], (38348 ^ _780086) ^ [_1516670, _1516672, _1516674] : [c_Wellfounded_Owf(_1516670, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1516670, _1516670), tc_HOL_Obool)), _1516672), _1516674)), -(c_Wellfounded_Owf(_1516670, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1516670, _1516670), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1516670, _1516670), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1516670, _1516670, _1516670), _1516672), _1516672)), hAPP(hAPP(c_Relation_Orel__comp(_1516670, _1516670, _1516670), _1516674), _1516672))), _1516674)))], (38354 ^ _780086) ^ [_1516869, _1516871, _1516873] : [c_Wellfounded_Owf(_1516869, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1516869, _1516869), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1516869, _1516869), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1516869, _1516869, _1516869), _1516871), _1516871)), hAPP(hAPP(c_Relation_Orel__comp(_1516869, _1516869, _1516869), _1516873), _1516871))), _1516873)), -(c_Wellfounded_Owf(_1516869, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1516869, _1516869), tc_HOL_Obool)), _1516871), _1516873)))], (38360 ^ _780086) ^ [_1517089, _1517091] : [c_Wellfounded_Owf(_1517089, _1517091), 38364 ^ _780086 : [(38365 ^ _780086) ^ [_1517225] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1517089, _1517089)), hAPP(hAPP(c_Product__Type_OPair(_1517089, _1517089), hAPP(_1517225, hAPP(c_Nat_OSuc, 38363 ^ [_1517089, _1517091, _1517225]))), hAPP(_1517225, 38363 ^ [_1517089, _1517091, _1517225]))), _1517091))]]], (38367 ^ _780086) ^ [_1517292, _1517294] : [38369 ^ _780086 : [(38370 ^ _780086) ^ [_1517317] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1517292, _1517292)), hAPP(hAPP(c_Product__Type_OPair(_1517292, _1517292), hAPP(38368 ^ [_1517292, _1517294], hAPP(c_Nat_OSuc, _1517317))), hAPP(38368 ^ [_1517292, _1517294], _1517317))), _1517294)))]], -(c_Wellfounded_Owf(_1517292, _1517294))], (38374 ^ _780086) ^ [_1517393, _1517395, _1517397] : [c_Wellfounded_Owf(_1517393, _1517395), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1517393, tc_HOL_Obool)), _1517397), hAPP(c_Relation_OImage(_1517393, _1517393, _1517395), _1517397))), -(_1517397 = c_Orderings_Obot__class_Obot(tc_fun(_1517393, tc_HOL_Obool)))], (38384 ^ _780086) ^ [_1517570, _1517572, _1517574] : [c_Wellfounded_Owf(_1517570, _1517572), c_Wellfounded_Owf(_1517570, _1517574), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1517570, _1517570), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1517570, _1517570, _1517570), _1517572), _1517574)), _1517572)), -(c_Wellfounded_Owf(_1517570, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1517570, _1517570), tc_HOL_Obool)), _1517572), _1517574)))], (38398 ^ _780086) ^ [_1517831] : [class_Orderings_Owellorder(_1517831), -(c_Wellfounded_Owf(_1517831, hAPP(c_Set_OCollect(tc_prod(_1517831, _1517831)), hAPP(c_Product__Type_Oprod_Oprod__case(_1517831, _1517831, tc_HOL_Obool), c_Orderings_Oord__class_Oless(_1517831)))))], (38404 ^ _780086) ^ [_1517953, _1517955] : [c_FunDef_Oreduction__pair(_1517953, _1517955), 38407 ^ _780086 : [(38408 ^ _780086) ^ [] : [-(c_Wellfounded_Owf(_1517953, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1517953, _1517953), tc_HOL_Obool), tc_fun(tc_prod(_1517953, _1517953), tc_HOL_Obool)), _1517955)))], (38410 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1517953, _1517953), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1517953, _1517953, _1517953), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1517953, _1517953), tc_HOL_Obool), tc_fun(tc_prod(_1517953, _1517953), tc_HOL_Obool)), _1517955)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1517953, _1517953), tc_HOL_Obool), tc_fun(tc_prod(_1517953, _1517953), tc_HOL_Obool)), _1517955))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1517953, _1517953), tc_HOL_Obool), tc_fun(tc_prod(_1517953, _1517953), tc_HOL_Obool)), _1517955))))]]], (38412 ^ _780086) ^ [_1518242, _1518244] : [-(c_FunDef_Oreduction__pair(_1518242, _1518244)), c_Wellfounded_Owf(_1518242, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1518242, _1518242), tc_HOL_Obool), tc_fun(tc_prod(_1518242, _1518242), tc_HOL_Obool)), _1518244)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1518242, _1518242), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1518242, _1518242, _1518242), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1518242, _1518242), tc_HOL_Obool), tc_fun(tc_prod(_1518242, _1518242), tc_HOL_Obool)), _1518244)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1518242, _1518242), tc_HOL_Obool), tc_fun(tc_prod(_1518242, _1518242), tc_HOL_Obool)), _1518244))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1518242, _1518242), tc_HOL_Obool), tc_fun(tc_prod(_1518242, _1518242), tc_HOL_Obool)), _1518244)))], (38422 ^ _780086) ^ [_1518563, _1518565, _1518567, _1518569] : [c_FunDef_Oreduction__pair(_1518563, _1518565), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1518563, _1518563), tc_HOL_Obool)), _1518567), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1518563, _1518563), tc_HOL_Obool), tc_fun(tc_prod(_1518563, _1518563), tc_HOL_Obool)), _1518565))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1518563, _1518563), tc_HOL_Obool)), _1518569), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1518563, _1518563), tc_HOL_Obool), tc_fun(tc_prod(_1518563, _1518563), tc_HOL_Obool)), _1518565))), c_Wellfounded_Owf(_1518563, _1518569), -(c_Wellfounded_Owf(_1518563, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1518563, _1518563), tc_HOL_Obool)), _1518567), _1518569)))], (38440 ^ _780086) ^ [_1518964, _1518966] : [c_Wellfounded_Owf(_1518964, _1518966), -(c_Wellfounded_Owf(tc_List_Olist(_1518964), c_List_Olenlex(_1518964, _1518966)))], (38446 ^ _780086) ^ [_1519051, _1519053, _1519055, _1519057] : [38448 ^ _780086 : [(38449 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1519051, 38447 ^ [_1519051, _1519053, _1519055, _1519057])))], (38451 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1519053, hAPP(_1519055, 38447 ^ [_1519051, _1519053, _1519055, _1519057]))), hAPP(_1519053, 38447 ^ [_1519051, _1519053, _1519055, _1519057])))]], -(c_Wellfounded_Owf(_1519057, hAPP(c_Set_OCollect(tc_prod(_1519057, _1519057)), hAPP(c_Product__Type_Oprod_Oprod__case(_1519057, _1519057, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1519057, tc_HOL_Obool), tc_fun(_1519057, tc_HOL_Obool), _1519057), hAPP(c_COMBS(_1519057, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1519057), c_fconj), _1519051))), hAPP(hAPP(c_COMBC(_1519057, tc_fun(_1519057, _1519057), tc_fun(_1519057, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1519057, tc_HOL_Obool), tc_fun(tc_fun(_1519057, _1519057), tc_fun(_1519057, tc_HOL_Obool)), _1519057), c_COMBB(_1519057, tc_HOL_Obool, _1519057)), c_fequal)), _1519055))))))], (38455 ^ _780086) ^ [_1519444, _1519446, _1519448, _1519450] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1519444), _1519446)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1519444), _1519448)), -(_1519448 = c_Orderings_Obot__class_Obot(tc_fun(_1519444, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1519444, tc_HOL_Obool), tc_fun(_1519444, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1519444, tc_HOL_Obool), tc_fun(_1519444, tc_HOL_Obool)), _1519446), _1519448)), c_Wellfounded_Omax__ext(_1519444, _1519450)))), 38469 ^ _780086 : [(38470 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1519444), 38468 ^ [_1519444, _1519446, _1519448, _1519450]), _1519446)))], (38472 ^ _780086) ^ [_1519849] : [hBOOL(hAPP(hAPP(c_member(_1519444), _1519849), _1519448)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1519444, _1519444)), hAPP(hAPP(c_Product__Type_OPair(_1519444, _1519444), 38468 ^ [_1519444, _1519446, _1519448, _1519450]), _1519849)), _1519450))]]], (38480 ^ _780086) ^ [] : [-(c_Wellfounded_Opred__nat = hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_fequal)), c_Nat_OSuc))))], (38482 ^ _780086) ^ [_1520093, _1520095] : [c_Wellfounded_Owf(_1520093, _1520095), -(c_Wellfounded_Owf(tc_List_Olist(_1520093), c_List_Olex(_1520093, _1520095)))], (38488 ^ _780086) ^ [_1520180, _1520182, _1520184] : [c_Wellfounded_Owf(_1520180, _1520182), -(c_Wellfounded_Owf(tc_List_Olist(_1520180), hAPP(c_List_Olexn(_1520180, _1520182), _1520184)))], (38494 ^ _780086) ^ [_1520275, _1520277] : [-(c_List_Olex(_1520275, _1520277) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(tc_List_Olist(_1520275), tc_List_Olist(_1520275)), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), c_List_Olexn(_1520275, _1520277)))], (38496 ^ _780086) ^ [_1520325, _1520327] : [-(hAPP(c_List_Olexn(_1520325, _1520327), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(_1520325), tc_List_Olist(_1520325)), tc_HOL_Obool)))], (38498 ^ _780086) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (38500 ^ _780086) ^ [_1520386, _1520388, _1520390, _1520392] : [38502 ^ _780086 : [(38503 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1520386, 38501 ^ [_1520386, _1520388, _1520390, _1520392])))], (38505 ^ _780086) ^ [] : [c_Wellfounded_Owf(_1520388, hAPP(_1520390, 38501 ^ [_1520386, _1520388, _1520390, _1520392]))]], -(c_Wellfounded_Owf(tc_prod(_1520392, _1520388), c_Recdef_Osame__fst(_1520392, _1520388, _1520386, _1520390)))], (38509 ^ _780086) ^ [_1520571] : [-(c_Nitpick_Ozero__frac(_1520571) = c_Nitpick_OAbs__Frac(_1520571, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (38511 ^ _780086) ^ [_1520599, _1520601, _1520603] : [-(hAPP(c_Relation_ORange(_1520599, _1520601), hAPP(c_Set_OCollect(tc_prod(_1520599, _1520601)), hAPP(c_Product__Type_Oprod_Oprod__case(_1520599, _1520601, tc_HOL_Obool), _1520603))) = hAPP(c_Set_OCollect(_1520601), hAPP(hAPP(c_COMBB(tc_fun(_1520599, tc_HOL_Obool), tc_HOL_Obool, _1520601), c_HOL_OEx(_1520599)), hAPP(c_COMBC(_1520599, _1520601, tc_HOL_Obool), _1520603))))], (38513 ^ _780086) ^ [_1520674, _1520676, _1520678, _1520680, _1520682] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1520674, _1520676)), hAPP(hAPP(c_Product__Type_OPair(_1520674, _1520676), _1520678), _1520680)), _1520682)), -(hBOOL(hAPP(hAPP(c_member(_1520676), _1520680), hAPP(c_Relation_ORange(_1520674, _1520676), _1520682))))], (38519 ^ _780086) ^ [_1520821, _1520823] : [-(hAPP(c_Relation_ORange(_1520821, _1520821), c_Relation_OId__on(_1520821, _1520823)) = _1520823)], (38521 ^ _780086) ^ [_1520855, _1520857, _1520859, _1520861] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1520855, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1520855, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1520857, _1520855), _1520859)), hAPP(c_Relation_ORange(_1520857, _1520855), _1520861))), hAPP(c_Relation_ORange(_1520857, _1520855), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1520857, _1520855), tc_HOL_Obool)), _1520859), _1520861)))))], (38523 ^ _780086) ^ [_1520937, _1520939, _1520941] : [-(hAPP(c_Relation_ORange(_1520937, _1520939), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1520937, _1520939), tc_HOL_Obool), _1520941)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1520937, _1520939), tc_HOL_Obool), tc_fun(_1520939, tc_HOL_Obool)), _1520941), c_Relation_ORange(_1520937, _1520939)))], (38525 ^ _780086) ^ [_1521018, _1521020, _1521022] : [hAPP(c_Relation_ORange(_1521018, _1521020), _1521022) = c_Orderings_Obot__class_Obot(tc_fun(_1521020, tc_HOL_Obool)), -(_1521022 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1521018, _1521020), tc_HOL_Obool)))], (38531 ^ _780086) ^ [_1521131, _1521133, _1521135] : [_1521135 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1521131, _1521133), tc_HOL_Obool)), -(hAPP(c_Relation_ORange(_1521131, _1521133), _1521135) = c_Orderings_Obot__class_Obot(tc_fun(_1521133, tc_HOL_Obool)))], (38537 ^ _780086) ^ [_1521250, _1521252] : [-(hAPP(c_Relation_ORange(_1521250, _1521252), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1521250, _1521252), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1521252, tc_HOL_Obool)))], (38539 ^ _780086) ^ [_1521294, _1521296, _1521298, _1521300] : [-(hAPP(c_Relation_ORange(_1521294, _1521296), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1521294, _1521296), tc_HOL_Obool)), _1521298), _1521300)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1521296, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1521294, _1521296), _1521298)), hAPP(c_Relation_ORange(_1521294, _1521296), _1521300)))], (38541 ^ _780086) ^ [_1521366, _1521368, _1521370] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1521366, _1521368)), _1521370)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1521368), hAPP(c_Relation_ORange(_1521366, _1521368), _1521370))))], (38547 ^ _780086) ^ [_1521479, _1521481, _1521483] : [-(hAPP(c_Set_Oimage(tc_prod(_1521479, _1521481), _1521481, c_Product__Type_Osnd(_1521479, _1521481)), _1521483) = hAPP(c_Relation_ORange(_1521479, _1521481), _1521483))], (38549 ^ _780086) ^ [_1521546, _1521548, _1521550, _1521552] : [hBOOL(hAPP(hAPP(c_member(_1521546), _1521548), hAPP(c_Relation_ORange(_1521550, _1521546), _1521552))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1521550, _1521546)), hAPP(hAPP(c_Product__Type_OPair(_1521550, _1521546), 38552 ^ [_1521546, _1521548, _1521550, _1521552]), _1521548)), _1521552)))], (38556 ^ _780086) ^ [_1521703, _1521705, _1521707, _1521709] : [38557 ^ _780086 : [(38558 ^ _780086) ^ [_1521778] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1521707, _1521703)), hAPP(hAPP(c_Product__Type_OPair(_1521707, _1521703), _1521778), _1521705)), _1521709))]], -(hBOOL(hAPP(hAPP(c_member(_1521703), _1521705), hAPP(c_Relation_ORange(_1521707, _1521703), _1521709))))], (38562 ^ _780086) ^ [_1521863, _1521865, _1521867, _1521869, _1521871] : [-(hAPP(c_Relation_ORange(_1521863, _1521865), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1521863, _1521865)), hAPP(hAPP(c_Product__Type_OPair(_1521863, _1521865), _1521867), _1521869)), _1521871)) = hAPP(hAPP(c_Set_Oinsert(_1521865), _1521869), hAPP(c_Relation_ORange(_1521863, _1521865), _1521871)))], (38564 ^ _780086) ^ [_1521934, _1521936, _1521938, _1521940] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1521934, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1521936, _1521934), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1521936, _1521934), tc_HOL_Obool)), _1521938), _1521940))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1521934, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1521936, _1521934), _1521938)), hAPP(c_Relation_ORange(_1521936, _1521934), _1521940)))))], (38566 ^ _780086) ^ [_1522016] : [-(c_Nitpick_Oone__frac(_1522016) = c_Nitpick_OAbs__Frac(_1522016, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (38568 ^ _780086) ^ [_1522044, _1522046] : [-(c_Nitpick_Onumber__of__frac(_1522044, _1522046) = c_Nitpick_OAbs__Frac(_1522044, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1522046), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (38570 ^ _780086) ^ [_1522102, _1522104, _1522106, _1522108] : [hBOOL(hAPP(c_Predicate_ORangeP(_1522102, _1522104, hAPP(hAPP(c_COMBC(_1522102, tc_fun(tc_prod(_1522102, _1522104), tc_HOL_Obool), tc_fun(_1522104, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1522104, tc_fun(tc_fun(tc_prod(_1522102, _1522104), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1522102, _1522104), tc_HOL_Obool), tc_fun(_1522104, tc_HOL_Obool)), _1522102), c_COMBC(_1522104, tc_fun(tc_prod(_1522102, _1522104), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1522104, tc_prod(_1522102, _1522104)), tc_fun(_1522104, tc_fun(tc_fun(tc_prod(_1522102, _1522104), tc_HOL_Obool), tc_HOL_Obool)), _1522102), hAPP(c_COMBB(tc_prod(_1522102, _1522104), tc_fun(tc_fun(tc_prod(_1522102, _1522104), tc_HOL_Obool), tc_HOL_Obool), _1522104), c_member(tc_prod(_1522102, _1522104)))), c_Product__Type_OPair(_1522102, _1522104)))), _1522106)), _1522108)), -(hBOOL(hAPP(hAPP(c_member(_1522104), _1522108), hAPP(c_Relation_ORange(_1522102, _1522104), _1522106))))], (38576 ^ _780086) ^ [_1522453, _1522455, _1522457, _1522459] : [hBOOL(hAPP(hAPP(c_member(_1522455), _1522459), hAPP(c_Relation_ORange(_1522453, _1522455), _1522457))), -(hBOOL(hAPP(c_Predicate_ORangeP(_1522453, _1522455, hAPP(hAPP(c_COMBC(_1522453, tc_fun(tc_prod(_1522453, _1522455), tc_HOL_Obool), tc_fun(_1522455, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1522455, tc_fun(tc_fun(tc_prod(_1522453, _1522455), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1522453, _1522455), tc_HOL_Obool), tc_fun(_1522455, tc_HOL_Obool)), _1522453), c_COMBC(_1522455, tc_fun(tc_prod(_1522453, _1522455), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1522455, tc_prod(_1522453, _1522455)), tc_fun(_1522455, tc_fun(tc_fun(tc_prod(_1522453, _1522455), tc_HOL_Obool), tc_HOL_Obool)), _1522453), hAPP(c_COMBB(tc_prod(_1522453, _1522455), tc_fun(tc_fun(tc_prod(_1522453, _1522455), tc_HOL_Obool), tc_HOL_Obool), _1522455), c_member(tc_prod(_1522453, _1522455)))), c_Product__Type_OPair(_1522453, _1522455)))), _1522457)), _1522459)))], (38582 ^ _780086) ^ [_1522810, _1522812, _1522814, _1522816, _1522818] : [hBOOL(hAPP(hAPP(_1522810, _1522812), _1522814)), -(hBOOL(hAPP(c_Predicate_ORangeP(_1522816, _1522818, _1522810), _1522814)))], (38588 ^ _780086) ^ [_1522936, _1522938, _1522940, _1522942] : [hBOOL(hAPP(c_Predicate_ORangeP(_1522936, _1522938, _1522940), _1522942)), -(hBOOL(hAPP(hAPP(_1522940, 38591 ^ [_1522936, _1522938, _1522940, _1522942]), _1522942)))], (38595 ^ _780086) ^ [_1523051, _1523053, _1523055, _1523057] : [38596 ^ _780086 : [(38597 ^ _780086) ^ [_1523105] : [hBOOL(hAPP(hAPP(_1523055, _1523105), _1523057))]], -(hBOOL(hAPP(c_Predicate_ORangeP(_1523051, _1523053, _1523055), _1523057)))], (38601 ^ _780086) ^ [_1523169, _1523171, _1523173] : [-(hAPP(hAPP(c_Nitpick_Ofrac(_1523169), _1523171), _1523173) = c_Nitpick_OAbs__Frac(_1523169, c_Nitpick_Onorm__frac(_1523171, _1523173)))], (38603 ^ _780086) ^ [_1523210, _1523212, _1523214, _1523216] : [hBOOL(hAPP(hAPP(c_member(_1523210), _1523212), hAPP(c_Relation_ORange(_1523214, _1523210), _1523216))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1523214, _1523210)), hAPP(hAPP(c_Product__Type_OPair(_1523214, _1523210), 38606 ^ [_1523210, _1523212, _1523214, _1523216]), _1523212)), _1523216)))], (38610 ^ _780086) ^ [_1523375, _1523377, _1523379] : [c_Wellfounded_Owf(_1523375, _1523377), c_Wellfounded_Owf(_1523375, _1523379), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1523375, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1523375, _1523375), _1523377)), hAPP(c_Relation_ORange(_1523375, _1523375), _1523379)) = c_Orderings_Obot__class_Obot(tc_fun(_1523375, tc_HOL_Obool)), -(c_Wellfounded_Owf(_1523375, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1523375, _1523375), tc_HOL_Obool)), _1523377), _1523379)))], (38624 ^ _780086) ^ [_1523646, _1523648, _1523650, _1523652, _1523654] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1523646, _1523648)), hAPP(hAPP(c_Product__Type_OPair(_1523646, _1523648), _1523650), _1523652)), _1523654)), -(hBOOL(hAPP(hAPP(c_member(_1523646), _1523650), hAPP(c_Relation_ODomain(_1523646, _1523648), _1523654))))], (38630 ^ _780086) ^ [_1523793, _1523795] : [-(hAPP(c_Relation_ODomain(_1523793, _1523793), c_Relation_OId__on(_1523793, _1523795)) = _1523795)], (38632 ^ _780086) ^ [_1523845, _1523847, _1523849] : [hAPP(c_Relation_ODomain(_1523845, _1523847), _1523849) = c_Orderings_Obot__class_Obot(tc_fun(_1523845, tc_HOL_Obool)), -(_1523849 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1523845, _1523847), tc_HOL_Obool)))], (38638 ^ _780086) ^ [_1523958, _1523960, _1523962] : [_1523962 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1523958, _1523960), tc_HOL_Obool)), -(hAPP(c_Relation_ODomain(_1523958, _1523960), _1523962) = c_Orderings_Obot__class_Obot(tc_fun(_1523958, tc_HOL_Obool)))], (38644 ^ _780086) ^ [_1524077, _1524079] : [-(hAPP(c_Relation_ODomain(_1524077, _1524079), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1524077, _1524079), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1524077, tc_HOL_Obool)))], (38646 ^ _780086) ^ [_1524121, _1524123, _1524125, _1524127] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1524121, _1524123), tc_HOL_Obool)), _1524125), _1524127)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1524121, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1524121, _1524123), _1524125)), hAPP(c_Relation_ODomain(_1524121, _1524123), _1524127))))], (38652 ^ _780086) ^ [_1524272, _1524274, _1524276, _1524278] : [-(hAPP(c_Relation_ODomain(_1524272, _1524274), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1524272, _1524274), tc_HOL_Obool)), _1524276), _1524278)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1524272, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1524272, _1524274), _1524276)), hAPP(c_Relation_ODomain(_1524272, _1524274), _1524278)))], (38654 ^ _780086) ^ [_1524344, _1524346, _1524348] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1524344, _1524346)), _1524348)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1524344), hAPP(c_Relation_ODomain(_1524344, _1524346), _1524348))))], (38660 ^ _780086) ^ [_1524457, _1524459, _1524461] : [-(hAPP(c_Set_Oimage(tc_prod(_1524457, _1524459), _1524457, c_Product__Type_Ofst(_1524457, _1524459)), _1524461) = hAPP(c_Relation_ODomain(_1524457, _1524459), _1524461))], (38662 ^ _780086) ^ [_1524524, _1524526, _1524528, _1524530] : [hBOOL(hAPP(hAPP(c_member(_1524524), _1524526), hAPP(c_Relation_ODomain(_1524524, _1524528), _1524530))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1524524, _1524528)), hAPP(hAPP(c_Product__Type_OPair(_1524524, _1524528), _1524526), 38665 ^ [_1524524, _1524526, _1524528, _1524530])), _1524530)))], (38669 ^ _780086) ^ [_1524681, _1524683, _1524685, _1524687] : [38670 ^ _780086 : [(38671 ^ _780086) ^ [_1524756] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1524681, _1524685)), hAPP(hAPP(c_Product__Type_OPair(_1524681, _1524685), _1524683), _1524756)), _1524687))]], -(hBOOL(hAPP(hAPP(c_member(_1524681), _1524683), hAPP(c_Relation_ODomain(_1524681, _1524685), _1524687))))], (38675 ^ _780086) ^ [_1524841, _1524843, _1524845, _1524847, _1524849] : [-(hAPP(c_Relation_ODomain(_1524841, _1524843), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1524841, _1524843)), hAPP(hAPP(c_Product__Type_OPair(_1524841, _1524843), _1524845), _1524847)), _1524849)) = hAPP(hAPP(c_Set_Oinsert(_1524841), _1524845), hAPP(c_Relation_ODomain(_1524841, _1524843), _1524849)))], (38677 ^ _780086) ^ [_1524912, _1524914, _1524916, _1524918] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1524912, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1524912, _1524914), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1524912, _1524914), tc_HOL_Obool)), _1524916), _1524918))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1524912, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1524912, _1524914), _1524916)), hAPP(c_Relation_ODomain(_1524912, _1524914), _1524918)))))], (38679 ^ _780086) ^ [_1524994, _1524996, _1524998, _1525000] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1524994, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1524994, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1524994, _1524996), _1524998)), hAPP(c_Relation_ODomain(_1524994, _1524996), _1525000))), hAPP(c_Relation_ODomain(_1524994, _1524996), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1524994, _1524996), tc_HOL_Obool)), _1524998), _1525000)))))], (38681 ^ _780086) ^ [_1525076, _1525078] : [-(hAPP(c_Relation_OField(_1525076), _1525078) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1525076, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1525076, _1525076), _1525078)), hAPP(c_Relation_ORange(_1525076, _1525076), _1525078)))], (38683 ^ _780086) ^ [_1525129, _1525131, _1525133] : [-(hAPP(c_Relation_ODomain(_1525129, _1525131), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1525129, _1525131), tc_HOL_Obool), _1525133)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1525129, _1525131), tc_HOL_Obool), tc_fun(_1525129, tc_HOL_Obool)), _1525133), c_Relation_ODomain(_1525129, _1525131)))], (38685 ^ _780086) ^ [_1525192, _1525194, _1525196] : [-(hAPP(c_Relation_ODomain(_1525192, _1525194), hAPP(c_Set_OCollect(tc_prod(_1525192, _1525194)), hAPP(c_Product__Type_Oprod_Oprod__case(_1525192, _1525194, tc_HOL_Obool), _1525196))) = hAPP(c_Set_OCollect(_1525192), hAPP(hAPP(c_COMBB(tc_fun(_1525194, tc_HOL_Obool), tc_HOL_Obool, _1525192), c_HOL_OEx(_1525194)), _1525196)))], (38687 ^ _780086) ^ [_1525281, _1525283, _1525285, _1525287] : [hBOOL(hAPP(c_Predicate_ODomainP(_1525281, _1525283, hAPP(hAPP(c_COMBC(_1525281, tc_fun(tc_prod(_1525281, _1525283), tc_HOL_Obool), tc_fun(_1525283, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1525283, tc_fun(tc_fun(tc_prod(_1525281, _1525283), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1525281, _1525283), tc_HOL_Obool), tc_fun(_1525283, tc_HOL_Obool)), _1525281), c_COMBC(_1525283, tc_fun(tc_prod(_1525281, _1525283), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1525283, tc_prod(_1525281, _1525283)), tc_fun(_1525283, tc_fun(tc_fun(tc_prod(_1525281, _1525283), tc_HOL_Obool), tc_HOL_Obool)), _1525281), hAPP(c_COMBB(tc_prod(_1525281, _1525283), tc_fun(tc_fun(tc_prod(_1525281, _1525283), tc_HOL_Obool), tc_HOL_Obool), _1525283), c_member(tc_prod(_1525281, _1525283)))), c_Product__Type_OPair(_1525281, _1525283)))), _1525285)), _1525287)), -(hBOOL(hAPP(hAPP(c_member(_1525281), _1525287), hAPP(c_Relation_ODomain(_1525281, _1525283), _1525285))))], (38693 ^ _780086) ^ [_1525632, _1525634, _1525636, _1525638] : [hBOOL(hAPP(hAPP(c_member(_1525632), _1525638), hAPP(c_Relation_ODomain(_1525632, _1525634), _1525636))), -(hBOOL(hAPP(c_Predicate_ODomainP(_1525632, _1525634, hAPP(hAPP(c_COMBC(_1525632, tc_fun(tc_prod(_1525632, _1525634), tc_HOL_Obool), tc_fun(_1525634, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1525634, tc_fun(tc_fun(tc_prod(_1525632, _1525634), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1525632, _1525634), tc_HOL_Obool), tc_fun(_1525634, tc_HOL_Obool)), _1525632), c_COMBC(_1525634, tc_fun(tc_prod(_1525632, _1525634), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1525634, tc_prod(_1525632, _1525634)), tc_fun(_1525634, tc_fun(tc_fun(tc_prod(_1525632, _1525634), tc_HOL_Obool), tc_HOL_Obool)), _1525632), hAPP(c_COMBB(tc_prod(_1525632, _1525634), tc_fun(tc_fun(tc_prod(_1525632, _1525634), tc_HOL_Obool), tc_HOL_Obool), _1525634), c_member(tc_prod(_1525632, _1525634)))), c_Product__Type_OPair(_1525632, _1525634)))), _1525636)), _1525638)))], (38699 ^ _780086) ^ [_1525989, _1525991, _1525993, _1525995] : [hBOOL(hAPP(hAPP(c_member(_1525989), _1525991), hAPP(c_Relation_ODomain(_1525989, _1525993), _1525995))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1525989, _1525993)), hAPP(hAPP(c_Product__Type_OPair(_1525989, _1525993), _1525991), 38702 ^ [_1525989, _1525991, _1525993, _1525995])), _1525995)))], (38706 ^ _780086) ^ [_1526154, _1526156, _1526158, _1526160, _1526162, _1526164] : [-(hAPP(c_Set_Oimage(_1526154, tc_prod(_1526156, _1526158), hAPP(hAPP(c_COMBS(_1526154, _1526158, tc_prod(_1526156, _1526158)), hAPP(hAPP(c_COMBB(_1526156, tc_fun(_1526158, tc_prod(_1526156, _1526158)), _1526154), c_Product__Type_OPair(_1526156, _1526158)), _1526160)), _1526162)), _1526164) = hAPP(hAPP(c_Product__Type_OSigma(_1526156, _1526158), hAPP(c_Set_Oimage(_1526154, _1526156, _1526160), _1526164)), hAPP(hAPP(c_COMBB(tc_fun(_1526154, tc_HOL_Obool), tc_fun(_1526158, tc_HOL_Obool), _1526156), c_Set_Oimage(_1526154, _1526158, _1526162)), hAPP(hAPP(c_COMBC(_1526156, tc_fun(_1526154, tc_HOL_Obool), tc_fun(_1526154, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1526154, tc_HOL_Obool), tc_fun(tc_fun(_1526154, tc_HOL_Obool), tc_fun(_1526154, tc_HOL_Obool)), _1526156), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1526154, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1526156, tc_HOL_Obool), tc_fun(_1526154, tc_HOL_Obool), _1526156), c_Set_Ovimage(_1526154, _1526156, _1526160)), hAPP(hAPP(c_COMBC(_1526156, tc_fun(_1526156, tc_HOL_Obool), tc_fun(_1526156, tc_HOL_Obool)), c_Set_Oinsert(_1526156)), c_Orderings_Obot__class_Obot(tc_fun(_1526156, tc_HOL_Obool)))))), _1526164))))], (38708 ^ _780086) ^ [_1526351, _1526353, _1526355, _1526357, _1526359] : [hBOOL(hAPP(hAPP(_1526351, _1526353), _1526355)), -(hBOOL(hAPP(c_Predicate_ODomainP(_1526357, _1526359, _1526351), _1526353)))], (38714 ^ _780086) ^ [_1526456, _1526458, _1526460, _1526462, _1526464, _1526466] : [hBOOL(hAPP(hAPP(c_member(_1526456), _1526458), _1526460)), hBOOL(hAPP(hAPP(c_member(_1526462), _1526464), hAPP(_1526466, _1526458))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1526456, _1526462)), hAPP(hAPP(c_Product__Type_OPair(_1526456, _1526462), _1526458), _1526464)), hAPP(hAPP(c_Product__Type_OSigma(_1526456, _1526462), _1526460), _1526466))))], (38724 ^ _780086) ^ [_1526691, _1526693, _1526695] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1526691, _1526693), c_Orderings_Obot__class_Obot(tc_fun(_1526691, tc_HOL_Obool))), _1526695) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1526691, _1526693), tc_HOL_Obool)))], (38726 ^ _780086) ^ [_1526740, _1526742, _1526744, _1526746, _1526748, _1526750] : [hBOOL(hAPP(hAPP(c_member(_1526740), _1526742), _1526744)), 38729 ^ _780086 : [(38730 ^ _780086) ^ [] : [hAPP(hAPP(c_Product__Type_OSigma(_1526746, _1526740), _1526748), hAPP(c_COMBK(tc_fun(_1526740, tc_HOL_Obool), _1526746), _1526744)) = hAPP(hAPP(c_Product__Type_OSigma(_1526746, _1526740), _1526750), hAPP(c_COMBK(tc_fun(_1526740, tc_HOL_Obool), _1526746), _1526744)), -(_1526748 = _1526750)], (38736 ^ _780086) ^ [] : [_1526748 = _1526750, -(hAPP(hAPP(c_Product__Type_OSigma(_1526746, _1526740), _1526748), hAPP(c_COMBK(tc_fun(_1526740, tc_HOL_Obool), _1526746), _1526744)) = hAPP(hAPP(c_Product__Type_OSigma(_1526746, _1526740), _1526750), hAPP(c_COMBK(tc_fun(_1526740, tc_HOL_Obool), _1526746), _1526744)))]]], (38742 ^ _780086) ^ [_1527093, _1527095, _1527097, _1527099] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1527093, _1527095), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1527093, tc_HOL_Obool), _1527097)), _1527099) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1527093, tc_HOL_Obool), tc_fun(tc_prod(_1527093, _1527095), tc_HOL_Obool)), _1527097), hAPP(hAPP(c_COMBC(tc_fun(_1527093, tc_HOL_Obool), tc_fun(_1527093, tc_fun(_1527095, tc_HOL_Obool)), tc_fun(tc_prod(_1527093, _1527095), tc_HOL_Obool)), c_Product__Type_OSigma(_1527093, _1527095)), _1527099)))], (38744 ^ _780086) ^ [_1527183, _1527185, _1527187, _1527189] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1527183, _1527185)), hAPP(hAPP(c_Product__Type_OSigma(_1527183, _1527185), _1527187), hAPP(c_COMBK(tc_fun(_1527185, tc_HOL_Obool), _1527183), _1527189))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1527183), _1527187)), hAPP(c_Finite__Set_Ocard(_1527185), _1527189)))], (38746 ^ _780086) ^ [_1527254, _1527256, _1527258, _1527260, _1527262, _1527264] : [class_Groups_Ocomm__monoid__add(_1527254), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1527256, _1527254), hAPP(hAPP(c_COMBC(_1527256, tc_fun(_1527258, tc_HOL_Obool), _1527254), hAPP(hAPP(c_COMBB(tc_fun(_1527258, _1527254), tc_fun(tc_fun(_1527258, tc_HOL_Obool), _1527254), _1527256), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1527258, _1527254)), _1527260)), _1527262)), _1527264) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1527256, _1527258), _1527254), hAPP(c_Product__Type_Oprod_Oprod__case(_1527256, _1527258, _1527254), _1527260)), hAPP(hAPP(c_Product__Type_OSigma(_1527256, _1527258), _1527264), hAPP(c_COMBK(tc_fun(_1527258, tc_HOL_Obool), _1527256), _1527262))))], (38762 ^ _780086) ^ [_1527682, _1527684, _1527686, _1527688] : [38763 ^ _780086 : [(38764 ^ _780086) ^ [] : [_1527686 = c_Orderings_Obot__class_Obot(tc_fun(_1527682, tc_HOL_Obool))], (38766 ^ _780086) ^ [] : [_1527688 = c_Orderings_Obot__class_Obot(tc_fun(_1527684, tc_HOL_Obool))]], -(hAPP(hAPP(c_Product__Type_OSigma(_1527682, _1527684), _1527686), hAPP(c_COMBK(tc_fun(_1527684, tc_HOL_Obool), _1527682), _1527688)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1527682, _1527684), tc_HOL_Obool)))], (38752 ^ _780086) ^ [_1527520, _1527522, _1527524, _1527526] : [hAPP(hAPP(c_Product__Type_OSigma(_1527520, _1527522), _1527524), hAPP(c_COMBK(tc_fun(_1527522, tc_HOL_Obool), _1527520), _1527526)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1527520, _1527522), tc_HOL_Obool)), -(_1527524 = c_Orderings_Obot__class_Obot(tc_fun(_1527520, tc_HOL_Obool))), -(_1527526 = c_Orderings_Obot__class_Obot(tc_fun(_1527522, tc_HOL_Obool)))], (38770 ^ _780086) ^ [_1527875, _1527877, _1527879] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1527875, _1527877), _1527879), hAPP(c_COMBK(tc_fun(_1527877, tc_HOL_Obool), _1527875), c_Orderings_Obot__class_Obot(tc_fun(_1527877, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1527875, _1527877), tc_HOL_Obool)))], (38772 ^ _780086) ^ [_1527933, _1527935, _1527937] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1527933, _1527935), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1527933, _1527935), _1527937), hAPP(c_COMBK(tc_fun(_1527935, tc_HOL_Obool), _1527933), c_Orderings_Otop__class_Otop(tc_fun(_1527935, tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(_1527933, _1527935), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1527933, tc_HOL_Obool)), _1527937)), hAPP(c_COMBK(tc_fun(_1527935, tc_HOL_Obool), _1527933), c_Orderings_Otop__class_Otop(tc_fun(_1527935, tc_HOL_Obool)))))], (38774 ^ _780086) ^ [_1528025, _1528027, _1528029] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1528025, _1528027), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1528025, _1528027), c_Orderings_Otop__class_Otop(tc_fun(_1528025, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1528027, tc_HOL_Obool), _1528025), _1528029))) = hAPP(hAPP(c_Product__Type_OSigma(_1528025, _1528027), c_Orderings_Otop__class_Otop(tc_fun(_1528025, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1528027, tc_HOL_Obool), _1528025), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1528027, tc_HOL_Obool)), _1528029))))], (38776 ^ _780086) ^ [_1528117, _1528119, _1528121, _1528123, _1528125, _1528127] : [class_Groups_Ocomm__monoid__mult(_1528117), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1528119, _1528117), hAPP(hAPP(c_COMBC(_1528119, tc_fun(_1528121, tc_HOL_Obool), _1528117), hAPP(hAPP(c_COMBB(tc_fun(_1528121, _1528117), tc_fun(tc_fun(_1528121, tc_HOL_Obool), _1528117), _1528119), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1528121, _1528117)), _1528123)), _1528125)), _1528127) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1528119, _1528121), _1528117), hAPP(c_Product__Type_Oprod_Oprod__case(_1528119, _1528121, _1528117), _1528123)), hAPP(hAPP(c_Product__Type_OSigma(_1528119, _1528121), _1528127), hAPP(c_COMBK(tc_fun(_1528121, tc_HOL_Obool), _1528119), _1528125))))], (38782 ^ _780086) ^ [_1528362, _1528364, _1528366, _1528368, _1528370] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1528362, _1528364), _1528366), hAPP(hAPP(c_COMBS(_1528362, tc_fun(_1528364, tc_HOL_Obool), tc_fun(_1528364, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1528364, tc_HOL_Obool), tc_fun(tc_fun(_1528364, tc_HOL_Obool), tc_fun(_1528364, tc_HOL_Obool)), _1528362), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1528364, tc_HOL_Obool))), _1528368)), _1528370)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1528362, _1528364), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1528362, _1528364), _1528366), _1528368)), hAPP(hAPP(c_Product__Type_OSigma(_1528362, _1528364), _1528366), _1528370)))], (38784 ^ _780086) ^ [_1528477, _1528479, _1528481, _1528483, _1528485] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1528477, _1528479), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1528477, tc_HOL_Obool)), _1528481), _1528483)), hAPP(c_COMBK(tc_fun(_1528479, tc_HOL_Obool), _1528477), _1528485)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1528477, _1528479), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1528477, _1528479), _1528481), hAPP(c_COMBK(tc_fun(_1528479, tc_HOL_Obool), _1528477), _1528485))), hAPP(hAPP(c_Product__Type_OSigma(_1528477, _1528479), _1528483), hAPP(c_COMBK(tc_fun(_1528479, tc_HOL_Obool), _1528477), _1528485))))], (38786 ^ _780086) ^ [_1528587, _1528589, _1528591, _1528593, _1528595] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1528587, _1528589), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1528587, tc_HOL_Obool)), _1528591), _1528593)), _1528595) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1528587, _1528589), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1528587, _1528589), _1528591), _1528595)), hAPP(hAPP(c_Product__Type_OSigma(_1528587, _1528589), _1528593), _1528595)))], (38788 ^ _780086) ^ [_1528670, _1528672, _1528674, _1528676, _1528678, _1528680, _1528682, _1528684] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1528670, _1528672), tc_HOL_Obool)), _1528674), hAPP(hAPP(c_Product__Type_OSigma(_1528670, _1528672), _1528676), hAPP(c_COMBK(tc_fun(_1528672, tc_HOL_Obool), _1528670), _1528678)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1528672, _1528680), tc_HOL_Obool)), _1528682), hAPP(hAPP(c_Product__Type_OSigma(_1528672, _1528680), _1528678), hAPP(c_COMBK(tc_fun(_1528680, tc_HOL_Obool), _1528672), _1528684)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1528670, _1528680), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1528670, _1528672, _1528680), _1528674), _1528682)), hAPP(hAPP(c_Product__Type_OSigma(_1528670, _1528680), _1528676), hAPP(c_COMBK(tc_fun(_1528680, tc_HOL_Obool), _1528670), _1528684)))))], (38798 ^ _780086) ^ [_1529029, _1529031, _1529033, _1529035] : [-(hAPP(c_Set_Oimage(tc_prod(_1529029, _1529031), tc_prod(_1529031, _1529029), hAPP(c_Product__Type_Oprod_Oprod__case(_1529029, _1529031, tc_prod(_1529031, _1529029)), hAPP(c_COMBC(_1529031, _1529029, tc_prod(_1529031, _1529029)), c_Product__Type_OPair(_1529031, _1529029)))), hAPP(hAPP(c_Product__Type_OSigma(_1529029, _1529031), _1529033), hAPP(c_COMBK(tc_fun(_1529031, tc_HOL_Obool), _1529029), _1529035))) = hAPP(hAPP(c_Product__Type_OSigma(_1529031, _1529029), _1529035), hAPP(c_COMBK(tc_fun(_1529029, tc_HOL_Obool), _1529031), _1529033)))], (38800 ^ _780086) ^ [_1529130, _1529132, _1529134, _1529136] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1529130), _1529132)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1529134), _1529136)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1529130, _1529134)), hAPP(hAPP(c_Product__Type_OSigma(_1529130, _1529134), _1529132), hAPP(c_COMBK(tc_fun(_1529134, tc_HOL_Obool), _1529130), _1529136)))))], (38810 ^ _780086) ^ [_1529333, _1529335, _1529337] : [c_Equiv__Relations_Oequiv(_1529333, _1529335, _1529337), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1529333, _1529333), tc_HOL_Obool)), _1529337), hAPP(hAPP(c_Product__Type_OSigma(_1529333, _1529333), _1529335), hAPP(c_COMBK(tc_fun(_1529333, tc_HOL_Obool), _1529333), _1529335)))))], (38816 ^ _780086) ^ [_1529476, _1529478, _1529480, _1529482, _1529484] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1529476, _1529478), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1529476, tc_HOL_Obool)), _1529480), _1529482)), _1529484) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1529476, _1529478), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1529476, _1529478), _1529480), _1529484)), hAPP(hAPP(c_Product__Type_OSigma(_1529476, _1529478), _1529482), _1529484)))], (38818 ^ _780086) ^ [_1529559, _1529561, _1529563, _1529565, _1529567] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1529559, _1529561), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1529559, tc_HOL_Obool)), _1529563), _1529565)), hAPP(c_COMBK(tc_fun(_1529561, tc_HOL_Obool), _1529559), _1529567)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1529559, _1529561), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1529559, _1529561), _1529563), hAPP(c_COMBK(tc_fun(_1529561, tc_HOL_Obool), _1529559), _1529567))), hAPP(hAPP(c_Product__Type_OSigma(_1529559, _1529561), _1529565), hAPP(c_COMBK(tc_fun(_1529561, tc_HOL_Obool), _1529559), _1529567))))], (38820 ^ _780086) ^ [_1529669, _1529671, _1529673, _1529675, _1529677] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1529669, _1529671), _1529673), hAPP(hAPP(c_COMBS(_1529669, tc_fun(_1529671, tc_HOL_Obool), tc_fun(_1529671, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529671, tc_HOL_Obool), tc_fun(tc_fun(_1529671, tc_HOL_Obool), tc_fun(_1529671, tc_HOL_Obool)), _1529669), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1529671, tc_HOL_Obool))), _1529675)), _1529677)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1529669, _1529671), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1529669, _1529671), _1529673), _1529675)), hAPP(hAPP(c_Product__Type_OSigma(_1529669, _1529671), _1529673), _1529677)))], (38822 ^ _780086) ^ [_1529784, _1529786] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1529784, _1529784), tc_HOL_Obool)), c_Relation_OId__on(_1529784, _1529786)), hAPP(hAPP(c_Product__Type_OSigma(_1529784, _1529784), _1529786), hAPP(c_COMBK(tc_fun(_1529784, tc_HOL_Obool), _1529784), _1529786)))))], (38824 ^ _780086) ^ [_1529843, _1529845, _1529847, _1529849, _1529851] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1529843, _1529845), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1529843, tc_HOL_Obool)), _1529847), _1529849)), _1529851) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1529843, _1529845), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1529843, _1529845), _1529847), _1529851)), hAPP(hAPP(c_Product__Type_OSigma(_1529843, _1529845), _1529849), _1529851)))], (38826 ^ _780086) ^ [_1529926, _1529928, _1529930, _1529932, _1529934] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1529926, _1529928), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1529926, tc_HOL_Obool)), _1529930), _1529932)), hAPP(c_COMBK(tc_fun(_1529928, tc_HOL_Obool), _1529926), _1529934)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1529926, _1529928), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1529926, _1529928), _1529930), hAPP(c_COMBK(tc_fun(_1529928, tc_HOL_Obool), _1529926), _1529934))), hAPP(hAPP(c_Product__Type_OSigma(_1529926, _1529928), _1529932), hAPP(c_COMBK(tc_fun(_1529928, tc_HOL_Obool), _1529926), _1529934))))], (38828 ^ _780086) ^ [_1530036, _1530038, _1530040, _1530042, _1530044] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1530036, _1530038), _1530040), hAPP(hAPP(c_COMBS(_1530036, tc_fun(_1530038, tc_HOL_Obool), tc_fun(_1530038, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1530038, tc_HOL_Obool), tc_fun(tc_fun(_1530038, tc_HOL_Obool), tc_fun(_1530038, tc_HOL_Obool)), _1530036), c_Groups_Ominus__class_Ominus(tc_fun(_1530038, tc_HOL_Obool))), _1530042)), _1530044)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1530036, _1530038), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1530036, _1530038), _1530040), _1530042)), hAPP(hAPP(c_Product__Type_OSigma(_1530036, _1530038), _1530040), _1530044)))], (38830 ^ _780086) ^ [_1530172, _1530174, _1530176, _1530178] : [hBOOL(hAPP(c_Predicate_ODomainP(_1530172, _1530174, _1530176), _1530178)), -(hBOOL(hAPP(hAPP(_1530176, _1530178), 38833 ^ [_1530172, _1530174, _1530176, _1530178])))], (38837 ^ _780086) ^ [_1530287, _1530289, _1530291, _1530293] : [38838 ^ _780086 : [(38839 ^ _780086) ^ [_1530341] : [hBOOL(hAPP(hAPP(_1530291, _1530293), _1530341))]], -(hBOOL(hAPP(c_Predicate_ODomainP(_1530287, _1530289, _1530291), _1530293)))], (38843 ^ _780086) ^ [_1530405, _1530407] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1530405, _1530407), c_Orderings_Otop__class_Otop(tc_fun(_1530405, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1530407, tc_HOL_Obool), _1530405), c_Orderings_Otop__class_Otop(tc_fun(_1530407, tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1530405, _1530407), tc_HOL_Obool)))], (38845 ^ _780086) ^ [_1530493, _1530495, _1530497, _1530499, _1530501, _1530503] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1530493, _1530495)), hAPP(hAPP(c_Product__Type_OPair(_1530493, _1530495), _1530497), _1530499)), hAPP(hAPP(c_Product__Type_OSigma(_1530493, _1530495), _1530501), _1530503))), 38848 ^ _780086 : [(38849 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1530493), _1530497), _1530501)))], (38851 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1530495), _1530499), hAPP(_1530503, _1530497))))]]], (38853 ^ _780086) ^ [_1530690, _1530692, _1530694, _1530696, _1530698, _1530700] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1530690, _1530692)), hAPP(hAPP(c_Product__Type_OPair(_1530690, _1530692), _1530694), _1530696)), hAPP(hAPP(c_Product__Type_OSigma(_1530690, _1530692), _1530698), _1530700)))), hBOOL(hAPP(hAPP(c_member(_1530690), _1530694), _1530698)), hBOOL(hAPP(hAPP(c_member(_1530692), _1530696), hAPP(_1530700, _1530694)))], (38863 ^ _780086) ^ [_1530927, _1530929, _1530931, _1530933, _1530935, _1530937] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1530927, _1530929)), hAPP(hAPP(c_Product__Type_OPair(_1530927, _1530929), _1530931), _1530933)), hAPP(hAPP(c_Product__Type_OSigma(_1530927, _1530929), _1530935), _1530937))), -(hBOOL(hAPP(hAPP(c_member(_1530927), _1530931), _1530935)))], (38869 ^ _780086) ^ [_1531082, _1531084, _1531086, _1531088, _1531090, _1531092] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1531082, _1531084)), hAPP(hAPP(c_Product__Type_OPair(_1531082, _1531084), _1531086), _1531088)), hAPP(hAPP(c_Product__Type_OSigma(_1531082, _1531084), _1531090), _1531092))), -(hBOOL(hAPP(hAPP(c_member(_1531084), _1531088), hAPP(_1531092, _1531086))))], (38875 ^ _780086) ^ [_1531243, _1531245, _1531247, _1531249, _1531251, _1531253] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1531243, _1531245)), hAPP(hAPP(c_Product__Type_OPair(_1531243, _1531245), _1531247), _1531249)), hAPP(hAPP(c_Product__Type_OSigma(_1531243, _1531245), _1531251), _1531253))), 38878 ^ _780086 : [(38879 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1531243), _1531247), _1531251)))], (38881 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1531245), _1531249), hAPP(_1531253, _1531247))))]]], (38883 ^ _780086) ^ [_1531448, _1531450, _1531452, _1531454] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1531448, _1531450)), hAPP(hAPP(c_Product__Type_OSigma(_1531448, _1531450), hAPP(hAPP(c_Set_Oinsert(_1531448), _1531452), c_Orderings_Obot__class_Obot(tc_fun(_1531448, tc_HOL_Obool)))), hAPP(c_COMBK(tc_fun(_1531450, tc_HOL_Obool), _1531448), _1531454))) = hAPP(c_Finite__Set_Ocard(_1531450), _1531454))], (38885 ^ _780086) ^ [_1531521, _1531523, _1531525, _1531527, _1531529, _1531531] : [hBOOL(hAPP(hAPP(c_member(_1531521), _1531523), _1531525)), 38888 ^ _780086 : [(38889 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1531527, _1531521), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1531527, _1531521), _1531529), hAPP(c_COMBK(tc_fun(_1531521, tc_HOL_Obool), _1531527), _1531525))), hAPP(hAPP(c_Product__Type_OSigma(_1531527, _1531521), _1531531), hAPP(c_COMBK(tc_fun(_1531521, tc_HOL_Obool), _1531527), _1531525)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1531527, tc_HOL_Obool)), _1531529), _1531531)))], (38895 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1531527, tc_HOL_Obool)), _1531529), _1531531)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1531527, _1531521), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1531527, _1531521), _1531529), hAPP(c_COMBK(tc_fun(_1531521, tc_HOL_Obool), _1531527), _1531525))), hAPP(hAPP(c_Product__Type_OSigma(_1531527, _1531521), _1531531), hAPP(c_COMBK(tc_fun(_1531521, tc_HOL_Obool), _1531527), _1531525)))))]]], (38901 ^ _780086) ^ [_1531943, _1531945, _1531947, _1531949, _1531951, _1531953] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1531943, _1531945), tc_HOL_Obool)), _1531947), hAPP(hAPP(c_Product__Type_OSigma(_1531943, _1531945), _1531949), hAPP(c_COMBK(tc_fun(_1531945, tc_HOL_Obool), _1531943), _1531951)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1531945, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1531943, _1531945, _1531947), _1531953)), _1531951)))], (38907 ^ _780086) ^ [_1532124, _1532126, _1532128, _1532130] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1532124, _1532126)), hAPP(hAPP(c_Product__Type_OSigma(_1532124, _1532126), _1532128), hAPP(c_COMBK(tc_fun(_1532126, tc_HOL_Obool), _1532124), _1532130)))), -(_1532130 = c_Orderings_Obot__class_Obot(tc_fun(_1532126, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1532124), _1532128)))], (38917 ^ _780086) ^ [_1532288, _1532290, _1532292, _1532294] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1532288, _1532290)), hAPP(hAPP(c_Product__Type_OSigma(_1532288, _1532290), _1532292), hAPP(c_COMBK(tc_fun(_1532290, tc_HOL_Obool), _1532288), _1532294)))), -(_1532292 = c_Orderings_Obot__class_Obot(tc_fun(_1532288, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1532290), _1532294)))], (38927 ^ _780086) ^ [_1532452, _1532454, _1532456, _1532458] : [-(hAPP(c_Set_OCollect(tc_prod(_1532452, _1532454)), hAPP(c_Product__Type_Oprod_Oprod__case(_1532452, _1532454, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1532452, tc_fun(_1532454, tc_HOL_Obool), tc_fun(_1532454, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1532454, tc_HOL_Obool), tc_fun(_1532454, tc_HOL_Obool)), _1532452), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1532454)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1532452), c_fconj), _1532456))), _1532458))) = hAPP(hAPP(c_Product__Type_OSigma(_1532452, _1532454), hAPP(c_Set_OCollect(_1532452), _1532456)), hAPP(c_COMBK(tc_fun(_1532454, tc_HOL_Obool), _1532452), hAPP(c_Set_OCollect(_1532454), _1532458))))], (38929 ^ _780086) ^ [_1532573, _1532575, _1532577, _1532579] : [-(hAPP(c_Set_OCollect(tc_prod(_1532573, _1532575)), hAPP(c_Product__Type_Oprod_Oprod__case(_1532573, _1532575, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1532573, tc_fun(_1532575, tc_HOL_Obool), tc_fun(_1532575, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1532575, tc_HOL_Obool), tc_fun(_1532575, tc_HOL_Obool)), _1532573), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1532575)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1532573), c_fconj), _1532577))), _1532579))) = hAPP(hAPP(c_Product__Type_OSigma(_1532573, _1532575), hAPP(c_Set_OCollect(_1532573), _1532577)), hAPP(hAPP(c_COMBB(tc_fun(_1532575, tc_HOL_Obool), tc_fun(_1532575, tc_HOL_Obool), _1532573), c_Set_OCollect(_1532575)), _1532579)))], (38931 ^ _780086) ^ [_1532713, _1532715, _1532717, _1532719] : [_1532713 = c_Orderings_Obot__class_Obot(tc_fun(_1532715, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1532717, _1532715), _1532717, c_Product__Type_Ofst(_1532717, _1532715)), hAPP(hAPP(c_Product__Type_OSigma(_1532717, _1532715), _1532719), hAPP(c_COMBK(tc_fun(_1532715, tc_HOL_Obool), _1532717), _1532713))) = c_Orderings_Obot__class_Obot(tc_fun(_1532717, tc_HOL_Obool)))], (38937 ^ _780086) ^ [_1532870, _1532872, _1532874, _1532876] : [-(_1532870 = c_Orderings_Obot__class_Obot(tc_fun(_1532872, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1532874, _1532872), _1532874, c_Product__Type_Ofst(_1532874, _1532872)), hAPP(hAPP(c_Product__Type_OSigma(_1532874, _1532872), _1532876), hAPP(c_COMBK(tc_fun(_1532872, tc_HOL_Obool), _1532874), _1532870))) = _1532876)], (38943 ^ _780086) ^ [_1532963, _1532965, _1532967, _1532969] : [_1532963 = c_Orderings_Obot__class_Obot(tc_fun(_1532965, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1532965, _1532967), _1532967, c_Product__Type_Osnd(_1532965, _1532967)), hAPP(hAPP(c_Product__Type_OSigma(_1532965, _1532967), _1532963), hAPP(c_COMBK(tc_fun(_1532967, tc_HOL_Obool), _1532965), _1532969))) = c_Orderings_Obot__class_Obot(tc_fun(_1532967, tc_HOL_Obool)))], (38949 ^ _780086) ^ [_1533120, _1533122, _1533124, _1533126] : [-(_1533120 = c_Orderings_Obot__class_Obot(tc_fun(_1533122, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1533122, _1533124), _1533124, c_Product__Type_Osnd(_1533122, _1533124)), hAPP(hAPP(c_Product__Type_OSigma(_1533122, _1533124), _1533120), hAPP(c_COMBK(tc_fun(_1533124, tc_HOL_Obool), _1533122), _1533126))) = _1533126)], (38955 ^ _780086) ^ [_1533198, _1533200, _1533202, _1533204, _1533206, _1533208] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1533198, _1533200), hAPP(hAPP(c_Set_Oinsert(_1533198), _1533202), _1533204)), hAPP(c_COMBK(tc_fun(_1533200, tc_HOL_Obool), _1533198), hAPP(hAPP(c_Set_Oinsert(_1533200), _1533206), _1533208))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(_1533198, _1533200)), hAPP(hAPP(c_Product__Type_OPair(_1533198, _1533200), _1533202), _1533206)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1533198, _1533200), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1533198, _1533200), _1533204), hAPP(c_COMBK(tc_fun(_1533200, tc_HOL_Obool), _1533198), hAPP(hAPP(c_Set_Oinsert(_1533200), _1533206), _1533208)))), hAPP(hAPP(c_Product__Type_OSigma(_1533198, _1533200), hAPP(hAPP(c_Set_Oinsert(_1533198), _1533202), _1533204)), hAPP(c_COMBK(tc_fun(_1533200, tc_HOL_Obool), _1533198), _1533208)))))], (38957 ^ _780086) ^ [_1533351, _1533353, _1533355, _1533357] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1533351), _1533353)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1533351, _1533351), tc_HOL_Obool)), _1533355), hAPP(hAPP(c_Product__Type_OSigma(_1533351, _1533351), _1533353), hAPP(c_COMBK(tc_fun(_1533351, tc_HOL_Obool), _1533351), _1533353)))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1533351, tc_HOL_Obool)), _1533357), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1533351), _1533353), _1533355))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1533351), _1533357)))], (38971 ^ _780086) ^ [_1533658, _1533660, _1533662, _1533664, _1533666, _1533668, _1533670, _1533672] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(_1533658, _1533660), tc_fun(tc_prod(_1533662, _1533664), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1533658, _1533660), _1533666), hAPP(c_COMBK(tc_fun(_1533660, tc_HOL_Obool), _1533658), _1533668))), hAPP(c_Product__Type_Oprod_Oprod__case(_1533658, _1533660, tc_fun(tc_prod(_1533662, _1533664), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1533658, tc_fun(_1533660, tc_fun(_1533662, tc_fun(_1533664, tc_HOL_Obool))), tc_fun(_1533660, tc_fun(tc_prod(_1533662, _1533664), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1533662, tc_fun(_1533664, tc_HOL_Obool)), tc_fun(tc_prod(_1533662, _1533664), tc_HOL_Obool)), tc_fun(tc_fun(_1533660, tc_fun(_1533662, tc_fun(_1533664, tc_HOL_Obool))), tc_fun(_1533660, tc_fun(tc_prod(_1533662, _1533664), tc_HOL_Obool))), _1533658), c_COMBB(tc_fun(_1533662, tc_fun(_1533664, tc_HOL_Obool)), tc_fun(tc_prod(_1533662, _1533664), tc_HOL_Obool), _1533660)), hAPP(hAPP(c_COMBB(tc_fun(_1533662, tc_HOL_Obool), tc_fun(tc_fun(_1533662, tc_fun(_1533664, tc_HOL_Obool)), tc_fun(tc_prod(_1533662, _1533664), tc_HOL_Obool)), _1533658), c_Product__Type_OSigma(_1533662, _1533664)), _1533670))), hAPP(hAPP(c_COMBB(tc_fun(_1533664, tc_HOL_Obool), tc_fun(_1533662, tc_fun(_1533664, tc_HOL_Obool)), _1533660), c_COMBK(tc_fun(_1533664, tc_HOL_Obool), _1533662)), _1533672)))) = hAPP(hAPP(c_Product__Type_OSigma(_1533662, _1533664), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1533658, tc_fun(_1533662, tc_HOL_Obool)), _1533666), _1533670)), hAPP(c_COMBK(tc_fun(_1533664, tc_HOL_Obool), _1533662), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1533660, tc_fun(_1533664, tc_HOL_Obool)), _1533668), _1533672))))], (38973 ^ _780086) ^ [_1533932, _1533934, _1533936, _1533938] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1533932, _1533934), _1533936), _1533938) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1533932, tc_fun(tc_prod(_1533932, _1533934), tc_HOL_Obool)), _1533936), hAPP(hAPP(c_COMBS(_1533932, tc_fun(_1533934, tc_fun(tc_prod(_1533932, _1533934), tc_HOL_Obool)), tc_fun(tc_prod(_1533932, _1533934), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1533934, tc_HOL_Obool), tc_fun(tc_fun(_1533934, tc_fun(tc_prod(_1533932, _1533934), tc_HOL_Obool)), tc_fun(tc_prod(_1533932, _1533934), tc_HOL_Obool)), _1533932), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1533934, tc_fun(tc_prod(_1533932, _1533934), tc_HOL_Obool))), _1533938)), hAPP(hAPP(c_COMBC(_1533932, tc_fun(tc_prod(_1533932, _1533934), tc_HOL_Obool), tc_fun(_1533934, tc_fun(tc_prod(_1533932, _1533934), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1533934, tc_fun(tc_fun(tc_prod(_1533932, _1533934), tc_HOL_Obool), tc_fun(tc_prod(_1533932, _1533934), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1533932, _1533934), tc_HOL_Obool), tc_fun(_1533934, tc_fun(tc_prod(_1533932, _1533934), tc_HOL_Obool))), _1533932), c_COMBC(_1533934, tc_fun(tc_prod(_1533932, _1533934), tc_HOL_Obool), tc_fun(tc_prod(_1533932, _1533934), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1533934, tc_prod(_1533932, _1533934)), tc_fun(_1533934, tc_fun(tc_fun(tc_prod(_1533932, _1533934), tc_HOL_Obool), tc_fun(tc_prod(_1533932, _1533934), tc_HOL_Obool))), _1533932), hAPP(c_COMBB(tc_prod(_1533932, _1533934), tc_fun(tc_fun(tc_prod(_1533932, _1533934), tc_HOL_Obool), tc_fun(tc_prod(_1533932, _1533934), tc_HOL_Obool)), _1533934), c_Set_Oinsert(tc_prod(_1533932, _1533934)))), c_Product__Type_OPair(_1533932, _1533934)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1533932, _1533934), tc_HOL_Obool))))))], (38975 ^ _780086) ^ [_1534212, _1534214, _1534216] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1534212), _1534214)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1534212, _1534212), tc_HOL_Obool)), _1534216), hAPP(hAPP(c_Product__Type_OSigma(_1534212, _1534212), _1534214), hAPP(c_COMBK(tc_fun(_1534212, tc_HOL_Obool), _1534212), _1534214)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1534212, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1534212), _1534214), _1534216))))], (38985 ^ _780086) ^ [_1534445, _1534447, _1534449, _1534451, _1534453, _1534455, _1534457] : [class_Rings_Osemiring__0(_1534445), c_Fun_Oinj__on(tc_prod(_1534447, _1534449), _1534445, hAPP(c_Product__Type_Oprod_Oprod__case(_1534447, _1534449, _1534445), hAPP(hAPP(c_COMBC(_1534447, tc_fun(_1534449, _1534445), tc_fun(_1534449, _1534445)), hAPP(hAPP(c_COMBB(tc_fun(_1534445, _1534445), tc_fun(tc_fun(_1534449, _1534445), tc_fun(_1534449, _1534445)), _1534447), c_COMBB(_1534445, _1534445, _1534449)), hAPP(hAPP(c_COMBB(_1534445, tc_fun(_1534445, _1534445), _1534447), c_Groups_Otimes__class_Otimes(_1534445)), _1534451))), _1534453)), hAPP(hAPP(c_Product__Type_OSigma(_1534447, _1534449), _1534455), hAPP(c_COMBK(tc_fun(_1534449, tc_HOL_Obool), _1534447), _1534457))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1534445), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1534447, _1534445), _1534451), _1534455)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1534449, _1534445), _1534453), _1534457)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1534445, _1534445), c_Fun_Oid(_1534445)), hAPP(c_Set_OCollect(_1534445), hAPP(hAPP(c_COMBB(tc_fun(_1534447, tc_HOL_Obool), tc_HOL_Obool, _1534445), c_HOL_OEx(_1534447)), hAPP(hAPP(c_COMBB(tc_fun(_1534447, tc_fun(_1534449, tc_HOL_Obool)), tc_fun(_1534447, tc_HOL_Obool), _1534445), hAPP(c_COMBB(tc_fun(_1534449, tc_HOL_Obool), tc_HOL_Obool, _1534447), c_HOL_OEx(_1534449))), hAPP(hAPP(c_COMBC(_1534445, tc_fun(_1534447, tc_fun(_1534449, tc_HOL_Obool)), tc_fun(_1534447, tc_fun(_1534449, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1534447, tc_fun(tc_fun(_1534449, tc_HOL_Obool), tc_fun(_1534449, tc_HOL_Obool))), tc_fun(tc_fun(_1534447, tc_fun(_1534449, tc_HOL_Obool)), tc_fun(_1534447, tc_fun(_1534449, tc_HOL_Obool))), _1534445), c_COMBS(_1534447, tc_fun(_1534449, tc_HOL_Obool), tc_fun(_1534449, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1534447, tc_fun(_1534449, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1534447, tc_fun(tc_fun(_1534449, tc_HOL_Obool), tc_fun(_1534449, tc_HOL_Obool))), _1534445), hAPP(c_COMBB(tc_fun(_1534449, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1534449, tc_HOL_Obool), tc_fun(_1534449, tc_HOL_Obool)), _1534447), c_COMBS(_1534449, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1534447, tc_fun(_1534449, tc_HOL_Obool)), tc_fun(_1534447, tc_fun(_1534449, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1534445), hAPP(c_COMBB(tc_fun(_1534449, tc_HOL_Obool), tc_fun(_1534449, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1534447), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1534449), c_fconj))), hAPP(hAPP(c_COMBC(_1534445, tc_fun(_1534447, tc_fun(_1534449, _1534445)), tc_fun(_1534447, tc_fun(_1534449, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1534449, _1534445), tc_fun(_1534449, tc_HOL_Obool)), tc_fun(tc_fun(_1534447, tc_fun(_1534449, _1534445)), tc_fun(_1534447, tc_fun(_1534449, tc_HOL_Obool))), _1534445), c_COMBB(tc_fun(_1534449, _1534445), tc_fun(_1534449, tc_HOL_Obool), _1534447)), hAPP(hAPP(c_COMBB(tc_fun(_1534445, tc_HOL_Obool), tc_fun(tc_fun(_1534449, _1534445), tc_fun(_1534449, tc_HOL_Obool)), _1534445), c_COMBB(_1534445, tc_HOL_Obool, _1534449)), c_fequal))), hAPP(hAPP(c_COMBC(_1534447, tc_fun(_1534449, _1534445), tc_fun(_1534449, _1534445)), hAPP(hAPP(c_COMBB(tc_fun(_1534445, _1534445), tc_fun(tc_fun(_1534449, _1534445), tc_fun(_1534449, _1534445)), _1534447), c_COMBB(_1534445, _1534445, _1534449)), hAPP(hAPP(c_COMBB(_1534445, tc_fun(_1534445, _1534445), _1534447), c_Groups_Otimes__class_Otimes(_1534445)), _1534451))), _1534453)))))), hAPP(hAPP(c_COMBC(_1534447, tc_fun(_1534449, tc_HOL_Obool), tc_fun(_1534449, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1534449, tc_HOL_Obool), tc_fun(_1534449, tc_HOL_Obool)), _1534447), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1534449)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1534447), c_fconj), hAPP(hAPP(c_COMBC(_1534447, tc_fun(_1534447, tc_HOL_Obool), tc_HOL_Obool), c_member(_1534447)), _1534455)))), hAPP(hAPP(c_COMBC(_1534449, tc_fun(_1534449, tc_HOL_Obool), tc_HOL_Obool), c_member(_1534449)), _1534457))))))))], (38996 ^ _780086) ^ [_1535720, _1535722, _1535724, _1535726] : [-(c_Fun_Oinj__on(_1535720, tc_prod(_1535722, _1535720), 38994 ^ [_1535720, _1535722, _1535724, _1535726], hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1535722, tc_fun(_1535720, tc_HOL_Obool)), _1535724), _1535726)))], (38998 ^ _780086) ^ [_1535774, _1535776, _1535778, _1535780] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1535776, _1535774), tc_HOL_Obool)), hAPP(c_Set_Oimage(_1535774, tc_prod(_1535776, _1535774), 38994 ^ [_1535774, _1535776, _1535778, _1535780]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1535776, tc_fun(_1535774, tc_HOL_Obool)), _1535778), _1535780))), hAPP(hAPP(c_Product__Type_OSigma(_1535776, _1535774), _1535778), _1535780))))], (39000 ^ _780086) ^ [_1535860, _1535862, _1535864, _1535866, _1535868, _1535870] : [class_Groups_Ocomm__monoid__mult(_1535860), hBOOL(hAPP(c_Finite__Set_Ofinite(_1535862), _1535864)), 39010 ^ _780086 : [(39011 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1535862), 39009 ^ [_1535860, _1535862, _1535864, _1535866, _1535868, _1535870]), _1535864)))], (39013 ^ _780086) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1535866), hAPP(_1535868, 39009 ^ [_1535860, _1535862, _1535864, _1535866, _1535868, _1535870])))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1535860, _1535862, c_Groups_Otimes__class_Otimes(_1535860)), hAPP(hAPP(c_COMBS(_1535862, tc_fun(_1535866, tc_HOL_Obool), _1535860), hAPP(hAPP(c_COMBC(_1535862, _1535860, tc_fun(tc_fun(_1535866, tc_HOL_Obool), _1535860)), hAPP(hAPP(c_COMBB(tc_fun(_1535866, _1535860), tc_fun(_1535860, tc_fun(tc_fun(_1535866, tc_HOL_Obool), _1535860)), _1535862), c_Finite__Set_Ofold__image(_1535860, _1535866, c_Groups_Otimes__class_Otimes(_1535860))), _1535870)), c_Groups_Oone__class_Oone(_1535860))), _1535868)), c_Groups_Oone__class_Oone(_1535860)), _1535864) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1535860, tc_prod(_1535862, _1535866), c_Groups_Otimes__class_Otimes(_1535860)), hAPP(c_Product__Type_Oprod_Oprod__case(_1535862, _1535866, _1535860), _1535870)), c_Groups_Oone__class_Oone(_1535860)), hAPP(hAPP(c_Product__Type_OSigma(_1535862, _1535866), _1535864), _1535868)))], (39017 ^ _780086) ^ [_1536417, _1536419] : [-(hAPP(c_Set_Oimage(_1536417, _1536417, c_Fun_Oid(_1536417)), _1536419) = _1536419)], (39019 ^ _780086) ^ [_1536451, _1536453] : [-(c_Fun_Oinj__on(_1536451, _1536451, c_Fun_Oid(_1536451), _1536453))], (39021 ^ _780086) ^ [_1536480, _1536482] : [-(hAPP(c_Set_Ovimage(_1536480, _1536480, c_Fun_Oid(_1536480)), _1536482) = _1536482)], (39023 ^ _780086) ^ [_1536514, _1536516] : [-(hAPP(c_Fun_Oid(_1536514), _1536516) = _1536516)], (39025 ^ _780086) ^ [_1536544, _1536546] : [-(hAPP(c_Fun_Oid(_1536544), _1536546) = _1536546)], (39027 ^ _780086) ^ [_1536574, _1536576] : [-(c_Product__Type_Oapsnd(_1536574, _1536574, _1536576, c_Fun_Oid(_1536574)) = c_Fun_Oid(tc_prod(_1536576, _1536574)))], (39029 ^ _780086) ^ [_1536611, _1536613] : [-(c_Product__Type_Oapfst(_1536611, _1536611, _1536613, c_Fun_Oid(_1536611)) = c_Fun_Oid(tc_prod(_1536611, _1536613)))], (39031 ^ _780086) ^ [] : [-(c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint))], (39033 ^ _780086) ^ [_1536666] : [-(hAPP(c_Set_Oimage(_1536666, _1536666, c_Fun_Oid(_1536666)), c_Orderings_Otop__class_Otop(tc_fun(_1536666, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1536666, tc_HOL_Obool)))], (39035 ^ _780086) ^ [_1536708, _1536710] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1536708, _1536710, tc_prod(_1536708, _1536710)), c_Product__Type_OPair(_1536708, _1536710)) = c_Fun_Oid(tc_prod(_1536708, _1536710)))], (39037 ^ _780086) ^ [_1536751, _1536753, _1536755, _1536757] : [class_Groups_Ocomm__monoid__add(_1536751), c_Fun_Oinj__on(_1536753, _1536751, _1536755, _1536757), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1536753, _1536751), _1536755), _1536757) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1536751, _1536751), c_Fun_Oid(_1536751)), hAPP(c_Set_Oimage(_1536753, _1536751, _1536755), _1536757)))], (39047 ^ _780086) ^ [_1536944, _1536946, _1536948, _1536950] : [class_Groups_Ocomm__monoid__mult(_1536944), c_Fun_Oinj__on(_1536946, _1536944, _1536948, _1536950), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1536946, _1536944), _1536948), _1536950) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1536944, _1536944), c_Fun_Oid(_1536944)), hAPP(c_Set_Oimage(_1536946, _1536944, _1536948), _1536950)))], (39057 ^ _780086) ^ [_1537137, _1537139, _1537141, _1537143, _1537145, _1537147] : [class_Groups_Ocomm__monoid__mult(_1537137), hBOOL(hAPP(c_Finite__Set_Ofinite(_1537139), _1537141)), 39067 ^ _780086 : [(39068 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1537139), 39066 ^ [_1537137, _1537139, _1537141, _1537143, _1537145, _1537147]), _1537141)))], (39070 ^ _780086) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1537143), hAPP(_1537145, 39066 ^ [_1537137, _1537139, _1537141, _1537143, _1537145, _1537147])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1537139, _1537137), hAPP(hAPP(c_COMBS(_1537139, tc_fun(_1537143, tc_HOL_Obool), _1537137), hAPP(hAPP(c_COMBB(tc_fun(_1537143, _1537137), tc_fun(tc_fun(_1537143, tc_HOL_Obool), _1537137), _1537139), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1537143, _1537137)), _1537147)), _1537145)), _1537141) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1537139, _1537143), _1537137), hAPP(c_Product__Type_Oprod_Oprod__case(_1537139, _1537143, _1537137), _1537147)), hAPP(hAPP(c_Product__Type_OSigma(_1537139, _1537143), _1537141), _1537145)))], (39074 ^ _780086) ^ [_1537614, _1537616, _1537618, _1537620, _1537622, _1537624] : [class_Groups_Ocomm__monoid__add(_1537614), hBOOL(hAPP(c_Finite__Set_Ofinite(_1537616), _1537618)), 39084 ^ _780086 : [(39085 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1537616), 39083 ^ [_1537614, _1537616, _1537618, _1537620, _1537622, _1537624]), _1537618)))], (39087 ^ _780086) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1537620), hAPP(_1537622, 39083 ^ [_1537614, _1537616, _1537618, _1537620, _1537622, _1537624])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1537616, _1537614), hAPP(hAPP(c_COMBS(_1537616, tc_fun(_1537620, tc_HOL_Obool), _1537614), hAPP(hAPP(c_COMBB(tc_fun(_1537620, _1537614), tc_fun(tc_fun(_1537620, tc_HOL_Obool), _1537614), _1537616), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1537620, _1537614)), _1537624)), _1537622)), _1537618) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1537616, _1537620), _1537614), hAPP(c_Product__Type_Oprod_Oprod__case(_1537616, _1537620, _1537614), _1537624)), hAPP(hAPP(c_Product__Type_OSigma(_1537616, _1537620), _1537618), _1537622)))], (39091 ^ _780086) ^ [_1538091, _1538093, _1538095, _1538097] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1538091), _1538093)), 39097 ^ _780086 : [(39098 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1538091), 39096 ^ [_1538091, _1538093, _1538095, _1538097]), _1538093)))], (39100 ^ _780086) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1538095), hAPP(_1538097, 39096 ^ [_1538091, _1538093, _1538095, _1538097])))]], -(hAPP(c_Finite__Set_Ocard(tc_prod(_1538091, _1538095)), hAPP(hAPP(c_Product__Type_OSigma(_1538091, _1538095), _1538093), _1538097)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1538091, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1538095, tc_HOL_Obool), tc_Nat_Onat, _1538091), c_Finite__Set_Ocard(_1538095)), _1538097)), _1538093))], (39104 ^ _780086) ^ [_1538428, _1538430, _1538432, _1538434] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1538428), _1538430)), 39110 ^ _780086 : [(39111 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1538428), 39109 ^ [_1538428, _1538430, _1538432, _1538434]), _1538430)))], (39113 ^ _780086) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1538432), hAPP(_1538434, 39109 ^ [_1538428, _1538430, _1538432, _1538434])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1538428, _1538432)), hAPP(hAPP(c_Product__Type_OSigma(_1538428, _1538432), _1538430), _1538434))))], (39117 ^ _780086) ^ [_1538715, _1538717, _1538719, _1538721, _1538723] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1538715, _1538717)), _1538719), hAPP(hAPP(c_Product__Type_OSigma(_1538715, _1538717), _1538721), _1538723))), 39121 ^ _780086 : [(39122 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1538715), 39120 ^ [_1538715, _1538717, _1538719, _1538721, _1538723]), _1538721)))], (39125 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1538717), 39123 ^ [_1538715, _1538717, _1538719, _1538721, _1538723]), hAPP(_1538723, 39120 ^ [_1538715, _1538717, _1538719, _1538721, _1538723]))))], (39127 ^ _780086) ^ [] : [-(_1538719 = hAPP(hAPP(c_Product__Type_OPair(_1538715, _1538717), 39120 ^ [_1538715, _1538717, _1538719, _1538721, _1538723]), 39123 ^ [_1538715, _1538717, _1538719, _1538721, _1538723]))]]], (39129 ^ _780086) ^ [_1539017, _1539019, _1539021, _1539023, _1539025, _1539027] : [hAPP(c_Set_Oimage(_1539017, _1539019, _1539021), c_Orderings_Otop__class_Otop(tc_fun(_1539017, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1539019, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1539023, _1539025, _1539027), c_Orderings_Otop__class_Otop(tc_fun(_1539023, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1539025, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1539017, _1539023), tc_prod(_1539019, _1539025), c_Product__Type_Omap__pair(_1539017, _1539019, _1539023, _1539025, _1539021, _1539027)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1539017, _1539023), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1539019, _1539025), tc_HOL_Obool)))], (39139 ^ _780086) ^ [_1539302, _1539304, _1539306, _1539308, _1539310, _1539312, _1539314, _1539316, _1539318] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1539302, _1539304)), hAPP(hAPP(c_Product__Type_OPair(_1539302, _1539304), _1539306), _1539308)), _1539310)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1539312, _1539314)), hAPP(hAPP(c_Product__Type_OPair(_1539312, _1539314), hAPP(_1539316, _1539306)), hAPP(_1539318, _1539308))), hAPP(c_Set_Oimage(tc_prod(_1539302, _1539304), tc_prod(_1539312, _1539314), c_Product__Type_Omap__pair(_1539302, _1539312, _1539304, _1539314, _1539316, _1539318)), _1539310))))], (39145 ^ _780086) ^ [_1539521, _1539523, _1539525, _1539527, _1539529, _1539531, _1539533, _1539535] : [-(hAPP(c_Product__Type_Omap__pair(_1539521, _1539523, _1539525, _1539527, _1539529, _1539531), hAPP(hAPP(c_Product__Type_OPair(_1539521, _1539525), _1539533), _1539535)) = hAPP(hAPP(c_Product__Type_OPair(_1539523, _1539527), hAPP(_1539529, _1539533)), hAPP(_1539531, _1539535)))], (39147 ^ _780086) ^ [_1539592, _1539594, _1539596] : [-(hAPP(c_Product__Type_Omap__pair(_1539592, _1539592, _1539594, _1539594, c_COMBI(_1539592), c_COMBI(_1539594)), _1539596) = _1539596)], (39149 ^ _780086) ^ [_1539633, _1539635, _1539637, _1539639, _1539641, _1539643, _1539645] : [-(hAPP(c_Product__Type_Osnd(_1539633, _1539635), hAPP(c_Product__Type_Omap__pair(_1539637, _1539633, _1539639, _1539635, _1539641, _1539643), _1539645)) = hAPP(_1539643, hAPP(c_Product__Type_Osnd(_1539637, _1539639), _1539645)))], (39151 ^ _780086) ^ [_1539693, _1539695, _1539697, _1539699, _1539701, _1539703, _1539705] : [-(hAPP(c_Product__Type_Ofst(_1539693, _1539695), hAPP(c_Product__Type_Omap__pair(_1539697, _1539693, _1539699, _1539695, _1539701, _1539703), _1539705)) = hAPP(_1539701, hAPP(c_Product__Type_Ofst(_1539697, _1539699), _1539705)))], (39153 ^ _780086) ^ [_1539753, _1539755] : [-(c_Product__Type_Omap__pair(_1539753, _1539753, _1539755, _1539755, c_COMBI(_1539753), c_COMBI(_1539755)) = c_Fun_Oid(tc_prod(_1539753, _1539755)))], (39155 ^ _780086) ^ [_1539794, _1539796, _1539798, _1539800] : [-(c_Product__Type_Oapsnd(_1539794, _1539796, _1539798, _1539800) = c_Product__Type_Omap__pair(_1539798, _1539798, _1539794, _1539796, c_Fun_Oid(_1539798), _1539800))], (39157 ^ _780086) ^ [_1539837, _1539839, _1539841, _1539843] : [-(c_Product__Type_Oapfst(_1539837, _1539839, _1539841, _1539843) = c_Product__Type_Omap__pair(_1539837, _1539839, _1539841, _1539841, _1539843, c_Fun_Oid(_1539841)))], (39159 ^ _780086) ^ [_1539880, _1539882] : [-(c_Product__Type_Omap__pair(_1539880, _1539880, _1539882, _1539882, c_Fun_Oid(_1539880), c_Fun_Oid(_1539882)) = c_Fun_Oid(tc_prod(_1539880, _1539882)))], (39161 ^ _780086) ^ [_1539921, _1539923, _1539925, _1539927, _1539929, _1539931] : [-(c_Product__Type_Omap__pair(_1539921, _1539923, _1539925, _1539927, _1539929, _1539931) = hAPP(c_Product__Type_Oprod_Oprod__case(_1539921, _1539925, tc_prod(_1539923, _1539927)), hAPP(hAPP(c_COMBC(_1539921, tc_fun(_1539925, _1539927), tc_fun(_1539925, tc_prod(_1539923, _1539927))), hAPP(hAPP(c_COMBB(tc_fun(_1539927, tc_prod(_1539923, _1539927)), tc_fun(tc_fun(_1539925, _1539927), tc_fun(_1539925, tc_prod(_1539923, _1539927))), _1539921), c_COMBB(_1539927, tc_prod(_1539923, _1539927), _1539925)), hAPP(hAPP(c_COMBB(_1539923, tc_fun(_1539927, tc_prod(_1539923, _1539927)), _1539921), c_Product__Type_OPair(_1539923, _1539927)), _1539929))), _1539931)))], (39163 ^ _780086) ^ [_1540044, _1540046, _1540048, _1540050, _1540052, _1540054, _1540056, _1540058, _1540060, _1540062] : [hAPP(c_Set_Oimage(_1540044, _1540046, _1540048), _1540050) = _1540052, hAPP(c_Set_Oimage(_1540054, _1540056, _1540058), _1540060) = _1540062, -(hAPP(c_Set_Oimage(tc_prod(_1540044, _1540054), tc_prod(_1540046, _1540056), c_Product__Type_Omap__pair(_1540044, _1540046, _1540054, _1540056, _1540048, _1540058)), hAPP(hAPP(c_Product__Type_OSigma(_1540044, _1540054), _1540050), hAPP(c_COMBK(tc_fun(_1540054, tc_HOL_Obool), _1540044), _1540060))) = hAPP(hAPP(c_Product__Type_OSigma(_1540046, _1540056), _1540052), hAPP(c_COMBK(tc_fun(_1540056, tc_HOL_Obool), _1540046), _1540062)))], (39173 ^ _780086) ^ [_1540345, _1540347, _1540349, _1540351] : [c_Wellfounded_Owf(_1540345, _1540347), c_Fun_Oinj__on(_1540345, _1540349, _1540351, c_Orderings_Otop__class_Otop(tc_fun(_1540345, tc_HOL_Obool))), -(c_Wellfounded_Owf(_1540349, hAPP(c_Set_Oimage(tc_prod(_1540345, _1540345), tc_prod(_1540349, _1540349), c_Product__Type_Omap__pair(_1540345, _1540349, _1540345, _1540349, _1540351, _1540351)), _1540347)))], (39183 ^ _780086) ^ [_1540536, _1540538, _1540540, _1540542, _1540544, _1540546, _1540548, _1540550] : [c_Fun_Oinj__on(_1540536, _1540538, _1540540, _1540542), c_Fun_Oinj__on(_1540544, _1540546, _1540548, _1540550), -(c_Fun_Oinj__on(tc_prod(_1540536, _1540544), tc_prod(_1540538, _1540546), c_Product__Type_Omap__pair(_1540536, _1540538, _1540544, _1540546, _1540540, _1540548), hAPP(hAPP(c_Product__Type_OSigma(_1540536, _1540544), _1540542), hAPP(c_COMBK(tc_fun(_1540544, tc_HOL_Obool), _1540536), _1540550))))], (39193 ^ _780086) ^ [_1540763, _1540765, _1540767, _1540769, _1540771, _1540773, _1540775, _1540777] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1540763, _1540765)), _1540767), hAPP(c_Set_Oimage(tc_prod(_1540769, _1540771), tc_prod(_1540763, _1540765), c_Product__Type_Omap__pair(_1540769, _1540763, _1540771, _1540765, _1540773, _1540775)), _1540777))), 39198 ^ _780086 : [(39199 ^ _780086) ^ [] : [-(_1540767 = hAPP(hAPP(c_Product__Type_OPair(_1540763, _1540765), hAPP(_1540773, 39196 ^ [_1540763, _1540765, _1540767, _1540769, _1540771, _1540773, _1540775, _1540777])), hAPP(_1540775, 39197 ^ [_1540763, _1540765, _1540767, _1540769, _1540771, _1540773, _1540775, _1540777])))], (39201 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1540769, _1540771)), hAPP(hAPP(c_Product__Type_OPair(_1540769, _1540771), 39196 ^ [_1540763, _1540765, _1540767, _1540769, _1540771, _1540773, _1540775, _1540777]), 39197 ^ [_1540763, _1540765, _1540767, _1540769, _1540771, _1540773, _1540775, _1540777])), _1540777)))]]], (39203 ^ _780086) ^ [_1541114, _1541116, _1541118] : [c_Relation_Orefl__on(_1541114, _1541116, _1541118), 39206 ^ _780086 : [(39207 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1541114, _1541114), tc_HOL_Obool)), _1541118), hAPP(hAPP(c_Product__Type_OSigma(_1541114, _1541114), _1541116), hAPP(c_COMBK(tc_fun(_1541114, tc_HOL_Obool), _1541114), _1541116)))))], (39209 ^ _780086) ^ [_1541296] : [hBOOL(hAPP(hAPP(c_member(_1541114), _1541296), _1541116)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1541114, _1541114)), hAPP(hAPP(c_Product__Type_OPair(_1541114, _1541114), _1541296), _1541296)), _1541118)))]]], (39215 ^ _780086) ^ [_1541431, _1541433, _1541435] : [-(c_Relation_Orefl__on(_1541431, _1541433, _1541435)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1541431, _1541431), tc_HOL_Obool)), _1541435), hAPP(hAPP(c_Product__Type_OSigma(_1541431, _1541431), _1541433), hAPP(c_COMBK(tc_fun(_1541431, tc_HOL_Obool), _1541431), _1541433)))), 39221 ^ _780086 : [(39222 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1541431), 39220 ^ [_1541431, _1541433, _1541435]), _1541433)))], (39224 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1541431, _1541431)), hAPP(hAPP(c_Product__Type_OPair(_1541431, _1541431), 39220 ^ [_1541431, _1541433, _1541435]), 39220 ^ [_1541431, _1541433, _1541435])), _1541435))]]], (39228 ^ _780086) ^ [_1541795, _1541797] : [c_Wellfounded_OwfP(_1541795, _1541797), -(c_Wellfounded_Owf(_1541795, hAPP(c_Set_OCollect(tc_prod(_1541795, _1541795)), hAPP(c_Product__Type_Oprod_Oprod__case(_1541795, _1541795, tc_HOL_Obool), _1541797))))], (39234 ^ _780086) ^ [_1541898, _1541900] : [c_Wellfounded_Owf(_1541898, hAPP(c_Set_OCollect(tc_prod(_1541898, _1541898)), hAPP(c_Product__Type_Oprod_Oprod__case(_1541898, _1541898, tc_HOL_Obool), _1541900))), -(c_Wellfounded_OwfP(_1541898, _1541900))], (39240 ^ _780086) ^ [_1542007] : [-(c_Wellfounded_OwfP(_1542007, hAPP(c_COMBK(tc_fun(_1542007, tc_HOL_Obool), _1542007), hAPP(c_COMBK(tc_HOL_Obool, _1542007), c_fFalse))))], (39242 ^ _780086) ^ [_1542045, _1542047] : [-(c_Relation_Orefl__on(_1542045, _1542047, c_Relation_OId__on(_1542045, _1542047)))], (39244 ^ _780086) ^ [_1542089, _1542091] : [c_Wellfounded_OwfP(_1542089, _1542091), 39247 ^ _780086 : [(39248 ^ _780086) ^ [_1542153] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(_1542089, _1542091), _1542153)))]]], (39250 ^ _780086) ^ [_1542181, _1542183] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1542181, _1542183), 39251 ^ [_1542181, _1542183])), -(c_Wellfounded_OwfP(_1542181, _1542183))], (39257 ^ _780086) ^ [_1542299, _1542301, _1542303] : [c_Wellfounded_OwfP(_1542299, _1542301), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1542299, _1542301), _1542303)))], (39263 ^ _780086) ^ [_1542388, _1542390, _1542392] : [c_Wellfounded_OwfP(_1542388, _1542390), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1542388, tc_fun(_1542388, tc_HOL_Obool))), _1542392), _1542390)), -(c_Wellfounded_OwfP(_1542388, _1542392))], (39273 ^ _780086) ^ [_1542547] : [-(c_Relation_Orefl__on(_1542547, c_Orderings_Obot__class_Obot(tc_fun(_1542547, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1542547, _1542547), tc_HOL_Obool))))], (39275 ^ _780086) ^ [_1542584, _1542586, _1542588, _1542590, _1542592] : [c_Relation_Orefl__on(_1542584, _1542586, _1542588), c_Relation_Orefl__on(_1542584, _1542590, _1542592), -(c_Relation_Orefl__on(_1542584, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1542584, tc_HOL_Obool)), _1542586), _1542590), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1542584, _1542584), tc_HOL_Obool)), _1542588), _1542592)))], (39285 ^ _780086) ^ [_1542781, _1542783, _1542785, _1542787, _1542789] : [c_Relation_Orefl__on(_1542781, _1542783, _1542785), c_Relation_Orefl__on(_1542781, _1542787, _1542789), -(c_Relation_Orefl__on(_1542781, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1542781, tc_HOL_Obool)), _1542783), _1542787), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1542781, _1542781), tc_HOL_Obool)), _1542785), _1542789)))], (39295 ^ _780086) ^ [_1542978, _1542980, _1542982, _1542984] : [c_Relation_Orefl__on(_1542978, _1542980, _1542982), hBOOL(hAPP(hAPP(c_member(_1542978), _1542984), _1542980)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1542978, _1542978)), hAPP(hAPP(c_Product__Type_OPair(_1542978, _1542978), _1542984), _1542984)), _1542982)))], (39305 ^ _780086) ^ [_1543169, _1543171, _1543173, _1543175, _1543177] : [c_Relation_Orefl__on(_1543169, _1543171, _1543173), hBOOL(hAPP(hAPP(c_member(tc_prod(_1543169, _1543169)), hAPP(hAPP(c_Product__Type_OPair(_1543169, _1543169), _1543175), _1543177)), _1543173)), -(hBOOL(hAPP(hAPP(c_member(_1543169), _1543175), _1543171)))], (39315 ^ _780086) ^ [_1543364, _1543366, _1543368, _1543370, _1543372] : [c_Relation_Orefl__on(_1543364, _1543366, _1543368), hBOOL(hAPP(hAPP(c_member(tc_prod(_1543364, _1543364)), hAPP(hAPP(c_Product__Type_OPair(_1543364, _1543364), _1543370), _1543372)), _1543368)), -(hBOOL(hAPP(hAPP(c_member(_1543364), _1543372), _1543366)))], (39325 ^ _780086) ^ [_1543559, _1543561] : [c_Wellfounded_Owf(_1543559, _1543561), -(c_Wellfounded_OwfP(_1543559, c_FunDef_Oin__rel(_1543559, _1543559, _1543561)))], (39331 ^ _780086) ^ [_1543659, _1543661] : [c_Wellfounded_OwfP(_1543659, hAPP(hAPP(c_COMBC(_1543659, tc_fun(tc_prod(_1543659, _1543659), tc_HOL_Obool), tc_fun(_1543659, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1543659, tc_fun(tc_fun(tc_prod(_1543659, _1543659), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1543659, _1543659), tc_HOL_Obool), tc_fun(_1543659, tc_HOL_Obool)), _1543659), c_COMBC(_1543659, tc_fun(tc_prod(_1543659, _1543659), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1543659, tc_prod(_1543659, _1543659)), tc_fun(_1543659, tc_fun(tc_fun(tc_prod(_1543659, _1543659), tc_HOL_Obool), tc_HOL_Obool)), _1543659), hAPP(c_COMBB(tc_prod(_1543659, _1543659), tc_fun(tc_fun(tc_prod(_1543659, _1543659), tc_HOL_Obool), tc_HOL_Obool), _1543659), c_member(tc_prod(_1543659, _1543659)))), c_Product__Type_OPair(_1543659, _1543659)))), _1543661)), -(c_Wellfounded_Owf(_1543659, _1543661))], (39337 ^ _780086) ^ [_1543968, _1543970] : [c_Wellfounded_Owf(_1543968, _1543970), -(c_Wellfounded_OwfP(_1543968, hAPP(hAPP(c_COMBC(_1543968, tc_fun(tc_prod(_1543968, _1543968), tc_HOL_Obool), tc_fun(_1543968, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1543968, tc_fun(tc_fun(tc_prod(_1543968, _1543968), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1543968, _1543968), tc_HOL_Obool), tc_fun(_1543968, tc_HOL_Obool)), _1543968), c_COMBC(_1543968, tc_fun(tc_prod(_1543968, _1543968), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1543968, tc_prod(_1543968, _1543968)), tc_fun(_1543968, tc_fun(tc_fun(tc_prod(_1543968, _1543968), tc_HOL_Obool), tc_HOL_Obool)), _1543968), hAPP(c_COMBB(tc_prod(_1543968, _1543968), tc_fun(tc_fun(tc_prod(_1543968, _1543968), tc_HOL_Obool), tc_HOL_Obool), _1543968), c_member(tc_prod(_1543968, _1543968)))), c_Product__Type_OPair(_1543968, _1543968)))), _1543970)))], (39343 ^ _780086) ^ [_1544298, _1544300] : [c_Predicate_Oreflp(_1544298, _1544300), -(c_Relation_Orefl__on(_1544298, c_Orderings_Otop__class_Otop(tc_fun(_1544298, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1544298, _1544298)), hAPP(c_Product__Type_Oprod_Oprod__case(_1544298, _1544298, tc_HOL_Obool), _1544300))))], (39349 ^ _780086) ^ [_1544413, _1544415] : [c_Relation_Orefl__on(_1544413, c_Orderings_Otop__class_Otop(tc_fun(_1544413, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1544413, _1544413)), hAPP(c_Product__Type_Oprod_Oprod__case(_1544413, _1544413, tc_HOL_Obool), _1544415))), -(c_Predicate_Oreflp(_1544413, _1544415))], (39355 ^ _780086) ^ [_1544534, _1544536, _1544538] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1544534, _1544534), tc_HOL_Obool)), _1544536), hAPP(hAPP(c_Product__Type_OSigma(_1544534, _1544534), _1544538), hAPP(c_COMBK(tc_fun(_1544534, tc_HOL_Obool), _1544534), _1544538)))), 39361 ^ _780086 : [(39362 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1544534), 39360 ^ [_1544534, _1544536, _1544538]), _1544538)))], (39364 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1544534, _1544534)), hAPP(hAPP(c_Product__Type_OPair(_1544534, _1544534), 39360 ^ [_1544534, _1544536, _1544538]), 39360 ^ [_1544534, _1544536, _1544538])), _1544536))]], -(c_Relation_Orefl__on(_1544534, _1544538, _1544536))], (39368 ^ _780086) ^ [_1544881, _1544883] : [c_Wellfounded_OwfP(_1544881, _1544883), -(c_Wellfounded_Oacyclic(_1544881, hAPP(c_Set_OCollect(tc_prod(_1544881, _1544881)), hAPP(c_Product__Type_Oprod_Oprod__case(_1544881, _1544881, tc_HOL_Obool), _1544883))))], (39374 ^ _780086) ^ [_1544988, _1544990, _1544992] : [c_Wellfounded_Oacyclic(_1544988, _1544990), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1544988, _1544988), tc_HOL_Obool)), _1544992), _1544990)), -(c_Wellfounded_Oacyclic(_1544988, _1544992))], (39384 ^ _780086) ^ [_1545147, _1545149, _1545151] : [c_Predicate_Oreflp(_1545147, _1545149), -(hBOOL(hAPP(hAPP(_1545149, _1545151), _1545151)))], (39390 ^ _780086) ^ [_1545236, _1545238] : [c_Wellfounded_Owf(_1545236, _1545238), -(c_Wellfounded_Oacyclic(_1545236, _1545238))], (39396 ^ _780086) ^ [_1545313, _1545315] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1545313, _1545313)), _1545315)), 39399 ^ _780086 : [(39400 ^ _780086) ^ [] : [c_Wellfounded_Owf(_1545313, _1545315), -(c_Wellfounded_Oacyclic(_1545313, _1545315))], (39406 ^ _780086) ^ [] : [c_Wellfounded_Oacyclic(_1545313, _1545315), -(c_Wellfounded_Owf(_1545313, _1545315))]]], (39412 ^ _780086) ^ [_1545534, _1545536] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1545534, _1545534)), _1545536)), c_Wellfounded_Oacyclic(_1545534, _1545536), -(c_Wellfounded_Owf(_1545534, _1545536))], (39422 ^ _780086) ^ [_1545692, _1545694] : [c_Nitpick_Owf_H(_1545692, _1545694), 39425 ^ _780086 : [(39426 ^ _780086) ^ [] : [-(c_Wellfounded_Oacyclic(_1545692, _1545694))], (39428 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1545692, _1545692)), _1545694))), -(c_Nitpick_Ounknown(tc_HOL_Obool))]]], (39434 ^ _780086) ^ [_1545812, _1545814] : [-(c_Nitpick_Owf_H(_1545812, _1545814)), c_Wellfounded_Oacyclic(_1545812, _1545814), 39439 ^ _780086 : [(39440 ^ _780086) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1545812, _1545812)), _1545814))], (39442 ^ _780086) ^ [] : [c_Nitpick_Ounknown(tc_HOL_Obool)]]], (39446 ^ _780086) ^ [_1545989, _1545991] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1545989), c_Int_OInteg)), hBOOL(hAPP(_1545991, hAPP(c_Int_ORep__Integ, 39451 ^ [_1545989, _1545991]))), -(hBOOL(hAPP(_1545991, _1545989)))], (39457 ^ _780086) ^ [_1546171] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1546171), c_Int_OInteg)), -(_1546171 = hAPP(c_Int_ORep__Integ, 39460 ^ [_1546171]))], (39480 ^ _780086) ^ [_1546913, _1546915, _1546917] : [-(c_Relation_Orefl__on(_1546913, _1546915, _1546917)), 39484 ^ _780086 : [(39485 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1546913, _1546913)), 39483 ^ [_1546913, _1546915, _1546917]), _1546917)))], (39487 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1546913, _1546913, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1546913, tc_fun(_1546913, tc_HOL_Obool), tc_fun(_1546913, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1546913, tc_HOL_Obool), tc_fun(_1546913, tc_HOL_Obool)), _1546913), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1546913)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1546913), c_fconj), hAPP(hAPP(c_COMBC(_1546913, tc_fun(_1546913, tc_HOL_Obool), tc_HOL_Obool), c_member(_1546913)), _1546915)))), hAPP(hAPP(c_COMBC(_1546913, tc_fun(_1546913, tc_HOL_Obool), tc_HOL_Obool), c_member(_1546913)), _1546915))), 39483 ^ [_1546913, _1546915, _1546917]))]], 39489 ^ _780086 : [(39490 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1546913), 39488 ^ [_1546913, _1546915, _1546917]), _1546915)))], (39492 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1546913, _1546913)), hAPP(hAPP(c_Product__Type_OPair(_1546913, _1546913), 39488 ^ [_1546913, _1546915, _1546917]), 39488 ^ [_1546913, _1546915, _1546917])), _1546917))]]], (39464 ^ _780086) ^ [_1546294, _1546296, _1546298] : [c_Relation_Orefl__on(_1546294, _1546296, _1546298), 39467 ^ _780086 : [(39468 ^ _780086) ^ [_1546505] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1546294, _1546294)), _1546505), _1546298)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1546294, _1546294, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1546294, tc_fun(_1546294, tc_HOL_Obool), tc_fun(_1546294, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1546294, tc_HOL_Obool), tc_fun(_1546294, tc_HOL_Obool)), _1546294), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1546294)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1546294), c_fconj), hAPP(hAPP(c_COMBC(_1546294, tc_fun(_1546294, tc_HOL_Obool), tc_HOL_Obool), c_member(_1546294)), _1546296)))), hAPP(hAPP(c_COMBC(_1546294, tc_fun(_1546294, tc_HOL_Obool), tc_HOL_Obool), c_member(_1546294)), _1546296))), _1546505)))], (39474 ^ _780086) ^ [_1546778] : [hBOOL(hAPP(hAPP(c_member(_1546294), _1546778), _1546296)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1546294, _1546294)), hAPP(hAPP(c_Product__Type_OPair(_1546294, _1546294), _1546778), _1546778)), _1546298)))]]], (39496 ^ _780086) ^ [_1547554, _1547556] : [39498 ^ _780086 : [(39499 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 39497 ^ [_1547554, _1547556]), c_Int_OInteg)))], (39501 ^ _780086) ^ [] : [hBOOL(hAPP(_1547554, hAPP(c_Int_OAbs__Integ, 39497 ^ [_1547554, _1547556])))]], -(hBOOL(hAPP(_1547554, _1547556)))], (39506 ^ _780086) ^ [_1547721] : [-(_1547721 = hAPP(c_Int_OAbs__Integ, 39504 ^ [_1547721]))], (39508 ^ _780086) ^ [_1547749] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 39504 ^ [_1547749]), c_Int_OInteg)))], (39510 ^ _780086) ^ [_1547784] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1547784, tc_HOL_Obool) = c_Set_OBall(_1547784))], (39512 ^ _780086) ^ [_1547812, _1547814, _1547816] : [hBOOL(hAPP(hAPP(c_member(_1547814), _1547812), c_Orderings_Obot__class_Obot(tc_fun(_1547814, tc_HOL_Obool)))), -(hBOOL(hAPP(_1547816, _1547812)))], (39528 ^ _780086) ^ [_1548120, _1548122, _1548124] : [39530 ^ _780086 : [(39531 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1548120), 39529 ^ [_1548120, _1548122, _1548124]), _1548124)))], (39533 ^ _780086) ^ [] : [hBOOL(hAPP(_1548122, 39529 ^ [_1548120, _1548122, _1548124]))]], -(hBOOL(hAPP(c_Predicate_OPowp(_1548120, _1548122), _1548124)))], (39518 ^ _780086) ^ [_1547937, _1547939, _1547941] : [hBOOL(hAPP(c_Predicate_OPowp(_1547937, _1547939), _1547941)), 39521 ^ _780086 : [(39522 ^ _780086) ^ [_1548021] : [hBOOL(hAPP(hAPP(c_member(_1547937), _1548021), _1547941)), -(hBOOL(hAPP(_1547939, _1548021)))]]], (39537 ^ _780086) ^ [_1548300, _1548302, _1548304, _1548306] : [-(hAPP(c_Set_OCollect(_1548300), hAPP(hAPP(c_COMBB(tc_fun(_1548302, tc_HOL_Obool), tc_HOL_Obool, _1548300), c_HOL_OAll(_1548302)), hAPP(hAPP(c_COMBB(tc_fun(_1548302, tc_HOL_Obool), tc_fun(_1548302, tc_HOL_Obool), _1548300), hAPP(c_COMBS(_1548302, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1548302), c_fimplies), hAPP(hAPP(c_COMBC(_1548302, tc_fun(_1548302, tc_HOL_Obool), tc_HOL_Obool), c_member(_1548302)), _1548304)))), _1548306))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1548302, tc_fun(_1548300, tc_HOL_Obool)), _1548304), hAPP(hAPP(c_COMBB(tc_fun(_1548300, tc_HOL_Obool), tc_fun(_1548300, tc_HOL_Obool), _1548302), c_Set_OCollect(_1548300)), hAPP(c_COMBC(_1548300, _1548302, tc_HOL_Obool), _1548306))))], (39549 ^ _780086) ^ [_1548831, _1548833, _1548835, _1548837] : [39551 ^ _780086 : [(39552 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1548831, _1548831)), 39550 ^ [_1548831, _1548833, _1548835, _1548837]), _1548835)))], (39554 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1548831, _1548831, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1548831, tc_fun(_1548831, _1548833), tc_fun(_1548831, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1548833, tc_HOL_Obool), tc_fun(tc_fun(_1548831, _1548833), tc_fun(_1548831, tc_HOL_Obool)), _1548831), c_COMBB(_1548833, tc_HOL_Obool, _1548831)), hAPP(hAPP(c_COMBB(_1548833, tc_fun(_1548833, tc_HOL_Obool), _1548831), c_fequal), _1548837))), _1548837)), 39550 ^ [_1548831, _1548833, _1548835, _1548837]))]], -(c_Equiv__Relations_Ocongruent(_1548831, _1548833, _1548835, _1548837))], (39539 ^ _780086) ^ [_1548455, _1548457, _1548459, _1548461] : [c_Equiv__Relations_Ocongruent(_1548455, _1548457, _1548459, _1548461), 39542 ^ _780086 : [(39543 ^ _780086) ^ [_1548600] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1548455, _1548455)), _1548600), _1548459)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1548455, _1548455, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1548455, tc_fun(_1548455, _1548457), tc_fun(_1548455, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1548457, tc_HOL_Obool), tc_fun(tc_fun(_1548455, _1548457), tc_fun(_1548455, tc_HOL_Obool)), _1548455), c_COMBB(_1548457, tc_HOL_Obool, _1548455)), hAPP(hAPP(c_COMBB(_1548457, tc_fun(_1548457, tc_HOL_Obool), _1548455), c_fequal), _1548461))), _1548461)), _1548600)))]]], (39558 ^ _780086) ^ [_1549206, _1549208, _1549210, _1549212] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1549206, tc_fun(_1549208, tc_HOL_Obool)), _1549210), _1549212) = hAPP(c_Set_OCollect(_1549208), hAPP(hAPP(c_COMBB(tc_fun(_1549206, tc_HOL_Obool), tc_HOL_Obool, _1549208), c_HOL_OAll(_1549206)), hAPP(hAPP(c_COMBB(tc_fun(_1549206, tc_HOL_Obool), tc_fun(_1549206, tc_HOL_Obool), _1549208), hAPP(c_COMBS(_1549206, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1549206), c_fimplies), hAPP(hAPP(c_COMBC(_1549206, tc_fun(_1549206, tc_HOL_Obool), tc_HOL_Obool), c_member(_1549206)), _1549210)))), hAPP(hAPP(c_COMBC(_1549208, tc_fun(_1549206, tc_fun(_1549208, tc_HOL_Obool)), tc_fun(_1549206, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1549208, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1549206, tc_fun(_1549208, tc_HOL_Obool)), tc_fun(_1549206, tc_HOL_Obool)), _1549208), c_COMBB(tc_fun(_1549208, tc_HOL_Obool), tc_HOL_Obool, _1549206)), c_member(_1549208))), _1549212)))))], (39560 ^ _780086) ^ [_1549371, _1549373] : [class_Complete__Lattice_Ocomplete__lattice(_1549371), -(c_Complete__Lattice_OSup__class_OSup(_1549371, _1549373) = c_Complete__Lattice_OInf__class_OInf(_1549371, hAPP(c_Set_OCollect(_1549371), hAPP(hAPP(c_COMBB(tc_fun(_1549371, tc_HOL_Obool), tc_HOL_Obool, _1549371), c_HOL_OAll(_1549371)), hAPP(hAPP(c_COMBB(tc_fun(_1549371, tc_HOL_Obool), tc_fun(_1549371, tc_HOL_Obool), _1549371), hAPP(c_COMBS(_1549371, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1549371), c_fimplies), hAPP(hAPP(c_COMBC(_1549371, tc_fun(_1549371, tc_HOL_Obool), tc_HOL_Obool), c_member(_1549371)), _1549373)))), hAPP(c_COMBC(_1549371, _1549371, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1549371)))))))], (39566 ^ _780086) ^ [_1549612, _1549614] : [class_Complete__Lattice_Ocomplete__lattice(_1549612), -(c_Complete__Lattice_OInf__class_OInf(_1549612, _1549614) = c_Complete__Lattice_OSup__class_OSup(_1549612, hAPP(c_Set_OCollect(_1549612), hAPP(hAPP(c_COMBB(tc_fun(_1549612, tc_HOL_Obool), tc_HOL_Obool, _1549612), c_HOL_OAll(_1549612)), hAPP(hAPP(c_COMBB(tc_fun(_1549612, tc_HOL_Obool), tc_fun(_1549612, tc_HOL_Obool), _1549612), hAPP(c_COMBS(_1549612, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1549612), c_fimplies), hAPP(hAPP(c_COMBC(_1549612, tc_fun(_1549612, tc_HOL_Obool), tc_HOL_Obool), c_member(_1549612)), _1549614)))), c_Orderings_Oord__class_Oless__eq(_1549612))))))], (39572 ^ _780086) ^ [_1549839, _1549841, _1549843] : [c_Wellfounded_OwfP(_1549839, hAPP(_1549841, 39573 ^ [_1549839, _1549841, _1549843])), 39580 ^ _780086 : [(39581 ^ _780086) ^ [] : [hAPP(_1549841, 39578 ^ [_1549839, _1549841, _1549843]) = hAPP(_1549841, 39579 ^ [_1549839, _1549841, _1549843])], (39583 ^ _780086) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1549839, tc_HOL_Obool)), c_Predicate_ODomainP(_1549839, _1549839, hAPP(_1549841, 39578 ^ [_1549839, _1549841, _1549843]))), c_Predicate_ORangeP(_1549839, _1549839, hAPP(_1549841, 39579 ^ [_1549839, _1549841, _1549843]))) = c_Orderings_Obot__class_Obot(tc_fun(_1549839, tc_HOL_Obool))]], -(c_Wellfounded_OwfP(_1549839, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1549843, tc_fun(_1549839, tc_fun(_1549839, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1549843, tc_HOL_Obool))), _1549841)))], (39587 ^ _780086) ^ [_1550279, _1550281, _1550283, _1550285, _1550287, _1550289] : [39590 ^ _780086 : [(39591 ^ _780086) ^ [] : [-(_1550279 = hAPP(hAPP(c_Product__Type_OPair(_1550281, _1550283), 39588 ^ [_1550279, _1550281, _1550283, _1550285, _1550287, _1550289]), 39589 ^ [_1550279, _1550281, _1550283, _1550285, _1550287, _1550289]))], (39593 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1550285), _1550287), hAPP(hAPP(_1550289, 39588 ^ [_1550279, _1550281, _1550283, _1550285, _1550287, _1550289]), 39589 ^ [_1550279, _1550281, _1550283, _1550285, _1550287, _1550289])))]], -(hBOOL(hAPP(hAPP(c_member(_1550285), _1550287), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1550281, _1550283, tc_fun(_1550285, tc_HOL_Obool)), _1550289), _1550279))))], (39597 ^ _780086) ^ [_1550604, _1550606, _1550608, _1550610, _1550612, _1550614] : [hBOOL(hAPP(hAPP(c_member(_1550604), _1550606), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1550608, _1550610, tc_fun(_1550604, tc_HOL_Obool)), _1550612), _1550614))), 39602 ^ _780086 : [(39603 ^ _780086) ^ [] : [-(_1550614 = hAPP(hAPP(c_Product__Type_OPair(_1550608, _1550610), 39600 ^ [_1550604, _1550606, _1550608, _1550610, _1550612, _1550614]), 39601 ^ [_1550604, _1550606, _1550608, _1550610, _1550612, _1550614]))], (39605 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1550604), _1550606), hAPP(hAPP(_1550612, 39600 ^ [_1550604, _1550606, _1550608, _1550610, _1550612, _1550614]), 39601 ^ [_1550604, _1550606, _1550608, _1550610, _1550612, _1550614]))))]]], (39607 ^ _780086) ^ [_1550873, _1550875] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1550873, tc_HOL_Obool), _1550875) = hAPP(c_Set_OCollect(_1550873), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1550873, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1550873), c_HOL_OAll(tc_fun(_1550873, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1550873, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1550873, tc_HOL_Obool), tc_HOL_Obool), _1550873), hAPP(c_COMBS(tc_fun(_1550873, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1550873, tc_HOL_Obool)), c_fimplies), hAPP(hAPP(c_COMBC(tc_fun(_1550873, tc_HOL_Obool), tc_fun(tc_fun(_1550873, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1550873, tc_HOL_Obool))), _1550875)))), c_member(_1550873)))))], (39609 ^ _780086) ^ [_1551001, _1551003, _1551005, _1551007, _1551009, _1551011] : [-(hAPP(c_Set_Ovimage(_1551001, tc_prod(_1551003, _1551005), _1551007), hAPP(hAPP(c_Product__Type_OSigma(_1551003, _1551005), _1551009), hAPP(c_COMBK(tc_fun(_1551005, tc_HOL_Obool), _1551003), _1551011))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1551001, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1551001, _1551003, hAPP(c_Fun_Ocomp(tc_prod(_1551003, _1551005), _1551003, _1551001, c_Product__Type_Ofst(_1551003, _1551005)), _1551007)), _1551009)), hAPP(c_Set_Ovimage(_1551001, _1551005, hAPP(c_Fun_Ocomp(tc_prod(_1551003, _1551005), _1551005, _1551001, c_Product__Type_Osnd(_1551003, _1551005)), _1551007)), _1551011)))], (39611 ^ _780086) ^ [_1551115, _1551117, _1551119] : [-(c_Hilbert__Choice_OEps(tc_prod(_1551115, _1551117), hAPP(c_Product__Type_Oprod_Oprod__case(_1551115, _1551117, tc_HOL_Obool), _1551119)) = c_Hilbert__Choice_OEps(tc_prod(_1551115, _1551117), hAPP(hAPP(c_COMBS(tc_prod(_1551115, _1551117), _1551117, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1551115, tc_fun(_1551117, tc_HOL_Obool), tc_prod(_1551115, _1551117)), _1551119), c_Product__Type_Ofst(_1551115, _1551117))), c_Product__Type_Osnd(_1551115, _1551117))))], (39613 ^ _780086) ^ [_1551196, _1551198] : [39615 ^ _780086 : [(39616 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1551196, tc_HOL_Obool)), 39614 ^ [_1551196, _1551198]), hAPP(c_Relation_OImage(_1551196, _1551196, _1551198), 39614 ^ [_1551196, _1551198]))))], (39618 ^ _780086) ^ [] : [39614 ^ [_1551196, _1551198] = c_Orderings_Obot__class_Obot(tc_fun(_1551196, tc_HOL_Obool))]], -(c_Wellfounded_Owf(_1551196, _1551198))], (39622 ^ _780086) ^ [_1551393, _1551395, _1551397] : [-(hAPP(c_Fun_Ocomp(_1551393, _1551393, _1551395, c_Fun_Oid(_1551393)), _1551397) = _1551397)], (39624 ^ _780086) ^ [_1551430, _1551432, _1551434] : [-(hAPP(c_Fun_Ocomp(_1551430, _1551432, _1551430, _1551434), c_Fun_Oid(_1551430)) = _1551434)], (39626 ^ _780086) ^ [_1551467, _1551469, _1551471, _1551473, _1551475, _1551477, _1551479] : [hAPP(c_Fun_Ocomp(_1551467, _1551469, _1551471, _1551473), _1551475) = hAPP(c_Fun_Ocomp(_1551469, _1551469, _1551471, c_Fun_Oid(_1551469)), _1551477), -(hAPP(_1551473, hAPP(_1551475, _1551479)) = hAPP(_1551477, _1551479))], (39632 ^ _780086) ^ [_1551608, _1551610, _1551612, _1551614] : [c_Finite__Set_Ofun__left__comm__idem(_1551608, _1551610, _1551612), -(hAPP(c_Fun_Ocomp(_1551610, _1551610, _1551610, hAPP(_1551612, _1551614)), hAPP(_1551612, _1551614)) = hAPP(_1551612, _1551614))], (39638 ^ _780086) ^ [_1551725, _1551727, _1551729, _1551731, _1551733, _1551735, _1551737] : [-(hAPP(c_Fun_Ocomp(_1551725, _1551727, _1551729, _1551731), c_Fun_Ofun__upd(_1551729, _1551725, _1551733, _1551735, _1551737)) = c_Fun_Ofun__upd(_1551729, _1551727, hAPP(c_Fun_Ocomp(_1551725, _1551727, _1551729, _1551731), _1551733), _1551735, hAPP(_1551731, _1551737)))], (39640 ^ _780086) ^ [_1551791, _1551793, _1551795, _1551797, _1551799, _1551801] : [-(hAPP(c_Set_Ovimage(_1551791, _1551793, hAPP(c_Fun_Ocomp(_1551795, _1551793, _1551791, _1551797), _1551799)), _1551801) = hAPP(c_Set_Ovimage(_1551791, _1551795, _1551799), hAPP(c_Set_Ovimage(_1551795, _1551793, _1551797), _1551801)))], (39642 ^ _780086) ^ [_1551853, _1551855, _1551857, _1551859, _1551861, _1551863, _1551865] : [-(hAPP(c_Fun_Ocomp(_1551853, _1551855, _1551857, _1551859), hAPP(c_Fun_Ocomp(_1551861, _1551853, _1551857, _1551863), _1551865)) = hAPP(c_Fun_Ocomp(_1551861, _1551855, _1551857, hAPP(c_Fun_Ocomp(_1551853, _1551855, _1551861, _1551859), _1551863)), _1551865))], (39644 ^ _780086) ^ [_1551920, _1551922, _1551924, _1551926, _1551928, _1551930] : [-(hAPP(hAPP(c_Fun_Ocomp(_1551920, _1551922, _1551924, _1551926), _1551928), _1551930) = hAPP(_1551926, hAPP(_1551928, _1551930)))], (39646 ^ _780086) ^ [_1551970, _1551972, _1551974, _1551976, _1551978, _1551980, _1551982, _1551984, _1551986] : [hAPP(c_Fun_Ocomp(_1551970, _1551972, _1551974, _1551976), _1551978) = hAPP(c_Fun_Ocomp(_1551980, _1551972, _1551974, _1551982), _1551984), -(hAPP(_1551976, hAPP(_1551978, _1551986)) = hAPP(_1551982, hAPP(_1551984, _1551986)))], (39652 ^ _780086) ^ [_1552117, _1552119, _1552121, _1552123, _1552125, _1552127, _1552129, _1552131] : [hAPP(c_Fun_Ocomp(_1552117, _1552119, _1552121, _1552123), _1552125) = hAPP(c_Fun_Ocomp(_1552127, _1552119, _1552121, _1552129), _1552131), 39655 ^ _780086 : [(39656 ^ _780086) ^ [_1552232] : [-(hAPP(_1552123, hAPP(_1552125, _1552232)) = hAPP(_1552129, hAPP(_1552131, _1552232)))]]], (39658 ^ _780086) ^ [_1552271, _1552273] : [39659 ^ _780086 : [(39660 ^ _780086) ^ [_1552317] : [hBOOL(hAPP(_1552271, _1552317))]], -(hBOOL(hAPP(_1552271, c_Hilbert__Choice_OEps(_1552273, _1552271))))], (39664 ^ _780086) ^ [_1552375, _1552377, _1552379] : [hBOOL(hAPP(_1552375, _1552377)), -(hBOOL(hAPP(_1552375, c_Hilbert__Choice_OEps(_1552379, _1552375))))], (39670 ^ _780086) ^ [_1552468, _1552470, _1552472, _1552474, _1552476, _1552478, _1552480, _1552482, _1552484, _1552486, _1552488] : [hAPP(_1552468, hAPP(_1552470, _1552472)) = hAPP(_1552474, hAPP(_1552476, _1552478)), -(hAPP(hAPP(c_Fun_Ocomp(_1552480, _1552482, _1552484, _1552468), _1552470), _1552472) = hAPP(hAPP(c_Fun_Ocomp(_1552486, _1552482, _1552488, _1552474), _1552476), _1552478))], (39676 ^ _780086) ^ [_1552631, _1552633, _1552635, _1552637, _1552639, _1552641, _1552643] : [hAPP(c_Fun_Ocomp(_1552631, _1552633, _1552635, _1552637), _1552639) = _1552641, -(hAPP(_1552637, hAPP(_1552639, _1552643)) = hAPP(_1552641, _1552643))], (39682 ^ _780086) ^ [_1552752, _1552754, _1552756, _1552758, _1552760] : [c_Finite__Set_Ofun__left__comm(_1552752, _1552754, _1552756), -(hAPP(c_Fun_Ocomp(_1552754, _1552754, _1552754, hAPP(_1552756, _1552758)), hAPP(_1552756, _1552760)) = hAPP(c_Fun_Ocomp(_1552754, _1552754, _1552754, hAPP(_1552756, _1552760)), hAPP(_1552756, _1552758)))], (39688 ^ _780086) ^ [_1552893, _1552895] : [39689 ^ _780086 : [(39690 ^ _780086) ^ [_1552939] : [hBOOL(hAPP(_1552893, _1552939))]], -(hBOOL(hAPP(_1552893, c_Hilbert__Choice_OEps(_1552895, _1552893))))], (39694 ^ _780086) ^ [_1553012, _1553014] : [hBOOL(hAPP(_1553012, c_Hilbert__Choice_OEps(_1553014, _1553012))), -(hBOOL(hAPP(_1553012, 39697 ^ [_1553012, _1553014])))], (39701 ^ _780086) ^ [_1553111, _1553113] : [39702 ^ _780086 : [(39703 ^ _780086) ^ [_1553157] : [hBOOL(hAPP(_1553111, _1553157))]], -(hBOOL(hAPP(_1553111, c_Hilbert__Choice_OEps(_1553113, _1553111))))], (39707 ^ _780086) ^ [_1553217, _1553219] : [-(c_Hilbert__Choice_OEps(_1553217, hAPP(hAPP(c_COMBC(_1553217, _1553217, tc_HOL_Obool), c_fequal), _1553219)) = _1553219)], (39709 ^ _780086) ^ [_1553255, _1553257] : [-(c_Hilbert__Choice_OEps(_1553255, hAPP(c_fequal, _1553257)) = _1553257)], (39711 ^ _780086) ^ [_1553286, _1553288, _1553290, _1553292, _1553294, _1553296] : [-(hAPP(hAPP(c_Fun_Ocomp(_1553286, _1553288, _1553290, hAPP(c_COMBK(_1553288, _1553286), _1553292)), _1553294), _1553296) = _1553292)], (39713 ^ _780086) ^ [_1553336, _1553338, _1553340, _1553342, _1553344, _1553346] : [-(hAPP(hAPP(c_Fun_Ocomp(_1553336, _1553338, _1553340, _1553342), _1553344), _1553346) = hAPP(_1553342, hAPP(_1553344, _1553346)))], (39715 ^ _780086) ^ [_1553386, _1553388, _1553390] : [39716 ^ _780086 : [(39717 ^ _780086) ^ [_1553440] : [hBOOL(hAPP(_1553386, _1553440))]], _1553388 = c_Hilbert__Choice_OEps(_1553390, _1553386), -(hBOOL(hAPP(_1553386, _1553388)))], (39725 ^ _780086) ^ [_1553546, _1553548, _1553550, _1553552, _1553554, _1553556, _1553558] : [-(hAPP(c_Product__Type_Oapsnd(_1553546, _1553548, _1553550, _1553552), hAPP(c_Product__Type_Oapsnd(_1553554, _1553546, _1553550, _1553556), _1553558)) = hAPP(c_Product__Type_Oapsnd(_1553554, _1553548, _1553550, hAPP(c_Fun_Ocomp(_1553546, _1553548, _1553554, _1553552), _1553556)), _1553558))], (39727 ^ _780086) ^ [_1553613, _1553615, _1553617, _1553619, _1553621, _1553623, _1553625] : [-(hAPP(c_Product__Type_Oapfst(_1553613, _1553615, _1553617, _1553619), hAPP(c_Product__Type_Oapfst(_1553621, _1553613, _1553617, _1553623), _1553625)) = hAPP(c_Product__Type_Oapfst(_1553621, _1553615, _1553617, hAPP(c_Fun_Ocomp(_1553613, _1553615, _1553621, _1553619), _1553623)), _1553625))], (39729 ^ _780086) ^ [_1553680, _1553682, _1553684, _1553686, _1553688, _1553690] : [c_Fun_Oinj__on(_1553680, _1553682, hAPP(c_Fun_Ocomp(_1553684, _1553682, _1553680, _1553686), _1553688), _1553690), -(c_Fun_Oinj__on(_1553680, _1553684, _1553688, _1553690))], (39735 ^ _780086) ^ [_1553789, _1553791, _1553793, _1553795, _1553797] : [c_Fun_Oinj__on(_1553789, _1553791, _1553793, c_Orderings_Otop__class_Otop(tc_fun(_1553789, tc_HOL_Obool))), c_Fun_Oinj__on(_1553795, _1553789, _1553797, c_Orderings_Otop__class_Otop(tc_fun(_1553795, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1553795, _1553791, hAPP(c_Fun_Ocomp(_1553789, _1553791, _1553795, _1553793), _1553797), c_Orderings_Otop__class_Otop(tc_fun(_1553795, tc_HOL_Obool))))], (39745 ^ _780086) ^ [_1553988, _1553990, _1553992, _1553994, _1553996] : [hAPP(c_Set_Oimage(_1553988, _1553990, _1553992), c_Orderings_Otop__class_Otop(tc_fun(_1553988, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1553990, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1553990, _1553994, _1553996), c_Orderings_Otop__class_Otop(tc_fun(_1553990, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1553994, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1553988, _1553994, hAPP(c_Fun_Ocomp(_1553990, _1553994, _1553988, _1553996), _1553992)), c_Orderings_Otop__class_Otop(tc_fun(_1553988, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1553994, tc_HOL_Obool)))], (39755 ^ _780086) ^ [_1554247, _1554249, _1554251, _1554253, _1554255, _1554257] : [c_Fun_Oinj__on(_1554247, _1554249, _1554251, _1554253), 39758 ^ _780086 : [(39759 ^ _780086) ^ [] : [c_Fun_Oinj__on(_1554249, _1554255, _1554257, hAPP(c_Set_Oimage(_1554247, _1554249, _1554251), _1554253)), -(c_Fun_Oinj__on(_1554247, _1554255, hAPP(c_Fun_Ocomp(_1554249, _1554255, _1554247, _1554257), _1554251), _1554253))], (39765 ^ _780086) ^ [] : [c_Fun_Oinj__on(_1554247, _1554255, hAPP(c_Fun_Ocomp(_1554249, _1554255, _1554247, _1554257), _1554251), _1554253), -(c_Fun_Oinj__on(_1554249, _1554255, _1554257, hAPP(c_Set_Oimage(_1554247, _1554249, _1554251), _1554253)))]]], (39771 ^ _780086) ^ [_1554539, _1554541, _1554543, _1554545, _1554547, _1554549] : [c_Fun_Oinj__on(_1554539, _1554541, _1554543, _1554545), c_Fun_Oinj__on(_1554541, _1554547, _1554549, hAPP(c_Set_Oimage(_1554539, _1554541, _1554543), _1554545)), -(c_Fun_Oinj__on(_1554539, _1554547, hAPP(c_Fun_Ocomp(_1554541, _1554547, _1554539, _1554549), _1554543), _1554545))], (39781 ^ _780086) ^ [_1554726, _1554728, _1554730, _1554732, _1554734, _1554736] : [c_Fun_Oinj__on(_1554726, _1554728, hAPP(c_Fun_Ocomp(_1554730, _1554728, _1554726, _1554732), _1554734), _1554736), -(c_Fun_Oinj__on(_1554730, _1554728, _1554732, hAPP(c_Set_Oimage(_1554726, _1554730, _1554734), _1554736)))], (39787 ^ _780086) ^ [_1554849, _1554851, _1554853, _1554855, _1554857, _1554859] : [-(hAPP(c_Set_Oimage(_1554849, _1554851, hAPP(c_Fun_Ocomp(_1554853, _1554851, _1554849, _1554855), _1554857)), _1554859) = hAPP(c_Set_Oimage(_1554853, _1554851, _1554855), hAPP(c_Set_Oimage(_1554849, _1554853, _1554857), _1554859)))], (39789 ^ _780086) ^ [_1554911, _1554913, _1554915, _1554917, _1554919, _1554921, _1554923, _1554925, _1554927, _1554929, _1554931] : [-(hAPP(c_Product__Type_Omap__pair(_1554911, _1554913, _1554915, _1554917, _1554919, _1554921), hAPP(c_Product__Type_Omap__pair(_1554923, _1554911, _1554925, _1554915, _1554927, _1554929), _1554931)) = hAPP(c_Product__Type_Omap__pair(_1554923, _1554913, _1554925, _1554917, hAPP(c_Fun_Ocomp(_1554911, _1554913, _1554923, _1554919), _1554927), hAPP(c_Fun_Ocomp(_1554915, _1554917, _1554925, _1554921), _1554929)), _1554931))], (39791 ^ _780086) ^ [_1555000, _1555002, _1555004, _1555006, _1555008, _1555010, _1555012, _1555014, _1555016, _1555018] : [-(c_Product__Type_Omap__pair(_1555000, _1555002, _1555004, _1555006, hAPP(c_Fun_Ocomp(_1555008, _1555002, _1555000, _1555010), _1555012), hAPP(c_Fun_Ocomp(_1555014, _1555006, _1555004, _1555016), _1555018)) = hAPP(c_Fun_Ocomp(tc_prod(_1555008, _1555014), tc_prod(_1555002, _1555006), tc_prod(_1555000, _1555004), c_Product__Type_Omap__pair(_1555008, _1555002, _1555014, _1555006, _1555010, _1555016)), c_Product__Type_Omap__pair(_1555000, _1555008, _1555004, _1555014, _1555012, _1555018)))], (39793 ^ _780086) ^ [_1555095, _1555097, _1555099, _1555101, _1555103, _1555105, _1555107, _1555109, _1555111, _1555113] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1555095, _1555097), tc_prod(_1555099, _1555101), tc_prod(_1555103, _1555105), c_Product__Type_Omap__pair(_1555095, _1555099, _1555097, _1555101, _1555107, _1555109)), c_Product__Type_Omap__pair(_1555103, _1555095, _1555105, _1555097, _1555111, _1555113)) = c_Product__Type_Omap__pair(_1555103, _1555099, _1555105, _1555101, hAPP(c_Fun_Ocomp(_1555095, _1555099, _1555103, _1555107), _1555111), hAPP(c_Fun_Ocomp(_1555097, _1555101, _1555105, _1555109), _1555113)))], (39795 ^ _780086) ^ [_1555190, _1555192, _1555194, _1555196, _1555198, _1555200] : [class_Groups_Ocomm__monoid__add(_1555190), c_Fun_Oinj__on(_1555192, _1555194, _1555196, _1555198), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1555194, _1555190), _1555200), hAPP(c_Set_Oimage(_1555192, _1555194, _1555196), _1555198)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1555192, _1555190), hAPP(c_Fun_Ocomp(_1555194, _1555190, _1555192, _1555200), _1555196)), _1555198))], (39805 ^ _780086) ^ [_1555403, _1555405, _1555407, _1555409, _1555411, _1555413] : [class_Groups_Ocomm__monoid__mult(_1555403), c_Fun_Oinj__on(_1555405, _1555407, _1555409, _1555411), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1555407, _1555403), _1555413), hAPP(c_Set_Oimage(_1555405, _1555407, _1555409), _1555411)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1555405, _1555403), hAPP(c_Fun_Ocomp(_1555407, _1555403, _1555405, _1555413), _1555409)), _1555411))], (39815 ^ _780086) ^ [_1555616, _1555618, _1555620, _1555622, _1555624, _1555626, _1555628, _1555630] : [class_Groups_Ocomm__monoid__mult(_1555616), c_Fun_Oinj__on(_1555618, _1555620, _1555622, _1555624), _1555626 = hAPP(c_Set_Oimage(_1555618, _1555620, _1555622), _1555624), _1555628 = hAPP(c_Fun_Ocomp(_1555620, _1555616, _1555618, _1555630), _1555622), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1555620, _1555616), _1555630), _1555626) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1555618, _1555616), _1555628), _1555624))], (39833 ^ _780086) ^ [_1555965, _1555967, _1555969, _1555971] : [-(c_Hilbert__Choice_OEps(tc_prod(_1555965, _1555967), hAPP(c_Product__Type_Oprod_Oprod__case(_1555965, _1555967, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1555965, tc_fun(_1555967, tc_HOL_Obool), tc_fun(_1555967, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1555967, tc_HOL_Obool), tc_fun(_1555967, tc_HOL_Obool)), _1555965), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1555967)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1555965), c_fconj), hAPP(c_fequal, _1555969)))), hAPP(c_fequal, _1555971)))) = hAPP(hAPP(c_Product__Type_OPair(_1555965, _1555967), _1555969), _1555971))], (39835 ^ _780086) ^ [_1556071, _1556073, _1556075] : [-(c_Hilbert__Choice_OEps(tc_prod(_1556071, _1556073), _1556075) = c_Hilbert__Choice_OEps(tc_prod(_1556071, _1556073), hAPP(c_Product__Type_Oprod_Oprod__case(_1556071, _1556073, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1556073, tc_prod(_1556071, _1556073)), tc_fun(_1556073, tc_HOL_Obool), _1556071), hAPP(c_COMBB(tc_prod(_1556071, _1556073), tc_HOL_Obool, _1556073), _1556075)), c_Product__Type_OPair(_1556071, _1556073)))))], (39837 ^ _780086) ^ [_1556149, _1556151, _1556153, _1556155, _1556157] : [class_Groups_Ocomm__monoid__add(_1556149), hBOOL(hAPP(c_Finite__Set_Ofinite(_1556151), _1556153)), c_Fun_Oinj__on(_1556151, _1556151, _1556155, _1556153), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1556151, _1556149), _1556157), hAPP(c_Set_Oimage(_1556151, _1556151, _1556155), _1556153)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1556151, _1556149), hAPP(c_Fun_Ocomp(_1556151, _1556149, _1556151, _1556157), _1556155)), _1556153))], (39851 ^ _780086) ^ [_1556424, _1556426, _1556428, _1556430, _1556432] : [class_Groups_Ocomm__monoid__mult(_1556424), hBOOL(hAPP(c_Finite__Set_Ofinite(_1556426), _1556428)), c_Fun_Oinj__on(_1556426, _1556426, _1556430, _1556428), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1556426, _1556424), _1556432), hAPP(c_Set_Oimage(_1556426, _1556426, _1556430), _1556428)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1556426, _1556424), hAPP(c_Fun_Ocomp(_1556426, _1556424, _1556426, _1556432), _1556430)), _1556428))], (39865 ^ _780086) ^ [_1556699, _1556701, _1556703, _1556705, _1556707, _1556709, _1556711] : [c_Fun_Oinj__on(_1556699, _1556701, _1556703, hAPP(c_Set_Oimage(_1556705, _1556699, _1556707), _1556709)), c_Fun_Oinj__on(_1556705, _1556699, _1556707, _1556709), hBOOL(hAPP(hAPP(c_member(_1556701), _1556711), hAPP(c_Set_Oimage(_1556699, _1556701, _1556703), hAPP(c_Set_Oimage(_1556705, _1556699, _1556707), _1556709)))), -(hAPP(c_Fun_Othe__inv__into(_1556705, _1556701, _1556709, hAPP(c_Fun_Ocomp(_1556699, _1556701, _1556705, _1556703), _1556707)), _1556711) = hAPP(hAPP(c_Fun_Ocomp(_1556699, _1556705, _1556701, c_Fun_Othe__inv__into(_1556705, _1556699, _1556709, _1556707)), c_Fun_Othe__inv__into(_1556699, _1556701, hAPP(c_Set_Oimage(_1556705, _1556699, _1556707), _1556709), _1556703)), _1556711))], (39879 ^ _780086) ^ [_1557062, _1557064, _1557066, _1557068, _1557070, _1557072, _1557074] : [class_Groups_Oab__semigroup__mult(_1557062), hBOOL(hAPP(c_Finite__Set_Ofinite(_1557064), _1557066)), c_Fun_Oinj__on(_1557064, _1557068, _1557070, _1557066), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1557062, _1557068, c_Groups_Otimes__class_Otimes(_1557062)), _1557072), _1557074), hAPP(c_Set_Oimage(_1557064, _1557068, _1557070), _1557066)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1557062, _1557064, c_Groups_Otimes__class_Otimes(_1557062)), hAPP(c_Fun_Ocomp(_1557068, _1557062, _1557064, _1557072), _1557070)), _1557074), _1557066))], (39893 ^ _780086) ^ [_1557373, _1557375, _1557377, _1557379, _1557381, _1557383] : [c_Finite__Set_Ofolding(_1557373, _1557375, _1557377, _1557379), hBOOL(hAPP(c_Finite__Set_Ofinite(_1557373), _1557381)), hBOOL(hAPP(hAPP(c_member(_1557373), _1557383), _1557381)), -(hAPP(_1557379, _1557381) = hAPP(c_Fun_Ocomp(_1557375, _1557375, _1557375, hAPP(_1557379, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1557373, tc_HOL_Obool)), _1557381), hAPP(hAPP(c_Set_Oinsert(_1557373), _1557383), c_Orderings_Obot__class_Obot(tc_fun(_1557373, tc_HOL_Obool)))))), hAPP(_1557377, _1557383)))], (39907 ^ _780086) ^ [_1557686, _1557688, _1557690, _1557692, _1557694, _1557696, _1557698, _1557700] : [c_Finite__Set_Ofolding__image(_1557686, _1557688, _1557690, _1557692, _1557694), hBOOL(hAPP(c_Finite__Set_Ofinite(_1557688), _1557696)), c_Fun_Oinj__on(_1557688, _1557688, _1557698, _1557696), -(hAPP(hAPP(_1557694, _1557700), hAPP(c_Set_Oimage(_1557688, _1557688, _1557698), _1557696)) = hAPP(hAPP(_1557694, hAPP(c_Fun_Ocomp(_1557688, _1557686, _1557688, _1557700), _1557698)), _1557696))], (39921 ^ _780086) ^ [_1557975, _1557977, _1557979, _1557981, _1557983, _1557985] : [c_Finite__Set_Ofolding(_1557975, _1557977, _1557979, _1557981), hBOOL(hAPP(c_Finite__Set_Ofinite(_1557975), _1557983)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1557975), _1557985)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1557975, tc_HOL_Obool)), _1557983), _1557985) = c_Orderings_Obot__class_Obot(tc_fun(_1557975, tc_HOL_Obool)), -(hAPP(_1557981, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1557975, tc_HOL_Obool)), _1557983), _1557985)) = hAPP(c_Fun_Ocomp(_1557977, _1557977, _1557977, hAPP(_1557981, _1557983)), hAPP(_1557981, _1557985)))], (39939 ^ _780086) ^ [_1558348, _1558350, _1558352, _1558354, _1558356, _1558358, _1558360, _1558362, _1558364, _1558366, _1558368] : [c_Finite__Set_Ofolding(_1558348, _1558350, _1558352, _1558354), -(hAPP(c_Fun_Ocomp(_1558356, _1558358, _1558360, _1558362), hAPP(c_Fun_Ocomp(_1558364, _1558356, _1558360, _1558366), _1558368)) = hAPP(c_Fun_Ocomp(_1558364, _1558358, _1558360, hAPP(c_Fun_Ocomp(_1558356, _1558358, _1558364, _1558362), _1558366)), _1558368))], (39945 ^ _780086) ^ [_1558511, _1558513, _1558515, _1558517, _1558519, _1558521] : [c_Finite__Set_Ofolding(_1558511, _1558513, _1558515, _1558517), -(hAPP(c_Fun_Ocomp(_1558513, _1558513, _1558513, hAPP(_1558515, _1558519)), hAPP(_1558515, _1558521)) = hAPP(c_Fun_Ocomp(_1558513, _1558513, _1558513, hAPP(_1558515, _1558521)), hAPP(_1558515, _1558519)))], (39951 ^ _780086) ^ [_1558656, _1558658, _1558660, _1558662, _1558664, _1558666, _1558668, _1558670] : [c_Finite__Set_Ofolding(_1558656, _1558658, _1558660, _1558662), -(hAPP(c_Fun_Ocomp(_1558658, _1558658, _1558664, hAPP(_1558660, _1558666)), hAPP(c_Fun_Ocomp(_1558658, _1558658, _1558664, hAPP(_1558660, _1558668)), _1558670)) = hAPP(c_Fun_Ocomp(_1558658, _1558658, _1558664, hAPP(_1558660, _1558668)), hAPP(c_Fun_Ocomp(_1558658, _1558658, _1558664, hAPP(_1558660, _1558666)), _1558670)))], (39957 ^ _780086) ^ [_1558837, _1558839, _1558841, _1558843, _1558845, _1558847] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1558837, tc_fun(_1558839, tc_HOL_Obool)), _1558841), hAPP(c_Fun_Ocomp(_1558843, tc_fun(_1558839, tc_HOL_Obool), _1558837, _1558845), _1558847)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1558843, tc_fun(_1558839, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1558837, _1558843, _1558847), _1558841)), _1558845))], (39959 ^ _780086) ^ [_1558912, _1558914, _1558916, _1558918, _1558920, _1558922] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1558912, _1558914), _1558912, tc_prod(_1558916, _1558918), c_Product__Type_Ofst(_1558912, _1558914)), c_Product__Type_Omap__pair(_1558916, _1558912, _1558918, _1558914, _1558920, _1558922)) = hAPP(c_Fun_Ocomp(_1558916, _1558912, tc_prod(_1558916, _1558918), _1558920), c_Product__Type_Ofst(_1558916, _1558918)))], (39961 ^ _780086) ^ [_1558983, _1558985, _1558987, _1558989, _1558991, _1558993] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1558983, _1558985), _1558985, tc_prod(_1558987, _1558989), c_Product__Type_Osnd(_1558983, _1558985)), c_Product__Type_Omap__pair(_1558987, _1558983, _1558989, _1558985, _1558991, _1558993)) = hAPP(c_Fun_Ocomp(_1558989, _1558985, tc_prod(_1558987, _1558989), _1558993), c_Product__Type_Osnd(_1558987, _1558989)))], (39963 ^ _780086) ^ [_1559054, _1559056, _1559058, _1559060, _1559062, _1559064, _1559066, _1559068] : [c_Finite__Set_Ofolding__image(_1559054, _1559056, _1559058, _1559060, _1559062), hBOOL(hAPP(c_Finite__Set_Ofinite(_1559056), _1559064)), -(hAPP(hAPP(_1559062, hAPP(hAPP(c_COMBS(_1559056, _1559054, _1559054), hAPP(hAPP(c_COMBB(_1559054, tc_fun(_1559054, _1559054), _1559056), _1559058), _1559066)), _1559068)), _1559064) = hAPP(hAPP(_1559058, hAPP(hAPP(_1559062, _1559066), _1559064)), hAPP(hAPP(_1559062, _1559068), _1559064)))], (39973 ^ _780086) ^ [_1559315, _1559317, _1559319, _1559321, _1559323, _1559325, _1559327] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1559315, _1559317, _1559319), hAPP(c_Fun_Ocomp(_1559321, tc_fun(_1559317, _1559319), _1559315, _1559323), _1559325)), _1559327) = hAPP(hAPP(_1559323, hAPP(_1559325, hAPP(c_Product__Type_Ofst(_1559315, _1559317), _1559327))), hAPP(c_Product__Type_Osnd(_1559315, _1559317), _1559327)))], (39975 ^ _780086) ^ [_1559392, _1559394, _1559396, _1559398, _1559400, _1559402] : [c_Finite__Set_Ofolding(_1559392, _1559394, _1559396, _1559398), hBOOL(hAPP(c_Finite__Set_Ofinite(_1559392), _1559400)), -(hAPP(c_Fun_Ocomp(_1559394, _1559394, _1559394, hAPP(_1559396, _1559402)), hAPP(_1559398, _1559400)) = hAPP(c_Fun_Ocomp(_1559394, _1559394, _1559394, hAPP(_1559398, _1559400)), hAPP(_1559396, _1559402)))], (39985 ^ _780086) ^ [_1559605, _1559607, _1559609, _1559611, _1559613, _1559615, _1559617, _1559619] : [c_Finite__Set_Ofolding(_1559605, _1559607, _1559609, _1559611), hBOOL(hAPP(c_Finite__Set_Ofinite(_1559605), _1559613)), -(hAPP(c_Fun_Ocomp(_1559607, _1559607, _1559615, hAPP(_1559609, _1559617)), hAPP(c_Fun_Ocomp(_1559607, _1559607, _1559615, hAPP(_1559611, _1559613)), _1559619)) = hAPP(c_Fun_Ocomp(_1559607, _1559607, _1559615, hAPP(_1559611, _1559613)), hAPP(c_Fun_Ocomp(_1559607, _1559607, _1559615, hAPP(_1559609, _1559617)), _1559619)))], (39995 ^ _780086) ^ [_1559858, _1559860, _1559862, _1559864, _1559866, _1559868] : [c_Finite__Set_Ofolding(_1559858, _1559860, _1559862, _1559864), hBOOL(hAPP(c_Finite__Set_Ofinite(_1559858), _1559866)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1559858), _1559868)), -(hAPP(c_Fun_Ocomp(_1559860, _1559860, _1559860, hAPP(_1559864, _1559868)), hAPP(_1559864, _1559866)) = hAPP(c_Fun_Ocomp(_1559860, _1559860, _1559860, hAPP(_1559864, _1559866)), hAPP(_1559864, _1559868)))], (40009 ^ _780086) ^ [_1560139, _1560141, _1560143, _1560145, _1560147, _1560149, _1560151, _1560153] : [c_Finite__Set_Ofolding(_1560139, _1560141, _1560143, _1560145), hBOOL(hAPP(c_Finite__Set_Ofinite(_1560139), _1560147)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1560139), _1560149)), -(hAPP(c_Fun_Ocomp(_1560141, _1560141, _1560151, hAPP(_1560145, _1560149)), hAPP(c_Fun_Ocomp(_1560141, _1560141, _1560151, hAPP(_1560145, _1560147)), _1560153)) = hAPP(c_Fun_Ocomp(_1560141, _1560141, _1560151, hAPP(_1560145, _1560147)), hAPP(c_Fun_Ocomp(_1560141, _1560141, _1560151, hAPP(_1560145, _1560149)), _1560153)))], (40023 ^ _780086) ^ [_1560464, _1560466, _1560468, _1560470] : [c_Finite__Set_Ofolding(_1560464, _1560466, _1560468, _1560470), -(hAPP(_1560470, c_Orderings_Obot__class_Obot(tc_fun(_1560464, tc_HOL_Obool))) = c_Fun_Oid(_1560466))], (40029 ^ _780086) ^ [_1560569, _1560571, _1560573, _1560575, _1560577, _1560579] : [c_Finite__Set_Ofolding(_1560569, _1560571, _1560573, _1560575), hBOOL(hAPP(c_Finite__Set_Ofinite(_1560569), _1560577)), -(hAPP(hAPP(_1560575, _1560577), _1560579) = hAPP(hAPP(c_Finite__Set_Ofold(_1560569, _1560571, _1560573), _1560579), _1560577))], (40039 ^ _780086) ^ [_1560758, _1560760, _1560762, _1560764, _1560766, _1560768, _1560770] : [c_Finite__Set_Ofolding__image(_1560758, _1560760, _1560762, _1560764, _1560766), hBOOL(hAPP(c_Finite__Set_Ofinite(_1560760), _1560768)), -(hAPP(hAPP(_1560766, _1560770), _1560768) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1560758, _1560760, _1560762), _1560770), _1560764), _1560768))], (40049 ^ _780086) ^ [_1560959, _1560961, _1560963, _1560965, _1560967, _1560969] : [c_Finite__Set_Ofolding(_1560959, _1560961, _1560963, _1560965), hBOOL(hAPP(c_Finite__Set_Ofinite(_1560959), _1560967)), -(hBOOL(hAPP(hAPP(c_member(_1560959), _1560969), _1560967))), -(hAPP(_1560965, hAPP(hAPP(c_Set_Oinsert(_1560959), _1560969), _1560967)) = hAPP(c_Fun_Ocomp(_1560961, _1560961, _1560961, hAPP(_1560965, _1560967)), hAPP(_1560963, _1560969)))], (40063 ^ _780086) ^ [_1561195, _1561197, _1561199, _1561201, _1561203, _1561205] : [c_Finite__Set_Ofolding(_1561195, _1561197, _1561199, _1561201), hBOOL(hAPP(c_Finite__Set_Ofinite(_1561195), _1561203)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1561195), _1561205)), -(hAPP(c_Fun_Ocomp(_1561197, _1561197, _1561197, hAPP(_1561201, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1561195, tc_HOL_Obool)), _1561203), _1561205))), hAPP(_1561201, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1561195, tc_HOL_Obool)), _1561203), _1561205))) = hAPP(c_Fun_Ocomp(_1561197, _1561197, _1561197, hAPP(_1561201, _1561203)), hAPP(_1561201, _1561205)))], (40077 ^ _780086) ^ [_1561520, _1561522, _1561524, _1561526, _1561528, _1561530] : [c_Finite__Set_Ofolding(_1561520, _1561522, _1561524, _1561526), hBOOL(hAPP(c_Finite__Set_Ofinite(_1561520), _1561528)), -(hAPP(_1561526, hAPP(hAPP(c_Set_Oinsert(_1561520), _1561530), _1561528)) = hAPP(c_Fun_Ocomp(_1561522, _1561522, _1561522, hAPP(_1561526, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1561520, tc_HOL_Obool)), _1561528), hAPP(hAPP(c_Set_Oinsert(_1561520), _1561530), c_Orderings_Obot__class_Obot(tc_fun(_1561520, tc_HOL_Obool)))))), hAPP(_1561524, _1561530)))], (40087 ^ _780086) ^ [_1561775, _1561777, _1561779, _1561781, _1561783, _1561785, _1561787] : [c_Hoare__Mirabelle_Ohoare__derivs(_1561775, _1561777, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1561775)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1561775), c_Hoare__Mirabelle_Opeek__and(_1561775, _1561779, _1561781)), _1561783), _1561785)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1561775), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_1561775, _1561777, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1561775)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1561775), c_Hoare__Mirabelle_Opeek__and(_1561775, _1561779, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate, c_fNot), _1561781))), _1561787), _1561785)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1561775), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_1561775, _1561777, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1561775)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1561775), _1561779), c_Com_Ocom_OCond(_1561781, _1561783, _1561787)), _1561785)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1561775), tc_HOL_Obool)))))], (40097 ^ _780086) ^ [_1562128, _1562130, _1562132, _1562134, _1562136] : [c_Hoare__Mirabelle_Ohoare__derivs(_1562128, _1562130, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1562128)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1562128), c_Hoare__Mirabelle_Opeek__and(_1562128, _1562132, _1562134)), _1562136), _1562132)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1562128), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_1562128, _1562130, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1562128)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1562128), _1562132), c_Com_Ocom_OWhile(_1562134, _1562136)), c_Hoare__Mirabelle_Opeek__and(_1562128, _1562132, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate, c_fNot), _1562134)))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1562128), tc_HOL_Obool)))))], (40103 ^ _780086) ^ [_1562355, _1562357, _1562359, _1562361, _1562363, _1562365] : [class_Groups_Ocomm__monoid__add(_1562355), hBOOL(hAPP(c_Finite__Set_Ofinite(_1562357), _1562359)), 40113 ^ _780086 : [(40114 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1562357), 40112 ^ [_1562355, _1562357, _1562359, _1562361, _1562363, _1562365]), _1562359)))], (40117 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1562357), 40115 ^ [_1562355, _1562357, _1562359, _1562361, _1562363, _1562365]), _1562359)))], (40119 ^ _780086) ^ [] : [40112 ^ [_1562355, _1562357, _1562359, _1562361, _1562363, _1562365] = 40115 ^ [_1562355, _1562357, _1562359, _1562361, _1562363, _1562365]], (40121 ^ _780086) ^ [] : [-(hAPP(_1562361, 40112 ^ [_1562355, _1562357, _1562359, _1562361, _1562363, _1562365]) = hAPP(_1562361, 40115 ^ [_1562355, _1562357, _1562359, _1562361, _1562363, _1562365]))], (40123 ^ _780086) ^ [] : [hAPP(_1562363, hAPP(_1562361, 40112 ^ [_1562355, _1562357, _1562359, _1562361, _1562363, _1562365])) = c_Groups_Ozero__class_Ozero(_1562355)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1562365, _1562355), _1562363), hAPP(c_Set_Oimage(_1562357, _1562365, _1562361), _1562359)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1562357, _1562355), hAPP(c_Fun_Ocomp(_1562365, _1562355, _1562357, _1562363), _1562361)), _1562359))], (40127 ^ _780086) ^ [_1563116, _1563118, _1563120, _1563122, _1563124] : [hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(_1563116, _1563118, _1563120), _1563122), _1563124)), 40130 ^ _780086 : [(40131 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(_1563118, _1563122), _1563124)))], (40133 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1563120, _1563124)))]]], (40135 ^ _780086) ^ [_1563253, _1563255, _1563257, _1563259, _1563261] : [-(hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(_1563253, _1563255, _1563257), _1563259), _1563261))), hBOOL(hAPP(hAPP(_1563255, _1563259), _1563261)), hBOOL(hAPP(_1563257, _1563261))], (40145 ^ _780086) ^ [_1563428, _1563430, _1563432, _1563434, _1563436, _1563438] : [c_Finite__Set_Ofolding__idem(_1563428, _1563430, _1563432, _1563434), hBOOL(hAPP(c_Finite__Set_Ofinite(_1563428), _1563436)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1563428), _1563438)), -(hAPP(_1563434, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1563428, tc_HOL_Obool)), _1563436), _1563438)) = hAPP(c_Fun_Ocomp(_1563430, _1563430, _1563430, hAPP(_1563434, _1563436)), hAPP(_1563434, _1563438)))], (40159 ^ _780086) ^ [_1563709, _1563711, _1563713, _1563715, _1563717, _1563719] : [c_Finite__Set_Ofolding__idem(_1563709, _1563711, _1563713, _1563715), hBOOL(hAPP(c_Finite__Set_Ofinite(_1563709), _1563717)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1563709, tc_HOL_Obool)), _1563719), _1563717)), -(hAPP(c_Fun_Ocomp(_1563711, _1563711, _1563711, hAPP(_1563715, _1563717)), hAPP(_1563715, _1563719)) = hAPP(_1563715, _1563717))], (40173 ^ _780086) ^ [_1563980, _1563982, _1563984, _1563986, _1563988, _1563990] : [c_Finite__Set_Ofolding__idem(_1563980, _1563982, _1563984, _1563986), hBOOL(hAPP(c_Finite__Set_Ofinite(_1563980), _1563988)), -(hAPP(_1563986, hAPP(hAPP(c_Set_Oinsert(_1563980), _1563990), _1563988)) = hAPP(c_Fun_Ocomp(_1563982, _1563982, _1563982, hAPP(_1563986, _1563988)), hAPP(_1563984, _1563990)))], (40183 ^ _780086) ^ [_1564187, _1564189, _1564191, _1564193, _1564195, _1564197, _1564199] : [c_Finite__Set_Ofolding__idem(_1564187, _1564189, _1564191, _1564193), -(hAPP(c_Fun_Ocomp(_1564189, _1564189, _1564195, hAPP(_1564191, _1564197)), hAPP(c_Fun_Ocomp(_1564189, _1564189, _1564195, hAPP(_1564191, _1564197)), _1564199)) = hAPP(c_Fun_Ocomp(_1564189, _1564189, _1564195, hAPP(_1564191, _1564197)), _1564199))], (40189 ^ _780086) ^ [_1564344, _1564346, _1564348, _1564350, _1564352] : [c_Finite__Set_Ofolding__idem(_1564344, _1564346, _1564348, _1564350), -(hAPP(c_Fun_Ocomp(_1564346, _1564346, _1564346, hAPP(_1564348, _1564352)), hAPP(_1564348, _1564352)) = hAPP(_1564348, _1564352))], (40195 ^ _780086) ^ [_1564465, _1564467, _1564469, _1564471, _1564473, _1564475] : [c_Finite__Set_Ofolding__idem(_1564465, _1564467, _1564469, _1564471), hBOOL(hAPP(c_Finite__Set_Ofinite(_1564465), _1564473)), hBOOL(hAPP(hAPP(c_member(_1564465), _1564475), _1564473)), -(hAPP(c_Fun_Ocomp(_1564467, _1564467, _1564467, hAPP(_1564471, _1564473)), hAPP(_1564469, _1564475)) = hAPP(_1564471, _1564473))], (40209 ^ _780086) ^ [_1564730, _1564732, _1564734, _1564736, _1564738, _1564740, _1564742, _1564744] : [class_Groups_Ocomm__monoid__mult(_1564730), c_Fun_Oinj__on(_1564732, _1564734, _1564736, _1564738), _1564740 = hAPP(c_Set_Oimage(_1564732, _1564734, _1564736), _1564738), 40223 ^ _780086 : [(40224 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1564732), 40222 ^ [_1564730, _1564732, _1564734, _1564736, _1564738, _1564740, _1564742, _1564744]), _1564738)))], (40226 ^ _780086) ^ [] : [hAPP(_1564742, 40222 ^ [_1564730, _1564732, _1564734, _1564736, _1564738, _1564740, _1564742, _1564744]) = hAPP(hAPP(c_Fun_Ocomp(_1564734, _1564730, _1564732, _1564744), _1564736), 40222 ^ [_1564730, _1564732, _1564734, _1564736, _1564738, _1564740, _1564742, _1564744])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1564734, _1564730), _1564744), _1564740) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1564732, _1564730), _1564742), _1564738))], (40230 ^ _780086) ^ [_1565238, _1565240, _1565242, _1565244, _1565246, _1565248] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1565238, tc_HOL_Obool)), _1565240), _1565242)), 40236 ^ _780086 : [(40237 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1565238), 40235 ^ [_1565238, _1565240, _1565242, _1565244, _1565246, _1565248]), _1565240)))], (40239 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1565244, tc_HOL_Obool)), hAPP(_1565246, 40235 ^ [_1565238, _1565240, _1565242, _1565244, _1565246, _1565248])), hAPP(_1565248, 40235 ^ [_1565238, _1565240, _1565242, _1565244, _1565246, _1565248])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1565238, _1565244), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1565238, _1565244), _1565240), _1565246)), hAPP(hAPP(c_Product__Type_OSigma(_1565238, _1565244), _1565242), _1565248))))], (40243 ^ _780086) ^ [_1565628, _1565630, _1565632] : [-(hBOOL(hAPP(hAPP(c_member(_1565628), _1565630), c_Wellfounded_Oacc(_1565628, _1565632)))), 40247 ^ _780086 : [(40248 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1565628, _1565628)), hAPP(hAPP(c_Product__Type_OPair(_1565628, _1565628), 40246 ^ [_1565628, _1565630, _1565632]), _1565630)), _1565632)))], (40250 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1565628), 40246 ^ [_1565628, _1565630, _1565632]), c_Wellfounded_Oacc(_1565628, _1565632)))]]], (40252 ^ _780086) ^ [_1565855, _1565857, _1565859] : [40254 ^ _780086 : [(40255 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1565855, _1565855)), hAPP(hAPP(c_Product__Type_OPair(_1565855, _1565855), 40253 ^ [_1565855, _1565857, _1565859]), _1565857)), _1565859)))], (40257 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1565855), 40253 ^ [_1565855, _1565857, _1565859]), c_Wellfounded_Oacc(_1565855, _1565859)))]], -(hBOOL(hAPP(hAPP(c_member(_1565855), _1565857), c_Wellfounded_Oacc(_1565855, _1565859))))], (40261 ^ _780086) ^ [_1566114, _1566116, _1566118, _1566120] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1566114, tc_HOL_Obool), tc_fun(_1566114, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1566114, tc_HOL_Obool), tc_fun(_1566114, tc_HOL_Obool)), _1566116), _1566118)), c_Wellfounded_Omax__ext(_1566114, _1566120))), 40264 ^ _780086 : [(40265 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1566114), _1566116)))], (40267 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1566114), _1566118)))], (40269 ^ _780086) ^ [] : [_1566118 = c_Orderings_Obot__class_Obot(tc_fun(_1566114, tc_HOL_Obool))], (40271 ^ _780086) ^ [_1566408] : [hBOOL(hAPP(hAPP(c_member(_1566114), _1566408), _1566116)), 40275 ^ _780086 : [(40276 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1566114), 40274 ^ [_1566114, _1566116, _1566118, _1566120, _1566408]), _1566118)))], (40278 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1566114, _1566114)), hAPP(hAPP(c_Product__Type_OPair(_1566114, _1566114), _1566408), 40274 ^ [_1566114, _1566116, _1566118, _1566120, _1566408])), _1566120)))]]]]], (40280 ^ _780086) ^ [_1566620, _1566622, _1566624, _1566626] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1566620, tc_HOL_Obool), tc_fun(_1566620, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1566620, tc_HOL_Obool), tc_fun(_1566620, tc_HOL_Obool)), _1566622), _1566624)), c_Wellfounded_Omax__ext(_1566620, _1566626)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1566620), _1566622)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1566620), _1566624)), -(_1566624 = c_Orderings_Obot__class_Obot(tc_fun(_1566620, tc_HOL_Obool))), 40294 ^ _780086 : [(40295 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1566620), 40293 ^ [_1566620, _1566622, _1566624, _1566626]), _1566622)))], (40297 ^ _780086) ^ [_1567025] : [hBOOL(hAPP(hAPP(c_member(_1566620), _1567025), _1566624)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1566620, _1566620)), hAPP(hAPP(c_Product__Type_OPair(_1566620, _1566620), 40293 ^ [_1566620, _1566622, _1566624, _1566626]), _1567025)), _1566626))]]], (40305 ^ _780086) ^ [_1567253, _1567255, _1567257] : [c_Wellfounded_Owf(_1567253, _1567255), hBOOL(hAPP(hAPP(c_member(tc_prod(_1567253, _1567253)), hAPP(hAPP(c_Product__Type_OPair(_1567253, _1567253), hAPP(_1567257, hAPP(c_Nat_OSuc, 40308 ^ [_1567253, _1567255, _1567257]))), hAPP(_1567257, 40308 ^ [_1567253, _1567255, _1567257]))), _1567255))], (40312 ^ _780086) ^ [_1567454, _1567456, _1567458, _1567460, _1567462, _1567464, _1567466] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1567454, _1567456, _1567458, _1567460), _1567462), _1567464), _1567466) = hAPP(hAPP(_1567464, hAPP(c_Product__Type_Ofst(_1567456, _1567458), hAPP(_1567462, _1567466))), hAPP(c_Product__Type_Osnd(_1567456, _1567458), hAPP(_1567462, _1567466))))], (40314 ^ _780086) ^ [_1567527, _1567529, _1567531, _1567533, _1567535, _1567537, _1567539, _1567541] : [class_Groups_Ocomm__monoid__add(_1567527), class_Orderings_Oord(_1567529), _1567531 = _1567533, _1567535 = _1567537, 40332 ^ _780086 : [(40333 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1567529), _1567533), 40331 ^ [_1567527, _1567529, _1567531, _1567533, _1567535, _1567537, _1567539, _1567541])))], (40335 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1567529), 40331 ^ [_1567527, _1567529, _1567531, _1567533, _1567535, _1567537, _1567539, _1567541]), _1567537)))], (40337 ^ _780086) ^ [] : [hAPP(_1567539, 40331 ^ [_1567527, _1567529, _1567531, _1567533, _1567535, _1567537, _1567539, _1567541]) = hAPP(_1567541, 40331 ^ [_1567527, _1567529, _1567531, _1567533, _1567535, _1567537, _1567539, _1567541])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1567529, _1567527), _1567539), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1567529, _1567531), _1567535)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1567529, _1567527), _1567541), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1567529, _1567533), _1567537)))], (40341 ^ _780086) ^ [_1568171, _1568173] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1568171), _1568173)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1568171), _1568173)))], (40347 ^ _780086) ^ [_1568276, _1568278] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1568276), _1568278)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1568276), _1568278)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (40353 ^ _780086) ^ [_1568387, _1568389, _1568391, _1568393, _1568395] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1568387, _1568389, _1568387, _1568391), hAPP(c_Product__Type_OPair(_1568389, _1568387), _1568393)), _1568395) = hAPP(_1568395, _1568393))], (40355 ^ _780086) ^ [_1568438, _1568440, _1568442, _1568444] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1568438, _1568440, _1568442, tc_prod(_1568440, _1568442)), _1568444), c_Product__Type_OPair(_1568440, _1568442)) = _1568444)], (40357 ^ _780086) ^ [_1568484, _1568486, _1568488, _1568490, _1568492, _1568494, _1568496, _1568498, _1568500] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1568484, _1568486, _1568488, _1568490), hAPP(hAPP(c_Product__Type_Oscomp(_1568484, _1568492, _1568494, tc_prod(_1568486, _1568488)), _1568496), _1568498)), _1568500) = hAPP(hAPP(c_Product__Type_Oscomp(_1568484, _1568492, _1568494, _1568490), _1568496), hAPP(hAPP(c_COMBC(_1568492, tc_fun(_1568486, tc_fun(_1568488, _1568490)), tc_fun(_1568494, _1568490)), hAPP(hAPP(c_COMBB(tc_fun(_1568494, tc_prod(_1568486, _1568488)), tc_fun(tc_fun(_1568486, tc_fun(_1568488, _1568490)), tc_fun(_1568494, _1568490)), _1568492), c_Product__Type_Oscomp(_1568494, _1568486, _1568488, _1568490)), _1568498)), _1568500)))], (40359 ^ _780086) ^ [_1568611, _1568613] : [c_Wellfounded_Owf(_1568611, _1568613), -(c_Wellfounded_Owf(_1568611, c_Transitive__Closure_Otrancl(_1568611, _1568613)))], (40365 ^ _780086) ^ [_1568694, _1568696, _1568698, _1568700, _1568702, _1568704, _1568706] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1568694, _1568696, _1568698, _1568700), _1568702), _1568704), _1568706) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1568696, _1568698, _1568700), _1568704), hAPP(_1568702, _1568706)))], (40367 ^ _780086) ^ [_1568756, _1568758, _1568760, _1568762, _1568764, _1568766, _1568768] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1568756, _1568758, _1568760, _1568762), _1568764), _1568766), _1568768) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1568758, _1568760, _1568762), _1568766), hAPP(_1568764, _1568768)))], (40369 ^ _780086) ^ [] : [-(c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (40371 ^ _780086) ^ [_1568851, _1568853] : [c_Wellfounded_Oacyclic(_1568851, _1568853), 40374 ^ _780086 : [(40375 ^ _780086) ^ [_1568936] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1568851, _1568851)), hAPP(hAPP(c_Product__Type_OPair(_1568851, _1568851), _1568936), _1568936)), c_Transitive__Closure_Otrancl(_1568851, _1568853)))]]], (40377 ^ _780086) ^ [_1568979, _1568981] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1568979, _1568979)), hAPP(hAPP(c_Product__Type_OPair(_1568979, _1568979), 40378 ^ [_1568979, _1568981]), 40378 ^ [_1568979, _1568981])), c_Transitive__Closure_Otrancl(_1568979, _1568981)))), -(c_Wellfounded_Oacyclic(_1568979, _1568981))], (40384 ^ _780086) ^ [_1569053, _1569055, _1569057, _1569059] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1569053, _1569053)), hAPP(hAPP(c_Product__Type_OPair(_1569053, _1569053), _1569055), _1569057)), _1569059)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1569053, _1569053)), hAPP(hAPP(c_Product__Type_OPair(_1569053, _1569053), _1569055), _1569057)), c_Transitive__Closure_Otrancl(_1569053, _1569059))))], (40390 ^ _780086) ^ [_1569216, _1569218] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1569216, _1569216), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1569216, _1569218)), hAPP(hAPP(c_Product__Type_OSigma(_1569216, _1569216), hAPP(c_Relation_OField(_1569216), _1569218)), hAPP(c_COMBK(tc_fun(_1569216, tc_HOL_Obool), _1569216), hAPP(c_Relation_OField(_1569216), _1569218))))))], (40392 ^ _780086) ^ [_1569285, _1569287, _1569289] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1569285, _1569285), tc_HOL_Obool)), _1569287), _1569289)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1569285, _1569285), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1569285, _1569285, _1569285), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1569285, _1569285), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1569285, _1569287)), _1569289)), _1569287)), _1569289)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1569285, _1569285), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1569285, _1569287)), _1569289)))], (40402 ^ _780086) ^ [_1569556, _1569558, _1569560] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1569556, _1569556)), _1569558), _1569560)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1569556, _1569556)), _1569558), c_Transitive__Closure_Otrancl(_1569556, _1569560))))], (40408 ^ _780086) ^ [_1569681] : [-(c_Transitive__Closure_Otrancl(_1569681, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1569681, _1569681), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1569681, _1569681), tc_HOL_Obool)))], (40410 ^ _780086) ^ [_1569723, _1569725] : [-(hAPP(c_Relation_ODomain(_1569723, _1569723), c_Transitive__Closure_Otrancl(_1569723, _1569725)) = hAPP(c_Relation_ODomain(_1569723, _1569723), _1569725))], (40412 ^ _780086) ^ [_1569763, _1569765] : [-(hAPP(c_Relation_ORange(_1569763, _1569763), c_Transitive__Closure_Otrancl(_1569763, _1569765)) = hAPP(c_Relation_ORange(_1569763, _1569763), _1569765))], (40414 ^ _780086) ^ [_1569818, _1569820] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1569818, _1569818)), c_Transitive__Closure_Otrancl(_1569818, _1569820))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1569818, _1569818)), _1569820)))], (40420 ^ _780086) ^ [_1569925, _1569927] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1569925, _1569925)), _1569927)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1569925, _1569925)), c_Transitive__Closure_Otrancl(_1569925, _1569927))))], (40426 ^ _780086) ^ [_1570038, _1570040, _1570042, _1570044, _1570046] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1570038, _1570038)), hAPP(hAPP(c_Product__Type_OPair(_1570038, _1570038), _1570040), _1570042)), c_Transitive__Closure_Otrancl(_1570038, _1570044))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1570038, _1570038)), hAPP(hAPP(c_Product__Type_OPair(_1570038, _1570038), _1570042), _1570046)), c_Transitive__Closure_Otrancl(_1570038, _1570044))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1570038, _1570038)), hAPP(hAPP(c_Product__Type_OPair(_1570038, _1570038), _1570040), _1570046)), c_Transitive__Closure_Otrancl(_1570038, _1570044))))], (40436 ^ _780086) ^ [_1570311, _1570313, _1570315, _1570317, _1570319] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1570311, _1570311)), hAPP(hAPP(c_Product__Type_OPair(_1570311, _1570311), _1570313), _1570315)), c_Transitive__Closure_Otrancl(_1570311, _1570317))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1570311, _1570311)), hAPP(hAPP(c_Product__Type_OPair(_1570311, _1570311), _1570315), _1570319)), _1570317)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1570311, _1570311)), hAPP(hAPP(c_Product__Type_OPair(_1570311, _1570311), _1570313), _1570319)), c_Transitive__Closure_Otrancl(_1570311, _1570317))))], (40446 ^ _780086) ^ [_1570578, _1570580, _1570582, _1570584, _1570586] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1570578, _1570578)), hAPP(hAPP(c_Product__Type_OPair(_1570578, _1570578), _1570580), _1570582)), _1570584)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1570578, _1570578)), hAPP(hAPP(c_Product__Type_OPair(_1570578, _1570578), _1570582), _1570586)), c_Transitive__Closure_Otrancl(_1570578, _1570584))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1570578, _1570578)), hAPP(hAPP(c_Product__Type_OPair(_1570578, _1570578), _1570580), _1570586)), c_Transitive__Closure_Otrancl(_1570578, _1570584))))], (40456 ^ _780086) ^ [_1570845, _1570847, _1570849, _1570851, _1570853] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1570845, _1570845)), hAPP(hAPP(c_Product__Type_OPair(_1570845, _1570845), _1570847), _1570849)), _1570851)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1570845, _1570845)), hAPP(hAPP(c_Product__Type_OPair(_1570845, _1570845), _1570849), _1570853)), _1570851)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1570845, _1570845)), hAPP(hAPP(c_Product__Type_OPair(_1570845, _1570845), _1570847), _1570853)), c_Transitive__Closure_Otrancl(_1570845, _1570851))))], (40466 ^ _780086) ^ [_1571106, _1571108, _1571110, _1571112] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1571106, _1571106)), _1571108), c_Transitive__Closure_Otrancl(_1571106, _1571110))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1571106, _1571106), tc_HOL_Obool)), _1571110), _1571112)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1571106, _1571106)), _1571108), c_Transitive__Closure_Otrancl(_1571106, _1571112))))], (40476 ^ _780086) ^ [_1571321, _1571323] : [-(c_Transitive__Closure_Otrancl(_1571321, _1571323) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1571321, _1571321), tc_HOL_Obool)), _1571323), hAPP(hAPP(c_Relation_Orel__comp(_1571321, _1571321, _1571321), c_Transitive__Closure_Otrancl(_1571321, _1571323)), _1571323)))], (40478 ^ _780086) ^ [_1571376, _1571378, _1571380] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1571376, _1571376), tc_HOL_Obool)), _1571378), hAPP(hAPP(c_Product__Type_OSigma(_1571376, _1571376), _1571380), hAPP(c_COMBK(tc_fun(_1571376, tc_HOL_Obool), _1571376), _1571380)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1571376, _1571376), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1571376, _1571378)), hAPP(hAPP(c_Product__Type_OSigma(_1571376, _1571376), _1571380), hAPP(c_COMBK(tc_fun(_1571376, tc_HOL_Obool), _1571376), _1571380)))))], (40484 ^ _780086) ^ [_1571603, _1571605, _1571607, _1571609, _1571611] : [_1571603 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Random_Oiterate(_1571605, _1571607, _1571603, _1571609), _1571611) = hAPP(c_Product__Type_OPair(_1571605, _1571607), _1571611))], (40490 ^ _780086) ^ [_1571708, _1571710, _1571712, _1571714, _1571716] : [-(_1571708 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_Random_Oiterate(_1571710, _1571712, _1571708, _1571714), _1571716) = hAPP(hAPP(c_Product__Type_Oscomp(_1571712, _1571710, _1571712, tc_prod(_1571710, _1571712)), hAPP(_1571714, _1571716)), c_Random_Oiterate(_1571710, _1571712, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1571708), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1571714)))], (40496 ^ _780086) ^ [_1571788, _1571790, _1571792, _1571794] : [-(c_Transitive__Closure_Otrancl(_1571788, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1571788, _1571788)), hAPP(hAPP(c_Product__Type_OPair(_1571788, _1571788), _1571790), _1571792)), _1571794)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1571788, _1571788), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1571788, _1571794)), hAPP(c_Set_OCollect(tc_prod(_1571788, _1571788)), hAPP(c_Product__Type_Oprod_Oprod__case(_1571788, _1571788, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1571788, tc_fun(_1571788, tc_HOL_Obool), tc_fun(_1571788, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1571788, tc_HOL_Obool), tc_fun(_1571788, tc_HOL_Obool)), _1571788), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1571788)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1571788), c_fconj), hAPP(hAPP(c_COMBC(_1571788, tc_fun(tc_prod(_1571788, _1571788), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1571788, _1571788), tc_fun(tc_fun(tc_prod(_1571788, _1571788), tc_HOL_Obool), tc_HOL_Obool), _1571788), c_member(tc_prod(_1571788, _1571788))), hAPP(hAPP(c_COMBC(_1571788, _1571788, tc_prod(_1571788, _1571788)), c_Product__Type_OPair(_1571788, _1571788)), _1571790))), c_Transitive__Closure_Ortrancl(_1571788, _1571794))))), hAPP(hAPP(c_COMBC(_1571788, tc_fun(tc_prod(_1571788, _1571788), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1571788, _1571788), tc_fun(tc_fun(tc_prod(_1571788, _1571788), tc_HOL_Obool), tc_HOL_Obool), _1571788), c_member(tc_prod(_1571788, _1571788))), hAPP(c_Product__Type_OPair(_1571788, _1571788), _1571792))), c_Transitive__Closure_Ortrancl(_1571788, _1571794)))))))], (40498 ^ _780086) ^ [_1572035, _1572037, _1572039] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1572035, _1572035)), _1572037), _1572039)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1572035, _1572035)), _1572037), c_Transitive__Closure_Ortrancl(_1572035, _1572039))))], (40504 ^ _780086) ^ [_1572160, _1572162, _1572164] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1572160, _1572160)), hAPP(hAPP(c_Product__Type_OPair(_1572160, _1572160), _1572162), _1572162)), c_Transitive__Closure_Ortrancl(_1572160, _1572164))))], (40506 ^ _780086) ^ [_1572209, _1572211, _1572213, _1572215] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1572209, _1572209)), hAPP(hAPP(c_Product__Type_OPair(_1572209, _1572209), _1572211), _1572213)), c_Transitive__Closure_Otrancl(_1572209, _1572215))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1572209, _1572209)), hAPP(hAPP(c_Product__Type_OPair(_1572209, _1572209), _1572211), _1572213)), c_Transitive__Closure_Ortrancl(_1572209, _1572215))))], (40512 ^ _780086) ^ [_1572378, _1572380] : [-(c_Transitive__Closure_Ortrancl(_1572378, c_Transitive__Closure_Otrancl(_1572378, _1572380)) = c_Transitive__Closure_Ortrancl(_1572378, _1572380))], (40514 ^ _780086) ^ [_1572412, _1572414] : [-(c_Transitive__Closure_Otrancl(_1572412, c_Transitive__Closure_Ortrancl(_1572412, _1572414)) = c_Transitive__Closure_Ortrancl(_1572412, _1572414))], (40516 ^ _780086) ^ [_1572446, _1572448] : [-(c_Transitive__Closure_Otrancl(_1572446, _1572448) = hAPP(hAPP(c_Relation_Orel__comp(_1572446, _1572446, _1572446), c_Transitive__Closure_Ortrancl(_1572446, _1572448)), _1572448))], (40518 ^ _780086) ^ [_1572487, _1572489] : [-(c_Transitive__Closure_Otrancl(_1572487, _1572489) = hAPP(hAPP(c_Relation_Orel__comp(_1572487, _1572487, _1572487), _1572489), c_Transitive__Closure_Ortrancl(_1572487, _1572489)))], (40520 ^ _780086) ^ [_1572528, _1572530] : [-(hAPP(c_Relation_ODomain(_1572528, _1572528), c_Transitive__Closure_Ortrancl(_1572528, _1572530)) = c_Orderings_Otop__class_Otop(tc_fun(_1572528, tc_HOL_Obool)))], (40522 ^ _780086) ^ [_1572567, _1572569] : [-(hAPP(c_Relation_ORange(_1572567, _1572567), c_Transitive__Closure_Ortrancl(_1572567, _1572569)) = c_Orderings_Otop__class_Otop(tc_fun(_1572567, tc_HOL_Obool)))], (40524 ^ _780086) ^ [_1572606, _1572608, _1572610, _1572612] : [40525 ^ _780086 : [(40526 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1572606, _1572606)), _1572608), c_Transitive__Closure_Ortrancl(_1572606, _1572610)))], (40528 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1572606, _1572606)), _1572608), c_Transitive__Closure_Ortrancl(_1572606, _1572612)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1572606, _1572606)), _1572608), c_Transitive__Closure_Ortrancl(_1572606, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1572606, _1572606), tc_HOL_Obool)), _1572610), _1572612)))))], (40532 ^ _780086) ^ [_1572831, _1572833] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1572831, _1572831, _1572831), _1572833), c_Transitive__Closure_Ortrancl(_1572831, _1572833)) = hAPP(hAPP(c_Relation_Orel__comp(_1572831, _1572831, _1572831), c_Transitive__Closure_Ortrancl(_1572831, _1572833)), _1572833))], (40534 ^ _780086) ^ [_1572882, _1572884] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1572882, _1572882, _1572882), c_Transitive__Closure_Ortrancl(_1572882, _1572884)), c_Transitive__Closure_Ortrancl(_1572882, _1572884)) = c_Transitive__Closure_Ortrancl(_1572882, _1572884))], (40536 ^ _780086) ^ [_1572926, _1572928, _1572930] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1572926, _1572926), tc_HOL_Obool)), _1572928), c_Transitive__Closure_Ortrancl(_1572926, _1572930))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1572926, _1572926), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1572926, _1572928)), c_Transitive__Closure_Ortrancl(_1572926, _1572930))))], (40542 ^ _780086) ^ [_1573075, _1573077, _1573079] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1573075, _1573075), tc_HOL_Obool)), _1573077), _1573079)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1573075, _1573075), tc_HOL_Obool)), _1573079), c_Transitive__Closure_Ortrancl(_1573075, _1573077))), -(c_Transitive__Closure_Ortrancl(_1573075, _1573079) = c_Transitive__Closure_Ortrancl(_1573075, _1573077))], (40552 ^ _780086) ^ [_1573278, _1573280, _1573282] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1573278, _1573278), tc_HOL_Obool)), _1573280), _1573282)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1573278, _1573278), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1573278, _1573280)), c_Transitive__Closure_Ortrancl(_1573278, _1573282))))], (40558 ^ _780086) ^ [_1573421, _1573423, _1573425] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1573421, _1573421), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1573421, _1573421), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1573421, _1573423)), c_Transitive__Closure_Ortrancl(_1573421, _1573425))), c_Transitive__Closure_Ortrancl(_1573421, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1573421, _1573421), tc_HOL_Obool)), _1573423), _1573425)))))], (40560 ^ _780086) ^ [_1573498, _1573500, _1573502] : [-(c_Transitive__Closure_Ortrancl(_1573498, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1573498, _1573498), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1573498, _1573500)), c_Transitive__Closure_Ortrancl(_1573498, _1573502))) = c_Transitive__Closure_Ortrancl(_1573498, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1573498, _1573498), tc_HOL_Obool)), _1573500), _1573502)))], (40562 ^ _780086) ^ [_1573565, _1573567, _1573569] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1573565, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1573565, _1573565, _1573567), _1573569)), _1573569)), -(hAPP(c_Relation_OImage(_1573565, _1573565, c_Transitive__Closure_Ortrancl(_1573565, _1573567)), _1573569) = _1573569)], (40568 ^ _780086) ^ [_1573698, _1573700] : [-(c_Transitive__Closure_Ortrancl(_1573698, c_Transitive__Closure_Ortrancl(_1573698, _1573700)) = c_Transitive__Closure_Ortrancl(_1573698, _1573700))], (40570 ^ _780086) ^ [_1573732, _1573734, _1573736, _1573738, _1573740] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1573732, _1573732)), hAPP(hAPP(c_Product__Type_OPair(_1573732, _1573732), _1573734), _1573736)), c_Transitive__Closure_Ortrancl(_1573732, _1573738))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1573732, _1573732)), hAPP(hAPP(c_Product__Type_OPair(_1573732, _1573732), _1573736), _1573740)), c_Transitive__Closure_Ortrancl(_1573732, _1573738))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1573732, _1573732)), hAPP(hAPP(c_Product__Type_OPair(_1573732, _1573732), _1573734), _1573740)), c_Transitive__Closure_Ortrancl(_1573732, _1573738))))], (40580 ^ _780086) ^ [_1574005, _1574007, _1574009, _1574011, _1574013] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1574005, _1574005)), hAPP(hAPP(c_Product__Type_OPair(_1574005, _1574005), _1574007), _1574009)), c_Transitive__Closure_Ortrancl(_1574005, _1574011))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1574005, _1574005)), hAPP(hAPP(c_Product__Type_OPair(_1574005, _1574005), _1574009), _1574013)), _1574011)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1574005, _1574005)), hAPP(hAPP(c_Product__Type_OPair(_1574005, _1574005), _1574007), _1574013)), c_Transitive__Closure_Ortrancl(_1574005, _1574011))))], (40590 ^ _780086) ^ [_1574272, _1574274, _1574276, _1574278, _1574280] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1574272, _1574272)), hAPP(hAPP(c_Product__Type_OPair(_1574272, _1574272), _1574274), _1574276)), _1574278)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1574272, _1574272)), hAPP(hAPP(c_Product__Type_OPair(_1574272, _1574272), _1574276), _1574280)), c_Transitive__Closure_Ortrancl(_1574272, _1574278))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1574272, _1574272)), hAPP(hAPP(c_Product__Type_OPair(_1574272, _1574272), _1574274), _1574280)), c_Transitive__Closure_Ortrancl(_1574272, _1574278))))], (40600 ^ _780086) ^ [_1574539, _1574541] : [-(c_Relation_Orefl__on(_1574539, c_Orderings_Otop__class_Otop(tc_fun(_1574539, tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1574539, _1574541)))], (40602 ^ _780086) ^ [_1574573, _1574575, _1574577, _1574579, _1574581] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1574573, _1574573)), hAPP(hAPP(c_Product__Type_OPair(_1574573, _1574573), _1574575), _1574577)), c_Transitive__Closure_Ortrancl(_1574573, _1574579))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1574573, _1574573)), hAPP(hAPP(c_Product__Type_OPair(_1574573, _1574573), _1574577), _1574581)), c_Transitive__Closure_Otrancl(_1574573, _1574579))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1574573, _1574573)), hAPP(hAPP(c_Product__Type_OPair(_1574573, _1574573), _1574575), _1574581)), c_Transitive__Closure_Otrancl(_1574573, _1574579))))], (40612 ^ _780086) ^ [_1574846, _1574848, _1574850, _1574852, _1574854] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1574846, _1574846)), hAPP(hAPP(c_Product__Type_OPair(_1574846, _1574846), _1574848), _1574850)), c_Transitive__Closure_Otrancl(_1574846, _1574852))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1574846, _1574846)), hAPP(hAPP(c_Product__Type_OPair(_1574846, _1574846), _1574850), _1574854)), c_Transitive__Closure_Ortrancl(_1574846, _1574852))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1574846, _1574846)), hAPP(hAPP(c_Product__Type_OPair(_1574846, _1574846), _1574848), _1574854)), c_Transitive__Closure_Otrancl(_1574846, _1574852))))], (40622 ^ _780086) ^ [_1575119, _1575121, _1575123, _1575125, _1575127] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1575119, _1575119)), hAPP(hAPP(c_Product__Type_OPair(_1575119, _1575119), _1575121), _1575123)), c_Transitive__Closure_Ortrancl(_1575119, _1575125))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1575119, _1575119)), hAPP(hAPP(c_Product__Type_OPair(_1575119, _1575119), _1575123), _1575127)), _1575125)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1575119, _1575119)), hAPP(hAPP(c_Product__Type_OPair(_1575119, _1575119), _1575121), _1575127)), c_Transitive__Closure_Otrancl(_1575119, _1575125))))], (40632 ^ _780086) ^ [_1575386, _1575388, _1575390, _1575392] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1575386, _1575386)), hAPP(hAPP(c_Product__Type_OPair(_1575386, _1575386), _1575388), _1575390)), c_Transitive__Closure_Ortrancl(_1575386, _1575392))), -(_1575388 = _1575390), 40639 ^ _780086 : [(40640 ^ _780086) ^ [] : [_1575388 = _1575390], (40642 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1575386, _1575386)), hAPP(hAPP(c_Product__Type_OPair(_1575386, _1575386), _1575388), _1575390)), c_Transitive__Closure_Otrancl(_1575386, _1575392))))]]], (40644 ^ _780086) ^ [_1575648, _1575650, _1575652, _1575654, _1575656] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1575648, _1575648)), hAPP(hAPP(c_Product__Type_OPair(_1575648, _1575648), _1575650), _1575652)), _1575654)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1575648, _1575648)), hAPP(hAPP(c_Product__Type_OPair(_1575648, _1575648), _1575652), _1575656)), c_Transitive__Closure_Ortrancl(_1575648, _1575654))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1575648, _1575648)), hAPP(hAPP(c_Product__Type_OPair(_1575648, _1575648), _1575650), _1575656)), c_Transitive__Closure_Otrancl(_1575648, _1575654))))], (40654 ^ _780086) ^ [_1575936, _1575938, _1575940, _1575942] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1575936, _1575936)), hAPP(hAPP(c_Product__Type_OPair(_1575936, _1575936), _1575938), _1575940)), c_Transitive__Closure_Ortrancl(_1575936, _1575942))), -(_1575938 = _1575940), 40661 ^ _780086 : [(40662 ^ _780086) ^ [] : [_1575938 = _1575940], (40664 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1575936, _1575936)), hAPP(hAPP(c_Product__Type_OPair(_1575936, _1575936), _1575938), _1575940)), c_Transitive__Closure_Otrancl(_1575936, _1575942))))]]], (40666 ^ _780086) ^ [_1576194, _1576196, _1576198, _1576200] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1576194, _1576194)), hAPP(hAPP(c_Product__Type_OPair(_1576194, _1576194), _1576196), _1576198)), c_Transitive__Closure_Ortrancl(_1576194, _1576200)))), 40667 ^ _780086 : [(40668 ^ _780086) ^ [] : [_1576196 = _1576198], (40670 ^ _780086) ^ [] : [-(_1576196 = _1576198), hBOOL(hAPP(hAPP(c_member(tc_prod(_1576194, _1576194)), hAPP(hAPP(c_Product__Type_OPair(_1576194, _1576194), _1576196), _1576198)), c_Transitive__Closure_Otrancl(_1576194, _1576200)))]]], (40678 ^ _780086) ^ [_1576459, _1576461, _1576463, _1576465] : [-(hBOOL(hAPP(hAPP(c_member(_1576459), _1576461), hAPP(c_Relation_ODomain(_1576459, _1576459), _1576463)))), 40681 ^ _780086 : [(40682 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1576459, _1576459)), hAPP(hAPP(c_Product__Type_OPair(_1576459, _1576459), _1576461), _1576465)), c_Transitive__Closure_Ortrancl(_1576459, _1576463))), -(_1576461 = _1576465)], (40688 ^ _780086) ^ [] : [_1576461 = _1576465, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1576459, _1576459)), hAPP(hAPP(c_Product__Type_OPair(_1576459, _1576459), _1576461), _1576465)), c_Transitive__Closure_Ortrancl(_1576459, _1576463))))]]], (40694 ^ _780086) ^ [_1576755, _1576757, _1576759, _1576761] : [hBOOL(hAPP(hAPP(c_member(_1576755), _1576757), c_Wellfounded_Oacc(_1576755, _1576759))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1576755, _1576755)), hAPP(hAPP(c_Product__Type_OPair(_1576755, _1576755), _1576761), _1576757)), c_Transitive__Closure_Ortrancl(_1576755, _1576759))), -(hBOOL(hAPP(hAPP(c_member(_1576755), _1576761), c_Wellfounded_Oacc(_1576755, _1576759))))], (40704 ^ _780086) ^ [_1576976, _1576978, _1576980, _1576982] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1576976, _1576976)), hAPP(hAPP(c_Product__Type_OPair(_1576976, _1576976), _1576978), _1576980)), c_Transitive__Closure_Ortrancl(_1576976, _1576982))), hBOOL(hAPP(hAPP(c_member(_1576976), _1576980), c_Wellfounded_Oacc(_1576976, _1576982))), -(hBOOL(hAPP(hAPP(c_member(_1576976), _1576978), c_Wellfounded_Oacc(_1576976, _1576982))))], (40714 ^ _780086) ^ [_1577218, _1577220, _1577222, _1577224] : [c_Wellfounded_Owf(_1577218, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1577218, _1577218)), hAPP(hAPP(c_Product__Type_OPair(_1577218, _1577218), _1577220), _1577222)), _1577224)), 40717 ^ _780086 : [(40718 ^ _780086) ^ [] : [-(c_Wellfounded_Owf(_1577218, _1577224))], (40720 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1577218, _1577218)), hAPP(hAPP(c_Product__Type_OPair(_1577218, _1577218), _1577222), _1577220)), c_Transitive__Closure_Ortrancl(_1577218, _1577224)))]]], (40722 ^ _780086) ^ [_1577413, _1577415, _1577417, _1577419] : [-(c_Wellfounded_Owf(_1577413, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1577413, _1577413)), hAPP(hAPP(c_Product__Type_OPair(_1577413, _1577413), _1577415), _1577417)), _1577419))), c_Wellfounded_Owf(_1577413, _1577419), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1577413, _1577413)), hAPP(hAPP(c_Product__Type_OPair(_1577413, _1577413), _1577417), _1577415)), c_Transitive__Closure_Ortrancl(_1577413, _1577419))))], (40732 ^ _780086) ^ [_1577660, _1577662, _1577664, _1577666] : [c_Wellfounded_Oacyclic(_1577660, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1577660, _1577660)), hAPP(hAPP(c_Product__Type_OPair(_1577660, _1577660), _1577662), _1577664)), _1577666)), 40735 ^ _780086 : [(40736 ^ _780086) ^ [] : [-(c_Wellfounded_Oacyclic(_1577660, _1577666))], (40738 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1577660, _1577660)), hAPP(hAPP(c_Product__Type_OPair(_1577660, _1577660), _1577664), _1577662)), c_Transitive__Closure_Ortrancl(_1577660, _1577666)))]]], (40740 ^ _780086) ^ [_1577855, _1577857, _1577859, _1577861] : [-(c_Wellfounded_Oacyclic(_1577855, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1577855, _1577855)), hAPP(hAPP(c_Product__Type_OPair(_1577855, _1577855), _1577857), _1577859)), _1577861))), c_Wellfounded_Oacyclic(_1577855, _1577861), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1577855, _1577855)), hAPP(hAPP(c_Product__Type_OPair(_1577855, _1577855), _1577859), _1577857)), c_Transitive__Closure_Ortrancl(_1577855, _1577861))))], (40750 ^ _780086) ^ [_1578096, _1578098] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1578096), _1578098)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1578096), _1578098)))], (40756 ^ _780086) ^ [_1578201, _1578203] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1578201), _1578203)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1578201), _1578203)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (40762 ^ _780086) ^ [_1578312, _1578314, _1578316, _1578318, _1578320] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1578312, _1578312)), hAPP(hAPP(c_Product__Type_OPair(_1578312, _1578312), _1578314), _1578316)), c_Transitive__Closure_Ortrancl(_1578312, _1578318))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1578312, _1578312), tc_HOL_Obool)), _1578318), hAPP(hAPP(c_Product__Type_OSigma(_1578312, _1578312), _1578320), hAPP(c_COMBK(tc_fun(_1578312, tc_HOL_Obool), _1578312), _1578320)))), -(_1578314 = _1578316), -(hBOOL(hAPP(hAPP(c_member(_1578312), _1578314), _1578320)))], (40776 ^ _780086) ^ [_1578595, _1578597] : [40777 ^ _780086 : [(40778 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1578595), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))], (40780 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1578597), _1578595))]], -(c_Random_Olog(_1578595, _1578597) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (40784 ^ _780086) ^ [_1578730, _1578732] : [-(c_Random_Olog(_1578730, _1578732) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), c_Random_Olog(_1578730, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1578732), _1578730)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1578730), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1578732), _1578730)))], (40794 ^ _780086) ^ [_1578812, _1578814, _1578816] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1578812), _1578814)), -(c_Random_Ominus__shift(_1578816, _1578812, _1578814) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1578816), _1578812)), _1578814))], (40800 ^ _780086) ^ [_1578927, _1578929, _1578931] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1578927), _1578929))), -(c_Random_Ominus__shift(_1578931, _1578927, _1578929) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1578927), _1578929))], (40806 ^ _780086) ^ [_1578991, _1578993] : [_1578991 = _1578993, -(c_Random_Oinc__shift(_1578991, _1578993) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (40812 ^ _780086) ^ [_1579068, _1579070] : [-(_1579068 = _1579070), -(c_Random_Oinc__shift(_1579068, _1579070) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1579070), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))], (40818 ^ _780086) ^ [_1579115, _1579117] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1579115)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Orange(_1579115), _1579117))), _1579115)))], (40824 ^ _780086) ^ [_1579222, _1579224, _1579226] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1579222, _1579222), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1579222, _1579222), _1579224)), c_Transitive__Closure_Ortrancl(_1579222, _1579224)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1579222, _1579222), tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1579222, _1579222)), hAPP(hAPP(c_Product__Type_OPair(_1579222, _1579222), _1579226), _1579226)), c_Transitive__Closure_Otrancl(_1579222, _1579224)))], (40830 ^ _780086) ^ [_1579408, _1579410, _1579412, _1579414, _1579416] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1579408, _1579408)), hAPP(hAPP(c_Product__Type_OPair(_1579408, _1579408), hAPP(_1579410, hAPP(c_Nat_OSuc, 40831 ^ [_1579408, _1579410, _1579412, _1579414, _1579416]))), hAPP(_1579410, 40831 ^ [_1579408, _1579410, _1579412, _1579414, _1579416]))), c_Transitive__Closure_Ortrancl(_1579408, _1579412))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1579408, _1579408)), hAPP(hAPP(c_Product__Type_OPair(_1579408, _1579408), hAPP(_1579410, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1579414), _1579416))), hAPP(_1579410, _1579414))), c_Transitive__Closure_Ortrancl(_1579408, _1579412))))], (40837 ^ _780086) ^ [_1579716, _1579718] : [c_Wellfounded_Oacyclic(_1579716, hAPP(c_Relation_Oconverse(_1579716, _1579716), _1579718)), -(c_Wellfounded_Oacyclic(_1579716, _1579718))], (40843 ^ _780086) ^ [_1579801, _1579803] : [c_Wellfounded_Oacyclic(_1579801, _1579803), -(c_Wellfounded_Oacyclic(_1579801, hAPP(c_Relation_Oconverse(_1579801, _1579801), _1579803)))], (40849 ^ _780086) ^ [_1579892, _1579894, _1579896, _1579898, _1579900] : [-(hAPP(c_Relation_Oconverse(_1579892, _1579894), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1579896, tc_fun(tc_prod(_1579892, _1579894), tc_HOL_Obool)), _1579898), _1579900)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1579896, tc_fun(tc_prod(_1579894, _1579892), tc_HOL_Obool)), _1579898), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1579892, _1579894), tc_HOL_Obool), tc_fun(tc_prod(_1579894, _1579892), tc_HOL_Obool), _1579896), c_Relation_Oconverse(_1579892, _1579894)), _1579900)))], (40851 ^ _780086) ^ [_1579984, _1579986, _1579988, _1579990, _1579992] : [-(hAPP(c_Relation_Oconverse(_1579984, _1579986), hAPP(hAPP(c_Relation_Orel__comp(_1579984, _1579988, _1579986), _1579990), _1579992)) = hAPP(hAPP(c_Relation_Orel__comp(_1579986, _1579988, _1579984), hAPP(c_Relation_Oconverse(_1579988, _1579986), _1579992)), hAPP(c_Relation_Oconverse(_1579984, _1579988), _1579990)))], (40853 ^ _780086) ^ [_1580053, _1580055, _1580057, _1580059] : [-(hAPP(c_Relation_Oconverse(_1580053, _1580055), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1580053, _1580055), tc_HOL_Obool)), _1580057), _1580059)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1580055, _1580053), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1580053, _1580055), _1580057)), hAPP(c_Relation_Oconverse(_1580053, _1580055), _1580059)))], (40855 ^ _780086) ^ [_1580128, _1580130] : [-(hAPP(c_Relation_Oconverse(_1580128, _1580128), c_Relation_OId__on(_1580128, _1580130)) = c_Relation_OId__on(_1580128, _1580130))], (40857 ^ _780086) ^ [_1580165, _1580167, _1580169, _1580171] : [-(hAPP(c_Relation_Oconverse(_1580165, _1580165), hAPP(hAPP(c_Relation_Oinv__image(_1580167, _1580165), _1580169), _1580171)) = hAPP(hAPP(c_Relation_Oinv__image(_1580167, _1580165), hAPP(c_Relation_Oconverse(_1580167, _1580167), _1580169)), _1580171))], (40859 ^ _780086) ^ [_1580224, _1580226, _1580228, _1580230] : [-(hAPP(c_Relation_Oconverse(_1580224, _1580226), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1580224, _1580226), tc_HOL_Obool)), _1580228), _1580230)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1580226, _1580224), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1580224, _1580226), _1580228)), hAPP(c_Relation_Oconverse(_1580224, _1580226), _1580230)))], (40861 ^ _780086) ^ [_1580299, _1580301, _1580303] : [-(hAPP(c_Relation_Oconverse(_1580299, _1580301), hAPP(c_Relation_Oconverse(_1580301, _1580299), _1580303)) = _1580303)], (40863 ^ _780086) ^ [_1580356, _1580358, _1580360] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1580356, _1580358)), hAPP(c_Relation_Oconverse(_1580358, _1580356), _1580360))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1580358, _1580356)), _1580360)))], (40869 ^ _780086) ^ [_1580471, _1580473, _1580475] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1580473, _1580471)), _1580475)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1580471, _1580473)), hAPP(c_Relation_Oconverse(_1580473, _1580471), _1580475))))], (40875 ^ _780086) ^ [_1580592, _1580594] : [-(hAPP(c_Relation_OField(_1580592), hAPP(c_Relation_Oconverse(_1580592, _1580592), _1580594)) = hAPP(c_Relation_OField(_1580592), _1580594))], (40877 ^ _780086) ^ [_1580657, _1580659, _1580661, _1580663, _1580665] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1580657, _1580659)), hAPP(hAPP(c_Product__Type_OPair(_1580657, _1580659), _1580661), _1580663)), hAPP(c_Relation_Oconverse(_1580659, _1580657), _1580665))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1580659, _1580657)), hAPP(hAPP(c_Product__Type_OPair(_1580659, _1580657), _1580663), _1580661)), _1580665)))], (40883 ^ _780086) ^ [_1580824, _1580826, _1580828, _1580830, _1580832] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1580826, _1580824)), hAPP(hAPP(c_Product__Type_OPair(_1580826, _1580824), _1580830), _1580828)), _1580832)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1580824, _1580826)), hAPP(hAPP(c_Product__Type_OPair(_1580824, _1580826), _1580828), _1580830)), hAPP(c_Relation_Oconverse(_1580826, _1580824), _1580832))))], (40889 ^ _780086) ^ [_1580997, _1580999, _1581001, _1581003, _1581005] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1580997, _1580999)), hAPP(hAPP(c_Product__Type_OPair(_1580997, _1580999), _1581001), _1581003)), _1581005)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1580999, _1580997)), hAPP(hAPP(c_Product__Type_OPair(_1580999, _1580997), _1581003), _1581001)), hAPP(c_Relation_Oconverse(_1580997, _1580999), _1581005))))], (40895 ^ _780086) ^ [_1581168, _1581170, _1581172, _1581174, _1581176] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1581168, _1581170)), hAPP(hAPP(c_Product__Type_OPair(_1581168, _1581170), _1581172), _1581174)), hAPP(c_Relation_Oconverse(_1581170, _1581168), _1581176))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1581170, _1581168)), hAPP(hAPP(c_Product__Type_OPair(_1581170, _1581168), _1581174), _1581172)), _1581176)))], (40901 ^ _780086) ^ [_1581357, _1581359, _1581361] : [c_Relation_Orefl__on(_1581357, _1581359, hAPP(c_Relation_Oconverse(_1581357, _1581357), _1581361)), -(c_Relation_Orefl__on(_1581357, _1581359, _1581361))], (40907 ^ _780086) ^ [_1581448, _1581450, _1581452] : [c_Relation_Orefl__on(_1581448, _1581450, _1581452), -(c_Relation_Orefl__on(_1581448, _1581450, hAPP(c_Relation_Oconverse(_1581448, _1581448), _1581452)))], (40913 ^ _780086) ^ [_1581545, _1581547, _1581549, _1581551, _1581553] : [-(hAPP(c_Relation_Oconverse(_1581545, _1581547), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1581549, tc_fun(tc_prod(_1581545, _1581547), tc_HOL_Obool)), _1581551), _1581553)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1581549, tc_fun(tc_prod(_1581547, _1581545), tc_HOL_Obool)), _1581551), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1581545, _1581547), tc_HOL_Obool), tc_fun(tc_prod(_1581547, _1581545), tc_HOL_Obool), _1581549), c_Relation_Oconverse(_1581545, _1581547)), _1581553)))], (40915 ^ _780086) ^ [_1581637, _1581639] : [-(c_Transitive__Closure_Otrancl(_1581637, hAPP(c_Relation_Oconverse(_1581637, _1581637), _1581639)) = hAPP(c_Relation_Oconverse(_1581637, _1581637), c_Transitive__Closure_Otrancl(_1581637, _1581639)))], (40917 ^ _780086) ^ [_1581680, _1581682] : [-(c_Transitive__Closure_Ortrancl(_1581680, hAPP(c_Relation_Oconverse(_1581680, _1581680), _1581682)) = hAPP(c_Relation_Oconverse(_1581680, _1581680), c_Transitive__Closure_Ortrancl(_1581680, _1581682)))], (40919 ^ _780086) ^ [_1581723, _1581725] : [c_Wellfounded_Owf(_1581723, hAPP(c_Relation_Oconverse(_1581723, _1581723), _1581725)), -(c_Wellfounded_Owf(_1581723, hAPP(c_Relation_Oconverse(_1581723, _1581723), c_Transitive__Closure_Otrancl(_1581723, _1581725))))], (40925 ^ _780086) ^ [_1581830, _1581832, _1581834] : [c_Equiv__Relations_Oequiv(_1581830, _1581832, _1581834), -(hAPP(hAPP(c_Relation_Orel__comp(_1581830, _1581830, _1581830), hAPP(c_Relation_Oconverse(_1581830, _1581830), _1581834)), _1581834) = _1581834)], (40931 ^ _780086) ^ [_1581943, _1581945, _1581947] : [-(hAPP(c_Relation_ORange(_1581943, _1581945), hAPP(c_Relation_Oconverse(_1581945, _1581943), _1581947)) = hAPP(c_Relation_ODomain(_1581945, _1581943), _1581947))], (40933 ^ _780086) ^ [_1581988, _1581990, _1581992] : [-(hAPP(c_Relation_ODomain(_1581988, _1581990), hAPP(c_Relation_Oconverse(_1581990, _1581988), _1581992)) = hAPP(c_Relation_ORange(_1581990, _1581988), _1581992))], (40935 ^ _780086) ^ [_1582033, _1582035, _1582037] : [-(hAPP(c_Relation_ORange(_1582033, _1582035), _1582037) = hAPP(c_Relation_ODomain(_1582035, _1582033), hAPP(c_Relation_Oconverse(_1582033, _1582035), _1582037)))], (40937 ^ _780086) ^ [_1582078, _1582080, _1582082, _1582084] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1582078, _1582078)), hAPP(hAPP(c_Product__Type_OPair(_1582078, _1582078), _1582080), _1582082)), c_Transitive__Closure_Ortrancl(_1582078, _1582084))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1582078, _1582078)), hAPP(hAPP(c_Product__Type_OPair(_1582078, _1582078), _1582082), _1582080)), c_Transitive__Closure_Ortrancl(_1582078, hAPP(c_Relation_Oconverse(_1582078, _1582078), _1582084)))))], (40943 ^ _780086) ^ [_1582259, _1582261, _1582263, _1582265] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1582259, _1582259)), hAPP(hAPP(c_Product__Type_OPair(_1582259, _1582259), _1582261), _1582263)), c_Transitive__Closure_Ortrancl(_1582259, hAPP(c_Relation_Oconverse(_1582259, _1582259), _1582265)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1582259, _1582259)), hAPP(hAPP(c_Product__Type_OPair(_1582259, _1582259), _1582263), _1582261)), c_Transitive__Closure_Ortrancl(_1582259, _1582265))))], (40949 ^ _780086) ^ [_1582440, _1582442, _1582444, _1582446] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1582440, _1582440)), hAPP(hAPP(c_Product__Type_OPair(_1582440, _1582440), _1582442), _1582444)), hAPP(c_Relation_Oconverse(_1582440, _1582440), c_Transitive__Closure_Otrancl(_1582440, _1582446)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1582440, _1582440)), hAPP(hAPP(c_Product__Type_OPair(_1582440, _1582440), _1582442), _1582444)), c_Transitive__Closure_Otrancl(_1582440, hAPP(c_Relation_Oconverse(_1582440, _1582440), _1582446)))))], (40955 ^ _780086) ^ [_1582633, _1582635, _1582637, _1582639] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1582633, _1582633)), hAPP(hAPP(c_Product__Type_OPair(_1582633, _1582633), _1582635), _1582637)), c_Transitive__Closure_Otrancl(_1582633, hAPP(c_Relation_Oconverse(_1582633, _1582633), _1582639)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1582633, _1582633)), hAPP(hAPP(c_Product__Type_OPair(_1582633, _1582633), _1582635), _1582637)), hAPP(c_Relation_Oconverse(_1582633, _1582633), c_Transitive__Closure_Otrancl(_1582633, _1582639)))))], (40961 ^ _780086) ^ [_1582850, _1582852, _1582854, _1582856, _1582858] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1582850, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1582852, _1582850, _1582854), _1582856)), _1582858)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1582852, tc_HOL_Obool)), _1582856), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1582852, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1582850, _1582852, hAPP(c_Relation_Oconverse(_1582852, _1582850), _1582854)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1582850, tc_HOL_Obool)), _1582858))))))], (40967 ^ _780086) ^ [_1583041, _1583043, _1583045, _1583047, _1583049] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1583043, tc_HOL_Obool)), _1583047), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1583043, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1583041, _1583043, hAPP(c_Relation_Oconverse(_1583043, _1583041), _1583045)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1583041, tc_HOL_Obool)), _1583049))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1583041, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1583043, _1583041, _1583045), _1583047)), _1583049)))], (40973 ^ _780086) ^ [_1583238, _1583240, _1583242] : [c_Relation_Orefl__on(_1583238, _1583240, _1583242), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1583238, _1583238), tc_HOL_Obool)), _1583242), hAPP(hAPP(c_Relation_Orel__comp(_1583238, _1583238, _1583238), hAPP(c_Relation_Oconverse(_1583238, _1583238), _1583242)), _1583242))))], (40979 ^ _780086) ^ [_1583377, _1583379, _1583381] : [hAPP(hAPP(c_Relation_Orel__comp(_1583377, _1583377, _1583377), hAPP(c_Relation_Oconverse(_1583377, _1583377), _1583379)), _1583379) = _1583379, hAPP(c_Relation_ODomain(_1583377, _1583377), _1583379) = _1583381, -(c_Equiv__Relations_Oequiv(_1583377, _1583381, _1583379))], (40989 ^ _780086) ^ [_1583556, _1583558] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1583556, _1583556)), _1583558)), c_Wellfounded_Oacyclic(_1583556, _1583558), -(c_Wellfounded_Owf(_1583556, hAPP(c_Relation_Oconverse(_1583556, _1583556), _1583558)))], (40999 ^ _780086) ^ [_1583711, _1583713, _1583715] : [-(hAPP(c_Relation_Oconverse(_1583711, _1583713), _1583715) = hAPP(c_Set_OCollect(tc_prod(_1583713, _1583711)), hAPP(c_Product__Type_Oprod_Oprod__case(_1583713, _1583711, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1583713, tc_fun(tc_prod(_1583711, _1583713), tc_HOL_Obool), tc_fun(_1583711, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1583711, tc_fun(tc_fun(tc_prod(_1583711, _1583713), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1583711, _1583713), tc_HOL_Obool), tc_fun(_1583711, tc_HOL_Obool)), _1583713), c_COMBC(_1583711, tc_fun(tc_prod(_1583711, _1583713), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1583711, tc_prod(_1583711, _1583713)), tc_fun(_1583711, tc_fun(tc_fun(tc_prod(_1583711, _1583713), tc_HOL_Obool), tc_HOL_Obool)), _1583713), hAPP(c_COMBB(tc_prod(_1583711, _1583713), tc_fun(tc_fun(tc_prod(_1583711, _1583713), tc_HOL_Obool), tc_HOL_Obool), _1583711), c_member(tc_prod(_1583711, _1583713)))), hAPP(c_COMBC(_1583711, _1583713, tc_prod(_1583711, _1583713)), c_Product__Type_OPair(_1583711, _1583713))))), _1583715))))], (41001 ^ _780086) ^ [_1583887, _1583889, _1583891, _1583893, _1583895, _1583897] : [c_Relation_Osingle__valued(_1583887, _1583889, hAPP(c_Relation_Oconverse(_1583889, _1583887), _1583891)), -(_1583893 = c_Orderings_Obot__class_Obot(tc_fun(_1583895, tc_HOL_Obool))), -(hAPP(c_Relation_OImage(_1583889, _1583887, _1583891), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1583895, tc_fun(_1583889, tc_HOL_Obool)), _1583893), _1583897)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1583895, tc_fun(_1583887, tc_HOL_Obool)), _1583893), hAPP(hAPP(c_COMBB(tc_fun(_1583889, tc_HOL_Obool), tc_fun(_1583887, tc_HOL_Obool), _1583895), c_Relation_OImage(_1583889, _1583887, _1583891)), _1583897)))], (41011 ^ _780086) ^ [_1584134, _1584136, _1584138, _1584140] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1584134, tc_fun(_1584134, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1584134, tc_fun(tc_prod(_1584134, _1584134), tc_HOL_Obool), tc_fun(_1584134, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1584134, tc_fun(tc_fun(tc_prod(_1584134, _1584134), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1584134, _1584134), tc_HOL_Obool), tc_fun(_1584134, tc_HOL_Obool)), _1584134), c_COMBC(_1584134, tc_fun(tc_prod(_1584134, _1584134), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1584134, tc_prod(_1584134, _1584134)), tc_fun(_1584134, tc_fun(tc_fun(tc_prod(_1584134, _1584134), tc_HOL_Obool), tc_HOL_Obool)), _1584134), hAPP(c_COMBB(tc_prod(_1584134, _1584134), tc_fun(tc_fun(tc_prod(_1584134, _1584134), tc_HOL_Obool), tc_HOL_Obool), _1584134), c_member(tc_prod(_1584134, _1584134)))), c_Product__Type_OPair(_1584134, _1584134)))), _1584136)), c_fequal), _1584138), _1584140)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584134, _1584134)), hAPP(hAPP(c_Product__Type_OPair(_1584134, _1584134), _1584138), _1584140)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1584134, _1584134), tc_HOL_Obool)), _1584136), c_Relation_OId(_1584134)))))], (41017 ^ _780086) ^ [_1584555, _1584557, _1584559, _1584561] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1584555, _1584555)), hAPP(hAPP(c_Product__Type_OPair(_1584555, _1584555), _1584559), _1584561)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1584555, _1584555), tc_HOL_Obool)), _1584557), c_Relation_OId(_1584555)))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1584555, tc_fun(_1584555, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1584555, tc_fun(tc_prod(_1584555, _1584555), tc_HOL_Obool), tc_fun(_1584555, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1584555, tc_fun(tc_fun(tc_prod(_1584555, _1584555), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1584555, _1584555), tc_HOL_Obool), tc_fun(_1584555, tc_HOL_Obool)), _1584555), c_COMBC(_1584555, tc_fun(tc_prod(_1584555, _1584555), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1584555, tc_prod(_1584555, _1584555)), tc_fun(_1584555, tc_fun(tc_fun(tc_prod(_1584555, _1584555), tc_HOL_Obool), tc_HOL_Obool)), _1584555), hAPP(c_COMBB(tc_prod(_1584555, _1584555), tc_fun(tc_fun(tc_prod(_1584555, _1584555), tc_HOL_Obool), tc_HOL_Obool), _1584555), c_member(tc_prod(_1584555, _1584555)))), c_Product__Type_OPair(_1584555, _1584555)))), _1584557)), c_fequal), _1584559), _1584561)))], (41023 ^ _780086) ^ [_1584982, _1584984] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584982, _1584982)), hAPP(hAPP(c_Product__Type_OPair(_1584982, _1584982), _1584984), _1584984)), c_Relation_OId(_1584982))))], (41025 ^ _780086) ^ [_1585028] : [-(hAPP(c_Relation_Oconverse(_1585028, _1585028), c_Relation_OId(_1585028)) = c_Relation_OId(_1585028))], (41027 ^ _780086) ^ [_1585061, _1585063, _1585065, _1585067] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1585061, _1585063), tc_HOL_Obool)), _1585065), _1585067)), c_Relation_Osingle__valued(_1585061, _1585063, _1585067), -(c_Relation_Osingle__valued(_1585061, _1585063, _1585065))], (41037 ^ _780086) ^ [_1585228, _1585230, _1585232, _1585234, _1585236] : [c_Relation_Osingle__valued(_1585228, _1585230, _1585232), c_Relation_Osingle__valued(_1585230, _1585234, _1585236), -(c_Relation_Osingle__valued(_1585228, _1585234, hAPP(hAPP(c_Relation_Orel__comp(_1585228, _1585230, _1585234), _1585232), _1585236)))], (41047 ^ _780086) ^ [_1585395] : [-(c_Relation_Osingle__valued(_1585395, _1585395, c_Relation_OId(_1585395)))], (41049 ^ _780086) ^ [_1585421, _1585423] : [-(hAPP(c_Relation_OImage(_1585421, _1585421, c_Relation_OId(_1585421)), _1585423) = _1585423)], (41051 ^ _780086) ^ [_1585455, _1585457, _1585459] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1585455, _1585455, _1585457), c_Relation_OId(_1585455)), _1585459) = _1585459)], (41053 ^ _780086) ^ [_1585494, _1585496, _1585498] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1585494, _1585496, _1585496), _1585498), c_Relation_OId(_1585496)) = _1585498)], (41055 ^ _780086) ^ [_1585533, _1585535] : [-(c_Relation_Osingle__valued(_1585533, _1585533, c_Relation_OId__on(_1585533, _1585535)))], (41057 ^ _780086) ^ [_1585580, _1585582, _1585584] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1585580, _1585580)), hAPP(hAPP(c_Product__Type_OPair(_1585580, _1585580), _1585582), _1585584)), c_Relation_OId(_1585580))), -(_1585582 = _1585584)], (41063 ^ _780086) ^ [_1585697, _1585699, _1585701] : [_1585699 = _1585701, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1585697, _1585697)), hAPP(hAPP(c_Product__Type_OPair(_1585697, _1585697), _1585699), _1585701)), c_Relation_OId(_1585697))))], (41069 ^ _780086) ^ [_1585820] : [-(hAPP(c_Relation_ODomain(_1585820, _1585820), c_Relation_OId(_1585820)) = c_Orderings_Otop__class_Otop(tc_fun(_1585820, tc_HOL_Obool)))], (41071 ^ _780086) ^ [_1585856] : [-(c_Transitive__Closure_Ortrancl(_1585856, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1585856, _1585856), tc_HOL_Obool))) = c_Relation_OId(_1585856))], (41073 ^ _780086) ^ [_1585892] : [-(hAPP(c_Relation_ORange(_1585892, _1585892), c_Relation_OId(_1585892)) = c_Orderings_Otop__class_Otop(tc_fun(_1585892, tc_HOL_Obool)))], (41075 ^ _780086) ^ [_1585928, _1585930] : [-(c_Transitive__Closure_Ortrancl(_1585928, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1585928, _1585928), tc_HOL_Obool)), _1585930), c_Relation_OId(_1585928))) = c_Transitive__Closure_Ortrancl(_1585928, _1585930))], (41077 ^ _780086) ^ [_1585975, _1585977] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1585975, _1585975), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1585975, _1585977)), c_Relation_OId(_1585975)) = c_Transitive__Closure_Ortrancl(_1585975, _1585977))], (41079 ^ _780086) ^ [_1586022] : [-(c_Relation_Orefl__on(_1586022, c_Orderings_Otop__class_Otop(tc_fun(_1586022, tc_HOL_Obool)), c_Relation_OId(_1586022)))], (41081 ^ _780086) ^ [_1586053, _1586055] : [-(c_Transitive__Closure_Ortrancl(_1586053, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1586053, _1586053), tc_HOL_Obool)), _1586055), c_Relation_OId(_1586053))) = c_Transitive__Closure_Ortrancl(_1586053, _1586055))], (41083 ^ _780086) ^ [_1586100, _1586102, _1586104, _1586106, _1586108, _1586110] : [c_Relation_Osingle__valued(_1586100, _1586102, _1586104), hBOOL(hAPP(hAPP(c_member(tc_prod(_1586100, _1586102)), hAPP(hAPP(c_Product__Type_OPair(_1586100, _1586102), _1586106), _1586108)), _1586104)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1586100, _1586102)), hAPP(hAPP(c_Product__Type_OPair(_1586100, _1586102), _1586106), _1586110)), _1586104)), -(_1586108 = _1586110)], (41111 ^ _780086) ^ [_1586775, _1586777, _1586779] : [41114 ^ _780086 : [(41115 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586775, _1586777)), hAPP(hAPP(c_Product__Type_OPair(_1586775, _1586777), 41112 ^ [_1586775, _1586777, _1586779]), 41113 ^ [_1586775, _1586777, _1586779])), _1586779)))], (41118 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586775, _1586777)), hAPP(hAPP(c_Product__Type_OPair(_1586775, _1586777), 41112 ^ [_1586775, _1586777, _1586779]), 41116 ^ [_1586775, _1586777, _1586779])), _1586779)))], (41120 ^ _780086) ^ [] : [41113 ^ [_1586775, _1586777, _1586779] = 41116 ^ [_1586775, _1586777, _1586779]]], -(c_Relation_Osingle__valued(_1586775, _1586777, _1586779))], (41097 ^ _780086) ^ [_1586401, _1586403, _1586405] : [c_Relation_Osingle__valued(_1586401, _1586403, _1586405), 41100 ^ _780086 : [(41101 ^ _780086) ^ [_1586522, _1586524] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1586401, _1586403)), hAPP(hAPP(c_Product__Type_OPair(_1586401, _1586403), _1586524), _1586522)), _1586405)), 41104 ^ _780086 : [(41105 ^ _780086) ^ [_1586648] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1586401, _1586403)), hAPP(hAPP(c_Product__Type_OPair(_1586401, _1586403), _1586524), _1586648)), _1586405)), -(_1586522 = _1586648)]]]]], (41124 ^ _780086) ^ [] : [-(c_FunDef_Opair__leq = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat)), tc_HOL_Obool)), c_FunDef_Opair__less), c_Relation_OId(tc_prod(tc_Nat_Onat, tc_Nat_Onat))))], (41126 ^ _780086) ^ [_1587163, _1587165] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1587163, _1587163), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1587163, _1587165)), c_Relation_OId(_1587163)) = c_Transitive__Closure_Ortrancl(_1587163, _1587165))], (41128 ^ _780086) ^ [_1587210, _1587212] : [-(c_Transitive__Closure_Otrancl(_1587210, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1587210, _1587210), tc_HOL_Obool)), _1587212), c_Relation_OId(_1587210))) = c_Transitive__Closure_Ortrancl(_1587210, _1587212))], (41130 ^ _780086) ^ [_1587257, _1587259] : [-(c_Transitive__Closure_Ortrancl(_1587257, _1587259) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1587257, _1587257), tc_HOL_Obool)), c_Relation_OId(_1587257)), hAPP(hAPP(c_Relation_Orel__comp(_1587257, _1587257, _1587257), c_Transitive__Closure_Ortrancl(_1587257, _1587259)), _1587259)))], (41132 ^ _780086) ^ [_1587314, _1587316] : [-(c_Relation_Orefl__on(_1587314, c_Orderings_Otop__class_Otop(tc_fun(_1587314, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1587314, _1587314), tc_HOL_Obool)), _1587316), c_Relation_OId(_1587314))))], (41134 ^ _780086) ^ [_1587361] : [-(c_Relation_OId(_1587361) = hAPP(c_Set_OCollect(tc_prod(_1587361, _1587361)), hAPP(hAPP(c_COMBB(tc_fun(_1587361, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1587361, _1587361)), c_HOL_OEx(_1587361)), hAPP(hAPP(c_COMBC(tc_prod(_1587361, _1587361), tc_fun(_1587361, tc_prod(_1587361, _1587361)), tc_fun(_1587361, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1587361, _1587361), tc_HOL_Obool), tc_fun(tc_fun(_1587361, tc_prod(_1587361, _1587361)), tc_fun(_1587361, tc_HOL_Obool)), tc_prod(_1587361, _1587361)), c_COMBB(tc_prod(_1587361, _1587361), tc_HOL_Obool, _1587361)), c_fequal)), hAPP(hAPP(c_COMBS(_1587361, _1587361, tc_prod(_1587361, _1587361)), c_Product__Type_OPair(_1587361, _1587361)), c_COMBI(_1587361))))))], (41136 ^ _780086) ^ [_1587490, _1587492] : [-(c_Relation_Oirrefl(_1587490, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1587490, _1587490), tc_HOL_Obool)), _1587492), c_Relation_OId(_1587490))))], (41138 ^ _780086) ^ [_1587531, _1587533, _1587535, _1587537, _1587539] : [c_Relation_Osingle__valued(_1587531, _1587531, _1587533), hBOOL(hAPP(hAPP(c_member(tc_prod(_1587531, _1587531)), hAPP(hAPP(c_Product__Type_OPair(_1587531, _1587531), _1587535), _1587537)), c_Transitive__Closure_Ortrancl(_1587531, _1587533))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1587531, _1587531)), hAPP(hAPP(c_Product__Type_OPair(_1587531, _1587531), _1587535), _1587539)), c_Transitive__Closure_Ortrancl(_1587531, _1587533))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587531, _1587531)), hAPP(hAPP(c_Product__Type_OPair(_1587531, _1587531), _1587537), _1587539)), c_Transitive__Closure_Ortrancl(_1587531, _1587533)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587531, _1587531)), hAPP(hAPP(c_Product__Type_OPair(_1587531, _1587531), _1587539), _1587537)), c_Transitive__Closure_Ortrancl(_1587531, _1587533))))], (41156 ^ _780086) ^ [_1587921, _1587923, _1587925, _1587927, _1587929] : [c_Relation_Osingle__valued(_1587921, _1587923, hAPP(c_Relation_Oconverse(_1587923, _1587921), _1587925)), -(hAPP(c_Relation_OImage(_1587923, _1587921, _1587925), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1587923, tc_HOL_Obool)), _1587927), _1587929)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1587921, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1587923, _1587921, _1587925), _1587927)), hAPP(c_Relation_OImage(_1587923, _1587921, _1587925), _1587929)))], (41162 ^ _780086) ^ [_1588104, _1588106, _1588108] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1588104, _1588104), tc_HOL_Obool)), c_Relation_OId(_1588104)), _1588106)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1588104, _1588104), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1588104, _1588104, _1588104), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1588104, _1588104), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1588104, _1588108)), _1588106)), _1588108)), _1588106)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1588104, _1588104), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1588104, _1588108)), _1588106)))], (41172 ^ _780086) ^ [_1588397, _1588399, _1588401] : [c_Relation_Ototal__on(_1588397, _1588399, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1588397, _1588397), tc_HOL_Obool)), _1588401), c_Relation_OId(_1588397))), -(c_Relation_Ototal__on(_1588397, _1588399, _1588401))], (41178 ^ _780086) ^ [_1588508, _1588510, _1588512] : [c_Relation_Ototal__on(_1588508, _1588510, _1588512), -(c_Relation_Ototal__on(_1588508, _1588510, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1588508, _1588508), tc_HOL_Obool)), _1588512), c_Relation_OId(_1588508))))], (41184 ^ _780086) ^ [_1588625, _1588627, _1588629] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1588625, _1588625)), _1588627), c_Transitive__Closure_Ortrancl(_1588625, _1588629))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1588625, _1588625)), _1588627), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1588625, _1588625), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_prod(_1588625, _1588625), tc_HOL_Obool), tc_fun(tc_prod(_1588625, _1588625), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1588625, _1588625), tc_HOL_Obool)), _1588629)))))], (41190 ^ _780086) ^ [_1588836, _1588838, _1588840] : [c_Relation_Osingle__valued(_1588836, _1588836, _1588838), -(c_Relation_Osingle__valued(_1588836, _1588836, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1588836, _1588836), tc_HOL_Obool), _1588840), _1588838)))], (41196 ^ _780086) ^ [_1588943, _1588945, _1588947, _1588949] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_fun(_1588943, _1588945), tc_fun(_1588943, _1588945)), _1588947), c_Fun_Ocomp(_1588945, _1588945, _1588943, _1588949)) = c_Fun_Ocomp(_1588945, _1588945, _1588943, hAPP(hAPP(c_Nat_Ocompow(_1588945, _1588945), _1588947), _1588949)))], (41198 ^ _780086) ^ [_1589006, _1589008, _1589010] : [c_Wellfounded_Owf(_1589006, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1589006, _1589006), tc_HOL_Obool), _1589008), _1589010)), -(c_Wellfounded_Owf(_1589006, _1589010))], (41204 ^ _780086) ^ [_1589109, _1589111, _1589113, _1589115] : [-(hAPP(hAPP(c_Nat_Ocompow(_1589109, _1589109), _1589111), hAPP(hAPP(c_Nat_Ocompow(_1589109, _1589109), _1589113), _1589115)) = hAPP(hAPP(c_Nat_Ocompow(_1589109, _1589109), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1589113), _1589111)), _1589115))], (41206 ^ _780086) ^ [_1589171, _1589173, _1589175, _1589177] : [-(hAPP(_1589171, hAPP(hAPP(hAPP(c_Nat_Ocompow(_1589173, _1589173), _1589175), _1589171), _1589177)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(_1589173, _1589173), _1589175), _1589171), hAPP(_1589171, _1589177)))], (41208 ^ _780086) ^ [_1589230, _1589232] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1589230, _1589230), tc_HOL_Obool), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1589232) = _1589232)], (41210 ^ _780086) ^ [_1589267, _1589269, _1589271] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1589267, _1589267, _1589267), _1589269), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1589267, _1589267), tc_HOL_Obool), _1589271), _1589269)) = hAPP(hAPP(c_Relation_Orel__comp(_1589267, _1589267, _1589267), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1589267, _1589267), tc_HOL_Obool), _1589271), _1589269)), _1589269))], (41212 ^ _780086) ^ [_1589338, _1589340, _1589342, _1589344] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1589338, _1589338)), _1589340), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1589338, _1589338), tc_HOL_Obool), _1589342), _1589344))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589338, _1589338)), _1589340), c_Transitive__Closure_Ortrancl(_1589338, _1589344))))], (41218 ^ _780086) ^ [_1589507, _1589509, _1589511] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1589507, _1589507)), _1589509), c_Transitive__Closure_Ortrancl(_1589507, _1589511))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589507, _1589507)), _1589509), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1589507, _1589507), tc_HOL_Obool), 41221 ^ [_1589507, _1589509, _1589511]), _1589511))))], (41225 ^ _780086) ^ [_1589666, _1589668, _1589670] : [41226 ^ _780086 : [(41227 ^ _780086) ^ [_1589742] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1589666, _1589666)), _1589668), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1589666, _1589666), tc_HOL_Obool), _1589742), _1589670)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589666, _1589666)), _1589668), c_Transitive__Closure_Ortrancl(_1589666, _1589670))))], (41231 ^ _780086) ^ [_1589830, _1589832, _1589834] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1589830, _1589830), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1589832)), _1589834) = hAPP(hAPP(c_Relation_Orel__comp(_1589830, _1589830, _1589830), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1589830, _1589830), tc_HOL_Obool), _1589832), _1589834)), _1589834))], (41233 ^ _780086) ^ [_1589894, _1589896, _1589898, _1589900] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1589894, _1589894), tc_HOL_Obool), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1589896), _1589898)), _1589900) = hAPP(hAPP(c_Relation_Orel__comp(_1589894, _1589894, _1589894), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1589894, _1589894), tc_HOL_Obool), _1589896), _1589900)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1589894, _1589894), tc_HOL_Obool), _1589898), _1589900)))], (41235 ^ _780086) ^ [_1589975, _1589977] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1589975, _1589975), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1589977) = c_Relation_OId(_1589975))], (41237 ^ _780086) ^ [_1590014, _1590016] : [-(c_Relation_Ototal__on(_1590014, c_Orderings_Obot__class_Obot(tc_fun(_1590014, tc_HOL_Obool)), _1590016))], (41239 ^ _780086) ^ [_1590063, _1590065, _1590067] : [c_Relation_Ototal__on(_1590063, _1590065, hAPP(c_Relation_Oconverse(_1590063, _1590063), _1590067)), -(c_Relation_Ototal__on(_1590063, _1590065, _1590067))], (41245 ^ _780086) ^ [_1590154, _1590156, _1590158] : [c_Relation_Ototal__on(_1590154, _1590156, _1590158), -(c_Relation_Ototal__on(_1590154, _1590156, hAPP(c_Relation_Oconverse(_1590154, _1590154), _1590158)))], (41251 ^ _780086) ^ [_1590251, _1590253, _1590255] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590251, _1590251)), hAPP(hAPP(c_Product__Type_OPair(_1590251, _1590251), _1590253), _1590253)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1590251, _1590251), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1590255))))], (41253 ^ _780086) ^ [_1590309, _1590311, _1590313, _1590315] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590309, _1590309)), hAPP(hAPP(c_Product__Type_OPair(_1590309, _1590309), _1590311), _1590313)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1590309, _1590309), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1590315))), -(_1590311 = _1590313)], (41259 ^ _780086) ^ [_1590452, _1590454, _1590456, _1590458, _1590460, _1590462] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590452, _1590452)), hAPP(hAPP(c_Product__Type_OPair(_1590452, _1590452), _1590454), _1590456)), _1590458)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1590452, _1590452)), hAPP(hAPP(c_Product__Type_OPair(_1590452, _1590452), _1590456), _1590460)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1590452, _1590452), tc_HOL_Obool), _1590462), _1590458))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590452, _1590452)), hAPP(hAPP(c_Product__Type_OPair(_1590452, _1590452), _1590454), _1590460)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1590452, _1590452), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1590462)), _1590458))))], (41269 ^ _780086) ^ [_1590765, _1590767, _1590769, _1590771, _1590773, _1590775] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590765, _1590765)), hAPP(hAPP(c_Product__Type_OPair(_1590765, _1590765), _1590767), _1590769)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1590765, _1590765), tc_HOL_Obool), _1590771), _1590773))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1590765, _1590765)), hAPP(hAPP(c_Product__Type_OPair(_1590765, _1590765), _1590769), _1590775)), _1590773)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590765, _1590765)), hAPP(hAPP(c_Product__Type_OPair(_1590765, _1590765), _1590767), _1590775)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1590765, _1590765), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1590771)), _1590773))))], (41279 ^ _780086) ^ [_1591078, _1591080, _1591082] : [-(hAPP(hAPP(c_Nat_Ocompow(_1591078, _1591078), hAPP(c_Nat_OSuc, _1591080)), _1591082) = hAPP(c_Fun_Ocomp(_1591078, _1591078, _1591078, _1591082), hAPP(hAPP(c_Nat_Ocompow(_1591078, _1591078), _1591080), _1591082)))], (41281 ^ _780086) ^ [_1591134, _1591136, _1591138, _1591140] : [-(hAPP(hAPP(c_Nat_Ocompow(_1591134, _1591134), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1591136), _1591138)), _1591140) = hAPP(c_Fun_Ocomp(_1591134, _1591134, _1591134, hAPP(hAPP(c_Nat_Ocompow(_1591134, _1591134), _1591136), _1591140)), hAPP(hAPP(c_Nat_Ocompow(_1591134, _1591134), _1591138), _1591140)))], (41283 ^ _780086) ^ [_1591204, _1591206] : [-(hAPP(hAPP(c_Nat_Ocompow(_1591204, _1591204), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1591206) = c_Fun_Oid(_1591204))], (41285 ^ _780086) ^ [_1591258, _1591260, _1591262] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1591258, _1591258)), _1591260), c_Transitive__Closure_Otrancl(_1591258, _1591262))), 41289 ^ _780086 : [(41290 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 41288 ^ [_1591258, _1591260, _1591262])))], (41292 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1591258, _1591258)), _1591260), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1591258, _1591258), tc_HOL_Obool), 41288 ^ [_1591258, _1591260, _1591262]), _1591262))))]]], (41294 ^ _780086) ^ [_1591456, _1591458, _1591460] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1591456, _1591456)), _1591458), c_Transitive__Closure_Otrancl(_1591456, _1591460)))), 41295 ^ _780086 : [(41296 ^ _780086) ^ [_1591535] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1591535)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1591456, _1591456)), _1591458), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1591456, _1591456), tc_HOL_Obool), _1591535), _1591460)))]]], (41326 ^ _780086) ^ [_1592213, _1592215, _1592217] : [41328 ^ _780086 : [(41329 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1592213), 41327 ^ [_1592213, _1592215, _1592217]), _1592215)))], (41332 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1592213), 41330 ^ [_1592213, _1592215, _1592217]), _1592215)))], (41334 ^ _780086) ^ [] : [41327 ^ [_1592213, _1592215, _1592217] = 41330 ^ [_1592213, _1592215, _1592217]], (41336 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1592213, _1592213)), hAPP(hAPP(c_Product__Type_OPair(_1592213, _1592213), 41327 ^ [_1592213, _1592215, _1592217]), 41330 ^ [_1592213, _1592215, _1592217])), _1592217))], (41338 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1592213, _1592213)), hAPP(hAPP(c_Product__Type_OPair(_1592213, _1592213), 41330 ^ [_1592213, _1592215, _1592217]), 41327 ^ [_1592213, _1592215, _1592217])), _1592217))]], -(c_Relation_Ototal__on(_1592213, _1592215, _1592217))], (41304 ^ _780086) ^ [_1591724, _1591726, _1591728] : [c_Relation_Ototal__on(_1591724, _1591726, _1591728), 41307 ^ _780086 : [(41308 ^ _780086) ^ [_1591868] : [hBOOL(hAPP(hAPP(c_member(_1591724), _1591868), _1591726)), 41311 ^ _780086 : [(41312 ^ _780086) ^ [_1592008] : [hBOOL(hAPP(hAPP(c_member(_1591724), _1592008), _1591726)), -(_1591868 = _1592008), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1591724, _1591724)), hAPP(hAPP(c_Product__Type_OPair(_1591724, _1591724), _1591868), _1592008)), _1591728))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1591724, _1591724)), hAPP(hAPP(c_Product__Type_OPair(_1591724, _1591724), _1592008), _1591868)), _1591728)))]]]]], (41342 ^ _780086) ^ [_1592795, _1592797] : [-(c_Transitive__Closure_Ortrancl(_1592795, _1592797) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1592795, _1592795), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_prod(_1592795, _1592795), tc_HOL_Obool), tc_fun(tc_prod(_1592795, _1592795), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1592795, _1592795), tc_HOL_Obool)), _1592797)))], (41344 ^ _780086) ^ [_1592866] : [-(c_Nat_Ofunpow(_1592866) = c_Nat_Ocompow(_1592866, _1592866))], (41346 ^ _780086) ^ [_1592894, _1592896, _1592898, _1592900, _1592902] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1592894, _1592894)), hAPP(hAPP(c_Product__Type_OPair(_1592894, _1592894), _1592896), _1592898)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1592894, _1592894), tc_HOL_Obool), _1592900), _1592902))), 41351 ^ _780086 : [(41352 ^ _780086) ^ [] : [-(_1592900 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41354 ^ _780086) ^ [] : [-(_1592896 = _1592898)]], 41357 ^ _780086 : [(41358 ^ _780086) ^ [] : [-(_1592900 = hAPP(c_Nat_OSuc, 41356 ^ [_1592894, _1592896, _1592898, _1592900, _1592902]))], (41360 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1592894, _1592894)), hAPP(hAPP(c_Product__Type_OPair(_1592894, _1592894), _1592896), 41355 ^ [_1592894, _1592896, _1592898, _1592900, _1592902])), _1592902)))], (41362 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1592894, _1592894)), hAPP(hAPP(c_Product__Type_OPair(_1592894, _1592894), 41355 ^ [_1592894, _1592896, _1592898, _1592900, _1592902]), _1592898)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1592894, _1592894), tc_HOL_Obool), 41356 ^ [_1592894, _1592896, _1592898, _1592900, _1592902]), _1592902))))]]], (41364 ^ _780086) ^ [_1593336, _1593338, _1593340, _1593342, _1593344] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1593336, _1593336)), hAPP(hAPP(c_Product__Type_OPair(_1593336, _1593336), _1593338), _1593340)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1593336, _1593336), tc_HOL_Obool), _1593342), _1593344))), 41369 ^ _780086 : [(41370 ^ _780086) ^ [] : [-(_1593342 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41372 ^ _780086) ^ [] : [-(_1593338 = _1593340)]], 41375 ^ _780086 : [(41376 ^ _780086) ^ [] : [-(_1593342 = hAPP(c_Nat_OSuc, 41374 ^ [_1593336, _1593338, _1593340, _1593342, _1593344]))], (41378 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1593336, _1593336)), hAPP(hAPP(c_Product__Type_OPair(_1593336, _1593336), _1593338), 41373 ^ [_1593336, _1593338, _1593340, _1593342, _1593344])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1593336, _1593336), tc_HOL_Obool), 41374 ^ [_1593336, _1593338, _1593340, _1593342, _1593344]), _1593344))))], (41380 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1593336, _1593336)), hAPP(hAPP(c_Product__Type_OPair(_1593336, _1593336), 41373 ^ [_1593336, _1593338, _1593340, _1593342, _1593344]), _1593340)), _1593344)))]]], (41382 ^ _780086) ^ [_1593774, _1593776] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1593774, _1593774)), hAPP(hAPP(c_Product__Type_OPair(_1593774, _1593774), 41383 ^ [_1593774, _1593776]), 41383 ^ [_1593774, _1593776])), c_Transitive__Closure_Otrancl(_1593774, _1593776)))), -(c_Wellfounded_Oacyclic(_1593774, _1593776))], (41389 ^ _780086) ^ [_1593846, _1593848, _1593850, _1593852, _1593854] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1593846, _1593846)), hAPP(hAPP(c_Product__Type_OPair(_1593846, _1593846), _1593848), _1593850)), c_Transitive__Closure_Ortrancl(_1593846, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1593846, _1593846), tc_HOL_Obool)), _1593852), _1593854)))), 41395 ^ _780086 : [(41396 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1593846, _1593846)), hAPP(hAPP(c_Product__Type_OPair(_1593846, _1593846), 41394 ^ [_1593846, _1593848, _1593850, _1593852, _1593854]), _1593850)), c_Transitive__Closure_Ortrancl(_1593846, _1593852))))], (41399 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1593846, _1593846)), hAPP(hAPP(c_Product__Type_OPair(_1593846, _1593846), 41397 ^ [_1593846, _1593848, _1593850, _1593852, _1593854]), 41394 ^ [_1593846, _1593848, _1593850, _1593852, _1593854])), _1593854)))], (41401 ^ _780086) ^ [] : [41397 ^ [_1593846, _1593848, _1593850, _1593852, _1593854] = 41394 ^ [_1593846, _1593848, _1593850, _1593852, _1593854]]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1593846, _1593846)), hAPP(hAPP(c_Product__Type_OPair(_1593846, _1593846), _1593848), _1593850)), c_Transitive__Closure_Ortrancl(_1593846, _1593852))))], (41405 ^ _780086) ^ [_1594405, _1594407, _1594409, _1594411, _1594413] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1594405, _1594405)), hAPP(hAPP(c_Product__Type_OPair(_1594405, _1594405), _1594407), _1594409)), c_Transitive__Closure_Ortrancl(_1594405, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1594405, _1594405), tc_HOL_Obool)), _1594411), _1594413)))), 41411 ^ _780086 : [(41412 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1594405, _1594405)), hAPP(hAPP(c_Product__Type_OPair(_1594405, _1594405), _1594407), 41410 ^ [_1594405, _1594407, _1594409, _1594411, _1594413])), c_Transitive__Closure_Ortrancl(_1594405, _1594411))))], (41415 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1594405, _1594405)), hAPP(hAPP(c_Product__Type_OPair(_1594405, _1594405), 41410 ^ [_1594405, _1594407, _1594409, _1594411, _1594413]), 41413 ^ [_1594405, _1594407, _1594409, _1594411, _1594413])), _1594413)))], (41417 ^ _780086) ^ [] : [41410 ^ [_1594405, _1594407, _1594409, _1594411, _1594413] = 41413 ^ [_1594405, _1594407, _1594409, _1594411, _1594413]]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1594405, _1594405)), hAPP(hAPP(c_Product__Type_OPair(_1594405, _1594405), _1594407), _1594409)), c_Transitive__Closure_Ortrancl(_1594405, _1594411))))], (41421 ^ _780086) ^ [_1594964, _1594966, _1594968, _1594970, _1594972] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1594964, _1594964)), hAPP(hAPP(c_Product__Type_OPair(_1594964, _1594964), _1594966), _1594968)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1594964, _1594964), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1594970)), _1594972))), 41425 ^ _780086 : [(41426 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1594964, _1594964)), hAPP(hAPP(c_Product__Type_OPair(_1594964, _1594964), _1594966), 41424 ^ [_1594964, _1594966, _1594968, _1594970, _1594972])), _1594972)))], (41428 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1594964, _1594964)), hAPP(hAPP(c_Product__Type_OPair(_1594964, _1594964), 41424 ^ [_1594964, _1594966, _1594968, _1594970, _1594972]), _1594968)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1594964, _1594964), tc_HOL_Obool), _1594970), _1594972))))]]], (41430 ^ _780086) ^ [_1595272, _1595274, _1595276, _1595278, _1595280] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1595272, _1595272)), hAPP(hAPP(c_Product__Type_OPair(_1595272, _1595272), _1595274), _1595276)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1595272, _1595272), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1595278)), _1595280))), 41434 ^ _780086 : [(41435 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1595272, _1595272)), hAPP(hAPP(c_Product__Type_OPair(_1595272, _1595272), _1595274), 41433 ^ [_1595272, _1595274, _1595276, _1595278, _1595280])), _1595280)))], (41437 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1595272, _1595272)), hAPP(hAPP(c_Product__Type_OPair(_1595272, _1595272), 41433 ^ [_1595272, _1595274, _1595276, _1595278, _1595280]), _1595276)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1595272, _1595272), tc_HOL_Obool), _1595278), _1595280))))]]], (41439 ^ _780086) ^ [_1595584, _1595586, _1595588, _1595590, _1595592] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1595584, _1595584)), hAPP(hAPP(c_Product__Type_OPair(_1595584, _1595584), _1595586), _1595588)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1595584, _1595584), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1595590)), _1595592))), 41443 ^ _780086 : [(41444 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1595584, _1595584)), hAPP(hAPP(c_Product__Type_OPair(_1595584, _1595584), _1595586), 41442 ^ [_1595584, _1595586, _1595588, _1595590, _1595592])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1595584, _1595584), tc_HOL_Obool), _1595590), _1595592))))], (41446 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1595584, _1595584)), hAPP(hAPP(c_Product__Type_OPair(_1595584, _1595584), 41442 ^ [_1595584, _1595586, _1595588, _1595590, _1595592]), _1595588)), _1595592)))]]], (41448 ^ _780086) ^ [_1595896, _1595898, _1595900, _1595902] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1595896, _1595896)), hAPP(hAPP(c_Product__Type_OPair(_1595896, _1595896), _1595898), _1595900)), c_Transitive__Closure_Otrancl(_1595896, _1595902))), 41452 ^ _780086 : [(41453 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1595896, _1595896)), hAPP(hAPP(c_Product__Type_OPair(_1595896, _1595896), _1595898), 41451 ^ [_1595896, _1595898, _1595900, _1595902])), c_Transitive__Closure_Ortrancl(_1595896, _1595902))))], (41455 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1595896, _1595896)), hAPP(hAPP(c_Product__Type_OPair(_1595896, _1595896), 41451 ^ [_1595896, _1595898, _1595900, _1595902]), _1595900)), _1595902)))]]], (41457 ^ _780086) ^ [_1596156, _1596158, _1596160, _1596162] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1596156, _1596156)), hAPP(hAPP(c_Product__Type_OPair(_1596156, _1596156), _1596158), _1596160)), c_Transitive__Closure_Otrancl(_1596156, _1596162))), 41461 ^ _780086 : [(41462 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1596156, _1596156)), hAPP(hAPP(c_Product__Type_OPair(_1596156, _1596156), _1596158), 41460 ^ [_1596156, _1596158, _1596160, _1596162])), _1596162)))], (41464 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1596156, _1596156)), hAPP(hAPP(c_Product__Type_OPair(_1596156, _1596156), 41460 ^ [_1596156, _1596158, _1596160, _1596162]), _1596160)), c_Transitive__Closure_Ortrancl(_1596156, _1596162))))]]], (41466 ^ _780086) ^ [_1596416, _1596418] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1596416, _1596416)), _1596418), c_Relation_OId(_1596416))), -(_1596418 = hAPP(hAPP(c_Product__Type_OPair(_1596416, _1596416), 41469 ^ [_1596416, _1596418]), 41469 ^ [_1596416, _1596418]))], (41473 ^ _780086) ^ [_1596558, _1596560, _1596562, _1596564] : [41475 ^ _780086 : [(41476 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1596558), 41474 ^ [_1596558, _1596560, _1596562, _1596564])))], (41478 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41474 ^ [_1596558, _1596560, _1596562, _1596564]), _1596560)))], (41480 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(_1596562, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 41474 ^ [_1596558, _1596560, _1596562, _1596564]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1596562, 41474 ^ [_1596558, _1596560, _1596562, _1596564])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1596558), _1596560)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1596562, _1596558)), _1596564)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1596564), hAPP(_1596562, _1596560))), 41494 ^ _780086 : [(41495 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1596558), 41493 ^ [_1596558, _1596560, _1596562, _1596564])))], (41497 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 41493 ^ [_1596558, _1596560, _1596562, _1596564]), _1596560)))], (41499 ^ _780086) ^ [] : [-(hAPP(_1596562, 41493 ^ [_1596558, _1596560, _1596562, _1596564]) = _1596564)]]], (41501 ^ _780086) ^ [_1597184, _1597186, _1597188] : [class_Divides_Osemiring__div(_1597184), -(_1597186 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1597184), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1597184), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1597184), _1597186), _1597188)), _1597188)), c_Divides_Odiv__class_Omod(_1597184, _1597186, _1597188)))], (41524 ^ _780086) ^ [_1597851, _1597853] : [-(c_Wellfounded_Owf(_1597851, _1597853)), 41527 ^ _780086 : [(41528 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1597851), 41526 ^ [_1597851, _1597853]), 41525 ^ [_1597851, _1597853])))], (41530 ^ _780086) ^ [_1598071] : [hBOOL(hAPP(hAPP(c_member(_1597851), _1598071), 41525 ^ [_1597851, _1597853])), 41534 ^ _780086 : [(41535 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1597851, _1597851)), hAPP(hAPP(c_Product__Type_OPair(_1597851, _1597851), 41533 ^ [_1597851, _1597853, _1598071]), _1598071)), _1597853)))], (41537 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1597851), 41533 ^ [_1597851, _1597853, _1598071]), 41525 ^ [_1597851, _1597853])))]]]]], (41507 ^ _780086) ^ [_1597332, _1597334] : [c_Wellfounded_Owf(_1597332, _1597334), 41510 ^ _780086 : [(41511 ^ _780086) ^ [_1597464] : [41512 ^ _780086 : [(41513 ^ _780086) ^ [_1597569] : [hBOOL(hAPP(hAPP(c_member(_1597332), _1597569), _1597464))]], 41515 ^ _780086 : [(41516 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1597332), 41514 ^ [_1597332, _1597334, _1597464]), _1597464)))], (41518 ^ _780086) ^ [_1597691] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1597332, _1597332)), hAPP(hAPP(c_Product__Type_OPair(_1597332, _1597332), _1597691), 41514 ^ [_1597332, _1597334, _1597464])), _1597334)), hBOOL(hAPP(hAPP(c_member(_1597332), _1597691), _1597464))]]]]], (41541 ^ _780086) ^ [_1598327, _1598329] : [-(hAPP(c_Set_OCollect(tc_Int_Oint), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fconj), hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), _1598327)) = hAPP(c_Set_OCollect(tc_Int_Oint), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fconj), hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), _1598329))), 41543 ^ _780086 : [(41544 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 41542 ^ [_1598327, _1598329])))], (41546 ^ _780086) ^ [] : [41547 ^ _780086 : [(41548 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1598327, 41542 ^ [_1598327, _1598329])))], (41550 ^ _780086) ^ [] : [hBOOL(hAPP(_1598329, 41542 ^ [_1598327, _1598329]))]], 41551 ^ _780086 : [(41552 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1598329, 41542 ^ [_1598327, _1598329])))], (41554 ^ _780086) ^ [] : [hBOOL(hAPP(_1598327, 41542 ^ [_1598327, _1598329]))]]]]], (41558 ^ _780086) ^ [_1598648, _1598650, _1598652, _1598654, _1598656] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1598648, tc_HOL_Obool)), _1598650), _1598652)), 41564 ^ _780086 : [(41565 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1598648), 41563 ^ [_1598648, _1598650, _1598652, _1598654, _1598656]), _1598650)))], (41567 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1598654, 41563 ^ [_1598648, _1598650, _1598652, _1598654, _1598656])))], (41569 ^ _780086) ^ [] : [hBOOL(hAPP(_1598656, 41563 ^ [_1598648, _1598650, _1598652, _1598654, _1598656]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1598648, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1598648, tc_HOL_Obool)), _1598650), hAPP(c_Set_OCollect(_1598648), _1598654))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1598648, tc_HOL_Obool)), _1598652), hAPP(c_Set_OCollect(_1598648), _1598656)))))], (41573 ^ _780086) ^ [_1599048, _1599050, _1599052] : [hBOOL(hAPP(hAPP(c_member(_1599048), _1599050), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1599048, tc_HOL_Obool), _1599052))), 41577 ^ _780086 : [(41578 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1599048), _1599050), 41576 ^ [_1599048, _1599050, _1599052])))], (41580 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1599048, tc_HOL_Obool)), 41576 ^ [_1599048, _1599050, _1599052]), _1599052)))]]], (41582 ^ _780086) ^ [_1599240, _1599242, _1599244, _1599246, _1599248, _1599250] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1599240, _1599242)), _1599244), hAPP(hAPP(c_Relation_Orel__comp(_1599240, _1599246, _1599242), _1599248), _1599250))), 41588 ^ _780086 : [(41589 ^ _780086) ^ [] : [-(_1599244 = hAPP(hAPP(c_Product__Type_OPair(_1599240, _1599242), 41585 ^ [_1599240, _1599242, _1599244, _1599246, _1599248, _1599250]), 41587 ^ [_1599240, _1599242, _1599244, _1599246, _1599248, _1599250]))], (41591 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1599240, _1599246)), hAPP(hAPP(c_Product__Type_OPair(_1599240, _1599246), 41585 ^ [_1599240, _1599242, _1599244, _1599246, _1599248, _1599250]), 41586 ^ [_1599240, _1599242, _1599244, _1599246, _1599248, _1599250])), _1599248)))], (41593 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1599246, _1599242)), hAPP(hAPP(c_Product__Type_OPair(_1599246, _1599242), 41586 ^ [_1599240, _1599242, _1599244, _1599246, _1599248, _1599250]), 41587 ^ [_1599240, _1599242, _1599244, _1599246, _1599248, _1599250])), _1599250)))]]], (41595 ^ _780086) ^ [_1599618, _1599620, _1599622, _1599624] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1599618, _1599620)), _1599622), hAPP(c_Relation_Oconverse(_1599620, _1599618), _1599624))), 41600 ^ _780086 : [(41601 ^ _780086) ^ [] : [-(_1599622 = hAPP(hAPP(c_Product__Type_OPair(_1599618, _1599620), 41599 ^ [_1599618, _1599620, _1599622, _1599624]), 41598 ^ [_1599618, _1599620, _1599622, _1599624]))], (41603 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1599620, _1599618)), hAPP(hAPP(c_Product__Type_OPair(_1599620, _1599618), 41598 ^ [_1599618, _1599620, _1599622, _1599624]), 41599 ^ [_1599618, _1599620, _1599622, _1599624])), _1599624)))]]], (41605 ^ _780086) ^ [_1599871, _1599873, _1599875] : [-(c_Nitpick_Oplus__frac(_1599871, _1599873, _1599875) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1599871), c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(_1599871), _1599873), hAPP(c_Nitpick_Odenom(_1599871), _1599875))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Int_Oint, _1599871), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, _1599871), tc_Int_Oint), c_Nitpick_Ofrac(_1599871)), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint)), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint), hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1599871), _1599873))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint)), hAPP(c_Nitpick_Odenom(_1599871), _1599873))))), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint), hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1599871), _1599875))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint)), hAPP(c_Nitpick_Odenom(_1599871), _1599875)))))), c_COMBI(tc_Int_Oint))))], (41607 ^ _780086) ^ [_1600002, _1600004, _1600006, _1600008] : [class_Rings_Olinordered__semidom(_1600002), 41613 ^ _780086 : [(41614 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1600004), 41612 ^ [_1600002, _1600004, _1600006, _1600008]), _1600006)))], (41616 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1600002), c_Groups_Ozero__class_Ozero(_1600002)), hAPP(_1600008, 41612 ^ [_1600002, _1600004, _1600006, _1600008])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1600002), c_Groups_Ozero__class_Ozero(_1600002)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1600004, _1600002), _1600008), _1600006))))], (41620 ^ _780086) ^ [_1600298, _1600300, _1600302] : [-(c_Nitpick_Otimes__frac(_1600298, _1600300, _1600302) = hAPP(hAPP(c_Nitpick_Ofrac(_1600298), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1600298), _1600300)), hAPP(c_Nitpick_Onum(_1600298), _1600302))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Odenom(_1600298), _1600300)), hAPP(c_Nitpick_Odenom(_1600298), _1600302))))], (41622 ^ _780086) ^ [_1600369, _1600371, _1600373] : [-(c_Nitpick_Oof__frac(_1600371, _1600369, _1600373) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1600369), hAPP(c_Int_Oring__1__class_Oof__int(_1600369), hAPP(c_Nitpick_Onum(_1600371), _1600373))), hAPP(c_Int_Oring__1__class_Oof__int(_1600369), hAPP(c_Nitpick_Odenom(_1600371), _1600373)))), class_Rings_Oinverse(_1600369), class_Rings_Oring__1(_1600369)], (41632 ^ _780086) ^ [_1600562, _1600564] : [-(c_Nitpick_Oinverse__frac(_1600562, _1600564) = hAPP(hAPP(c_Nitpick_Ofrac(_1600562), hAPP(c_Nitpick_Odenom(_1600562), _1600564)), hAPP(c_Nitpick_Onum(_1600562), _1600564)))], (41634 ^ _780086) ^ [_1600608, _1600610] : [-(c_Nitpick_Ouminus__frac(_1600608, _1600610) = c_Nitpick_OAbs__Frac(_1600608, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1600608), _1600610))), hAPP(c_Nitpick_Odenom(_1600608), _1600610))))], (41636 ^ _780086) ^ [_1600676, _1600678, _1600680] : [c_Nitpick_Oless__frac(_1600676, _1600678, _1600680), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1600676), c_Nitpick_Oplus__frac(_1600676, _1600678, c_Nitpick_Ouminus__frac(_1600676, _1600680)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (41642 ^ _780086) ^ [_1600787, _1600789, _1600791] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1600787), c_Nitpick_Oplus__frac(_1600787, _1600789, c_Nitpick_Ouminus__frac(_1600787, _1600791)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__frac(_1600787, _1600789, _1600791))], (41648 ^ _780086) ^ [_1600922, _1600924, _1600926] : [c_Nitpick_Oless__eq__frac(_1600922, _1600924, _1600926), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1600922), c_Nitpick_Oplus__frac(_1600922, _1600924, c_Nitpick_Ouminus__frac(_1600922, _1600926)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (41654 ^ _780086) ^ [_1601033, _1601035, _1601037] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1601033), c_Nitpick_Oplus__frac(_1601033, _1601035, c_Nitpick_Ouminus__frac(_1601033, _1601037)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__eq__frac(_1601033, _1601035, _1601037))], (41660 ^ _780086) ^ [_1601150] : [-(c_Nitpick_Onum(_1601150) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1601150, c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1601150)))], (41662 ^ _780086) ^ [_1601185] : [-(c_Nitpick_Odenom(_1601185) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1601185, c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1601185)))], (41664 ^ _780086) ^ [_1601220, _1601222, _1601224] : [-(c_Product__Type_Ointernal__split(_1601220, _1601222, _1601224) = c_Product__Type_Oprod_Oprod__case(_1601220, _1601222, _1601224))], (41666 ^ _780086) ^ [_1601255, _1601257, _1601259, _1601261] : [class_Rings_Olinordered__semidom(_1601255), 41672 ^ _780086 : [(41673 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1601257), 41671 ^ [_1601255, _1601257, _1601259, _1601261]), _1601259)))], (41675 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1601255), c_Groups_Ozero__class_Ozero(_1601255)), hAPP(_1601261, 41671 ^ [_1601255, _1601257, _1601259, _1601261])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1601255), c_Groups_Ozero__class_Ozero(_1601255)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1601257, _1601255), _1601261), _1601259))))], (41679 ^ _780086) ^ [_1601551, _1601553, _1601555, _1601557, _1601559, _1601561] : [-(hAPP(hAPP(c_Product__Type_Ointernal__split(_1601551, _1601553, _1601555), _1601557), hAPP(hAPP(c_Product__Type_OPair(_1601551, _1601553), _1601559), _1601561)) = hAPP(hAPP(_1601557, _1601559), _1601561))], (41681 ^ _780086) ^ [] : [-(c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41683 ^ _780086) ^ [] : [-(c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41685 ^ _780086) ^ [_1601645, _1601647] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 41686 ^ [_1601645, _1601647]), hAPP(_1601645, 41686 ^ [_1601645, _1601647]))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_OCollect(tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)), _1601645)), _1601647)))))], (41692 ^ _780086) ^ [_1601805, _1601807] : [-(c_List_Olenlex(_1601805, _1601807) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, tc_List_Olist(_1601805)), tc_List_Olist(_1601805)), c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_List_Olist(_1601805), c_Wellfounded_Oless__than, c_List_Olex(_1601805, _1601807))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1601805), tc_List_Olist(_1601805), tc_prod(tc_Nat_Onat, tc_List_Olist(_1601805))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_List_Olist(_1601805), tc_prod(tc_Nat_Onat, tc_List_Olist(_1601805))), tc_List_Olist(_1601805)), c_Product__Type_OPair(tc_Nat_Onat, tc_List_Olist(_1601805))), c_Nat_Osize__class_Osize(tc_List_Olist(_1601805)))), c_COMBI(tc_List_Olist(_1601805)))))], (41694 ^ _780086) ^ [_1601912, _1601914, _1601916] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1601912)), _1601914) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1601912)), _1601916)), _1601914 = _1601916], (41700 ^ _780086) ^ [_1602004, _1602006, _1602008, _1602010, _1602012] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602004), tc_List_Olist(_1602004))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602004), tc_List_Olist(_1602004)), _1602006), _1602008)), hAPP(c_List_Olexn(_1602004, _1602010), _1602012))), 41703 ^ _780086 : [(41704 ^ _780086) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1602004)), _1602006) = _1602012)], (41706 ^ _780086) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1602004)), _1602008) = _1602012)]]], (41708 ^ _780086) ^ [_1602207, _1602209] : [-(c_List_Olenlex(_1602207, _1602209) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1602207), tc_List_Olist(_1602207))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1602207), tc_List_Olist(_1602207), tc_HOL_Obool), hAPP(hAPP(c_COMBS(tc_List_Olist(_1602207), tc_fun(tc_List_Olist(_1602207), tc_HOL_Obool), tc_fun(tc_List_Olist(_1602207), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1602207), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1602207), tc_HOL_Obool), tc_fun(tc_List_Olist(_1602207), tc_HOL_Obool)), tc_List_Olist(_1602207)), c_COMBS(tc_List_Olist(_1602207), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1602207), tc_HOL_Obool), tc_fun(tc_List_Olist(_1602207), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1602207)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1602207)), c_fdisj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1602207), tc_fun(tc_List_Olist(_1602207), tc_Nat_Onat), tc_fun(tc_List_Olist(_1602207), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1602207), tc_Nat_Onat), tc_fun(tc_List_Olist(_1602207), tc_HOL_Obool)), tc_List_Olist(_1602207)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1602207))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1602207)), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1602207))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1602207)))))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1602207), tc_fun(tc_List_Olist(_1602207), tc_HOL_Obool), tc_fun(tc_List_Olist(_1602207), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1602207), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1602207), tc_HOL_Obool), tc_fun(tc_List_Olist(_1602207), tc_HOL_Obool)), tc_List_Olist(_1602207)), c_COMBS(tc_List_Olist(_1602207), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1602207), tc_HOL_Obool), tc_fun(tc_List_Olist(_1602207), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1602207)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1602207)), c_fconj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1602207), tc_fun(tc_List_Olist(_1602207), tc_Nat_Onat), tc_fun(tc_List_Olist(_1602207), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1602207), tc_Nat_Onat), tc_fun(tc_List_Olist(_1602207), tc_HOL_Obool)), tc_List_Olist(_1602207)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1602207))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1602207)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1602207))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1602207)))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1602207), tc_fun(tc_prod(tc_List_Olist(_1602207), tc_List_Olist(_1602207)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1602207), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1602207), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1602207), tc_List_Olist(_1602207)), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1602207), tc_List_Olist(_1602207)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1602207), tc_HOL_Obool)), tc_List_Olist(_1602207)), c_COMBC(tc_List_Olist(_1602207), tc_fun(tc_prod(tc_List_Olist(_1602207), tc_List_Olist(_1602207)), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1602207), tc_prod(tc_List_Olist(_1602207), tc_List_Olist(_1602207))), tc_fun(tc_List_Olist(_1602207), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1602207), tc_List_Olist(_1602207)), tc_HOL_Obool), tc_HOL_Obool)), tc_List_Olist(_1602207)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1602207), tc_List_Olist(_1602207)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1602207), tc_List_Olist(_1602207)), tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1602207)), c_member(tc_prod(tc_List_Olist(_1602207), tc_List_Olist(_1602207))))), c_Product__Type_OPair(tc_List_Olist(_1602207), tc_List_Olist(_1602207))))), c_List_Olex(_1602207, _1602209)))))))], (41710 ^ _780086) ^ [_1602763, _1602765, _1602767] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1602763)), c_List_Osublist(_1602763, _1602765, _1602767)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_Set_OCollect(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1602763)), _1602765)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1602767)))))], (41712 ^ _780086) ^ [_1602829, _1602831, _1602833] : [-(hAPP(c_List_Olexn(_1602829, _1602831), hAPP(c_Nat_OSuc, _1602833)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(_1602829), tc_List_Olist(_1602829)), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_prod(tc_prod(_1602829, tc_List_Olist(_1602829)), tc_prod(_1602829, tc_List_Olist(_1602829))), tc_prod(tc_List_Olist(_1602829), tc_List_Olist(_1602829)), c_Product__Type_Omap__pair(tc_prod(_1602829, tc_List_Olist(_1602829)), tc_List_Olist(_1602829), tc_prod(_1602829, tc_List_Olist(_1602829)), tc_List_Olist(_1602829), hAPP(c_Product__Type_Oprod_Oprod__case(_1602829, tc_List_Olist(_1602829), tc_List_Olist(_1602829)), c_List_Olist_OCons(_1602829)), hAPP(c_Product__Type_Oprod_Oprod__case(_1602829, tc_List_Olist(_1602829), tc_List_Olist(_1602829)), c_List_Olist_OCons(_1602829)))), c_Wellfounded_Olex__prod(_1602829, tc_List_Olist(_1602829), _1602831, hAPP(c_List_Olexn(_1602829, _1602831), _1602833)))), hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1602829), tc_List_Olist(_1602829))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1602829), tc_List_Olist(_1602829), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1602829), tc_fun(tc_List_Olist(_1602829), tc_HOL_Obool), tc_fun(tc_List_Olist(_1602829), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1602829), tc_HOL_Obool), tc_fun(tc_List_Olist(_1602829), tc_HOL_Obool)), tc_List_Olist(_1602829)), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1602829))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1602829)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1602829), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1602829)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1602829)))), hAPP(c_Nat_OSuc, _1602833))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1602829), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1602829)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1602829)))), hAPP(c_Nat_OSuc, _1602833)))))))], (41714 ^ _780086) ^ [_1603120, _1603122, _1603124, _1603126] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1603120)), _1603122)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1603120)), _1603124))), _1603122 = hAPP(hAPP(c_List_Olist_OCons(_1603120), _1603126), _1603124)], (41720 ^ _780086) ^ [_1603271, _1603273, _1603275] : [_1603271 = hAPP(hAPP(c_List_Olist_OCons(_1603273), _1603275), _1603271)], (41722 ^ _780086) ^ [_1603321, _1603323, _1603325] : [hAPP(hAPP(c_List_Olist_OCons(_1603321), _1603323), _1603325) = _1603325], (41724 ^ _780086) ^ [_1603380, _1603382, _1603384, _1603386, _1603388] : [hAPP(hAPP(c_List_Olist_OCons(_1603380), _1603382), _1603384) = hAPP(hAPP(c_List_Olist_OCons(_1603380), _1603386), _1603388), 41727 ^ _780086 : [(41728 ^ _780086) ^ [] : [-(_1603382 = _1603386)], (41730 ^ _780086) ^ [] : [-(_1603384 = _1603388)]]], (41732 ^ _780086) ^ [_1603517, _1603519, _1603521, _1603523, _1603525] : [-(hAPP(hAPP(c_List_Olist_OCons(_1603517), _1603519), _1603521) = hAPP(hAPP(c_List_Olist_OCons(_1603517), _1603523), _1603525)), _1603519 = _1603523, _1603521 = _1603525], (41742 ^ _780086) ^ [_1603692, _1603694, _1603696] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1603692)), hAPP(hAPP(c_List_Olist_OCons(_1603692), _1603694), _1603696)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1603692)), _1603696)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (41744 ^ _780086) ^ [_1603774, _1603776, _1603778, _1603780, _1603782, _1603784] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1603774), tc_List_Olist(_1603774))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1603774), tc_List_Olist(_1603774)), hAPP(hAPP(c_List_Olist_OCons(_1603774), _1603776), _1603778)), hAPP(hAPP(c_List_Olist_OCons(_1603774), _1603780), _1603782))), c_List_Olex(_1603774, _1603784))), 41749 ^ _780086 : [(41750 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1603774, _1603774)), hAPP(hAPP(c_Product__Type_OPair(_1603774, _1603774), _1603776), _1603780)), _1603784)))], (41752 ^ _780086) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1603774)), _1603778) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1603774)), _1603782))]], 41753 ^ _780086 : [(41754 ^ _780086) ^ [] : [-(_1603776 = _1603780)], (41756 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1603774), tc_List_Olist(_1603774))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1603774), tc_List_Olist(_1603774)), _1603778), _1603782)), c_List_Olex(_1603774, _1603784))))]]], (41758 ^ _780086) ^ [_1604172, _1604174, _1604176, _1604178, _1604180, _1604182] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1604172), tc_List_Olist(_1604172))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1604172), tc_List_Olist(_1604172)), hAPP(hAPP(c_List_Olist_OCons(_1604172), _1604174), _1604176)), hAPP(hAPP(c_List_Olist_OCons(_1604172), _1604178), _1604180))), c_List_Olex(_1604172, _1604182)))), 41759 ^ _780086 : [(41760 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1604172, _1604172)), hAPP(hAPP(c_Product__Type_OPair(_1604172, _1604172), _1604174), _1604178)), _1604182)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1604172)), _1604176) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1604172)), _1604180)], (41766 ^ _780086) ^ [] : [_1604174 = _1604178, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1604172), tc_List_Olist(_1604172))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1604172), tc_List_Olist(_1604172)), _1604176), _1604180)), c_List_Olex(_1604172, _1604182)))]]], (41774 ^ _780086) ^ [_1604628, _1604630, _1604632] : [-(c_List_Oset__Cons(_1604628, _1604630, _1604632) = hAPP(c_Set_OCollect(tc_List_Olist(_1604628)), hAPP(hAPP(c_COMBB(tc_fun(_1604628, tc_HOL_Obool), tc_HOL_Obool, tc_List_Olist(_1604628)), c_HOL_OEx(_1604628)), hAPP(hAPP(c_COMBB(tc_fun(_1604628, tc_fun(tc_List_Olist(_1604628), tc_HOL_Obool)), tc_fun(_1604628, tc_HOL_Obool), tc_List_Olist(_1604628)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1604628), tc_HOL_Obool), tc_HOL_Obool, _1604628), c_HOL_OEx(tc_List_Olist(_1604628)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1604628), tc_fun(_1604628, tc_fun(tc_List_Olist(_1604628), tc_HOL_Obool)), tc_fun(_1604628, tc_fun(tc_List_Olist(_1604628), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1604628, tc_fun(tc_fun(tc_List_Olist(_1604628), tc_HOL_Obool), tc_fun(tc_List_Olist(_1604628), tc_HOL_Obool))), tc_fun(tc_fun(_1604628, tc_fun(tc_List_Olist(_1604628), tc_HOL_Obool)), tc_fun(_1604628, tc_fun(tc_List_Olist(_1604628), tc_HOL_Obool))), tc_List_Olist(_1604628)), c_COMBS(_1604628, tc_fun(tc_List_Olist(_1604628), tc_HOL_Obool), tc_fun(tc_List_Olist(_1604628), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1604628, tc_fun(tc_List_Olist(_1604628), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1604628, tc_fun(tc_fun(tc_List_Olist(_1604628), tc_HOL_Obool), tc_fun(tc_List_Olist(_1604628), tc_HOL_Obool))), tc_List_Olist(_1604628)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1604628), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1604628), tc_HOL_Obool), tc_fun(tc_List_Olist(_1604628), tc_HOL_Obool)), _1604628), c_COMBS(tc_List_Olist(_1604628), tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1604628, tc_fun(tc_List_Olist(_1604628), tc_HOL_Obool)), tc_fun(_1604628, tc_fun(tc_List_Olist(_1604628), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_List_Olist(_1604628)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1604628), tc_HOL_Obool), tc_fun(tc_List_Olist(_1604628), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1604628), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1604628)), c_fconj))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1604628), tc_fun(_1604628, tc_fun(tc_List_Olist(_1604628), tc_List_Olist(_1604628))), tc_fun(_1604628, tc_fun(tc_List_Olist(_1604628), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(_1604628), tc_List_Olist(_1604628)), tc_fun(tc_List_Olist(_1604628), tc_HOL_Obool)), tc_fun(tc_fun(_1604628, tc_fun(tc_List_Olist(_1604628), tc_List_Olist(_1604628))), tc_fun(_1604628, tc_fun(tc_List_Olist(_1604628), tc_HOL_Obool))), tc_List_Olist(_1604628)), c_COMBB(tc_fun(tc_List_Olist(_1604628), tc_List_Olist(_1604628)), tc_fun(tc_List_Olist(_1604628), tc_HOL_Obool), _1604628)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1604628), tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1604628), tc_List_Olist(_1604628)), tc_fun(tc_List_Olist(_1604628), tc_HOL_Obool)), tc_List_Olist(_1604628)), c_COMBB(tc_List_Olist(_1604628), tc_HOL_Obool, tc_List_Olist(_1604628))), c_fequal))), c_List_Olist_OCons(_1604628)))))), hAPP(hAPP(c_COMBC(_1604628, tc_fun(tc_List_Olist(_1604628), tc_HOL_Obool), tc_fun(tc_List_Olist(_1604628), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1604628), tc_HOL_Obool), tc_fun(tc_List_Olist(_1604628), tc_HOL_Obool)), _1604628), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1604628))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1604628), c_fconj), hAPP(hAPP(c_COMBC(_1604628, tc_fun(_1604628, tc_HOL_Obool), tc_HOL_Obool), c_member(_1604628)), _1604630)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1604628), tc_fun(tc_List_Olist(_1604628), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1604628))), _1604632)))))))], (41776 ^ _780086) ^ [_1605178, _1605180, _1605182, _1605184] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1605178), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1605180), _1605182))), -(hAPP(c_Random_Opick(_1605180, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1605180)), _1605182), _1605184)), _1605178) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1605180), _1605182))], (41782 ^ _780086) ^ [_1605321, _1605323, _1605325, _1605327] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1605321), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1605323), _1605325)))), -(hAPP(c_Random_Opick(_1605323, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1605323)), _1605325), _1605327)), _1605321) = hAPP(c_Random_Opick(_1605323, _1605327), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1605321), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1605323), _1605325))))], (41788 ^ _780086) ^ [_1605409, _1605411, _1605413] : [-(c_Random_Oselect__weight(_1605409, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1605409)), hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1605409), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1605411)), _1605413)) = c_Random_Oselect__weight(_1605409, _1605413))], (41790 ^ _780086) ^ [_1605489, _1605491, _1605493, _1605495, _1605497, _1605499] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1605489), tc_List_Olist(_1605489))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1605489), tc_List_Olist(_1605489)), hAPP(hAPP(c_List_Olist_OCons(_1605489), _1605491), _1605493)), hAPP(hAPP(c_List_Olist_OCons(_1605489), _1605495), _1605497))), c_List_Olexord(_1605489, _1605499))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1605489, _1605489)), hAPP(hAPP(c_Product__Type_OPair(_1605489, _1605489), _1605491), _1605495)), _1605499))), 41797 ^ _780086 : [(41798 ^ _780086) ^ [] : [-(_1605491 = _1605495)], (41800 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1605489), tc_List_Olist(_1605489))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1605489), tc_List_Olist(_1605489)), _1605493), _1605497)), c_List_Olexord(_1605489, _1605499))))]]], (41802 ^ _780086) ^ [_1605816, _1605818, _1605820, _1605822, _1605824, _1605826] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1605816), tc_List_Olist(_1605816))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1605816), tc_List_Olist(_1605816)), hAPP(hAPP(c_List_Olist_OCons(_1605816), _1605818), _1605820)), hAPP(hAPP(c_List_Olist_OCons(_1605816), _1605822), _1605824))), c_List_Olexord(_1605816, _1605826)))), 41803 ^ _780086 : [(41804 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1605816, _1605816)), hAPP(hAPP(c_Product__Type_OPair(_1605816, _1605816), _1605818), _1605822)), _1605826))], (41806 ^ _780086) ^ [] : [_1605818 = _1605822, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1605816), tc_List_Olist(_1605816))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1605816), tc_List_Olist(_1605816)), _1605820), _1605824)), c_List_Olexord(_1605816, _1605826)))]]], (41814 ^ _780086) ^ [_1606210, _1606212, _1606214, _1606216] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1606210), tc_List_Olist(_1606210))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1606210), tc_List_Olist(_1606210)), _1606212), _1606214)), c_List_Olex(_1606210, _1606216))), 41817 ^ _780086 : [(41818 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1606210), tc_List_Olist(_1606210))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1606210), tc_List_Olist(_1606210)), _1606212), _1606214)), c_List_Olexord(_1606210, _1606216))))], (41820 ^ _780086) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606210)), _1606212) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606210)), _1606214))]]], (41822 ^ _780086) ^ [_1606461, _1606463, _1606465, _1606467] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1606461), tc_List_Olist(_1606461))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1606461), tc_List_Olist(_1606461)), _1606463), _1606465)), c_List_Olex(_1606461, _1606467)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1606461), tc_List_Olist(_1606461))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1606461), tc_List_Olist(_1606461)), _1606463), _1606465)), c_List_Olexord(_1606461, _1606467))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606461)), _1606463) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606461)), _1606465)], (41832 ^ _780086) ^ [_1606748, _1606750, _1606752, _1606754, _1606756, _1606758] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1606748, _1606748)), hAPP(hAPP(c_Product__Type_OPair(_1606748, _1606748), _1606750), _1606752)), c_Transitive__Closure_Ortrancl(_1606748, _1606754))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1606748), tc_List_Olist(_1606748))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1606748), tc_List_Olist(_1606748)), _1606756), _1606758)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1606748), c_List_Olistrel1(_1606748, _1606754)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1606748), tc_List_Olist(_1606748))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1606748), tc_List_Olist(_1606748)), hAPP(hAPP(c_List_Olist_OCons(_1606748), _1606750), _1606756)), hAPP(hAPP(c_List_Olist_OCons(_1606748), _1606752), _1606758))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1606748), c_List_Olistrel1(_1606748, _1606754)))))], (41842 ^ _780086) ^ [_1607109, _1607111, _1607113, _1607115] : [-(c_List_Olist_Olist__size(_1607109, _1607111, hAPP(hAPP(c_List_Olist_OCons(_1607109), _1607113), _1607115)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1607111, _1607113)), c_List_Olist_Olist__size(_1607109, _1607111, _1607115))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (41844 ^ _780086) ^ [_1607169, _1607171, _1607173, _1607175] : [hBOOL(hAPP(hAPP(c_member(_1607169), _1607171), c_Wellfounded_Oacc(_1607169, _1607173))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1607169)), _1607175), c_Wellfounded_Oacc(tc_List_Olist(_1607169), c_List_Olistrel1(_1607169, _1607173)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1607169)), hAPP(hAPP(c_List_Olist_OCons(_1607169), _1607171), _1607175)), c_Wellfounded_Oacc(tc_List_Olist(_1607169), c_List_Olistrel1(_1607169, _1607173)))))], (41854 ^ _780086) ^ [_1607410, _1607412, _1607414] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1607410, _1607410), tc_HOL_Obool)), _1607412), _1607414)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1607410), tc_List_Olist(_1607410)), tc_HOL_Obool)), c_List_Olistrel1(_1607410, _1607412)), c_List_Olistrel1(_1607410, _1607414))))], (41860 ^ _780086) ^ [_1607561, _1607563] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1607561), tc_List_Olist(_1607561)), tc_HOL_Obool)), c_List_Olistrel1(_1607561, c_Transitive__Closure_Ortrancl(_1607561, _1607563))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1607561), c_List_Olistrel1(_1607561, _1607563)))))], (41862 ^ _780086) ^ [_1607617, _1607619] : [-(c_List_Olistrel1(_1607617, hAPP(c_Relation_Oconverse(_1607617, _1607617), _1607619)) = hAPP(c_Relation_Oconverse(tc_List_Olist(_1607617), tc_List_Olist(_1607617)), c_List_Olistrel1(_1607617, _1607619)))], (41864 ^ _780086) ^ [_1607664, _1607666, _1607668, _1607670, _1607672] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1607664), tc_List_Olist(_1607664))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1607664), tc_List_Olist(_1607664)), _1607666), _1607668)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1607664), c_List_Olistrel1(_1607664, _1607670)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1607664), tc_List_Olist(_1607664))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1607664), tc_List_Olist(_1607664)), hAPP(hAPP(c_List_Olist_OCons(_1607664), _1607672), _1607666)), hAPP(hAPP(c_List_Olist_OCons(_1607664), _1607672), _1607668))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1607664), c_List_Olistrel1(_1607664, _1607670)))))], (41870 ^ _780086) ^ [_1607919, _1607921, _1607923, _1607925, _1607927] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1607919), tc_List_Olist(_1607919))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1607919), tc_List_Olist(_1607919)), _1607921), _1607923)), c_List_Olistrel1(_1607919, _1607925))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1607919), tc_List_Olist(_1607919))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1607919), tc_List_Olist(_1607919)), hAPP(hAPP(c_List_Olist_OCons(_1607919), _1607927), _1607921)), hAPP(hAPP(c_List_Olist_OCons(_1607919), _1607927), _1607923))), c_List_Olistrel1(_1607919, _1607925))))], (41876 ^ _780086) ^ [_1608154, _1608156, _1608158, _1608160] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1608154), tc_List_Olist(_1608154))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1608154), tc_List_Olist(_1608154)), _1608156), _1608158)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1608154), c_List_Olistrel1(_1608154, _1608160)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608154)), _1608156) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608154)), _1608158))], (41882 ^ _780086) ^ [_1608333, _1608335, _1608337, _1608339] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1608333), tc_List_Olist(_1608333))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1608333), tc_List_Olist(_1608333)), _1608335), _1608337)), c_List_Olistrel1(_1608333, _1608339))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608333)), _1608335) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608333)), _1608337))], (41888 ^ _780086) ^ [_1608523, _1608525, _1608527, _1608529] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1608523), tc_List_Olist(_1608523))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1608523), tc_List_Olist(_1608523)), _1608525), _1608527)), c_List_Olistrel1(_1608523, hAPP(c_Relation_Oconverse(_1608523, _1608523), _1608529)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1608523), tc_List_Olist(_1608523))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1608523), tc_List_Olist(_1608523)), _1608525), _1608527)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1608523), tc_List_Olist(_1608523)), c_List_Olistrel1(_1608523, _1608529)))))], (41894 ^ _780086) ^ [_1608752, _1608754, _1608756, _1608758] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1608752), tc_List_Olist(_1608752))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1608752), tc_List_Olist(_1608752)), _1608754), _1608756)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1608752), tc_List_Olist(_1608752)), c_List_Olistrel1(_1608752, _1608758)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1608752), tc_List_Olist(_1608752))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1608752), tc_List_Olist(_1608752)), _1608754), _1608756)), c_List_Olistrel1(_1608752, hAPP(c_Relation_Oconverse(_1608752, _1608752), _1608758)))))], (41900 ^ _780086) ^ [_1608987, _1608989, _1608991, _1608993, _1608995] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1608987, _1608987)), hAPP(hAPP(c_Product__Type_OPair(_1608987, _1608987), _1608989), _1608991)), _1608993)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1608987), tc_List_Olist(_1608987))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1608987), tc_List_Olist(_1608987)), hAPP(hAPP(c_List_Olist_OCons(_1608987), _1608989), _1608995)), hAPP(hAPP(c_List_Olist_OCons(_1608987), _1608991), _1608995))), c_List_Olistrel1(_1608987, _1608993))))], (41906 ^ _780086) ^ [_1609227, _1609229, _1609231, _1609233, _1609235, _1609237] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1609227), tc_List_Olist(_1609227))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1609227), tc_List_Olist(_1609227)), hAPP(hAPP(c_List_Olist_OCons(_1609227), _1609229), _1609231)), hAPP(hAPP(c_List_Olist_OCons(_1609227), _1609233), _1609235))), c_List_Olistrel1(_1609227, _1609237))), 41911 ^ _780086 : [(41912 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1609227, _1609227)), hAPP(hAPP(c_Product__Type_OPair(_1609227, _1609227), _1609229), _1609233)), _1609237)))], (41914 ^ _780086) ^ [] : [-(_1609231 = _1609235)]], 41915 ^ _780086 : [(41916 ^ _780086) ^ [] : [-(_1609229 = _1609233)], (41918 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1609227), tc_List_Olist(_1609227))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1609227), tc_List_Olist(_1609227)), _1609231), _1609235)), c_List_Olistrel1(_1609227, _1609237))))]]], (41920 ^ _780086) ^ [_1609597, _1609599, _1609601, _1609603, _1609605, _1609607] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1609597), tc_List_Olist(_1609597))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1609597), tc_List_Olist(_1609597)), hAPP(hAPP(c_List_Olist_OCons(_1609597), _1609599), _1609601)), hAPP(hAPP(c_List_Olist_OCons(_1609597), _1609603), _1609605))), c_List_Olistrel1(_1609597, _1609607)))), 41921 ^ _780086 : [(41922 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1609597, _1609597)), hAPP(hAPP(c_Product__Type_OPair(_1609597, _1609597), _1609599), _1609603)), _1609607)), _1609601 = _1609605], (41928 ^ _780086) ^ [] : [_1609599 = _1609603, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1609597), tc_List_Olist(_1609597))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1609597), tc_List_Olist(_1609597)), _1609601), _1609605)), c_List_Olistrel1(_1609597, _1609607)))]]], (41936 ^ _780086) ^ [_1610025, _1610027, _1610029, _1610031] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1610025), tc_List_Olist(_1610025), c_List_Olistrel(_1610025, _1610027)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1610025)), hAPP(hAPP(c_List_Olist_OCons(_1610025), _1610029), _1610031)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1610025), tc_HOL_Obool)))) = c_List_Oset__Cons(_1610025, hAPP(c_Relation_OImage(_1610025, _1610025, _1610027), hAPP(hAPP(c_Set_Oinsert(_1610025), _1610029), c_Orderings_Obot__class_Obot(tc_fun(_1610025, tc_HOL_Obool)))), hAPP(c_Relation_OImage(tc_List_Olist(_1610025), tc_List_Olist(_1610025), c_List_Olistrel(_1610025, _1610027)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1610025)), _1610031), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1610025), tc_HOL_Obool))))))], (41938 ^ _780086) ^ [_1610147, _1610149, _1610151] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1610147, _1610147)), hAPP(hAPP(c_Product__Type_OPair(_1610147, _1610147), 41939 ^ [_1610147, _1610149, _1610151]), 41939 ^ [_1610147, _1610149, _1610151])), _1610149))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1610147), tc_List_Olist(_1610147))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1610147), tc_List_Olist(_1610147)), _1610151), _1610151)), c_List_Olexord(_1610147, _1610149)))], (41945 ^ _780086) ^ [_1610322, _1610324, _1610326] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1610322), tc_List_Olist(_1610322))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1610322), tc_List_Olist(_1610322)), _1610324), _1610324)), c_List_Olistrel(_1610322, c_Transitive__Closure_Ortrancl(_1610322, _1610326)))))], (41947 ^ _780086) ^ [_1610382, _1610384, _1610386] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1610382, _1610382), tc_HOL_Obool)), _1610384), _1610386)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1610382), tc_List_Olist(_1610382)), tc_HOL_Obool)), c_List_Olistrel(_1610382, _1610384)), c_List_Olistrel(_1610382, _1610386))))], (41953 ^ _780086) ^ [_1610533, _1610535] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1610533), tc_List_Olist(_1610533)), tc_HOL_Obool)), c_List_Olistrel(_1610533, _1610535)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1610533), c_List_Olistrel1(_1610533, _1610535)))))], (41955 ^ _780086) ^ [_1610586, _1610588, _1610590, _1610592] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1610586), tc_List_Olist(_1610586))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1610586), tc_List_Olist(_1610586)), _1610588), _1610590)), c_List_Olistrel(_1610586, _1610592))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1610586)), _1610588) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1610586)), _1610590))], (41961 ^ _780086) ^ [_1610755, _1610757, _1610759, _1610761, _1610763] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1610755), tc_List_Olist(_1610755))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1610755), tc_List_Olist(_1610755)), _1610757), _1610759)), c_List_Olistrel(_1610755, c_Transitive__Closure_Ortrancl(_1610755, _1610761)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1610755), tc_List_Olist(_1610755))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1610755), tc_List_Olist(_1610755)), _1610759), _1610763)), c_List_Olistrel(_1610755, c_Transitive__Closure_Ortrancl(_1610755, _1610761)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1610755), tc_List_Olist(_1610755))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1610755), tc_List_Olist(_1610755)), _1610757), _1610763)), c_List_Olistrel(_1610755, c_Transitive__Closure_Ortrancl(_1610755, _1610761)))))], (41971 ^ _780086) ^ [_1611094, _1611096] : [-(c_List_Olistrel(_1611094, c_Transitive__Closure_Ortrancl(_1611094, _1611096)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(_1611094), c_List_Olistrel1(_1611094, _1611096)))], (41973 ^ _780086) ^ [_1611133, _1611135, _1611137, _1611139] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1611133), tc_List_Olist(_1611133))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1611133), tc_List_Olist(_1611133)), _1611135), _1611137)), c_List_Olistrel1(_1611133, _1611139))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1611133), tc_List_Olist(_1611133))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1611133), tc_List_Olist(_1611133)), _1611135), _1611137)), c_List_Olistrel(_1611133, c_Transitive__Closure_Ortrancl(_1611133, _1611139)))))], (41979 ^ _780086) ^ [_1611340, _1611342, _1611344] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1611340, _1611340), tc_HOL_Obool)), _1611342), _1611344)), c_Relation_Orefl__on(_1611340, c_Orderings_Otop__class_Otop(tc_fun(_1611340, tc_HOL_Obool)), _1611344), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1611340), tc_List_Olist(_1611340)), tc_HOL_Obool)), c_List_Olistrel1(_1611340, _1611342)), c_List_Olistrel(_1611340, _1611344))))], (41989 ^ _780086) ^ [_1611557, _1611559, _1611561, _1611563] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1611557), tc_List_Olist(_1611557))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1611557), tc_List_Olist(_1611557)), _1611559), _1611561)), c_List_Olistrel(_1611557, _1611563))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1611557), tc_List_Olist(_1611557))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1611557), tc_List_Olist(_1611557)), _1611559), _1611561)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1611557), c_List_Olistrel1(_1611557, _1611563)))))], (41995 ^ _780086) ^ [_1611768, _1611770, _1611772, _1611774, _1611776, _1611778] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1611768, _1611768)), hAPP(hAPP(c_Product__Type_OPair(_1611768, _1611768), _1611770), _1611772)), _1611774)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1611768), tc_List_Olist(_1611768))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1611768), tc_List_Olist(_1611768)), _1611776), _1611778)), c_List_Olistrel(_1611768, _1611774))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1611768), tc_List_Olist(_1611768))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1611768), tc_List_Olist(_1611768)), hAPP(hAPP(c_List_Olist_OCons(_1611768), _1611770), _1611776)), hAPP(hAPP(c_List_Olist_OCons(_1611768), _1611772), _1611778))), c_List_Olistrel(_1611768, _1611774))))], (42005 ^ _780086) ^ [_1612124, _1612126, _1612128, _1612130] : [c_List_Olistrelp(_1612124, hAPP(hAPP(c_COMBC(_1612124, tc_fun(tc_prod(_1612124, _1612124), tc_HOL_Obool), tc_fun(_1612124, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1612124, tc_fun(tc_fun(tc_prod(_1612124, _1612124), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1612124, _1612124), tc_HOL_Obool), tc_fun(_1612124, tc_HOL_Obool)), _1612124), c_COMBC(_1612124, tc_fun(tc_prod(_1612124, _1612124), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1612124, tc_prod(_1612124, _1612124)), tc_fun(_1612124, tc_fun(tc_fun(tc_prod(_1612124, _1612124), tc_HOL_Obool), tc_HOL_Obool)), _1612124), hAPP(c_COMBB(tc_prod(_1612124, _1612124), tc_fun(tc_fun(tc_prod(_1612124, _1612124), tc_HOL_Obool), tc_HOL_Obool), _1612124), c_member(tc_prod(_1612124, _1612124)))), c_Product__Type_OPair(_1612124, _1612124)))), _1612126), _1612128, _1612130), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1612124), tc_List_Olist(_1612124))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1612124), tc_List_Olist(_1612124)), _1612128), _1612130)), c_List_Olistrel(_1612124, _1612126))))], (42011 ^ _780086) ^ [_1612501, _1612503, _1612505, _1612507] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1612501), tc_List_Olist(_1612501))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1612501), tc_List_Olist(_1612501)), _1612505), _1612507)), c_List_Olistrel(_1612501, _1612503))), -(c_List_Olistrelp(_1612501, hAPP(hAPP(c_COMBC(_1612501, tc_fun(tc_prod(_1612501, _1612501), tc_HOL_Obool), tc_fun(_1612501, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1612501, tc_fun(tc_fun(tc_prod(_1612501, _1612501), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1612501, _1612501), tc_HOL_Obool), tc_fun(_1612501, tc_HOL_Obool)), _1612501), c_COMBC(_1612501, tc_fun(tc_prod(_1612501, _1612501), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1612501, tc_prod(_1612501, _1612501)), tc_fun(_1612501, tc_fun(tc_fun(tc_prod(_1612501, _1612501), tc_HOL_Obool), tc_HOL_Obool)), _1612501), hAPP(c_COMBB(tc_prod(_1612501, _1612501), tc_fun(tc_fun(tc_prod(_1612501, _1612501), tc_HOL_Obool), tc_HOL_Obool), _1612501), c_member(tc_prod(_1612501, _1612501)))), c_Product__Type_OPair(_1612501, _1612501)))), _1612503), _1612505, _1612507))], (42017 ^ _780086) ^ [_1612884, _1612886, _1612888, _1612890, _1612892] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1612884), tc_List_Olist(_1612884))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1612884), tc_List_Olist(_1612884)), _1612886), hAPP(hAPP(c_List_Olist_OCons(_1612884), _1612888), _1612890))), c_List_Olistrel(_1612884, _1612892))), 42022 ^ _780086 : [(42023 ^ _780086) ^ [] : [-(_1612886 = hAPP(hAPP(c_List_Olist_OCons(_1612884), 42020 ^ [_1612884, _1612886, _1612888, _1612890, _1612892]), 42021 ^ [_1612884, _1612886, _1612888, _1612890, _1612892]))], (42025 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1612884, _1612884)), hAPP(hAPP(c_Product__Type_OPair(_1612884, _1612884), 42020 ^ [_1612884, _1612886, _1612888, _1612890, _1612892]), _1612888)), _1612892)))], (42027 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1612884), tc_List_Olist(_1612884))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1612884), tc_List_Olist(_1612884)), 42021 ^ [_1612884, _1612886, _1612888, _1612890, _1612892]), _1612890)), c_List_Olistrel(_1612884, _1612892))))]]], (42029 ^ _780086) ^ [_1613273, _1613275, _1613277, _1613279, _1613281, _1613283] : [hBOOL(hAPP(hAPP(_1613273, _1613275), _1613277)), c_List_Olistrelp(_1613279, _1613273, _1613281, _1613283), -(c_List_Olistrelp(_1613279, _1613273, hAPP(hAPP(c_List_Olist_OCons(_1613279), _1613275), _1613281), hAPP(hAPP(c_List_Olist_OCons(_1613279), _1613277), _1613283)))], (42039 ^ _780086) ^ [_1613495, _1613497, _1613499, _1613501, _1613503, _1613505] : [c_List_Olistrelp(_1613495, _1613497, hAPP(hAPP(c_List_Olist_OCons(_1613495), _1613499), _1613501), hAPP(hAPP(c_List_Olist_OCons(_1613495), _1613503), _1613505)), 42042 ^ _780086 : [(42043 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(_1613497, _1613499), _1613503)))], (42045 ^ _780086) ^ [] : [-(c_List_Olistrelp(_1613495, _1613497, _1613501, _1613505))]]], (42047 ^ _780086) ^ [_1613652, _1613654, _1613656, _1613658, _1613660, _1613662] : [-(c_List_Olistrelp(_1613652, _1613654, hAPP(hAPP(c_List_Olist_OCons(_1613652), _1613656), _1613658), hAPP(hAPP(c_List_Olist_OCons(_1613652), _1613660), _1613662))), hBOOL(hAPP(hAPP(_1613654, _1613656), _1613660)), c_List_Olistrelp(_1613652, _1613654, _1613658, _1613662)], (42057 ^ _780086) ^ [_1613849, _1613851, _1613853, _1613855, _1613857] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1613849), tc_List_Olist(_1613849))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1613849), tc_List_Olist(_1613849)), hAPP(hAPP(c_List_Olist_OCons(_1613849), _1613851), _1613853)), _1613855)), c_List_Olistrel(_1613849, _1613857))), 42062 ^ _780086 : [(42063 ^ _780086) ^ [] : [-(_1613855 = hAPP(hAPP(c_List_Olist_OCons(_1613849), 42060 ^ [_1613849, _1613851, _1613853, _1613855, _1613857]), 42061 ^ [_1613849, _1613851, _1613853, _1613855, _1613857]))], (42065 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1613849, _1613849)), hAPP(hAPP(c_Product__Type_OPair(_1613849, _1613849), _1613851), 42060 ^ [_1613849, _1613851, _1613853, _1613855, _1613857])), _1613857)))], (42067 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1613849), tc_List_Olist(_1613849))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1613849), tc_List_Olist(_1613849)), _1613853), 42061 ^ [_1613849, _1613851, _1613853, _1613855, _1613857])), c_List_Olistrel(_1613849, _1613857))))]]], (42069 ^ _780086) ^ [_1614238, _1614240, _1614242] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1614238, _1614238), tc_HOL_Obool)), _1614240), hAPP(hAPP(c_Product__Type_OSigma(_1614238, _1614238), _1614242), hAPP(c_COMBK(tc_fun(_1614238, tc_HOL_Obool), _1614238), _1614242)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1614238), tc_List_Olist(_1614238)), tc_HOL_Obool)), c_List_Olistrel(_1614238, _1614240)), hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(_1614238), tc_List_Olist(_1614238)), c_List_Olists(_1614238, _1614242)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1614238), tc_HOL_Obool), tc_List_Olist(_1614238)), c_List_Olists(_1614238, _1614242))))))], (42075 ^ _780086) ^ [_1614483] : [-(c_List_Olists(_1614483, c_Orderings_Otop__class_Otop(tc_fun(_1614483, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1614483), tc_HOL_Obool)))], (42077 ^ _780086) ^ [_1614521, _1614523, _1614525] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1614521, tc_HOL_Obool)), _1614523), _1614525)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1614521), tc_HOL_Obool)), c_List_Olists(_1614521, _1614523)), c_List_Olists(_1614521, _1614525))))], (42083 ^ _780086) ^ [_1614656, _1614658, _1614660] : [c_Equiv__Relations_Oequiv(_1614656, _1614658, _1614660), -(c_Equiv__Relations_Oequiv(tc_List_Olist(_1614656), c_List_Olists(_1614656, _1614658), c_List_Olistrel(_1614656, _1614660)))], (42089 ^ _780086) ^ [_1614755, _1614757, _1614759] : [c_Relation_Orefl__on(_1614755, _1614757, _1614759), -(c_Relation_Orefl__on(tc_List_Olist(_1614755), c_List_Olists(_1614755, _1614757), c_List_Olistrel(_1614755, _1614759)))], (42095 ^ _780086) ^ [_1614875, _1614877, _1614879, _1614881] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1614875)), hAPP(hAPP(c_List_Olist_OCons(_1614875), _1614877), _1614879)), c_List_Olists(_1614875, _1614881))), 42098 ^ _780086 : [(42099 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1614875), _1614877), _1614881)))], (42101 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1614875)), _1614879), c_List_Olists(_1614875, _1614881))))]]], (42103 ^ _780086) ^ [_1615056, _1615058, _1615060, _1615062] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1615056)), hAPP(hAPP(c_List_Olist_OCons(_1615056), _1615058), _1615060)), c_List_Olists(_1615056, _1615062)))), hBOOL(hAPP(hAPP(c_member(_1615056), _1615058), _1615062)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1615056)), _1615060), c_List_Olists(_1615056, _1615062)))], (42113 ^ _780086) ^ [_1615273, _1615275, _1615277] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1615273)), _1615275), c_List_Olists(_1615273, c_Wellfounded_Oacc(_1615273, _1615277)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1615273)), _1615275), c_Wellfounded_Oacc(tc_List_Olist(_1615273), c_List_Olistrel1(_1615273, _1615277)))))], (42119 ^ _780086) ^ [_1615416, _1615418, _1615420] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1615416)), _1615418), c_Wellfounded_Oacc(tc_List_Olist(_1615416), c_List_Olistrel1(_1615416, _1615420)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1615416)), _1615418), c_List_Olists(_1615416, c_Wellfounded_Oacc(_1615416, _1615420)))))], (42125 ^ _780086) ^ [_1615580, _1615582, _1615584, _1615586] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1615580), tc_List_Olist(_1615580))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1615580), tc_List_Olist(_1615580)), _1615582), _1615584)), c_List_Olistrel(_1615580, _1615586))), 42128 ^ _780086 : [(42129 ^ _780086) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615580)), _1615582) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615580)), _1615584))], (42131 ^ _780086) ^ [_1615809] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1615809), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615580)), _1615582))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1615580, _1615580)), hAPP(hAPP(c_Product__Type_OPair(_1615580, _1615580), hAPP(hAPP(c_List_Onth(_1615580), _1615582), _1615809)), hAPP(hAPP(c_List_Onth(_1615580), _1615584), _1615809))), _1615586)))]]], (42137 ^ _780086) ^ [_1615988, _1615990, _1615992, _1615994] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1615988), tc_List_Olist(_1615988))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1615988), tc_List_Olist(_1615988)), _1615990), _1615992)), c_List_Olistrel(_1615988, _1615994)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615988)), _1615990) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615988)), _1615992), 42143 ^ _780086 : [(42144 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42142 ^ [_1615988, _1615990, _1615992, _1615994]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615988)), _1615990))))], (42146 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1615988, _1615988)), hAPP(hAPP(c_Product__Type_OPair(_1615988, _1615988), hAPP(hAPP(c_List_Onth(_1615988), _1615990), 42142 ^ [_1615988, _1615990, _1615992, _1615994])), hAPP(hAPP(c_List_Onth(_1615988), _1615992), 42142 ^ [_1615988, _1615990, _1615992, _1615994]))), _1615994))]]], (42150 ^ _780086) ^ [_1616432, _1616434, _1616436, _1616438] : [42153 ^ _780086 : [(42154 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1616432, _1616432)), hAPP(hAPP(c_Product__Type_OPair(_1616432, _1616432), 42151 ^ [_1616432, _1616434, _1616436, _1616438]), 42152 ^ [_1616432, _1616434, _1616436, _1616438])), _1616434))], (42156 ^ _780086) ^ [] : [42151 ^ [_1616432, _1616434, _1616436, _1616438] = 42152 ^ [_1616432, _1616434, _1616436, _1616438]], (42158 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1616432, _1616432)), hAPP(hAPP(c_Product__Type_OPair(_1616432, _1616432), 42152 ^ [_1616432, _1616434, _1616436, _1616438]), 42151 ^ [_1616432, _1616434, _1616436, _1616438])), _1616434))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1616432), tc_List_Olist(_1616432))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1616432), tc_List_Olist(_1616432)), _1616436), _1616438)), c_List_Olexord(_1616432, _1616434)))), -(_1616436 = _1616438), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1616432), tc_List_Olist(_1616432))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1616432), tc_List_Olist(_1616432)), _1616438), _1616436)), c_List_Olexord(_1616432, _1616434))))], (42170 ^ _780086) ^ [_1616988] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1616988)), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1616988), tc_HOL_Obool))))], (42172 ^ _780086) ^ [_1617042, _1617044, _1617046] : [_1617042 = _1617044, 42175 ^ _780086 : [(42176 ^ _780086) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617046)), _1617042) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617046)), _1617044))], (42178 ^ _780086) ^ [_1617190] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1617190), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617046)), _1617042))), -(hAPP(hAPP(c_List_Onth(_1617046), _1617042), _1617190) = hAPP(hAPP(c_List_Onth(_1617046), _1617044), _1617190))]]], (42184 ^ _780086) ^ [_1617329, _1617331, _1617333] : [-(_1617329 = _1617331), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617333)), _1617329) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617333)), _1617331), 42190 ^ _780086 : [(42191 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42189 ^ [_1617329, _1617331, _1617333]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617333)), _1617329))))], (42193 ^ _780086) ^ [] : [hAPP(hAPP(c_List_Onth(_1617333), _1617329), 42189 ^ [_1617329, _1617331, _1617333]) = hAPP(hAPP(c_List_Onth(_1617333), _1617331), 42189 ^ [_1617329, _1617331, _1617333])]]], (42197 ^ _780086) ^ [_1617644, _1617646, _1617648] : [-(hAPP(hAPP(c_List_Onth(_1617644), hAPP(hAPP(c_List_Olist_OCons(_1617644), _1617646), _1617648)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1617646)], (42199 ^ _780086) ^ [_1617687, _1617689, _1617691, _1617693] : [-(hAPP(hAPP(c_List_Onth(_1617687), hAPP(hAPP(c_List_Olist_OCons(_1617687), _1617689), _1617691)), hAPP(c_Nat_OSuc, _1617693)) = hAPP(hAPP(c_List_Onth(_1617687), _1617691), _1617693))], (42201 ^ _780086) ^ [_1617743, _1617745, _1617747, _1617749] : [-(hAPP(hAPP(c_List_Onth(_1617743), hAPP(hAPP(c_List_Olist_OCons(_1617743), _1617745), _1617747)), _1617749) = c_Nat_Onat_Onat__case(_1617743, _1617745, hAPP(c_List_Onth(_1617743), _1617747), _1617749))], (42203 ^ _780086) ^ [_1617813, _1617815, _1617817, _1617819] : [_1617813 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1617815), hAPP(hAPP(c_List_Olist_OCons(_1617815), _1617817), _1617819)), _1617813) = _1617817)], (42209 ^ _780086) ^ [_1617920, _1617922, _1617924, _1617926] : [-(_1617920 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1617922), hAPP(hAPP(c_List_Olist_OCons(_1617922), _1617924), _1617926)), _1617920) = hAPP(hAPP(c_List_Onth(_1617922), _1617926), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1617920), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (42215 ^ _780086) ^ [_1618007, _1618009, _1618011, _1618013] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1618007) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1618009), hAPP(hAPP(c_List_Olist_OCons(_1618009), _1618011), _1618013)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1618007)) = _1618011)], (42221 ^ _780086) ^ [_1618126, _1618128, _1618130, _1618132] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1618126) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1618128), hAPP(hAPP(c_List_Olist_OCons(_1618128), _1618130), _1618132)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1618126)) = hAPP(hAPP(c_List_Onth(_1618128), _1618132), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1618126)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (42227 ^ _780086) ^ [_1618228, _1618230, _1618232, _1618234] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1618228), tc_List_Olist(_1618228))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1618228), tc_List_Olist(_1618228)), _1618230), _1618232)), c_List_Olexord(_1618228, _1618234))), 42232 ^ _780086 : [(42233 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1618228)), _1618230)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1618228)), _1618232))))], (42235 ^ _780086) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1618228), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1618228)), _1618230)), _1618232) = _1618230)]], 42237 ^ _780086 : [(42238 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42236 ^ [_1618228, _1618230, _1618232, _1618234]), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1618228)), _1618230)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1618228)), _1618232)))))], (42240 ^ _780086) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1618228), 42236 ^ [_1618228, _1618230, _1618232, _1618234]), _1618230) = hAPP(hAPP(c_List_Otake(_1618228), 42236 ^ [_1618228, _1618230, _1618232, _1618234]), _1618232))], (42242 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1618228, _1618228)), hAPP(hAPP(c_Product__Type_OPair(_1618228, _1618228), hAPP(hAPP(c_List_Onth(_1618228), _1618230), 42236 ^ [_1618228, _1618230, _1618232, _1618234])), hAPP(hAPP(c_List_Onth(_1618228), _1618232), 42236 ^ [_1618228, _1618230, _1618232, _1618234]))), _1618234)))]]], (42244 ^ _780086) ^ [_1618768, _1618770, _1618772, _1618774] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1618768), tc_List_Olist(_1618768))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1618768), tc_List_Olist(_1618768)), _1618770), _1618772)), c_List_Olexord(_1618768, _1618774)))), 42245 ^ _780086 : [(42246 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1618768)), _1618770)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1618768)), _1618772))), hAPP(hAPP(c_List_Otake(_1618768), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1618768)), _1618770)), _1618772) = _1618770], (42252 ^ _780086) ^ [_1619075] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1619075), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1618768)), _1618770)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1618768)), _1618772)))), hAPP(hAPP(c_List_Otake(_1618768), _1619075), _1618770) = hAPP(hAPP(c_List_Otake(_1618768), _1619075), _1618772), hBOOL(hAPP(hAPP(c_member(tc_prod(_1618768, _1618768)), hAPP(hAPP(c_Product__Type_OPair(_1618768, _1618768), hAPP(hAPP(c_List_Onth(_1618768), _1618770), _1619075)), hAPP(hAPP(c_List_Onth(_1618768), _1618772), _1619075))), _1618774))]]], (42264 ^ _780086) ^ [_1619429, _1619431, _1619433] : [-(hAPP(c_List_Oset(_1619429), c_List_Osublist(_1619429, _1619431, _1619433)) = hAPP(c_Set_OCollect(_1619429), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1619429), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1619429, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1619429), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1619429), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1619429, tc_fun(tc_Nat_Onat, _1619429), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1619429, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1619429), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1619429), c_COMBB(_1619429, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1619429), _1619431))))), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1619429)), _1619431)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1619433))))))], (42266 ^ _780086) ^ [_1619573, _1619575] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1619573), hAPP(c_List_Oset(_1619573), _1619575))))], (42268 ^ _780086) ^ [_1619607, _1619609, _1619611] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1619607, tc_HOL_Obool)), hAPP(c_List_Oset(_1619607), _1619609)), hAPP(c_List_Oset(_1619607), hAPP(hAPP(c_List_Olist_OCons(_1619607), _1619611), _1619609)))))], (42270 ^ _780086) ^ [_1619662, _1619664, _1619666] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1619662)), _1619664)), _1619666)), -(hAPP(hAPP(c_List_Otake(_1619662), _1619666), _1619664) = _1619664)], (42276 ^ _780086) ^ [_1619781, _1619783, _1619785] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1619781, tc_HOL_Obool)), hAPP(c_List_Oset(_1619781), hAPP(hAPP(c_List_Otake(_1619781), _1619783), _1619785))), hAPP(c_List_Oset(_1619781), _1619785))))], (42278 ^ _780086) ^ [_1619836, _1619838, _1619840, _1619842] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1619836), _1619838)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1619840, tc_HOL_Obool)), hAPP(c_List_Oset(_1619840), hAPP(hAPP(c_List_Otake(_1619840), _1619836), _1619842))), hAPP(c_List_Oset(_1619840), hAPP(hAPP(c_List_Otake(_1619840), _1619838), _1619842)))))], (42284 ^ _780086) ^ [_1619999, _1620001, _1620003] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1619999, tc_HOL_Obool)), hAPP(c_List_Oset(_1619999), c_List_Osublist(_1619999, _1620001, _1620003))), hAPP(c_List_Oset(_1619999), _1620001))))], (42286 ^ _780086) ^ [_1620050, _1620052, _1620054, _1620056] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1620050), _1620052)), -(hAPP(hAPP(c_List_Onth(_1620054), hAPP(hAPP(c_List_Otake(_1620054), _1620052), _1620056)), _1620050) = hAPP(hAPP(c_List_Onth(_1620054), _1620056), _1620050))], (42292 ^ _780086) ^ [_1620188, _1620190, _1620192, _1620194] : [-(hBOOL(hAPP(hAPP(c_member(_1620188), _1620190), hAPP(c_List_Oset(_1620188), _1620192)))), hBOOL(hAPP(hAPP(c_member(_1620188), _1620190), hAPP(c_List_Oset(_1620188), c_List_Osublist(_1620188, _1620192, _1620194))))], (42298 ^ _780086) ^ [_1620312, _1620314, _1620316, _1620318] : [hBOOL(hAPP(hAPP(c_member(_1620312), _1620314), hAPP(c_List_Oset(_1620312), hAPP(hAPP(c_List_Otake(_1620312), _1620316), _1620318)))), -(hBOOL(hAPP(hAPP(c_member(_1620312), _1620314), hAPP(c_List_Oset(_1620312), _1620318))))], (42304 ^ _780086) ^ [_1620457, _1620459, _1620461, _1620463] : [hBOOL(hAPP(hAPP(c_member(_1620457), _1620459), hAPP(c_List_Oset(_1620457), c_List_Osublist(_1620457, _1620461, _1620463)))), -(hBOOL(hAPP(hAPP(c_member(_1620457), _1620459), hAPP(c_List_Oset(_1620457), _1620461))))], (42310 ^ _780086) ^ [_1620594, _1620596, _1620598, _1620600] : [hBOOL(hAPP(hAPP(c_member(_1620594), _1620596), hAPP(c_List_Oset(_1620594), hAPP(hAPP(c_List_Olist_OCons(_1620594), _1620598), _1620600)))), -(_1620596 = _1620598), -(hBOOL(hAPP(hAPP(c_member(_1620594), _1620596), hAPP(c_List_Oset(_1620594), _1620600))))], (42320 ^ _780086) ^ [_1620752, _1620754, _1620756, _1620758] : [-(hAPP(hAPP(c_List_Otake(_1620752), hAPP(c_Nat_OSuc, _1620754)), hAPP(hAPP(c_List_Olist_OCons(_1620752), _1620756), _1620758)) = hAPP(hAPP(c_List_Olist_OCons(_1620752), _1620756), hAPP(hAPP(c_List_Otake(_1620752), _1620754), _1620758)))], (42322 ^ _780086) ^ [_1620816, _1620818, _1620820] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1620816)), hAPP(hAPP(c_List_Otake(_1620816), _1620818), _1620820)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1620816)), _1620820)), _1620818))], (42324 ^ _780086) ^ [_1620871, _1620873, _1620875, _1620877] : [-(hAPP(hAPP(c_List_Otake(_1620871), _1620873), hAPP(hAPP(c_List_Otake(_1620871), _1620875), _1620877)) = hAPP(hAPP(c_List_Otake(_1620871), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1620873), _1620875)), _1620877))], (42326 ^ _780086) ^ [_1620930, _1620932, _1620934] : [-(hAPP(c_List_Oset(_1620930), hAPP(hAPP(c_List_Olist_OCons(_1620930), _1620932), _1620934)) = hAPP(hAPP(c_Set_Oinsert(_1620930), _1620932), hAPP(c_List_Oset(_1620930), _1620934)))], (42328 ^ _780086) ^ [_1620983, _1620985, _1620987] : [-(c_List_Osublist(_1620983, _1620985, hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1620987)) = hAPP(hAPP(c_List_Otake(_1620983), _1620987), _1620985))], (42330 ^ _780086) ^ [_1621025, _1621027] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1621025), hAPP(c_List_Oset(_1621025), _1621027))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621025)), _1621027))))], (42332 ^ _780086) ^ [_1621090, _1621092, _1621094] : [42334 ^ _780086 : [(42335 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1621090), 42333 ^ [_1621090, _1621092, _1621094]), hAPP(c_List_Oset(_1621090), _1621092))))], (42337 ^ _780086) ^ [] : [hBOOL(hAPP(_1621094, 42333 ^ [_1621090, _1621092, _1621094]))]], 42338 ^ _780086 : [(42339 ^ _780086) ^ [_1621274] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1621274), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621090)), _1621092))), -(hBOOL(hAPP(_1621094, hAPP(hAPP(c_List_Onth(_1621090), _1621092), _1621274))))]]], (42345 ^ _780086) ^ [_1621401, _1621403, _1621405] : [42347 ^ _780086 : [(42348 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42346 ^ [_1621401, _1621403, _1621405]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621401)), _1621403))))], (42350 ^ _780086) ^ [] : [hBOOL(hAPP(_1621405, hAPP(hAPP(c_List_Onth(_1621401), _1621403), 42346 ^ [_1621401, _1621403, _1621405])))]], 42351 ^ _780086 : [(42352 ^ _780086) ^ [_1621603] : [hBOOL(hAPP(hAPP(c_member(_1621401), _1621603), hAPP(c_List_Oset(_1621401), _1621403))), -(hBOOL(hAPP(_1621405, _1621603)))]]], (42358 ^ _780086) ^ [_1621720, _1621722, _1621724, _1621726, _1621728] : [hBOOL(hAPP(hAPP(c_member(_1621720), _1621722), hAPP(c_List_Oset(_1621720), _1621724))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1621726), hAPP(_1621728, _1621722))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1621726), c_List_Olist_Olist__size(_1621720, _1621728, _1621724))))], (42368 ^ _780086) ^ [_1621919, _1621921, _1621923, _1621925, _1621927] : [hBOOL(hAPP(hAPP(c_member(_1621919), _1621921), hAPP(c_List_Oset(_1621919), _1621923))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1621925), hAPP(_1621927, _1621921))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1621925), c_List_Olist_Olist__size(_1621919, _1621927, _1621923))))], (42388 ^ _780086) ^ [_1622363, _1622365, _1622367] : [42390 ^ _780086 : [(42391 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1622363), 42389 ^ [_1622363, _1622365, _1622367]), hAPP(c_List_Oset(_1622363), _1622365))))], (42393 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1622363), 42389 ^ [_1622363, _1622365, _1622367]), _1622367))]], -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1622363)), _1622365), c_List_Olists(_1622363, _1622367))))], (42378 ^ _780086) ^ [_1622136, _1622138, _1622140] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1622136)), _1622138), c_List_Olists(_1622136, _1622140))), 42381 ^ _780086 : [(42382 ^ _780086) ^ [_1622244] : [hBOOL(hAPP(hAPP(c_member(_1622136), _1622244), hAPP(c_List_Oset(_1622136), _1622138))), -(hBOOL(hAPP(hAPP(c_member(_1622136), _1622244), _1622140)))]]], (42397 ^ _780086) ^ [_1622583, _1622585, _1622587] : [hBOOL(hAPP(hAPP(c_member(_1622583), _1622585), hAPP(c_List_Oset(_1622583), _1622587))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622583)), _1622587))))], (42403 ^ _780086) ^ [_1622704, _1622706, _1622708] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1622704), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622706)), _1622708))), -(hBOOL(hAPP(hAPP(c_member(_1622706), hAPP(hAPP(c_List_Onth(_1622706), _1622708), _1622704)), hAPP(c_List_Oset(_1622706), _1622708))))], (42409 ^ _780086) ^ [_1622865, _1622867, _1622869] : [hBOOL(hAPP(hAPP(c_member(_1622865), _1622867), hAPP(c_List_Oset(_1622865), _1622869))), 42413 ^ _780086 : [(42414 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42412 ^ [_1622865, _1622867, _1622869]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622865)), _1622869))))], (42416 ^ _780086) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1622865), _1622869), 42412 ^ [_1622865, _1622867, _1622869]) = _1622867)]]], (42418 ^ _780086) ^ [_1623053, _1623055, _1623057] : [-(hBOOL(hAPP(hAPP(c_member(_1623053), _1623055), hAPP(c_List_Oset(_1623053), _1623057)))), 42419 ^ _780086 : [(42420 ^ _780086) ^ [_1623127] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1623127), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1623053)), _1623057))), hAPP(hAPP(c_List_Onth(_1623053), _1623057), _1623127) = _1623055]]], (42428 ^ _780086) ^ [_1623289, _1623291] : [-(c_List_Olists(_1623289, _1623291) = hAPP(c_Set_OCollect(tc_List_Olist(_1623289)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1623289), tc_fun(_1623289, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1623289, tc_HOL_Obool), tc_fun(tc_fun(_1623289, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1623289)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1623289, tc_HOL_Obool))), c_List_Oset(_1623289))), _1623291)))], (42430 ^ _780086) ^ [_1623367, _1623369] : [-(hAPP(c_List_Oset(_1623367), _1623369) = hAPP(c_Set_OCollect(_1623367), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1623367), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1623367, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1623367), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1623367), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1623367, tc_fun(tc_Nat_Onat, _1623367), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1623367, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1623367), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1623367), c_COMBB(_1623367, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1623367), _1623369))))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1623367)), _1623369))))))], (42432 ^ _780086) ^ [_1623493, _1623495, _1623497] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1623493), _1623495)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1623493)), hAPP(c_Set_OCollect(tc_List_Olist(_1623493)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1623493), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1623493)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1623493), tc_fun(_1623493, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1623493, tc_HOL_Obool), tc_fun(tc_fun(_1623493, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1623493)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1623493, tc_HOL_Obool))), c_List_Oset(_1623493))), _1623495))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1623493), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1623493)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1623493)))), _1623497))))))], (42438 ^ _780086) ^ [_1623796, _1623798, _1623800] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1623796), _1623798)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1623796)), hAPP(c_Set_OCollect(tc_List_Olist(_1623796)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1623796), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1623796)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1623796), tc_fun(_1623796, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1623796, tc_HOL_Obool), tc_fun(tc_fun(_1623796, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1623796)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1623796, tc_HOL_Obool))), c_List_Oset(_1623796))), _1623798))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1623796), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1623796)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1623796)))), _1623800))))))], (42444 ^ _780086) ^ [_1624120, _1624122, _1624124, _1624126] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1624120), tc_List_Olist(_1624120))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1624120), tc_List_Olist(_1624120)), _1624122), _1624124)), c_List_Olistrel(_1624120, _1624126))), 42447 ^ _780086 : [(42448 ^ _780086) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1624120)), _1624122) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1624120)), _1624124))], (42450 ^ _780086) ^ [_1624456] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1624120, _1624120)), _1624456), hAPP(c_List_Oset(tc_prod(_1624120, _1624120)), hAPP(hAPP(c_List_Ozip(_1624120, _1624120), _1624122), _1624124)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1624120, _1624120, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1624120, tc_fun(tc_prod(_1624120, _1624120), tc_HOL_Obool), tc_fun(_1624120, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1624120, tc_fun(tc_fun(tc_prod(_1624120, _1624120), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1624120, _1624120), tc_HOL_Obool), tc_fun(_1624120, tc_HOL_Obool)), _1624120), c_COMBC(_1624120, tc_fun(tc_prod(_1624120, _1624120), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1624120, tc_prod(_1624120, _1624120)), tc_fun(_1624120, tc_fun(tc_fun(tc_prod(_1624120, _1624120), tc_HOL_Obool), tc_HOL_Obool)), _1624120), hAPP(c_COMBB(tc_prod(_1624120, _1624120), tc_fun(tc_fun(tc_prod(_1624120, _1624120), tc_HOL_Obool), tc_HOL_Obool), _1624120), c_member(tc_prod(_1624120, _1624120)))), c_Product__Type_OPair(_1624120, _1624120)))), _1624126)), _1624456)))]]], (42456 ^ _780086) ^ [_1624849, _1624851, _1624853, _1624855] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1624849), tc_List_Olist(_1624849))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1624849), tc_List_Olist(_1624849)), _1624851), _1624853)), c_List_Olistrel(_1624849, _1624855)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1624849)), _1624851) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1624849)), _1624853), 42462 ^ _780086 : [(42463 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1624849, _1624849)), 42461 ^ [_1624849, _1624851, _1624853, _1624855]), hAPP(c_List_Oset(tc_prod(_1624849, _1624849)), hAPP(hAPP(c_List_Ozip(_1624849, _1624849), _1624851), _1624853)))))], (42465 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1624849, _1624849, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1624849, tc_fun(tc_prod(_1624849, _1624849), tc_HOL_Obool), tc_fun(_1624849, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1624849, tc_fun(tc_fun(tc_prod(_1624849, _1624849), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1624849, _1624849), tc_HOL_Obool), tc_fun(_1624849, tc_HOL_Obool)), _1624849), c_COMBC(_1624849, tc_fun(tc_prod(_1624849, _1624849), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1624849, tc_prod(_1624849, _1624849)), tc_fun(_1624849, tc_fun(tc_fun(tc_prod(_1624849, _1624849), tc_HOL_Obool), tc_HOL_Obool)), _1624849), hAPP(c_COMBB(tc_prod(_1624849, _1624849), tc_fun(tc_fun(tc_prod(_1624849, _1624849), tc_HOL_Obool), tc_HOL_Obool), _1624849), c_member(tc_prod(_1624849, _1624849)))), c_Product__Type_OPair(_1624849, _1624849)))), _1624855)), 42461 ^ [_1624849, _1624851, _1624853, _1624855]))]]], (42469 ^ _780086) ^ [_1625587, _1625589, _1625591, _1625593] : [-(hAPP(c_List_Oset(tc_prod(_1625587, _1625589)), hAPP(hAPP(c_List_Ozip(_1625587, _1625589), _1625591), _1625593)) = hAPP(c_Set_OCollect(tc_prod(_1625587, _1625589)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1625587, _1625589)), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1625587, _1625589), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_prod(_1625587, _1625589)), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_prod(_1625587, _1625589)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(tc_prod(_1625587, _1625589), tc_fun(tc_Nat_Onat, tc_prod(_1625587, _1625589)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1625587, _1625589), tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_prod(_1625587, _1625589)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_prod(_1625587, _1625589)), c_COMBB(tc_prod(_1625587, _1625589), tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1625589, tc_prod(_1625587, _1625589)), hAPP(hAPP(c_COMBB(_1625587, tc_fun(_1625589, tc_prod(_1625587, _1625589)), tc_Nat_Onat), c_Product__Type_OPair(_1625587, _1625589)), hAPP(c_List_Onth(_1625587), _1625591))), hAPP(c_List_Onth(_1625589), _1625593)))))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625587)), _1625591)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625589)), _1625593)))))))], (42471 ^ _780086) ^ [_1625812, _1625814, _1625816, _1625818, _1625820] : [-(hAPP(hAPP(c_List_Otake(tc_prod(_1625812, _1625814)), _1625816), hAPP(hAPP(c_List_Ozip(_1625812, _1625814), _1625818), _1625820)) = hAPP(hAPP(c_List_Ozip(_1625812, _1625814), hAPP(hAPP(c_List_Otake(_1625812), _1625816), _1625818)), hAPP(hAPP(c_List_Otake(_1625814), _1625816), _1625820)))], (42473 ^ _780086) ^ [_1625888, _1625890, _1625892, _1625894] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(_1625888, _1625890))), hAPP(hAPP(c_List_Ozip(_1625888, _1625890), _1625892), _1625894)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625888)), _1625892)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625890)), _1625894)))], (42475 ^ _780086) ^ [_1625956, _1625958, _1625960, _1625962, _1625964, _1625966] : [-(hAPP(hAPP(c_List_Ozip(_1625956, _1625958), hAPP(hAPP(c_List_Olist_OCons(_1625956), _1625960), _1625962)), hAPP(hAPP(c_List_Olist_OCons(_1625958), _1625964), _1625966)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1625956, _1625958)), hAPP(hAPP(c_Product__Type_OPair(_1625956, _1625958), _1625960), _1625964)), hAPP(hAPP(c_List_Ozip(_1625956, _1625958), _1625962), _1625966)))], (42477 ^ _780086) ^ [_1626061, _1626063, _1626065] : [_1626061 = _1626063, 42480 ^ _780086 : [(42481 ^ _780086) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626065)), _1626061) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626065)), _1626063))], (42483 ^ _780086) ^ [_1626217] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1626065, _1626065)), _1626217), hAPP(c_List_Oset(tc_prod(_1626065, _1626065)), hAPP(hAPP(c_List_Ozip(_1626065, _1626065), _1626061), _1626063)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1626065, _1626065, tc_HOL_Obool), c_fequal), _1626217)))]]], (42489 ^ _780086) ^ [_1626372, _1626374, _1626376] : [-(_1626372 = _1626374), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626376)), _1626372) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626376)), _1626374), 42495 ^ _780086 : [(42496 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1626376, _1626376)), 42494 ^ [_1626372, _1626374, _1626376]), hAPP(c_List_Oset(tc_prod(_1626376, _1626376)), hAPP(hAPP(c_List_Ozip(_1626376, _1626376), _1626372), _1626374)))))], (42498 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1626376, _1626376, tc_HOL_Obool), c_fequal), 42494 ^ [_1626372, _1626374, _1626376]))]]], (42502 ^ _780086) ^ [_1626707, _1626709, _1626711, _1626713] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1626707, _1626707)), hAPP(hAPP(c_Product__Type_OPair(_1626707, _1626707), _1626709), _1626711)), hAPP(c_List_Oset(tc_prod(_1626707, _1626707)), hAPP(hAPP(c_List_Ozip(_1626707, _1626707), _1626713), _1626713)))), 42505 ^ _780086 : [(42506 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1626707), _1626709), hAPP(c_List_Oset(_1626707), _1626713))))], (42508 ^ _780086) ^ [] : [-(_1626709 = _1626711)]]], (42510 ^ _780086) ^ [_1626906, _1626908, _1626910, _1626912] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1626906, _1626906)), hAPP(hAPP(c_Product__Type_OPair(_1626906, _1626906), _1626908), _1626910)), hAPP(c_List_Oset(tc_prod(_1626906, _1626906)), hAPP(hAPP(c_List_Ozip(_1626906, _1626906), _1626912), _1626912))))), hBOOL(hAPP(hAPP(c_member(_1626906), _1626908), hAPP(c_List_Oset(_1626906), _1626912))), _1626908 = _1626910], (42520 ^ _780086) ^ [_1627141, _1627143, _1627145, _1627147, _1627149, _1627151] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1627141, _1627143)), hAPP(hAPP(c_Product__Type_OPair(_1627141, _1627143), _1627145), _1627147)), hAPP(c_List_Oset(tc_prod(_1627141, _1627143)), hAPP(hAPP(c_List_Ozip(_1627141, _1627143), _1627149), _1627151)))), -(hBOOL(hAPP(hAPP(c_member(_1627141), _1627145), hAPP(c_List_Oset(_1627141), _1627149))))], (42526 ^ _780086) ^ [_1627322, _1627324, _1627326, _1627328, _1627330, _1627332] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1627322, _1627324)), hAPP(hAPP(c_Product__Type_OPair(_1627322, _1627324), _1627326), _1627328)), hAPP(c_List_Oset(tc_prod(_1627322, _1627324)), hAPP(hAPP(c_List_Ozip(_1627322, _1627324), _1627330), _1627332)))), -(hBOOL(hAPP(hAPP(c_member(_1627324), _1627328), hAPP(c_List_Oset(_1627324), _1627332))))], (42532 ^ _780086) ^ [_1627503, _1627505, _1627507, _1627509, _1627511, _1627513] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1627503, _1627505)), hAPP(hAPP(c_Product__Type_OPair(_1627503, _1627505), _1627507), _1627509)), hAPP(c_List_Oset(tc_prod(_1627503, _1627505)), hAPP(hAPP(c_List_Ozip(_1627503, _1627505), _1627511), _1627513)))), 42535 ^ _780086 : [(42536 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1627503), _1627507), hAPP(c_List_Oset(_1627503), _1627511))))], (42538 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1627505), _1627509), hAPP(c_List_Oset(_1627505), _1627513))))]]], (42540 ^ _780086) ^ [_1627738, _1627740, _1627742, _1627744, _1627746] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1627738), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627740)), _1627742))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1627738), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627744)), _1627746))), -(hAPP(hAPP(c_List_Onth(tc_prod(_1627740, _1627744)), hAPP(hAPP(c_List_Ozip(_1627740, _1627744), _1627742), _1627746)), _1627738) = hAPP(hAPP(c_Product__Type_OPair(_1627740, _1627744), hAPP(hAPP(c_List_Onth(_1627740), _1627742), _1627738)), hAPP(hAPP(c_List_Onth(_1627744), _1627746), _1627738)))], (42550 ^ _780086) ^ [_1628017, _1628019] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1628017, _1628019) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1628017), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1628019), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (42552 ^ _780086) ^ [_1628064, _1628066] : [class_Groups_Ocomm__monoid__add(_1628064), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1628064), _1628066) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1628064), hAPP(c_List_Onth(_1628064), _1628066)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628064)), _1628066))))], (42558 ^ _780086) ^ [_1628197, _1628199] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1628197, _1628199) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1628197, _1628199)))], (42560 ^ _780086) ^ [_1628232, _1628234] : [-(hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1628232, _1628234)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1628232, _1628234))], (42572 ^ _780086) ^ [_1628447] : [42574 ^ _780086 : [(42575 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 42573 ^ [_1628447]), hAPP(c_List_Oset(tc_Nat_Onat), _1628447))))], (42577 ^ _780086) ^ [] : [42573 ^ [_1628447] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1628447) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42562 ^ _780086) ^ [_1628279] : [hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1628279) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 42565 ^ _780086 : [(42566 ^ _780086) ^ [_1628354] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1628354), hAPP(c_List_Oset(tc_Nat_Onat), _1628279))), -(_1628354 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (42581 ^ _780086) ^ [_1628603, _1628605] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1628603), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1628605))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1628605), _1628603)), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1628605))))], (42587 ^ _780086) ^ [_1628724, _1628726, _1628728] : [class_Groups_Omonoid__add(_1628724), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1628724), hAPP(hAPP(c_List_Olist_OCons(_1628724), _1628726), _1628728)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1628724), _1628726), hAPP(c_List_Omonoid__add__class_Olistsum(_1628724), _1628728)))], (42593 ^ _780086) ^ [_1628853, _1628855] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1628853), _1628855) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1628853, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1628855), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (42595 ^ _780086) ^ [_1628896, _1628898] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1628896, _1628898) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1628896), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1628898)))], (42597 ^ _780086) ^ [_1628949] : [c_List_Onat__list(_1628949), -(c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1628949)))], (42603 ^ _780086) ^ [_1629022] : [c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1629022)), -(c_List_Onat__list(_1629022))], (42609 ^ _780086) ^ [_1629101, _1629103, _1629105, _1629107] : [42611 ^ _780086 : [(42612 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1629101), 42610 ^ [_1629101, _1629103, _1629105, _1629107]), hAPP(c_List_Oset(_1629101), _1629103))))], (42614 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1629105, 42610 ^ [_1629101, _1629103, _1629105, _1629107])), hAPP(_1629107, 42610 ^ [_1629101, _1629103, _1629105, _1629107])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_List_Olist_Olist__size(_1629101, _1629105, _1629103)), c_List_Olist_Olist__size(_1629101, _1629107, _1629103))))], (42618 ^ _780086) ^ [_1629351, _1629353, _1629355] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1629351), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1629353))), -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat, _1629353), _1629351), _1629355)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1629353)), _1629355)), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1629353), _1629351)))], (42624 ^ _780086) ^ [_1629512, _1629514, _1629516] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1629512), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629514)), _1629516))), -(c_List_Obutlast(_1629514, hAPP(hAPP(c_List_Otake(_1629514), _1629512), _1629516)) = hAPP(hAPP(c_List_Otake(_1629514), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1629512), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1629516))], (42630 ^ _780086) ^ [_1629665, _1629667, _1629669, _1629671] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629665)), _1629667)), _1629669)), -(hAPP(hAPP(c_List_Olist__update(_1629665, _1629667), _1629669), _1629671) = _1629667)], (42636 ^ _780086) ^ [_1629784, _1629786, _1629788, _1629790, _1629792] : [-(_1629784 = _1629786), -(hAPP(hAPP(c_List_Onth(_1629788), hAPP(hAPP(c_List_Olist__update(_1629788, _1629790), _1629784), _1629792)), _1629786) = hAPP(hAPP(c_List_Onth(_1629788), _1629790), _1629786))], (42642 ^ _780086) ^ [_1629851, _1629853, _1629855] : [-(hAPP(hAPP(c_List_Olist__update(_1629851, _1629853), _1629855), hAPP(hAPP(c_List_Onth(_1629851), _1629853), _1629855)) = _1629853)], (42644 ^ _780086) ^ [_1629895, _1629897, _1629899, _1629901] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629895)), hAPP(hAPP(c_List_Olist__update(_1629895, _1629897), _1629899), _1629901)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629895)), _1629897))], (42646 ^ _780086) ^ [_1629962, _1629964, _1629966, _1629968] : [_1629962 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629964)), _1629966)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Obutlast(_1629964, hAPP(hAPP(c_List_Olist__update(_1629964, _1629966), _1629962), _1629968)) = c_List_Obutlast(_1629964, _1629966))], (42652 ^ _780086) ^ [_1630093, _1630095, _1630097, _1630099] : [-(_1630093 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630095)), _1630097)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Obutlast(_1630095, hAPP(hAPP(c_List_Olist__update(_1630095, _1630097), _1630093), _1630099)) = hAPP(hAPP(c_List_Olist__update(_1630095, c_List_Obutlast(_1630095, _1630097)), _1630093), _1630099))], (42658 ^ _780086) ^ [_1630172, _1630174, _1630176, _1630178, _1630180, _1630182, _1630184] : [-(hAPP(hAPP(c_List_Ozip(_1630172, _1630174), hAPP(hAPP(c_List_Olist__update(_1630172, _1630176), _1630178), _1630180)), hAPP(hAPP(c_List_Olist__update(_1630174, _1630182), _1630178), _1630184)) = hAPP(hAPP(c_List_Olist__update(tc_prod(_1630172, _1630174), hAPP(hAPP(c_List_Ozip(_1630172, _1630174), _1630176), _1630182)), _1630178), hAPP(hAPP(c_Product__Type_OPair(_1630172, _1630174), _1630180), _1630184)))], (42660 ^ _780086) ^ [_1630264, _1630266, _1630268, _1630270, _1630272, _1630274] : [-(hAPP(hAPP(c_List_Olist__update(tc_prod(_1630264, _1630266), hAPP(hAPP(c_List_Ozip(_1630264, _1630266), _1630268), _1630270)), _1630272), _1630274) = hAPP(hAPP(c_List_Ozip(_1630264, _1630266), hAPP(hAPP(c_List_Olist__update(_1630264, _1630268), _1630272), hAPP(c_Product__Type_Ofst(_1630264, _1630266), _1630274))), hAPP(hAPP(c_List_Olist__update(_1630266, _1630270), _1630272), hAPP(c_Product__Type_Osnd(_1630264, _1630266), _1630274))))], (42662 ^ _780086) ^ [_1630357, _1630359, _1630361, _1630363, _1630365] : [-(hAPP(hAPP(c_List_Olist__update(_1630357, hAPP(hAPP(c_List_Olist__update(_1630357, _1630359), _1630361), _1630363)), _1630361), _1630365) = hAPP(hAPP(c_List_Olist__update(_1630357, _1630359), _1630361), _1630365))], (42664 ^ _780086) ^ [_1630411, _1630413, _1630415, _1630417, _1630419, _1630421] : [-(_1630411 = _1630413), -(hAPP(hAPP(c_List_Olist__update(_1630415, hAPP(hAPP(c_List_Olist__update(_1630415, _1630417), _1630411), _1630419)), _1630413), _1630421) = hAPP(hAPP(c_List_Olist__update(_1630415, hAPP(hAPP(c_List_Olist__update(_1630415, _1630417), _1630413), _1630421)), _1630411), _1630419))], (42670 ^ _780086) ^ [_1630491, _1630493, _1630495, _1630497, _1630499] : [-(hAPP(hAPP(c_List_Olist__update(_1630491, hAPP(hAPP(c_List_Olist_OCons(_1630491), _1630493), _1630495)), _1630497), _1630499) = c_Nat_Onat_Onat__case(tc_List_Olist(_1630491), hAPP(hAPP(c_List_Olist_OCons(_1630491), _1630499), _1630495), hAPP(hAPP(c_COMBB(tc_List_Olist(_1630491), tc_List_Olist(_1630491), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1630491), _1630493)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1630491, tc_List_Olist(_1630491)), c_List_Olist__update(_1630491, _1630495)), _1630499)), _1630497))], (42672 ^ _780086) ^ [_1630588, _1630590, _1630592, _1630594] : [-(hAPP(hAPP(c_List_Olist__update(_1630588, hAPP(hAPP(c_List_Olist_OCons(_1630588), _1630590), _1630592)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1630594) = hAPP(hAPP(c_List_Olist_OCons(_1630588), _1630594), _1630592))], (42674 ^ _780086) ^ [_1630642, _1630644, _1630646, _1630648, _1630650] : [-(hAPP(hAPP(c_List_Olist__update(_1630642, hAPP(hAPP(c_List_Olist_OCons(_1630642), _1630644), _1630646)), hAPP(c_Nat_OSuc, _1630648)), _1630650) = hAPP(hAPP(c_List_Olist_OCons(_1630642), _1630644), hAPP(hAPP(c_List_Olist__update(_1630642, _1630646), _1630648), _1630650)))], (42676 ^ _780086) ^ [_1630710, _1630712, _1630714] : [hBOOL(hAPP(hAPP(c_member(_1630710), _1630712), hAPP(c_List_Oset(_1630710), c_List_Obutlast(_1630710, _1630714)))), -(hBOOL(hAPP(hAPP(c_member(_1630710), _1630712), hAPP(c_List_Oset(_1630710), _1630714))))], (42682 ^ _780086) ^ [_1630843, _1630845, _1630847, _1630849, _1630851] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1630843, tc_HOL_Obool)), hAPP(c_List_Oset(_1630843), _1630845)), _1630847)), hBOOL(hAPP(hAPP(c_member(_1630843), _1630849), _1630847)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1630843, tc_HOL_Obool)), hAPP(c_List_Oset(_1630843), hAPP(hAPP(c_List_Olist__update(_1630843, _1630845), _1630851), _1630849))), _1630847)))], (42692 ^ _780086) ^ [_1631076, _1631078, _1631080, _1631082] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1631076, tc_HOL_Obool)), hAPP(c_List_Oset(_1631076), hAPP(hAPP(c_List_Olist__update(_1631076, _1631078), _1631080), _1631082))), hAPP(hAPP(c_Set_Oinsert(_1631076), _1631082), hAPP(c_List_Oset(_1631076), _1631078)))))], (42694 ^ _780086) ^ [_1631142, _1631144, _1631146, _1631148, _1631150] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1631142), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1631144)), _1631146))), 42697 ^ _780086 : [(42698 ^ _780086) ^ [] : [_1631142 = _1631148, -(hAPP(hAPP(c_List_Onth(_1631144), hAPP(hAPP(c_List_Olist__update(_1631144, _1631146), _1631142), _1631150)), _1631148) = _1631150)], (42704 ^ _780086) ^ [] : [-(_1631142 = _1631148), -(hAPP(hAPP(c_List_Onth(_1631144), hAPP(hAPP(c_List_Olist__update(_1631144, _1631146), _1631142), _1631150)), _1631148) = hAPP(hAPP(c_List_Onth(_1631144), _1631146), _1631148))]]], (42710 ^ _780086) ^ [_1631438, _1631440, _1631442, _1631444] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1631438), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1631440)), _1631442))), 42713 ^ _780086 : [(42714 ^ _780086) ^ [] : [hAPP(hAPP(c_List_Olist__update(_1631440, _1631442), _1631438), _1631444) = _1631442, -(hAPP(hAPP(c_List_Onth(_1631440), _1631442), _1631438) = _1631444)], (42720 ^ _780086) ^ [] : [hAPP(hAPP(c_List_Onth(_1631440), _1631442), _1631438) = _1631444, -(hAPP(hAPP(c_List_Olist__update(_1631440, _1631442), _1631438), _1631444) = _1631442)]]], (42726 ^ _780086) ^ [_1631732, _1631734, _1631736, _1631738] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1631732), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1631734)), _1631736))), -(hAPP(hAPP(c_List_Onth(_1631734), hAPP(hAPP(c_List_Olist__update(_1631734, _1631736), _1631732), _1631738)), _1631732) = _1631738)], (42732 ^ _780086) ^ [_1631871, _1631873, _1631875] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1631871), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1631873)), _1631875))), -(hAPP(hAPP(c_List_Otake(_1631873), _1631871), c_List_Obutlast(_1631873, _1631875)) = hAPP(hAPP(c_List_Otake(_1631873), _1631871), _1631875))], (42738 ^ _780086) ^ [_1632012, _1632014] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632012)), c_List_Obutlast(_1632012, _1632014)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632012)), _1632014)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (42740 ^ _780086) ^ [_1632060, _1632062, _1632064, _1632066] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1632060), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632062)), _1632064))), -(hBOOL(hAPP(hAPP(c_member(_1632062), _1632066), hAPP(c_List_Oset(_1632062), hAPP(hAPP(c_List_Olist__update(_1632062, _1632064), _1632060), _1632066)))))], (42746 ^ _780086) ^ [_1632207, _1632209] : [-(c_List_Obutlast(_1632207, _1632209) = hAPP(hAPP(c_List_Otake(_1632207), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632207)), _1632209)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1632209))], (42748 ^ _780086) ^ [_1632277, _1632279, _1632281, _1632283] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1632277), tc_List_Olist(_1632277))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1632277), tc_List_Olist(_1632277)), _1632279), _1632281)), c_List_Olistrel1(_1632277, _1632283))), 42753 ^ _780086 : [(42754 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1632277, _1632277)), hAPP(hAPP(c_Product__Type_OPair(_1632277, _1632277), hAPP(hAPP(c_List_Onth(_1632277), _1632279), 42752 ^ [_1632277, _1632279, _1632281, _1632283])), 42751 ^ [_1632277, _1632279, _1632281, _1632283])), _1632283)))], (42756 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42752 ^ [_1632277, _1632279, _1632281, _1632283]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632277)), _1632279))))], (42758 ^ _780086) ^ [] : [-(_1632281 = hAPP(hAPP(c_List_Olist__update(_1632277, _1632279), 42752 ^ [_1632277, _1632279, _1632281, _1632283]), 42751 ^ [_1632277, _1632279, _1632281, _1632283]))]]], (42760 ^ _780086) ^ [_1632625, _1632627, _1632629, _1632631] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1632625), tc_List_Olist(_1632625))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1632625), tc_List_Olist(_1632625)), _1632627), _1632629)), c_List_Olistrel1(_1632625, _1632631)))), 42761 ^ _780086 : [(42762 ^ _780086) ^ [_1632758, _1632760] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1632625, _1632625)), hAPP(hAPP(c_Product__Type_OPair(_1632625, _1632625), hAPP(hAPP(c_List_Onth(_1632625), _1632627), _1632758)), _1632760)), _1632631)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1632758), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632625)), _1632627))), _1632629 = hAPP(hAPP(c_List_Olist__update(_1632625, _1632627), _1632758), _1632760)]]], (42774 ^ _780086) ^ [_1633058, _1633060, _1633062, _1633064] : [hBOOL(hAPP(c_List_Odistinct(_1633058), _1633060)), -(hBOOL(hAPP(hAPP(c_member(_1633058), _1633062), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1633058, tc_HOL_Obool)), hAPP(c_List_Oset(_1633058), _1633060)), hAPP(hAPP(c_Set_Oinsert(_1633058), hAPP(hAPP(c_List_Onth(_1633058), _1633060), _1633064)), c_Orderings_Obot__class_Obot(tc_fun(_1633058, tc_HOL_Obool))))))), -(hBOOL(hAPP(c_List_Odistinct(_1633058), hAPP(hAPP(c_List_Olist__update(_1633058, _1633060), _1633064), _1633062))))], (42784 ^ _780086) ^ [_1633276, _1633278] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint), c_List_Oupto(_1633276, _1633278))))], (42786 ^ _780086) ^ [_1633306, _1633308, _1633310] : [hBOOL(hAPP(c_List_Odistinct(_1633306), _1633308)), -(hBOOL(hAPP(c_List_Odistinct(_1633306), hAPP(hAPP(c_List_Otake(_1633306), _1633310), _1633308))))], (42792 ^ _780086) ^ [_1633417, _1633419, _1633421] : [hBOOL(hAPP(c_List_Odistinct(_1633417), _1633419)), -(hBOOL(hAPP(c_List_Odistinct(_1633417), c_List_Osublist(_1633417, _1633419, _1633421))))], (42798 ^ _780086) ^ [_1633520, _1633522, _1633524, _1633526] : [hBOOL(hAPP(c_List_Odistinct(_1633520), _1633522)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1633520, _1633524)), hAPP(hAPP(c_List_Ozip(_1633520, _1633524), _1633522), _1633526))))], (42804 ^ _780086) ^ [_1633641, _1633643, _1633645, _1633647] : [hBOOL(hAPP(c_List_Odistinct(_1633641), _1633643)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1633645, _1633641)), hAPP(hAPP(c_List_Ozip(_1633645, _1633641), _1633647), _1633643))))], (42810 ^ _780086) ^ [_1633780, _1633782, _1633784] : [hBOOL(hAPP(c_List_Odistinct(_1633780), hAPP(hAPP(c_List_Olist_OCons(_1633780), _1633782), _1633784))), 42813 ^ _780086 : [(42814 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1633780), _1633782), hAPP(c_List_Oset(_1633780), _1633784)))], (42816 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1633780), _1633784)))]]], (42818 ^ _780086) ^ [_1633947, _1633949, _1633951] : [-(hBOOL(hAPP(c_List_Odistinct(_1633947), hAPP(hAPP(c_List_Olist_OCons(_1633947), _1633949), _1633951)))), -(hBOOL(hAPP(hAPP(c_member(_1633947), _1633949), hAPP(c_List_Oset(_1633947), _1633951)))), hBOOL(hAPP(c_List_Odistinct(_1633947), _1633951))], (42828 ^ _780086) ^ [_1634141, _1634143] : [hAPP(c_Finite__Set_Ocard(_1634141), hAPP(c_List_Oset(_1634141), _1634143)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1634141)), _1634143), -(hBOOL(hAPP(c_List_Odistinct(_1634141), _1634143)))], (42834 ^ _780086) ^ [_1634260, _1634262] : [hBOOL(hAPP(c_List_Odistinct(_1634260), _1634262)), -(hAPP(c_Finite__Set_Ocard(_1634260), hAPP(c_List_Oset(_1634260), _1634262)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1634260)), _1634262))], (42858 ^ _780086) ^ [_1634854, _1634856] : [42860 ^ _780086 : [(42861 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42859 ^ [_1634854, _1634856]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1634854)), _1634856))))], (42864 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42862 ^ [_1634854, _1634856]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1634854)), _1634856))))], (42866 ^ _780086) ^ [] : [42859 ^ [_1634854, _1634856] = 42862 ^ [_1634854, _1634856]], (42868 ^ _780086) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1634854), _1634856), 42859 ^ [_1634854, _1634856]) = hAPP(hAPP(c_List_Onth(_1634854), _1634856), 42862 ^ [_1634854, _1634856]))]], -(hBOOL(hAPP(c_List_Odistinct(_1634854), _1634856)))], (42840 ^ _780086) ^ [_1634394, _1634396] : [hBOOL(hAPP(c_List_Odistinct(_1634394), _1634396)), 42843 ^ _780086 : [(42844 ^ _780086) ^ [_1634526] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1634526), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1634394)), _1634396))), 42847 ^ _780086 : [(42848 ^ _780086) ^ [_1634653] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1634653), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1634394)), _1634396))), -(_1634526 = _1634653), hAPP(hAPP(c_List_Onth(_1634394), _1634396), _1634526) = hAPP(hAPP(c_List_Onth(_1634394), _1634396), _1634653)]]]]], (42872 ^ _780086) ^ [_1635286, _1635288, _1635290, _1635292] : [hBOOL(hAPP(c_List_Odistinct(_1635286), _1635288)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1635290), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1635286)), _1635288))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1635292), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1635286)), _1635288))), 42883 ^ _780086 : [(42884 ^ _780086) ^ [] : [hAPP(hAPP(c_List_Onth(_1635286), _1635288), _1635290) = hAPP(hAPP(c_List_Onth(_1635286), _1635288), _1635292), -(_1635290 = _1635292)], (42890 ^ _780086) ^ [] : [_1635290 = _1635292, -(hAPP(hAPP(c_List_Onth(_1635286), _1635288), _1635290) = hAPP(hAPP(c_List_Onth(_1635286), _1635288), _1635292))]]], (42896 ^ _780086) ^ [_1635721, _1635723] : [class_Groups_Ocomm__monoid__add(_1635721), hBOOL(hAPP(c_List_Odistinct(_1635721), _1635723)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1635721), _1635723) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1635721, _1635721), c_COMBI(_1635721)), hAPP(c_List_Oset(_1635721), _1635723)))], (42906 ^ _780086) ^ [_1635907, _1635909] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1635907), _1635909)), -(c_Nitpick_Ocard_H(_1635907, _1635909) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1635907)), c_Hilbert__Choice_OEps(tc_List_Olist(_1635907), hAPP(hAPP(c_COMBS(tc_List_Olist(_1635907), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1635907)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1635907), tc_fun(_1635907, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1635907, tc_HOL_Obool), tc_fun(tc_fun(_1635907, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1635907)), c_fequal), c_List_Oset(_1635907))), _1635909))), c_List_Odistinct(_1635907)))))], (42912 ^ _780086) ^ [_1636144, _1636146] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1636144), _1636146))), -(c_Nitpick_Ocard_H(_1636144, _1636146) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42918 ^ _780086) ^ [_1636189, _1636191, _1636193, _1636195] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1636189), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1636191)), _1636193))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1636189), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1636191)), _1636195))), 42928 ^ _780086 : [(42929 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42927 ^ [_1636189, _1636191, _1636193, _1636195]), _1636189)))], (42931 ^ _780086) ^ [] : [hAPP(hAPP(c_List_Onth(_1636191), _1636193), 42927 ^ [_1636189, _1636191, _1636193, _1636195]) = hAPP(hAPP(c_List_Onth(_1636191), _1636195), 42927 ^ [_1636189, _1636191, _1636193, _1636195])]], -(hAPP(hAPP(c_List_Otake(_1636191), _1636189), _1636193) = hAPP(hAPP(c_List_Otake(_1636191), _1636189), _1636195))], (42935 ^ _780086) ^ [_1636606, _1636608, _1636610] : [hBOOL(hAPP(c_List_Odistinct(_1636606), _1636608)), -(hAPP(c_List_Oset(_1636606), c_List_Oremove1(_1636606, _1636610, _1636608)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1636606, tc_HOL_Obool)), hAPP(c_List_Oset(_1636606), _1636608)), hAPP(hAPP(c_Set_Oinsert(_1636606), _1636610), c_Orderings_Obot__class_Obot(tc_fun(_1636606, tc_HOL_Obool)))))], (42941 ^ _780086) ^ [_1636784, _1636786, _1636788, _1636790] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1636784) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1636786), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1636784)), hAPP(hAPP(c_List_Olist_OCons(_1636786), _1636788), _1636790)) = c_List_Olist_ONil(_1636786))], (42947 ^ _780086) ^ [_1636907, _1636909, _1636911, _1636913] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1636907) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1636909), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1636907)), hAPP(hAPP(c_List_Olist_OCons(_1636909), _1636911), _1636913)) = hAPP(hAPP(c_List_Olist_OCons(_1636909), _1636911), hAPP(hAPP(c_List_Otake(_1636909), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1636907)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1636913)))], (42953 ^ _780086) ^ [_1636996, _1636998] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1636996)), c_List_Olist_ONil(_1636996)), c_List_Olists(_1636996, _1636998))))], (42955 ^ _780086) ^ [_1637035, _1637037, _1637039] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1637035), tc_List_Olist(_1637035))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1637035), tc_List_Olist(_1637035)), c_List_Olist_ONil(_1637035)), _1637037)), c_List_Olistrel(_1637035, _1637039))), -(_1637037 = c_List_Olist_ONil(_1637035))], (42961 ^ _780086) ^ [_1637182, _1637184, _1637186] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1637182), tc_List_Olist(_1637182))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1637182), tc_List_Olist(_1637182)), _1637184), c_List_Olist_ONil(_1637182))), c_List_Olistrel(_1637182, _1637186))), -(_1637184 = c_List_Olist_ONil(_1637182))], (42967 ^ _780086) ^ [_1637328, _1637330] : [-(_1637328 = c_List_Olist_ONil(_1637330)), hBOOL(hAPP(c_List_Odistinct(_1637330), _1637328)), -(hBOOL(hAPP(c_List_Odistinct(_1637330), c_List_Obutlast(_1637330, _1637328))))], (42977 ^ _780086) ^ [_1637479, _1637481, _1637483] : [hBOOL(hAPP(c_List_Odistinct(_1637479), _1637481)), -(hBOOL(hAPP(c_List_Odistinct(_1637479), c_List_Oremove1(_1637479, _1637483, _1637481))))], (42983 ^ _780086) ^ [_1637582] : [-(hBOOL(hAPP(c_List_Odistinct(_1637582), c_List_Olist_ONil(_1637582))))], (42985 ^ _780086) ^ [_1637611] : [-(c_List_Obutlast(_1637611, c_List_Olist_ONil(_1637611)) = c_List_Olist_ONil(_1637611))], (42987 ^ _780086) ^ [_1637653, _1637655, _1637657] : [_1637653 = c_List_Olist_ONil(_1637655), -(c_List_Obutlast(_1637655, hAPP(hAPP(c_List_Olist_OCons(_1637655), _1637657), _1637653)) = c_List_Olist_ONil(_1637655))], (42993 ^ _780086) ^ [_1637756, _1637758, _1637760] : [-(_1637756 = c_List_Olist_ONil(_1637758)), -(c_List_Obutlast(_1637758, hAPP(hAPP(c_List_Olist_OCons(_1637758), _1637760), _1637756)) = hAPP(hAPP(c_List_Olist_OCons(_1637758), _1637760), c_List_Obutlast(_1637758, _1637756)))], (42999 ^ _780086) ^ [_1637835, _1637837, _1637839] : [c_List_Olist_ONil(_1637835) = hAPP(hAPP(c_List_Olist_OCons(_1637835), _1637837), _1637839)], (43001 ^ _780086) ^ [_1637887, _1637889, _1637891] : [hAPP(hAPP(c_List_Olist_OCons(_1637887), _1637889), _1637891) = c_List_Olist_ONil(_1637887)], (43003 ^ _780086) ^ [_1637939, _1637941, _1637943, _1637945] : [_1637939 = _1637941, -(c_List_Oremove1(_1637943, _1637939, hAPP(hAPP(c_List_Olist_OCons(_1637943), _1637941), _1637945)) = _1637945)], (43009 ^ _780086) ^ [_1638038, _1638040, _1638042, _1638044] : [-(_1638038 = _1638040), -(c_List_Oremove1(_1638042, _1638038, hAPP(hAPP(c_List_Olist_OCons(_1638042), _1638040), _1638044)) = hAPP(hAPP(c_List_Olist_OCons(_1638042), _1638040), c_List_Oremove1(_1638042, _1638038, _1638044)))], (43015 ^ _780086) ^ [_1638104, _1638106] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1638104), _1638106)), -(c_List_Oupto(_1638106, _1638104) = c_List_Olist_ONil(tc_Int_Oint))], (43031 ^ _780086) ^ [_1638327, _1638329, _1638331] : [43032 ^ _780086 : [(43033 ^ _780086) ^ [] : [_1638329 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (43035 ^ _780086) ^ [] : [_1638331 = c_List_Olist_ONil(_1638327)]], -(hAPP(hAPP(c_List_Otake(_1638327), _1638329), _1638331) = c_List_Olist_ONil(_1638327))], (43021 ^ _780086) ^ [_1638215, _1638217, _1638219] : [hAPP(hAPP(c_List_Otake(_1638215), _1638217), _1638219) = c_List_Olist_ONil(_1638215), -(_1638217 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1638219 = c_List_Olist_ONil(_1638215))], (43039 ^ _780086) ^ [_1638470, _1638472] : [-(hAPP(hAPP(c_List_Otake(_1638470), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1638472) = c_List_Olist_ONil(_1638470))], (43041 ^ _780086) ^ [_1638505, _1638507] : [-(hAPP(hAPP(c_List_Otake(_1638505), _1638507), c_List_Olist_ONil(_1638505)) = c_List_Olist_ONil(_1638505))], (43043 ^ _780086) ^ [_1638542, _1638544] : [-(c_List_Osublist(_1638542, c_List_Olist_ONil(_1638542), _1638544) = c_List_Olist_ONil(_1638542))], (43045 ^ _780086) ^ [_1638575, _1638577, _1638579, _1638581] : [-(c_List_Oremove1(_1638575, _1638577, c_List_Oremove1(_1638575, _1638579, _1638581)) = c_List_Oremove1(_1638575, _1638579, c_List_Oremove1(_1638575, _1638577, _1638581)))], (43047 ^ _780086) ^ [_1638620, _1638622] : [-(c_List_Oremove1(_1638620, _1638622, c_List_Olist_ONil(_1638620)) = c_List_Olist_ONil(_1638620))], (43049 ^ _780086) ^ [_1638653, _1638655] : [-(c_List_Olistrelp(_1638653, _1638655, c_List_Olist_ONil(_1638653), c_List_Olist_ONil(_1638653)))], (43051 ^ _780086) ^ [_1638684, _1638686] : [-(c_List_Olistrelp(_1638684, _1638686, c_List_Olist_ONil(_1638684), c_List_Olist_ONil(_1638684)))], (43053 ^ _780086) ^ [_1638715, _1638717, _1638719] : [-(hAPP(hAPP(c_List_Ozip(_1638715, _1638717), c_List_Olist_ONil(_1638715)), _1638719) = c_List_Olist_ONil(tc_prod(_1638715, _1638717)))], (43055 ^ _780086) ^ [_1638758, _1638760, _1638762] : [-(hAPP(hAPP(c_List_Ozip(_1638758, _1638760), _1638762), c_List_Olist_ONil(_1638760)) = c_List_Olist_ONil(tc_prod(_1638758, _1638760)))], (43057 ^ _780086) ^ [_1638801] : [class_Groups_Omonoid__add(_1638801), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1638801), c_List_Olist_ONil(_1638801)) = c_Groups_Ozero__class_Ozero(_1638801))], (43063 ^ _780086) ^ [_1638907, _1638909] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1638907)), _1638909) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1638909 = c_List_Olist_ONil(_1638907))], (43069 ^ _780086) ^ [_1638998, _1639000] : [_1639000 = c_List_Olist_ONil(_1638998), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1638998)), _1639000) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43075 ^ _780086) ^ [_1639095] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639095)), c_List_Olist_ONil(_1639095)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43077 ^ _780086) ^ [_1639142, _1639144] : [hAPP(c_List_Oset(_1639142), _1639144) = c_Orderings_Obot__class_Obot(tc_fun(_1639142, tc_HOL_Obool)), -(_1639144 = c_List_Olist_ONil(_1639142))], (43083 ^ _780086) ^ [_1639239, _1639241] : [_1639241 = c_List_Olist_ONil(_1639239), -(hAPP(c_List_Oset(_1639239), _1639241) = c_Orderings_Obot__class_Obot(tc_fun(_1639239, tc_HOL_Obool)))], (43089 ^ _780086) ^ [_1639357, _1639359] : [c_Orderings_Obot__class_Obot(tc_fun(_1639357, tc_HOL_Obool)) = hAPP(c_List_Oset(_1639357), _1639359), -(_1639359 = c_List_Olist_ONil(_1639357))], (43095 ^ _780086) ^ [_1639454, _1639456] : [_1639456 = c_List_Olist_ONil(_1639454), -(c_Orderings_Obot__class_Obot(tc_fun(_1639454, tc_HOL_Obool)) = hAPP(c_List_Oset(_1639454), _1639456))], (43101 ^ _780086) ^ [_1639557] : [-(hAPP(c_List_Oset(_1639557), c_List_Olist_ONil(_1639557)) = c_Orderings_Obot__class_Obot(tc_fun(_1639557, tc_HOL_Obool)))], (43103 ^ _780086) ^ [_1639592, _1639594] : [-(c_List_Olist_Olist__size(_1639592, _1639594, c_List_Olist_ONil(_1639592)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43105 ^ _780086) ^ [_1639623, _1639625, _1639627] : [-(hAPP(hAPP(c_List_Olist__update(_1639623, c_List_Olist_ONil(_1639623)), _1639625), _1639627) = c_List_Olist_ONil(_1639623))], (43107 ^ _780086) ^ [_1639663, _1639665, _1639667] : [-(hAPP(hAPP(c_List_Olist__update(_1639663, c_List_Olist_ONil(_1639663)), _1639665), _1639667) = c_List_Olist_ONil(_1639663))], (43109 ^ _780086) ^ [_1639724, _1639726, _1639728, _1639730] : [hAPP(hAPP(c_List_Olist__update(_1639724, _1639726), _1639728), _1639730) = c_List_Olist_ONil(_1639724), -(_1639726 = c_List_Olist_ONil(_1639724))], (43115 ^ _780086) ^ [_1639827, _1639829, _1639831, _1639833] : [_1639829 = c_List_Olist_ONil(_1639827), -(hAPP(hAPP(c_List_Olist__update(_1639827, _1639829), _1639831), _1639833) = c_List_Olist_ONil(_1639827))], (43121 ^ _780086) ^ [_1639932, _1639934, _1639936] : [-(hBOOL(hAPP(hAPP(c_member(_1639932), _1639934), hAPP(c_List_Oset(_1639932), _1639936)))), -(c_List_Oremove1(_1639932, _1639934, _1639936) = _1639936)], (43127 ^ _780086) ^ [_1639985, _1639987, _1639989, _1639991] : [-(hBOOL(hAPP(hAPP(c_member(_1639985), _1639987), hAPP(c_List_Oset(_1639985), _1639989)))), hBOOL(hAPP(hAPP(c_member(_1639985), _1639987), hAPP(c_List_Oset(_1639985), c_List_Oremove1(_1639985, _1639991, _1639989))))], (43133 ^ _780086) ^ [_1640108, _1640110, _1640112, _1640114] : [-(_1640108 = _1640110), 43136 ^ _780086 : [(43137 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1640112), _1640108), hAPP(c_List_Oset(_1640112), c_List_Oremove1(_1640112, _1640110, _1640114)))), -(hBOOL(hAPP(hAPP(c_member(_1640112), _1640108), hAPP(c_List_Oset(_1640112), _1640114))))], (43143 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1640112), _1640108), hAPP(c_List_Oset(_1640112), _1640114))), -(hBOOL(hAPP(hAPP(c_member(_1640112), _1640108), hAPP(c_List_Oset(_1640112), c_List_Oremove1(_1640112, _1640110, _1640114)))))]]], (43149 ^ _780086) ^ [_1640409, _1640411] : [-(c_List_Osublist(_1640409, _1640411, c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))) = c_List_Olist_ONil(_1640409))], (43151 ^ _780086) ^ [_1640440, _1640442, _1640444] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1640440, tc_HOL_Obool)), hAPP(c_List_Oset(_1640440), c_List_Oremove1(_1640440, _1640442, _1640444))), hAPP(c_List_Oset(_1640440), _1640444))))], (43153 ^ _780086) ^ [_1640506, _1640508] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1640506)), _1640508))), _1640508 = c_List_Olist_ONil(_1640506)], (43159 ^ _780086) ^ [_1640600, _1640602] : [-(_1640602 = c_List_Olist_ONil(_1640600)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1640600)), _1640602))))], (43165 ^ _780086) ^ [_1640649, _1640651, _1640653] : [-(hAPP(hAPP(c_List_Otake(_1640649), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1640649), _1640651), _1640653)) = hAPP(hAPP(c_List_Olist_OCons(_1640649), _1640651), c_List_Olist_ONil(_1640649)))], (43167 ^ _780086) ^ [_1640717, _1640719, _1640721] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1640717), tc_List_Olist(_1640717))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1640717), tc_List_Olist(_1640717)), c_List_Olist_ONil(_1640717)), _1640719)), c_List_Olistrel1(_1640717, _1640721)))], (43169 ^ _780086) ^ [_1640791, _1640793, _1640795] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1640791), tc_List_Olist(_1640791))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1640791), tc_List_Olist(_1640791)), _1640793), c_List_Olist_ONil(_1640791))), c_List_Olistrel1(_1640791, _1640795)))], (43171 ^ _780086) ^ [_1640850, _1640852] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1640850), tc_List_Olist(_1640850))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1640850), tc_List_Olist(_1640850)), c_List_Olist_ONil(_1640850)), c_List_Olist_ONil(_1640850))), c_List_Olistrel(_1640850, _1640852))))], (43173 ^ _780086) ^ [_1640924, _1640926, _1640928] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1640924), tc_List_Olist(_1640924))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1640924), tc_List_Olist(_1640924)), _1640926), c_List_Olist_ONil(_1640924))), c_List_Olexord(_1640924, _1640928)))], (43175 ^ _780086) ^ [_1640998, _1641000, _1641002] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1640998), tc_List_Olist(_1640998))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1640998), tc_List_Olist(_1640998)), c_List_Olist_ONil(_1640998)), _1641000)), c_List_Olex(_1640998, _1641002)))], (43177 ^ _780086) ^ [_1641072, _1641074, _1641076] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1641072), tc_List_Olist(_1641072))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1641072), tc_List_Olist(_1641072)), _1641074), c_List_Olist_ONil(_1641072))), c_List_Olex(_1641072, _1641076)))], (43179 ^ _780086) ^ [_1641131, _1641133, _1641135, _1641137] : [-(hAPP(hAPP(c_List_Otake(_1641131), _1641133), hAPP(hAPP(c_List_Olist_OCons(_1641131), _1641135), _1641137)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1641131), c_List_Olist_ONil(_1641131), hAPP(hAPP(c_COMBB(tc_List_Olist(_1641131), tc_List_Olist(_1641131), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1641131), _1641135)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1641131), tc_List_Olist(_1641131)), c_List_Otake(_1641131)), _1641137)), _1641133))], (43181 ^ _780086) ^ [_1641229, _1641231] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1641229), _1641231)), -(c_List_Oupto(_1641229, _1641231) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1641229), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1641229), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1641231)))], (43187 ^ _780086) ^ [_1641346, _1641348] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1641346), _1641348))), -(c_List_Oupto(_1641346, _1641348) = c_List_Olist_ONil(tc_Int_Oint))], (43193 ^ _780086) ^ [_1641404, _1641406, _1641408] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1641404)), -(c_List_Osublist(_1641406, hAPP(hAPP(c_List_Olist_OCons(_1641406), _1641408), c_List_Olist_ONil(_1641406)), _1641404) = hAPP(hAPP(c_List_Olist_OCons(_1641406), _1641408), c_List_Olist_ONil(_1641406)))], (43199 ^ _780086) ^ [_1641529, _1641531, _1641533] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1641529))), -(c_List_Osublist(_1641531, hAPP(hAPP(c_List_Olist_OCons(_1641531), _1641533), c_List_Olist_ONil(_1641531)), _1641529) = c_List_Olist_ONil(_1641531))], (43205 ^ _780086) ^ [_1641587] : [-(c_List_Olists(_1641587, c_Orderings_Obot__class_Obot(tc_fun(_1641587, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1641587)), c_List_Olist_ONil(_1641587)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1641587), tc_HOL_Obool))))], (43207 ^ _780086) ^ [_1641652, _1641654, _1641656, _1641658] : [_1641652 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1641654), _1641652), hAPP(hAPP(c_List_Olist_OCons(_1641654), _1641656), _1641658)) = c_List_Olist_ONil(_1641654))], (43213 ^ _780086) ^ [_1641763, _1641765, _1641767, _1641769] : [-(_1641763 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1641765), _1641763), hAPP(hAPP(c_List_Olist_OCons(_1641765), _1641767), _1641769)) = hAPP(hAPP(c_List_Olist_OCons(_1641765), _1641767), hAPP(hAPP(c_List_Otake(_1641765), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1641763), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1641769)))], (43219 ^ _780086) ^ [_1641852, _1641854] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1641852)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1641854))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1641852), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1641854)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1641852)), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1641852)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1641854))))], (43225 ^ _780086) ^ [_1642011, _1642013] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1642011)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1642013)))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1642011), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1642013)) = c_List_Olist_ONil(tc_Int_Oint))], (43231 ^ _780086) ^ [_1642069, _1642071] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1642069), tc_List_Olist(_1642069), c_List_Olistrel(_1642069, _1642071)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1642069)), c_List_Olist_ONil(_1642069)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1642069), tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1642069)), c_List_Olist_ONil(_1642069)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1642069), tc_HOL_Obool))))], (43233 ^ _780086) ^ [_1642146, _1642148] : [-(c_List_Oset__Cons(_1642146, _1642148, hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1642146)), c_List_Olist_ONil(_1642146)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1642146), tc_HOL_Obool)))) = hAPP(c_Set_Oimage(_1642146, tc_List_Olist(_1642146), hAPP(hAPP(c_COMBC(_1642146, tc_List_Olist(_1642146), tc_List_Olist(_1642146)), c_List_Olist_OCons(_1642146)), c_List_Olist_ONil(_1642146))), _1642148))], (43235 ^ _780086) ^ [_1642233, _1642235, _1642237] : [hBOOL(hAPP(hAPP(c_member(_1642233), _1642235), hAPP(c_List_Oset(_1642233), _1642237))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642233)), c_List_Oremove1(_1642233, _1642235, _1642237)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642233)), _1642237)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (43241 ^ _780086) ^ [_1642378, _1642380, _1642382] : [-(hBOOL(hAPP(hAPP(c_member(_1642378), _1642380), hAPP(c_List_Oset(_1642378), _1642382)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642378)), c_List_Oremove1(_1642378, _1642380, _1642382)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642378)), _1642382))], (43247 ^ _780086) ^ [_1642448, _1642450] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_List_Oupto__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1642448), _1642450))), 43250 ^ _780086 : [(43251 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1642448), _1642450)), -(c_List_Oupto(_1642448, _1642450) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1642448), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1642448), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1642450)))], (43257 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1642448), _1642450))), -(c_List_Oupto(_1642448, _1642450) = c_List_Olist_ONil(tc_Int_Oint))]]], (43263 ^ _780086) ^ [_1642698, _1642700, _1642702] : [-(_1642698 = c_List_Olist_ONil(_1642700)), -(hBOOL(hAPP(hAPP(c_member(_1642700), hAPP(c_Product__Type_Ofst(_1642700, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect(_1642700, _1642698), _1642702))), hAPP(c_List_Oset(_1642700), _1642698))))], (43269 ^ _780086) ^ [_1642762] : [-(c_List_Olistset(_1642762, c_List_Olist_ONil(tc_fun(_1642762, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1642762)), c_List_Olist_ONil(_1642762)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1642762), tc_HOL_Obool))))], (43271 ^ _780086) ^ [_1642812, _1642814, _1642816, _1642818, _1642820] : [-(hAPP(hAPP(c_List_Ozip(_1642812, _1642814), _1642816), hAPP(hAPP(c_List_Olist_OCons(_1642814), _1642818), _1642820)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1642812, _1642814)), _1642812, c_List_Olist_ONil(tc_prod(_1642812, _1642814)), hAPP(hAPP(c_COMBC(_1642812, tc_fun(tc_List_Olist(_1642812), tc_List_Olist(tc_prod(_1642812, _1642814))), tc_fun(tc_List_Olist(_1642812), tc_List_Olist(tc_prod(_1642812, _1642814)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1642812, _1642814)), tc_List_Olist(tc_prod(_1642812, _1642814))), tc_fun(tc_fun(tc_List_Olist(_1642812), tc_List_Olist(tc_prod(_1642812, _1642814))), tc_fun(tc_List_Olist(_1642812), tc_List_Olist(tc_prod(_1642812, _1642814)))), _1642812), c_COMBB(tc_List_Olist(tc_prod(_1642812, _1642814)), tc_List_Olist(tc_prod(_1642812, _1642814)), tc_List_Olist(_1642812))), hAPP(hAPP(c_COMBB(tc_prod(_1642812, _1642814), tc_fun(tc_List_Olist(tc_prod(_1642812, _1642814)), tc_List_Olist(tc_prod(_1642812, _1642814))), _1642812), c_List_Olist_OCons(tc_prod(_1642812, _1642814))), hAPP(hAPP(c_COMBC(_1642812, _1642814, tc_prod(_1642812, _1642814)), c_Product__Type_OPair(_1642812, _1642814)), _1642818)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1642812), tc_List_Olist(_1642814), tc_List_Olist(tc_prod(_1642812, _1642814))), c_List_Ozip(_1642812, _1642814)), _1642820))), _1642816))], (43273 ^ _780086) ^ [_1643039, _1643041, _1643043, _1643045, _1643047, _1643049] : [-(hAPP(c_List_Olist_Olist__case(_1643039, _1643041, _1643043, _1643045), hAPP(hAPP(c_List_Olist_OCons(_1643041), _1643047), _1643049)) = hAPP(hAPP(_1643045, _1643047), _1643049))], (43275 ^ _780086) ^ [_1643094, _1643096, _1643098, _1643100] : [-(hAPP(c_List_Olist_Olist__case(_1643094, _1643096, _1643098, _1643100), c_List_Olist_ONil(_1643096)) = _1643098)], (43277 ^ _780086) ^ [_1643133, _1643135, _1643137] : [-(c_List_Olistset(_1643133, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1643133, tc_HOL_Obool)), _1643135), _1643137)) = c_List_Oset__Cons(_1643133, _1643135, c_List_Olistset(_1643133, _1643137)))], (43279 ^ _780086) ^ [_1643181, _1643183, _1643185, _1643187, _1643189] : [-(hAPP(hAPP(c_List_Ozip(_1643181, _1643183), hAPP(hAPP(c_List_Olist_OCons(_1643181), _1643185), _1643187)), _1643189) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1643181, _1643183)), _1643183, c_List_Olist_ONil(tc_prod(_1643181, _1643183)), hAPP(hAPP(c_COMBC(_1643183, tc_fun(tc_List_Olist(_1643183), tc_List_Olist(tc_prod(_1643181, _1643183))), tc_fun(tc_List_Olist(_1643183), tc_List_Olist(tc_prod(_1643181, _1643183)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1643181, _1643183)), tc_List_Olist(tc_prod(_1643181, _1643183))), tc_fun(tc_fun(tc_List_Olist(_1643183), tc_List_Olist(tc_prod(_1643181, _1643183))), tc_fun(tc_List_Olist(_1643183), tc_List_Olist(tc_prod(_1643181, _1643183)))), _1643183), c_COMBB(tc_List_Olist(tc_prod(_1643181, _1643183)), tc_List_Olist(tc_prod(_1643181, _1643183)), tc_List_Olist(_1643183))), hAPP(hAPP(c_COMBB(tc_prod(_1643181, _1643183), tc_fun(tc_List_Olist(tc_prod(_1643181, _1643183)), tc_List_Olist(tc_prod(_1643181, _1643183))), _1643183), c_List_Olist_OCons(tc_prod(_1643181, _1643183))), hAPP(c_Product__Type_OPair(_1643181, _1643183), _1643185)))), hAPP(c_List_Ozip(_1643181, _1643183), _1643187))), _1643189))], (43281 ^ _780086) ^ [_1643382, _1643384, _1643386] : [class_Orderings_Olinorder(_1643382), hBOOL(hAPP(c_Finite__Set_Ofinite(_1643382), _1643384)), -(c_List_Olinorder__class_Osorted__list__of__set(_1643382, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1643382, tc_HOL_Obool)), _1643384), hAPP(hAPP(c_Set_Oinsert(_1643382), _1643386), c_Orderings_Obot__class_Obot(tc_fun(_1643382, tc_HOL_Obool))))) = c_List_Oremove1(_1643382, _1643386, c_List_Olinorder__class_Osorted__list__of__set(_1643382, _1643384)))], (43291 ^ _780086) ^ [_1643589, _1643591, _1643593] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_List_Oupto__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1643589), _1643591))), -(hBOOL(hAPP(hAPP(_1643593, _1643589), _1643591))), 43298 ^ _780086 : [(43299 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_List_Oupto__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), 43296 ^ [_1643589, _1643591, _1643593]), 43297 ^ [_1643589, _1643591, _1643593]))))], (43307 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(_1643593, 43296 ^ [_1643589, _1643591, _1643593]), 43297 ^ [_1643589, _1643591, _1643593]))], (43301 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 43296 ^ [_1643589, _1643591, _1643593]), 43297 ^ [_1643589, _1643591, _1643593])), -(hBOOL(hAPP(hAPP(_1643593, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 43296 ^ [_1643589, _1643591, _1643593]), c_Groups_Oone__class_Oone(tc_Int_Oint))), 43297 ^ [_1643589, _1643591, _1643593])))]]], (43311 ^ _780086) ^ [_1644080] : [class_Orderings_Olinorder(_1644080), -(c_List_Olinorder__class_Osorted__list__of__set(_1644080, c_Orderings_Obot__class_Obot(tc_fun(_1644080, tc_HOL_Obool))) = c_List_Olist_ONil(_1644080))], (43317 ^ _780086) ^ [_1644191, _1644193, _1644195, _1644197, _1644199] : [_1644191 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1644193, _1644195, _1644197), _1644191), _1644199) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1644195), _1644193), c_List_Olist_ONil(_1644195)), _1644199))], (43323 ^ _780086) ^ [_1644314, _1644316, _1644318, _1644320, _1644322] : [-(_1644314 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1644316, _1644318, _1644320), _1644314), _1644322) = c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(_1644318), _1644316), tc_prod(_1644318, _1644316), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1644318), _1644316), c_List_Olist_ONil(_1644318)), _1644322), hAPP(c_Product__Type_Oprod_Oprod__case(_1644318, _1644316, tc_prod(tc_List_Olist(_1644318), _1644316)), hAPP(hAPP(c_COMBC(_1644318, tc_fun(_1644316, tc_prod(tc_List_Olist(_1644318), _1644316)), tc_fun(_1644316, tc_prod(tc_List_Olist(_1644318), _1644316))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(_1644318), _1644316), tc_prod(tc_List_Olist(_1644318), _1644316)), tc_fun(tc_fun(_1644316, tc_prod(tc_List_Olist(_1644318), _1644316)), tc_fun(_1644316, tc_prod(tc_List_Olist(_1644318), _1644316))), _1644318), c_COMBB(tc_prod(tc_List_Olist(_1644318), _1644316), tc_prod(tc_List_Olist(_1644318), _1644316), _1644316)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1644318), tc_fun(_1644316, tc_prod(tc_List_Olist(_1644318), _1644316))), tc_fun(tc_prod(tc_List_Olist(_1644318), _1644316), tc_prod(tc_List_Olist(_1644318), _1644316)), _1644318), c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1644318), _1644316, tc_prod(tc_List_Olist(_1644318), _1644316))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1644318), tc_List_Olist(_1644318)), tc_fun(tc_List_Olist(_1644318), tc_fun(_1644316, tc_prod(tc_List_Olist(_1644318), _1644316))), _1644318), hAPP(c_COMBB(tc_List_Olist(_1644318), tc_fun(_1644316, tc_prod(tc_List_Olist(_1644318), _1644316)), tc_List_Olist(_1644318)), c_Product__Type_OPair(tc_List_Olist(_1644318), _1644316))), c_List_Olist_OCons(_1644318))))), hAPP(c_Lazy__Sequence_Oanamorph(_1644316, _1644318, _1644320), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1644314), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))))), hAPP(_1644320, _1644322)))], (43329 ^ _780086) ^ [_1644608, _1644610, _1644612, _1644614] : [-(c_List_Osublist(_1644608, hAPP(hAPP(c_List_Olist_OCons(_1644608), _1644610), _1644612), _1644614) = hAPP(hAPP(c_List_Oappend(_1644608), hAPP(hAPP(hAPP(c_If(tc_List_Olist(_1644608)), hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1644614)), hAPP(hAPP(c_List_Olist_OCons(_1644608), _1644610), c_List_Olist_ONil(_1644608))), c_List_Olist_ONil(_1644608))), c_List_Osublist(_1644608, _1644612, hAPP(c_Set_OCollect(tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), tc_Nat_Onat), c_member(tc_Nat_Onat)), c_Nat_OSuc)), _1644614)))))], (43331 ^ _780086) ^ [_1644719, _1644721, _1644723, _1644725, _1644727] : [hAPP(hAPP(c_List_Oappend(_1644719), _1644721), _1644723) = hAPP(hAPP(c_List_Olist_OCons(_1644719), _1644725), _1644727), 43336 ^ _780086 : [(43337 ^ _780086) ^ [] : [-(_1644721 = c_List_Olist_ONil(_1644719))], (43339 ^ _780086) ^ [] : [-(_1644723 = hAPP(hAPP(c_List_Olist_OCons(_1644719), _1644725), _1644727))]], 43341 ^ _780086 : [(43342 ^ _780086) ^ [] : [-(_1644721 = hAPP(hAPP(c_List_Olist_OCons(_1644719), _1644725), 43340 ^ [_1644719, _1644721, _1644723, _1644725, _1644727]))], (43344 ^ _780086) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1644719), 43340 ^ [_1644719, _1644721, _1644723, _1644725, _1644727]), _1644723) = _1644727)]]], (43346 ^ _780086) ^ [_1645012, _1645014, _1645016, _1645018, _1645020] : [-(hAPP(hAPP(c_List_Oappend(_1645012), _1645014), _1645016) = hAPP(hAPP(c_List_Olist_OCons(_1645012), _1645018), _1645020)), 43347 ^ _780086 : [(43348 ^ _780086) ^ [] : [_1645014 = c_List_Olist_ONil(_1645012), _1645016 = hAPP(hAPP(c_List_Olist_OCons(_1645012), _1645018), _1645020)], (43354 ^ _780086) ^ [_1645195] : [_1645014 = hAPP(hAPP(c_List_Olist_OCons(_1645012), _1645018), _1645195), hAPP(hAPP(c_List_Oappend(_1645012), _1645195), _1645016) = _1645020]]], (43362 ^ _780086) ^ [_1645383, _1645385, _1645387, _1645389, _1645391] : [hAPP(hAPP(c_List_Olist_OCons(_1645383), _1645385), _1645387) = hAPP(hAPP(c_List_Oappend(_1645383), _1645389), _1645391), 43367 ^ _780086 : [(43368 ^ _780086) ^ [] : [-(_1645389 = c_List_Olist_ONil(_1645383))], (43370 ^ _780086) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1645383), _1645385), _1645387) = _1645391)]], 43372 ^ _780086 : [(43373 ^ _780086) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1645383), _1645385), 43371 ^ [_1645383, _1645385, _1645387, _1645389, _1645391]) = _1645389)], (43375 ^ _780086) ^ [] : [-(_1645387 = hAPP(hAPP(c_List_Oappend(_1645383), 43371 ^ [_1645383, _1645385, _1645387, _1645389, _1645391]), _1645391))]]], (43377 ^ _780086) ^ [_1645676, _1645678, _1645680, _1645682, _1645684] : [-(hAPP(hAPP(c_List_Olist_OCons(_1645676), _1645678), _1645680) = hAPP(hAPP(c_List_Oappend(_1645676), _1645682), _1645684)), 43378 ^ _780086 : [(43379 ^ _780086) ^ [] : [_1645682 = c_List_Olist_ONil(_1645676), hAPP(hAPP(c_List_Olist_OCons(_1645676), _1645678), _1645680) = _1645684], (43385 ^ _780086) ^ [_1645859] : [hAPP(hAPP(c_List_Olist_OCons(_1645676), _1645678), _1645859) = _1645682, _1645680 = hAPP(hAPP(c_List_Oappend(_1645676), _1645859), _1645684)]]], (43393 ^ _780086) ^ [_1646047, _1646049, _1646051, _1646053, _1646055] : [hAPP(hAPP(c_List_Oappend(_1646047), _1646049), hAPP(hAPP(c_List_Olist_OCons(_1646047), _1646051), c_List_Olist_ONil(_1646047))) = hAPP(hAPP(c_List_Oappend(_1646047), _1646053), hAPP(hAPP(c_List_Olist_OCons(_1646047), _1646055), c_List_Olist_ONil(_1646047))), 43396 ^ _780086 : [(43397 ^ _780086) ^ [] : [-(_1646049 = _1646053)], (43399 ^ _780086) ^ [] : [-(_1646051 = _1646055)]]], (43401 ^ _780086) ^ [_1646224, _1646226, _1646228, _1646230, _1646232] : [-(hAPP(hAPP(c_List_Oappend(_1646224), _1646226), hAPP(hAPP(c_List_Olist_OCons(_1646224), _1646228), c_List_Olist_ONil(_1646224))) = hAPP(hAPP(c_List_Oappend(_1646224), _1646230), hAPP(hAPP(c_List_Olist_OCons(_1646224), _1646232), c_List_Olist_ONil(_1646224)))), _1646226 = _1646230, _1646228 = _1646232], (43411 ^ _780086) ^ [_1646439, _1646441, _1646443, _1646445] : [-(hAPP(hAPP(c_List_Oappend(_1646439), hAPP(hAPP(c_List_Olist_OCons(_1646439), _1646441), _1646443)), _1646445) = hAPP(hAPP(c_List_Olist_OCons(_1646439), _1646441), hAPP(hAPP(c_List_Oappend(_1646439), _1646443), _1646445)))], (43413 ^ _780086) ^ [_1646500, _1646502, _1646504, _1646506, _1646508, _1646510] : [hAPP(hAPP(c_List_Olist_OCons(_1646500), _1646502), _1646504) = _1646506, _1646508 = hAPP(hAPP(c_List_Oappend(_1646500), _1646504), _1646510), -(hAPP(hAPP(c_List_Olist_OCons(_1646500), _1646502), _1646508) = hAPP(hAPP(c_List_Oappend(_1646500), _1646506), _1646510))], (43423 ^ _780086) ^ [_1646730, _1646732, _1646734, _1646736] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1646730)), hAPP(hAPP(c_List_Oappend(_1646730), _1646732), _1646734)), c_List_Olists(_1646730, _1646736))), 43426 ^ _780086 : [(43427 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1646730)), _1646732), c_List_Olists(_1646730, _1646736))))], (43429 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1646730)), _1646734), c_List_Olists(_1646730, _1646736))))]]], (43431 ^ _780086) ^ [_1646921, _1646923, _1646925, _1646927] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1646921)), hAPP(hAPP(c_List_Oappend(_1646921), _1646923), _1646925)), c_List_Olists(_1646921, _1646927)))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1646921)), _1646923), c_List_Olists(_1646921, _1646927))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1646921)), _1646925), c_List_Olists(_1646921, _1646927)))], (43441 ^ _780086) ^ [_1647148, _1647150, _1647152, _1647154, _1647156, _1647158] : [hAPP(hAPP(c_List_Oappend(_1647148), _1647150), _1647152) = _1647154, _1647156 = hAPP(hAPP(c_List_Oappend(_1647148), _1647152), _1647158), -(hAPP(hAPP(c_List_Oappend(_1647148), _1647150), _1647156) = hAPP(hAPP(c_List_Oappend(_1647148), _1647154), _1647158))], (43451 ^ _780086) ^ [_1647378, _1647380, _1647382, _1647384] : [hAPP(hAPP(c_List_Oappend(_1647378), _1647380), _1647382) = hAPP(hAPP(c_List_Oappend(_1647378), _1647384), _1647382), -(_1647380 = _1647384)], (43457 ^ _780086) ^ [_1647487, _1647489, _1647491, _1647493] : [_1647489 = _1647493, -(hAPP(hAPP(c_List_Oappend(_1647487), _1647489), _1647491) = hAPP(hAPP(c_List_Oappend(_1647487), _1647493), _1647491))], (43463 ^ _780086) ^ [_1647623, _1647625, _1647627, _1647629] : [hAPP(hAPP(c_List_Oappend(_1647623), _1647625), _1647627) = hAPP(hAPP(c_List_Oappend(_1647623), _1647625), _1647629), -(_1647627 = _1647629)], (43469 ^ _780086) ^ [_1647732, _1647734, _1647736, _1647738] : [_1647736 = _1647738, -(hAPP(hAPP(c_List_Oappend(_1647732), _1647734), _1647736) = hAPP(hAPP(c_List_Oappend(_1647732), _1647734), _1647738))], (43475 ^ _780086) ^ [_1647871, _1647873, _1647875, _1647877, _1647879] : [hAPP(hAPP(c_List_Oappend(_1647871), _1647873), _1647875) = hAPP(hAPP(c_List_Oappend(_1647871), _1647877), _1647879), 43481 ^ _780086 : [(43482 ^ _780086) ^ [] : [-(_1647873 = hAPP(hAPP(c_List_Oappend(_1647871), _1647877), 43478 ^ [_1647871, _1647873, _1647875, _1647877, _1647879]))], (43484 ^ _780086) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1647871), 43478 ^ [_1647871, _1647873, _1647875, _1647877, _1647879]), _1647875) = _1647879)]], 43485 ^ _780086 : [(43486 ^ _780086) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1647871), _1647873), 43478 ^ [_1647871, _1647873, _1647875, _1647877, _1647879]) = _1647877)], (43488 ^ _780086) ^ [] : [-(_1647875 = hAPP(hAPP(c_List_Oappend(_1647871), 43478 ^ [_1647871, _1647873, _1647875, _1647877, _1647879]), _1647879))]]], (43490 ^ _780086) ^ [_1648202, _1648204, _1648206, _1648208, _1648210] : [-(hAPP(hAPP(c_List_Oappend(_1648202), _1648204), _1648206) = hAPP(hAPP(c_List_Oappend(_1648202), _1648208), _1648210)), 43491 ^ _780086 : [(43492 ^ _780086) ^ [_1648314] : [_1648204 = hAPP(hAPP(c_List_Oappend(_1648202), _1648208), _1648314), hAPP(hAPP(c_List_Oappend(_1648202), _1648314), _1648206) = _1648210], (43498 ^ _780086) ^ [_1648426] : [hAPP(hAPP(c_List_Oappend(_1648202), _1648204), _1648426) = _1648208, _1648206 = hAPP(hAPP(c_List_Oappend(_1648202), _1648426), _1648210)]]], (43506 ^ _780086) ^ [_1648590, _1648592, _1648594, _1648596] : [-(hAPP(hAPP(c_List_Oappend(_1648590), hAPP(hAPP(c_List_Oappend(_1648590), _1648592), _1648594)), _1648596) = hAPP(hAPP(c_List_Oappend(_1648590), _1648592), hAPP(hAPP(c_List_Oappend(_1648590), _1648594), _1648596)))], (43508 ^ _780086) ^ [_1648651, _1648653, _1648655] : [class_Groups_Omonoid__add(_1648651), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1648651), hAPP(hAPP(c_List_Oappend(_1648651), _1648653), _1648655)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1648651), hAPP(c_List_Omonoid__add__class_Olistsum(_1648651), _1648653)), hAPP(c_List_Omonoid__add__class_Olistsum(_1648651), _1648655)))], (43514 ^ _780086) ^ [_1648790, _1648792, _1648794] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648790)), hAPP(hAPP(c_List_Oappend(_1648790), _1648792), _1648794)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648790)), _1648792)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648790)), _1648794)))], (43516 ^ _780086) ^ [_1648852, _1648854, _1648856, _1648858, _1648860, _1648862] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648852)), _1648854) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648856)), _1648858), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648852)), _1648860) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648856)), _1648862), -(hAPP(hAPP(c_List_Ozip(_1648852, _1648856), hAPP(hAPP(c_List_Oappend(_1648852), _1648854), _1648860)), hAPP(hAPP(c_List_Oappend(_1648856), _1648858), _1648862)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1648852, _1648856)), hAPP(hAPP(c_List_Ozip(_1648852, _1648856), _1648854), _1648858)), hAPP(hAPP(c_List_Ozip(_1648852, _1648856), _1648860), _1648862)))], (43526 ^ _780086) ^ [_1649161, _1649163, _1649165] : [-(hAPP(c_List_Oset(_1649161), hAPP(hAPP(c_List_Oappend(_1649161), _1649163), _1649165)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1649161, tc_HOL_Obool)), hAPP(c_List_Oset(_1649161), _1649163)), hAPP(c_List_Oset(_1649161), _1649165)))], (43528 ^ _780086) ^ [_1649222, _1649224] : [-(hAPP(hAPP(c_List_Oappend(_1649222), c_List_Olist_ONil(_1649222)), _1649224) = _1649224)], (43530 ^ _780086) ^ [_1649275, _1649277, _1649279] : [c_List_Olist_ONil(_1649275) = hAPP(hAPP(c_List_Oappend(_1649275), _1649277), _1649279), 43533 ^ _780086 : [(43534 ^ _780086) ^ [] : [-(_1649277 = c_List_Olist_ONil(_1649275))], (43536 ^ _780086) ^ [] : [-(_1649279 = c_List_Olist_ONil(_1649275))]]], (43538 ^ _780086) ^ [_1649404, _1649406, _1649408] : [-(c_List_Olist_ONil(_1649404) = hAPP(hAPP(c_List_Oappend(_1649404), _1649406), _1649408)), _1649406 = c_List_Olist_ONil(_1649404), _1649408 = c_List_Olist_ONil(_1649404)], (43548 ^ _780086) ^ [_1649567, _1649569] : [-(hAPP(hAPP(c_List_Oappend(_1649567), _1649569), c_List_Olist_ONil(_1649567)) = _1649569)], (43550 ^ _780086) ^ [_1649620, _1649622, _1649624] : [_1649620 = hAPP(hAPP(c_List_Oappend(_1649622), _1649620), _1649624), -(_1649624 = c_List_Olist_ONil(_1649622))], (43556 ^ _780086) ^ [_1649715, _1649717, _1649719] : [_1649719 = c_List_Olist_ONil(_1649717), -(_1649715 = hAPP(hAPP(c_List_Oappend(_1649717), _1649715), _1649719))], (43562 ^ _780086) ^ [_1649834, _1649836, _1649838] : [_1649834 = hAPP(hAPP(c_List_Oappend(_1649836), _1649838), _1649834), -(_1649838 = c_List_Olist_ONil(_1649836))], (43568 ^ _780086) ^ [_1649929, _1649931, _1649933] : [_1649933 = c_List_Olist_ONil(_1649931), -(_1649929 = hAPP(hAPP(c_List_Oappend(_1649931), _1649933), _1649929))], (43574 ^ _780086) ^ [_1650048, _1650050, _1650052] : [hAPP(hAPP(c_List_Oappend(_1650048), _1650050), _1650052) = c_List_Olist_ONil(_1650048), 43577 ^ _780086 : [(43578 ^ _780086) ^ [] : [-(_1650050 = c_List_Olist_ONil(_1650048))], (43580 ^ _780086) ^ [] : [-(_1650052 = c_List_Olist_ONil(_1650048))]]], (43582 ^ _780086) ^ [_1650177, _1650179, _1650181] : [-(hAPP(hAPP(c_List_Oappend(_1650177), _1650179), _1650181) = c_List_Olist_ONil(_1650177)), _1650179 = c_List_Olist_ONil(_1650177), _1650181 = c_List_Olist_ONil(_1650177)], (43592 ^ _780086) ^ [_1650358, _1650360, _1650362] : [hAPP(hAPP(c_List_Oappend(_1650358), _1650360), _1650362) = _1650360, -(_1650362 = c_List_Olist_ONil(_1650358))], (43598 ^ _780086) ^ [_1650453, _1650455, _1650457] : [_1650457 = c_List_Olist_ONil(_1650453), -(hAPP(hAPP(c_List_Oappend(_1650453), _1650455), _1650457) = _1650455)], (43604 ^ _780086) ^ [_1650572, _1650574, _1650576] : [hAPP(hAPP(c_List_Oappend(_1650572), _1650574), _1650576) = _1650576, -(_1650574 = c_List_Olist_ONil(_1650572))], (43610 ^ _780086) ^ [_1650667, _1650669, _1650671] : [_1650669 = c_List_Olist_ONil(_1650667), -(hAPP(hAPP(c_List_Oappend(_1650667), _1650669), _1650671) = _1650671)], (43616 ^ _780086) ^ [_1650768, _1650770, _1650772] : [_1650768 = _1650770, -(_1650768 = hAPP(hAPP(c_List_Oappend(_1650772), c_List_Olist_ONil(_1650772)), _1650770))], (43622 ^ _780086) ^ [_1650879, _1650881, _1650883] : [_1650879 = c_List_Olist_ONil(_1650881), -(c_List_Obutlast(_1650881, hAPP(hAPP(c_List_Oappend(_1650881), _1650883), _1650879)) = c_List_Obutlast(_1650881, _1650883))], (43628 ^ _780086) ^ [_1650984, _1650986, _1650988] : [-(_1650984 = c_List_Olist_ONil(_1650986)), -(c_List_Obutlast(_1650986, hAPP(hAPP(c_List_Oappend(_1650986), _1650988), _1650984)) = hAPP(hAPP(c_List_Oappend(_1650986), _1650988), c_List_Obutlast(_1650986, _1650984)))], (43634 ^ _780086) ^ [_1651048, _1651050, _1651052, _1651054] : [-(hAPP(hAPP(c_List_Onth(_1651048), hAPP(hAPP(c_List_Oappend(_1651048), _1651050), hAPP(hAPP(c_List_Olist_OCons(_1651048), _1651052), _1651054))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651048)), _1651050)) = _1651052)], (43636 ^ _780086) ^ [_1651108, _1651110, _1651112, _1651114] : [-(hAPP(hAPP(c_List_Onth(_1651108), hAPP(hAPP(c_List_Oappend(_1651108), _1651110), _1651112)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651108)), _1651110)), _1651114)) = hAPP(hAPP(c_List_Onth(_1651108), _1651112), _1651114))], (43638 ^ _780086) ^ [_1651174, _1651176, _1651178, _1651180] : [-(hAPP(hAPP(c_List_Otake(_1651174), _1651176), hAPP(hAPP(c_List_Oappend(_1651174), _1651178), _1651180)) = hAPP(hAPP(c_List_Oappend(_1651174), hAPP(hAPP(c_List_Otake(_1651174), _1651176), _1651178)), hAPP(hAPP(c_List_Otake(_1651174), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1651176), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651174)), _1651178))), _1651180)))], (43640 ^ _780086) ^ [_1651256, _1651258, _1651260, _1651262, _1651264] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1651256), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651258)), _1651260))), -(hAPP(hAPP(c_List_Olist__update(_1651258, hAPP(hAPP(c_List_Oappend(_1651258), _1651260), _1651262)), _1651256), _1651264) = hAPP(hAPP(c_List_Oappend(_1651258), hAPP(hAPP(c_List_Olist__update(_1651258, _1651260), _1651256), _1651264)), _1651262))], (43646 ^ _780086) ^ [_1651431, _1651433, _1651435, _1651437, _1651439] : [-(hAPP(hAPP(c_List_Olist__update(_1651431, hAPP(hAPP(c_List_Oappend(_1651431), _1651433), hAPP(hAPP(c_List_Olist_OCons(_1651431), _1651435), _1651437))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651431)), _1651433)), _1651439) = hAPP(hAPP(c_List_Oappend(_1651431), _1651433), hAPP(hAPP(c_List_Olist_OCons(_1651431), _1651439), _1651437)))], (43648 ^ _780086) ^ [_1651525, _1651527, _1651529, _1651531] : [hBOOL(hAPP(hAPP(c_member(_1651525), _1651527), hAPP(c_List_Oset(_1651525), _1651529))), -(c_List_Oremove1(_1651525, _1651527, hAPP(hAPP(c_List_Oappend(_1651525), _1651529), _1651531)) = hAPP(hAPP(c_List_Oappend(_1651525), c_List_Oremove1(_1651525, _1651527, _1651529)), _1651531))], (43654 ^ _780086) ^ [_1651672, _1651674, _1651676, _1651678] : [-(hBOOL(hAPP(hAPP(c_member(_1651672), _1651674), hAPP(c_List_Oset(_1651672), _1651676)))), -(c_List_Oremove1(_1651672, _1651674, hAPP(hAPP(c_List_Oappend(_1651672), _1651676), _1651678)) = hAPP(hAPP(c_List_Oappend(_1651672), _1651676), c_List_Oremove1(_1651672, _1651674, _1651678)))], (43660 ^ _780086) ^ [_1651750, _1651752, _1651754, _1651756] : [43661 ^ _780086 : [(43662 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1651750), _1651752), hAPP(c_List_Oset(_1651750), c_List_Obutlast(_1651750, _1651754))))], (43664 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1651750), _1651752), hAPP(c_List_Oset(_1651750), c_List_Obutlast(_1651750, _1651756))))]], -(hBOOL(hAPP(hAPP(c_member(_1651750), _1651752), hAPP(c_List_Oset(_1651750), c_List_Obutlast(_1651750, hAPP(hAPP(c_List_Oappend(_1651750), _1651754), _1651756))))))], (43668 ^ _780086) ^ [_1651975, _1651977, _1651979] : [-(c_List_Obutlast(_1651975, hAPP(hAPP(c_List_Oappend(_1651975), _1651977), hAPP(hAPP(c_List_Olist_OCons(_1651975), _1651979), c_List_Olist_ONil(_1651975)))) = _1651977)], (43670 ^ _780086) ^ [_1652023, _1652025, _1652027, _1652029, _1652031, _1652033] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1652023), tc_List_Olist(_1652023))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1652023), tc_List_Olist(_1652023)), hAPP(hAPP(c_List_Oappend(_1652023), _1652025), _1652031)), hAPP(hAPP(c_List_Oappend(_1652023), _1652027), _1652033))), c_List_Olistrel1(_1652023, _1652029)))), 43671 ^ _780086 : [(43672 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1652023), tc_List_Olist(_1652023))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1652023), tc_List_Olist(_1652023)), _1652025), _1652027)), c_List_Olistrel1(_1652023, _1652029))), _1652031 = _1652033], (43678 ^ _780086) ^ [] : [_1652025 = _1652027, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1652023), tc_List_Olist(_1652023))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1652023), tc_List_Olist(_1652023)), _1652031), _1652033)), c_List_Olistrel1(_1652023, _1652029)))]]], (43686 ^ _780086) ^ [_1652471, _1652473, _1652475, _1652477, _1652479] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1652471), tc_List_Olist(_1652471))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1652471), tc_List_Olist(_1652471)), _1652473), _1652475)), c_List_Olexord(_1652471, _1652477))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1652471), tc_List_Olist(_1652471))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1652471), tc_List_Olist(_1652471)), hAPP(hAPP(c_List_Oappend(_1652471), _1652479), _1652473)), hAPP(hAPP(c_List_Oappend(_1652471), _1652479), _1652475))), c_List_Olexord(_1652471, _1652477))))], (43692 ^ _780086) ^ [_1652724, _1652726, _1652728] : [hBOOL(hAPP(c_List_Odistinct(_1652724), hAPP(hAPP(c_List_Oappend(_1652724), _1652726), _1652728))), 43695 ^ _780086 : [(43696 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1652724), _1652726)))], (43698 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1652724), _1652728)))], (43700 ^ _780086) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1652724, tc_HOL_Obool)), hAPP(c_List_Oset(_1652724), _1652726)), hAPP(c_List_Oset(_1652724), _1652728)) = c_Orderings_Obot__class_Obot(tc_fun(_1652724, tc_HOL_Obool)))]]], (43702 ^ _780086) ^ [_1652941, _1652943, _1652945] : [-(hBOOL(hAPP(c_List_Odistinct(_1652941), hAPP(hAPP(c_List_Oappend(_1652941), _1652943), _1652945)))), hBOOL(hAPP(c_List_Odistinct(_1652941), _1652943)), hBOOL(hAPP(c_List_Odistinct(_1652941), _1652945)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1652941, tc_HOL_Obool)), hAPP(c_List_Oset(_1652941), _1652943)), hAPP(c_List_Oset(_1652941), _1652945)) = c_Orderings_Obot__class_Obot(tc_fun(_1652941, tc_HOL_Obool))], (43716 ^ _780086) ^ [_1653237, _1653239, _1653241, _1653243] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1653237), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653239)), _1653241))), -(hAPP(hAPP(c_List_Onth(_1653239), hAPP(hAPP(c_List_Oappend(_1653239), _1653241), _1653243)), _1653237) = hAPP(hAPP(c_List_Onth(_1653239), _1653241), _1653237))], (43722 ^ _780086) ^ [_1653384, _1653386, _1653388, _1653390] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1653384), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653386)), _1653388)))), -(hAPP(hAPP(c_List_Onth(_1653386), hAPP(hAPP(c_List_Oappend(_1653386), _1653388), _1653390)), _1653384) = hAPP(hAPP(c_List_Onth(_1653386), _1653390), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1653384), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653386)), _1653388))))], (43728 ^ _780086) ^ [_1653493, _1653495, _1653497, _1653499, _1653501] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1653493), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653495)), _1653497))), -(hAPP(hAPP(c_List_Olist__update(_1653495, hAPP(hAPP(c_List_Oappend(_1653495), _1653497), _1653499)), _1653493), _1653501) = hAPP(hAPP(c_List_Oappend(_1653495), hAPP(hAPP(c_List_Olist__update(_1653495, _1653497), _1653493), _1653501)), _1653499))], (43734 ^ _780086) ^ [_1653662, _1653664, _1653666, _1653668, _1653670] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1653662), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653664)), _1653666)))), -(hAPP(hAPP(c_List_Olist__update(_1653664, hAPP(hAPP(c_List_Oappend(_1653664), _1653666), _1653668)), _1653662), _1653670) = hAPP(hAPP(c_List_Oappend(_1653664), _1653666), hAPP(hAPP(c_List_Olist__update(_1653664, _1653668), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1653662), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653664)), _1653666))), _1653670)))], (43740 ^ _780086) ^ [_1653765, _1653767, _1653769, _1653771] : [-(c_List_Osublist(_1653765, hAPP(hAPP(c_List_Oappend(_1653765), _1653767), _1653769), _1653771) = hAPP(hAPP(c_List_Oappend(_1653765), c_List_Osublist(_1653765, _1653767, _1653771)), c_List_Osublist(_1653765, _1653769, hAPP(c_Set_OCollect(tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), tc_Nat_Onat), c_member(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653765)), _1653767)))), _1653771)))))], (43742 ^ _780086) ^ [_1653844, _1653846, _1653848, _1653850, _1653852, _1653854, _1653856, _1653858] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1653844, _1653844)), hAPP(hAPP(c_Product__Type_OPair(_1653844, _1653844), _1653846), _1653848)), _1653850)), _1653852 = hAPP(hAPP(c_List_Oappend(_1653844), _1653854), hAPP(hAPP(c_List_Olist_OCons(_1653844), _1653846), _1653856)), _1653858 = hAPP(hAPP(c_List_Oappend(_1653844), _1653854), hAPP(hAPP(c_List_Olist_OCons(_1653844), _1653848), _1653856)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1653844), tc_List_Olist(_1653844))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1653844), tc_List_Olist(_1653844)), _1653852), _1653858)), c_List_Olistrel1(_1653844, _1653850))))], (43756 ^ _780086) ^ [_1654223, _1654225, _1654227, _1654229, _1654231, _1654233, _1654235] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1654223, _1654223)), hAPP(hAPP(c_Product__Type_OPair(_1654223, _1654223), _1654225), _1654227)), _1654229)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1654223), tc_List_Olist(_1654223))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1654223), tc_List_Olist(_1654223)), hAPP(hAPP(c_List_Oappend(_1654223), _1654231), hAPP(hAPP(c_List_Olist_OCons(_1654223), _1654225), _1654233))), hAPP(hAPP(c_List_Oappend(_1654223), _1654231), hAPP(hAPP(c_List_Olist_OCons(_1654223), _1654227), _1654235)))), c_List_Olexord(_1654223, _1654229))))], (43762 ^ _780086) ^ [_1654472, _1654474, _1654476] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1654472), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654474)), _1654476))), -(hAPP(hAPP(c_List_Otake(_1654474), hAPP(c_Nat_OSuc, _1654472)), _1654476) = hAPP(hAPP(c_List_Oappend(_1654474), hAPP(hAPP(c_List_Otake(_1654474), _1654472), _1654476)), hAPP(hAPP(c_List_Olist_OCons(_1654474), hAPP(hAPP(c_List_Onth(_1654474), _1654476), _1654472)), c_List_Olist_ONil(_1654474))))], (43768 ^ _780086) ^ [_1654692, _1654694, _1654696, _1654698, _1654700, _1654702] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1654692), tc_List_Olist(_1654692))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1654692), tc_List_Olist(_1654692)), hAPP(hAPP(c_List_Oappend(_1654692), _1654694), hAPP(hAPP(c_List_Olist_OCons(_1654692), _1654696), c_List_Olist_ONil(_1654692)))), hAPP(hAPP(c_List_Oappend(_1654692), _1654698), hAPP(hAPP(c_List_Olist_OCons(_1654692), _1654700), c_List_Olist_ONil(_1654692))))), c_List_Olistrel1(_1654692, _1654702))), 43773 ^ _780086 : [(43774 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1654692), tc_List_Olist(_1654692))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1654692), tc_List_Olist(_1654692)), _1654694), _1654698)), c_List_Olistrel1(_1654692, _1654702))))], (43776 ^ _780086) ^ [] : [-(_1654696 = _1654700)]], 43777 ^ _780086 : [(43778 ^ _780086) ^ [] : [-(_1654694 = _1654698)], (43780 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1654692, _1654692)), hAPP(hAPP(c_Product__Type_OPair(_1654692, _1654692), _1654696), _1654700)), _1654702)))]]], (43782 ^ _780086) ^ [_1655102, _1655104, _1655106, _1655108, _1655110, _1655112] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1655102), tc_List_Olist(_1655102))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1655102), tc_List_Olist(_1655102)), hAPP(hAPP(c_List_Oappend(_1655102), _1655104), hAPP(hAPP(c_List_Olist_OCons(_1655102), _1655106), c_List_Olist_ONil(_1655102)))), hAPP(hAPP(c_List_Oappend(_1655102), _1655108), hAPP(hAPP(c_List_Olist_OCons(_1655102), _1655110), c_List_Olist_ONil(_1655102))))), c_List_Olistrel1(_1655102, _1655112)))), 43783 ^ _780086 : [(43784 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1655102), tc_List_Olist(_1655102))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1655102), tc_List_Olist(_1655102)), _1655104), _1655108)), c_List_Olistrel1(_1655102, _1655112))), _1655106 = _1655110], (43790 ^ _780086) ^ [] : [_1655104 = _1655108, hBOOL(hAPP(hAPP(c_member(tc_prod(_1655102, _1655102)), hAPP(hAPP(c_Product__Type_OPair(_1655102, _1655102), _1655106), _1655110)), _1655112))]]], (43798 ^ _780086) ^ [_1655570, _1655572, _1655574, _1655576] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1655570), tc_List_Olist(_1655570))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1655570), tc_List_Olist(_1655570)), _1655572), _1655574)), c_List_Olistrel1(_1655570, _1655576))), 43803 ^ _780086 : [(43804 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1655570, _1655570)), hAPP(hAPP(c_Product__Type_OPair(_1655570, _1655570), 43801 ^ [_1655570, _1655572, _1655574, _1655576]), 43802 ^ [_1655570, _1655572, _1655574, _1655576])), _1655576)))], (43808 ^ _780086) ^ [] : [-(_1655572 = hAPP(hAPP(c_List_Oappend(_1655570), 43805 ^ [_1655570, _1655572, _1655574, _1655576]), hAPP(hAPP(c_List_Olist_OCons(_1655570), 43801 ^ [_1655570, _1655572, _1655574, _1655576]), 43806 ^ [_1655570, _1655572, _1655574, _1655576])))], (43810 ^ _780086) ^ [] : [-(_1655574 = hAPP(hAPP(c_List_Oappend(_1655570), 43805 ^ [_1655570, _1655572, _1655574, _1655576]), hAPP(hAPP(c_List_Olist_OCons(_1655570), 43802 ^ [_1655570, _1655572, _1655574, _1655576]), 43806 ^ [_1655570, _1655572, _1655574, _1655576])))]]], (43812 ^ _780086) ^ [_1655975, _1655977, _1655979, _1655981, _1655983] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1655975), tc_List_Olist(_1655975))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1655975), tc_List_Olist(_1655975)), hAPP(hAPP(c_List_Oappend(_1655975), _1655977), _1655979)), hAPP(hAPP(c_List_Oappend(_1655975), _1655977), _1655981))), c_List_Olexord(_1655975, _1655983))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1655975, _1655975)), hAPP(hAPP(c_Product__Type_OPair(_1655975, _1655975), 43817 ^ [_1655975, _1655977, _1655979, _1655981, _1655983]), 43817 ^ [_1655975, _1655977, _1655979, _1655981, _1655983])), _1655983))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1655975), tc_List_Olist(_1655975))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1655975), tc_List_Olist(_1655975)), _1655979), _1655981)), c_List_Olexord(_1655975, _1655983))))], (43823 ^ _780086) ^ [_1656294, _1656296] : [-(hAPP(c_List_Orotate1(_1656294), _1656296) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1656294), _1656294, c_List_Olist_ONil(_1656294), hAPP(hAPP(c_COMBB(tc_List_Olist(_1656294), tc_fun(tc_List_Olist(_1656294), tc_List_Olist(_1656294)), _1656294), hAPP(c_COMBC(tc_List_Olist(_1656294), tc_List_Olist(_1656294), tc_List_Olist(_1656294)), c_List_Oappend(_1656294))), hAPP(hAPP(c_COMBC(_1656294, tc_List_Olist(_1656294), tc_List_Olist(_1656294)), c_List_Olist_OCons(_1656294)), c_List_Olist_ONil(_1656294)))), _1656296))], (43825 ^ _780086) ^ [_1656388, _1656390, _1656392, _1656394] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1656388), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656390)), _1656392))), -(hAPP(hAPP(c_List_Olist__update(_1656390, _1656392), _1656388), _1656394) = hAPP(hAPP(c_List_Oappend(_1656390), hAPP(hAPP(c_List_Otake(_1656390), _1656388), _1656392)), hAPP(hAPP(c_List_Olist_OCons(_1656390), _1656394), hAPP(hAPP(c_List_Odrop(_1656390), hAPP(c_Nat_OSuc, _1656388)), _1656392))))], (43831 ^ _780086) ^ [_1656581, _1656583, _1656585] : [-(hAPP(hAPP(c_List_Oappend(_1656581), hAPP(hAPP(c_List_Otake(_1656581), _1656583), _1656585)), hAPP(hAPP(c_List_Odrop(_1656581), _1656583), _1656585)) = _1656585)], (43833 ^ _780086) ^ [_1656632, _1656634, _1656636] : [-(hAPP(hAPP(c_List_Odrop(_1656632), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1656632), _1656634), _1656636)) = _1656636)], (43835 ^ _780086) ^ [_1656675, _1656677, _1656679, _1656681] : [-(hAPP(hAPP(c_List_Odrop(_1656675), hAPP(c_Nat_OSuc, _1656677)), hAPP(hAPP(c_List_Olist_OCons(_1656675), _1656679), _1656681)) = hAPP(hAPP(c_List_Odrop(_1656675), _1656677), _1656681))], (43837 ^ _780086) ^ [_1656731, _1656733, _1656735, _1656737, _1656739] : [hAPP(hAPP(c_List_Odrop(_1656731), _1656733), _1656735) = hAPP(hAPP(c_List_Olist_OCons(_1656731), _1656737), _1656739), -(hAPP(hAPP(c_List_Onth(_1656731), _1656735), _1656733) = _1656737)], (43843 ^ _780086) ^ [_1656862, _1656864, _1656866] : [hBOOL(hAPP(c_List_Odistinct(_1656862), _1656864)), -(hBOOL(hAPP(c_List_Odistinct(_1656862), hAPP(hAPP(c_List_Odrop(_1656862), _1656866), _1656864))))], (43849 ^ _780086) ^ [_1656988, _1656990] : [hBOOL(hAPP(c_List_Odistinct(_1656988), hAPP(c_List_Orotate1(_1656988), _1656990))), -(hBOOL(hAPP(c_List_Odistinct(_1656988), _1656990)))], (43855 ^ _780086) ^ [_1657087, _1657089] : [hBOOL(hAPP(c_List_Odistinct(_1657087), _1657089)), -(hBOOL(hAPP(c_List_Odistinct(_1657087), hAPP(c_List_Orotate1(_1657087), _1657089))))], (43861 ^ _780086) ^ [_1657192, _1657194, _1657196] : [-(c_List_Obutlast(_1657192, hAPP(hAPP(c_List_Odrop(_1657192), _1657194), _1657196)) = hAPP(hAPP(c_List_Odrop(_1657192), _1657194), c_List_Obutlast(_1657192, _1657196)))], (43863 ^ _780086) ^ [_1657241, _1657243, _1657245] : [-(hAPP(hAPP(c_List_Odrop(_1657241), _1657243), c_List_Obutlast(_1657241, _1657245)) = c_List_Obutlast(_1657241, hAPP(hAPP(c_List_Odrop(_1657241), _1657243), _1657245)))], (43865 ^ _780086) ^ [_1657290, _1657292, _1657294, _1657296] : [-(hAPP(hAPP(c_List_Odrop(_1657290), _1657292), hAPP(hAPP(c_List_Otake(_1657290), _1657294), _1657296)) = hAPP(hAPP(c_List_Otake(_1657290), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1657294), _1657292)), hAPP(hAPP(c_List_Odrop(_1657290), _1657292), _1657296)))], (43867 ^ _780086) ^ [_1657357, _1657359, _1657361, _1657363] : [-(hAPP(hAPP(c_List_Otake(_1657357), _1657359), hAPP(hAPP(c_List_Odrop(_1657357), _1657361), _1657363)) = hAPP(hAPP(c_List_Odrop(_1657357), _1657361), hAPP(hAPP(c_List_Otake(_1657357), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1657359), _1657361)), _1657363)))], (43869 ^ _780086) ^ [_1657424, _1657426] : [-(hAPP(hAPP(c_List_Odrop(_1657424), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1657426) = _1657426)], (43871 ^ _780086) ^ [_1657457, _1657459, _1657461, _1657463] : [-(hAPP(hAPP(c_List_Odrop(_1657457), _1657459), hAPP(hAPP(c_List_Odrop(_1657457), _1657461), _1657463)) = hAPP(hAPP(c_List_Odrop(_1657457), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1657459), _1657461)), _1657463))], (43873 ^ _780086) ^ [_1657516, _1657518, _1657520, _1657522, _1657524] : [-(hAPP(hAPP(c_List_Odrop(tc_prod(_1657516, _1657518)), _1657520), hAPP(hAPP(c_List_Ozip(_1657516, _1657518), _1657522), _1657524)) = hAPP(hAPP(c_List_Ozip(_1657516, _1657518), hAPP(hAPP(c_List_Odrop(_1657516), _1657520), _1657522)), hAPP(hAPP(c_List_Odrop(_1657518), _1657520), _1657524)))], (43875 ^ _780086) ^ [_1657592, _1657594, _1657596] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1657592)), hAPP(hAPP(c_List_Odrop(_1657592), _1657594), _1657596)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1657592)), _1657596)), _1657594))], (43877 ^ _780086) ^ [_1657647, _1657649] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1657647)), hAPP(c_List_Orotate1(_1657647), _1657649)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1657647)), _1657649))], (43879 ^ _780086) ^ [_1657691, _1657693] : [-(hAPP(c_List_Oset(_1657691), hAPP(c_List_Orotate1(_1657691), _1657693)) = hAPP(c_List_Oset(_1657691), _1657693))], (43881 ^ _780086) ^ [_1657731, _1657733, _1657735, _1657737] : [hBOOL(hAPP(hAPP(c_member(_1657731), _1657733), hAPP(c_List_Oset(_1657731), hAPP(hAPP(c_List_Odrop(_1657731), _1657735), _1657737)))), -(hBOOL(hAPP(hAPP(c_member(_1657731), _1657733), hAPP(c_List_Oset(_1657731), _1657737))))], (43887 ^ _780086) ^ [_1657876, _1657878, _1657880] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1657876, tc_HOL_Obool)), hAPP(c_List_Oset(_1657876), hAPP(hAPP(c_List_Odrop(_1657876), _1657878), _1657880))), hAPP(c_List_Oset(_1657876), _1657880))))], (43889 ^ _780086) ^ [_1657931, _1657933] : [-(hAPP(hAPP(c_List_Odrop(_1657931), _1657933), c_List_Olist_ONil(_1657931)) = c_List_Olist_ONil(_1657931))], (43891 ^ _780086) ^ [_1657983, _1657985] : [hAPP(c_List_Orotate1(_1657983), _1657985) = c_List_Olist_ONil(_1657983), -(_1657985 = c_List_Olist_ONil(_1657983))], (43897 ^ _780086) ^ [_1658074, _1658076] : [_1658076 = c_List_Olist_ONil(_1658074), -(hAPP(c_List_Orotate1(_1658074), _1658076) = c_List_Olist_ONil(_1658074))], (43903 ^ _780086) ^ [_1658171, _1658173, _1658175, _1658177] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1658171), _1658173)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1658175, tc_HOL_Obool)), hAPP(c_List_Oset(_1658175), hAPP(hAPP(c_List_Odrop(_1658175), _1658173), _1658177))), hAPP(c_List_Oset(_1658175), hAPP(hAPP(c_List_Odrop(_1658175), _1658171), _1658177)))))], (43909 ^ _780086) ^ [_1658352, _1658354, _1658356] : [hAPP(hAPP(c_List_Odrop(_1658352), _1658354), _1658356) = c_List_Olist_ONil(_1658352), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658352)), _1658356)), _1658354)))], (43915 ^ _780086) ^ [_1658471, _1658473, _1658475] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658471)), _1658475)), _1658473)), -(hAPP(hAPP(c_List_Odrop(_1658471), _1658473), _1658475) = c_List_Olist_ONil(_1658471))], (43921 ^ _780086) ^ [_1658596, _1658598, _1658600] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658596)), _1658598)), _1658600)), -(hAPP(hAPP(c_List_Odrop(_1658596), _1658600), _1658598) = c_List_Olist_ONil(_1658596))], (43927 ^ _780086) ^ [_1658719, _1658721, _1658723, _1658725] : [-(hAPP(hAPP(c_List_Odrop(_1658719), _1658721), hAPP(hAPP(c_List_Oappend(_1658719), _1658723), _1658725)) = hAPP(hAPP(c_List_Oappend(_1658719), hAPP(hAPP(c_List_Odrop(_1658719), _1658721), _1658723)), hAPP(hAPP(c_List_Odrop(_1658719), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1658721), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658719)), _1658723))), _1658725)))], (43929 ^ _780086) ^ [_1658822, _1658824, _1658826, _1658828] : [hAPP(hAPP(c_List_Oappend(_1658822), _1658824), _1658826) = _1658828, 43932 ^ _780086 : [(43933 ^ _780086) ^ [] : [-(_1658824 = hAPP(hAPP(c_List_Otake(_1658822), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658822)), _1658824)), _1658828))], (43935 ^ _780086) ^ [] : [-(_1658826 = hAPP(hAPP(c_List_Odrop(_1658822), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658822)), _1658824)), _1658828))]]], (43937 ^ _780086) ^ [_1659001, _1659003, _1659005, _1659007] : [-(hAPP(hAPP(c_List_Oappend(_1659001), _1659003), _1659005) = _1659007), _1659003 = hAPP(hAPP(c_List_Otake(_1659001), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659001)), _1659003)), _1659007), _1659005 = hAPP(hAPP(c_List_Odrop(_1659001), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659001)), _1659003)), _1659007)], (43947 ^ _780086) ^ [_1659216, _1659218, _1659220, _1659222] : [-(hAPP(hAPP(c_List_Odrop(_1659216), _1659218), hAPP(hAPP(c_List_Olist_OCons(_1659216), _1659220), _1659222)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1659216), hAPP(hAPP(c_List_Olist_OCons(_1659216), _1659220), _1659222), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1659216), tc_List_Olist(_1659216)), c_List_Odrop(_1659216)), _1659222), _1659218))], (43949 ^ _780086) ^ [_1659307, _1659309, _1659311, _1659313] : [_1659307 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1659309), _1659307), hAPP(hAPP(c_List_Olist_OCons(_1659309), _1659311), _1659313)) = hAPP(hAPP(c_List_Olist_OCons(_1659309), _1659311), _1659313))], (43955 ^ _780086) ^ [_1659430, _1659432, _1659434, _1659436] : [-(_1659430 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1659432), _1659430), hAPP(hAPP(c_List_Olist_OCons(_1659432), _1659434), _1659436)) = hAPP(hAPP(c_List_Odrop(_1659432), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1659430), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1659436))], (43961 ^ _780086) ^ [_1659502, _1659504, _1659506, _1659508] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1659502), _1659504)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659506)), _1659508))), -(hAPP(hAPP(c_List_Onth(_1659506), hAPP(hAPP(c_List_Odrop(_1659506), _1659502), _1659508)), _1659504) = hAPP(hAPP(c_List_Onth(_1659506), _1659508), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1659502), _1659504)))], (43967 ^ _780086) ^ [_1659703, _1659705, _1659707, _1659709, _1659711] : [hAPP(hAPP(c_List_Oappend(_1659703), _1659705), _1659707) = hAPP(hAPP(c_List_Oappend(_1659703), _1659709), _1659711), 43970 ^ _780086 : [(43971 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659703)), _1659705)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659703)), _1659709))), 43974 ^ _780086 : [(43975 ^ _780086) ^ [] : [-(_1659705 = hAPP(hAPP(c_List_Otake(_1659703), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659703)), _1659705)), _1659709))], (43977 ^ _780086) ^ [] : [-(_1659707 = hAPP(hAPP(c_List_Oappend(_1659703), hAPP(hAPP(c_List_Odrop(_1659703), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659703)), _1659705)), _1659709)), _1659711))]]], (43979 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659703)), _1659705)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659703)), _1659709)))), 43982 ^ _780086 : [(43983 ^ _780086) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1659703), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659703)), _1659709)), _1659705) = _1659709)], (43985 ^ _780086) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1659703), hAPP(hAPP(c_List_Odrop(_1659703), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659703)), _1659709)), _1659705)), _1659707) = _1659711)]]]]], (43987 ^ _780086) ^ [_1660216, _1660218, _1660220, _1660222, _1660224] : [-(hAPP(hAPP(c_List_Oappend(_1660216), _1660218), _1660220) = hAPP(hAPP(c_List_Oappend(_1660216), _1660222), _1660224)), 43990 ^ _780086 : [(43991 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660216)), _1660218)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660216)), _1660222))))], (43993 ^ _780086) ^ [] : [_1660218 = hAPP(hAPP(c_List_Otake(_1660216), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660216)), _1660218)), _1660222), _1660220 = hAPP(hAPP(c_List_Oappend(_1660216), hAPP(hAPP(c_List_Odrop(_1660216), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660216)), _1660218)), _1660222)), _1660224)]], 43998 ^ _780086 : [(43999 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660216)), _1660218)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660216)), _1660222)))], (44001 ^ _780086) ^ [] : [hAPP(hAPP(c_List_Otake(_1660216), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660216)), _1660222)), _1660218) = _1660222, hAPP(hAPP(c_List_Oappend(_1660216), hAPP(hAPP(c_List_Odrop(_1660216), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660216)), _1660222)), _1660218)), _1660220) = _1660224]]], (44009 ^ _780086) ^ [_1660804, _1660806, _1660808] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1660804), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660806)), _1660808))), -(hAPP(hAPP(c_List_Olist_OCons(_1660806), hAPP(hAPP(c_List_Onth(_1660806), _1660808), _1660804)), hAPP(hAPP(c_List_Odrop(_1660806), hAPP(c_Nat_OSuc, _1660804)), _1660808)) = hAPP(hAPP(c_List_Odrop(_1660806), _1660804), _1660808))], (44015 ^ _780086) ^ [_1660975, _1660977, _1660979, _1660981] : [-(hAPP(c_List_Orotate1(_1660975), c_List_Olist_ONil(_1660975)) = c_List_Olist_ONil(_1660975))], (44017 ^ _780086) ^ [_1661010, _1661012, _1661014, _1661016] : [-(hAPP(c_List_Orotate1(_1661012), hAPP(hAPP(c_List_Olist_OCons(_1661012), _1661014), _1661016)) = hAPP(hAPP(c_List_Oappend(_1661012), _1661016), hAPP(hAPP(c_List_Olist_OCons(_1661012), _1661014), c_List_Olist_ONil(_1661012))))], (44019 ^ _780086) ^ [_1661087, _1661089, _1661091, _1661093] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1661087) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1661089), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1661087)), hAPP(hAPP(c_List_Olist_OCons(_1661089), _1661091), _1661093)) = hAPP(hAPP(c_List_Olist_OCons(_1661089), _1661091), _1661093))], (44025 ^ _780086) ^ [_1661222, _1661224, _1661226, _1661228] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1661222) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1661224), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1661222)), hAPP(hAPP(c_List_Olist_OCons(_1661224), _1661226), _1661228)) = hAPP(hAPP(c_List_Odrop(_1661224), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1661222)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1661228))], (44031 ^ _780086) ^ [_1661303, _1661305, _1661307, _1661309] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1661303), _1661305)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661307)), _1661309))), -(hAPP(hAPP(c_List_Otake(_1661307), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1661303), _1661305)), _1661309) = hAPP(hAPP(c_List_Oappend(_1661307), hAPP(hAPP(c_List_Otake(_1661307), _1661303), _1661309)), hAPP(hAPP(c_List_Otake(_1661307), _1661305), hAPP(hAPP(c_List_Odrop(_1661307), _1661303), _1661309))))], (44037 ^ _780086) ^ [_1661512, _1661514] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661512)), _1661514)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate1(_1661512), _1661514) = _1661514)], (44043 ^ _780086) ^ [_1661623, _1661625, _1661627, _1661629, _1661631] : [-(hAPP(hAPP(c_List_Ozip(_1661623, _1661625), _1661627), hAPP(hAPP(c_List_Oappend(_1661625), _1661629), _1661631)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1661623, _1661625)), hAPP(hAPP(c_List_Ozip(_1661623, _1661625), hAPP(hAPP(c_List_Otake(_1661623), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661625)), _1661629)), _1661627)), _1661629)), hAPP(hAPP(c_List_Ozip(_1661623, _1661625), hAPP(hAPP(c_List_Odrop(_1661623), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661625)), _1661629)), _1661627)), _1661631)))], (44045 ^ _780086) ^ [_1661730, _1661732, _1661734, _1661736, _1661738] : [-(hAPP(hAPP(c_List_Ozip(_1661730, _1661732), hAPP(hAPP(c_List_Oappend(_1661730), _1661734), _1661736)), _1661738) = hAPP(hAPP(c_List_Oappend(tc_prod(_1661730, _1661732)), hAPP(hAPP(c_List_Ozip(_1661730, _1661732), _1661734), hAPP(hAPP(c_List_Otake(_1661732), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661730)), _1661734)), _1661738))), hAPP(hAPP(c_List_Ozip(_1661730, _1661732), _1661736), hAPP(hAPP(c_List_Odrop(_1661732), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661730)), _1661734)), _1661738))))], (44047 ^ _780086) ^ [_1661837, _1661839, _1661841] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1661837), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661839)), _1661841))), -(_1661841 = hAPP(hAPP(c_List_Oappend(_1661839), hAPP(hAPP(c_List_Otake(_1661839), _1661837), _1661841)), hAPP(hAPP(c_List_Olist_OCons(_1661839), hAPP(hAPP(c_List_Onth(_1661839), _1661841), _1661837)), hAPP(hAPP(c_List_Odrop(_1661839), hAPP(c_Nat_OSuc, _1661837)), _1661841))))], (44053 ^ _780086) ^ [_1662026, _1662028, _1662030] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1662026), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662028)), _1662030))), -(hAPP(hAPP(c_List_Oappend(_1662028), hAPP(hAPP(c_List_Otake(_1662028), _1662026), _1662030)), hAPP(hAPP(c_List_Olist_OCons(_1662028), hAPP(c_List_Ohd(_1662028), hAPP(hAPP(c_List_Odrop(_1662028), _1662026), _1662030))), c_List_Olist_ONil(_1662028))) = hAPP(hAPP(c_List_Otake(_1662028), hAPP(c_Nat_OSuc, _1662026)), _1662030))], (44059 ^ _780086) ^ [_1662228, _1662230, _1662232] : [-(_1662228 = c_List_Olist_ONil(_1662230)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1662232), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662230)), _1662228))), -(hAPP(c_List_Ohd(_1662230), hAPP(hAPP(c_List_Odrop(_1662230), _1662232), _1662228)) = hAPP(hAPP(c_List_Onth(_1662230), _1662228), _1662232))], (44069 ^ _780086) ^ [_1662427, _1662429, _1662431] : [-(hAPP(c_List_Ohd(_1662427), hAPP(hAPP(c_List_Olist_OCons(_1662427), _1662429), _1662431)) = _1662429)], (44071 ^ _780086) ^ [_1662463, _1662465, _1662467] : [-(_1662463 = c_List_Olist_ONil(_1662465)), -(hAPP(c_List_Ohd(_1662465), hAPP(hAPP(c_List_Oappend(_1662465), _1662463), _1662467)) = hAPP(c_List_Ohd(_1662465), _1662463))], (44077 ^ _780086) ^ [_1662533, _1662535, _1662537] : [_1662533 = c_List_Olist_ONil(_1662535), -(hAPP(c_List_Ohd(_1662535), hAPP(hAPP(c_List_Oappend(_1662535), _1662533), _1662537)) = hAPP(c_List_Ohd(_1662535), _1662537))], (44083 ^ _780086) ^ [_1662646, _1662648, _1662650] : [-(_1662646 = c_List_Olist_ONil(_1662648)), -(hAPP(c_List_Ohd(_1662648), hAPP(hAPP(c_List_Oappend(_1662648), _1662646), _1662650)) = hAPP(c_List_Ohd(_1662648), _1662646))], (44089 ^ _780086) ^ [_1662702, _1662704] : [-(_1662702 = c_List_Olist_ONil(_1662704)), -(hBOOL(hAPP(hAPP(c_member(_1662704), hAPP(c_List_Ohd(_1662704), _1662702)), hAPP(c_List_Oset(_1662704), _1662702))))], (44095 ^ _780086) ^ [_1662753, _1662755] : [-(_1662753 = c_List_Olist_ONil(_1662755)), -(hAPP(c_List_Ohd(_1662755), _1662753) = hAPP(hAPP(c_List_Onth(_1662755), _1662753), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (44101 ^ _780086) ^ [_1662800, _1662802] : [-(_1662800 = c_List_Olist_ONil(_1662802)), -(hAPP(c_List_Orotate1(_1662802), _1662800) = hAPP(hAPP(c_List_Oappend(_1662802), hAPP(c_List_Otl(_1662802), _1662800)), hAPP(hAPP(c_List_Olist_OCons(_1662802), hAPP(c_List_Ohd(_1662802), _1662800)), c_List_Olist_ONil(_1662802))))], (44107 ^ _780086) ^ [_1662867, _1662869, _1662871] : [-(_1662867 = c_List_Olist_ONil(_1662869)), -(hAPP(c_List_Ohd(_1662869), hAPP(c_List_Orotate(_1662869, _1662871), _1662867)) = hAPP(hAPP(c_List_Onth(_1662869), _1662867), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1662871, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662869)), _1662867))))], (44113 ^ _780086) ^ [_1662937, _1662939, _1662941] : [-(hAPP(hAPP(c_List_Odrop(_1662937), _1662939), hAPP(c_List_Otl(_1662937), _1662941)) = hAPP(c_List_Otl(_1662937), hAPP(hAPP(c_List_Odrop(_1662937), _1662939), _1662941)))], (44115 ^ _780086) ^ [_1662990, _1662992, _1662994] : [-(hAPP(c_List_Otl(_1662990), hAPP(hAPP(c_List_Odrop(_1662990), _1662992), _1662994)) = hAPP(hAPP(c_List_Odrop(_1662990), _1662992), hAPP(c_List_Otl(_1662990), _1662994)))], (44117 ^ _780086) ^ [_1663043, _1663045, _1663047] : [-(hAPP(c_List_Otl(_1663043), hAPP(hAPP(c_List_Olist_OCons(_1663043), _1663045), _1663047)) = _1663047)], (44119 ^ _780086) ^ [_1663083, _1663085] : [hBOOL(hAPP(c_List_Odistinct(_1663083), _1663085)), -(hBOOL(hAPP(c_List_Odistinct(_1663083), hAPP(c_List_Otl(_1663083), _1663085))))], (44125 ^ _780086) ^ [_1663204, _1663206, _1663208] : [hBOOL(hAPP(c_List_Odistinct(_1663204), hAPP(c_List_Orotate(_1663204, _1663206), _1663208))), -(hBOOL(hAPP(c_List_Odistinct(_1663204), _1663208)))], (44131 ^ _780086) ^ [_1663307, _1663309, _1663311] : [hBOOL(hAPP(c_List_Odistinct(_1663307), _1663311)), -(hBOOL(hAPP(c_List_Odistinct(_1663307), hAPP(c_List_Orotate(_1663307, _1663309), _1663311))))], (44137 ^ _780086) ^ [_1663416, _1663418, _1663420] : [-(c_List_Orotate(_1663416, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1663418), _1663420)) = hAPP(c_Fun_Ocomp(tc_List_Olist(_1663416), tc_List_Olist(_1663416), tc_List_Olist(_1663416), c_List_Orotate(_1663416, _1663418)), c_List_Orotate(_1663416, _1663420)))], (44139 ^ _780086) ^ [_1663472] : [-(c_List_Orotate(_1663472, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(_1663472)))], (44141 ^ _780086) ^ [_1663502, _1663504, _1663506, _1663508] : [-(hAPP(c_List_Orotate(_1663502, _1663504), hAPP(c_List_Orotate(_1663502, _1663506), _1663508)) = hAPP(c_List_Orotate(_1663502, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1663504), _1663506)), _1663508))], (44143 ^ _780086) ^ [_1663555, _1663557, _1663559] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1663555)), hAPP(c_List_Orotate(_1663555, _1663557), _1663559)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1663555)), _1663559))], (44145 ^ _780086) ^ [_1663602, _1663604, _1663606] : [-(hAPP(c_List_Oset(_1663602), hAPP(c_List_Orotate(_1663602, _1663604), _1663606)) = hAPP(c_List_Oset(_1663602), _1663606))], (44147 ^ _780086) ^ [_1663645] : [-(hAPP(c_List_Otl(_1663645), c_List_Olist_ONil(_1663645)) = c_List_Olist_ONil(_1663645))], (44149 ^ _780086) ^ [_1663695, _1663697, _1663699] : [hAPP(c_List_Orotate(_1663695, _1663697), _1663699) = c_List_Olist_ONil(_1663695), -(_1663699 = c_List_Olist_ONil(_1663695))], (44155 ^ _780086) ^ [_1663790, _1663792, _1663794] : [_1663794 = c_List_Olist_ONil(_1663790), -(hAPP(c_List_Orotate(_1663790, _1663792), _1663794) = c_List_Olist_ONil(_1663790))], (44161 ^ _780086) ^ [_1663891, _1663893, _1663895] : [-(hAPP(c_List_Orotate1(_1663891), hAPP(c_List_Orotate(_1663891, _1663893), _1663895)) = hAPP(c_List_Orotate(_1663891, _1663893), hAPP(c_List_Orotate1(_1663891), _1663895)))], (44163 ^ _780086) ^ [_1663940, _1663942] : [-(c_List_Orotate(_1663940, _1663942) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(_1663940), tc_List_Olist(_1663940)), _1663942), c_List_Orotate1(_1663940)))], (44165 ^ _780086) ^ [_1663979, _1663981, _1663983] : [-(_1663979 = c_List_Olist_ONil(_1663981)), -(hAPP(c_List_Otl(_1663981), hAPP(hAPP(c_List_Oappend(_1663981), _1663979), _1663983)) = hAPP(hAPP(c_List_Oappend(_1663981), hAPP(c_List_Otl(_1663981), _1663979)), _1663983))], (44171 ^ _780086) ^ [_1664045, _1664047, _1664049] : [-(hAPP(hAPP(c_List_Otake(_1664045), _1664047), hAPP(c_List_Otl(_1664045), _1664049)) = hAPP(c_List_Otl(_1664045), hAPP(hAPP(c_List_Otake(_1664045), hAPP(c_Nat_OSuc, _1664047)), _1664049)))], (44173 ^ _780086) ^ [_1664101, _1664103, _1664105] : [-(hAPP(c_List_Orotate(_1664101, _1664103), _1664105) = hAPP(c_List_Orotate(_1664101, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1664103, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664101)), _1664105))), _1664105))], (44175 ^ _780086) ^ [_1664151, _1664153, _1664155] : [-(hAPP(hAPP(c_List_Odrop(_1664151), hAPP(c_Nat_OSuc, _1664153)), _1664155) = hAPP(hAPP(c_List_Odrop(_1664151), _1664153), hAPP(c_List_Otl(_1664151), _1664155)))], (44177 ^ _780086) ^ [_1664202, _1664204, _1664206] : [-(hAPP(c_List_Orotate(_1664202, hAPP(c_Nat_OSuc, _1664204)), _1664206) = hAPP(c_List_Orotate1(_1664202), hAPP(c_List_Orotate(_1664202, _1664204), _1664206)))], (44179 ^ _780086) ^ [_1664249, _1664251, _1664253] : [-(hAPP(c_List_Otl(_1664249), hAPP(hAPP(c_List_Oappend(_1664249), _1664251), _1664253)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1664249), _1664249, hAPP(c_List_Otl(_1664249), _1664253), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1664249), tc_List_Olist(_1664249)), _1664249), hAPP(hAPP(c_COMBC(tc_List_Olist(_1664249), tc_List_Olist(_1664249), tc_List_Olist(_1664249)), c_List_Oappend(_1664249)), _1664253))), _1664251))], (44181 ^ _780086) ^ [_1664335, _1664337, _1664339] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1664335, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664337)), _1664339)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Orotate(_1664337, _1664335), _1664339) = _1664339)], (44187 ^ _780086) ^ [_1664448, _1664450, _1664452] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664448)), _1664450)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate(_1664448, _1664452), _1664450) = _1664450)], (44193 ^ _780086) ^ [_1664563, _1664565] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664563)), hAPP(c_List_Otl(_1664563), _1664565)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664563)), _1664565)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (44195 ^ _780086) ^ [_1664613, _1664615, _1664617] : [-(hAPP(c_List_Otl(_1664613), hAPP(hAPP(c_List_Otake(_1664613), _1664615), _1664617)) = hAPP(hAPP(c_List_Otake(_1664613), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1664615), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_List_Otl(_1664613), _1664617)))], (44197 ^ _780086) ^ [_1664668, _1664670, _1664672] : [-(_1664668 = c_List_Olist_ONil(_1664670)), -(hAPP(hAPP(c_List_Otake(_1664670), hAPP(c_Nat_OSuc, _1664672)), _1664668) = hAPP(hAPP(c_List_Olist_OCons(_1664670), hAPP(c_List_Ohd(_1664670), _1664668)), hAPP(hAPP(c_List_Otake(_1664670), _1664672), hAPP(c_List_Otl(_1664670), _1664668))))], (44203 ^ _780086) ^ [_1664745, _1664747, _1664749] : [-(hAPP(c_List_Orotate(_1664745, _1664747), _1664749) = hAPP(hAPP(c_List_Oappend(_1664745), hAPP(hAPP(c_List_Odrop(_1664745), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1664747, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664745)), _1664749))), _1664749)), hAPP(hAPP(c_List_Otake(_1664745), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1664747, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664745)), _1664749))), _1664749)))], (44205 ^ _780086) ^ [_1664824, _1664826] : [class_Lattices_Oab__semigroup__idem__mult(_1664824), -(_1664826 = c_List_Olist_ONil(_1664824)), -(hAPP(c_Finite__Set_Ofold1(_1664824, c_Groups_Otimes__class_Otimes(_1664824)), hAPP(c_List_Oset(_1664824), _1664826)) = hAPP(c_List_Ofoldl(_1664824, _1664824, c_Groups_Otimes__class_Otimes(_1664824), hAPP(c_List_Ohd(_1664824), _1664826)), hAPP(c_List_Otl(_1664824), _1664826)))], (44215 ^ _780086) ^ [_1664984, _1664986, _1664988, _1664990] : [44216 ^ _780086 : [(44217 ^ _780086) ^ [_1665081, _1665083] : [_1664984 = hAPP(hAPP(c_List_Olist_OCons(_1664986), _1665083), _1665081)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1664986), tc_List_Olist(_1664986))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1664986), tc_List_Olist(_1664986)), _1664988), hAPP(hAPP(c_List_Oappend(_1664986), _1664988), _1664984))), c_List_Olexord(_1664986, _1664990))))], (44221 ^ _780086) ^ [_1665180, _1665182, _1665184, _1665186] : [-(hAPP(c_List_Ofoldl(_1665180, _1665182, _1665184, _1665186), c_List_Olist_ONil(_1665182)) = _1665186)], (44223 ^ _780086) ^ [_1665219, _1665221, _1665223] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1665219), _1665221)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1665219), hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1665221), _1665223))))], (44229 ^ _780086) ^ [_1665334, _1665336, _1665338, _1665340] : [class_Groups_Osemigroup__add(_1665334), -(hAPP(c_List_Ofoldl(_1665334, _1665334, c_Groups_Oplus__class_Oplus(_1665334), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1665334), _1665336), _1665338)), _1665340) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1665334), _1665336), hAPP(c_List_Ofoldl(_1665334, _1665334, c_Groups_Oplus__class_Oplus(_1665334), _1665338), _1665340)))], (44235 ^ _780086) ^ [_1665485, _1665487, _1665489] : [class_Groups_Omonoid__add(_1665485), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1665485), _1665487), hAPP(c_List_Ofoldl(_1665485, _1665485, c_Groups_Oplus__class_Oplus(_1665485), c_Groups_Ozero__class_Ozero(_1665485)), _1665489)) = hAPP(c_List_Ofoldl(_1665485, _1665485, c_Groups_Oplus__class_Oplus(_1665485), _1665487), _1665489))], (44241 ^ _780086) ^ [_1665622, _1665624, _1665626, _1665628, _1665630, _1665632] : [-(hAPP(c_List_Ofoldl(_1665622, _1665624, _1665626, _1665628), hAPP(hAPP(c_List_Olist_OCons(_1665624), _1665630), _1665632)) = hAPP(c_List_Ofoldl(_1665622, _1665624, _1665626, hAPP(hAPP(_1665626, _1665628), _1665630)), _1665632))], (44243 ^ _780086) ^ [_1665685, _1665687, _1665689, _1665691, _1665693, _1665695] : [-(hAPP(c_List_Ofoldl(_1665685, _1665687, _1665689, _1665691), hAPP(hAPP(c_List_Oappend(_1665687), _1665693), _1665695)) = hAPP(c_List_Ofoldl(_1665685, _1665687, _1665689, hAPP(c_List_Ofoldl(_1665685, _1665687, _1665689, _1665691), _1665693)), _1665695))], (44245 ^ _780086) ^ [_1665750] : [class_Groups_Omonoid__add(_1665750), -(c_List_Omonoid__add__class_Olistsum(_1665750) = c_List_Ofoldl(_1665750, _1665750, c_Groups_Oplus__class_Oplus(_1665750), c_Groups_Ozero__class_Ozero(_1665750)))], (44251 ^ _780086) ^ [_1665860, _1665862] : [hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1665860), _1665862) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 44254 ^ _780086 : [(44255 ^ _780086) ^ [] : [-(_1665860 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44257 ^ _780086) ^ [_1665974] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1665974), hAPP(c_List_Oset(tc_Nat_Onat), _1665862))), -(_1665974 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (44263 ^ _780086) ^ [_1666071, _1666073] : [-(hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1666071), _1666073) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1666071 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 44269 ^ _780086 : [(44270 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 44268 ^ [_1666071, _1666073]), hAPP(c_List_Oset(tc_Nat_Onat), _1666073))))], (44272 ^ _780086) ^ [] : [44268 ^ [_1666071, _1666073] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (44276 ^ _780086) ^ [_1666297, _1666299, _1666301, _1666303, _1666305] : [c_Finite__Set_Ofun__left__comm__idem(_1666297, _1666299, _1666301), -(hAPP(hAPP(c_Finite__Set_Ofold(_1666297, _1666299, _1666301), _1666303), hAPP(c_List_Oset(_1666297), _1666305)) = hAPP(c_List_Ofoldl(_1666299, _1666297, hAPP(c_COMBC(_1666297, _1666299, _1666299), _1666301), _1666303), _1666305))], (44282 ^ _780086) ^ [_1666442, _1666444] : [class_Complete__Lattice_Ocomplete__lattice(_1666442), -(c_Complete__Lattice_OSup__class_OSup(_1666442, hAPP(c_List_Oset(_1666442), _1666444)) = hAPP(c_List_Ofoldl(_1666442, _1666442, c_Lattices_Osemilattice__sup__class_Osup(_1666442), c_Orderings_Obot__class_Obot(_1666442)), _1666444))], (44288 ^ _780086) ^ [_1666557, _1666559] : [class_Complete__Lattice_Ocomplete__lattice(_1666557), -(c_Complete__Lattice_OInf__class_OInf(_1666557, hAPP(c_List_Oset(_1666557), _1666559)) = hAPP(c_List_Ofoldl(_1666557, _1666557, c_Lattices_Osemilattice__inf__class_Oinf(_1666557), c_Orderings_Otop__class_Otop(_1666557)), _1666559))], (44294 ^ _780086) ^ [_1666672, _1666674, _1666676] : [class_Lattices_Olattice(_1666672), -(c_Big__Operators_Olattice__class_OSup__fin(_1666672, hAPP(c_List_Oset(_1666672), hAPP(hAPP(c_List_Olist_OCons(_1666672), _1666674), _1666676))) = hAPP(c_List_Ofoldl(_1666672, _1666672, c_Lattices_Osemilattice__sup__class_Osup(_1666672), _1666674), _1666676))], (44300 ^ _780086) ^ [_1666801, _1666803, _1666805] : [class_Lattices_Olattice(_1666801), -(c_Big__Operators_Olattice__class_OInf__fin(_1666801, hAPP(c_List_Oset(_1666801), hAPP(hAPP(c_List_Olist_OCons(_1666801), _1666803), _1666805))) = hAPP(c_List_Ofoldl(_1666801, _1666801, c_Lattices_Osemilattice__inf__class_Oinf(_1666801), _1666803), _1666805))], (44306 ^ _780086) ^ [_1666930, _1666932, _1666934] : [class_Orderings_Olinorder(_1666930), -(c_Big__Operators_Olinorder__class_OMin(_1666930, hAPP(c_List_Oset(_1666930), hAPP(hAPP(c_List_Olist_OCons(_1666930), _1666932), _1666934))) = hAPP(c_List_Ofoldl(_1666930, _1666930, c_Orderings_Oord__class_Omin(_1666930), _1666932), _1666934))], (44312 ^ _780086) ^ [_1667059, _1667061, _1667063] : [class_Orderings_Olinorder(_1667059), -(c_Big__Operators_Olinorder__class_OMax(_1667059, hAPP(c_List_Oset(_1667059), hAPP(hAPP(c_List_Olist_OCons(_1667059), _1667061), _1667063))) = hAPP(c_List_Ofoldl(_1667059, _1667059, c_Orderings_Oord__class_Omax(_1667059), _1667061), _1667063))], (44318 ^ _780086) ^ [_1667188, _1667190, _1667192] : [class_Orderings_Olinorder(_1667188), -(c_Big__Operators_Olattice_OInf__fin(_1667188, c_Orderings_Oord__class_Omin(_1667188), hAPP(c_List_Oset(_1667188), hAPP(hAPP(c_List_Olist_OCons(_1667188), _1667190), _1667192))) = hAPP(c_List_Ofoldl(_1667188, _1667188, c_Orderings_Oord__class_Omin(_1667188), _1667190), _1667192))], (44324 ^ _780086) ^ [_1667323, _1667325, _1667327] : [class_Orderings_Olinorder(_1667323), -(c_Big__Operators_Olattice_OSup__fin(_1667323, c_Orderings_Oord__class_Omax(_1667323), hAPP(c_List_Oset(_1667323), hAPP(hAPP(c_List_Olist_OCons(_1667323), _1667325), _1667327))) = hAPP(c_List_Ofoldl(_1667323, _1667323, c_Orderings_Oord__class_Omax(_1667323), _1667325), _1667327))], (44330 ^ _780086) ^ [_1667458, _1667460, _1667462, _1667464] : [class_Complete__Lattice_Ocomplete__lattice(_1667458), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1667460, _1667458), hAPP(c_List_Oset(_1667460), _1667462)), _1667464) = hAPP(c_List_Ofoldl(_1667458, _1667460, hAPP(c_COMBC(_1667460, _1667458, _1667458), hAPP(hAPP(c_COMBB(_1667458, tc_fun(_1667458, _1667458), _1667460), c_Lattices_Osemilattice__sup__class_Osup(_1667458)), _1667464)), c_Orderings_Obot__class_Obot(_1667458)), _1667462))], (44336 ^ _780086) ^ [_1667629, _1667631, _1667633, _1667635] : [class_Complete__Lattice_Ocomplete__lattice(_1667629), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1667631, _1667629), hAPP(c_List_Oset(_1667631), _1667633)), _1667635) = hAPP(c_List_Ofoldl(_1667629, _1667631, hAPP(c_COMBC(_1667631, _1667629, _1667629), hAPP(hAPP(c_COMBB(_1667629, tc_fun(_1667629, _1667629), _1667631), c_Lattices_Osemilattice__inf__class_Oinf(_1667629)), _1667635)), c_Orderings_Otop__class_Otop(_1667629)), _1667633))], (44342 ^ _780086) ^ [_1667800, _1667802] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1667800), hAPP(c_List_Oset(tc_Nat_Onat), _1667802))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1667800), hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1667802))))], (44348 ^ _780086) ^ [_1667909, _1667911, _1667913] : [class_Orderings_Olinorder(_1667909), hBOOL(hAPP(c_Finite__Set_Ofinite(_1667909), _1667911)), -(c_List_Olinorder__class_Osorted__list__of__set(_1667909, hAPP(hAPP(c_Set_Oinsert(_1667909), _1667913), _1667911)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1667909, _1667909, c_COMBI(_1667909)), _1667913), c_List_Olinorder__class_Osorted__list__of__set(_1667909, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1667909, tc_HOL_Obool)), _1667911), hAPP(hAPP(c_Set_Oinsert(_1667909), _1667913), c_Orderings_Obot__class_Obot(tc_fun(_1667909, tc_HOL_Obool)))))))], (44358 ^ _780086) ^ [_1668166, _1668168, _1668170] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1668166), tc_List_Olist(_1668166))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1668166), tc_List_Olist(_1668166)), c_List_Olist_ONil(_1668166)), _1668168)), c_List_Olexord(_1668166, _1668170))), -(_1668168 = hAPP(hAPP(c_List_Olist_OCons(_1668166), 44361 ^ [_1668166, _1668168, _1668170]), 44362 ^ [_1668166, _1668168, _1668170]))], (44366 ^ _780086) ^ [_1668349, _1668351, _1668353] : [44367 ^ _780086 : [(44368 ^ _780086) ^ [_1668438, _1668440] : [_1668351 = hAPP(hAPP(c_List_Olist_OCons(_1668349), _1668440), _1668438)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1668349), tc_List_Olist(_1668349))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1668349), tc_List_Olist(_1668349)), c_List_Olist_ONil(_1668349)), _1668351)), c_List_Olexord(_1668349, _1668353))))], (44372 ^ _780086) ^ [_1668533, _1668535, _1668537, _1668539] : [class_Orderings_Olinorder(_1668533), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1668535, _1668533, _1668537), _1668539), c_List_Olist_ONil(_1668535)) = hAPP(hAPP(c_List_Olist_OCons(_1668535), _1668539), c_List_Olist_ONil(_1668535)))], (44378 ^ _780086) ^ [_1668656, _1668658, _1668660, _1668662, _1668664, _1668666] : [class_Orderings_Olinorder(_1668656), 44381 ^ _780086 : [(44382 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1668656), hAPP(_1668658, _1668660)), hAPP(_1668658, _1668662))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1668664, _1668656, _1668658), _1668660), hAPP(hAPP(c_List_Olist_OCons(_1668664), _1668662), _1668666)) = hAPP(hAPP(c_List_Olist_OCons(_1668664), _1668660), hAPP(hAPP(c_List_Olist_OCons(_1668664), _1668662), _1668666)))], (44388 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1668656), hAPP(_1668658, _1668660)), hAPP(_1668658, _1668662)))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1668664, _1668656, _1668658), _1668660), hAPP(hAPP(c_List_Olist_OCons(_1668664), _1668662), _1668666)) = hAPP(hAPP(c_List_Olist_OCons(_1668664), _1668662), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1668664, _1668656, _1668658), _1668660), _1668666)))]]], (44394 ^ _780086) ^ [_1669038, _1669040, _1669042, _1669044, _1669046] : [class_Orderings_Olinorder(_1669038), -(hAPP(c_List_Oset(_1669040), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1669040, _1669038, _1669042), _1669044), _1669046)) = hAPP(hAPP(c_Set_Oinsert(_1669040), _1669044), hAPP(c_List_Oset(_1669040), _1669046)))], (44400 ^ _780086) ^ [_1669175, _1669177, _1669179, _1669181, _1669183] : [class_Orderings_Olinorder(_1669175), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1669177)), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1669177, _1669175, _1669179), _1669181), _1669183)) = hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1669177)), _1669183)))], (44406 ^ _780086) ^ [_1669310] : [class_Orderings_Olinorder(_1669310), -(c_Finite__Set_Ofun__left__comm(_1669310, tc_List_Olist(_1669310), c_List_Olinorder__class_Oinsort__key(_1669310, _1669310, c_COMBI(_1669310))))], (44412 ^ _780086) ^ [_1669401, _1669403, _1669405, _1669407] : [class_Orderings_Olinorder(_1669401), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1669401, _1669401, c_COMBI(_1669401)), _1669403), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1669401, _1669401, c_COMBI(_1669401)), _1669405), _1669407)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1669401, _1669401, c_COMBI(_1669401)), _1669405), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1669401, _1669401, c_COMBI(_1669401)), _1669403), _1669407)))], (44418 ^ _780086) ^ [_1669576, _1669578, _1669580, _1669582, _1669584, _1669586] : [class_Orderings_Olinorder(_1669576), -(hAPP(_1669578, _1669580) = hAPP(_1669578, _1669582)), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1669584, _1669576, _1669578), _1669582), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1669584, _1669576, _1669578), _1669580), _1669586)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1669584, _1669576, _1669578), _1669580), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1669584, _1669576, _1669578), _1669582), _1669586)))], (44428 ^ _780086) ^ [_1669766, _1669768, _1669770] : [class_Orderings_Olinorder(_1669766), -(c_List_Oremove1(_1669766, _1669768, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1669766, _1669766, c_COMBI(_1669766)), _1669768), _1669770)) = _1669770)], (44434 ^ _780086) ^ [_1669875, _1669877, _1669879, _1669881, _1669883] : [class_Orderings_Olinorder(_1669875), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1669877, _1669875, _1669879), _1669881), _1669883) = c_List_Olist_ONil(_1669877)], (44440 ^ _780086) ^ [_1669981, _1669983, _1669985, _1669987, _1669989] : [class_Orderings_Olinorder(_1669981), 44443 ^ _780086 : [(44444 ^ _780086) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1669983), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1669983, _1669981, _1669985), _1669987), _1669989))), 44447 ^ _780086 : [(44448 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1669983), _1669987), hAPP(c_List_Oset(_1669983), _1669989)))], (44450 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1669983), _1669989)))]]], (44452 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1669983), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1669983, _1669981, _1669985), _1669987), _1669989)))), -(hBOOL(hAPP(hAPP(c_member(_1669983), _1669987), hAPP(c_List_Oset(_1669983), _1669989)))), hBOOL(hAPP(c_List_Odistinct(_1669983), _1669989))]]], (44462 ^ _780086) ^ [_1670383, _1670385, _1670387, _1670389, _1670391] : [class_Orderings_Olinorder(_1670383), -(hBOOL(hAPP(hAPP(c_member(_1670383), hAPP(_1670385, _1670387)), hAPP(c_Set_Oimage(_1670389, _1670383, _1670385), hAPP(c_List_Oset(_1670389), _1670391))))), -(c_List_Olinorder__class_Oinsort__insert__key(_1670389, _1670383, _1670385, _1670387, _1670391) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1670389, _1670383, _1670385), _1670387), _1670391))], (44472 ^ _780086) ^ [_1670555, _1670557, _1670559] : [class_Orderings_Olinorder(_1670555), -(hBOOL(hAPP(hAPP(c_member(_1670555), _1670557), hAPP(c_List_Oset(_1670555), _1670559)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1670555, _1670555, c_COMBI(_1670555), _1670557, _1670559) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1670555, _1670555, c_COMBI(_1670555)), _1670557), _1670559))], (44482 ^ _780086) ^ [_1670711, _1670713, _1670715, _1670717, _1670719] : [class_Orderings_Olinorder(_1670711), hBOOL(hAPP(c_List_Odistinct(_1670713), _1670715)), -(hBOOL(hAPP(c_List_Odistinct(_1670713), c_List_Olinorder__class_Oinsort__insert__key(_1670713, _1670711, _1670717, _1670719, _1670715))))], (44492 ^ _780086) ^ [_1670878, _1670880, _1670882] : [class_Orderings_Olinorder(_1670878), hBOOL(hAPP(hAPP(c_member(_1670878), _1670880), hAPP(c_List_Oset(_1670878), _1670882))), -(c_List_Olinorder__class_Oinsort__insert__key(_1670878, _1670878, c_COMBI(_1670878), _1670880, _1670882) = _1670882)], (44502 ^ _780086) ^ [_1671049, _1671051, _1671053] : [class_Orderings_Olinorder(_1671049), -(hAPP(c_List_Oset(_1671049), c_List_Olinorder__class_Oinsort__insert__key(_1671049, _1671049, c_COMBI(_1671049), _1671051, _1671053)) = hAPP(hAPP(c_Set_Oinsert(_1671049), _1671051), hAPP(c_List_Oset(_1671049), _1671053)))], (44508 ^ _780086) ^ [_1671178, _1671180, _1671182, _1671184, _1671186] : [class_Orderings_Olinorder(_1671178), hBOOL(hAPP(hAPP(c_member(_1671178), hAPP(_1671180, _1671182)), hAPP(c_Set_Oimage(_1671184, _1671178, _1671180), hAPP(c_List_Oset(_1671184), _1671186)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1671184, _1671178, _1671180, _1671182, _1671186) = _1671186)], (44518 ^ _780086) ^ [_1671372, _1671374, _1671376, _1671378] : [-(_1671372 = c_List_Olist_ONil(_1671374)), 44521 ^ _780086 : [(44522 ^ _780086) ^ [] : [_1671376 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1671374)), _1671372)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Olast(_1671374, hAPP(hAPP(c_List_Olist__update(_1671374, _1671372), _1671376), _1671378)) = _1671378)], (44528 ^ _780086) ^ [] : [-(_1671376 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1671374)), _1671372)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Olast(_1671374, hAPP(hAPP(c_List_Olist__update(_1671374, _1671372), _1671376), _1671378)) = c_List_Olast(_1671374, _1671372))]]], (44534 ^ _780086) ^ [_1671658, _1671660] : [-(_1671658 = c_List_Olist_ONil(_1671660)), -(c_List_Olast(_1671660, _1671658) = hAPP(hAPP(c_List_Onth(_1671660), _1671658), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1671660)), _1671658)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (44540 ^ _780086) ^ [_1671732, _1671734, _1671736] : [_1671732 = c_List_Olist_ONil(_1671734), -(c_List_Olast(_1671734, hAPP(hAPP(c_List_Olist_OCons(_1671734), _1671736), _1671732)) = _1671736)], (44546 ^ _780086) ^ [_1671831, _1671833, _1671835] : [-(_1671831 = c_List_Olist_ONil(_1671833)), -(c_List_Olast(_1671833, hAPP(hAPP(c_List_Olist_OCons(_1671833), _1671835), _1671831)) = c_List_Olast(_1671833, _1671831))], (44552 ^ _780086) ^ [_1671883, _1671885, _1671887] : [-(_1671883 = c_List_Olist_ONil(_1671885)), -(c_List_Olast(_1671885, hAPP(hAPP(c_List_Olist_OCons(_1671885), _1671887), _1671883)) = c_List_Olast(_1671885, _1671883))], (44558 ^ _780086) ^ [_1671937, _1671939, _1671941] : [_1671937 = c_List_Olist_ONil(_1671939), -(c_List_Olast(_1671939, hAPP(hAPP(c_List_Olist_OCons(_1671939), _1671941), _1671937)) = _1671941)], (44564 ^ _780086) ^ [_1672054, _1672056, _1672058] : [_1672054 = c_List_Olist_ONil(_1672056), -(c_List_Olast(_1672056, hAPP(hAPP(c_List_Oappend(_1672056), _1672058), _1672054)) = c_List_Olast(_1672056, _1672058))], (44570 ^ _780086) ^ [_1672159, _1672161, _1672163] : [-(_1672159 = c_List_Olist_ONil(_1672161)), -(c_List_Olast(_1672161, hAPP(hAPP(c_List_Oappend(_1672161), _1672163), _1672159)) = c_List_Olast(_1672161, _1672159))], (44576 ^ _780086) ^ [_1672211, _1672213, _1672215] : [-(_1672211 = c_List_Olist_ONil(_1672213)), -(c_List_Olast(_1672213, hAPP(hAPP(c_List_Oappend(_1672213), _1672215), _1672211)) = c_List_Olast(_1672213, _1672211))], (44582 ^ _780086) ^ [_1672265, _1672267, _1672269] : [_1672265 = c_List_Olist_ONil(_1672267), -(c_List_Olast(_1672267, hAPP(hAPP(c_List_Oappend(_1672267), _1672269), _1672265)) = c_List_Olast(_1672267, _1672269))], (44588 ^ _780086) ^ [_1672372, _1672374] : [-(_1672372 = c_List_Olist_ONil(_1672374)), -(hBOOL(hAPP(hAPP(c_member(_1672374), c_List_Olast(_1672374, _1672372)), hAPP(c_List_Oset(_1672374), _1672372))))], (44594 ^ _780086) ^ [_1672425, _1672427, _1672429] : [-(c_List_Olast(_1672425, hAPP(hAPP(c_List_Oappend(_1672425), _1672427), hAPP(hAPP(c_List_Olist_OCons(_1672425), _1672429), c_List_Olist_ONil(_1672425)))) = _1672429)], (44596 ^ _780086) ^ [_1672473, _1672475, _1672477] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1672473), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672475)), _1672477))), -(c_List_Olast(_1672475, hAPP(hAPP(c_List_Odrop(_1672475), _1672473), _1672477)) = c_List_Olast(_1672475, _1672477))], (44602 ^ _780086) ^ [_1672600, _1672602] : [-(_1672600 = c_List_Olist_ONil(_1672602)), -(hAPP(hAPP(c_List_Oappend(_1672602), c_List_Obutlast(_1672602, _1672600)), hAPP(hAPP(c_List_Olist_OCons(_1672602), c_List_Olast(_1672602, _1672600)), c_List_Olist_ONil(_1672602))) = _1672600)], (44608 ^ _780086) ^ [_1672683, _1672685, _1672687, _1672689] : [hAPP(hAPP(c_List_Oappend(_1672683), _1672685), hAPP(hAPP(c_List_Olist_OCons(_1672683), _1672687), c_List_Olist_ONil(_1672683))) = _1672689, 44611 ^ _780086 : [(44612 ^ _780086) ^ [] : [_1672689 = c_List_Olist_ONil(_1672683)], (44614 ^ _780086) ^ [] : [-(c_List_Obutlast(_1672683, _1672689) = _1672685)], (44616 ^ _780086) ^ [] : [-(c_List_Olast(_1672683, _1672689) = _1672687)]]], (44618 ^ _780086) ^ [_1672872, _1672874, _1672876, _1672878] : [-(hAPP(hAPP(c_List_Oappend(_1672872), _1672874), hAPP(hAPP(c_List_Olist_OCons(_1672872), _1672876), c_List_Olist_ONil(_1672872))) = _1672878), -(_1672878 = c_List_Olist_ONil(_1672872)), c_List_Obutlast(_1672872, _1672878) = _1672874, c_List_Olast(_1672872, _1672878) = _1672876], (44632 ^ _780086) ^ [_1673140, _1673142, _1673144] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1673140)), _1673142), c_List_Olists(_1673140, _1673144))), -(_1673142 = c_List_Olist_ONil(_1673140)), 44641 ^ _780086 : [(44642 ^ _780086) ^ [] : [-(_1673142 = hAPP(hAPP(c_List_Olist_OCons(_1673140), 44639 ^ [_1673140, _1673142, _1673144]), 44640 ^ [_1673140, _1673142, _1673144]))], (44644 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1673140), 44639 ^ [_1673140, _1673142, _1673144]), _1673144)))], (44646 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1673140)), 44640 ^ [_1673140, _1673142, _1673144]), c_List_Olists(_1673140, _1673144))))]]], (44648 ^ _780086) ^ [_1673423, _1673425, _1673427] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1673423)), _1673425), c_List_Olists(_1673423, _1673427)))), 44649 ^ _780086 : [(44650 ^ _780086) ^ [] : [_1673425 = c_List_Olist_ONil(_1673423)], (44652 ^ _780086) ^ [_1673551, _1673553] : [_1673425 = hAPP(hAPP(c_List_Olist_OCons(_1673423), _1673553), _1673551), hBOOL(hAPP(hAPP(c_member(_1673423), _1673553), _1673427)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1673423)), _1673551), c_List_Olists(_1673423, _1673427)))]]], (44664 ^ _780086) ^ [_1673785, _1673787] : [-(_1673785 = c_List_Olist_ONil(_1673787)), -(c_Random_Oselect__weight(_1673787, hAPP(hAPP(c_List_Omap(_1673787, tc_prod(tc_Code__Numeral_Ocode__numeral, _1673787)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1673787), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1673785)) = c_Random_Oselect(_1673787, _1673785))], (44670 ^ _780086) ^ [_1673847, _1673849, _1673851] : [c_Fun_Oinj__on(_1673847, _1673849, _1673851, c_Orderings_Otop__class_Otop(tc_fun(_1673847, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1673847), tc_List_Olist(_1673849), hAPP(c_List_Omap(_1673847, _1673849), _1673851), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1673847), tc_HOL_Obool))))], (44676 ^ _780086) ^ [_1673974, _1673976, _1673978, _1673980] : [-(_1673974 = c_List_Olist_ONil(_1673976)), -(c_List_Olast(_1673978, hAPP(hAPP(c_List_Omap(_1673976, _1673978), _1673980), _1673974)) = hAPP(_1673980, c_List_Olast(_1673976, _1673974)))], (44682 ^ _780086) ^ [_1674034, _1674036, _1674038, _1674040, _1674042, _1674044, _1674046] : [-(hAPP(c_List_Ofoldl(_1674034, _1674036, _1674038, _1674040), hAPP(hAPP(c_List_Omap(_1674042, _1674036), _1674044), _1674046)) = hAPP(c_List_Ofoldl(_1674034, _1674042, hAPP(hAPP(c_COMBC(_1674034, tc_fun(_1674042, _1674036), tc_fun(_1674042, _1674034)), hAPP(hAPP(c_COMBB(tc_fun(_1674036, _1674034), tc_fun(tc_fun(_1674042, _1674036), tc_fun(_1674042, _1674034)), _1674034), c_COMBB(_1674036, _1674034, _1674042)), _1674038)), _1674044), _1674040), _1674046))], (44684 ^ _780086) ^ [_1674136, _1674138, _1674140, _1674142, _1674144] : [-(hAPP(c_List_Orotate(_1674136, _1674138), hAPP(hAPP(c_List_Omap(_1674140, _1674136), _1674142), _1674144)) = hAPP(hAPP(c_List_Omap(_1674140, _1674136), _1674142), hAPP(c_List_Orotate(_1674140, _1674138), _1674144)))], (44686 ^ _780086) ^ [_1674197, _1674199, _1674201, _1674203] : [-(hAPP(hAPP(c_List_Omap(_1674197, _1674199), _1674201), hAPP(c_List_Otl(_1674197), _1674203)) = hAPP(c_List_Otl(_1674199), hAPP(hAPP(c_List_Omap(_1674197, _1674199), _1674201), _1674203)))], (44688 ^ _780086) ^ [_1674254, _1674256, _1674258, _1674260, _1674262, _1674264] : [-(hAPP(hAPP(c_List_Ozip(_1674254, _1674256), _1674258), hAPP(hAPP(c_List_Omap(_1674260, _1674256), _1674262), _1674264)) = hAPP(hAPP(c_List_Omap(tc_prod(_1674254, _1674260), tc_prod(_1674254, _1674256)), hAPP(c_Product__Type_Oprod_Oprod__case(_1674254, _1674260, tc_prod(_1674254, _1674256)), hAPP(hAPP(c_COMBC(_1674254, tc_fun(_1674260, _1674256), tc_fun(_1674260, tc_prod(_1674254, _1674256))), hAPP(hAPP(c_COMBB(tc_fun(_1674256, tc_prod(_1674254, _1674256)), tc_fun(tc_fun(_1674260, _1674256), tc_fun(_1674260, tc_prod(_1674254, _1674256))), _1674254), c_COMBB(_1674256, tc_prod(_1674254, _1674256), _1674260)), c_Product__Type_OPair(_1674254, _1674256))), _1674262))), hAPP(hAPP(c_List_Ozip(_1674254, _1674260), _1674258), _1674264)))], (44690 ^ _780086) ^ [_1674396, _1674398, _1674400, _1674402, _1674404, _1674406, _1674408, _1674410] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1674396, _1674398), _1674400), _1674402), hAPP(hAPP(c_List_Ozip(_1674396, _1674398), _1674404), hAPP(hAPP(c_List_Omap(_1674406, _1674398), _1674408), _1674410))) = hAPP(hAPP(c_List_Omap(tc_prod(_1674396, _1674406), _1674400), hAPP(c_Product__Type_Oprod_Oprod__case(_1674396, _1674406, _1674400), hAPP(hAPP(c_COMBB(tc_fun(_1674406, tc_prod(_1674396, _1674398)), tc_fun(_1674406, _1674400), _1674396), hAPP(c_COMBB(tc_prod(_1674396, _1674398), _1674400, _1674406), _1674402)), hAPP(hAPP(c_COMBC(_1674396, tc_fun(_1674406, _1674398), tc_fun(_1674406, tc_prod(_1674396, _1674398))), hAPP(hAPP(c_COMBB(tc_fun(_1674398, tc_prod(_1674396, _1674398)), tc_fun(tc_fun(_1674406, _1674398), tc_fun(_1674406, tc_prod(_1674396, _1674398))), _1674396), c_COMBB(_1674398, tc_prod(_1674396, _1674398), _1674406)), c_Product__Type_OPair(_1674396, _1674398))), _1674408)))), hAPP(hAPP(c_List_Ozip(_1674396, _1674406), _1674404), _1674410)))], (44692 ^ _780086) ^ [_1674577, _1674579, _1674581, _1674583, _1674585, _1674587, _1674589, _1674591] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1674577, _1674579), _1674581), _1674583), hAPP(hAPP(c_List_Ozip(_1674577, _1674579), hAPP(hAPP(c_List_Omap(_1674585, _1674577), _1674587), _1674589)), _1674591)) = hAPP(hAPP(c_List_Omap(tc_prod(_1674585, _1674579), _1674581), hAPP(c_Product__Type_Oprod_Oprod__case(_1674585, _1674579, _1674581), hAPP(hAPP(c_COMBB(tc_fun(_1674579, tc_prod(_1674577, _1674579)), tc_fun(_1674579, _1674581), _1674585), hAPP(c_COMBB(tc_prod(_1674577, _1674579), _1674581, _1674579), _1674583)), hAPP(hAPP(c_COMBB(_1674577, tc_fun(_1674579, tc_prod(_1674577, _1674579)), _1674585), c_Product__Type_OPair(_1674577, _1674579)), _1674587)))), hAPP(hAPP(c_List_Ozip(_1674585, _1674579), _1674589), _1674591)))], (44694 ^ _780086) ^ [_1674720, _1674722, _1674724, _1674726, _1674728, _1674730] : [-(hAPP(hAPP(c_List_Ozip(_1674720, _1674722), hAPP(hAPP(c_List_Omap(_1674724, _1674720), _1674726), _1674728)), _1674730) = hAPP(hAPP(c_List_Omap(tc_prod(_1674724, _1674722), tc_prod(_1674720, _1674722)), hAPP(c_Product__Type_Oprod_Oprod__case(_1674724, _1674722, tc_prod(_1674720, _1674722)), hAPP(hAPP(c_COMBB(_1674720, tc_fun(_1674722, tc_prod(_1674720, _1674722)), _1674724), c_Product__Type_OPair(_1674720, _1674722)), _1674726))), hAPP(hAPP(c_List_Ozip(_1674724, _1674722), _1674728), _1674730)))], (44696 ^ _780086) ^ [_1674824, _1674826, _1674828, _1674830, _1674832, _1674834, _1674836, _1674838] : [-(hAPP(hAPP(c_List_Ozip(_1674824, _1674826), hAPP(hAPP(c_List_Omap(_1674828, _1674824), _1674830), _1674832)), hAPP(hAPP(c_List_Omap(_1674834, _1674826), _1674836), _1674838)) = hAPP(hAPP(c_List_Omap(tc_prod(_1674828, _1674834), tc_prod(_1674824, _1674826)), hAPP(c_Product__Type_Oprod_Oprod__case(_1674828, _1674834, tc_prod(_1674824, _1674826)), hAPP(hAPP(c_COMBC(_1674828, tc_fun(_1674834, _1674826), tc_fun(_1674834, tc_prod(_1674824, _1674826))), hAPP(hAPP(c_COMBB(tc_fun(_1674826, tc_prod(_1674824, _1674826)), tc_fun(tc_fun(_1674834, _1674826), tc_fun(_1674834, tc_prod(_1674824, _1674826))), _1674828), c_COMBB(_1674826, tc_prod(_1674824, _1674826), _1674834)), hAPP(hAPP(c_COMBB(_1674824, tc_fun(_1674826, tc_prod(_1674824, _1674826)), _1674828), c_Product__Type_OPair(_1674824, _1674826)), _1674830))), _1674836))), hAPP(hAPP(c_List_Ozip(_1674828, _1674834), _1674832), _1674838)))], (44698 ^ _780086) ^ [_1674995, _1674997] : [-(hAPP(hAPP(c_List_Ozip(_1674995, _1674995), _1674997), _1674997) = hAPP(hAPP(c_List_Omap(_1674995, tc_prod(_1674995, _1674995)), hAPP(hAPP(c_COMBS(_1674995, _1674995, tc_prod(_1674995, _1674995)), c_Product__Type_OPair(_1674995, _1674995)), c_COMBI(_1674995))), _1674997))], (44700 ^ _780086) ^ [_1675080, _1675082, _1675084, _1675086] : [hAPP(hAPP(c_List_Omap(_1675080, _1675082), _1675084), _1675086) = c_List_Olist_ONil(_1675082), -(_1675086 = c_List_Olist_ONil(_1675080))], (44706 ^ _780086) ^ [_1675183, _1675185, _1675187, _1675189] : [_1675189 = c_List_Olist_ONil(_1675183), -(hAPP(hAPP(c_List_Omap(_1675183, _1675185), _1675187), _1675189) = c_List_Olist_ONil(_1675185))], (44712 ^ _780086) ^ [_1675292, _1675294, _1675296] : [-(hAPP(hAPP(c_List_Omap(_1675292, _1675294), _1675296), c_List_Olist_ONil(_1675292)) = c_List_Olist_ONil(_1675294))], (44714 ^ _780086) ^ [_1675353, _1675355, _1675357, _1675359] : [c_List_Olist_ONil(_1675353) = hAPP(hAPP(c_List_Omap(_1675355, _1675353), _1675357), _1675359), -(_1675359 = c_List_Olist_ONil(_1675355))], (44720 ^ _780086) ^ [_1675456, _1675458, _1675460, _1675462] : [_1675462 = c_List_Olist_ONil(_1675458), -(c_List_Olist_ONil(_1675456) = hAPP(hAPP(c_List_Omap(_1675458, _1675456), _1675460), _1675462))], (44726 ^ _780086) ^ [_1675565, _1675567, _1675569, _1675571, _1675573, _1675575] : [-(hAPP(hAPP(c_List_Omap(_1675565, _1675567), _1675569), hAPP(hAPP(c_List_Olist__update(_1675565, _1675571), _1675573), _1675575)) = hAPP(hAPP(c_List_Olist__update(_1675567, hAPP(hAPP(c_List_Omap(_1675565, _1675567), _1675569), _1675571)), _1675573), hAPP(_1675569, _1675575)))], (44738 ^ _780086) ^ [_1675905, _1675907, _1675909, _1675911, _1675913] : [44740 ^ _780086 : [(44741 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1675905), 44739 ^ [_1675905, _1675907, _1675909, _1675911, _1675913]), hAPP(c_List_Oset(_1675905), _1675911))))], (44743 ^ _780086) ^ [] : [hAPP(_1675909, 44739 ^ [_1675905, _1675907, _1675909, _1675911, _1675913]) = hAPP(_1675913, 44739 ^ [_1675905, _1675907, _1675909, _1675911, _1675913])]], -(hAPP(hAPP(c_List_Omap(_1675905, _1675907), _1675909), _1675911) = hAPP(hAPP(c_List_Omap(_1675905, _1675907), _1675913), _1675911))], (44728 ^ _780086) ^ [_1675661, _1675663, _1675665, _1675667, _1675669] : [hAPP(hAPP(c_List_Omap(_1675661, _1675663), _1675665), _1675667) = hAPP(hAPP(c_List_Omap(_1675661, _1675663), _1675669), _1675667), 44731 ^ _780086 : [(44732 ^ _780086) ^ [_1675784] : [hBOOL(hAPP(hAPP(c_member(_1675661), _1675784), hAPP(c_List_Oset(_1675661), _1675667))), -(hAPP(_1675665, _1675784) = hAPP(_1675669, _1675784))]]], (44747 ^ _780086) ^ [_1676162, _1676164, _1676166, _1676168, _1676170, _1676172, _1676174] : [hAPP(hAPP(c_List_Omap(_1676162, _1676164), _1676166), _1676168) = hAPP(hAPP(c_List_Omap(_1676170, _1676164), _1676172), _1676174), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676162)), _1676168) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676170)), _1676174))], (44753 ^ _780086) ^ [_1676313, _1676315, _1676317, _1676319] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676313)), hAPP(hAPP(c_List_Omap(_1676315, _1676313), _1676317), _1676319)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676315)), _1676319))], (44755 ^ _780086) ^ [_1676365, _1676367, _1676369, _1676371, _1676373] : [class_Groups_Ocomm__monoid__add(_1676365), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1676365), hAPP(hAPP(c_List_Omap(_1676367, _1676365), hAPP(hAPP(c_COMBS(_1676367, _1676365, _1676365), hAPP(hAPP(c_COMBB(_1676365, tc_fun(_1676365, _1676365), _1676367), c_Groups_Oplus__class_Oplus(_1676365)), _1676369)), _1676371)), _1676373)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1676365), hAPP(c_List_Omonoid__add__class_Olistsum(_1676365), hAPP(hAPP(c_List_Omap(_1676367, _1676365), _1676369), _1676373))), hAPP(c_List_Omonoid__add__class_Olistsum(_1676365), hAPP(hAPP(c_List_Omap(_1676367, _1676365), _1676371), _1676373))))], (44761 ^ _780086) ^ [_1676596, _1676598, _1676600, _1676602, _1676604] : [class_Groups_Oab__group__add(_1676596), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1676596), hAPP(hAPP(c_List_Omap(_1676598, _1676596), hAPP(hAPP(c_COMBS(_1676598, _1676596, _1676596), hAPP(hAPP(c_COMBB(_1676596, tc_fun(_1676596, _1676596), _1676598), c_Groups_Ominus__class_Ominus(_1676596)), _1676600)), _1676602)), _1676604)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1676596), hAPP(c_List_Omonoid__add__class_Olistsum(_1676596), hAPP(hAPP(c_List_Omap(_1676598, _1676596), _1676600), _1676604))), hAPP(c_List_Omonoid__add__class_Olistsum(_1676596), hAPP(hAPP(c_List_Omap(_1676598, _1676596), _1676602), _1676604))))], (44767 ^ _780086) ^ [_1676827, _1676829, _1676831] : [class_Groups_Omonoid__add(_1676827), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1676827), hAPP(hAPP(c_List_Omap(_1676829, _1676827), hAPP(c_COMBK(_1676827, _1676829), c_Groups_Ozero__class_Ozero(_1676827))), _1676831)) = c_Groups_Ozero__class_Ozero(_1676827))], (44773 ^ _780086) ^ [_1676952, _1676954, _1676956, _1676958, _1676960] : [class_Rings_Osemiring__0(_1676952), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1676952), hAPP(hAPP(c_List_Omap(_1676954, _1676952), hAPP(hAPP(c_COMBB(_1676952, _1676952, _1676954), hAPP(c_Groups_Otimes__class_Otimes(_1676952), _1676956)), _1676958)), _1676960)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1676952), _1676956), hAPP(c_List_Omonoid__add__class_Olistsum(_1676952), hAPP(hAPP(c_List_Omap(_1676954, _1676952), _1676958), _1676960))))], (44779 ^ _780086) ^ [_1677135, _1677137, _1677139, _1677141, _1677143] : [class_Rings_Osemiring__0(_1677135), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1677135), hAPP(hAPP(c_List_Omap(_1677137, _1677135), hAPP(hAPP(c_COMBC(_1677137, _1677135, _1677135), hAPP(hAPP(c_COMBB(_1677135, tc_fun(_1677135, _1677135), _1677137), c_Groups_Otimes__class_Otimes(_1677135)), _1677139)), _1677141)), _1677143)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1677135), hAPP(c_List_Omonoid__add__class_Olistsum(_1677135), hAPP(hAPP(c_List_Omap(_1677137, _1677135), _1677139), _1677143))), _1677141))], (44785 ^ _780086) ^ [_1677338, _1677340, _1677342, _1677344, _1677346] : [c_Fun_Oinj__on(_1677338, _1677340, _1677342, c_Orderings_Otop__class_Otop(tc_fun(_1677338, tc_HOL_Obool))), 44788 ^ _780086 : [(44789 ^ _780086) ^ [] : [hAPP(hAPP(c_List_Omap(_1677338, _1677340), _1677342), _1677344) = hAPP(hAPP(c_List_Omap(_1677338, _1677340), _1677342), _1677346), -(_1677344 = _1677346)], (44795 ^ _780086) ^ [] : [_1677344 = _1677346, -(hAPP(hAPP(c_List_Omap(_1677338, _1677340), _1677342), _1677344) = hAPP(hAPP(c_List_Omap(_1677338, _1677340), _1677342), _1677346))]]], (44801 ^ _780086) ^ [_1677631, _1677633, _1677635, _1677637, _1677639] : [hAPP(hAPP(c_List_Omap(_1677631, _1677633), _1677635), _1677637) = hAPP(hAPP(c_List_Omap(_1677631, _1677633), _1677635), _1677639), c_Fun_Oinj__on(_1677631, _1677633, _1677635, c_Orderings_Otop__class_Otop(tc_fun(_1677631, tc_HOL_Obool))), -(_1677637 = _1677639)], (44811 ^ _780086) ^ [_1677822, _1677824] : [-(hAPP(hAPP(c_List_Omap(_1677822, _1677822), c_COMBI(_1677822)), _1677824) = _1677824)], (44813 ^ _780086) ^ [_1677858, _1677860, _1677862, _1677864, _1677866] : [-(hAPP(hAPP(c_List_Otake(_1677858), _1677860), hAPP(hAPP(c_List_Omap(_1677862, _1677858), _1677864), _1677866)) = hAPP(hAPP(c_List_Omap(_1677862, _1677858), _1677864), hAPP(hAPP(c_List_Otake(_1677862), _1677860), _1677866)))], (44815 ^ _780086) ^ [_1677923, _1677925, _1677927, _1677929] : [-(hAPP(hAPP(c_List_Omap(_1677923, _1677925), _1677927), c_List_Obutlast(_1677923, _1677929)) = c_List_Obutlast(_1677925, hAPP(hAPP(c_List_Omap(_1677923, _1677925), _1677927), _1677929)))], (44817 ^ _780086) ^ [_1677976, _1677978, _1677980, _1677982] : [-(hAPP(c_List_Oset(_1677976), hAPP(hAPP(c_List_Omap(_1677978, _1677976), _1677980), _1677982)) = hAPP(c_Set_Oimage(_1677978, _1677976, _1677980), hAPP(c_List_Oset(_1677978), _1677982)))], (44819 ^ _780086) ^ [_1678031, _1678033, _1678035, _1678037, _1678039] : [-(hAPP(hAPP(c_List_Omap(_1678031, _1678033), _1678035), hAPP(hAPP(c_List_Olist_OCons(_1678031), _1678037), _1678039)) = hAPP(hAPP(c_List_Olist_OCons(_1678033), hAPP(_1678035, _1678037)), hAPP(hAPP(c_List_Omap(_1678031, _1678033), _1678035), _1678039)))], (44821 ^ _780086) ^ [_1678099, _1678101, _1678103, _1678105, _1678107] : [-(hAPP(hAPP(c_List_Omap(_1678099, _1678101), _1678103), hAPP(hAPP(c_List_Oappend(_1678099), _1678105), _1678107)) = hAPP(hAPP(c_List_Oappend(_1678101), hAPP(hAPP(c_List_Omap(_1678099, _1678101), _1678103), _1678105)), hAPP(hAPP(c_List_Omap(_1678099, _1678101), _1678103), _1678107)))], (44823 ^ _780086) ^ [_1678169, _1678171, _1678173, _1678175] : [-(_1678169 = c_List_Olist_ONil(_1678171)), -(hAPP(c_List_Ohd(_1678173), hAPP(hAPP(c_List_Omap(_1678171, _1678173), _1678175), _1678169)) = hAPP(_1678175, hAPP(c_List_Ohd(_1678171), _1678169)))], (44829 ^ _780086) ^ [_1678233, _1678235, _1678237, _1678239, _1678241] : [-(hAPP(hAPP(c_List_Odrop(_1678233), _1678235), hAPP(hAPP(c_List_Omap(_1678237, _1678233), _1678239), _1678241)) = hAPP(hAPP(c_List_Omap(_1678237, _1678233), _1678239), hAPP(hAPP(c_List_Odrop(_1678237), _1678235), _1678241)))], (44831 ^ _780086) ^ [_1678298, _1678300, _1678302, _1678304, _1678306] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1678298), tc_List_Olist(_1678300), tc_List_Olist(_1678302), hAPP(c_List_Omap(_1678298, _1678300), _1678304)), hAPP(c_List_Omap(_1678302, _1678298), _1678306)) = hAPP(c_List_Omap(_1678302, _1678300), hAPP(c_Fun_Ocomp(_1678298, _1678300, _1678302, _1678304), _1678306)))], (44833 ^ _780086) ^ [_1678369, _1678371, _1678373, _1678375, _1678377] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1678369), tc_List_Olist(_1678371), tc_List_Olist(_1678373), hAPP(c_List_Omap(_1678369, _1678371), _1678375)), hAPP(c_List_Omap(_1678373, _1678369), _1678377)) = hAPP(c_List_Omap(_1678373, _1678371), hAPP(c_Fun_Ocomp(_1678369, _1678371, _1678373, _1678375), _1678377)))], (44835 ^ _780086) ^ [_1678440, _1678442, _1678444, _1678446, _1678448, _1678450] : [-(hAPP(hAPP(c_List_Omap(_1678440, _1678442), _1678444), hAPP(hAPP(c_List_Omap(_1678446, _1678440), _1678448), _1678450)) = hAPP(hAPP(c_List_Omap(_1678446, _1678442), hAPP(c_Fun_Ocomp(_1678440, _1678442, _1678446, _1678444), _1678448)), _1678450))], (44837 ^ _780086) ^ [_1678508, _1678510, _1678512, _1678514, _1678516, _1678518] : [-(hAPP(hAPP(c_List_Omap(_1678508, _1678510), _1678512), hAPP(hAPP(c_List_Omap(_1678514, _1678508), _1678516), _1678518)) = hAPP(hAPP(c_List_Omap(_1678514, _1678510), hAPP(c_Fun_Ocomp(_1678508, _1678510, _1678514, _1678512), _1678516)), _1678518))], (44839 ^ _780086) ^ [_1678576] : [-(hAPP(c_List_Omap(_1678576, _1678576), c_COMBI(_1678576)) = c_Fun_Oid(tc_List_Olist(_1678576)))], (44841 ^ _780086) ^ [_1678611] : [-(hAPP(c_List_Omap(_1678611, _1678611), c_Fun_Oid(_1678611)) = c_Fun_Oid(tc_List_Olist(_1678611)))], (44843 ^ _780086) ^ [_1678646, _1678648, _1678650, _1678652, _1678654] : [-(c_List_Olist_Olist__size(_1678646, _1678648, hAPP(hAPP(c_List_Omap(_1678650, _1678646), _1678652), _1678654)) = c_List_Olist_Olist__size(_1678650, hAPP(c_Fun_Ocomp(_1678646, tc_Nat_Onat, _1678650, _1678648), _1678652), _1678654))], (44845 ^ _780086) ^ [_1678702, _1678704, _1678706, _1678708, _1678710] : [c_Fun_Oinj__on(_1678702, _1678704, _1678706, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1678702, tc_HOL_Obool)), hAPP(c_List_Oset(_1678702), _1678708)), hAPP(c_List_Oset(_1678702), _1678710))), 44848 ^ _780086 : [(44849 ^ _780086) ^ [] : [hAPP(hAPP(c_List_Omap(_1678702, _1678704), _1678706), _1678708) = hAPP(hAPP(c_List_Omap(_1678702, _1678704), _1678706), _1678710), -(_1678708 = _1678710)], (44855 ^ _780086) ^ [] : [_1678708 = _1678710, -(hAPP(hAPP(c_List_Omap(_1678702, _1678704), _1678706), _1678708) = hAPP(hAPP(c_List_Omap(_1678702, _1678704), _1678706), _1678710))]]], (44861 ^ _780086) ^ [_1679027, _1679029, _1679031, _1679033, _1679035] : [hAPP(hAPP(c_List_Omap(_1679027, _1679029), _1679031), _1679033) = hAPP(hAPP(c_List_Omap(_1679027, _1679029), _1679031), _1679035), c_Fun_Oinj__on(_1679027, _1679029, _1679031, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1679027, tc_HOL_Obool)), hAPP(c_List_Oset(_1679027), _1679033)), hAPP(c_List_Oset(_1679027), _1679035))), -(_1679033 = _1679035)], (44871 ^ _780086) ^ [_1679250, _1679252, _1679254, _1679256, _1679258] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1679250), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1679252)), _1679254))), -(hAPP(hAPP(c_List_Onth(_1679256), hAPP(hAPP(c_List_Omap(_1679252, _1679256), _1679258), _1679254)), _1679250) = hAPP(_1679258, hAPP(hAPP(c_List_Onth(_1679252), _1679254), _1679250)))], (44877 ^ _780086) ^ [_1679409, _1679411, _1679413, _1679415, _1679417, _1679419] : [-(hBOOL(hAPP(hAPP(c_member(_1679409), _1679411), hAPP(c_List_Oset(_1679409), _1679413)))), -(hAPP(hAPP(c_List_Omap(_1679409, _1679415), c_Fun_Ofun__upd(_1679409, _1679415, _1679417, _1679411, _1679419)), _1679413) = hAPP(hAPP(c_List_Omap(_1679409, _1679415), _1679417), _1679413))], (44883 ^ _780086) ^ [_1679510, _1679512, _1679514, _1679516] : [hBOOL(hAPP(c_List_Odistinct(_1679510), hAPP(hAPP(c_List_Omap(_1679512, _1679510), _1679514), _1679516))), 44886 ^ _780086 : [(44887 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1679512), _1679516)))], (44889 ^ _780086) ^ [] : [-(c_Fun_Oinj__on(_1679512, _1679510, _1679514, hAPP(c_List_Oset(_1679512), _1679516)))]]], (44891 ^ _780086) ^ [_1679661, _1679663, _1679665, _1679667] : [-(hBOOL(hAPP(c_List_Odistinct(_1679661), hAPP(hAPP(c_List_Omap(_1679663, _1679661), _1679665), _1679667)))), hBOOL(hAPP(c_List_Odistinct(_1679663), _1679667)), c_Fun_Oinj__on(_1679663, _1679661, _1679665, hAPP(c_List_Oset(_1679663), _1679667))], (44901 ^ _780086) ^ [_1679848, _1679850] : [class_Groups_Oordered__ab__group__add__abs(_1679848), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1679848), hAPP(c_Groups_Oabs__class_Oabs(_1679848), hAPP(c_List_Omonoid__add__class_Olistsum(_1679848), _1679850))), hAPP(c_List_Omonoid__add__class_Olistsum(_1679848), hAPP(hAPP(c_List_Omap(_1679848, _1679848), c_Groups_Oabs__class_Oabs(_1679848)), _1679850)))))], (44907 ^ _780086) ^ [_1679989, _1679991, _1679993, _1679995] : [class_Groups_Oab__group__add(_1679989), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1679989), hAPP(c_List_Omonoid__add__class_Olistsum(_1679989), hAPP(hAPP(c_List_Omap(_1679991, _1679989), _1679993), _1679995))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1679989), hAPP(hAPP(c_List_Omap(_1679991, _1679989), hAPP(c_Fun_Ocomp(_1679989, _1679989, _1679991, c_Groups_Ouminus__class_Ouminus(_1679989)), _1679993)), _1679995)))], (44913 ^ _780086) ^ [_1680154, _1680156, _1680158, _1680160] : [c_Fun_Oinj__on(_1680154, _1680156, _1680158, c_Complete__Lattice_OSup__class_OSup(tc_fun(_1680154, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_List_Olist(_1680154), tc_fun(_1680154, tc_HOL_Obool), c_List_Oset(_1680154)), _1680160))), -(c_Fun_Oinj__on(tc_List_Olist(_1680154), tc_List_Olist(_1680156), hAPP(c_List_Omap(_1680154, _1680156), _1680158), _1680160))], (44919 ^ _780086) ^ [_1680303, _1680305, _1680307] : [c_Fun_Oinj__on(tc_List_Olist(_1680303), tc_List_Olist(_1680305), hAPP(c_List_Omap(_1680303, _1680305), _1680307), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1680303), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1680303, _1680305, _1680307, c_Orderings_Otop__class_Otop(tc_fun(_1680303, tc_HOL_Obool))))], (44925 ^ _780086) ^ [_1680452, _1680454, _1680456] : [c_Fun_Oinj__on(tc_List_Olist(_1680452), tc_List_Olist(_1680454), hAPP(c_List_Omap(_1680452, _1680454), _1680456), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1680452), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1680452, _1680454, _1680456, c_Orderings_Otop__class_Otop(tc_fun(_1680452, tc_HOL_Obool))))], (44931 ^ _780086) ^ [_1680579, _1680581, _1680583] : [c_Fun_Oinj__on(_1680579, _1680581, _1680583, c_Orderings_Otop__class_Otop(tc_fun(_1680579, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1680579), tc_List_Olist(_1680581), hAPP(c_List_Omap(_1680579, _1680581), _1680583), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1680579), tc_HOL_Obool))))], (44937 ^ _780086) ^ [_1680712, _1680714, _1680716, _1680718] : [class_Groups_Ocomm__monoid__add(_1680712), hBOOL(hAPP(c_List_Odistinct(_1680714), _1680716)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1680712), hAPP(hAPP(c_List_Omap(_1680714, _1680712), _1680718), _1680716)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1680714, _1680712), _1680718), hAPP(c_List_Oset(_1680714), _1680716)))], (44947 ^ _780086) ^ [_1680911, _1680913, _1680915, _1680917] : [class_Rings_Osemiring__1(_1680911), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1680911), hAPP(hAPP(c_List_Omap(_1680913, _1680911), hAPP(c_COMBK(_1680911, _1680913), _1680915)), _1680917)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1680911), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1680911), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1680913)), _1680917))), _1680915))], (44953 ^ _780086) ^ [_1681070, _1681072, _1681074, _1681076, _1681078] : [class_Groups_Ocomm__monoid__add(_1681070), hBOOL(hAPP(hAPP(c_member(_1681072), _1681074), hAPP(c_List_Oset(_1681072), _1681076))), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1681070), hAPP(hAPP(c_List_Omap(_1681072, _1681070), _1681078), _1681076)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1681070), hAPP(_1681078, _1681074)), hAPP(c_List_Omonoid__add__class_Olistsum(_1681070), hAPP(hAPP(c_List_Omap(_1681072, _1681070), _1681078), c_List_Oremove1(_1681072, _1681074, _1681076)))))], (44963 ^ _780086) ^ [_1681319, _1681321, _1681323, _1681325] : [class_Groups_Ocomm__monoid__add(_1681319), 44966 ^ _780086 : [(44967 ^ _780086) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1681321), _1681323)), -(c_Nitpick_Osetsum_H(_1681321, _1681319, _1681325, _1681323) = hAPP(c_List_Omonoid__add__class_Olistsum(_1681319), hAPP(hAPP(c_List_Omap(_1681321, _1681319), _1681325), c_Hilbert__Choice_OEps(tc_List_Olist(_1681321), hAPP(hAPP(c_COMBS(tc_List_Olist(_1681321), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1681321)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1681321), tc_fun(_1681321, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1681321, tc_HOL_Obool), tc_fun(tc_fun(_1681321, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1681321)), c_fequal), c_List_Oset(_1681321))), _1681323))), c_List_Odistinct(_1681321))))))], (44973 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1681321), _1681323))), -(c_Nitpick_Osetsum_H(_1681321, _1681319, _1681325, _1681323) = c_Groups_Ozero__class_Ozero(_1681319))]]], (44979 ^ _780086) ^ [_1681707, _1681709, _1681711] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1681707), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681709)), _1681711))), -(hAPP(c_Random_Opick(_1681709, hAPP(hAPP(c_List_Omap(_1681709, tc_prod(tc_Code__Numeral_Ocode__numeral, _1681709)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1681709), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1681711)), hAPP(c_Code__Numeral_Oof__nat, _1681707)) = hAPP(hAPP(c_List_Onth(_1681709), _1681711), _1681707))], (44985 ^ _780086) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (44987 ^ _780086) ^ [_1681898, _1681900] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1681898)), hAPP(c_Code__Numeral_Oof__nat, _1681900)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1681898), _1681900)))], (44989 ^ _780086) ^ [_1681959, _1681961] : [hAPP(c_Code__Numeral_Oof__nat, _1681959) = hAPP(c_Code__Numeral_Oof__nat, _1681961), -(_1681959 = _1681961)], (44995 ^ _780086) ^ [_1682044, _1682046] : [_1682044 = _1682046, -(hAPP(c_Code__Numeral_Oof__nat, _1682044) = hAPP(c_Code__Numeral_Oof__nat, _1682046))], (45001 ^ _780086) ^ [] : [-(c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral))], (45003 ^ _780086) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (45005 ^ _780086) ^ [_1682186, _1682188] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1682186)), hAPP(c_Code__Numeral_Oof__nat, _1682188))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1682186), _1682188)))], (45011 ^ _780086) ^ [_1682291, _1682293] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1682291), _1682293)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1682291)), hAPP(c_Code__Numeral_Oof__nat, _1682293))))], (45017 ^ _780086) ^ [_1682402, _1682404] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1682402), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1682404), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), 45024 ^ _780086 : [(45025 ^ _780086) ^ [] : [hAPP(c_Code__Numeral_Oof__nat, _1682402) = hAPP(c_Code__Numeral_Oof__nat, _1682404), -(_1682402 = _1682404)], (45031 ^ _780086) ^ [] : [_1682402 = _1682404, -(hAPP(c_Code__Numeral_Oof__nat, _1682402) = hAPP(c_Code__Numeral_Oof__nat, _1682404))]]], (45037 ^ _780086) ^ [_1682699, _1682701, _1682703, _1682705] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682699)), _1682701) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682703)), _1682705), -(hAPP(hAPP(c_List_Omap(tc_prod(_1682699, _1682703), _1682699), c_Product__Type_Ofst(_1682699, _1682703)), hAPP(hAPP(c_List_Ozip(_1682699, _1682703), _1682701), _1682705)) = _1682701)], (45043 ^ _780086) ^ [_1682856, _1682858, _1682860, _1682862] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682856)), _1682858) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682860)), _1682862), -(hAPP(hAPP(c_List_Omap(tc_prod(_1682856, _1682860), _1682860), c_Product__Type_Osnd(_1682856, _1682860)), hAPP(hAPP(c_List_Ozip(_1682856, _1682860), _1682858), _1682862)) = _1682862)], (45049 ^ _780086) ^ [] : [-(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Code__Numeral_Ocode__numeral, tc_Int_Oint, c_Code__Numeral_Oof__nat), c_Int_Onat))], (45051 ^ _780086) ^ [_1683031, _1683033, _1683035] : [-(hAPP(hAPP(c_List_Ozip(_1683031, _1683033), hAPP(hAPP(c_List_Omap(tc_prod(_1683031, _1683033), _1683031), c_Product__Type_Ofst(_1683031, _1683033)), _1683035)), hAPP(hAPP(c_List_Omap(tc_prod(_1683031, _1683033), _1683033), c_Product__Type_Osnd(_1683031, _1683033)), _1683035)) = _1683035)], (45053 ^ _780086) ^ [_1683097, _1683099] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1683097)), hAPP(c_Code__Numeral_Oof__nat, _1683099)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1683097), _1683099)))], (45055 ^ _780086) ^ [_1683158, _1683160] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1683158)), hAPP(c_Code__Numeral_Oof__nat, _1683160))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1683158), _1683160)))], (45061 ^ _780086) ^ [_1683263, _1683265] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1683263), _1683265)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1683263)), hAPP(c_Code__Numeral_Oof__nat, _1683265))))], (45067 ^ _780086) ^ [_1683374, _1683376, _1683378] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1683374), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1683376), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1683376)), _1683378)))), -(hBOOL(hAPP(hAPP(c_member(_1683376), hAPP(c_Random_Opick(_1683376, _1683378), _1683374)), hAPP(c_List_Oset(_1683376), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1683376), _1683376), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1683376)), _1683378)))))], (45073 ^ _780086) ^ [_1683565, _1683567, _1683569, _1683571, _1683573] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683565)), _1683567) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683569)), _1683571), 45076 ^ _780086 : [(45077 ^ _780086) ^ [] : [hAPP(hAPP(c_List_Ozip(_1683565, _1683569), _1683567), _1683571) = _1683573, 45080 ^ _780086 : [(45081 ^ _780086) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1683565, _1683569), _1683565), c_Product__Type_Ofst(_1683565, _1683569)), _1683573) = _1683567)], (45083 ^ _780086) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1683565, _1683569), _1683569), c_Product__Type_Osnd(_1683565, _1683569)), _1683573) = _1683571)]]], (45085 ^ _780086) ^ [] : [-(hAPP(hAPP(c_List_Ozip(_1683565, _1683569), _1683567), _1683571) = _1683573), hAPP(hAPP(c_List_Omap(tc_prod(_1683565, _1683569), _1683565), c_Product__Type_Ofst(_1683565, _1683569)), _1683573) = _1683567, hAPP(hAPP(c_List_Omap(tc_prod(_1683565, _1683569), _1683569), c_Product__Type_Osnd(_1683565, _1683569)), _1683573) = _1683571]]], (45095 ^ _780086) ^ [_1684013, _1684015, _1684017] : [-(c_List_Olist_Olist__size(_1684013, _1684015, _1684017) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(_1684013, tc_Nat_Onat), _1684015), _1684017))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684013)), _1684017)))], (45097 ^ _780086) ^ [_1684075] : [-(_1684075 = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1684075)))], (45103 ^ _780086) ^ [_1684107] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1684107)), _1684107 = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (45109 ^ _780086) ^ [_1684189, _1684191, _1684193, _1684195] : [class_Groups_Ocomm__monoid__add(_1684189), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1684189), _1684191), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1684193, _1684195))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1684189), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1684189), _1684191), c_List_Oupto(_1684193, _1684195))))], (45115 ^ _780086) ^ [_1684332, _1684334, _1684336, _1684338] : [class_Groups_Ocomm__monoid__add(_1684332), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1684332), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1684332), _1684334), c_List_Oupto(_1684336, _1684338))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1684332), _1684334), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1684336, _1684338))))], (45121 ^ _780086) ^ [_1684475, _1684477, _1684479] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1684475), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1684475)), _1684477)))), -(hBOOL(hAPP(hAPP(c_member(_1684475), hAPP(c_Product__Type_Ofst(_1684475, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect__weight(_1684475, _1684477), _1684479))), hAPP(c_List_Oset(_1684475), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1684475), _1684475), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1684475)), _1684477)))))], (45127 ^ _780086) ^ [_1684672, _1684674] : [-(c_Random_Oselect__weight(_1684672, _1684674) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1684672, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random_Orange(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1684672), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1684672)), _1684674)))), hAPP(hAPP(c_COMBB(_1684672, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1684672, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1684672, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random_Opick(_1684672, _1684674))))], (45129 ^ _780086) ^ [_1684756, _1684758] : [-(c_Random_Oselect(_1684756, _1684758) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1684756, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random_Orange(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684756)), _1684758)))), hAPP(hAPP(c_COMBB(_1684756, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1684756, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1684756, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1684756, tc_Code__Numeral_Ocode__numeral), hAPP(c_List_Onth(_1684756), _1684758)), c_Code__Numeral_Onat__of))))], (45131 ^ _780086) ^ [_1684844, _1684846] : [-(hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, hAPP(c_Code__Numeral_Oof__nat, _1684844)), hAPP(c_Code__Numeral_Oof__nat, _1684846)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1684844), _1684846)))], (45133 ^ _780086) ^ [_1684890, _1684892] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), _1684890), _1684892) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1684890)), hAPP(c_Code__Numeral_Onat__of, _1684892))))], (45135 ^ _780086) ^ [_1684936] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1684936)) = _1684936)], (45137 ^ _780086) ^ [_1684965] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1684965)) = _1684965)], (45139 ^ _780086) ^ [_1684994] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Code__Numeral_Oof__nat, _1684994)) = _1684994)], (45141 ^ _780086) ^ [_1685038, _1685040] : [hAPP(c_Code__Numeral_Onat__of, _1685038) = hAPP(c_Code__Numeral_Onat__of, _1685040), -(_1685038 = _1685040)], (45147 ^ _780086) ^ [_1685123, _1685125] : [_1685123 = _1685125, -(hAPP(c_Code__Numeral_Onat__of, _1685123) = hAPP(c_Code__Numeral_Onat__of, _1685125))], (45153 ^ _780086) ^ [_1685229, _1685231] : [hAPP(c_Code__Numeral_Onat__of, _1685229) = hAPP(c_Code__Numeral_Onat__of, _1685231), -(_1685229 = _1685231)], (45159 ^ _780086) ^ [_1685314, _1685316] : [_1685314 = _1685316, -(hAPP(c_Code__Numeral_Onat__of, _1685314) = hAPP(c_Code__Numeral_Onat__of, _1685316))], (45165 ^ _780086) ^ [] : [-(c_Typedef_Otype__definition(tc_Code__Numeral_Ocode__numeral, tc_Nat_Onat, c_Code__Numeral_Onat__of, c_Code__Numeral_Oof__nat, c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (45167 ^ _780086) ^ [_1685438, _1685440] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1685438), _1685440)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1685438)), hAPP(c_Code__Numeral_Onat__of, _1685440))))], (45173 ^ _780086) ^ [_1685543, _1685545] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1685543)), hAPP(c_Code__Numeral_Onat__of, _1685545))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1685543), _1685545)))], (45179 ^ _780086) ^ [_1685654] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1685654)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (45181 ^ _780086) ^ [_1685685] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), _1685685)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1685685))], (45183 ^ _780086) ^ [] : [-(c_Code__Numeral_Oint__of = hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Int_Oint, tc_Code__Numeral_Ocode__numeral, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), c_Code__Numeral_Onat__of))], (45185 ^ _780086) ^ [_1685750, _1685752] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1685750), _1685752)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1685750)), hAPP(c_Code__Numeral_Onat__of, _1685752))))], (45191 ^ _780086) ^ [_1685855, _1685857] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1685855)), hAPP(c_Code__Numeral_Onat__of, _1685857))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1685855), _1685857)))], (45197 ^ _780086) ^ [_1685966] : [-(hAPP(c_Code__Numeral_Onat__of, _1685966) = c_Code__Numeral_Onat__of__aux(_1685966, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (45199 ^ _780086) ^ [_1685995, _1685997] : [-(c_Code__Numeral_Onat__of__aux(_1685995, _1685997) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1685995)), _1685997))], (45201 ^ _780086) ^ [_1686032] : [-(c_Code__Numeral_OSuc__code__numeral(_1686032) = hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Nat_OSuc, hAPP(c_Code__Numeral_Onat__of, _1686032))))], (45203 ^ _780086) ^ [_1686066, _1686068] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1686066), _1686068) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1686066)), hAPP(c_Code__Numeral_Onat__of, _1686068))))], (45205 ^ _780086) ^ [_1686112] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1686112), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), -(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Code__Numeral_Oof__nat, _1686112)) = _1686112)], (45211 ^ _780086) ^ [_1686209, _1686211] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1686209), _1686211) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1686209)), hAPP(c_Code__Numeral_Onat__of, _1686211))))], (45213 ^ _780086) ^ [_1686255, _1686257] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1686255), _1686257) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1686255)), hAPP(c_Code__Numeral_Onat__of, _1686257))))], (45215 ^ _780086) ^ [] : [-(c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral))], (45217 ^ _780086) ^ [_1686319, _1686321] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1686319), _1686321) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, _1686319), _1686321))], (45219 ^ _780086) ^ [_1686356, _1686358] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1686356, _1686358) = hAPP(c_Code__Numeral_Oof__nat, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Code__Numeral_Onat__of, _1686356), hAPP(c_Code__Numeral_Onat__of, _1686358))))], (45221 ^ _780086) ^ [_1686394] : [-(_1686394 = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1686394)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_Code__Numeral_Onat__of, _1686394))))], (45227 ^ _780086) ^ [_1686445, _1686447, _1686449, _1686451, _1686453] : [class_Groups_Omonoid__add(_1686445), class_Groups_Oordered__ab__semigroup__add(_1686445), 45237 ^ _780086 : [(45238 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1686447), 45236 ^ [_1686445, _1686447, _1686449, _1686451, _1686453]), hAPP(c_List_Oset(_1686447), _1686449))))], (45240 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1686445), hAPP(_1686451, 45236 ^ [_1686445, _1686447, _1686449, _1686451, _1686453])), hAPP(_1686453, 45236 ^ [_1686445, _1686447, _1686449, _1686451, _1686453])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1686445), hAPP(c_List_Omonoid__add__class_Olistsum(_1686445), hAPP(hAPP(c_List_Omap(_1686447, _1686445), _1686451), _1686449))), hAPP(c_List_Omonoid__add__class_Olistsum(_1686445), hAPP(hAPP(c_List_Omap(_1686447, _1686445), _1686453), _1686449)))))], (45244 ^ _780086) ^ [_1686869, _1686871] : [-(hAPP(c_New__DSequence_Opos__not__seq(_1686869), _1686871) = c_Lazy__Sequence_Ohb__not__seq(hAPP(_1686869, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))), _1686871))))], (45246 ^ _780086) ^ [_1686907, _1686909, _1686911, _1686913, _1686915] : [c_List_Opartition(_1686907, _1686909, _1686911) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1686907), tc_List_Olist(_1686907)), _1686913), _1686915), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1686907, tc_HOL_Obool)), hAPP(c_List_Oset(_1686907), _1686913)), hAPP(c_List_Oset(_1686907), _1686915)) = hAPP(c_List_Oset(_1686907), _1686911))], (45252 ^ _780086) ^ [_1687076, _1687078, _1687080, _1687082] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1687076)), _1687078), c_List_Olists(_1687076, _1687080))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1687076)), _1687078), c_List_Olists(_1687076, _1687082))), -(hBOOL(hAPP(c_List_Olistsp(_1687076, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1687076, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1687076, tc_fun(_1687076, tc_HOL_Obool), tc_HOL_Obool), c_member(_1687076)), _1687080)), hAPP(hAPP(c_COMBC(_1687076, tc_fun(_1687076, tc_HOL_Obool), tc_HOL_Obool), c_member(_1687076)), _1687082))), _1687078)))], (45262 ^ _780086) ^ [_1687353, _1687355] : [-(hBOOL(hAPP(c_List_Olistsp(_1687353, _1687355), c_List_Olist_ONil(_1687353))))], (45264 ^ _780086) ^ [_1687385, _1687387] : [-(hBOOL(hAPP(c_List_Olistsp(_1687385, _1687387), c_List_Olist_ONil(_1687385))))], (45276 ^ _780086) ^ [_1687633, _1687635, _1687637] : [45278 ^ _780086 : [(45279 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1687633), 45277 ^ [_1687633, _1687635, _1687637]), hAPP(c_List_Oset(_1687633), _1687637))))], (45281 ^ _780086) ^ [] : [hBOOL(hAPP(_1687635, 45277 ^ [_1687633, _1687635, _1687637]))]], -(hBOOL(hAPP(c_List_Olistsp(_1687633, _1687635), _1687637)))], (45266 ^ _780086) ^ [_1687435, _1687437, _1687439] : [hBOOL(hAPP(c_List_Olistsp(_1687435, _1687437), _1687439)), 45269 ^ _780086 : [(45270 ^ _780086) ^ [_1687524] : [hBOOL(hAPP(hAPP(c_member(_1687435), _1687524), hAPP(c_List_Oset(_1687435), _1687439))), -(hBOOL(hAPP(_1687437, _1687524)))]]], (45285 ^ _780086) ^ [_1687844, _1687846, _1687848, _1687850] : [hBOOL(hAPP(c_List_Olistsp(_1687844, hAPP(hAPP(c_COMBS(_1687844, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1687844), c_fconj), _1687846)), _1687848)), _1687850)), 45288 ^ _780086 : [(45289 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1687844, _1687846), _1687850)))], (45291 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1687844, _1687848), _1687850)))]]], (45293 ^ _780086) ^ [_1688017, _1688019, _1688021, _1688023] : [-(hBOOL(hAPP(c_List_Olistsp(_1688017, hAPP(hAPP(c_COMBS(_1688017, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1688017), c_fconj), _1688019)), _1688021)), _1688023))), hBOOL(hAPP(c_List_Olistsp(_1688017, _1688019), _1688023)), hBOOL(hAPP(c_List_Olistsp(_1688017, _1688021), _1688023))], (45303 ^ _780086) ^ [_1688226, _1688228, _1688230, _1688232] : [hBOOL(hAPP(c_List_Olistsp(_1688226, _1688228), _1688230)), hBOOL(hAPP(c_List_Olistsp(_1688226, _1688232), _1688230)), -(hBOOL(hAPP(c_List_Olistsp(_1688226, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1688226, tc_HOL_Obool)), _1688228), _1688232)), _1688230)))], (45313 ^ _780086) ^ [_1688415, _1688417, _1688419] : [-(c_List_Olistsp(_1688415, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1688415, tc_HOL_Obool)), _1688417), _1688419)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1688415), tc_HOL_Obool)), c_List_Olistsp(_1688415, _1688417)), c_List_Olistsp(_1688415, _1688419)))], (45315 ^ _780086) ^ [_1688496, _1688498, _1688500, _1688502] : [hBOOL(hAPP(c_List_Olistsp(_1688496, _1688498), hAPP(hAPP(c_List_Olist_OCons(_1688496), _1688500), _1688502))), 45318 ^ _780086 : [(45319 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1688498, _1688500)))], (45321 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1688496, _1688498), _1688502)))]]], (45323 ^ _780086) ^ [_1688639, _1688641, _1688643, _1688645] : [-(hBOOL(hAPP(c_List_Olistsp(_1688639, _1688641), hAPP(hAPP(c_List_Olist_OCons(_1688639), _1688643), _1688645)))), hBOOL(hAPP(_1688641, _1688643)), hBOOL(hAPP(c_List_Olistsp(_1688639, _1688641), _1688645))], (45333 ^ _780086) ^ [_1688839, _1688841, _1688843, _1688845] : [hBOOL(hAPP(c_List_Olistsp(_1688839, _1688841), hAPP(hAPP(c_List_Oappend(_1688839), _1688843), _1688845))), 45336 ^ _780086 : [(45337 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1688839, _1688841), _1688843)))], (45339 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1688839, _1688841), _1688845)))]]], (45341 ^ _780086) ^ [_1688988, _1688990, _1688992, _1688994] : [-(hBOOL(hAPP(c_List_Olistsp(_1688988, _1688990), hAPP(hAPP(c_List_Oappend(_1688988), _1688992), _1688994)))), hBOOL(hAPP(c_List_Olistsp(_1688988, _1688990), _1688992)), hBOOL(hAPP(c_List_Olistsp(_1688988, _1688990), _1688994))], (45351 ^ _780086) ^ [_1689173, _1689175, _1689177] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1689173, tc_HOL_Obool)), _1689175), _1689177)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1689173), tc_HOL_Obool)), c_List_Olistsp(_1689173, _1689175)), c_List_Olistsp(_1689173, _1689177))))], (45357 ^ _780086) ^ [_1689308, _1689310, _1689312, _1689314, _1689316] : [c_List_Opartition(_1689308, _1689310, _1689312) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1689308), tc_List_Olist(_1689308)), _1689314), _1689316), 45360 ^ _780086 : [(45361 ^ _780086) ^ [_1689461] : [hBOOL(hAPP(hAPP(c_member(_1689308), _1689461), hAPP(c_List_Oset(_1689308), _1689314))), -(hBOOL(hAPP(_1689310, _1689461)))], (45367 ^ _780086) ^ [_1689570] : [hBOOL(hAPP(hAPP(c_member(_1689308), _1689570), hAPP(c_List_Oset(_1689308), _1689316))), hBOOL(hAPP(_1689310, _1689570))]]], (45373 ^ _780086) ^ [_1689690, _1689692] : [-(c_List_Opartition(_1689690, _1689692, c_List_Olist_ONil(_1689690)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1689690), tc_List_Olist(_1689690)), c_List_Olist_ONil(_1689690)), c_List_Olist_ONil(_1689690)))], (45375 ^ _780086) ^ [_1689756, _1689758, _1689760] : [hBOOL(hAPP(c_List_Olistsp(_1689756, hAPP(hAPP(c_COMBC(_1689756, tc_fun(_1689756, tc_HOL_Obool), tc_HOL_Obool), c_member(_1689756)), _1689758)), _1689760)), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1689756)), _1689760), c_List_Olists(_1689756, _1689758))))], (45381 ^ _780086) ^ [_1689895, _1689897, _1689899] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1689895)), _1689899), c_List_Olists(_1689895, _1689897))), -(hBOOL(hAPP(c_List_Olistsp(_1689895, hAPP(hAPP(c_COMBC(_1689895, tc_fun(_1689895, tc_HOL_Obool), tc_HOL_Obool), c_member(_1689895)), _1689897)), _1689899)))], (45387 ^ _780086) ^ [_1690040, _1690042, _1690044, _1690046] : [-(c_List_Opartition(_1690040, _1690042, hAPP(hAPP(c_List_Olist_OCons(_1690040), _1690044), _1690046)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1690040), tc_List_Olist(_1690040), tc_prod(tc_List_Olist(_1690040), tc_List_Olist(_1690040))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1690040), tc_fun(tc_List_Olist(_1690040), tc_prod(tc_List_Olist(_1690040), tc_List_Olist(_1690040))), tc_fun(tc_List_Olist(_1690040), tc_prod(tc_List_Olist(_1690040), tc_List_Olist(_1690040)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1690040), tc_fun(tc_prod(tc_List_Olist(_1690040), tc_List_Olist(_1690040)), tc_prod(tc_List_Olist(_1690040), tc_List_Olist(_1690040)))), tc_fun(tc_fun(tc_List_Olist(_1690040), tc_prod(tc_List_Olist(_1690040), tc_List_Olist(_1690040))), tc_fun(tc_List_Olist(_1690040), tc_prod(tc_List_Olist(_1690040), tc_List_Olist(_1690040)))), tc_List_Olist(_1690040)), c_COMBS(tc_List_Olist(_1690040), tc_prod(tc_List_Olist(_1690040), tc_List_Olist(_1690040)), tc_prod(tc_List_Olist(_1690040), tc_List_Olist(_1690040)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1690040), tc_prod(tc_List_Olist(_1690040), tc_List_Olist(_1690040))), tc_fun(tc_List_Olist(_1690040), tc_fun(tc_prod(tc_List_Olist(_1690040), tc_List_Olist(_1690040)), tc_prod(tc_List_Olist(_1690040), tc_List_Olist(_1690040)))), tc_List_Olist(_1690040)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1690040), tc_List_Olist(_1690040)), tc_fun(tc_prod(tc_List_Olist(_1690040), tc_List_Olist(_1690040)), tc_prod(tc_List_Olist(_1690040), tc_List_Olist(_1690040))), tc_List_Olist(_1690040)), hAPP(c_If(tc_prod(tc_List_Olist(_1690040), tc_List_Olist(_1690040))), hAPP(_1690042, _1690044)))), hAPP(hAPP(c_COMBB(tc_List_Olist(_1690040), tc_fun(tc_List_Olist(_1690040), tc_prod(tc_List_Olist(_1690040), tc_List_Olist(_1690040))), tc_List_Olist(_1690040)), c_Product__Type_OPair(tc_List_Olist(_1690040), tc_List_Olist(_1690040))), hAPP(c_List_Olist_OCons(_1690040), _1690044))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1690040), tc_fun(tc_List_Olist(_1690040), tc_List_Olist(_1690040)), tc_fun(tc_List_Olist(_1690040), tc_prod(tc_List_Olist(_1690040), tc_List_Olist(_1690040)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1690040), tc_prod(tc_List_Olist(_1690040), tc_List_Olist(_1690040))), tc_fun(tc_fun(tc_List_Olist(_1690040), tc_List_Olist(_1690040)), tc_fun(tc_List_Olist(_1690040), tc_prod(tc_List_Olist(_1690040), tc_List_Olist(_1690040)))), tc_List_Olist(_1690040)), c_COMBB(tc_List_Olist(_1690040), tc_prod(tc_List_Olist(_1690040), tc_List_Olist(_1690040)), tc_List_Olist(_1690040))), c_Product__Type_OPair(tc_List_Olist(_1690040), tc_List_Olist(_1690040)))), hAPP(c_List_Olist_OCons(_1690040), _1690044)))), c_List_Opartition(_1690040, _1690042, _1690046)))], (45389 ^ _780086) ^ [_1690459, _1690461, _1690463] : [-(c_List_Olistsp(_1690459, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1690459, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1690459, tc_fun(_1690459, tc_HOL_Obool), tc_HOL_Obool), c_member(_1690459)), _1690461)), hAPP(hAPP(c_COMBC(_1690459, tc_fun(_1690459, tc_HOL_Obool), tc_HOL_Obool), c_member(_1690459)), _1690463))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1690459), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1690459), tc_fun(tc_List_Olist(_1690459), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1690459))), c_List_Olists(_1690459, _1690461))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1690459), tc_fun(tc_List_Olist(_1690459), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1690459))), c_List_Olists(_1690459, _1690463))))], (45391 ^ _780086) ^ [_1690591, _1690593, _1690595, _1690597, _1690599] : [-(c_Enum_Oproduct(_1690591, _1690593, hAPP(hAPP(c_List_Olist_OCons(_1690591), _1690595), _1690597), _1690599) = hAPP(hAPP(c_List_Oappend(tc_prod(_1690591, _1690593)), hAPP(hAPP(c_List_Omap(_1690593, tc_prod(_1690591, _1690593)), hAPP(c_Product__Type_OPair(_1690591, _1690593), _1690595)), _1690599)), c_Enum_Oproduct(_1690591, _1690593, _1690597, _1690599)))], (45393 ^ _780086) ^ [_1690693, _1690695, _1690697, _1690699, _1690701] : [c_List_Olist__all2(_1690693, _1690695, _1690697, _1690699, _1690701), 45396 ^ _780086 : [(45397 ^ _780086) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690693)), _1690699) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690695)), _1690701))], (45399 ^ _780086) ^ [_1690859] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1690693, _1690695)), _1690859), hAPP(c_List_Oset(tc_prod(_1690693, _1690695)), hAPP(hAPP(c_List_Ozip(_1690693, _1690695), _1690699), _1690701)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1690693, _1690695, tc_HOL_Obool), _1690697), _1690859)))]]], (45405 ^ _780086) ^ [_1691018, _1691020, _1691022, _1691024, _1691026] : [-(c_List_Olist__all2(_1691018, _1691020, _1691022, _1691024, _1691026)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691018)), _1691024) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691020)), _1691026), 45411 ^ _780086 : [(45412 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1691018, _1691020)), 45410 ^ [_1691018, _1691020, _1691022, _1691024, _1691026]), hAPP(c_List_Oset(tc_prod(_1691018, _1691020)), hAPP(hAPP(c_List_Ozip(_1691018, _1691020), _1691024), _1691026)))))], (45414 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1691018, _1691020, tc_HOL_Obool), _1691022), 45410 ^ [_1691018, _1691020, _1691022, _1691024, _1691026]))]]], (45418 ^ _780086) ^ [_1691389, _1691391, _1691393, _1691395, _1691397, _1691399, _1691401] : [c_List_Olist__all2(_1691389, _1691391, _1691393, hAPP(hAPP(c_List_Omap(_1691395, _1691389), _1691397), _1691399), _1691401), -(c_List_Olist__all2(_1691395, _1691391, hAPP(hAPP(c_COMBB(_1691389, tc_fun(_1691391, tc_HOL_Obool), _1691395), _1691393), _1691397), _1691399, _1691401))], (45424 ^ _780086) ^ [_1691528, _1691530, _1691532, _1691534, _1691536, _1691538, _1691540] : [c_List_Olist__all2(_1691534, _1691530, hAPP(hAPP(c_COMBB(_1691528, tc_fun(_1691530, tc_HOL_Obool), _1691534), _1691532), _1691536), _1691538, _1691540), -(c_List_Olist__all2(_1691528, _1691530, _1691532, hAPP(hAPP(c_List_Omap(_1691534, _1691528), _1691536), _1691538), _1691540))], (45430 ^ _780086) ^ [_1691703, _1691705, _1691707, _1691709, _1691711, _1691713, _1691715] : [c_List_Olist__all2(_1691703, _1691705, _1691707, _1691709, hAPP(hAPP(c_List_Omap(_1691711, _1691705), _1691713), _1691715)), -(c_List_Olist__all2(_1691703, _1691711, hAPP(hAPP(c_COMBC(_1691703, tc_fun(_1691711, _1691705), tc_fun(_1691711, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1691705, tc_HOL_Obool), tc_fun(tc_fun(_1691711, _1691705), tc_fun(_1691711, tc_HOL_Obool)), _1691703), c_COMBB(_1691705, tc_HOL_Obool, _1691711)), _1691707)), _1691713), _1691709, _1691715))], (45436 ^ _780086) ^ [_1691900, _1691902, _1691904, _1691906, _1691908, _1691910, _1691912] : [c_List_Olist__all2(_1691900, _1691908, hAPP(hAPP(c_COMBC(_1691900, tc_fun(_1691908, _1691902), tc_fun(_1691908, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1691902, tc_HOL_Obool), tc_fun(tc_fun(_1691908, _1691902), tc_fun(_1691908, tc_HOL_Obool)), _1691900), c_COMBB(_1691902, tc_HOL_Obool, _1691908)), _1691904)), _1691910), _1691906, _1691912), -(c_List_Olist__all2(_1691900, _1691902, _1691904, _1691906, hAPP(hAPP(c_List_Omap(_1691908, _1691902), _1691910), _1691912)))], (45442 ^ _780086) ^ [_1692103, _1692105, _1692107, _1692109, _1692111, _1692113] : [c_List_Olist__all2(_1692103, _1692105, _1692107, _1692109, _1692111), -(c_List_Olist__all2(_1692103, _1692105, _1692107, hAPP(hAPP(c_List_Odrop(_1692103), _1692113), _1692109), hAPP(hAPP(c_List_Odrop(_1692105), _1692113), _1692111)))], (45448 ^ _780086) ^ [_1692232, _1692234, _1692236, _1692238, _1692240, _1692242, _1692244] : [c_List_Olist__all2(_1692232, _1692234, _1692236, _1692238, _1692240), c_List_Olist__all2(_1692232, _1692234, _1692236, _1692242, _1692244), -(c_List_Olist__all2(_1692232, _1692234, _1692236, hAPP(hAPP(c_List_Oappend(_1692232), _1692238), _1692242), hAPP(hAPP(c_List_Oappend(_1692234), _1692240), _1692244)))], (45458 ^ _780086) ^ [_1692431, _1692433, _1692435, _1692437, _1692439, _1692441, _1692443] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1692431)), _1692433) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1692435)), _1692437), 45461 ^ _780086 : [(45462 ^ _780086) ^ [] : [c_List_Olist__all2(_1692431, _1692435, _1692439, hAPP(hAPP(c_List_Oappend(_1692431), _1692433), _1692441), hAPP(hAPP(c_List_Oappend(_1692435), _1692437), _1692443)), 45465 ^ _780086 : [(45466 ^ _780086) ^ [] : [-(c_List_Olist__all2(_1692431, _1692435, _1692439, _1692433, _1692437))], (45468 ^ _780086) ^ [] : [-(c_List_Olist__all2(_1692431, _1692435, _1692439, _1692441, _1692443))]]], (45470 ^ _780086) ^ [] : [-(c_List_Olist__all2(_1692431, _1692435, _1692439, hAPP(hAPP(c_List_Oappend(_1692431), _1692433), _1692441), hAPP(hAPP(c_List_Oappend(_1692435), _1692437), _1692443))), c_List_Olist__all2(_1692431, _1692435, _1692439, _1692433, _1692437), c_List_Olist__all2(_1692431, _1692435, _1692439, _1692441, _1692443)]]], (45480 ^ _780086) ^ [_1692883, _1692885, _1692887, _1692889, _1692891, _1692893, _1692895] : [c_List_Olist__all2(_1692883, _1692885, _1692887, hAPP(hAPP(c_List_Olist_OCons(_1692883), _1692889), _1692891), hAPP(hAPP(c_List_Olist_OCons(_1692885), _1692893), _1692895)), 45483 ^ _780086 : [(45484 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(_1692887, _1692889), _1692893)))], (45486 ^ _780086) ^ [] : [-(c_List_Olist__all2(_1692883, _1692885, _1692887, _1692891, _1692895))]]], (45488 ^ _780086) ^ [_1693046, _1693048, _1693050, _1693052, _1693054, _1693056, _1693058] : [-(c_List_Olist__all2(_1693046, _1693048, _1693050, hAPP(hAPP(c_List_Olist_OCons(_1693046), _1693052), _1693054), hAPP(hAPP(c_List_Olist_OCons(_1693048), _1693056), _1693058))), hBOOL(hAPP(hAPP(_1693050, _1693052), _1693056)), c_List_Olist__all2(_1693046, _1693048, _1693050, _1693054, _1693058)], (45498 ^ _780086) ^ [_1693251, _1693253, _1693255, _1693257, _1693259, _1693261] : [c_List_Olist__all2(_1693251, _1693253, _1693255, _1693257, _1693259), -(c_List_Olist__all2(_1693251, _1693253, _1693255, hAPP(hAPP(c_List_Otake(_1693251), _1693261), _1693257), hAPP(hAPP(c_List_Otake(_1693253), _1693261), _1693259)))], (45504 ^ _780086) ^ [_1693398, _1693400, _1693402] : [_1693398 = _1693400, -(c_List_Olist__all2(_1693402, _1693402, c_fequal, _1693398, _1693400))], (45510 ^ _780086) ^ [_1693479, _1693481, _1693483] : [c_List_Olist__all2(_1693483, _1693483, c_fequal, _1693479, _1693481), -(_1693479 = _1693481)], (45516 ^ _780086) ^ [_1693566, _1693568, _1693570, _1693572, _1693574] : [c_List_Olist__all2(_1693566, _1693568, _1693570, _1693572, _1693574), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693566)), _1693572) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693568)), _1693574))], (45522 ^ _780086) ^ [_1693704, _1693706, _1693708, _1693710] : [c_List_Olist__all2(_1693704, _1693706, _1693708, c_List_Olist_ONil(_1693704), _1693710), -(_1693710 = c_List_Olist_ONil(_1693706))], (45528 ^ _780086) ^ [_1693795, _1693797, _1693799, _1693801] : [_1693801 = c_List_Olist_ONil(_1693797), -(c_List_Olist__all2(_1693795, _1693797, _1693799, c_List_Olist_ONil(_1693795), _1693801))], (45534 ^ _780086) ^ [_1693913, _1693915, _1693917, _1693919] : [c_List_Olist__all2(_1693913, _1693915, _1693917, _1693919, c_List_Olist_ONil(_1693915)), -(_1693919 = c_List_Olist_ONil(_1693913))], (45540 ^ _780086) ^ [_1694004, _1694006, _1694008, _1694010] : [_1694010 = c_List_Olist_ONil(_1694004), -(c_List_Olist__all2(_1694004, _1694006, _1694008, _1694010, c_List_Olist_ONil(_1694006)))], (45546 ^ _780086) ^ [_1694101, _1694103, _1694105] : [-(c_Enum_Oproduct(_1694101, _1694103, c_List_Olist_ONil(_1694101), _1694105) = c_List_Olist_ONil(tc_prod(_1694101, _1694103)))], (45548 ^ _780086) ^ [_1694164, _1694166, _1694168, _1694170, _1694172] : [c_List_Olist__all2(_1694164, _1694166, _1694168, _1694170, _1694172), 45551 ^ _780086 : [(45552 ^ _780086) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694164)), _1694170) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694166)), _1694172))], (45554 ^ _780086) ^ [_1694327] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1694327), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694164)), _1694170))), -(hBOOL(hAPP(hAPP(_1694168, hAPP(hAPP(c_List_Onth(_1694164), _1694170), _1694327)), hAPP(hAPP(c_List_Onth(_1694166), _1694172), _1694327))))]]], (45560 ^ _780086) ^ [_1694480, _1694482, _1694484, _1694486, _1694488] : [-(c_List_Olist__all2(_1694480, _1694482, _1694484, _1694486, _1694488)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694480)), _1694486) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694482)), _1694488), 45566 ^ _780086 : [(45567 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 45565 ^ [_1694480, _1694482, _1694484, _1694486, _1694488]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694480)), _1694486))))], (45569 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(_1694484, hAPP(hAPP(c_List_Onth(_1694480), _1694486), 45565 ^ [_1694480, _1694482, _1694484, _1694486, _1694488])), hAPP(hAPP(c_List_Onth(_1694482), _1694488), 45565 ^ [_1694480, _1694482, _1694484, _1694486, _1694488])))]]], (45573 ^ _780086) ^ [_1694840, _1694842, _1694844, _1694846, _1694848, _1694850] : [c_List_Olist__all2(_1694840, _1694842, _1694844, _1694846, _1694848), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1694850), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694840)), _1694846))), -(hBOOL(hAPP(hAPP(_1694844, hAPP(hAPP(c_List_Onth(_1694840), _1694846), _1694850)), hAPP(hAPP(c_List_Onth(_1694842), _1694848), _1694850))))], (45583 ^ _780086) ^ [_1695057, _1695059, _1695061, _1695063, _1695065, _1695067] : [c_List_Olist__all2(_1695057, _1695059, _1695061, _1695063, _1695065), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1695067), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695059)), _1695065))), -(hBOOL(hAPP(hAPP(_1695061, hAPP(hAPP(c_List_Onth(_1695057), _1695063), _1695067)), hAPP(hAPP(c_List_Onth(_1695059), _1695065), _1695067))))], (45593 ^ _780086) ^ [_1695274, _1695276, _1695278, _1695280, _1695282, _1695284, _1695286, _1695288] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1695274), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695276)), _1695278))), c_List_Olist__all2(_1695276, _1695280, _1695282, _1695278, _1695284), hBOOL(hAPP(hAPP(_1695282, _1695286), _1695288)), -(c_List_Olist__all2(_1695276, _1695280, _1695282, hAPP(hAPP(c_List_Olist__update(_1695276, _1695278), _1695274), _1695286), hAPP(hAPP(c_List_Olist__update(_1695280, _1695284), _1695274), _1695288)))], (45607 ^ _780086) ^ [_1695573, _1695575, _1695577, _1695579, _1695581, _1695583, _1695585, _1695587] : [c_List_Olist__all2(_1695573, _1695575, _1695577, _1695579, _1695581), hBOOL(hAPP(hAPP(_1695577, _1695583), _1695585)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1695587), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695575)), _1695581))), -(c_List_Olist__all2(_1695573, _1695575, _1695577, hAPP(hAPP(c_List_Olist__update(_1695573, _1695579), _1695587), _1695583), hAPP(hAPP(c_List_Olist__update(_1695575, _1695581), _1695587), _1695585)))], (45621 ^ _780086) ^ [_1695872, _1695874, _1695876, _1695878] : [hBOOL(hAPP(c_List_Odistinct(_1695872), _1695874)), hBOOL(hAPP(c_List_Odistinct(_1695876), _1695878)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1695872, _1695876)), c_Enum_Oproduct(_1695872, _1695876, _1695874, _1695878))))], (45631 ^ _780086) ^ [_1696049, _1696051, _1696053, _1696055] : [-(hAPP(c_List_Oset(tc_prod(_1696049, _1696051)), c_Enum_Oproduct(_1696049, _1696051, _1696053, _1696055)) = hAPP(hAPP(c_Product__Type_OSigma(_1696049, _1696051), hAPP(c_List_Oset(_1696049), _1696053)), hAPP(c_COMBK(tc_fun(_1696051, tc_HOL_Obool), _1696049), hAPP(c_List_Oset(_1696051), _1696055))))], (45633 ^ _780086) ^ [_1696119, _1696121] : [-(hAPP(c_Set_Oimage(tc_List_Olist(_1696119), tc_fun(_1696119, tc_HOL_Obool), c_List_Oset(_1696119)), hAPP(c_List_Oset(tc_List_Olist(_1696119)), c_Enum_Osublists(_1696119, _1696121))) = hAPP(c_Set_OPow(_1696119), hAPP(c_List_Oset(_1696119), _1696121)))], (45635 ^ _780086) ^ [_1696178, _1696180] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1696178))), c_Enum_Osublists(_1696178, _1696180)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696178)), _1696180)))], (45637 ^ _780086) ^ [_1696225] : [-(c_Enum_Osublists(_1696225, c_List_Olist_ONil(_1696225)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1696225)), c_List_Olist_ONil(_1696225)), c_List_Olist_ONil(tc_List_Olist(_1696225))))], (45639 ^ _780086) ^ [_1696269, _1696271, _1696273] : [-(c_Enum_Osublists(_1696269, hAPP(hAPP(c_List_Olist_OCons(_1696269), _1696271), _1696273)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(_1696269)), tc_List_Olist(tc_List_Olist(_1696269))), c_Enum_Osublists(_1696269, _1696273)), hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(_1696269)), tc_List_Olist(tc_List_Olist(_1696269)), tc_List_Olist(tc_List_Olist(_1696269))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(_1696269)), tc_fun(tc_List_Olist(tc_List_Olist(_1696269)), tc_List_Olist(tc_List_Olist(_1696269))), tc_List_Olist(tc_List_Olist(_1696269))), c_List_Oappend(tc_List_Olist(_1696269))), hAPP(c_List_Omap(tc_List_Olist(_1696269), tc_List_Olist(_1696269)), hAPP(c_List_Olist_OCons(_1696269), _1696271)))), c_COMBI(tc_List_Olist(tc_List_Olist(_1696269))))))], (45641 ^ _780086) ^ [_1696403, _1696405] : [hBOOL(hAPP(c_List_Odistinct(_1696403), _1696405)), -(hBOOL(hAPP(c_List_Odistinct(tc_fun(_1696403, tc_HOL_Obool)), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1696403), tc_fun(_1696403, tc_HOL_Obool)), c_List_Oset(_1696403)), c_Enum_Osublists(_1696403, _1696405)))))], (45647 ^ _780086) ^ [_1696540, _1696542, _1696544] : [-(hAPP(c_List_Oset(tc_List_Olist(_1696540)), c_Enum_On__lists(_1696540, _1696542, _1696544)) = hAPP(c_Set_OCollect(tc_List_Olist(_1696540)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1696540), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1696540)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1696540), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1696540)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1696540)))), _1696542))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1696540), tc_fun(_1696540, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1696540, tc_HOL_Obool), tc_fun(tc_fun(_1696540, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1696540)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1696540, tc_HOL_Obool))), c_List_Oset(_1696540))), hAPP(c_List_Oset(_1696540), _1696544)))))], (45649 ^ _780086) ^ [_1696685, _1696687] : [-(c_Enum_Oenum__the(_1696685, _1696687) = c_HOL_OThe(_1696685, _1696687))], (45651 ^ _780086) ^ [_1696716, _1696718, _1696720] : [hBOOL(hAPP(c_List_Odistinct(_1696716), _1696718)), -(hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1696716)), c_Enum_On__lists(_1696716, _1696720, _1696718))))], (45657 ^ _780086) ^ [_1696832, _1696834] : [_1696832 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Enum_On__lists(_1696834, _1696832, c_List_Olist_ONil(_1696834)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1696834)), c_List_Olist_ONil(_1696834)), c_List_Olist_ONil(tc_List_Olist(_1696834))))], (45663 ^ _780086) ^ [_1696947, _1696949] : [-(_1696947 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Enum_On__lists(_1696949, _1696947, c_List_Olist_ONil(_1696949)) = c_List_Olist_ONil(tc_List_Olist(_1696949)))], (45669 ^ _780086) ^ [_1696995, _1696997] : [-(c_Enum_On__lists(_1696995, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1696997) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1696995)), c_List_Olist_ONil(_1696995)), c_List_Olist_ONil(tc_List_Olist(_1696995))))], (45671 ^ _780086) ^ [_1697040, _1697042, _1697044] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1697040))), c_Enum_On__lists(_1697040, _1697042, _1697044)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697040)), _1697044)), _1697042))], (45673 ^ _780086) ^ [_1697093, _1697095, _1697097, _1697099] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1697093)), _1697095), hAPP(c_List_Oset(tc_List_Olist(_1697093)), c_Enum_On__lists(_1697093, _1697097, _1697099)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697093)), _1697095) = _1697097)], (45679 ^ _780086) ^ [_1697228, _1697230, _1697232, _1697234, _1697236] : [45681 ^ _780086 : [(45682 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1697228, _1697230)), 45680 ^ [_1697228, _1697230, _1697232, _1697234, _1697236]), hAPP(c_List_Oset(tc_prod(_1697228, _1697230)), hAPP(hAPP(c_List_Ozip(_1697228, _1697230), _1697232), _1697234)))))], (45684 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1697228, _1697230, tc_HOL_Obool), _1697236), 45680 ^ [_1697228, _1697230, _1697232, _1697234, _1697236]))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697228)), _1697232) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697230)), _1697234), -(c_List_Olist__all2(_1697228, _1697230, _1697236, _1697232, _1697234))], (45692 ^ _780086) ^ [_1697567, _1697569, _1697571, _1697573] : [45694 ^ _780086 : [(45695 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 45693 ^ [_1697567, _1697569, _1697571, _1697573]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697567)), _1697569))))], (45697 ^ _780086) ^ [] : [hBOOL(hAPP(_1697571, hAPP(hAPP(c_List_Onth(_1697567), _1697569), 45693 ^ [_1697567, _1697569, _1697571, _1697573])))]], hBOOL(hAPP(hAPP(c_member(_1697567), _1697573), hAPP(c_List_Oset(_1697567), _1697569))), -(hBOOL(hAPP(_1697571, _1697573)))], (45705 ^ _780086) ^ [_1697863, _1697865, _1697867, _1697869, _1697871] : [c_Finite__Set_Ofun__left__comm(_1697863, _1697865, _1697867), -(hAPP(hAPP(c_Finite__Set_Ofold(_1697863, _1697865, _1697867), _1697869), hAPP(c_List_Oset(_1697863), _1697871)) = hAPP(c_List_Ofoldl(_1697865, _1697863, hAPP(c_COMBC(_1697863, _1697865, _1697865), _1697867), _1697869), c_List_Oremdups(_1697863, _1697871)))], (45711 ^ _780086) ^ [_1698014, _1698016, _1698018, _1698020, _1698022] : [c_Fun_Oinj__on(_1698014, _1698016, _1698018, hAPP(hAPP(c_Set_Oinsert(_1698014), _1698020), hAPP(c_List_Oset(_1698014), _1698022))), -(hAPP(hAPP(c_List_Omap(_1698014, _1698016), _1698018), hAPP(c_List_OremoveAll(_1698014, _1698020), _1698022)) = hAPP(c_List_OremoveAll(_1698016, hAPP(_1698018, _1698020)), hAPP(hAPP(c_List_Omap(_1698014, _1698016), _1698018), _1698022)))], (45717 ^ _780086) ^ [_1698193, _1698195] : [-(hBOOL(hAPP(c_List_Odistinct(_1698193), c_List_Oremdups(_1698193, _1698195))))], (45719 ^ _780086) ^ [_1698225, _1698227] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698225)), c_List_Oremdups(_1698225, _1698227))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698225)), _1698227))))], (45721 ^ _780086) ^ [_1698272, _1698274] : [hBOOL(hAPP(c_List_Odistinct(_1698272), _1698274)), -(c_List_Oremdups(_1698272, _1698274) = _1698274)], (45727 ^ _780086) ^ [_1698363, _1698365, _1698367] : [hBOOL(hAPP(c_List_Odistinct(_1698363), _1698365)), -(hBOOL(hAPP(c_List_Odistinct(_1698363), hAPP(c_List_OremoveAll(_1698363, _1698367), _1698365))))], (45733 ^ _780086) ^ [_1698485, _1698487] : [c_List_Oremdups(_1698485, _1698487) = _1698487, -(hBOOL(hAPP(c_List_Odistinct(_1698485), _1698487)))], (45739 ^ _780086) ^ [_1698572, _1698574] : [hBOOL(hAPP(c_List_Odistinct(_1698572), _1698574)), -(c_List_Oremdups(_1698572, _1698574) = _1698574)], (45745 ^ _780086) ^ [_1698665, _1698667] : [-(hAPP(c_List_Oset(_1698665), c_List_Oremdups(_1698665, _1698667)) = hAPP(c_List_Oset(_1698665), _1698667))], (45747 ^ _780086) ^ [_1698718, _1698720] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698718)), c_List_Oremdups(_1698718, _1698720)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698718)), _1698720), -(c_List_Oremdups(_1698718, _1698720) = _1698720)], (45753 ^ _780086) ^ [_1698831, _1698833] : [c_List_Oremdups(_1698831, _1698833) = _1698833, -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698831)), c_List_Oremdups(_1698831, _1698833)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698831)), _1698833))], (45759 ^ _780086) ^ [_1698950, _1698952] : [-(c_List_Oremdups(_1698950, c_List_Oremdups(_1698950, _1698952)) = c_List_Oremdups(_1698950, _1698952))], (45761 ^ _780086) ^ [_1698999, _1699001] : [c_List_Oremdups(_1698999, _1699001) = c_List_Olist_ONil(_1698999), -(_1699001 = c_List_Olist_ONil(_1698999))], (45767 ^ _780086) ^ [_1699086, _1699088] : [_1699088 = c_List_Olist_ONil(_1699086), -(c_List_Oremdups(_1699086, _1699088) = c_List_Olist_ONil(_1699086))], (45773 ^ _780086) ^ [_1699179, _1699181] : [-(hAPP(c_List_OremoveAll(_1699179, _1699181), c_List_Olist_ONil(_1699179)) = c_List_Olist_ONil(_1699179))], (45775 ^ _780086) ^ [_1699229, _1699231] : [c_List_Olist_ONil(_1699229) = c_List_Oremdups(_1699229, _1699231), -(_1699231 = c_List_Olist_ONil(_1699229))], (45781 ^ _780086) ^ [_1699316, _1699318] : [_1699318 = c_List_Olist_ONil(_1699316), -(c_List_Olist_ONil(_1699316) = c_List_Oremdups(_1699316, _1699318))], (45787 ^ _780086) ^ [_1699409] : [-(c_List_Oremdups(_1699409, c_List_Olist_ONil(_1699409)) = c_List_Olist_ONil(_1699409))], (45789 ^ _780086) ^ [_1699454, _1699456, _1699458, _1699460] : [_1699454 = _1699456, -(hAPP(c_List_OremoveAll(_1699458, _1699454), hAPP(hAPP(c_List_Olist_OCons(_1699458), _1699456), _1699460)) = hAPP(c_List_OremoveAll(_1699458, _1699454), _1699460))], (45795 ^ _780086) ^ [_1699569, _1699571, _1699573, _1699575] : [-(_1699569 = _1699571), -(hAPP(c_List_OremoveAll(_1699573, _1699569), hAPP(hAPP(c_List_Olist_OCons(_1699573), _1699571), _1699575)) = hAPP(hAPP(c_List_Olist_OCons(_1699573), _1699571), hAPP(c_List_OremoveAll(_1699573, _1699569), _1699575)))], (45801 ^ _780086) ^ [_1699639, _1699641, _1699643, _1699645] : [-(hAPP(c_List_OremoveAll(_1699639, _1699641), hAPP(hAPP(c_List_Oappend(_1699639), _1699643), _1699645)) = hAPP(hAPP(c_List_Oappend(_1699639), hAPP(c_List_OremoveAll(_1699639, _1699641), _1699643)), hAPP(c_List_OremoveAll(_1699639, _1699641), _1699645)))], (45803 ^ _780086) ^ [_1699702, _1699704, _1699706, _1699708] : [-(c_List_Oremdups(_1699702, hAPP(hAPP(c_List_Omap(_1699704, _1699702), _1699706), c_List_Oremdups(_1699704, _1699708))) = c_List_Oremdups(_1699702, hAPP(hAPP(c_List_Omap(_1699704, _1699702), _1699706), _1699708)))], (45805 ^ _780086) ^ [_1699758, _1699760, _1699762] : [hBOOL(hAPP(c_List_Odistinct(_1699758), _1699760)), -(c_List_Oremove1(_1699758, _1699762, c_List_Oremdups(_1699758, _1699760)) = c_List_Oremdups(_1699758, c_List_Oremove1(_1699758, _1699762, _1699760)))], (45811 ^ _780086) ^ [_1699869, _1699871, _1699873] : [-(hBOOL(hAPP(hAPP(c_member(_1699869), _1699871), hAPP(c_List_Oset(_1699869), _1699873)))), -(hAPP(c_List_OremoveAll(_1699869, _1699871), _1699873) = _1699873)], (45817 ^ _780086) ^ [_1699925, _1699927, _1699929] : [hBOOL(hAPP(c_List_Odistinct(_1699925), _1699927)), -(c_List_Oremove1(_1699925, _1699929, _1699927) = hAPP(c_List_OremoveAll(_1699925, _1699929), _1699927))], (45823 ^ _780086) ^ [_1700044, _1700046, _1700048] : [hBOOL(hAPP(hAPP(c_member(_1700044), _1700046), hAPP(c_List_Oset(_1700044), _1700048))), -(c_List_Oremdups(_1700044, hAPP(hAPP(c_List_Olist_OCons(_1700044), _1700046), _1700048)) = c_List_Oremdups(_1700044, _1700048))], (45829 ^ _780086) ^ [_1700169, _1700171, _1700173] : [-(hBOOL(hAPP(hAPP(c_member(_1700169), _1700171), hAPP(c_List_Oset(_1700169), _1700173)))), -(c_List_Oremdups(_1700169, hAPP(hAPP(c_List_Olist_OCons(_1700169), _1700171), _1700173)) = hAPP(hAPP(c_List_Olist_OCons(_1700169), _1700171), c_List_Oremdups(_1700169, _1700173)))], (45835 ^ _780086) ^ [_1700243, _1700245] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700243)), c_List_Oremdups(_1700243, _1700245)) = hAPP(c_Finite__Set_Ocard(_1700243), hAPP(c_List_Oset(_1700243), _1700245)))], (45837 ^ _780086) ^ [_1700288, _1700290, _1700292, _1700294, _1700296] : [c_Fun_Oinj__on(_1700288, _1700290, _1700292, c_Orderings_Otop__class_Otop(tc_fun(_1700288, tc_HOL_Obool))), -(hAPP(hAPP(c_List_Omap(_1700288, _1700290), _1700292), hAPP(c_List_OremoveAll(_1700288, _1700294), _1700296)) = hAPP(c_List_OremoveAll(_1700290, hAPP(_1700292, _1700294)), hAPP(hAPP(c_List_Omap(_1700288, _1700290), _1700292), _1700296)))], (45843 ^ _780086) ^ [_1700451, _1700453, _1700455] : [-(hAPP(c_List_Oset(_1700451), hAPP(c_List_OremoveAll(_1700451, _1700453), _1700455)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1700451, tc_HOL_Obool)), hAPP(c_List_Oset(_1700451), _1700455)), hAPP(hAPP(c_Set_Oinsert(_1700451), _1700453), c_Orderings_Obot__class_Obot(tc_fun(_1700451, tc_HOL_Obool)))))], (45845 ^ _780086) ^ [_1700518, _1700520] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700518)), c_List_Oremdups(_1700518, c_List_Oconcat(_1700518, _1700520))) = hAPP(c_Finite__Set_Ocard(_1700518), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1700518), tc_fun(_1700518, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1700518)), _1700520)), c_List_Oset(_1700518))))], (45847 ^ _780086) ^ [_1700584, _1700586] : [class_Orderings_Olinorder(_1700584), -(c_List_Olinorder__class_Osorted__list__of__set(_1700584, hAPP(c_List_Oset(_1700584), _1700586)) = c_List_Olinorder__class_Osort__key(_1700584, _1700584, c_COMBI(_1700584), c_List_Oremdups(_1700584, _1700586)))], (45853 ^ _780086) ^ [_1700695, _1700697, _1700699] : [class_Orderings_Olinorder(_1700695), -(c_List_Olinorder__class_Osort__key(_1700697, _1700695, _1700699, c_List_Olist_ONil(_1700697)) = c_List_Olist_ONil(_1700697))], (45859 ^ _780086) ^ [_1700790, _1700792, _1700794] : [-(hAPP(c_List_Ofoldl(tc_List_Olist(_1700790), tc_List_Olist(_1700790), c_List_Oappend(_1700790), _1700792), _1700794) = hAPP(hAPP(c_List_Oappend(_1700790), _1700792), c_List_Oconcat(_1700790, _1700794)))], (45861 ^ _780086) ^ [_1700842, _1700844] : [-(c_List_Oconcat(_1700842, _1700844) = hAPP(c_List_Ofoldl(tc_List_Olist(_1700842), tc_List_Olist(_1700842), c_List_Oappend(_1700842), c_List_Olist_ONil(_1700842)), _1700844))], (45863 ^ _780086) ^ [_1700886, _1700888, _1700890, _1700892] : [class_Orderings_Olinorder(_1700886), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700888)), c_List_Olinorder__class_Osort__key(_1700888, _1700886, _1700890, _1700892)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700888)), _1700892))], (45869 ^ _780086) ^ [_1701003, _1701005, _1701007, _1701009] : [class_Orderings_Olinorder(_1701003), -(hAPP(c_List_Oset(_1701005), c_List_Olinorder__class_Osort__key(_1701005, _1701003, _1701007, _1701009)) = hAPP(c_List_Oset(_1701005), _1701009))], (45875 ^ _780086) ^ [_1701112, _1701114, _1701116, _1701118] : [class_Orderings_Olinorder(_1701112), 45878 ^ _780086 : [(45879 ^ _780086) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1701114), c_List_Olinorder__class_Osort__key(_1701114, _1701112, _1701116, _1701118))), -(hBOOL(hAPP(c_List_Odistinct(_1701114), _1701118)))], (45885 ^ _780086) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1701114), _1701118)), -(hBOOL(hAPP(c_List_Odistinct(_1701114), c_List_Olinorder__class_Osort__key(_1701114, _1701112, _1701116, _1701118))))]]], (45891 ^ _780086) ^ [_1701368] : [-(c_List_Oconcat(_1701368, c_List_Olist_ONil(tc_List_Olist(_1701368))) = c_List_Olist_ONil(_1701368))], (45893 ^ _780086) ^ [_1701400, _1701402, _1701404] : [-(c_List_Oconcat(_1701400, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1701400)), _1701402), _1701404)) = hAPP(hAPP(c_List_Oappend(_1701400), _1701402), c_List_Oconcat(_1701400, _1701404)))], (45905 ^ _780086) ^ [_1701672, _1701674] : [45907 ^ _780086 : [(45908 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1701672)), 45906 ^ [_1701672, _1701674]), hAPP(c_List_Oset(tc_List_Olist(_1701672)), _1701674))))], (45910 ^ _780086) ^ [] : [45906 ^ [_1701672, _1701674] = c_List_Olist_ONil(_1701672)]], -(c_List_Oconcat(_1701672, _1701674) = c_List_Olist_ONil(_1701672))], (45895 ^ _780086) ^ [_1701466, _1701468] : [c_List_Oconcat(_1701466, _1701468) = c_List_Olist_ONil(_1701466), 45898 ^ _780086 : [(45899 ^ _780086) ^ [_1701557] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1701466)), _1701557), hAPP(c_List_Oset(tc_List_Olist(_1701466)), _1701468))), -(_1701557 = c_List_Olist_ONil(_1701466))]]], (45924 ^ _780086) ^ [_1702084, _1702086] : [45926 ^ _780086 : [(45927 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1702084)), 45925 ^ [_1702084, _1702086]), hAPP(c_List_Oset(tc_List_Olist(_1702084)), _1702086))))], (45929 ^ _780086) ^ [] : [45925 ^ [_1702084, _1702086] = c_List_Olist_ONil(_1702084)]], -(c_List_Olist_ONil(_1702084) = c_List_Oconcat(_1702084, _1702086))], (45914 ^ _780086) ^ [_1701878, _1701880] : [c_List_Olist_ONil(_1701878) = c_List_Oconcat(_1701878, _1701880), 45917 ^ _780086 : [(45918 ^ _780086) ^ [_1701969] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1701878)), _1701969), hAPP(c_List_Oset(tc_List_Olist(_1701878)), _1701880))), -(_1701969 = c_List_Olist_ONil(_1701878))]]], (45933 ^ _780086) ^ [_1702275, _1702277, _1702279, _1702281] : [-(hAPP(hAPP(c_List_Omap(_1702275, _1702277), _1702279), c_List_Oconcat(_1702275, _1702281)) = c_List_Oconcat(_1702277, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1702275), tc_List_Olist(_1702277)), hAPP(c_List_Omap(_1702275, _1702277), _1702279)), _1702281)))], (45935 ^ _780086) ^ [_1702338, _1702340] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702338)), c_List_Oconcat(_1702338, _1702340)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1702338), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1702338))), _1702340)))], (45937 ^ _780086) ^ [_1702391, _1702393] : [-(hAPP(c_List_Oset(_1702391), c_List_Oconcat(_1702391, _1702393)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1702391), tc_fun(_1702391, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1702391)), _1702393)), c_List_Oset(_1702391)))], (45939 ^ _780086) ^ [_1702447, _1702449, _1702451, _1702453, _1702455] : [class_Orderings_Olinorder(_1702447), -(c_List_Olinorder__class_Osort__key(_1702449, _1702447, _1702451, hAPP(hAPP(c_List_Olist_OCons(_1702449), _1702453), _1702455)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1702449, _1702447, _1702451), _1702453), c_List_Olinorder__class_Osort__key(_1702449, _1702447, _1702451, _1702455)))], (45945 ^ _780086) ^ [_1702584, _1702586, _1702588] : [-(c_List_Oconcat(_1702584, hAPP(hAPP(c_List_Oappend(tc_List_Olist(_1702584)), _1702586), _1702588)) = hAPP(hAPP(c_List_Oappend(_1702584), c_List_Oconcat(_1702584, _1702586)), c_List_Oconcat(_1702584, _1702588)))], (45947 ^ _780086) ^ [_1702638, _1702640] : [class_Orderings_Olinorder(_1702638), -(c_List_Olinorder__class_Osort__key(_1702638, _1702638, c_COMBI(_1702638), _1702640) = hAPP(c_List_Ofoldl(tc_List_Olist(_1702638), _1702638, hAPP(c_COMBC(_1702638, tc_List_Olist(_1702638), tc_List_Olist(_1702638)), c_List_Olinorder__class_Oinsort__key(_1702638, _1702638, c_COMBI(_1702638))), c_List_Olist_ONil(_1702638)), _1702640))], (45953 ^ _780086) ^ [_1702785, _1702787, _1702789] : [c_List_Oconcat(_1702785, _1702787) = c_List_Oconcat(_1702785, _1702789), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1702785))), _1702787) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1702785))), _1702789), 45963 ^ _780086 : [(45964 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1702785), tc_List_Olist(_1702785))), 45962 ^ [_1702785, _1702787, _1702789]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1702785), tc_List_Olist(_1702785))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1702785), tc_List_Olist(_1702785)), _1702787), _1702789)))))], (45966 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1702785), tc_List_Olist(_1702785), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1702785), tc_fun(tc_List_Olist(_1702785), tc_Nat_Onat), tc_fun(tc_List_Olist(_1702785), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1702785), tc_Nat_Onat), tc_fun(tc_List_Olist(_1702785), tc_HOL_Obool)), tc_List_Olist(_1702785)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1702785))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1702785)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1702785))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1702785)))), 45962 ^ [_1702785, _1702787, _1702789]))]], -(_1702787 = _1702789)], (45970 ^ _780086) ^ [_1703426, _1703428, _1703430] : [45972 ^ _780086 : [(45973 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1703426), tc_List_Olist(_1703426))), 45971 ^ [_1703426, _1703428, _1703430]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1703426), tc_List_Olist(_1703426))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1703426), tc_List_Olist(_1703426)), _1703428), _1703430)))))], (45975 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1703426), tc_List_Olist(_1703426), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1703426), tc_fun(tc_List_Olist(_1703426), tc_Nat_Onat), tc_fun(tc_List_Olist(_1703426), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1703426), tc_Nat_Onat), tc_fun(tc_List_Olist(_1703426), tc_HOL_Obool)), tc_List_Olist(_1703426)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1703426))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1703426)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1703426))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1703426)))), 45971 ^ [_1703426, _1703428, _1703430]))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1703426))), _1703428) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1703426))), _1703430), 45980 ^ _780086 : [(45981 ^ _780086) ^ [] : [c_List_Oconcat(_1703426, _1703428) = c_List_Oconcat(_1703426, _1703430), -(_1703428 = _1703430)], (45987 ^ _780086) ^ [] : [_1703428 = _1703430, -(c_List_Oconcat(_1703426, _1703428) = c_List_Oconcat(_1703426, _1703430))]]], (45993 ^ _780086) ^ [_1704153, _1704155, _1704157, _1704159] : [-(c_List_Oconcat(_1704153, hAPP(hAPP(c_List_Omap(_1704155, tc_List_Olist(_1704153)), hAPP(hAPP(c_COMBC(_1704155, tc_List_Olist(_1704153), tc_List_Olist(_1704153)), hAPP(hAPP(c_COMBB(_1704153, tc_fun(tc_List_Olist(_1704153), tc_List_Olist(_1704153)), _1704155), c_List_Olist_OCons(_1704153)), _1704157)), c_List_Olist_ONil(_1704153))), _1704159)) = hAPP(hAPP(c_List_Omap(_1704155, _1704153), _1704157), _1704159))], (45995 ^ _780086) ^ [_1704240, _1704242, _1704244] : [-(c_Enum_On__lists(_1704240, hAPP(c_Nat_OSuc, _1704242), _1704244) = c_List_Oconcat(tc_List_Olist(_1704240), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1704240), tc_List_Olist(tc_List_Olist(_1704240))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1704240), tc_List_Olist(_1704240), tc_List_Olist(tc_List_Olist(_1704240))), hAPP(hAPP(c_COMBB(tc_fun(_1704240, tc_List_Olist(_1704240)), tc_fun(tc_List_Olist(_1704240), tc_List_Olist(tc_List_Olist(_1704240))), tc_List_Olist(_1704240)), c_List_Omap(_1704240, tc_List_Olist(_1704240))), hAPP(c_COMBC(_1704240, tc_List_Olist(_1704240), tc_List_Olist(_1704240)), c_List_Olist_OCons(_1704240)))), _1704244)), c_Enum_On__lists(_1704240, _1704242, _1704244))))], (45997 ^ _780086) ^ [_1704360, _1704362, _1704364, _1704366] : [-(c_List_Otranspose(_1704360, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1704360)), hAPP(hAPP(c_List_Olist_OCons(_1704360), _1704362), _1704364)), _1704366)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1704360)), hAPP(hAPP(c_List_Olist_OCons(_1704360), _1704362), c_List_Oconcat(_1704360, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1704360), tc_List_Olist(_1704360)), c_List_Olist_Olist__case(tc_List_Olist(_1704360), _1704360, c_List_Olist_ONil(_1704360), hAPP(hAPP(c_COMBB(tc_List_Olist(_1704360), tc_fun(tc_List_Olist(_1704360), tc_List_Olist(_1704360)), _1704360), c_COMBK(tc_List_Olist(_1704360), tc_List_Olist(_1704360))), hAPP(hAPP(c_COMBC(_1704360, tc_List_Olist(_1704360), tc_List_Olist(_1704360)), c_List_Olist_OCons(_1704360)), c_List_Olist_ONil(_1704360))))), _1704366)))), c_List_Otranspose(_1704360, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1704360)), _1704364), c_List_Oconcat(tc_List_Olist(_1704360), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1704360), tc_List_Olist(tc_List_Olist(_1704360))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1704360)), _1704360, c_List_Olist_ONil(tc_List_Olist(_1704360)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1704360), tc_List_Olist(tc_List_Olist(_1704360))), _1704360), hAPP(hAPP(c_COMBC(tc_List_Olist(_1704360), tc_List_Olist(tc_List_Olist(_1704360)), tc_List_Olist(tc_List_Olist(_1704360))), c_List_Olist_OCons(tc_List_Olist(_1704360))), c_List_Olist_ONil(tc_List_Olist(_1704360)))))), _1704366))))))], (45999 ^ _780086) ^ [_1704586, _1704588] : [-(c_List_Oconcat(_1704586, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1704586), tc_List_Olist(_1704586)), c_List_Olist_Olist__case(tc_List_Olist(_1704586), _1704586, c_List_Olist_ONil(_1704586), hAPP(hAPP(c_COMBB(tc_List_Olist(_1704586), tc_fun(tc_List_Olist(_1704586), tc_List_Olist(_1704586)), _1704586), c_COMBK(tc_List_Olist(_1704586), tc_List_Olist(_1704586))), hAPP(hAPP(c_COMBC(_1704586, tc_List_Olist(_1704586), tc_List_Olist(_1704586)), c_List_Olist_OCons(_1704586)), c_List_Olist_ONil(_1704586))))), _1704588)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1704586), _1704586), c_List_Ohd(_1704586)), hAPP(c_List_Ofilter(tc_List_Olist(_1704586), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1704586)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1704586), tc_List_Olist(_1704586), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1704586)))), _1704588)))], (46001 ^ _780086) ^ [_1704729, _1704731, _1704733] : [-(hAPP(c_List_Ofilter(_1704729, _1704731), c_List_Oconcat(_1704729, _1704733)) = c_List_Oconcat(_1704729, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1704729), tc_List_Olist(_1704729)), c_List_Ofilter(_1704729, _1704731)), _1704733)))], (46003 ^ _780086) ^ [_1704784, _1704786, _1704788, _1704790, _1704792] : [class_Orderings_Olinorder(_1704784), -(hAPP(c_List_Ofilter(_1704786, _1704788), c_List_Olinorder__class_Osort__key(_1704786, _1704784, _1704790, _1704792)) = c_List_Olinorder__class_Osort__key(_1704786, _1704784, _1704790, hAPP(c_List_Ofilter(_1704786, _1704788), _1704792)))], (46009 ^ _780086) ^ [_1704909, _1704911, _1704913] : [hBOOL(hAPP(c_List_Odistinct(_1704909), _1704911)), -(hBOOL(hAPP(c_List_Odistinct(_1704909), hAPP(c_List_Ofilter(_1704909, _1704913), _1704911))))], (46015 ^ _780086) ^ [_1705016, _1705018, _1705020] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1705016, tc_HOL_Obool)), hAPP(c_List_Oset(_1705016), hAPP(c_List_Ofilter(_1705016, _1705018), _1705020))), hAPP(c_List_Oset(_1705016), _1705020))))], (46027 ^ _780086) ^ [_1705287, _1705289, _1705291] : [46029 ^ _780086 : [(46030 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1705287), 46028 ^ [_1705287, _1705289, _1705291]), hAPP(c_List_Oset(_1705287), _1705291))))], (46032 ^ _780086) ^ [] : [hBOOL(hAPP(_1705289, 46028 ^ [_1705287, _1705289, _1705291]))]], -(hAPP(c_List_Ofilter(_1705287, _1705289), _1705291) = _1705291)], (46017 ^ _780086) ^ [_1705087, _1705089, _1705091] : [hAPP(c_List_Ofilter(_1705087, _1705089), _1705091) = _1705091, 46020 ^ _780086 : [(46021 ^ _780086) ^ [_1705178] : [hBOOL(hAPP(hAPP(c_member(_1705087), _1705178), hAPP(c_List_Oset(_1705087), _1705091))), -(hBOOL(hAPP(_1705089, _1705178)))]]], (46036 ^ _780086) ^ [_1705479, _1705481, _1705483] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705479)), hAPP(c_List_Ofilter(_1705479, _1705481), _1705483))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705479)), hAPP(c_List_Ofilter(_1705479, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1705479), c_fNot), _1705481)), _1705483))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705479)), _1705483))], (46038 ^ _780086) ^ [_1705555, _1705557, _1705559] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705555)), hAPP(c_List_Ofilter(_1705555, _1705557), _1705559))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705555)), _1705559))))], (46040 ^ _780086) ^ [_1705607, _1705609, _1705611] : [-(hAPP(c_Product__Type_Ofst(tc_List_Olist(_1705607), tc_List_Olist(_1705607)), c_List_Opartition(_1705607, _1705609, _1705611)) = hAPP(c_List_Ofilter(_1705607, _1705609), _1705611))], (46042 ^ _780086) ^ [_1705654, _1705656, _1705658, _1705660] : [-(hAPP(c_List_Ofilter(_1705654, _1705656), hAPP(c_List_Ofilter(_1705654, _1705658), _1705660)) = hAPP(c_List_Ofilter(_1705654, hAPP(hAPP(c_COMBS(_1705654, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1705654), c_fconj), _1705658)), _1705656)), _1705660))], (46044 ^ _780086) ^ [_1705721, _1705723, _1705725, _1705727] : [-(hAPP(c_List_Ofilter(_1705721, _1705723), c_List_Oremove1(_1705721, _1705725, _1705727)) = c_List_Oremove1(_1705721, _1705725, hAPP(c_List_Ofilter(_1705721, _1705723), _1705727)))], (46046 ^ _780086) ^ [_1705766, _1705768, _1705770, _1705772] : [-(hBOOL(hAPP(_1705766, _1705768))), -(c_List_Oremove1(_1705770, _1705768, hAPP(c_List_Ofilter(_1705770, _1705766), _1705772)) = hAPP(c_List_Ofilter(_1705770, _1705766), _1705772))], (46052 ^ _780086) ^ [_1705824, _1705826, _1705828, _1705830, _1705832, _1705834] : [class_Orderings_Olinorder(_1705824), -(hBOOL(hAPP(_1705826, _1705828))), -(hAPP(c_List_Ofilter(_1705830, _1705826), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1705830, _1705824, _1705832), _1705828), _1705834)) = hAPP(c_List_Ofilter(_1705830, _1705826), _1705834))], (46062 ^ _780086) ^ [_1705970, _1705972, _1705974, _1705976, _1705978] : [-(hAPP(c_List_Ofilter(_1705970, _1705972), hAPP(hAPP(c_List_Omap(_1705974, _1705970), _1705976), _1705978)) = hAPP(hAPP(c_List_Omap(_1705974, _1705970), _1705976), hAPP(c_List_Ofilter(_1705974, hAPP(c_Fun_Ocomp(_1705970, tc_HOL_Obool, _1705974, _1705972), _1705976)), _1705978)))], (46064 ^ _780086) ^ [_1706039, _1706041] : [-(hAPP(c_List_Ofilter(_1706039, _1706041), c_List_Olist_ONil(_1706039)) = c_List_Olist_ONil(_1706039))], (46066 ^ _780086) ^ [_1706074] : [-(c_List_Otranspose(_1706074, c_List_Olist_ONil(tc_List_Olist(_1706074))) = c_List_Olist_ONil(tc_List_Olist(_1706074)))], (46068 ^ _780086) ^ [_1706123, _1706125, _1706127, _1706129] : [hBOOL(hAPP(_1706123, _1706125)), -(hAPP(c_List_Ofilter(_1706127, _1706123), hAPP(hAPP(c_List_Olist_OCons(_1706127), _1706125), _1706129)) = hAPP(hAPP(c_List_Olist_OCons(_1706127), _1706125), hAPP(c_List_Ofilter(_1706127, _1706123), _1706129)))], (46074 ^ _780086) ^ [_1706258, _1706260, _1706262, _1706264] : [-(hBOOL(hAPP(_1706258, _1706260))), -(hAPP(c_List_Ofilter(_1706262, _1706258), hAPP(hAPP(c_List_Olist_OCons(_1706262), _1706260), _1706264)) = hAPP(c_List_Ofilter(_1706262, _1706258), _1706264))], (46080 ^ _780086) ^ [_1706322, _1706324, _1706326, _1706328] : [-(hAPP(c_List_Ofilter(_1706322, _1706324), hAPP(hAPP(c_List_Oappend(_1706322), _1706326), _1706328)) = hAPP(hAPP(c_List_Oappend(_1706322), hAPP(c_List_Ofilter(_1706322, _1706324), _1706326)), hAPP(c_List_Ofilter(_1706322, _1706324), _1706328)))], (46092 ^ _780086) ^ [_1706608, _1706610, _1706612] : [46094 ^ _780086 : [(46095 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1706608), 46093 ^ [_1706608, _1706610, _1706612]), hAPP(c_List_Oset(_1706608), _1706612))))], (46097 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1706610, 46093 ^ [_1706608, _1706610, _1706612])))]], -(hAPP(c_List_Ofilter(_1706608, _1706610), _1706612) = c_List_Olist_ONil(_1706608))], (46082 ^ _780086) ^ [_1706403, _1706405, _1706407] : [hAPP(c_List_Ofilter(_1706403, _1706405), _1706407) = c_List_Olist_ONil(_1706403), 46085 ^ _780086 : [(46086 ^ _780086) ^ [_1706500] : [hBOOL(hAPP(hAPP(c_member(_1706403), _1706500), hAPP(c_List_Oset(_1706403), _1706407))), hBOOL(hAPP(_1706405, _1706500))]]], (46101 ^ _780086) ^ [_1706725, _1706727, _1706729] : [-(c_List_Oremdups(_1706725, hAPP(c_List_Ofilter(_1706725, _1706727), _1706729)) = hAPP(c_List_Ofilter(_1706725, _1706727), c_List_Oremdups(_1706725, _1706729)))], (46103 ^ _780086) ^ [_1706766, _1706768, _1706770, _1706772] : [-(hBOOL(hAPP(_1706766, _1706768))), -(hAPP(c_List_OremoveAll(_1706770, _1706768), hAPP(c_List_Ofilter(_1706770, _1706766), _1706772)) = hAPP(c_List_Ofilter(_1706770, _1706766), _1706772))], (46109 ^ _780086) ^ [_1706826, _1706828] : [-(c_List_OremoveAll(_1706826, _1706828) = c_List_Ofilter(_1706826, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1706826), c_fNot), hAPP(c_fequal, _1706828))))], (46111 ^ _780086) ^ [_1706870, _1706872, _1706874] : [-(hAPP(c_Product__Type_Osnd(tc_List_Olist(_1706870), tc_List_Olist(_1706870)), c_List_Opartition(_1706870, _1706872, _1706874)) = hAPP(c_List_Ofilter(_1706870, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1706870, c_fNot), _1706872)), _1706874))], (46113 ^ _780086) ^ [_1706925, _1706927] : [-(c_List_Otranspose(_1706925, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1706925)), c_List_Olist_ONil(_1706925)), _1706927)) = c_List_Otranspose(_1706925, _1706927))], (46115 ^ _780086) ^ [_1706968, _1706970, _1706972] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1706968), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1706970))), c_List_Otranspose(_1706970, _1706972)))), -(hAPP(hAPP(c_List_Onth(tc_List_Olist(_1706970)), c_List_Otranspose(_1706970, _1706972)), _1706968) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1706970), _1706970), hAPP(hAPP(c_COMBC(tc_List_Olist(_1706970), tc_Nat_Onat, _1706970), c_List_Onth(_1706970)), _1706968)), hAPP(c_List_Ofilter(tc_List_Olist(_1706970), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1706970)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1706968)), c_Nat_Osize__class_Osize(tc_List_Olist(_1706970)))), _1706972)))], (46121 ^ _780086) ^ [_1707211, _1707213, _1707215, _1707217] : [-(c_List_Otranspose(_1707211, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1707213), tc_List_Olist(_1707211)), hAPP(c_List_Omap(_1707213, _1707211), _1707215)), _1707217)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1707213), tc_List_Olist(_1707211)), hAPP(c_List_Omap(_1707213, _1707211), _1707215)), c_List_Otranspose(_1707213, _1707217)))], (46123 ^ _780086) ^ [_1707284, _1707286, _1707288] : [-(hAPP(c_List_Oset(_1707284), hAPP(c_List_Ofilter(_1707284, _1707286), _1707288)) = hAPP(c_Set_OCollect(_1707284), hAPP(hAPP(c_COMBS(_1707284, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1707284), c_fconj), hAPP(hAPP(c_COMBC(_1707284, tc_fun(_1707284, tc_HOL_Obool), tc_HOL_Obool), c_member(_1707284)), hAPP(c_List_Oset(_1707284), _1707288)))), _1707286)))], (46125 ^ _780086) ^ [_1707367, _1707369, _1707371, _1707373, _1707375] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707367)), hAPP(c_List_Ofilter(_1707367, _1707369), hAPP(hAPP(c_List_Omap(_1707371, _1707367), _1707373), _1707375))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707371)), hAPP(c_List_Ofilter(_1707371, hAPP(c_Fun_Ocomp(_1707367, tc_HOL_Obool, _1707371, _1707369), _1707373)), _1707375)))], (46127 ^ _780086) ^ [_1707441, _1707443, _1707445, _1707447] : [hBOOL(hAPP(hAPP(c_member(_1707441), _1707443), hAPP(c_List_Oset(_1707441), _1707445))), -(hBOOL(hAPP(_1707447, _1707443))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707441)), hAPP(c_List_Ofilter(_1707441, _1707447), _1707445))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707441)), _1707445))))], (46137 ^ _780086) ^ [_1707615, _1707617, _1707619] : [-(c_List_Opartition(_1707615, _1707617, _1707619) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1707615), tc_List_Olist(_1707615)), hAPP(c_List_Ofilter(_1707615, _1707617), _1707619)), hAPP(c_List_Ofilter(_1707615, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1707615, c_fNot), _1707617)), _1707619)))], (46139 ^ _780086) ^ [_1707679, _1707681, _1707683] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1707679, tc_HOL_Obool)), hAPP(c_List_Oset(_1707679), _1707681)), hAPP(hAPP(c_Set_Oinsert(_1707679), _1707683), c_Orderings_Obot__class_Obot(tc_fun(_1707679, tc_HOL_Obool)))) = hAPP(c_List_Oset(_1707679), hAPP(c_List_Ofilter(_1707679, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1707679), c_fNot), hAPP(hAPP(c_COMBC(_1707679, _1707679, tc_HOL_Obool), c_fequal), _1707683))), _1707681)))], (46141 ^ _780086) ^ [_1707766, _1707768, _1707770] : [hBOOL(hAPP(c_List_Odistinct(_1707766), _1707768)), -(hAPP(c_List_Ofilter(_1707766, hAPP(hAPP(c_COMBC(_1707766, tc_fun(_1707766, tc_HOL_Obool), tc_HOL_Obool), c_member(_1707766)), hAPP(c_List_Oset(_1707766), c_List_Osublist(_1707766, _1707768, _1707770)))), _1707768) = c_List_Osublist(_1707766, _1707768, _1707770))], (46157 ^ _780086) ^ [_1708146, _1708148] : [46159 ^ _780086 : [(46160 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1708146)), 46158 ^ [_1708146, _1708148]), hAPP(c_List_Oset(tc_List_Olist(_1708146)), _1708148))))], (46162 ^ _780086) ^ [] : [46158 ^ [_1708146, _1708148] = c_List_Olist_ONil(_1708146)]], -(c_List_Otranspose(_1708146, _1708148) = c_List_Olist_ONil(tc_List_Olist(_1708146)))], (46147 ^ _780086) ^ [_1707936, _1707938] : [c_List_Otranspose(_1707936, _1707938) = c_List_Olist_ONil(tc_List_Olist(_1707936)), 46150 ^ _780086 : [(46151 ^ _780086) ^ [_1708031] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1707936)), _1708031), hAPP(c_List_Oset(tc_List_Olist(_1707936)), _1707938))), -(_1708031 = c_List_Olist_ONil(_1707936))]]], (46166 ^ _780086) ^ [_1708341, _1708343, _1708345] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1708341)), hAPP(c_List_Ofilter(_1708341, _1708343), _1708345)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_Set_OCollect(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1708341)), _1708345)))), hAPP(hAPP(c_COMBB(_1708341, tc_HOL_Obool, tc_Nat_Onat), _1708343), hAPP(c_List_Onth(_1708341), _1708345))))))], (46168 ^ _780086) ^ [_1708421, _1708423] : [-(c_List_Oconcat(tc_List_Olist(_1708421), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1708421), tc_List_Olist(tc_List_Olist(_1708421))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1708421)), _1708421, c_List_Olist_ONil(tc_List_Olist(_1708421)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1708421), tc_List_Olist(tc_List_Olist(_1708421))), _1708421), hAPP(hAPP(c_COMBC(tc_List_Olist(_1708421), tc_List_Olist(tc_List_Olist(_1708421)), tc_List_Olist(tc_List_Olist(_1708421))), c_List_Olist_OCons(tc_List_Olist(_1708421))), c_List_Olist_ONil(tc_List_Olist(_1708421)))))), _1708423)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1708421), tc_List_Olist(_1708421)), c_List_Otl(_1708421)), hAPP(c_List_Ofilter(tc_List_Olist(_1708421), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1708421)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1708421), tc_List_Olist(_1708421), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1708421)))), _1708423)))], (46170 ^ _780086) ^ [_1708573, _1708575, _1708577, _1708579] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1708573)), c_List_Otranspose__rel(_1708573)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1708573)), hAPP(hAPP(c_List_Olist_OCons(_1708573), _1708575), _1708577)), _1708579))), -(c_List_Otranspose(_1708573, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1708573)), hAPP(hAPP(c_List_Olist_OCons(_1708573), _1708575), _1708577)), _1708579)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1708573)), hAPP(hAPP(c_List_Olist_OCons(_1708573), _1708575), c_List_Oconcat(_1708573, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1708573), tc_List_Olist(_1708573)), c_List_Olist_Olist__case(tc_List_Olist(_1708573), _1708573, c_List_Olist_ONil(_1708573), hAPP(hAPP(c_COMBB(tc_List_Olist(_1708573), tc_fun(tc_List_Olist(_1708573), tc_List_Olist(_1708573)), _1708573), c_COMBK(tc_List_Olist(_1708573), tc_List_Olist(_1708573))), hAPP(hAPP(c_COMBC(_1708573, tc_List_Olist(_1708573), tc_List_Olist(_1708573)), c_List_Olist_OCons(_1708573)), c_List_Olist_ONil(_1708573))))), _1708579)))), c_List_Otranspose(_1708573, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1708573)), _1708577), c_List_Oconcat(tc_List_Olist(_1708573), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1708573), tc_List_Olist(tc_List_Olist(_1708573))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1708573)), _1708573, c_List_Olist_ONil(tc_List_Olist(_1708573)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1708573), tc_List_Olist(tc_List_Olist(_1708573))), _1708573), hAPP(hAPP(c_COMBC(tc_List_Olist(_1708573), tc_List_Olist(tc_List_Olist(_1708573)), tc_List_Olist(tc_List_Olist(_1708573))), c_List_Olist_OCons(tc_List_Olist(_1708573))), c_List_Olist_ONil(tc_List_Olist(_1708573)))))), _1708579))))))], (46176 ^ _780086) ^ [_1709106, _1709108] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1709106)), c_List_Otranspose__rel(_1709106)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1709106)), c_List_Olist_ONil(_1709106)), _1709108))), -(c_List_Otranspose(_1709106, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1709106)), c_List_Olist_ONil(_1709106)), _1709108)) = c_List_Otranspose(_1709106, _1709108))], (46182 ^ _780086) ^ [_1709265, _1709267, _1709269, _1709271] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1709265, tc_Nat_Onat), _1709265), c_Product__Type_Ofst(_1709265, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1709265, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1709265, tc_Nat_Onat)), _1709267), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_prod(_1709265, tc_Nat_Onat)), c_Nat_OSuc), c_Product__Type_Osnd(_1709265, tc_Nat_Onat)))), hAPP(hAPP(c_List_Ozip(_1709265, tc_Nat_Onat), _1709269), _1709271))) = hAPP(hAPP(c_List_Omap(tc_prod(_1709265, tc_Nat_Onat), _1709265), c_Product__Type_Ofst(_1709265, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1709265, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1709265, tc_Nat_Onat)), _1709267), c_Product__Type_Osnd(_1709265, tc_Nat_Onat))), hAPP(hAPP(c_List_Ozip(_1709265, tc_Nat_Onat), _1709269), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), _1709271)))))], (46184 ^ _780086) ^ [_1709408, _1709410] : [-(c_Random_Oselect__weight(_1709408, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1709408), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1709408, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1709408, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1709408)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1709410)) = c_Random_Oselect__weight(_1709408, _1709410))], (46186 ^ _780086) ^ [_1709471, _1709473] : [-(c_Random_Opick(_1709471, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1709471), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1709471, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1709471, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1709471)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1709473)) = c_Random_Opick(_1709471, _1709473))], (46188 ^ _780086) ^ [_1709534] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1709534)), c_List_Otranspose__rel(_1709534)), c_List_Olist_ONil(tc_List_Olist(_1709534)))), -(c_List_Otranspose(_1709534, c_List_Olist_ONil(tc_List_Olist(_1709534))) = c_List_Olist_ONil(tc_List_Olist(_1709534)))], (46194 ^ _780086) ^ [_1709661, _1709663] : [-(c_List_Ofoldr(tc_List_Olist(_1709661), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1709661)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1709661))), c_List_Otranspose(_1709661, _1709663), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1709661))), hAPP(c_List_Ofilter(tc_List_Olist(_1709661), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1709661)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1709661), tc_List_Olist(_1709661), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1709661)))), _1709663)))], (46196 ^ _780086) ^ [_1709758, _1709760, _1709762, _1709764] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709758)), _1709760))), c_List_Ofoldr(tc_List_Olist(_1709762), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1709762)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1709762))), _1709764, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709758)), _1709760)), c_List_Ofoldr(tc_List_Olist(_1709762), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1709762)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1709762), tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1709762)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1709762)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_List_Ofilter(tc_List_Olist(_1709762), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1709762)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1709762), tc_List_Olist(_1709762), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1709762)))), _1709764), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (46198 ^ _780086) ^ [_1709927, _1709929, _1709931, _1709933] : [-(c_List_Ofoldr(_1709927, _1709929, _1709931, c_List_Olist_ONil(_1709927), _1709933) = _1709933)], (46200 ^ _780086) ^ [_1709964, _1709966, _1709968, _1709970, _1709972, _1709974] : [-(c_List_Ofoldr(_1709964, _1709966, _1709968, hAPP(hAPP(c_List_Olist_OCons(_1709964), _1709970), _1709972), _1709974) = hAPP(hAPP(_1709968, _1709970), c_List_Ofoldr(_1709964, _1709966, _1709968, _1709972, _1709974)))], (46202 ^ _780086) ^ [_1710023, _1710025, _1710027, _1710029, _1710031, _1710033] : [-(c_List_Ofoldr(_1710023, _1710025, _1710027, hAPP(hAPP(c_List_Oappend(_1710023), _1710029), _1710031), _1710033) = c_List_Ofoldr(_1710023, _1710025, _1710027, _1710029, c_List_Ofoldr(_1710023, _1710025, _1710027, _1710031, _1710033)))], (46204 ^ _780086) ^ [_1710082, _1710084, _1710086] : [class_Groups_Oab__semigroup__add(_1710082), -(c_List_Ofoldr(_1710082, _1710082, c_Groups_Oplus__class_Oplus(_1710082), _1710084, _1710086) = hAPP(c_List_Ofoldl(_1710082, _1710082, c_Groups_Oplus__class_Oplus(_1710082), _1710086), _1710084))], (46210 ^ _780086) ^ [_1710195, _1710197, _1710199, _1710201, _1710203, _1710205, _1710207] : [-(c_List_Ofoldr(_1710195, _1710197, _1710199, hAPP(hAPP(c_List_Omap(_1710201, _1710195), _1710203), _1710205), _1710207) = c_List_Ofoldr(_1710201, _1710197, hAPP(c_Fun_Ocomp(_1710195, tc_fun(_1710197, _1710197), _1710201, _1710199), _1710203), _1710205, _1710207))], (46212 ^ _780086) ^ [_1710262, _1710264] : [class_Groups_Omonoid__add(_1710262), -(hAPP(c_List_Ofoldl(_1710262, _1710262, c_Groups_Oplus__class_Oplus(_1710262), c_Groups_Ozero__class_Ozero(_1710262)), _1710264) = c_List_Ofoldr(_1710262, _1710262, c_Groups_Oplus__class_Oplus(_1710262), _1710264, c_Groups_Ozero__class_Ozero(_1710262)))], (46218 ^ _780086) ^ [_1710381, _1710383, _1710385] : [class_Groups_Omonoid__add(_1710381), -(hAPP(c_List_Ofoldl(_1710381, _1710381, c_Groups_Oplus__class_Oplus(_1710381), _1710383), _1710385) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1710381), _1710383), c_List_Ofoldr(_1710381, _1710381, c_Groups_Oplus__class_Oplus(_1710381), _1710385, c_Groups_Ozero__class_Ozero(_1710381))))], (46224 ^ _780086) ^ [_1710514, _1710516] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1710514))), c_List_Otranspose(_1710514, _1710516)) = c_List_Ofoldr(tc_List_Olist(_1710514), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1710514)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1710514))), _1710516, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (46226 ^ _780086) ^ [_1710575, _1710577, _1710579] : [-(c_List_Osublist(_1710575, _1710577, _1710579) = hAPP(hAPP(c_List_Omap(tc_prod(_1710575, tc_Nat_Onat), _1710575), c_Product__Type_Ofst(_1710575, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1710575, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1710575, tc_Nat_Onat), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), tc_prod(_1710575, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1710575, tc_Nat_Onat))), _1710579)), hAPP(hAPP(c_List_Ozip(_1710575, tc_Nat_Onat), _1710577), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710575)), _1710577))))))], (46228 ^ _780086) ^ [_1710678, _1710680, _1710682, _1710684] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1710678, tc_Nat_Onat), _1710678), c_Product__Type_Ofst(_1710678, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1710678, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1710678, tc_Nat_Onat), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), tc_prod(_1710678, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1710678, tc_Nat_Onat))), _1710680)), hAPP(hAPP(c_List_Ozip(_1710678, tc_Nat_Onat), _1710682), c_List_Oupt(_1710684, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1710684), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710678)), _1710682)))))) = hAPP(hAPP(c_List_Omap(tc_prod(_1710678, tc_Nat_Onat), _1710678), c_Product__Type_Ofst(_1710678, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1710678, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1710678, tc_Nat_Onat), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), tc_prod(_1710678, tc_Nat_Onat)), c_member(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1710678, tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_prod(_1710678, tc_Nat_Onat)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Product__Type_Osnd(_1710678, tc_Nat_Onat))), _1710684))), _1710680)), hAPP(hAPP(c_List_Ozip(_1710678, tc_Nat_Onat), _1710682), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710678)), _1710682))))))], (46230 ^ _780086) ^ [_1710883, _1710885] : [-(hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1710883, _1710885)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1710883), _1710885))], (46232 ^ _780086) ^ [_1710920, _1710922] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1710920), _1710922) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1710920, _1710922)))], (46234 ^ _780086) ^ [_1710957, _1710959] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1710957), _1710959)), -(c_List_Oupt(_1710957, hAPP(c_Nat_OSuc, _1710959)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1710957, _1710959)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1710959), c_List_Olist_ONil(tc_Nat_Onat))))], (46240 ^ _780086) ^ [_1711095, _1711097] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1711095), _1711097)), -(c_List_Oupt(_1711095, hAPP(c_Nat_OSuc, _1711097)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1711095, _1711097)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1711097), c_List_Olist_ONil(tc_Nat_Onat))))], (46246 ^ _780086) ^ [_1711218, _1711220] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1711218), _1711220))), -(c_List_Oupt(_1711218, hAPP(c_Nat_OSuc, _1711220)) = c_List_Olist_ONil(tc_Nat_Onat))], (46252 ^ _780086) ^ [_1711267, _1711269, _1711271] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1711267), _1711269)), -(c_List_Oupt(_1711267, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1711269), _1711271)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1711267, _1711269)), c_List_Oupt(_1711269, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1711269), _1711271))))], (46258 ^ _780086) ^ [_1711419, _1711421] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1711419), _1711421)), -(c_List_Oupt(_1711419, _1711421) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1711419), c_List_Oupt(hAPP(c_Nat_OSuc, _1711419), _1711421)))], (46264 ^ _780086) ^ [_1711530, _1711532] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1711530), _1711532))), -(c_List_Oupt(_1711530, _1711532) = c_List_Olist_ONil(tc_Nat_Onat))], (46270 ^ _780086) ^ [_1711576, _1711578] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1711576), _1711578)), -(c_List_Oupt(_1711576, _1711578) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1711576), c_List_Oupt(hAPP(c_Nat_OSuc, _1711576), _1711578)))], (46286 ^ _780086) ^ [_1711810, _1711812] : [46287 ^ _780086 : [(46288 ^ _780086) ^ [] : [_1711812 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (46290 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1711812), _1711810))]], -(c_List_Oupt(_1711810, _1711812) = c_List_Olist_ONil(tc_Nat_Onat))], (46276 ^ _780086) ^ [_1711708, _1711710] : [c_List_Oupt(_1711708, _1711710) = c_List_Olist_ONil(tc_Nat_Onat), -(_1711710 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1711710), _1711708)))], (46294 ^ _780086) ^ [_1711943, _1711945] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1711943), _1711945)), -(c_List_Oupt(_1711945, _1711943) = c_List_Olist_ONil(tc_Nat_Onat))], (46300 ^ _780086) ^ [_1712036] : [-(c_List_Oupt(_1712036, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat))], (46302 ^ _780086) ^ [_1712062, _1712064, _1712066] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1712062), _1712064)), _1712066)), -(hAPP(hAPP(c_List_Otake(tc_Nat_Onat), _1712064), c_List_Oupt(_1712062, _1712066)) = c_List_Oupt(_1712062, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1712062), _1712064)))], (46308 ^ _780086) ^ [_1712199, _1712201] : [-(c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1712199), _1712201)) = c_List_Oupt(_1712199, _1712201))], (46310 ^ _780086) ^ [_1712236, _1712238] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1712236), _1712238)), -(hAPP(c_List_Ohd(tc_Nat_Onat), c_List_Oupt(_1712236, _1712238)) = _1712236)], (46316 ^ _780086) ^ [_1712335, _1712337, _1712339] : [-(hAPP(hAPP(c_List_Odrop(tc_Nat_Onat), _1712335), c_List_Oupt(_1712337, _1712339)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1712337), _1712335), _1712339))], (46318 ^ _780086) ^ [_1712380, _1712382] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat), c_List_Oupt(_1712380, _1712382))))], (46320 ^ _780086) ^ [_1712410, _1712412] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), c_List_Oupt(_1712410, _1712412)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1712412), _1712410))], (46322 ^ _780086) ^ [_1712456, _1712458] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1712456)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1712458))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1712456), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1712458)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1712456)), c_List_Oupt(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1712456)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1712458))))], (46328 ^ _780086) ^ [_1712609, _1712611] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1712609)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1712611)))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1712609), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1712611)) = c_List_Olist_ONil(tc_Nat_Onat))], (46334 ^ _780086) ^ [_1712688, _1712690, _1712692, _1712694] : [c_List_Oupt(_1712688, _1712690) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1712692), _1712694), 46337 ^ _780086 : [(46338 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1712688), _1712690)))], (46340 ^ _780086) ^ [] : [-(_1712688 = _1712692)], (46342 ^ _780086) ^ [] : [-(c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1712688), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1712690) = _1712694)]]], (46344 ^ _780086) ^ [_1712861, _1712863, _1712865, _1712867] : [-(c_List_Oupt(_1712861, _1712863) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1712865), _1712867)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1712861), _1712863)), _1712861 = _1712865, c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1712861), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1712863) = _1712867], (46358 ^ _780086) ^ [_1713102, _1713104] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1713102), _1713104)), -(c_List_Olast(tc_Nat_Onat, c_List_Oupt(_1713102, _1713104)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1713104), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (46364 ^ _780086) ^ [_1713213, _1713215] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), c_List_Oupt(_1713213, _1713215)) = c_List_Oupt(hAPP(c_Nat_OSuc, _1713213), hAPP(c_Nat_OSuc, _1713215)))], (46366 ^ _780086) ^ [_1713253, _1713255] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1713253, _1713255) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1713253, hAPP(c_Nat_OSuc, _1713255))))], (46368 ^ _780086) ^ [_1713291] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1713291) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1713291)))], (46370 ^ _780086) ^ [_1713323, _1713325, _1713327] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1713323), _1713325)), _1713327)), -(hAPP(hAPP(c_List_Onth(tc_Nat_Onat), c_List_Oupt(_1713323, _1713327)), _1713325) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1713323), _1713325))], (46376 ^ _780086) ^ [_1713454, _1713456] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1713454, _1713456) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1713454), hAPP(c_Nat_OSuc, _1713456))))], (46378 ^ _780086) ^ [_1713495, _1713497] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1713495, _1713497) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1713495), _1713497)))], (46380 ^ _780086) ^ [_1713533] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1713533) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1713533))))], (46382 ^ _780086) ^ [_1713568, _1713570] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1713568), hAPP(c_List_Onth(_1713568), _1713570)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1713568)), _1713570))) = _1713570)], (46384 ^ _780086) ^ [_1713617, _1713619, _1713621, _1713623] : [class_Groups_Ocomm__monoid__add(_1713617), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1713617), _1713619), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1713621, _1713623))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1713617), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1713617), _1713619), c_List_Oupt(_1713621, _1713623))))], (46390 ^ _780086) ^ [_1713760, _1713762, _1713764, _1713766] : [class_Groups_Ocomm__monoid__add(_1713760), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1713760), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1713760), _1713762), c_List_Oupt(_1713764, _1713766))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1713760), _1713762), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1713764, _1713766))))], (46396 ^ _780086) ^ [_1713903, _1713905, _1713907, _1713909, _1713911] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1713903), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1713905), _1713907))), -(hAPP(hAPP(c_List_Onth(_1713909), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1713909), _1713911), c_List_Oupt(_1713907, _1713905))), _1713903) = hAPP(_1713911, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1713907), _1713903)))], (46402 ^ _780086) ^ [_1714066, _1714068, _1714070] : [46403 ^ _780086 : [(46404 ^ _780086) ^ [] : [-(_1714066 = c_List_Olist_ONil(tc_List_Olist(_1714068)))], (46406 ^ _780086) ^ [] : [_1714070 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], 46410 ^ _780086 : [(46411 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46409 ^ [_1714066, _1714068, _1714070]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1714068))), _1714066))))], (46413 ^ _780086) ^ [] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1714068)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1714068)), _1714066), 46409 ^ [_1714066, _1714068, _1714070])) = _1714070]], -(c_List_Otranspose(_1714068, _1714066) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_List_Olist(_1714068)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1714068)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, _1714068), tc_fun(tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1714068)), tc_Nat_Onat), c_List_Omap(tc_Nat_Onat, _1714068)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, _1714068), hAPP(hAPP(c_COMBB(tc_List_Olist(_1714068), tc_fun(tc_Nat_Onat, _1714068), tc_Nat_Onat), c_List_Onth(_1714068)), hAPP(c_List_Onth(tc_List_Olist(_1714068)), _1714066))))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1714068))), _1714066)))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1714070)))], (46417 ^ _780086) ^ [_1714576, _1714578, _1714580, _1714582, _1714584] : [class_Orderings_Olinorder(_1714576), hBOOL(hAPP(hAPP(c_member(_1714578), _1714580), hAPP(c_List_Oset(_1714578), _1714582))), c_List_Olinorder__class_Osorted(_1714576, hAPP(hAPP(c_List_Omap(_1714578, _1714576), _1714584), _1714582)), hAPP(c_List_Ohd(_1714578), hAPP(c_List_Ofilter(_1714578, hAPP(hAPP(c_COMBB(_1714576, tc_HOL_Obool, _1714578), hAPP(c_fequal, hAPP(_1714584, _1714580))), _1714584)), _1714582)) = _1714580, -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1714578, _1714576, _1714584), _1714580), c_List_Oremove1(_1714578, _1714580, _1714582)) = _1714582)], (46435 ^ _780086) ^ [_1714955] : [class_Orderings_Olinorder(_1714955), -(c_List_Olinorder__class_Osorted(_1714955, c_List_Olist_ONil(_1714955)))], (46441 ^ _780086) ^ [_1715032, _1715034] : [class_Orderings_Olinorder(_1715032), -(c_List_Olinorder__class_Osorted(_1715032, hAPP(hAPP(c_List_Olist_OCons(_1715032), _1715034), c_List_Olist_ONil(_1715032))))], (46447 ^ _780086) ^ [_1715127, _1715129] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, c_List_Oupt(_1715127, _1715129)))], (46449 ^ _780086) ^ [_1715155, _1715157] : [class_Orderings_Olinorder(_1715155), -(c_List_Olinorder__class_Osorted(_1715155, c_List_Olinorder__class_Osort__key(_1715155, _1715155, c_COMBI(_1715155), _1715157)))], (46455 ^ _780086) ^ [_1715244, _1715246, _1715248] : [class_Orderings_Olinorder(_1715244), c_List_Olinorder__class_Osorted(_1715244, _1715246), -(c_List_Olinorder__class_Osorted(_1715244, c_List_Olinorder__class_Oinsort__insert__key(_1715244, _1715244, c_COMBI(_1715244), _1715248, _1715246)))], (46465 ^ _780086) ^ [_1715391, _1715393, _1715395] : [class_Orderings_Olinorder(_1715391), c_List_Olinorder__class_Osorted(_1715391, _1715393), -(c_List_Olinorder__class_Osorted(_1715391, hAPP(hAPP(c_List_Odrop(_1715391), _1715395), _1715393)))], (46475 ^ _780086) ^ [_1715538, _1715540] : [-(c_List_Olinorder__class_Osorted(tc_Int_Oint, c_List_Oupto(_1715538, _1715540)))], (46477 ^ _780086) ^ [_1715566, _1715568, _1715570] : [class_Orderings_Olinorder(_1715566), c_List_Olinorder__class_Osorted(_1715566, _1715568), -(c_List_Olinorder__class_Osorted(_1715566, hAPP(hAPP(c_List_Otake(_1715566), _1715570), _1715568)))], (46487 ^ _780086) ^ [_1715713, _1715715, _1715717] : [class_Orderings_Olinorder(_1715713), c_List_Olinorder__class_Osorted(_1715713, _1715715), -(c_List_Olinorder__class_Osorted(_1715713, c_List_Oremove1(_1715713, _1715717, _1715715)))], (46497 ^ _780086) ^ [_1715852, _1715854] : [class_Orderings_Olinorder(_1715852), c_List_Olinorder__class_Osorted(_1715852, _1715854), -(c_List_Olinorder__class_Osorted(_1715852, hAPP(c_List_Otl(_1715852), _1715854)))], (46507 ^ _780086) ^ [_1715989, _1715991, _1715993] : [class_Orderings_Olinorder(_1715989), 46510 ^ _780086 : [(46511 ^ _780086) ^ [] : [c_List_Olinorder__class_Osorted(_1715989, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1715989, _1715989, c_COMBI(_1715989)), _1715991), _1715993)), -(c_List_Olinorder__class_Osorted(_1715989, _1715993))], (46517 ^ _780086) ^ [] : [c_List_Olinorder__class_Osorted(_1715989, _1715993), -(c_List_Olinorder__class_Osorted(_1715989, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1715989, _1715989, c_COMBI(_1715989)), _1715991), _1715993)))]]], (46523 ^ _780086) ^ [_1716236, _1716238] : [class_Orderings_Olinorder(_1716236), -(_1716238 = c_List_Olist_ONil(_1716236)), c_List_Olinorder__class_Osorted(_1716236, _1716238), -(c_List_Olinorder__class_Osorted(_1716236, c_List_Obutlast(_1716236, _1716238)))], (46537 ^ _780086) ^ [_1716428] : [class_Orderings_Olinorder(_1716428), -(c_List_Olinorder__class_Osorted(_1716428, c_List_Olist_ONil(_1716428)))], (46543 ^ _780086) ^ [_1716505, _1716507, _1716509, _1716511] : [class_Orderings_Olinorder(_1716505), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1716505), _1716507), _1716509)), c_List_Olinorder__class_Osorted(_1716505, hAPP(hAPP(c_List_Olist_OCons(_1716505), _1716509), _1716511)), -(c_List_Olinorder__class_Osorted(_1716505, hAPP(hAPP(c_List_Olist_OCons(_1716505), _1716507), hAPP(hAPP(c_List_Olist_OCons(_1716505), _1716509), _1716511))))], (46557 ^ _780086) ^ [_1716758, _1716760, _1716762, _1716764] : [class_Orderings_Olinorder(_1716758), 46560 ^ _780086 : [(46561 ^ _780086) ^ [] : [c_List_Olinorder__class_Osorted(_1716758, hAPP(hAPP(c_List_Olist_OCons(_1716758), _1716760), hAPP(hAPP(c_List_Olist_OCons(_1716758), _1716762), _1716764))), 46564 ^ _780086 : [(46565 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1716758), _1716760), _1716762)))], (46567 ^ _780086) ^ [] : [-(c_List_Olinorder__class_Osorted(_1716758, hAPP(hAPP(c_List_Olist_OCons(_1716758), _1716762), _1716764)))]]], (46569 ^ _780086) ^ [] : [-(c_List_Olinorder__class_Osorted(_1716758, hAPP(hAPP(c_List_Olist_OCons(_1716758), _1716760), hAPP(hAPP(c_List_Olist_OCons(_1716758), _1716762), _1716764)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1716758), _1716760), _1716762)), c_List_Olinorder__class_Osorted(_1716758, hAPP(hAPP(c_List_Olist_OCons(_1716758), _1716762), _1716764))]]], (46579 ^ _780086) ^ [_1717144, _1717146] : [class_Orderings_Olinorder(_1717144), c_List_Olinorder__class_Osorted(_1717144, _1717146), -(c_List_Olinorder__class_Osorted(_1717144, c_List_Oremdups(_1717144, _1717146)))], (46589 ^ _780086) ^ [_1717277, _1717279, _1717281] : [class_Orderings_Olinorder(_1717277), c_List_Olinorder__class_Osorted(_1717277, _1717279), hBOOL(hAPP(c_List_Odistinct(_1717277), _1717279)), c_List_Olinorder__class_Osorted(_1717277, _1717281), hBOOL(hAPP(c_List_Odistinct(_1717277), _1717281)), hAPP(c_List_Oset(_1717277), _1717279) = hAPP(c_List_Oset(_1717277), _1717281), -(_1717279 = _1717281)], (46615 ^ _780086) ^ [_1717660, _1717662, _1717664, _1717666] : [class_Orderings_Olinorder(_1717660), -(c_List_Olinorder__class_Osorted(_1717660, hAPP(hAPP(c_List_Omap(_1717662, _1717660), _1717664), c_List_Olinorder__class_Osort__key(_1717662, _1717660, _1717664, _1717666))))], (46621 ^ _780086) ^ [_1717767, _1717769, _1717771, _1717773, _1717775] : [class_Orderings_Olinorder(_1717767), c_List_Olinorder__class_Osorted(_1717767, hAPP(hAPP(c_List_Omap(_1717769, _1717767), _1717771), _1717773)), -(c_List_Olinorder__class_Osorted(_1717767, hAPP(hAPP(c_List_Omap(_1717769, _1717767), _1717771), c_List_Olinorder__class_Oinsort__insert__key(_1717769, _1717767, _1717771, _1717775, _1717773))))], (46631 ^ _780086) ^ [_1717954, _1717956, _1717958, _1717960, _1717962] : [class_Orderings_Olinorder(_1717954), c_List_Olinorder__class_Osorted(_1717954, hAPP(hAPP(c_List_Omap(_1717956, _1717954), _1717958), _1717960)), -(c_List_Olinorder__class_Osorted(_1717954, hAPP(hAPP(c_List_Omap(_1717956, _1717954), _1717958), c_List_Oremove1(_1717956, _1717962, _1717960))))], (46641 ^ _780086) ^ [_1718137, _1718139, _1718141, _1718143, _1718145] : [class_Orderings_Olinorder(_1718137), 46644 ^ _780086 : [(46645 ^ _780086) ^ [] : [c_List_Olinorder__class_Osorted(_1718137, hAPP(hAPP(c_List_Omap(_1718139, _1718137), _1718141), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1718139, _1718137, _1718141), _1718143), _1718145))), -(c_List_Olinorder__class_Osorted(_1718137, hAPP(hAPP(c_List_Omap(_1718139, _1718137), _1718141), _1718145)))], (46651 ^ _780086) ^ [] : [c_List_Olinorder__class_Osorted(_1718137, hAPP(hAPP(c_List_Omap(_1718139, _1718137), _1718141), _1718145)), -(c_List_Olinorder__class_Osorted(_1718137, hAPP(hAPP(c_List_Omap(_1718139, _1718137), _1718141), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1718139, _1718137, _1718141), _1718143), _1718145))))]]], (46657 ^ _780086) ^ [_1718444, _1718446, _1718448, _1718450, _1718452] : [class_Orderings_Olinorder(_1718444), c_List_Olinorder__class_Osorted(_1718444, hAPP(hAPP(c_List_Omap(_1718446, _1718444), _1718448), _1718450)), -(c_List_Olinorder__class_Osorted(_1718444, hAPP(hAPP(c_List_Omap(_1718446, _1718444), _1718448), hAPP(c_List_Ofilter(_1718446, _1718452), _1718450))))], (46667 ^ _780086) ^ [_1718631, _1718633, _1718635, _1718637, _1718639] : [class_Orderings_Olinorder(_1718631), -(c_List_Olinorder__class_Osorted(_1718631, hAPP(hAPP(c_List_Omap(_1718633, _1718631), _1718635), hAPP(c_List_Ofilter(_1718633, hAPP(hAPP(c_COMBC(_1718633, _1718631, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1718631, tc_fun(_1718631, tc_HOL_Obool), _1718633), c_fequal), _1718635)), hAPP(_1718637, _1718639))), _1718639))))], (46673 ^ _780086) ^ [_1718794, _1718796, _1718798] : [class_Orderings_Olinorder(_1718794), -(c_List_Olinorder__class_Osorted(_1718794, hAPP(c_List_Ofilter(_1718794, hAPP(hAPP(c_COMBC(_1718794, _1718794, tc_HOL_Obool), c_fequal), hAPP(_1718796, _1718798))), _1718798)))], (46679 ^ _780086) ^ [_1718909, _1718911, _1718913] : [class_Orderings_Olinorder(_1718909), 46682 ^ _780086 : [(46683 ^ _780086) ^ [] : [c_List_Olinorder__class_Osorted(_1718909, hAPP(hAPP(c_List_Olist_OCons(_1718909), _1718911), _1718913)), 46686 ^ _780086 : [(46687 ^ _780086) ^ [] : [-(c_List_Olinorder__class_Osorted(_1718909, _1718913))], (46689 ^ _780086) ^ [_1719095] : [hBOOL(hAPP(hAPP(c_member(_1718909), _1719095), hAPP(c_List_Oset(_1718909), _1718913))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1718909), _1718911), _1719095)))]]], (46695 ^ _780086) ^ [] : [-(c_List_Olinorder__class_Osorted(_1718909, hAPP(hAPP(c_List_Olist_OCons(_1718909), _1718911), _1718913))), c_List_Olinorder__class_Osorted(_1718909, _1718913), 46701 ^ _780086 : [(46702 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1718909), 46700 ^ [_1718909, _1718911, _1718913]), hAPP(c_List_Oset(_1718909), _1718913))))], (46704 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1718909), _1718911), 46700 ^ [_1718909, _1718911, _1718913]))]]]]], (46708 ^ _780086) ^ [_1719434, _1719436, _1719438] : [class_Orderings_Olinorder(_1719434), 46711 ^ _780086 : [(46712 ^ _780086) ^ [] : [c_List_Olinorder__class_Osorted(_1719434, hAPP(hAPP(c_List_Oappend(_1719434), _1719436), _1719438)), 46715 ^ _780086 : [(46716 ^ _780086) ^ [] : [-(c_List_Olinorder__class_Osorted(_1719434, _1719436))], (46718 ^ _780086) ^ [] : [-(c_List_Olinorder__class_Osorted(_1719434, _1719438))], (46720 ^ _780086) ^ [_1719670] : [hBOOL(hAPP(hAPP(c_member(_1719434), _1719670), hAPP(c_List_Oset(_1719434), _1719436))), 46723 ^ _780086 : [(46724 ^ _780086) ^ [_1719780] : [hBOOL(hAPP(hAPP(c_member(_1719434), _1719780), hAPP(c_List_Oset(_1719434), _1719438))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1719434), _1719670), _1719780)))]]]]], (46730 ^ _780086) ^ [] : [-(c_List_Olinorder__class_Osorted(_1719434, hAPP(hAPP(c_List_Oappend(_1719434), _1719436), _1719438))), c_List_Olinorder__class_Osorted(_1719434, _1719436), c_List_Olinorder__class_Osorted(_1719434, _1719438), 46740 ^ _780086 : [(46741 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1719434), 46739 ^ [_1719434, _1719436, _1719438]), hAPP(c_List_Oset(_1719434), _1719436))))], (46744 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1719434), 46742 ^ [_1719434, _1719436, _1719438]), hAPP(c_List_Oset(_1719434), _1719438))))], (46746 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1719434), 46739 ^ [_1719434, _1719436, _1719438]), 46742 ^ [_1719434, _1719436, _1719438]))]]]]], (46750 ^ _780086) ^ [_1720282, _1720284, _1720286, _1720288, _1720290, _1720292] : [class_Orderings_Olinorder(_1720282), c_List_Olinorder__class_Osorted(_1720282, hAPP(hAPP(c_List_Omap(_1720284, _1720282), _1720286), _1720288)), hBOOL(hAPP(_1720290, _1720292)), -(hAPP(c_List_Ofilter(_1720284, _1720290), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1720284, _1720282, _1720286), _1720292), _1720288)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1720284, _1720282, _1720286), _1720292), hAPP(c_List_Ofilter(_1720284, _1720290), _1720288)))], (46764 ^ _780086) ^ [_1720571, _1720573, _1720575] : [class_Orderings_Olinorder(_1720571), 46767 ^ _780086 : [(46768 ^ _780086) ^ [] : [c_List_Olinorder__class_Osorted(_1720571, hAPP(hAPP(c_List_Olist_OCons(_1720571), _1720573), _1720575)), 46771 ^ _780086 : [(46778 ^ _780086) ^ [] : [-(c_List_Olinorder__class_Osorted(_1720571, _1720575))], (46772 ^ _780086) ^ [_1720739] : [hBOOL(hAPP(hAPP(c_member(_1720571), _1720739), hAPP(c_List_Oset(_1720571), _1720575))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1720571), _1720573), _1720739)))]]], (46780 ^ _780086) ^ [] : [-(c_List_Olinorder__class_Osorted(_1720571, hAPP(hAPP(c_List_Olist_OCons(_1720571), _1720573), _1720575))), 46784 ^ _780086 : [(46785 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1720571), 46783 ^ [_1720571, _1720573, _1720575]), hAPP(c_List_Oset(_1720571), _1720575))))], (46787 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1720571), _1720573), 46783 ^ [_1720571, _1720573, _1720575]))]], c_List_Olinorder__class_Osorted(_1720571, _1720575)]]], (46793 ^ _780086) ^ [_1721097, _1721099] : [class_Orderings_Olinorder(_1721097), hBOOL(hAPP(c_Finite__Set_Ofinite(_1721097), _1721099)), 46800 ^ _780086 : [(46801 ^ _780086) ^ [] : [-(hAPP(c_List_Oset(_1721097), c_List_Olinorder__class_Osorted__list__of__set(_1721097, _1721099)) = _1721099)], (46803 ^ _780086) ^ [] : [-(c_List_Olinorder__class_Osorted(_1721097, c_List_Olinorder__class_Osorted__list__of__set(_1721097, _1721099)))], (46805 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1721097), c_List_Olinorder__class_Osorted__list__of__set(_1721097, _1721099))))]]], (46807 ^ _780086) ^ [_1721318, _1721320, _1721322] : [class_Orderings_Olinorder(_1721318), hBOOL(hAPP(hAPP(c_member(_1721318), _1721320), hAPP(c_List_Oset(_1721318), _1721322))), c_List_Olinorder__class_Osorted(_1721318, _1721322), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1721318, _1721318, c_COMBI(_1721318)), _1721320), c_List_Oremove1(_1721318, _1721320, _1721322)) = _1721322)], (46821 ^ _780086) ^ [_1721559, _1721561] : [class_Orderings_Olinorder(_1721559), 46824 ^ _780086 : [(46839 ^ _780086) ^ [] : [46841 ^ _780086 : [(46842 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46840 ^ [_1721559, _1721561]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721559)), _1721561))))], (46845 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 46843 ^ [_1721559, _1721561]), 46840 ^ [_1721559, _1721561])))], (46847 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1721559), hAPP(hAPP(c_List_Onth(_1721559), _1721561), 46843 ^ [_1721559, _1721561])), hAPP(hAPP(c_List_Onth(_1721559), _1721561), 46840 ^ [_1721559, _1721561])))]], -(c_List_Olinorder__class_Osorted(_1721559, _1721561))], (46825 ^ _780086) ^ [] : [c_List_Olinorder__class_Osorted(_1721559, _1721561), 46828 ^ _780086 : [(46829 ^ _780086) ^ [_1721730] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1721730), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721559)), _1721561))), 46832 ^ _780086 : [(46833 ^ _780086) ^ [_1721847] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1721847), _1721730)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1721559), hAPP(hAPP(c_List_Onth(_1721559), _1721561), _1721847)), hAPP(hAPP(c_List_Onth(_1721559), _1721561), _1721730))))]]]]]]], (46851 ^ _780086) ^ [_1722283, _1722285, _1722287, _1722289] : [class_Orderings_Olinorder(_1722283), c_List_Olinorder__class_Osorted(_1722283, _1722285), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1722287), _1722289)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1722289), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722283)), _1722285))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1722283), hAPP(hAPP(c_List_Onth(_1722283), _1722285), _1722287)), hAPP(hAPP(c_List_Onth(_1722283), _1722285), _1722289))))], (46869 ^ _780086) ^ [_1722610, _1722612, _1722614, _1722616, _1722618] : [class_Orderings_Olinorder(_1722610), c_Fun_Oinj__on(_1722612, _1722610, _1722614, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1722612, tc_HOL_Obool)), hAPP(c_List_Oset(_1722612), _1722616)), hAPP(c_List_Oset(_1722612), _1722618))), c_List_Olinorder__class_Osorted(_1722610, hAPP(hAPP(c_List_Omap(_1722612, _1722610), _1722614), _1722616)), hBOOL(hAPP(c_List_Odistinct(_1722610), hAPP(hAPP(c_List_Omap(_1722612, _1722610), _1722614), _1722616))), c_List_Olinorder__class_Osorted(_1722610, hAPP(hAPP(c_List_Omap(_1722612, _1722610), _1722614), _1722618)), hBOOL(hAPP(c_List_Odistinct(_1722610), hAPP(hAPP(c_List_Omap(_1722612, _1722610), _1722614), _1722618))), hAPP(c_List_Oset(_1722612), _1722616) = hAPP(c_List_Oset(_1722612), _1722618), -(_1722616 = _1722618)], (46899 ^ _780086) ^ [_1723193, _1723195, _1723197] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1723193), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1723193))), _1723195))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1723197), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1723193))), _1723195))), -(hAPP(hAPP(c_List_Omap(tc_List_Olist(_1723193), _1723193), hAPP(hAPP(c_COMBC(tc_List_Olist(_1723193), tc_Nat_Onat, _1723193), c_List_Onth(_1723193)), _1723197)), hAPP(c_List_Ofilter(tc_List_Olist(_1723193), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1723193)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1723197)), c_Nat_Osize__class_Osize(tc_List_Olist(_1723193)))), c_List_Otranspose(_1723193, _1723195))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(_1723193)), _1723195), _1723197))], (46909 ^ _780086) ^ [_1723520, _1723522, _1723524, _1723526] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1723520), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1723520))), _1723522))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1723524), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1723520))), c_List_Otranspose(_1723520, _1723522)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1723526), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1723520))), hAPP(c_List_Ofilter(tc_List_Olist(_1723520), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1723520)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1723524)), c_Nat_Osize__class_Osize(tc_List_Olist(_1723520)))), _1723522)))), -(hAPP(hAPP(c_List_Onth(_1723520), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1723520)), c_List_Otranspose(_1723520, _1723522)), _1723524)), _1723526) = hAPP(hAPP(c_List_Onth(_1723520), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1723520)), _1723522), _1723526)), _1723524))], (46923 ^ _780086) ^ [_1723943, _1723945] : [-(c_Fun_Oinj__on(tc_List_Olist(_1723943), tc_List_Olist(_1723943), c_List_Orev(_1723943), _1723945))], (46925 ^ _780086) ^ [_1723991, _1723993] : [hBOOL(hAPP(c_List_Odistinct(_1723991), hAPP(c_List_Orev(_1723991), _1723993))), -(hBOOL(hAPP(c_List_Odistinct(_1723991), _1723993)))], (46931 ^ _780086) ^ [_1724090, _1724092] : [hBOOL(hAPP(c_List_Odistinct(_1724090), _1724092)), -(hBOOL(hAPP(c_List_Odistinct(_1724090), hAPP(c_List_Orev(_1724090), _1724092))))], (46937 ^ _780086) ^ [_1724210, _1724212] : [hAPP(c_List_Orev(_1724210), _1724212) = c_List_Olist_ONil(_1724210), -(_1724212 = c_List_Olist_ONil(_1724210))], (46943 ^ _780086) ^ [_1724301, _1724303] : [_1724303 = c_List_Olist_ONil(_1724301), -(hAPP(c_List_Orev(_1724301), _1724303) = c_List_Olist_ONil(_1724301))], (46949 ^ _780086) ^ [_1724413, _1724415] : [c_List_Olist_ONil(_1724413) = hAPP(c_List_Orev(_1724413), _1724415), -(_1724415 = c_List_Olist_ONil(_1724413))], (46955 ^ _780086) ^ [_1724504, _1724506] : [_1724506 = c_List_Olist_ONil(_1724504), -(c_List_Olist_ONil(_1724504) = hAPP(c_List_Orev(_1724504), _1724506))], (46961 ^ _780086) ^ [_1724601] : [-(hAPP(c_List_Orev(_1724601), c_List_Olist_ONil(_1724601)) = c_List_Olist_ONil(_1724601))], (46963 ^ _780086) ^ [_1724651, _1724653, _1724655] : [hAPP(hAPP(c_List_Olist_OCons(_1724651), _1724653), c_List_Olist_ONil(_1724651)) = hAPP(c_List_Orev(_1724651), _1724655), -(_1724655 = hAPP(hAPP(c_List_Olist_OCons(_1724651), _1724653), c_List_Olist_ONil(_1724651)))], (46969 ^ _780086) ^ [_1724776, _1724778, _1724780] : [_1724780 = hAPP(hAPP(c_List_Olist_OCons(_1724776), _1724778), c_List_Olist_ONil(_1724776)), -(hAPP(hAPP(c_List_Olist_OCons(_1724776), _1724778), c_List_Olist_ONil(_1724776)) = hAPP(c_List_Orev(_1724776), _1724780))], (46975 ^ _780086) ^ [_1724925, _1724927, _1724929] : [hAPP(c_List_Orev(_1724925), _1724927) = hAPP(hAPP(c_List_Olist_OCons(_1724925), _1724929), c_List_Olist_ONil(_1724925)), -(_1724927 = hAPP(hAPP(c_List_Olist_OCons(_1724925), _1724929), c_List_Olist_ONil(_1724925)))], (46981 ^ _780086) ^ [_1725050, _1725052, _1725054] : [_1725052 = hAPP(hAPP(c_List_Olist_OCons(_1725050), _1725054), c_List_Olist_ONil(_1725050)), -(hAPP(c_List_Orev(_1725050), _1725052) = hAPP(hAPP(c_List_Olist_OCons(_1725050), _1725054), c_List_Olist_ONil(_1725050)))], (46987 ^ _780086) ^ [_1725181, _1725183, _1725185] : [-(hAPP(c_List_Orev(_1725181), hAPP(hAPP(c_List_Oappend(_1725181), _1725183), _1725185)) = hAPP(hAPP(c_List_Oappend(_1725181), hAPP(c_List_Orev(_1725181), _1725185)), hAPP(c_List_Orev(_1725181), _1725183)))], (46989 ^ _780086) ^ [_1725239, _1725241] : [-(hAPP(c_List_Orev(_1725239), c_List_Oconcat(_1725239, _1725241)) = c_List_Oconcat(_1725239, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1725239), tc_List_Olist(_1725239)), c_List_Orev(_1725239)), hAPP(c_List_Orev(tc_List_Olist(_1725239)), _1725241))))], (46991 ^ _780086) ^ [_1725297, _1725299, _1725301, _1725303] : [-(hAPP(c_List_Orev(_1725297), hAPP(hAPP(c_List_Omap(_1725299, _1725297), _1725301), _1725303)) = hAPP(hAPP(c_List_Omap(_1725299, _1725297), _1725301), hAPP(c_List_Orev(_1725299), _1725303)))], (46993 ^ _780086) ^ [_1725354, _1725356, _1725358] : [-(hAPP(c_List_Orev(_1725354), hAPP(c_List_Ofilter(_1725354, _1725356), _1725358)) = hAPP(c_List_Ofilter(_1725354, _1725356), hAPP(c_List_Orev(_1725354), _1725358)))], (46995 ^ _780086) ^ [_1725403, _1725405, _1725407, _1725409] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725403)), _1725405) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725407)), _1725409), -(hAPP(hAPP(c_List_Ozip(_1725403, _1725407), hAPP(c_List_Orev(_1725403), _1725405)), hAPP(c_List_Orev(_1725407), _1725409)) = hAPP(c_List_Orev(tc_prod(_1725403, _1725407)), hAPP(hAPP(c_List_Ozip(_1725403, _1725407), _1725405), _1725409)))], (47001 ^ _780086) ^ [_1725584, _1725586] : [-(hAPP(c_List_Oset(_1725584), hAPP(c_List_Orev(_1725584), _1725586)) = hAPP(c_List_Oset(_1725584), _1725586))], (47003 ^ _780086) ^ [_1725648, _1725650, _1725652, _1725654, _1725656] : [c_List_Olist__all2(_1725648, _1725650, _1725652, hAPP(c_List_Orev(_1725648), _1725654), hAPP(c_List_Orev(_1725650), _1725656)), -(c_List_Olist__all2(_1725648, _1725650, _1725652, _1725654, _1725656))], (47009 ^ _780086) ^ [_1725759, _1725761, _1725763, _1725765, _1725767] : [c_List_Olist__all2(_1725759, _1725761, _1725763, _1725765, _1725767), -(c_List_Olist__all2(_1725759, _1725761, _1725763, hAPP(c_List_Orev(_1725759), _1725765), hAPP(c_List_Orev(_1725761), _1725767)))], (47015 ^ _780086) ^ [_1725900, _1725902, _1725904, _1725906, _1725908] : [c_List_Olist__all2(_1725900, _1725902, _1725904, hAPP(c_List_Orev(_1725900), _1725906), _1725908), -(c_List_Olist__all2(_1725900, _1725902, _1725904, _1725906, hAPP(c_List_Orev(_1725902), _1725908)))], (47021 ^ _780086) ^ [_1726011, _1726013, _1726015, _1726017, _1726019] : [c_List_Olist__all2(_1726011, _1726013, _1726015, _1726017, hAPP(c_List_Orev(_1726013), _1726019)), -(c_List_Olist__all2(_1726011, _1726013, _1726015, hAPP(c_List_Orev(_1726011), _1726017), _1726019))], (47027 ^ _780086) ^ [_1726128, _1726130] : [-(hAPP(c_List_Orev(_1726128), hAPP(c_List_Orev(_1726128), _1726130)) = _1726130)], (47029 ^ _780086) ^ [_1726181, _1726183, _1726185] : [hAPP(c_List_Orev(_1726181), _1726183) = _1726185, -(_1726183 = hAPP(c_List_Orev(_1726181), _1726185))], (47035 ^ _780086) ^ [_1726276, _1726278, _1726280] : [_1726278 = hAPP(c_List_Orev(_1726276), _1726280), -(hAPP(c_List_Orev(_1726276), _1726278) = _1726280)], (47041 ^ _780086) ^ [_1726395, _1726397, _1726399] : [hAPP(c_List_Orev(_1726395), _1726397) = hAPP(c_List_Orev(_1726395), _1726399), -(_1726397 = _1726399)], (47047 ^ _780086) ^ [_1726490, _1726492, _1726494] : [_1726492 = _1726494, -(hAPP(c_List_Orev(_1726490), _1726492) = hAPP(c_List_Orev(_1726490), _1726494))], (47053 ^ _780086) ^ [_1726591, _1726593] : [class_Groups_Ocomm__monoid__add(_1726591), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1726591), hAPP(c_List_Orev(_1726591), _1726593)) = hAPP(c_List_Omonoid__add__class_Olistsum(_1726591), _1726593))], (47059 ^ _780086) ^ [_1726696, _1726698] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726696)), hAPP(c_List_Orev(_1726696), _1726698)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726696)), _1726698))], (47061 ^ _780086) ^ [_1726740, _1726742, _1726744, _1726746, _1726748] : [-(c_List_Ofoldr(_1726740, _1726742, _1726744, _1726746, _1726748) = hAPP(c_List_Ofoldl(_1726742, _1726740, hAPP(c_COMBC(_1726740, _1726742, _1726742), _1726744), _1726748), hAPP(c_List_Orev(_1726740), _1726746)))], (47063 ^ _780086) ^ [_1726797, _1726799, _1726801, _1726803, _1726805] : [-(hAPP(c_List_Ofoldl(_1726797, _1726799, _1726801, _1726803), _1726805) = c_List_Ofoldr(_1726799, _1726797, hAPP(c_COMBC(_1726797, _1726799, _1726797), _1726801), hAPP(c_List_Orev(_1726799), _1726805), _1726803))], (47065 ^ _780086) ^ [_1726875, _1726877, _1726879, _1726881] : [hAPP(c_List_Orev(_1726875), _1726877) = hAPP(hAPP(c_List_Olist_OCons(_1726875), _1726879), _1726881), -(_1726877 = hAPP(hAPP(c_List_Oappend(_1726875), hAPP(c_List_Orev(_1726875), _1726881)), hAPP(hAPP(c_List_Olist_OCons(_1726875), _1726879), c_List_Olist_ONil(_1726875))))], (47071 ^ _780086) ^ [_1727024, _1727026, _1727028, _1727030] : [_1727026 = hAPP(hAPP(c_List_Oappend(_1727024), hAPP(c_List_Orev(_1727024), _1727030)), hAPP(hAPP(c_List_Olist_OCons(_1727024), _1727028), c_List_Olist_ONil(_1727024))), -(hAPP(c_List_Orev(_1727024), _1727026) = hAPP(hAPP(c_List_Olist_OCons(_1727024), _1727028), _1727030))], (47077 ^ _780086) ^ [_1727179, _1727181, _1727183] : [-(hAPP(c_List_Orev(_1727179), hAPP(hAPP(c_List_Olist_OCons(_1727179), _1727181), _1727183)) = hAPP(hAPP(c_List_Oappend(_1727179), hAPP(c_List_Orev(_1727179), _1727183)), hAPP(hAPP(c_List_Olist_OCons(_1727179), _1727181), c_List_Olist_ONil(_1727179))))], (47079 ^ _780086) ^ [_1727238, _1727240] : [-(_1727238 = c_List_Olist_ONil(_1727240)), -(hAPP(c_List_Ohd(_1727240), hAPP(c_List_Orev(_1727240), _1727238)) = c_List_Olast(_1727240, _1727238))], (47085 ^ _780086) ^ [_1727285, _1727287] : [-(_1727285 = c_List_Olist_ONil(_1727287)), -(c_List_Olast(_1727287, hAPP(c_List_Orev(_1727287), _1727285)) = hAPP(c_List_Ohd(_1727287), _1727285))], (47091 ^ _780086) ^ [_1727336, _1727338] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1727336), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1727336))), c_List_Otranspose(_1727336, _1727338)))))], (47093 ^ _780086) ^ [_1727382, _1727384] : [-(hAPP(c_List_Orev(_1727382), _1727384) = hAPP(c_List_Ofoldl(tc_List_Olist(_1727382), _1727382, hAPP(c_COMBC(_1727382, tc_List_Olist(_1727382), tc_List_Olist(_1727382)), c_List_Olist_OCons(_1727382)), c_List_Olist_ONil(_1727382)), _1727384))], (47095 ^ _780086) ^ [_1727437, _1727439, _1727441] : [-(hAPP(c_List_Orev(_1727437), hAPP(hAPP(c_List_Odrop(_1727437), _1727439), _1727441)) = hAPP(hAPP(c_List_Otake(_1727437), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727437)), _1727441)), _1727439)), hAPP(c_List_Orev(_1727437), _1727441)))], (47097 ^ _780086) ^ [_1727503, _1727505, _1727507] : [-(hAPP(c_List_Orev(_1727503), hAPP(hAPP(c_List_Otake(_1727503), _1727505), _1727507)) = hAPP(hAPP(c_List_Odrop(_1727503), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727503)), _1727507)), _1727505)), hAPP(c_List_Orev(_1727503), _1727507)))], (47099 ^ _780086) ^ [_1727569, _1727571, _1727573] : [-(hAPP(c_List_Orotate(_1727569, _1727571), hAPP(c_List_Orev(_1727569), _1727573)) = hAPP(c_List_Orev(_1727569), hAPP(c_List_Orotate(_1727569, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727569)), _1727573)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1727571, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727569)), _1727573)))), _1727573)))], (47101 ^ _780086) ^ [_1727642, _1727644, _1727646] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1727642), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727644)), _1727646))), -(hAPP(hAPP(c_List_Onth(_1727644), hAPP(c_List_Orev(_1727644), _1727646)), _1727642) = hAPP(hAPP(c_List_Onth(_1727644), _1727646), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727644)), _1727646)), hAPP(c_Nat_OSuc, _1727642))))], (47107 ^ _780086) ^ [_1727819, _1727821, _1727823, _1727825] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1727819), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727821)), _1727823))), -(hAPP(c_List_Orev(_1727821), hAPP(hAPP(c_List_Olist__update(_1727821, _1727823), _1727819), _1727825)) = hAPP(hAPP(c_List_Olist__update(_1727821, hAPP(c_List_Orev(_1727821), _1727823)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727821)), _1727823)), _1727819)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1727825))], (47113 ^ _780086) ^ [_1728018, _1728020, _1728022, _1728024] : [class_Orderings_Olinorder(_1728018), c_List_Olinorder__class_Osorted(_1728018, hAPP(c_List_Orev(_1728018), _1728020)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1728022), _1728024)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1728024), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728018)), _1728020))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1728018), hAPP(hAPP(c_List_Onth(_1728018), _1728020), _1728024)), hAPP(hAPP(c_List_Onth(_1728018), _1728020), _1728022))))], (47131 ^ _780086) ^ [_1728355, _1728357, _1728359] : [class_Orderings_Olinorder(_1728355), c_List_Olinorder__class_Osorted(_1728355, hAPP(c_List_Orev(_1728355), _1728357)), 47138 ^ _780086 : [(47139 ^ _780086) ^ [] : [_1728357 = c_List_Olist_ONil(_1728355), -(c_List_Ofoldr(_1728355, _1728355, c_Orderings_Oord__class_Omax(_1728355), _1728357, _1728359) = _1728359)], (47145 ^ _780086) ^ [] : [-(_1728357 = c_List_Olist_ONil(_1728355)), -(c_List_Ofoldr(_1728355, _1728355, c_Orderings_Oord__class_Omax(_1728355), _1728357, _1728359) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1728355), hAPP(hAPP(c_List_Onth(_1728355), _1728357), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1728359))]]], (47151 ^ _780086) ^ [_1728669, _1728671] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1728669), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1728669))), _1728671))), 47154 ^ _780086 : [(47155 ^ _780086) ^ [] : [_1728671 = c_List_Olist_ONil(tc_List_Olist(_1728669)), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1728669))), c_List_Otranspose(_1728669, _1728671)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (47161 ^ _780086) ^ [] : [-(_1728671 = c_List_Olist_ONil(tc_List_Olist(_1728669))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1728669))), c_List_Otranspose(_1728669, _1728671)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728669)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1728669)), _1728671), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (47167 ^ _780086) ^ [_1728979, _1728981, _1728983] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1728979), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1728979))), _1728981))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1728983), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1728979))), _1728981))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1728979))), hAPP(c_List_Ofilter(tc_List_Olist(_1728979), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1728979)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1728983)), c_Nat_Osize__class_Osize(tc_List_Olist(_1728979)))), c_List_Otranspose(_1728979, _1728981))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728979)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1728979)), _1728981), _1728983)))], (47177 ^ _780086) ^ [_1729288, _1729290] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1729288), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1729288))), _1729290))), -(c_List_Otranspose(_1729288, c_List_Otranspose(_1729288, _1729290)) = c_List_OtakeWhile(tc_List_Olist(_1729288), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1729288)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1729288), tc_List_Olist(_1729288), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1729288))), _1729290))], (47183 ^ _780086) ^ [] : [-(c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)))], (47185 ^ _780086) ^ [_1729499, _1729501, _1729503] : [class_Orderings_Olinorder(_1729499), c_List_Olinorder__class_Osorted(_1729499, _1729501), -(c_List_Olinorder__class_Osorted(_1729499, c_List_OtakeWhile(_1729499, _1729503, _1729501)))], (47195 ^ _780086) ^ [_1729638, _1729640, _1729642] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729638)), c_List_OtakeWhile(_1729638, _1729640, _1729642))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729638)), _1729642))))], (47197 ^ _780086) ^ [_1729688, _1729690, _1729692, _1729694] : [hBOOL(hAPP(hAPP(c_member(_1729688), _1729690), hAPP(c_List_Oset(_1729688), c_List_OtakeWhile(_1729688, _1729692, _1729694)))), 47200 ^ _780086 : [(47201 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1729688), _1729690), hAPP(c_List_Oset(_1729688), _1729694))))], (47203 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1729692, _1729690)))]]], (47215 ^ _780086) ^ [_1730069, _1730071, _1730073] : [47217 ^ _780086 : [(47218 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1730069), 47216 ^ [_1730069, _1730071, _1730073]), hAPP(c_List_Oset(_1730069), _1730073))))], (47220 ^ _780086) ^ [] : [hBOOL(hAPP(_1730071, 47216 ^ [_1730069, _1730071, _1730073]))]], -(c_List_OtakeWhile(_1730069, _1730071, _1730073) = _1730073)], (47205 ^ _780086) ^ [_1729873, _1729875, _1729877] : [c_List_OtakeWhile(_1729873, _1729875, _1729877) = _1729877, 47208 ^ _780086 : [(47209 ^ _780086) ^ [_1729960] : [hBOOL(hAPP(hAPP(c_member(_1729873), _1729960), hAPP(c_List_Oset(_1729873), _1729877))), -(hBOOL(hAPP(_1729875, _1729960)))]]], (47224 ^ _780086) ^ [_1730257, _1730259, _1730261, _1730263, _1730265] : [-(hAPP(hAPP(c_List_Ozip(_1730257, _1730259), _1730261), c_List_OtakeWhile(_1730259, _1730263, _1730265)) = c_List_OtakeWhile(tc_prod(_1730257, _1730259), hAPP(c_Fun_Ocomp(_1730259, tc_HOL_Obool, tc_prod(_1730257, _1730259), _1730263), c_Product__Type_Osnd(_1730257, _1730259)), hAPP(hAPP(c_List_Ozip(_1730257, _1730259), _1730261), _1730265)))], (47226 ^ _780086) ^ [_1730331, _1730333, _1730335, _1730337, _1730339] : [-(hAPP(hAPP(c_List_Ozip(_1730331, _1730333), c_List_OtakeWhile(_1730331, _1730335, _1730337)), _1730339) = c_List_OtakeWhile(tc_prod(_1730331, _1730333), hAPP(c_Fun_Ocomp(_1730331, tc_HOL_Obool, tc_prod(_1730331, _1730333), _1730335), c_Product__Type_Ofst(_1730331, _1730333)), hAPP(hAPP(c_List_Ozip(_1730331, _1730333), _1730337), _1730339)))], (47228 ^ _780086) ^ [_1730405, _1730407, _1730409, _1730411, _1730413] : [-(c_List_OtakeWhile(_1730405, _1730407, hAPP(hAPP(c_List_Omap(_1730409, _1730405), _1730411), _1730413)) = hAPP(hAPP(c_List_Omap(_1730409, _1730405), _1730411), c_List_OtakeWhile(_1730409, hAPP(c_Fun_Ocomp(_1730405, tc_HOL_Obool, _1730409, _1730407), _1730411), _1730413)))], (47230 ^ _780086) ^ [_1730466, _1730468, _1730470, _1730472, _1730474] : [-(hBOOL(hAPP(_1730466, _1730468))), -(c_List_OtakeWhile(_1730470, _1730466, hAPP(hAPP(c_List_Oappend(_1730470), _1730472), hAPP(hAPP(c_List_Olist_OCons(_1730470), _1730468), _1730474))) = c_List_OtakeWhile(_1730470, _1730466, _1730472))], (47236 ^ _780086) ^ [_1730549, _1730551, _1730553, _1730555] : [hBOOL(hAPP(_1730549, _1730551)), -(c_List_OtakeWhile(_1730553, _1730549, hAPP(hAPP(c_List_Olist_OCons(_1730553), _1730551), _1730555)) = hAPP(hAPP(c_List_Olist_OCons(_1730553), _1730551), c_List_OtakeWhile(_1730553, _1730549, _1730555)))], (47242 ^ _780086) ^ [_1730676, _1730678, _1730680, _1730682] : [-(hBOOL(hAPP(_1730676, _1730678))), -(c_List_OtakeWhile(_1730680, _1730676, hAPP(hAPP(c_List_Olist_OCons(_1730680), _1730678), _1730682)) = c_List_Olist_ONil(_1730680))], (47248 ^ _780086) ^ [_1730734, _1730736] : [-(c_List_OtakeWhile(_1730734, _1730736, c_List_Olist_ONil(_1730734)) = c_List_Olist_ONil(_1730734))], (47250 ^ _780086) ^ [_1730767, _1730769, _1730771] : [-(c_List_OtakeWhile(_1730767, _1730769, _1730771) = hAPP(hAPP(c_List_Otake(_1730767), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730767)), c_List_OtakeWhile(_1730767, _1730769, _1730771))), _1730771))], (47252 ^ _780086) ^ [_1730817, _1730819, _1730821] : [hBOOL(hAPP(c_List_Odistinct(_1730817), _1730819)), -(hBOOL(hAPP(c_List_Odistinct(_1730817), c_List_OtakeWhile(_1730817, _1730821, _1730819))))], (47258 ^ _780086) ^ [_1730920] : [-(c_List_Oreturn__list(_1730920) = hAPP(hAPP(c_List_Omap(tc_Int_Oint, tc_Nat_Onat), c_Int_Onat), _1730920))], (47260 ^ _780086) ^ [_1730948, _1730950, _1730952, _1730954, _1730956] : [hBOOL(hAPP(hAPP(c_member(_1730948), _1730950), hAPP(c_List_Oset(_1730948), _1730952))), -(hBOOL(hAPP(_1730954, _1730950))), -(c_List_OtakeWhile(_1730948, _1730954, hAPP(hAPP(c_List_Oappend(_1730948), _1730952), _1730956)) = c_List_OtakeWhile(_1730948, _1730954, _1730952))], (47270 ^ _780086) ^ [_1731106, _1731108, _1731110, _1731112] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1731106), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731108)), c_List_OtakeWhile(_1731108, _1731110, _1731112)))), -(hAPP(hAPP(c_List_Onth(_1731108), c_List_OtakeWhile(_1731108, _1731110, _1731112)), _1731106) = hAPP(hAPP(c_List_Onth(_1731108), _1731112), _1731106))], (47276 ^ _780086) ^ [_1731259, _1731261, _1731263] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731259)), c_List_OtakeWhile(_1731259, _1731261, _1731263))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731259)), _1731263))), hBOOL(hAPP(_1731261, hAPP(hAPP(c_List_Onth(_1731259), _1731263), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731259)), c_List_OtakeWhile(_1731259, _1731261, _1731263)))))], (47282 ^ _780086) ^ [_1731426, _1731428] : [-(_1731426 = c_List_Olist_ONil(_1731428)), hBOOL(hAPP(c_List_Odistinct(_1731428), _1731426)), -(c_List_OtakeWhile(_1731428, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1731428), c_fNot), hAPP(hAPP(c_COMBC(_1731428, _1731428, tc_HOL_Obool), c_fequal), c_List_Olast(_1731428, _1731426))), _1731426) = c_List_Obutlast(_1731428, _1731426))], (47292 ^ _780086) ^ [_1731623, _1731625, _1731627, _1731629, _1731631] : [class_Orderings_Olinorder(_1731623), c_List_Olinorder__class_Osorted(_1731623, hAPP(c_List_Orev(_1731623), hAPP(hAPP(c_List_Omap(_1731625, _1731623), _1731627), _1731629))), -(hAPP(c_List_Ofilter(_1731625, hAPP(hAPP(c_COMBB(_1731623, tc_HOL_Obool, _1731625), hAPP(c_Orderings_Oord__class_Oless(_1731623), _1731631)), _1731627)), _1731629) = c_List_OtakeWhile(_1731625, hAPP(hAPP(c_COMBB(_1731623, tc_HOL_Obool, _1731625), hAPP(c_Orderings_Oord__class_Oless(_1731623), _1731631)), _1731627), _1731629))], (47302 ^ _780086) ^ [_1731870] : [c_List_Onat__list(_1731870), -(c_List_Oembed__list(c_List_Oreturn__list(_1731870)) = _1731870)], (47308 ^ _780086) ^ [_1731951, _1731953] : [-(hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), _1731951), _1731953) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint), c_List_Oembed__list(_1731951)), c_List_Oembed__list(_1731953))))], (47310 ^ _780086) ^ [_1731994] : [-(c_List_Oembed__list(_1731994) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Int_Oint), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1731994))], (47312 ^ _780086) ^ [_1732022, _1732024, _1732026] : [hBOOL(hAPP(c_List_Odistinct(_1732022), _1732024)), hBOOL(hAPP(hAPP(c_member(_1732022), _1732026), hAPP(c_List_Oset(_1732022), _1732024))), -(c_List_OtakeWhile(_1732022, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1732022), c_fNot), hAPP(hAPP(c_COMBC(_1732022, _1732022, tc_HOL_Obool), c_fequal), _1732026)), hAPP(c_List_Orev(_1732022), _1732024)) = hAPP(c_List_Orev(_1732022), hAPP(c_List_Otl(_1732022), c_List_OdropWhile(_1732022, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1732022), c_fNot), hAPP(hAPP(c_COMBC(_1732022, _1732022, tc_HOL_Obool), c_fequal), _1732026)), _1732024))))], (47322 ^ _780086) ^ [_1732313, _1732315, _1732317] : [hBOOL(hAPP(c_List_Odistinct(_1732313), _1732315)), hBOOL(hAPP(hAPP(c_member(_1732313), _1732317), hAPP(c_List_Oset(_1732313), _1732315))), -(c_List_OdropWhile(_1732313, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1732313), c_fNot), hAPP(hAPP(c_COMBC(_1732313, _1732313, tc_HOL_Obool), c_fequal), _1732317)), hAPP(c_List_Orev(_1732313), _1732315)) = hAPP(hAPP(c_List_Olist_OCons(_1732313), _1732317), hAPP(c_List_Orev(_1732313), c_List_OtakeWhile(_1732313, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1732313), c_fNot), hAPP(hAPP(c_COMBC(_1732313, _1732313, tc_HOL_Obool), c_fequal), _1732317)), _1732315))))], (47332 ^ _780086) ^ [_1732610, _1732612, _1732614] : [-(hAPP(hAPP(c_List_Oappend(_1732610), c_List_OtakeWhile(_1732610, _1732612, _1732614)), c_List_OdropWhile(_1732610, _1732612, _1732614)) = _1732614)], (47334 ^ _780086) ^ [_1732652, _1732654, _1732656] : [-(c_List_OdropWhile(_1732652, _1732654, _1732656) = c_List_Olist_ONil(_1732652)), hBOOL(hAPP(_1732654, hAPP(c_List_Ohd(_1732652), c_List_OdropWhile(_1732652, _1732654, _1732656))))], (47340 ^ _780086) ^ [_1732758, _1732760, _1732762] : [class_Orderings_Olinorder(_1732758), c_List_Olinorder__class_Osorted(_1732758, _1732760), -(c_List_Olinorder__class_Osorted(_1732758, c_List_OdropWhile(_1732758, _1732762, _1732760)))], (47350 ^ _780086) ^ [_1732897, _1732899, _1732901] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732897)), c_List_OdropWhile(_1732897, _1732899, _1732901))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732897)), _1732901))))], (47362 ^ _780086) ^ [_1733165, _1733167, _1733169] : [47364 ^ _780086 : [(47365 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1733165), 47363 ^ [_1733165, _1733167, _1733169]), hAPP(c_List_Oset(_1733165), _1733169))))], (47367 ^ _780086) ^ [] : [hBOOL(hAPP(_1733167, 47363 ^ [_1733165, _1733167, _1733169]))]], -(c_List_OdropWhile(_1733165, _1733167, _1733169) = c_List_Olist_ONil(_1733165))], (47352 ^ _780086) ^ [_1732965, _1732967, _1732969] : [c_List_OdropWhile(_1732965, _1732967, _1732969) = c_List_Olist_ONil(_1732965), 47355 ^ _780086 : [(47356 ^ _780086) ^ [_1733056] : [hBOOL(hAPP(hAPP(c_member(_1732965), _1733056), hAPP(c_List_Oset(_1732965), _1732969))), -(hBOOL(hAPP(_1732967, _1733056)))]]], (47371 ^ _780086) ^ [_1733372, _1733374, _1733376, _1733378] : [hBOOL(hAPP(_1733372, _1733374)), -(c_List_OdropWhile(_1733376, _1733372, hAPP(hAPP(c_List_Olist_OCons(_1733376), _1733374), _1733378)) = c_List_OdropWhile(_1733376, _1733372, _1733378))], (47377 ^ _780086) ^ [_1733483, _1733485, _1733487, _1733489] : [-(hBOOL(hAPP(_1733483, _1733485))), -(c_List_OdropWhile(_1733487, _1733483, hAPP(hAPP(c_List_Olist_OCons(_1733487), _1733485), _1733489)) = hAPP(hAPP(c_List_Olist_OCons(_1733487), _1733485), _1733489))], (47383 ^ _780086) ^ [_1733547, _1733549] : [-(c_List_OdropWhile(_1733547, _1733549, c_List_Olist_ONil(_1733547)) = c_List_Olist_ONil(_1733547))], (47385 ^ _780086) ^ [_1733580, _1733582, _1733584] : [hBOOL(hAPP(c_List_Odistinct(_1733580), _1733582)), -(hBOOL(hAPP(c_List_Odistinct(_1733580), c_List_OdropWhile(_1733580, _1733584, _1733582))))], (47391 ^ _780086) ^ [_1733683, _1733685, _1733687, _1733689, _1733691] : [-(c_List_OdropWhile(_1733683, _1733685, hAPP(hAPP(c_List_Omap(_1733687, _1733683), _1733689), _1733691)) = hAPP(hAPP(c_List_Omap(_1733687, _1733683), _1733689), c_List_OdropWhile(_1733687, hAPP(c_Fun_Ocomp(_1733683, tc_HOL_Obool, _1733687, _1733685), _1733689), _1733691)))], (47393 ^ _780086) ^ [_1733748, _1733750, _1733752, _1733754, _1733756] : [hBOOL(hAPP(hAPP(c_member(_1733748), _1733750), hAPP(c_List_Oset(_1733748), _1733752))), -(hBOOL(hAPP(_1733754, _1733750))), -(c_List_OdropWhile(_1733748, _1733754, hAPP(hAPP(c_List_Oappend(_1733748), _1733752), _1733756)) = hAPP(hAPP(c_List_Oappend(_1733748), c_List_OdropWhile(_1733748, _1733754, _1733752)), _1733756))], (47403 ^ _780086) ^ [_1733946, _1733948, _1733950, _1733952, _1733954] : [c_List_OdropWhile(_1733946, _1733948, _1733950) = hAPP(hAPP(c_List_Olist_OCons(_1733946), _1733952), _1733954), 47406 ^ _780086 : [(47407 ^ _780086) ^ [] : [-(_1733950 = hAPP(hAPP(c_List_Oappend(_1733946), c_List_OtakeWhile(_1733946, _1733948, _1733950)), hAPP(hAPP(c_List_Olist_OCons(_1733946), _1733952), _1733954)))], (47409 ^ _780086) ^ [] : [hBOOL(hAPP(_1733948, _1733952))]]], (47411 ^ _780086) ^ [_1734127, _1734129, _1734131, _1734133, _1734135] : [-(c_List_OdropWhile(_1734127, _1734129, _1734131) = hAPP(hAPP(c_List_Olist_OCons(_1734127), _1734133), _1734135)), _1734131 = hAPP(hAPP(c_List_Oappend(_1734127), c_List_OtakeWhile(_1734127, _1734129, _1734131)), hAPP(hAPP(c_List_Olist_OCons(_1734127), _1734133), _1734135)), -(hBOOL(hAPP(_1734129, _1734133)))], (47421 ^ _780086) ^ [_1734341, _1734343, _1734345] : [-(c_List_OdropWhile(_1734341, _1734343, _1734345) = hAPP(hAPP(c_List_Odrop(_1734341), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734341)), c_List_OtakeWhile(_1734341, _1734343, _1734345))), _1734345))], (47423 ^ _780086) ^ [_1734391, _1734393, _1734395, _1734397] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1734391), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734393)), c_List_OdropWhile(_1734393, _1734395, _1734397)))), -(hAPP(hAPP(c_List_Onth(_1734393), c_List_OdropWhile(_1734393, _1734395, _1734397)), _1734391) = hAPP(hAPP(c_List_Onth(_1734393), _1734397), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1734391), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734393)), c_List_OtakeWhile(_1734393, _1734395, _1734397)))))], (47429 ^ _780086) ^ [_1734578, _1734580, _1734582, _1734584, _1734586] : [class_Groups_Omonoid__add(_1734578), 47435 ^ _780086 : [(47436 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1734580), 47434 ^ [_1734578, _1734580, _1734582, _1734584, _1734586]), hAPP(c_List_Oset(_1734580), _1734582))))], (47438 ^ _780086) ^ [] : [hBOOL(hAPP(_1734584, 47434 ^ [_1734578, _1734580, _1734582, _1734584, _1734586]))], (47440 ^ _780086) ^ [] : [hAPP(_1734586, 47434 ^ [_1734578, _1734580, _1734582, _1734584, _1734586]) = c_Groups_Ozero__class_Ozero(_1734578)]], -(hAPP(c_List_Omonoid__add__class_Olistsum(_1734578), hAPP(hAPP(c_List_Omap(_1734580, _1734578), _1734586), hAPP(c_List_Ofilter(_1734580, _1734584), _1734582))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1734578), hAPP(hAPP(c_List_Omap(_1734580, _1734578), _1734586), _1734582)))], (47444 ^ _780086) ^ [_1734969, _1734971] : [class_Orderings_Olinorder(_1734969), 47451 ^ _780086 : [(47452 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 47449 ^ [_1734969, _1734971]), 47450 ^ [_1734969, _1734971])))], (47454 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47450 ^ [_1734969, _1734971]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734969)), _1734971))))], (47456 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1734969), hAPP(hAPP(c_List_Onth(_1734969), _1734971), 47449 ^ [_1734969, _1734971])), hAPP(hAPP(c_List_Onth(_1734969), _1734971), 47450 ^ [_1734969, _1734971])))]], -(c_List_Olinorder__class_Osorted(_1734969, _1734971))], (47460 ^ _780086) ^ [_1735340, _1735342, _1735344] : [47462 ^ _780086 : [(47463 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1735340), 47461 ^ [_1735340, _1735342, _1735344]), hAPP(c_List_Oset(_1735340), c_List_OdropWhile(_1735340, _1735342, _1735344)))))], (47465 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1735342, 47461 ^ [_1735340, _1735342, _1735344])))]], -(c_List_OtakeWhile(_1735340, _1735342, _1735344) = hAPP(c_List_Ofilter(_1735340, _1735342), _1735344))], (47469 ^ _780086) ^ [_1735461, _1735463, _1735465, _1735467] : [47471 ^ _780086 : [(47472 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47470 ^ [_1735461, _1735463, _1735465, _1735467]), _1735461)))], (47474 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47470 ^ [_1735461, _1735463, _1735465, _1735467]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735463)), _1735465))))], (47476 ^ _780086) ^ [] : [hBOOL(hAPP(_1735467, hAPP(hAPP(c_List_Onth(_1735463), _1735465), 47470 ^ [_1735461, _1735463, _1735465, _1735467])))]], 47479 ^ _780086 : [(47480 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1735461), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735463)), _1735465))))], (47482 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1735467, hAPP(hAPP(c_List_Onth(_1735463), _1735465), _1735461))))]], -(c_List_OtakeWhile(_1735463, _1735467, _1735465) = hAPP(hAPP(c_List_Otake(_1735463), _1735461), _1735465))], (47486 ^ _780086) ^ [_1735865, _1735867, _1735869, _1735871] : [47488 ^ _780086 : [(47489 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47487 ^ [_1735865, _1735867, _1735869, _1735871]), _1735865)))], (47491 ^ _780086) ^ [] : [hBOOL(hAPP(_1735867, hAPP(hAPP(c_List_Onth(_1735869), _1735871), 47487 ^ [_1735865, _1735867, _1735869, _1735871])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1735865), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735869)), _1735871))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1735865), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735869)), c_List_OtakeWhile(_1735869, _1735867, _1735871)))))], (47499 ^ _780086) ^ [_1736173, _1736175] : [class_Orderings_Olinorder(_1736173), 47502 ^ _780086 : [(47503 ^ _780086) ^ [] : [c_List_Olinorder__class_Osorted(_1736173, _1736175), -(_1736175 = c_List_Olist_ONil(_1736173)), 47512 ^ _780086 : [(47513 ^ _780086) ^ [] : [-(_1736175 = hAPP(hAPP(c_List_Olist_OCons(_1736173), 47511 ^ [_1736173, _1736175]), 47510 ^ [_1736173, _1736175]))], (47521 ^ _780086) ^ [] : [-(c_List_Olinorder__class_Osorted(_1736173, 47510 ^ [_1736173, _1736175]))], (47515 ^ _780086) ^ [_1736507] : [hBOOL(hAPP(hAPP(c_member(_1736173), _1736507), hAPP(c_List_Oset(_1736173), 47510 ^ [_1736173, _1736175]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1736173), 47511 ^ [_1736173, _1736175]), _1736507)))]]], (47523 ^ _780086) ^ [] : [-(c_List_Olinorder__class_Osorted(_1736173, _1736175)), 47524 ^ _780086 : [(47525 ^ _780086) ^ [] : [_1736175 = c_List_Olist_ONil(_1736173)], (47527 ^ _780086) ^ [_1736733, _1736735] : [_1736175 = hAPP(hAPP(c_List_Olist_OCons(_1736173), _1736733), _1736735), 47533 ^ _780086 : [(47534 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1736173), 47532 ^ [_1736173, _1736175, _1736733, _1736735]), hAPP(c_List_Oset(_1736173), _1736735))))], (47536 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1736173), _1736733), 47532 ^ [_1736173, _1736175, _1736733, _1736735]))]], c_List_Olinorder__class_Osorted(_1736173, _1736735)]]]]], (47542 ^ _780086) ^ [_1737054, _1737056, _1737058] : [hBOOL(hAPP(hAPP(c_member(_1737054), _1737056), hAPP(c_List_Oset(_1737054), _1737058))), -(c_List_Oinsert(_1737054, _1737056, _1737058) = _1737058)], (47548 ^ _780086) ^ [_1737159, _1737161, _1737163] : [-(hBOOL(hAPP(hAPP(c_member(_1737159), _1737161), hAPP(c_List_Oset(_1737159), _1737163)))), -(c_List_Oinsert(_1737159, _1737161, _1737163) = hAPP(hAPP(c_List_Olist_OCons(_1737159), _1737161), _1737163))], (47554 ^ _780086) ^ [_1737219, _1737221, _1737223] : [-(hBOOL(hAPP(hAPP(c_member(_1737219), _1737221), hAPP(c_List_Oset(_1737219), _1737223)))), -(c_List_Oinsert(_1737219, _1737221, _1737223) = hAPP(hAPP(c_List_Olist_OCons(_1737219), _1737221), _1737223))], (47560 ^ _780086) ^ [_1737281, _1737283, _1737285] : [-(c_List_Oinsert(_1737281, _1737283, c_List_Oremdups(_1737281, _1737285)) = c_List_Oremdups(_1737281, c_List_Oinsert(_1737281, _1737283, _1737285)))], (47562 ^ _780086) ^ [_1737322, _1737324, _1737326] : [hBOOL(hAPP(c_List_Odistinct(_1737322), _1737324)), -(hBOOL(hAPP(c_List_Odistinct(_1737322), c_List_Oinsert(_1737322, _1737326, _1737324))))], (47568 ^ _780086) ^ [_1737425, _1737427, _1737429] : [hBOOL(hAPP(hAPP(c_member(_1737425), _1737427), hAPP(c_List_Oset(_1737425), _1737429))), -(c_List_Oinsert(_1737425, _1737427, _1737429) = _1737429)], (47574 ^ _780086) ^ [_1737536, _1737538, _1737540] : [-(hAPP(c_List_Oset(_1737536), c_List_Oinsert(_1737536, _1737538, _1737540)) = hAPP(hAPP(c_Set_Oinsert(_1737536), _1737538), hAPP(c_List_Oset(_1737536), _1737540)))], (47576 ^ _780086) ^ [_1737585, _1737587] : [-(c_List_Oinsert(_1737585, _1737587, c_List_Olist_ONil(_1737585)) = hAPP(hAPP(c_List_Olist_OCons(_1737585), _1737587), c_List_Olist_ONil(_1737585)))], (47578 ^ _780086) ^ [_1737626, _1737628, _1737630, _1737632] : [-(c_List_Omaps(_1737626, _1737628, _1737630, _1737632) = c_List_Oconcat(_1737628, hAPP(hAPP(c_List_Omap(_1737626, tc_List_Olist(_1737628)), _1737630), _1737632)))], (47580 ^ _780086) ^ [_1737674, _1737676, _1737678, _1737680] : [-(c_List_Oconcat(_1737674, hAPP(hAPP(c_List_Omap(_1737676, tc_List_Olist(_1737674)), _1737678), _1737680)) = c_List_Omaps(_1737676, _1737674, _1737678, _1737680))], (47582 ^ _780086) ^ [_1737722, _1737724, _1737726] : [-(c_List_Omaps(_1737722, _1737724, _1737726, c_List_Olist_ONil(_1737722)) = c_List_Olist_ONil(_1737724))], (47584 ^ _780086) ^ [_1737758, _1737760, _1737762, _1737764, _1737766] : [-(c_List_Omaps(_1737758, _1737760, _1737762, hAPP(hAPP(c_List_Olist_OCons(_1737758), _1737764), _1737766)) = hAPP(hAPP(c_List_Oappend(_1737760), hAPP(_1737762, _1737764)), c_List_Omaps(_1737758, _1737760, _1737762, _1737766)))], (47586 ^ _780086) ^ [_1737818, _1737820] : [hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1737818)), _1737820)), 47592 ^ _780086 : [(47593 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1737818)), 47591 ^ [_1737818, _1737820]), hAPP(c_List_Oset(tc_List_Olist(_1737818)), _1737820))))], (47595 ^ _780086) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1737818), 47591 ^ [_1737818, _1737820]))]], 47599 ^ _780086 : [(47600 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1737818)), 47598 ^ [_1737818, _1737820]), hAPP(c_List_Oset(tc_List_Olist(_1737818)), _1737820))))], (47603 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1737818)), 47601 ^ [_1737818, _1737820]), hAPP(c_List_Oset(tc_List_Olist(_1737818)), _1737820))))], (47605 ^ _780086) ^ [] : [47598 ^ [_1737818, _1737820] = 47601 ^ [_1737818, _1737820]], (47607 ^ _780086) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1737818, tc_HOL_Obool)), hAPP(c_List_Oset(_1737818), 47598 ^ [_1737818, _1737820])), hAPP(c_List_Oset(_1737818), 47601 ^ [_1737818, _1737820])) = c_Orderings_Obot__class_Obot(tc_fun(_1737818, tc_HOL_Obool))]], -(hBOOL(hAPP(c_List_Odistinct(_1737818), c_List_Oconcat(_1737818, _1737820))))], (47611 ^ _780086) ^ [_1738535, _1738537, _1738539, _1738541, _1738543] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1738535, _1738537)), hAPP(_1738535, _1738539))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1738541, _1738541)), hAPP(hAPP(c_Product__Type_OPair(_1738541, _1738541), _1738537), _1738539)), c_List_Omeasures(_1738541, _1738543))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1738541, _1738541)), hAPP(hAPP(c_Product__Type_OPair(_1738541, _1738541), _1738537), _1738539)), c_List_Omeasures(_1738541, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1738541, tc_Nat_Onat)), _1738535), _1738543)))))], (47621 ^ _780086) ^ [_1738808, _1738810] : [-(c_Wellfounded_Owf(_1738808, c_List_Omeasures(_1738808, _1738810)))], (47623 ^ _780086) ^ [_1738851, _1738853, _1738855] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1738851, _1738851)), hAPP(hAPP(c_Product__Type_OPair(_1738851, _1738851), _1738853), _1738855)), c_List_Omeasures(_1738851, c_List_Olist_ONil(tc_fun(_1738851, tc_Nat_Onat)))))], (47625 ^ _780086) ^ [_1738905, _1738907] : [-(c_List_Omeasures(_1738905, _1738907) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat), _1738905), c_List_Olex(tc_Nat_Onat, c_Wellfounded_Oless__than)), hAPP(hAPP(c_COMBC(_1738905, tc_List_Olist(tc_fun(_1738905, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1738905, tc_Nat_Onat), tc_Nat_Onat), tc_fun(tc_List_Olist(tc_fun(_1738905, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), _1738905), c_List_Omap(tc_fun(_1738905, tc_Nat_Onat), tc_Nat_Onat)), hAPP(c_COMBC(tc_fun(_1738905, tc_Nat_Onat), _1738905, tc_Nat_Onat), c_COMBI(tc_fun(_1738905, tc_Nat_Onat))))), _1738907)))], (47627 ^ _780086) ^ [_1739026, _1739028, _1739030, _1739032, _1739034] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1739026, _1739026)), hAPP(hAPP(c_Product__Type_OPair(_1739026, _1739026), _1739028), _1739030)), c_List_Omeasures(_1739026, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1739026, tc_Nat_Onat)), _1739032), _1739034)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1739032, _1739028)), hAPP(_1739032, _1739030)))), 47634 ^ _780086 : [(47635 ^ _780086) ^ [] : [-(hAPP(_1739032, _1739028) = hAPP(_1739032, _1739030))], (47637 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1739026, _1739026)), hAPP(hAPP(c_Product__Type_OPair(_1739026, _1739026), _1739028), _1739030)), c_List_Omeasures(_1739026, _1739034))))]]], (47639 ^ _780086) ^ [_1739305, _1739307, _1739309, _1739311, _1739313] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1739305, _1739305)), hAPP(hAPP(c_Product__Type_OPair(_1739305, _1739305), _1739307), _1739309)), c_List_Omeasures(_1739305, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1739305, tc_Nat_Onat)), _1739311), _1739313))))), 47640 ^ _780086 : [(47641 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1739311, _1739307)), hAPP(_1739311, _1739309)))], (47643 ^ _780086) ^ [] : [hAPP(_1739311, _1739307) = hAPP(_1739311, _1739309), hBOOL(hAPP(hAPP(c_member(tc_prod(_1739305, _1739305)), hAPP(hAPP(c_Product__Type_OPair(_1739305, _1739305), _1739307), _1739309)), c_List_Omeasures(_1739305, _1739313)))]]], (47651 ^ _780086) ^ [_1739628, _1739630, _1739632, _1739634, _1739636] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1739628, _1739630)), hAPP(_1739628, _1739632))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1739634, _1739634)), hAPP(hAPP(c_Product__Type_OPair(_1739634, _1739634), _1739630), _1739632)), c_List_Omeasures(_1739634, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1739634, tc_Nat_Onat)), _1739628), _1739636)))))], (47657 ^ _780086) ^ [_1739799, _1739801, _1739803, _1739805, _1739807, _1739809, _1739811, _1739813] : [47659 ^ _780086 : [(47660 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1739799), 47658 ^ [_1739799, _1739801, _1739803, _1739805, _1739807, _1739809, _1739811, _1739813]), hAPP(c_List_Oset(_1739799), _1739801))))], (47662 ^ _780086) ^ [] : [hAPP(c_Fun_Ocomp(_1739803, _1739803, _1739805, hAPP(_1739807, 47658 ^ [_1739799, _1739801, _1739803, _1739805, _1739807, _1739809, _1739811, _1739813])), _1739809) = hAPP(c_Fun_Ocomp(_1739805, _1739803, _1739805, _1739809), hAPP(_1739811, 47658 ^ [_1739799, _1739801, _1739803, _1739805, _1739807, _1739809, _1739811, _1739813]))]], -(hAPP(c_List_Ofoldl(_1739803, _1739799, hAPP(c_COMBC(_1739799, _1739803, _1739803), _1739807), hAPP(_1739809, _1739813)), _1739801) = hAPP(_1739809, hAPP(c_List_Ofoldl(_1739805, _1739799, hAPP(c_COMBC(_1739799, _1739805, _1739805), _1739811), _1739813), _1739801)))], (47666 ^ _780086) ^ [_1740168, _1740170, _1740172, _1740174] : [class_Orderings_Oorder(_1740168), class_Enum_Oenum(_1740170), 47673 ^ _780086 : [(47674 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1740170, _1740168)), _1740172), _1740174)), 47677 ^ _780086 : [(47678 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1740170, _1740168)), _1740172), _1740174)))], (47680 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1740170), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1740170), c_fNot), hAPP(hAPP(c_COMBS(_1740170, _1740168, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1740168, tc_fun(_1740168, tc_HOL_Obool), _1740170), c_fequal), _1740172)), _1740174)))))]]], (47682 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1740170, _1740168)), _1740172), _1740174))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1740170, _1740168)), _1740172), _1740174)), hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1740170), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1740170), c_fNot), hAPP(hAPP(c_COMBS(_1740170, _1740168, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1740168, tc_fun(_1740168, tc_HOL_Obool), _1740170), c_fequal), _1740172)), _1740174))))]]], (47692 ^ _780086) ^ [_1740688, _1740690, _1740692] : [class_Enum_Oenum(_1740688), class_Enum_Oenum(_1740690), 47699 ^ _780086 : [(47700 ^ _780086) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1740690, _1740688)), _1740692)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1740690), hAPP(hAPP(c_COMBB(tc_fun(_1740688, tc_HOL_Obool), tc_HOL_Obool, _1740690), c_Enum_Oenum__class_Oenum__ex(_1740688)), hAPP(hAPP(c_COMBB(tc_fun(_1740688, tc_prod(_1740690, _1740688)), tc_fun(_1740688, tc_HOL_Obool), _1740690), hAPP(c_COMBB(tc_prod(_1740690, _1740688), tc_HOL_Obool, _1740688), _1740692)), c_Product__Type_OPair(_1740690, _1740688))))))], (47706 ^ _780086) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1740690), hAPP(hAPP(c_COMBB(tc_fun(_1740688, tc_HOL_Obool), tc_HOL_Obool, _1740690), c_Enum_Oenum__class_Oenum__ex(_1740688)), hAPP(hAPP(c_COMBB(tc_fun(_1740688, tc_prod(_1740690, _1740688)), tc_fun(_1740688, tc_HOL_Obool), _1740690), hAPP(c_COMBB(tc_prod(_1740690, _1740688), tc_HOL_Obool, _1740688), _1740692)), c_Product__Type_OPair(_1740690, _1740688))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1740690, _1740688)), _1740692)))]]], (47712 ^ _780086) ^ [_1741127, _1741129] : [class_Enum_Oenum(_1741127), 47715 ^ _780086 : [(47716 ^ _780086) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1741127), _1741129)), -(hBOOL(hAPP(_1741129, 47719 ^ [_1741127, _1741129])))], (47723 ^ _780086) ^ [] : [47724 ^ _780086 : [(47725 ^ _780086) ^ [_1741307] : [hBOOL(hAPP(_1741129, _1741307))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1741127), _1741129)))]]], (47729 ^ _780086) ^ [_1741370, _1741372] : [class_Enum_Oenum(_1741370), 47732 ^ _780086 : [(47733 ^ _780086) ^ [] : [47734 ^ _780086 : [(47735 ^ _780086) ^ [_1741472] : [hBOOL(hAPP(_1741372, _1741472))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1741370), _1741372)))], (47739 ^ _780086) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1741370), _1741372)), -(hBOOL(hAPP(_1741372, 47742 ^ [_1741370, _1741372])))]]], (47746 ^ _780086) ^ [_1741613, _1741615, _1741617, _1741619, _1741621] : [47747 ^ _780086 : [(47748 ^ _780086) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741613)), hAPP(hAPP(c_List_Otake(_1741613), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741613)), _1741615)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741617)), _1741619))), _1741615)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741617)), hAPP(hAPP(c_List_Otake(_1741617), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741613)), _1741615)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741617)), _1741619))), _1741619)))], (47750 ^ _780086) ^ [] : [hBOOL(hAPP(_1741621, hAPP(hAPP(c_List_Ozip(_1741613, _1741617), hAPP(hAPP(c_List_Otake(_1741613), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741613)), _1741615)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741617)), _1741619))), _1741615)), hAPP(hAPP(c_List_Otake(_1741617), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741613)), _1741615)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741617)), _1741619))), _1741619))))]], -(hBOOL(hAPP(_1741621, hAPP(hAPP(c_List_Ozip(_1741613, _1741617), _1741615), _1741619))))], (47754 ^ _780086) ^ [_1742025, _1742027, _1742029, _1742031] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_1742025, _1742027, _1742029, _1742031) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(_1742025, _1742027), _1742029), _1742031)))], (47756 ^ _780086) ^ [_1742070, _1742072, _1742074, _1742076] : [47758 ^ _780086 : [(47759 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1742070), 47757 ^ [_1742070, _1742072, _1742074, _1742076]), hAPP(c_List_Oset(_1742070), _1742072))))], (47761 ^ _780086) ^ [] : [hBOOL(hAPP(_1742074, 47757 ^ [_1742070, _1742072, _1742074, _1742076]))]], -(c_List_OdropWhile(_1742070, _1742074, hAPP(hAPP(c_List_Oappend(_1742070), _1742072), _1742076)) = c_List_OdropWhile(_1742070, _1742074, _1742076))], (47765 ^ _780086) ^ [_1742288, _1742290, _1742292, _1742294, _1742296] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742288)), _1742290) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742292)), _1742294), 47771 ^ _780086 : [(47772 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47770 ^ [_1742288, _1742290, _1742292, _1742294, _1742296]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742288)), _1742290))))], (47774 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(_1742296, hAPP(hAPP(c_List_Onth(_1742288), _1742290), 47770 ^ [_1742288, _1742290, _1742292, _1742294, _1742296])), hAPP(hAPP(c_List_Onth(_1742292), _1742294), 47770 ^ [_1742288, _1742290, _1742292, _1742294, _1742296])))]], -(c_List_Olist__all2(_1742288, _1742292, _1742296, _1742290, _1742294))], (47778 ^ _780086) ^ [_1742646, _1742648] : [class_Orderings_Olinorder(_1742646), hBOOL(hAPP(c_Finite__Set_Ofinite(_1742646), _1742648)), 47786 ^ _780086 : [(47787 ^ _780086) ^ [] : [-(hAPP(c_List_Oset(_1742646), 47785 ^ [_1742646, _1742648]) = _1742648)], (47789 ^ _780086) ^ [] : [-(c_List_Olinorder__class_Osorted(_1742646, 47785 ^ [_1742646, _1742648]))], (47791 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1742646), 47785 ^ [_1742646, _1742648])))], (47793 ^ _780086) ^ [_1742972] : [-(_1742972 = 47785 ^ [_1742646, _1742648]), hAPP(c_List_Oset(_1742646), _1742972) = _1742648, c_List_Olinorder__class_Osorted(_1742646, _1742972), hBOOL(hAPP(c_List_Odistinct(_1742646), _1742972))]]], (47807 ^ _780086) ^ [_1743203, _1743205, _1743207, _1743209] : [47809 ^ _780086 : [(47810 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1743203), 47808 ^ [_1743203, _1743205, _1743207, _1743209]), hAPP(c_List_Oset(_1743203), _1743205))))], (47812 ^ _780086) ^ [] : [hBOOL(hAPP(_1743207, 47808 ^ [_1743203, _1743205, _1743207, _1743209]))]], -(c_List_OtakeWhile(_1743203, _1743207, hAPP(hAPP(c_List_Oappend(_1743203), _1743205), _1743209)) = hAPP(hAPP(c_List_Oappend(_1743203), _1743205), c_List_OtakeWhile(_1743203, _1743207, _1743209)))], (47816 ^ _780086) ^ [_1743437, _1743439, _1743441, _1743443, _1743445] : [class_Orderings_Olinorder(_1743437), 47822 ^ _780086 : [(47823 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1743439), 47821 ^ [_1743437, _1743439, _1743441, _1743443, _1743445]), hAPP(c_List_Oset(_1743439), _1743441))))], (47825 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1743437), hAPP(_1743443, _1743445)), hAPP(_1743443, 47821 ^ [_1743437, _1743439, _1743441, _1743443, _1743445])))]], -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1743439, _1743437, _1743443), _1743445), _1743441) = hAPP(hAPP(c_List_Olist_OCons(_1743439), _1743445), _1743441))], (47829 ^ _780086) ^ [_1743780, _1743782, _1743784, _1743786, _1743788] : [hAPP(hAPP(c_List_Olist_OCons(_1743780), _1743782), _1743784) = hAPP(c_List_Ofilter(_1743780, _1743786), _1743788), 47834 ^ _780086 : [(47835 ^ _780086) ^ [] : [-(_1743788 = hAPP(hAPP(c_List_Oappend(_1743780), 47832 ^ [_1743780, _1743782, _1743784, _1743786, _1743788]), hAPP(hAPP(c_List_Olist_OCons(_1743780), _1743782), 47833 ^ [_1743780, _1743782, _1743784, _1743786, _1743788])))], (47843 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1743786, _1743782)))], (47845 ^ _780086) ^ [] : [-(_1743784 = hAPP(c_List_Ofilter(_1743780, _1743786), 47833 ^ [_1743780, _1743782, _1743784, _1743786, _1743788]))], (47837 ^ _780086) ^ [_1744094] : [hBOOL(hAPP(hAPP(c_member(_1743780), _1744094), hAPP(c_List_Oset(_1743780), 47832 ^ [_1743780, _1743782, _1743784, _1743786, _1743788]))), hBOOL(hAPP(_1743786, _1744094))]]], (47847 ^ _780086) ^ [_1744298, _1744300, _1744302, _1744304, _1744306] : [-(hAPP(hAPP(c_List_Olist_OCons(_1744298), _1744300), _1744302) = hAPP(c_List_Ofilter(_1744298, _1744304), _1744306)), 47848 ^ _780086 : [(47849 ^ _780086) ^ [_1744426, _1744428] : [_1744306 = hAPP(hAPP(c_List_Oappend(_1744298), _1744428), hAPP(hAPP(c_List_Olist_OCons(_1744298), _1744300), _1744426)), 47855 ^ _780086 : [(47856 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1744298), 47854 ^ [_1744298, _1744300, _1744302, _1744304, _1744306, _1744426, _1744428]), hAPP(c_List_Oset(_1744298), _1744428))))], (47858 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1744304, 47854 ^ [_1744298, _1744300, _1744302, _1744304, _1744306, _1744426, _1744428])))]], hBOOL(hAPP(_1744304, _1744300)), _1744302 = hAPP(c_List_Ofilter(_1744298, _1744304), _1744426)]]], (47868 ^ _780086) ^ [_1744848, _1744850, _1744852, _1744854, _1744856] : [hAPP(c_List_Ofilter(_1744848, _1744850), _1744852) = hAPP(hAPP(c_List_Olist_OCons(_1744848), _1744854), _1744856), 47873 ^ _780086 : [(47874 ^ _780086) ^ [] : [-(_1744852 = hAPP(hAPP(c_List_Oappend(_1744848), 47871 ^ [_1744848, _1744850, _1744852, _1744854, _1744856]), hAPP(hAPP(c_List_Olist_OCons(_1744848), _1744854), 47872 ^ [_1744848, _1744850, _1744852, _1744854, _1744856])))], (47882 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1744850, _1744854)))], (47884 ^ _780086) ^ [] : [-(_1744856 = hAPP(c_List_Ofilter(_1744848, _1744850), 47872 ^ [_1744848, _1744850, _1744852, _1744854, _1744856]))], (47876 ^ _780086) ^ [_1745162] : [hBOOL(hAPP(hAPP(c_member(_1744848), _1745162), hAPP(c_List_Oset(_1744848), 47871 ^ [_1744848, _1744850, _1744852, _1744854, _1744856]))), hBOOL(hAPP(_1744850, _1745162))]]], (47886 ^ _780086) ^ [_1745366, _1745368, _1745370, _1745372, _1745374] : [-(hAPP(c_List_Ofilter(_1745366, _1745368), _1745370) = hAPP(hAPP(c_List_Olist_OCons(_1745366), _1745372), _1745374)), 47887 ^ _780086 : [(47888 ^ _780086) ^ [_1745494, _1745496] : [_1745370 = hAPP(hAPP(c_List_Oappend(_1745366), _1745496), hAPP(hAPP(c_List_Olist_OCons(_1745366), _1745372), _1745494)), 47894 ^ _780086 : [(47895 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1745366), 47893 ^ [_1745366, _1745368, _1745370, _1745372, _1745374, _1745494, _1745496]), hAPP(c_List_Oset(_1745366), _1745496))))], (47897 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1745368, 47893 ^ [_1745366, _1745368, _1745370, _1745372, _1745374, _1745494, _1745496])))]], hBOOL(hAPP(_1745368, _1745372)), _1745374 = hAPP(c_List_Ofilter(_1745366, _1745368), _1745494)]]], (47907 ^ _780086) ^ [_1745892, _1745894, _1745896, _1745898] : [class_Orderings_Oorder(_1745892), class_Enum_Oenum(_1745894), 47914 ^ _780086 : [(47915 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1745894, _1745892)), _1745896), _1745898)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1745894), hAPP(hAPP(c_COMBS(_1745894, _1745892, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1745892, tc_fun(_1745892, tc_HOL_Obool), _1745894), c_Orderings_Oord__class_Oless__eq(_1745892)), _1745896)), _1745898))))], (47921 ^ _780086) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1745894), hAPP(hAPP(c_COMBS(_1745894, _1745892, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1745892, tc_fun(_1745892, tc_HOL_Obool), _1745894), c_Orderings_Oord__class_Oless__eq(_1745892)), _1745896)), _1745898))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1745894, _1745892)), _1745896), _1745898)))]]], (47927 ^ _780086) ^ [_1746282, _1746284] : [class_Enum_Oenum(_1746282), 47930 ^ _780086 : [(47931 ^ _780086) ^ [] : [hBOOL(hAPP(_1746284, 47932 ^ [_1746282, _1746284])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1746282), _1746284)))], (47938 ^ _780086) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1746282), _1746284)), 47941 ^ _780086 : [(47942 ^ _780086) ^ [_1746500] : [-(hBOOL(hAPP(_1746284, _1746500)))]]]]], (47944 ^ _780086) ^ [_1746535, _1746537] : [class_Enum_Oenum(_1746535), 47947 ^ _780086 : [(47948 ^ _780086) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1746535), _1746537)), 47951 ^ _780086 : [(47952 ^ _780086) ^ [_1746661] : [-(hBOOL(hAPP(_1746537, _1746661)))]]], (47954 ^ _780086) ^ [] : [hBOOL(hAPP(_1746537, 47955 ^ [_1746535, _1746537])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1746535), _1746537)))]]], (47961 ^ _780086) ^ [_1746788, _1746790, _1746792] : [class_Enum_Oenum(_1746788), class_Enum_Oenum(_1746790), 47968 ^ _780086 : [(47969 ^ _780086) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1746790, _1746788)), _1746792)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1746790), hAPP(hAPP(c_COMBB(tc_fun(_1746788, tc_HOL_Obool), tc_HOL_Obool, _1746790), c_Enum_Oenum__class_Oenum__all(_1746788)), hAPP(hAPP(c_COMBB(tc_fun(_1746788, tc_prod(_1746790, _1746788)), tc_fun(_1746788, tc_HOL_Obool), _1746790), hAPP(c_COMBB(tc_prod(_1746790, _1746788), tc_HOL_Obool, _1746788), _1746792)), c_Product__Type_OPair(_1746790, _1746788))))))], (47975 ^ _780086) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1746790), hAPP(hAPP(c_COMBB(tc_fun(_1746788, tc_HOL_Obool), tc_HOL_Obool, _1746790), c_Enum_Oenum__class_Oenum__all(_1746788)), hAPP(hAPP(c_COMBB(tc_fun(_1746788, tc_prod(_1746790, _1746788)), tc_fun(_1746788, tc_HOL_Obool), _1746790), hAPP(c_COMBB(tc_prod(_1746790, _1746788), tc_HOL_Obool, _1746788), _1746792)), c_Product__Type_OPair(_1746790, _1746788))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1746790, _1746788)), _1746792)))]]], (47981 ^ _780086) ^ [_1747227, _1747229, _1747231, _1747233] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1747227), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1747229)), _1747231))), 47987 ^ _780086 : [(47988 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1747229), 47986 ^ [_1747227, _1747229, _1747231, _1747233]), hAPP(c_List_Oset(_1747229), _1747231))))], (47990 ^ _780086) ^ [] : [hBOOL(hAPP(_1747233, 47986 ^ [_1747227, _1747229, _1747231, _1747233]))]], -(hBOOL(hAPP(_1747233, hAPP(hAPP(c_List_Onth(_1747229), _1747231), _1747227))))], (47994 ^ _780086) ^ [_1747513, _1747515, _1747517] : [class_Orderings_Olinorder(_1747513), 48000 ^ _780086 : [(48001 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1747513), 47999 ^ [_1747513, _1747515, _1747517]), hAPP(c_List_Oset(_1747513), _1747515))))], (48003 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1747513), _1747517), 47999 ^ [_1747513, _1747515, _1747517]))]], c_List_Olinorder__class_Osorted(_1747513, _1747515), -(c_List_Olinorder__class_Osorted(_1747513, hAPP(hAPP(c_List_Olist_OCons(_1747513), _1747517), _1747515)))], (48011 ^ _780086) ^ [_1747847, _1747849, _1747851] : [c_List_Olist__ex(_1747847, _1747849, _1747851), 48015 ^ _780086 : [(48016 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48014 ^ [_1747847, _1747849, _1747851]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1747847)), _1747851))))], (48018 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1747849, hAPP(hAPP(c_List_Onth(_1747847), _1747851), 48014 ^ [_1747847, _1747849, _1747851]))))]]], (48020 ^ _780086) ^ [_1748017, _1748019, _1748021] : [-(c_List_Olist__ex(_1748017, _1748019, _1748021)), 48021 ^ _780086 : [(48022 ^ _780086) ^ [_1748082] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1748082), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1748017)), _1748021))), hBOOL(hAPP(_1748019, hAPP(hAPP(c_List_Onth(_1748017), _1748021), _1748082)))]]], (48030 ^ _780086) ^ [_1748255, _1748257, _1748259] : [hBOOL(hAPP(hAPP(c_member(_1748255), _1748257), hAPP(c_List_Oset(_1748255), _1748259))), -(_1748259 = hAPP(hAPP(c_List_Oappend(_1748255), 48033 ^ [_1748255, _1748257, _1748259]), hAPP(hAPP(c_List_Olist_OCons(_1748255), _1748257), 48034 ^ [_1748255, _1748257, _1748259])))], (48038 ^ _780086) ^ [_1748414, _1748416, _1748418] : [48039 ^ _780086 : [(48040 ^ _780086) ^ [_1748491, _1748493] : [_1748418 = hAPP(hAPP(c_List_Oappend(_1748414), _1748493), hAPP(hAPP(c_List_Olist_OCons(_1748414), _1748416), _1748491))]], -(hBOOL(hAPP(hAPP(c_member(_1748414), _1748416), hAPP(c_List_Oset(_1748414), _1748418))))], (48044 ^ _780086) ^ [_1748586, _1748588] : [c_List_Olist__ex(_1748586, _1748588, c_List_Olist_ONil(_1748586))], (48056 ^ _780086) ^ [_1748747, _1748749, _1748751, _1748753] : [48057 ^ _780086 : [(48058 ^ _780086) ^ [] : [c_List_Olist__ex(_1748747, _1748749, _1748751)], (48060 ^ _780086) ^ [] : [c_List_Olist__ex(_1748747, _1748749, _1748753)]], -(c_List_Olist__ex(_1748747, _1748749, hAPP(hAPP(c_List_Oappend(_1748747), _1748751), _1748753)))], (48046 ^ _780086) ^ [_1748635, _1748637, _1748639, _1748641] : [c_List_Olist__ex(_1748635, _1748637, hAPP(hAPP(c_List_Oappend(_1748635), _1748639), _1748641)), -(c_List_Olist__ex(_1748635, _1748637, _1748639)), -(c_List_Olist__ex(_1748635, _1748637, _1748641))], (48064 ^ _780086) ^ [_1748908, _1748910, _1748912] : [c_List_Olist__ex(_1748908, _1748910, _1748912), 48068 ^ _780086 : [(48069 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1748908), 48067 ^ [_1748908, _1748910, _1748912]), hAPP(c_List_Oset(_1748908), _1748912))))], (48071 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1748910, 48067 ^ [_1748908, _1748910, _1748912])))]]], (48073 ^ _780086) ^ [_1749062, _1749064, _1749066] : [-(c_List_Olist__ex(_1749062, _1749064, _1749066)), 48074 ^ _780086 : [(48075 ^ _780086) ^ [_1749119] : [hBOOL(hAPP(hAPP(c_member(_1749062), _1749119), hAPP(c_List_Oset(_1749062), _1749066))), hBOOL(hAPP(_1749064, _1749119))]]], (48083 ^ _780086) ^ [_1749276, _1749278, _1749280] : [c_List_Olist__ex(_1749276, _1749278, hAPP(c_List_Orev(_1749276), _1749280)), -(c_List_Olist__ex(_1749276, _1749278, _1749280))], (48089 ^ _780086) ^ [_1749365, _1749367, _1749369] : [c_List_Olist__ex(_1749365, _1749367, _1749369), -(c_List_Olist__ex(_1749365, _1749367, hAPP(c_List_Orev(_1749365), _1749369)))], (48105 ^ _780086) ^ [_1749595, _1749597, _1749599, _1749601] : [48106 ^ _780086 : [(48107 ^ _780086) ^ [] : [hBOOL(hAPP(_1749597, _1749599))], (48109 ^ _780086) ^ [] : [c_List_Olist__ex(_1749595, _1749597, _1749601)]], -(c_List_Olist__ex(_1749595, _1749597, hAPP(hAPP(c_List_Olist_OCons(_1749595), _1749599), _1749601)))], (48095 ^ _780086) ^ [_1749481, _1749483, _1749485, _1749487] : [c_List_Olist__ex(_1749481, _1749483, hAPP(hAPP(c_List_Olist_OCons(_1749481), _1749485), _1749487)), -(hBOOL(hAPP(_1749483, _1749485))), -(c_List_Olist__ex(_1749481, _1749483, _1749487))], (48113 ^ _780086) ^ [_1749758, _1749760, _1749762] : [hBOOL(hAPP(hAPP(c_member(_1749758), _1749760), hAPP(c_List_Oset(_1749758), _1749762))), 48118 ^ _780086 : [(48119 ^ _780086) ^ [] : [-(_1749762 = hAPP(hAPP(c_List_Oappend(_1749758), 48116 ^ [_1749758, _1749760, _1749762]), hAPP(hAPP(c_List_Olist_OCons(_1749758), _1749760), 48117 ^ [_1749758, _1749760, _1749762])))], (48121 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1749758), _1749760), hAPP(c_List_Oset(_1749758), 48116 ^ [_1749758, _1749760, _1749762])))]]], (48123 ^ _780086) ^ [_1750013, _1750015, _1750017] : [-(hBOOL(hAPP(hAPP(c_member(_1750013), _1750015), hAPP(c_List_Oset(_1750013), _1750017)))), 48124 ^ _780086 : [(48125 ^ _780086) ^ [_1750102] : [48126 ^ _780086 : [(48127 ^ _780086) ^ [_1750175] : [_1750017 = hAPP(hAPP(c_List_Oappend(_1750013), _1750102), hAPP(hAPP(c_List_Olist_OCons(_1750013), _1750015), _1750175))]], -(hBOOL(hAPP(hAPP(c_member(_1750013), _1750015), hAPP(c_List_Oset(_1750013), _1750102))))]]], (48133 ^ _780086) ^ [_1750314, _1750316, _1750318] : [hBOOL(hAPP(hAPP(c_member(_1750314), _1750316), hAPP(c_List_Oset(_1750314), _1750318))), 48138 ^ _780086 : [(48139 ^ _780086) ^ [] : [-(_1750318 = hAPP(hAPP(c_List_Oappend(_1750314), 48136 ^ [_1750314, _1750316, _1750318]), hAPP(hAPP(c_List_Olist_OCons(_1750314), _1750316), 48137 ^ [_1750314, _1750316, _1750318])))], (48141 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1750314), _1750316), hAPP(c_List_Oset(_1750314), 48137 ^ [_1750314, _1750316, _1750318])))]]], (48143 ^ _780086) ^ [_1750569, _1750571, _1750573] : [-(hBOOL(hAPP(hAPP(c_member(_1750569), _1750571), hAPP(c_List_Oset(_1750569), _1750573)))), 48144 ^ _780086 : [(48145 ^ _780086) ^ [_1750658, _1750660] : [_1750573 = hAPP(hAPP(c_List_Oappend(_1750569), _1750660), hAPP(hAPP(c_List_Olist_OCons(_1750569), _1750571), _1750658)), -(hBOOL(hAPP(hAPP(c_member(_1750569), _1750571), hAPP(c_List_Oset(_1750569), _1750658))))]]], (48163 ^ _780086) ^ [_1751073, _1751075, _1751077] : [48165 ^ _780086 : [(48166 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48164 ^ [_1751073, _1751075, _1751077]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1751073)), _1751077))))], (48168 ^ _780086) ^ [] : [hBOOL(hAPP(_1751075, hAPP(hAPP(c_List_Onth(_1751073), _1751077), 48164 ^ [_1751073, _1751075, _1751077])))]], -(c_List_Olist__all(_1751073, _1751075, _1751077))], (48153 ^ _780086) ^ [_1750859, _1750861, _1750863] : [c_List_Olist__all(_1750859, _1750861, _1750863), 48156 ^ _780086 : [(48157 ^ _780086) ^ [_1750948] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1750948), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1750859)), _1750863))), -(hBOOL(hAPP(_1750861, hAPP(hAPP(c_List_Onth(_1750859), _1750863), _1750948))))]]], (48172 ^ _780086) ^ [] : [-(c_FunDef_Ois__measure(tc_Int_Oint, hAPP(c_Fun_Ocomp(tc_Int_Oint, tc_Nat_Onat, tc_Int_Oint, c_Int_Onat), c_Groups_Oabs__class_Oabs(tc_Int_Oint))))], (48174 ^ _780086) ^ [_1751299, _1751301] : [-(c_List_Olist__all(_1751299, _1751301, c_List_Olist_ONil(_1751299)))], (48176 ^ _780086) ^ [_1751348, _1751350, _1751352, _1751354] : [c_List_Olist__all(_1751348, _1751350, hAPP(hAPP(c_List_Oappend(_1751348), _1751352), _1751354)), 48179 ^ _780086 : [(48180 ^ _780086) ^ [] : [-(c_List_Olist__all(_1751348, _1751350, _1751352))], (48182 ^ _780086) ^ [] : [-(c_List_Olist__all(_1751348, _1751350, _1751354))]]], (48184 ^ _780086) ^ [_1751473, _1751475, _1751477, _1751479] : [-(c_List_Olist__all(_1751473, _1751475, hAPP(hAPP(c_List_Oappend(_1751473), _1751477), _1751479))), c_List_Olist__all(_1751473, _1751475, _1751477), c_List_Olist__all(_1751473, _1751475, _1751479)], (48194 ^ _780086) ^ [_1751634] : [class_Nat_Osize(_1751634), -(c_FunDef_Ois__measure(_1751634, c_Nat_Osize__class_Osize(_1751634)))], (48200 ^ _780086) ^ [_1751711, _1751713] : [-(c_FunDef_Ois__measure(_1751711, _1751713))], (48202 ^ _780086) ^ [_1751736, _1751738] : [-(c_FunDef_Ois__measure(_1751736, _1751738))], (48204 ^ _780086) ^ [_1751761, _1751763] : [-(c_FunDef_Ois__measure(_1751761, _1751763))], (48216 ^ _780086) ^ [_1751994, _1751996, _1751998] : [48218 ^ _780086 : [(48219 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1751994), 48217 ^ [_1751994, _1751996, _1751998]), hAPP(c_List_Oset(_1751994), _1751998))))], (48221 ^ _780086) ^ [] : [hBOOL(hAPP(_1751996, 48217 ^ [_1751994, _1751996, _1751998]))]], -(c_List_Olist__all(_1751994, _1751996, _1751998))], (48206 ^ _780086) ^ [_1751804, _1751806, _1751808] : [c_List_Olist__all(_1751804, _1751806, _1751808), 48209 ^ _780086 : [(48210 ^ _780086) ^ [_1751885] : [hBOOL(hAPP(hAPP(c_member(_1751804), _1751885), hAPP(c_List_Oset(_1751804), _1751808))), -(hBOOL(hAPP(_1751806, _1751885)))]]], (48225 ^ _780086) ^ [_1752176, _1752178, _1752180] : [c_FunDef_Ois__measure(_1752176, _1752178), -(c_FunDef_Ois__measure(tc_prod(_1752176, _1752180), hAPP(hAPP(c_COMBB(_1752176, tc_Nat_Onat, tc_prod(_1752176, _1752180)), _1752178), c_Product__Type_Ofst(_1752176, _1752180))))], (48231 ^ _780086) ^ [_1752293, _1752295, _1752297] : [c_FunDef_Ois__measure(_1752293, _1752295), -(c_FunDef_Ois__measure(tc_prod(_1752297, _1752293), hAPP(hAPP(c_COMBB(_1752293, tc_Nat_Onat, tc_prod(_1752297, _1752293)), _1752295), c_Product__Type_Osnd(_1752297, _1752293))))], (48237 ^ _780086) ^ [_1752428, _1752430, _1752432] : [c_List_Olist__all(_1752428, _1752430, hAPP(c_List_Orev(_1752428), _1752432)), -(c_List_Olist__all(_1752428, _1752430, _1752432))], (48243 ^ _780086) ^ [_1752517, _1752519, _1752521] : [c_List_Olist__all(_1752517, _1752519, _1752521), -(c_List_Olist__all(_1752517, _1752519, hAPP(c_List_Orev(_1752517), _1752521)))], (48249 ^ _780086) ^ [_1752633, _1752635, _1752637, _1752639] : [c_List_Olist__all(_1752633, _1752635, hAPP(hAPP(c_List_Olist_OCons(_1752633), _1752637), _1752639)), 48252 ^ _780086 : [(48253 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1752635, _1752637)))], (48255 ^ _780086) ^ [] : [-(c_List_Olist__all(_1752633, _1752635, _1752639))]]], (48257 ^ _780086) ^ [_1752760, _1752762, _1752764, _1752766] : [-(c_List_Olist__all(_1752760, _1752762, hAPP(hAPP(c_List_Olist_OCons(_1752760), _1752764), _1752766))), hBOOL(hAPP(_1752762, _1752764)), c_List_Olist__all(_1752760, _1752762, _1752766)], (48267 ^ _780086) ^ [_1752941, _1752943, _1752945] : [48269 ^ _780086 : [(48270 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1752941), 48268 ^ [_1752941, _1752943, _1752945]), hAPP(c_List_Oset(_1752941), _1752943))))], (48272 ^ _780086) ^ [] : [hBOOL(hAPP(_1752945, 48268 ^ [_1752941, _1752943, _1752945]))]], -(c_List_Olist__all(_1752941, _1752945, _1752943))], (48276 ^ _780086) ^ [_1753117, _1753119, _1753121] : [c_List_Olist__all(_1753117, _1753121, _1753119), 48279 ^ _780086 : [(48280 ^ _780086) ^ [_1753198] : [hBOOL(hAPP(hAPP(c_member(_1753117), _1753198), hAPP(c_List_Oset(_1753117), _1753119))), -(hBOOL(hAPP(_1753121, _1753198)))]]], (48296 ^ _780086) ^ [_1753521, _1753523, _1753525] : [48298 ^ _780086 : [(48299 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1753521), 48297 ^ [_1753521, _1753523, _1753525]), hAPP(c_List_Oset(_1753521), _1753525))))], (48301 ^ _780086) ^ [] : [hBOOL(hAPP(_1753523, 48297 ^ [_1753521, _1753523, _1753525]))]], -(c_List_Olist__all(_1753521, _1753523, _1753525))], (48286 ^ _780086) ^ [_1753331, _1753333, _1753335] : [c_List_Olist__all(_1753331, _1753333, _1753335), 48289 ^ _780086 : [(48290 ^ _780086) ^ [_1753412] : [hBOOL(hAPP(hAPP(c_member(_1753331), _1753412), hAPP(c_List_Oset(_1753331), _1753335))), -(hBOOL(hAPP(_1753333, _1753412)))]]], (48321 ^ _780086) ^ [_1754000, _1754002, _1754004, _1754006] : [-(c_List_Olist__ex1(_1754000, _1754002, hAPP(hAPP(c_List_Olist_OCons(_1754000), _1754004), _1754006))), 48324 ^ _780086 : [(48325 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1754002, _1754004)))], (48327 ^ _780086) ^ [] : [c_List_Olist__all(_1754000, hAPP(hAPP(c_COMBS(_1754000, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1754000), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1754000), c_fNot), _1754002))), hAPP(c_fequal, _1754004)), _1754006)]], 48328 ^ _780086 : [(48329 ^ _780086) ^ [] : [hBOOL(hAPP(_1754002, _1754004))], (48331 ^ _780086) ^ [] : [c_List_Olist__ex1(_1754000, _1754002, _1754006)]]], (48305 ^ _780086) ^ [_1753724, _1753726, _1753728, _1753730] : [c_List_Olist__ex1(_1753724, _1753726, hAPP(hAPP(c_List_Olist_OCons(_1753724), _1753728), _1753730)), 48308 ^ _780086 : [(48309 ^ _780086) ^ [] : [hBOOL(hAPP(_1753726, _1753728)), -(c_List_Olist__all(_1753724, hAPP(hAPP(c_COMBS(_1753724, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1753724), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1753724), c_fNot), _1753726))), hAPP(c_fequal, _1753728)), _1753730))], (48315 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1753726, _1753728))), -(c_List_Olist__ex1(_1753724, _1753726, _1753730))]]], (48335 ^ _780086) ^ [] : [-(c_Nat__Transfer_Otransfer__morphism(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_COMBK(tc_HOL_Obool, tc_Nat_Onat), c_fTrue)))], (48337 ^ _780086) ^ [_1754338, _1754340] : [c_List_Olist__ex1(_1754338, _1754340, c_List_Olist_ONil(_1754338))], (48339 ^ _780086) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48341 ^ _780086) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48343 ^ _780086) ^ [_1754420, _1754422, _1754424] : [c_List_Olist__ex1(_1754420, _1754422, _1754424), 48347 ^ _780086 : [(48348 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1754420), 48346 ^ [_1754420, _1754422, _1754424]), hAPP(c_List_Oset(_1754420), _1754424))))], (48350 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1754422, 48346 ^ [_1754420, _1754422, _1754424])))], (48352 ^ _780086) ^ [_1754666] : [-(_1754666 = 48346 ^ [_1754420, _1754422, _1754424]), hBOOL(hAPP(hAPP(c_member(_1754420), _1754666), hAPP(c_List_Oset(_1754420), _1754424))), hBOOL(hAPP(_1754422, _1754666))]]], (48362 ^ _780086) ^ [_1754853, _1754855, _1754857] : [-(c_List_Olist__ex1(_1754853, _1754855, _1754857)), 48363 ^ _780086 : [(48364 ^ _780086) ^ [_1754947] : [hBOOL(hAPP(hAPP(c_member(_1754853), _1754947), hAPP(c_List_Oset(_1754853), _1754857))), hBOOL(hAPP(_1754855, _1754947)), 48372 ^ _780086 : [(48373 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1754853), 48371 ^ [_1754853, _1754855, _1754857, _1754947]), hAPP(c_List_Oset(_1754853), _1754857))))], (48375 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1754855, 48371 ^ [_1754853, _1754855, _1754857, _1754947])))], (48377 ^ _780086) ^ [] : [48371 ^ [_1754853, _1754855, _1754857, _1754947] = _1754947]]]]], (48381 ^ _780086) ^ [_1755300, _1755302, _1755304, _1755306, _1755308] : [_1755300 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1755302, _1755304, _1755306, _1755308), _1755300) = c_Lazy__Sequence_Ohit__bound(_1755304))], (48387 ^ _780086) ^ [_1755397, _1755399, _1755401, _1755403, _1755405] : [-(_1755397 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1755399, _1755401, _1755403, _1755405), _1755397) = c_Lazy__Sequence_Ohb__bind(_1755399, _1755401, hAPP(_1755403, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1755397), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBC(_1755399, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1755401))), _1755405), _1755397)))], (48393 ^ _780086) ^ [_1755495, _1755497, _1755499, _1755501, _1755503] : [_1755495 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Opos__decr__bind(_1755497, _1755499, _1755501, _1755503), _1755495) = c_Lazy__Sequence_Oempty(_1755499))], (48399 ^ _780086) ^ [_1755592, _1755594, _1755596, _1755598, _1755600] : [-(_1755592 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Opos__decr__bind(_1755594, _1755596, _1755598, _1755600), _1755592) = hAPP(c_Lazy__Sequence_Obind(_1755594, _1755596, hAPP(_1755598, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1755592), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), hAPP(hAPP(c_COMBC(_1755594, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1755596)), _1755600), _1755592)))], (48405 ^ _780086) ^ [_1755672, _1755674, _1755676, _1755678, _1755680, _1755682, _1755684] : [-(c_New__Random__Sequence_Oneg__decr__bind(_1755672, _1755674, _1755676, _1755678, _1755680, _1755682, _1755684) = c_New__DSequence_Oneg__decr__bind(_1755672, _1755674, hAPP(hAPP(hAPP(_1755676, _1755680), _1755682), _1755684), hAPP(hAPP(c_COMBC(_1755672, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1755674)))), hAPP(hAPP(c_COMBC(_1755672, tc_Code__Numeral_Ocode__numeral, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1755674))))), hAPP(hAPP(c_COMBC(_1755672, tc_Code__Numeral_Ocode__numeral, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1755674)))))), _1755678), _1755680)), _1755682)), _1755684)))], (48407 ^ _780086) ^ [_1755789, _1755791, _1755793, _1755795, _1755797, _1755799, _1755801] : [-(c_New__Random__Sequence_Opos__decr__bind(_1755789, _1755791, _1755793, _1755795, _1755797, _1755799, _1755801) = c_New__DSequence_Opos__decr__bind(_1755789, _1755791, hAPP(hAPP(hAPP(_1755793, _1755797), _1755799), _1755801), hAPP(hAPP(c_COMBC(_1755789, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1755791))), hAPP(hAPP(c_COMBC(_1755789, tc_Code__Numeral_Ocode__numeral, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1755791)))), hAPP(hAPP(c_COMBC(_1755789, tc_Code__Numeral_Ocode__numeral, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1755791))))), _1755795), _1755797)), _1755799)), _1755801)))], (48409 ^ _780086) ^ [_1755900, _1755902, _1755904, _1755906, _1755908] : [-(hAPP(c_New__DSequence_Oneg__bind(_1755900, _1755902, _1755904, _1755906), _1755908) = c_Lazy__Sequence_Ohb__bind(_1755900, _1755902, hAPP(_1755904, _1755908), hAPP(hAPP(c_COMBC(_1755900, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1755902))), _1755906), _1755908)))], (48411 ^ _780086) ^ [_1755961, _1755963] : [-(hAPP(c_New__DSequence_Opos__empty(_1755961), _1755963) = c_Lazy__Sequence_Oempty(_1755961))], (48413 ^ _780086) ^ [_1755993, _1755995, _1755997, _1755999] : [-(c_New__Random__Sequence_Opos__empty(_1755993, _1755995, _1755997, _1755999) = c_New__DSequence_Opos__empty(_1755993))], (48415 ^ _780086) ^ [_1756029, _1756031, _1756033, _1756035, _1756037, _1756039, _1756041] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(_1756029, _1756031, _1756033, _1756035), _1756037), _1756039), _1756041) = c_New__DSequence_Oneg__bind(_1756029, _1756031, hAPP(hAPP(hAPP(_1756033, _1756037), _1756039), _1756041), hAPP(hAPP(c_COMBC(_1756029, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1756031)))), hAPP(hAPP(c_COMBC(_1756029, tc_Code__Numeral_Ocode__numeral, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1756031))))), hAPP(hAPP(c_COMBC(_1756029, tc_Code__Numeral_Ocode__numeral, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1756031)))))), _1756035), _1756037)), _1756039)), _1756041)))], (48417 ^ _780086) ^ [_1756152, _1756154, _1756156, _1756158, _1756160] : [-(hAPP(c_New__DSequence_Opos__bind(_1756152, _1756154, _1756156, _1756158), _1756160) = hAPP(c_Lazy__Sequence_Obind(_1756152, _1756154, hAPP(_1756156, _1756160)), hAPP(hAPP(c_COMBC(_1756152, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1756154)), _1756158), _1756160)))], (48419 ^ _780086) ^ [_1756213, _1756215, _1756217, _1756219] : [-(c_New__Random__Sequence_Oneg__map(_1756213, _1756215, _1756217, _1756219) = c_New__Random__Sequence_Oneg__bind(_1756213, _1756215, _1756219, hAPP(c_Fun_Ocomp(_1756215, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1756215)))))), _1756213, c_New__Random__Sequence_Oneg__single(_1756215)), _1756217)))], (48421 ^ _780086) ^ [_1756278, _1756280, _1756282, _1756284, _1756286] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(_1756278), _1756280), _1756282), _1756284), _1756286) = c_New__DSequence_Oneg__single(_1756278, _1756280))], (48423 ^ _780086) ^ [_1756326, _1756328, _1756330, _1756332, _1756334, _1756336, _1756338] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(_1756326, _1756328, _1756330, _1756332), _1756334), _1756336), _1756338) = c_New__DSequence_Opos__bind(_1756326, _1756328, hAPP(hAPP(hAPP(_1756330, _1756334), _1756336), _1756338), hAPP(hAPP(c_COMBC(_1756326, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1756328))), hAPP(hAPP(c_COMBC(_1756326, tc_Code__Numeral_Ocode__numeral, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1756328)))), hAPP(hAPP(c_COMBC(_1756326, tc_Code__Numeral_Ocode__numeral, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1756328))))), _1756332), _1756334)), _1756336)), _1756338)))], (48425 ^ _780086) ^ [_1756443, _1756445, _1756447] : [-(hAPP(c_New__DSequence_Oneg__single(_1756443, _1756445), _1756447) = c_Lazy__Sequence_Ohb__single(_1756443, _1756445))], (48427 ^ _780086) ^ [_1756479, _1756481, _1756483, _1756485] : [-(c_New__Random__Sequence_Opos__map(_1756479, _1756481, _1756483, _1756485) = c_New__Random__Sequence_Opos__bind(_1756479, _1756481, _1756485, hAPP(c_Fun_Ocomp(_1756481, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1756481))))), _1756479, c_New__Random__Sequence_Opos__single(_1756481)), _1756483)))], (48429 ^ _780086) ^ [_1756542, _1756544, _1756546, _1756548, _1756550] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(_1756542), _1756544), _1756546), _1756548), _1756550) = c_New__DSequence_Opos__single(_1756542, _1756544))], (48431 ^ _780086) ^ [_1756590, _1756592, _1756594] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1756590)), c_List_Osplice(_1756590, _1756592, _1756594)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1756590)), _1756592)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1756590)), _1756594)))], (48433 ^ _780086) ^ [_1756648, _1756650, _1756652, _1756654, _1756656] : [-(c_List_Osplice(_1756648, hAPP(hAPP(c_List_Olist_OCons(_1756648), _1756650), _1756652), hAPP(hAPP(c_List_Olist_OCons(_1756648), _1756654), _1756656)) = hAPP(hAPP(c_List_Olist_OCons(_1756648), _1756650), hAPP(hAPP(c_List_Olist_OCons(_1756648), _1756654), c_List_Osplice(_1756648, _1756652, _1756656))))], (48435 ^ _780086) ^ [_1756719, _1756721] : [-(c_List_Osplice(_1756719, c_List_Olist_ONil(_1756719), _1756721) = _1756721)], (48437 ^ _780086) ^ [_1756750, _1756752] : [-(c_List_Osplice(_1756750, _1756752, c_List_Olist_ONil(_1756750)) = _1756752)], (48439 ^ _780086) ^ [_1756781, _1756783, _1756785] : [-(c_List_Osplice(_1756781, hAPP(hAPP(c_List_Olist_OCons(_1756781), _1756783), _1756785), c_List_Olist_ONil(_1756781)) = hAPP(hAPP(c_List_Olist_OCons(_1756781), _1756783), _1756785))], (48441 ^ _780086) ^ [_1756830, _1756832, _1756834] : [-(hAPP(c_New__DSequence_Opos__single(_1756830, _1756832), _1756834) = hAPP(c_Lazy__Sequence_Osingle(_1756830), _1756832))], (48443 ^ _780086) ^ [_1756883, _1756885] : [c_Wellfounded_Oacyclic(_1756883, hAPP(c_Set_OCollect(tc_prod(_1756883, _1756883)), hAPP(c_Product__Type_Oprod_Oprod__case(_1756883, _1756883, tc_HOL_Obool), c_Predicate_Oconversep(_1756883, _1756883, _1756885)))), -(c_Wellfounded_Oacyclic(_1756883, hAPP(c_Set_OCollect(tc_prod(_1756883, _1756883)), hAPP(c_Product__Type_Oprod_Oprod__case(_1756883, _1756883, tc_HOL_Obool), _1756885))))], (48449 ^ _780086) ^ [_1757024, _1757026] : [c_Wellfounded_Oacyclic(_1757024, hAPP(c_Set_OCollect(tc_prod(_1757024, _1757024)), hAPP(c_Product__Type_Oprod_Oprod__case(_1757024, _1757024, tc_HOL_Obool), _1757026))), -(c_Wellfounded_Oacyclic(_1757024, hAPP(c_Set_OCollect(tc_prod(_1757024, _1757024)), hAPP(c_Product__Type_Oprod_Oprod__case(_1757024, _1757024, tc_HOL_Obool), c_Predicate_Oconversep(_1757024, _1757024, _1757026)))))], (48455 ^ _780086) ^ [_1757189, _1757191, _1757193] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1757189, _1757189, hAPP(hAPP(c_COMBB(tc_fun(_1757189, tc_HOL_Obool), tc_fun(_1757189, tc_HOL_Obool), _1757189), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1757189), c_fNot)), c_fequal)), _1757191), _1757193)), _1757191 = _1757193], (48461 ^ _780086) ^ [_1757327, _1757329, _1757331] : [-(_1757329 = _1757331), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1757327, _1757327, hAPP(hAPP(c_COMBB(tc_fun(_1757327, tc_HOL_Obool), tc_fun(_1757327, tc_HOL_Obool), _1757327), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1757327), c_fNot)), c_fequal)), _1757329), _1757331)))], (48467 ^ _780086) ^ [_1757399, _1757401, _1757403, _1757405, _1757407] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1757399, _1757401, _1757403), _1757405), _1757407)), -(hBOOL(hAPP(hAPP(_1757403, _1757407), _1757405)))], (48473 ^ _780086) ^ [_1757510, _1757512, _1757514, _1757516, _1757518] : [hBOOL(hAPP(hAPP(_1757510, _1757512), _1757514)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1757516, _1757518, _1757510), _1757514), _1757512)))], (48479 ^ _780086) ^ [_1757645, _1757647, _1757649, _1757651, _1757653] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1757645, _1757647, _1757649), _1757651), _1757653)), -(hBOOL(hAPP(hAPP(_1757649, _1757653), _1757651)))], (48485 ^ _780086) ^ [_1757752, _1757754, _1757756, _1757758, _1757760] : [hBOOL(hAPP(hAPP(_1757756, _1757760), _1757758)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1757752, _1757754, _1757756), _1757758), _1757760)))], (48491 ^ _780086) ^ [_1757889, _1757891, _1757893, _1757895, _1757897] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1757889, _1757891, _1757893), _1757895), _1757897)), -(hBOOL(hAPP(hAPP(_1757893, _1757897), _1757895)))], (48497 ^ _780086) ^ [_1757996, _1757998, _1758000, _1758002, _1758004] : [hBOOL(hAPP(hAPP(_1758000, _1758004), _1758002)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1757996, _1757998, _1758000), _1758002), _1758004)))], (48503 ^ _780086) ^ [_1758109, _1758111, _1758113] : [-(c_Predicate_Oconversep(_1758109, _1758111, c_Predicate_Oconversep(_1758111, _1758109, _1758113)) = _1758113)], (48505 ^ _780086) ^ [_1758144] : [-(c_Predicate_Oconversep(_1758144, _1758144, c_fequal) = c_fequal)], (48507 ^ _780086) ^ [_1758171, _1758173, _1758175, _1758177, _1758179] : [-(c_Predicate_Oconversep(_1758171, _1758173, c_Predicate_Opred__comp(_1758171, _1758175, _1758173, _1758177, _1758179)) = c_Predicate_Opred__comp(_1758173, _1758175, _1758171, c_Predicate_Oconversep(_1758175, _1758173, _1758179), c_Predicate_Oconversep(_1758171, _1758175, _1758177)))], (48509 ^ _780086) ^ [_1758226, _1758228, _1758230, _1758232] : [-(c_Predicate_Oconversep(_1758226, _1758228, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1758226, tc_fun(_1758228, tc_HOL_Obool))), _1758230), _1758232)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1758228, tc_fun(_1758226, tc_HOL_Obool))), c_Predicate_Oconversep(_1758226, _1758228, _1758230)), c_Predicate_Oconversep(_1758226, _1758228, _1758232)))], (48511 ^ _780086) ^ [_1758295, _1758297, _1758299, _1758301] : [-(c_Predicate_Oconversep(_1758295, _1758297, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1758295, tc_fun(_1758297, tc_HOL_Obool))), _1758299), _1758301)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1758297, tc_fun(_1758295, tc_HOL_Obool))), c_Predicate_Oconversep(_1758295, _1758297, _1758299)), c_Predicate_Oconversep(_1758295, _1758297, _1758301)))], (48513 ^ _780086) ^ [_1758388, _1758390, _1758392, _1758394, _1758396] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1758388, _1758390, hAPP(hAPP(c_COMBC(_1758388, tc_fun(tc_prod(_1758388, _1758390), tc_HOL_Obool), tc_fun(_1758390, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1758390, tc_fun(tc_fun(tc_prod(_1758388, _1758390), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1758388, _1758390), tc_HOL_Obool), tc_fun(_1758390, tc_HOL_Obool)), _1758388), c_COMBC(_1758390, tc_fun(tc_prod(_1758388, _1758390), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1758390, tc_prod(_1758388, _1758390)), tc_fun(_1758390, tc_fun(tc_fun(tc_prod(_1758388, _1758390), tc_HOL_Obool), tc_HOL_Obool)), _1758388), hAPP(c_COMBB(tc_prod(_1758388, _1758390), tc_fun(tc_fun(tc_prod(_1758388, _1758390), tc_HOL_Obool), tc_HOL_Obool), _1758390), c_member(tc_prod(_1758388, _1758390)))), c_Product__Type_OPair(_1758388, _1758390)))), _1758392)), _1758394), _1758396)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1758390, _1758388)), hAPP(hAPP(c_Product__Type_OPair(_1758390, _1758388), _1758394), _1758396)), hAPP(c_Relation_Oconverse(_1758388, _1758390), _1758392))))], (48519 ^ _780086) ^ [_1758771, _1758773, _1758775, _1758777, _1758779] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1758773, _1758771)), hAPP(hAPP(c_Product__Type_OPair(_1758773, _1758771), _1758777), _1758779)), hAPP(c_Relation_Oconverse(_1758771, _1758773), _1758775))), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1758771, _1758773, hAPP(hAPP(c_COMBC(_1758771, tc_fun(tc_prod(_1758771, _1758773), tc_HOL_Obool), tc_fun(_1758773, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1758773, tc_fun(tc_fun(tc_prod(_1758771, _1758773), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1758771, _1758773), tc_HOL_Obool), tc_fun(_1758773, tc_HOL_Obool)), _1758771), c_COMBC(_1758773, tc_fun(tc_prod(_1758771, _1758773), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1758773, tc_prod(_1758771, _1758773)), tc_fun(_1758773, tc_fun(tc_fun(tc_prod(_1758771, _1758773), tc_HOL_Obool), tc_HOL_Obool)), _1758771), hAPP(c_COMBB(tc_prod(_1758771, _1758773), tc_fun(tc_fun(tc_prod(_1758771, _1758773), tc_HOL_Obool), tc_HOL_Obool), _1758773), c_member(tc_prod(_1758771, _1758773)))), c_Product__Type_OPair(_1758771, _1758773)))), _1758775)), _1758777), _1758779)))], (48525 ^ _780086) ^ [_1759160, _1759162, _1759164, _1759166] : [-(c_Lazy__Sequence_Oproduct(_1759160, _1759162, _1759164, _1759166) = hAPP(c_Lazy__Sequence_Obind(_1759160, tc_prod(_1759160, _1759162), _1759164), hAPP(hAPP(c_COMBB(tc_fun(_1759162, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1759160, _1759162))), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1759160, _1759162)), _1759160), c_Lazy__Sequence_Obind(_1759162, tc_prod(_1759160, _1759162), _1759166)), hAPP(hAPP(c_COMBB(tc_fun(_1759162, tc_prod(_1759160, _1759162)), tc_fun(_1759162, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1759160, _1759162))), _1759160), hAPP(c_COMBB(tc_prod(_1759160, _1759162), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1759160, _1759162)), _1759162), c_Lazy__Sequence_Osingle(tc_prod(_1759160, _1759162)))), c_Product__Type_OPair(_1759160, _1759162)))))], (48527 ^ _780086) ^ [_1759277, _1759279, _1759281] : [-(_1759277 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Otl(_1759279), c_List_Oreplicate(_1759279, _1759277, _1759281)) = c_List_Oreplicate(_1759279, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1759277), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1759281))], (48533 ^ _780086) ^ [_1759334, _1759336, _1759338] : [-(c_List_Oreplicate(_1759334, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759334)), hAPP(c_List_Ofilter(_1759334, hAPP(c_fequal, _1759336)), _1759338)), _1759336) = hAPP(c_List_Ofilter(_1759334, hAPP(c_fequal, _1759336)), _1759338))], (48535 ^ _780086) ^ [_1759390, _1759392, _1759394] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759390)), c_List_Oreplicate(_1759390, _1759392, _1759394)) = _1759392)], (48537 ^ _780086) ^ [_1759428, _1759430, _1759432, _1759434] : [-(hAPP(hAPP(c_List_Omap(_1759428, _1759430), hAPP(c_COMBK(_1759430, _1759428), _1759432)), _1759434) = c_List_Oreplicate(_1759430, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759428)), _1759434), _1759432))], (48539 ^ _780086) ^ [_1759483, _1759485, _1759487, _1759489] : [-(hAPP(hAPP(c_List_Oappend(_1759483), c_List_Oreplicate(_1759483, _1759485, _1759487)), hAPP(hAPP(c_List_Olist_OCons(_1759483), _1759487), _1759489)) = hAPP(hAPP(c_List_Olist_OCons(_1759483), _1759487), hAPP(hAPP(c_List_Oappend(_1759483), c_List_Oreplicate(_1759483, _1759485, _1759487)), _1759489)))], (48541 ^ _780086) ^ [_1759552, _1759554, _1759556] : [-(c_List_Oreplicate(_1759552, hAPP(c_Nat_OSuc, _1759554), _1759556) = hAPP(hAPP(c_List_Olist_OCons(_1759552), _1759556), c_List_Oreplicate(_1759552, _1759554, _1759556)))], (48543 ^ _780086) ^ [_1759598, _1759600, _1759602] : [-(hAPP(c_List_Orev(_1759598), c_List_Oreplicate(_1759598, _1759600, _1759602)) = c_List_Oreplicate(_1759598, _1759600, _1759602))], (48545 ^ _780086) ^ [_1759638, _1759640, _1759642, _1759644] : [-(hAPP(hAPP(c_List_Odrop(_1759638), _1759640), c_List_Oreplicate(_1759638, _1759642, _1759644)) = c_List_Oreplicate(_1759638, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1759642), _1759640), _1759644))], (48547 ^ _780086) ^ [_1759685, _1759687, _1759689] : [-(_1759685 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Ohd(_1759687), c_List_Oreplicate(_1759687, _1759685, _1759689)) = _1759689)], (48553 ^ _780086) ^ [_1759732, _1759734, _1759736, _1759738] : [-(hAPP(hAPP(c_List_Otake(_1759732), _1759734), c_List_Oreplicate(_1759732, _1759736, _1759738)) = c_List_Oreplicate(_1759732, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1759734), _1759736), _1759738))], (48555 ^ _780086) ^ [_1759779, _1759781, _1759783] : [-(_1759779 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_List_Olast(_1759781, c_List_Oreplicate(_1759781, _1759779, _1759783)) = _1759783)], (48561 ^ _780086) ^ [_1759824, _1759826, _1759828, _1759830, _1759832, _1759834] : [-(hAPP(hAPP(c_List_Ozip(_1759824, _1759826), c_List_Oreplicate(_1759824, _1759828, _1759830)), c_List_Oreplicate(_1759826, _1759832, _1759834)) = c_List_Oreplicate(tc_prod(_1759824, _1759826), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1759828), _1759832), hAPP(hAPP(c_Product__Type_OPair(_1759824, _1759826), _1759830), _1759834)))], (48563 ^ _780086) ^ [_1759917, _1759919, _1759921, _1759923] : [48570 ^ _780086 : [(48571 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1759923, _1759921)))], (48573 ^ _780086) ^ [] : [_1759919 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], 48564 ^ _780086 : [(48565 ^ _780086) ^ [_1759989] : [hBOOL(hAPP(hAPP(c_member(_1759917), _1759989), hAPP(c_List_Oset(_1759917), c_List_Oreplicate(_1759917, _1759919, _1759921)))), hBOOL(hAPP(_1759923, _1759989))]]], (48575 ^ _780086) ^ [_1760159, _1760161, _1760163, _1760165] : [48583 ^ _780086 : [(48584 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1760159), 48582 ^ [_1760159, _1760161, _1760163, _1760165]), hAPP(c_List_Oset(_1760159), c_List_Oreplicate(_1760159, _1760161, _1760163)))))], (48586 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1760165, 48582 ^ [_1760159, _1760161, _1760163, _1760165])))]], hBOOL(hAPP(_1760165, _1760163)), -(_1760161 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48588 ^ _780086) ^ [_1760415, _1760417, _1760419, _1760421] : [48590 ^ _780086 : [(48591 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1760415), 48589 ^ [_1760415, _1760417, _1760419, _1760421]), hAPP(c_List_Oset(_1760415), c_List_Oreplicate(_1760415, _1760417, _1760419)))))], (48593 ^ _780086) ^ [] : [hBOOL(hAPP(_1760421, 48589 ^ [_1760415, _1760417, _1760419, _1760421]))]], -(hBOOL(hAPP(_1760421, _1760419))), -(_1760417 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48601 ^ _780086) ^ [_1760622, _1760624, _1760626, _1760628] : [48602 ^ _780086 : [(48603 ^ _780086) ^ [] : [hBOOL(hAPP(_1760628, _1760626))], (48605 ^ _780086) ^ [] : [_1760624 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], 48606 ^ _780086 : [(48607 ^ _780086) ^ [_1760747] : [hBOOL(hAPP(hAPP(c_member(_1760622), _1760747), hAPP(c_List_Oset(_1760622), c_List_Oreplicate(_1760622, _1760624, _1760626)))), -(hBOOL(hAPP(_1760628, _1760747)))]]], (48613 ^ _780086) ^ [_1760898, _1760900, _1760902, _1760904, _1760906] : [c_List_Oreplicate(_1760898, _1760900, _1760902) = c_List_Oreplicate(_1760898, _1760904, _1760906), 48616 ^ _780086 : [(48617 ^ _780086) ^ [] : [-(_1760900 = _1760904)], (48619 ^ _780086) ^ [] : [-(_1760900 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1760902 = _1760906)]]], (48625 ^ _780086) ^ [_1761034, _1761036, _1761038, _1761040, _1761042] : [-(c_List_Oreplicate(_1761034, _1761036, _1761038) = c_List_Oreplicate(_1761034, _1761040, _1761042)), _1761036 = _1761040, 48630 ^ _780086 : [(48631 ^ _780086) ^ [] : [_1761036 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (48633 ^ _780086) ^ [] : [_1761038 = _1761042]]], (48637 ^ _780086) ^ [_1761233, _1761235, _1761237, _1761239] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1761233), _1761235)), -(hAPP(hAPP(c_List_Onth(_1761237), c_List_Oreplicate(_1761237, _1761235, _1761239)), _1761233) = _1761239)], (48643 ^ _780086) ^ [_1761348, _1761350, _1761352, _1761354] : [-(hAPP(hAPP(c_List_Oappend(_1761348), c_List_Oreplicate(_1761348, _1761350, _1761352)), c_List_Oreplicate(_1761348, _1761354, _1761352)) = hAPP(hAPP(c_List_Oappend(_1761348), c_List_Oreplicate(_1761348, _1761354, _1761352)), c_List_Oreplicate(_1761348, _1761350, _1761352)))], (48645 ^ _780086) ^ [_1761409, _1761411, _1761413, _1761415] : [-(c_List_Oreplicate(_1761409, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1761411), _1761413), _1761415) = hAPP(hAPP(c_List_Oappend(_1761409), c_List_Oreplicate(_1761409, _1761411, _1761415)), c_List_Oreplicate(_1761409, _1761413, _1761415)))], (48647 ^ _780086) ^ [_1761479, _1761481, _1761483, _1761485] : [hBOOL(hAPP(_1761479, _1761481)), -(hAPP(c_List_Ofilter(_1761483, _1761479), c_List_Oreplicate(_1761483, _1761485, _1761481)) = c_List_Oreplicate(_1761483, _1761485, _1761481))], (48653 ^ _780086) ^ [_1761586, _1761588, _1761590, _1761592] : [-(hBOOL(hAPP(_1761586, _1761588))), -(hAPP(c_List_Ofilter(_1761590, _1761586), c_List_Oreplicate(_1761590, _1761592, _1761588)) = c_List_Olist_ONil(_1761590))], (48659 ^ _780086) ^ [_1761642, _1761644] : [-(c_List_Oconcat(_1761642, c_List_Oreplicate(tc_List_Olist(_1761642), _1761644, c_List_Olist_ONil(_1761642))) = c_List_Olist_ONil(_1761642))], (48661 ^ _780086) ^ [_1761680, _1761682] : [-(c_List_Oreplicate(_1761680, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1761682) = c_List_Olist_ONil(_1761680))], (48663 ^ _780086) ^ [_1761729, _1761731, _1761733] : [c_List_Olist_ONil(_1761729) = c_List_Oreplicate(_1761729, _1761731, _1761733), -(_1761731 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48669 ^ _780086) ^ [_1761816, _1761818, _1761820] : [_1761818 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_List_Olist_ONil(_1761816) = c_List_Oreplicate(_1761816, _1761818, _1761820))], (48675 ^ _780086) ^ [_1761927, _1761929, _1761931] : [c_List_Oreplicate(_1761927, _1761929, _1761931) = c_List_Olist_ONil(_1761927), -(_1761929 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48681 ^ _780086) ^ [_1762014, _1762016, _1762018] : [_1762016 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_List_Oreplicate(_1762014, _1762016, _1762018) = c_List_Olist_ONil(_1762014))], (48687 ^ _780086) ^ [_1762107, _1762109, _1762111, _1762113, _1762115] : [-(hAPP(hAPP(c_List_Omap(_1762107, _1762109), _1762111), c_List_Oreplicate(_1762107, _1762113, _1762115)) = c_List_Oreplicate(_1762109, _1762113, hAPP(_1762111, _1762115)))], (48689 ^ _780086) ^ [_1762179, _1762181, _1762183, _1762185] : [hBOOL(hAPP(hAPP(c_member(_1762179), _1762181), hAPP(c_List_Oset(_1762179), c_List_Oreplicate(_1762179, _1762183, _1762185)))), 48692 ^ _780086 : [(48693 ^ _780086) ^ [] : [-(_1762181 = _1762185)], (48695 ^ _780086) ^ [] : [_1762183 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (48697 ^ _780086) ^ [_1762322, _1762324, _1762326, _1762328] : [-(hBOOL(hAPP(hAPP(c_member(_1762322), _1762324), hAPP(c_List_Oset(_1762322), c_List_Oreplicate(_1762322, _1762326, _1762328))))), _1762324 = _1762328, -(_1762326 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48707 ^ _780086) ^ [_1762496, _1762498, _1762500] : [-(hAPP(hAPP(c_List_Oappend(_1762496), c_List_Oreplicate(_1762496, _1762498, _1762500)), hAPP(hAPP(c_List_Olist_OCons(_1762496), _1762500), c_List_Olist_ONil(_1762496))) = hAPP(hAPP(c_List_Olist_OCons(_1762496), _1762500), c_List_Oreplicate(_1762496, _1762498, _1762500)))], (48709 ^ _780086) ^ [_1762557, _1762559, _1762561] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1762557), hAPP(c_COMBK(_1762557, tc_Nat_Onat), _1762559)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1762561)) = c_List_Oreplicate(_1762557, _1762561, _1762559))], (48711 ^ _780086) ^ [_1762602, _1762604, _1762606] : [-(_1762602 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Oset(_1762604), c_List_Oreplicate(_1762604, _1762602, _1762606)) = hAPP(hAPP(c_Set_Oinsert(_1762604), _1762606), c_Orderings_Obot__class_Obot(tc_fun(_1762604, tc_HOL_Obool))))], (48717 ^ _780086) ^ [_1762674, _1762676, _1762678] : [_1762674 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Oset(_1762676), c_List_Oreplicate(_1762676, _1762674, _1762678)) = c_Orderings_Obot__class_Obot(tc_fun(_1762676, tc_HOL_Obool)))], (48723 ^ _780086) ^ [_1762775, _1762777, _1762779] : [-(_1762775 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Oset(_1762777), c_List_Oreplicate(_1762777, _1762775, _1762779)) = hAPP(hAPP(c_Set_Oinsert(_1762777), _1762779), c_Orderings_Obot__class_Obot(tc_fun(_1762777, tc_HOL_Obool))))], (48729 ^ _780086) ^ [_1762837, _1762839, _1762841] : [-(hAPP(c_List_Oset(_1762837), c_List_Oreplicate(_1762837, hAPP(c_Nat_OSuc, _1762839), _1762841)) = hAPP(hAPP(c_Set_Oinsert(_1762837), _1762841), c_Orderings_Obot__class_Obot(tc_fun(_1762837, tc_HOL_Obool))))], (48731 ^ _780086) ^ [_1762889, _1762891] : [class_Lazy__Sequence_Osmall__lazy(_1762889), -(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1762889), _1762891) = c_Lazy__Sequence_Oappend(tc_List_Olist(_1762889), hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(_1762889)), c_List_Olist_ONil(_1762889)), hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1762889))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1762891)), hAPP(c_Lazy__Sequence_Obind(tc_prod(_1762889, tc_List_Olist(_1762889)), tc_List_Olist(_1762889), c_Lazy__Sequence_Oproduct(_1762889, tc_List_Olist(_1762889), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1762889, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1762891), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1762889), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1762891), c_Groups_Oone__class_Oone(tc_Int_Oint))))), hAPP(c_Product__Type_Oprod_Oprod__case(_1762889, tc_List_Olist(_1762889), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1762889))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1762889), tc_List_Olist(_1762889)), tc_fun(tc_List_Olist(_1762889), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1762889))), _1762889), hAPP(c_COMBB(tc_List_Olist(_1762889), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1762889)), tc_List_Olist(_1762889)), c_Lazy__Sequence_Osingle(tc_List_Olist(_1762889)))), c_List_Olist_OCons(_1762889))))), c_Lazy__Sequence_Oempty(tc_List_Olist(_1762889)))))], (48737 ^ _780086) ^ [_1763250, _1763252] : [-(c_Predicate_Opred__comp(_1763250, _1763250, _1763250, c_fequal, c_Predicate_Opred__comp(_1763250, _1763250, _1763250, _1763252, c_fequal)) = _1763252)], (48739 ^ _780086) ^ [_1763287, _1763289, _1763291] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(_1763287, _1763289), _1763291) = c_Lazy__Sequence_Oproduct(_1763287, _1763289, c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1763287, _1763291), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1763289, _1763291))), class_Lazy__Sequence_Osmall__lazy(_1763287), class_Lazy__Sequence_Osmall__lazy(_1763289)], (48749 ^ _780086) ^ [_1763450, _1763452, _1763454, _1763456] : [-(hAPP(c_New__DSequence_Opos__union(_1763450, _1763452, _1763454), _1763456) = c_Lazy__Sequence_Oappend(_1763450, hAPP(_1763452, _1763456), hAPP(_1763454, _1763456)))], (48751 ^ _780086) ^ [_1763496, _1763498, _1763500] : [class_Fields_Olinordered__field(_1763496), 48757 ^ _780086 : [(48758 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1763496), c_Groups_Ozero__class_Ozero(_1763496)), 48756 ^ [_1763496, _1763498, _1763500])))], (48760 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1763496), _1763498), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1763496), _1763500), 48756 ^ [_1763496, _1763498, _1763500])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1763496), _1763498), _1763500)))], (48764 ^ _780086) ^ [_1763774, _1763776, _1763778, _1763780, _1763782, _1763784] : [-(c_New__Random__Sequence_Opos__union(_1763774, _1763776, _1763778, _1763780, _1763782, _1763784) = c_New__DSequence_Opos__union(_1763774, hAPP(hAPP(hAPP(_1763776, _1763780), _1763782), _1763784), hAPP(hAPP(hAPP(_1763778, _1763780), _1763782), _1763784)))], (48766 ^ _780086) ^ [_1763845, _1763847] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1763845), _1763847)), -(c_Lazy__Sequence_Osmall__lazy_H(_1763845, _1763847) = c_Lazy__Sequence_Oempty(tc_Int_Oint))], (48772 ^ _780086) ^ [_1763932, _1763934] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1763932), _1763934))), -(c_Lazy__Sequence_Osmall__lazy_H(_1763932, _1763934) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1763934), c_Lazy__Sequence_Osmall__lazy_H(_1763932, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1763934), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (48778 ^ _780086) ^ [_1763994] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint, _1763994) = c_Lazy__Sequence_Osmall__lazy_H(_1763994, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1763994)))], (48780 ^ _780086) ^ [_1764026, _1764028] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_Lazy__Sequence_Osmall__lazy_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1764026), _1764028))), 48783 ^ _780086 : [(48784 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1764026), _1764028)), -(c_Lazy__Sequence_Osmall__lazy_H(_1764026, _1764028) = c_Lazy__Sequence_Oempty(tc_Int_Oint))], (48790 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1764026), _1764028))), -(c_Lazy__Sequence_Osmall__lazy_H(_1764026, _1764028) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1764028), c_Lazy__Sequence_Osmall__lazy_H(_1764026, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1764028), c_Groups_Oone__class_Oone(tc_Int_Oint)))))]]], (48796 ^ _780086) ^ [_1764282, _1764284, _1764286] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1764282)), c_Lazy__Sequence_Olazy__sequence_OInsert(_1764282, _1764284, _1764286)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1764282)), _1764286)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (48798 ^ _780086) ^ [_1764333, _1764335, _1764337, _1764339] : [-(c_Lazy__Sequence_Oappend(_1764333, c_Lazy__Sequence_Olazy__sequence_OInsert(_1764333, _1764335, _1764337), _1764339) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1764333, _1764335, c_Lazy__Sequence_Oappend(_1764333, _1764337, _1764339)))], (48800 ^ _780086) ^ [_1764402, _1764404, _1764406, _1764408, _1764410] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1764402, _1764404, _1764406) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1764402, _1764408, _1764410), 48803 ^ _780086 : [(48804 ^ _780086) ^ [] : [-(_1764404 = _1764408)], (48806 ^ _780086) ^ [] : [-(_1764406 = _1764410)]]], (48808 ^ _780086) ^ [_1764523, _1764525, _1764527, _1764529, _1764531] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_1764523, _1764525, _1764527) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1764523, _1764529, _1764531)), _1764525 = _1764529, _1764527 = _1764531], (48818 ^ _780086) ^ [_1764682, _1764684, _1764686, _1764688] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1764682, _1764684), c_Lazy__Sequence_Olazy__sequence_OInsert(_1764682, _1764686, _1764688)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1764684, _1764686)), hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1764682, _1764684), _1764688))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (48820 ^ _780086) ^ [_1764742, _1764744, _1764746] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_Lazy__Sequence_Osmall__lazy_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1764742), _1764744))), -(hBOOL(hAPP(hAPP(_1764746, _1764742), _1764744))), 48827 ^ _780086 : [(48828 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_Lazy__Sequence_Osmall__lazy_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), 48825 ^ [_1764742, _1764744, _1764746]), 48826 ^ [_1764742, _1764744, _1764746]))))], (48836 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(_1764746, 48825 ^ [_1764742, _1764744, _1764746]), 48826 ^ [_1764742, _1764744, _1764746]))], (48830 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 48825 ^ [_1764742, _1764744, _1764746]), 48826 ^ [_1764742, _1764744, _1764746]))), -(hBOOL(hAPP(hAPP(_1764746, 48825 ^ [_1764742, _1764744, _1764746]), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 48826 ^ [_1764742, _1764744, _1764746]), c_Groups_Oone__class_Oone(tc_Int_Oint)))))]]], (48840 ^ _780086) ^ [_1765194, _1765196] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1765194)), _1765196) = c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1765194, tc_Lazy__Sequence_Olazy__sequence(_1765194)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1765194, tc_Lazy__Sequence_Olazy__sequence(_1765194), tc_Nat_Onat), hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1765194), tc_Nat_Onat), _1765194), hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1765194), tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_Lazy__Sequence_Olazy__sequence(_1765194)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1765194)))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(c_Lazy__Sequence_Oyield(_1765194), _1765196)))], (48842 ^ _780086) ^ [_1765290, _1765292, _1765294] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1765290, _1765292), _1765294) = c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1765290, tc_Lazy__Sequence_Olazy__sequence(_1765290)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1765290, tc_Lazy__Sequence_Olazy__sequence(_1765290), tc_Nat_Onat), hAPP(hAPP(c_COMBC(_1765290, tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1765290), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1765290), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), tc_fun(tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1765290), tc_Nat_Onat)), _1765290), c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1765290), tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1765290), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1765290), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), _1765290), hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_Lazy__Sequence_Olazy__sequence(_1765290)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat))), hAPP(hAPP(c_COMBC(_1765290, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1765290), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1765290), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1765290), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1765290), tc_Nat_Onat)), _1765290), c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Lazy__Sequence_Olazy__sequence(_1765290))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), _1765290), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1765292))), c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1765290, _1765292))))), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_Lazy__Sequence_Oyield(_1765290), _1765294)))], (48844 ^ _780086) ^ [_1765483, _1765485, _1765487, _1765489, _1765491] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1765483, _1765485, _1765487, _1765489, _1765491) = c_Option_Ooption_Ooption__case(_1765483, tc_prod(_1765485, tc_Lazy__Sequence_Olazy__sequence(_1765485)), _1765487, hAPP(c_Product__Type_Oprod_Oprod__case(_1765485, tc_Lazy__Sequence_Olazy__sequence(_1765485), _1765483), _1765489), hAPP(c_Lazy__Sequence_Oyield(_1765485), _1765491)))], (48846 ^ _780086) ^ [_1765545] : [-(c_Lazy__Sequence_Oyieldn(_1765545) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(_1765545), _1765545, c_Lazy__Sequence_Oyield(_1765545)))], (48848 ^ _780086) ^ [_1765578, _1765580, _1765582, _1765584, _1765586, _1765588] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1765578, _1765580, _1765582, _1765584, c_Lazy__Sequence_Olazy__sequence_OInsert(_1765580, _1765586, _1765588)) = hAPP(hAPP(_1765584, _1765586), _1765588))], (48850 ^ _780086) ^ [_1765627, _1765629, _1765631, _1765633, _1765635] : [48852 ^ _780086 : [(48853 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1765627), 48851 ^ [_1765627, _1765629, _1765631, _1765633, _1765635]), _1765629)))], (48855 ^ _780086) ^ [] : [c_Relation_Orefl__on(_1765631, hAPP(_1765633, 48851 ^ [_1765627, _1765629, _1765631, _1765633, _1765635]), hAPP(_1765635, 48851 ^ [_1765627, _1765629, _1765631, _1765633, _1765635]))]], -(c_Relation_Orefl__on(_1765631, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1765627, tc_fun(_1765631, tc_HOL_Obool)), _1765629), _1765633), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1765627, tc_fun(tc_prod(_1765631, _1765631), tc_HOL_Obool)), _1765629), _1765635)))], (48859 ^ _780086) ^ [_1765913, _1765915, _1765917] : [hBOOL(hAPP(hAPP(c_member(_1765913), _1765915), hAPP(c_List_Oset(_1765913), _1765917))), -(hBOOL(hAPP(hAPP(c_List_Omember(_1765913), _1765917), _1765915)))], (48865 ^ _780086) ^ [_1766026, _1766028, _1766030] : [hBOOL(hAPP(hAPP(c_List_Omember(_1766026), _1766030), _1766028)), -(hBOOL(hAPP(hAPP(c_member(_1766026), _1766028), hAPP(c_List_Oset(_1766026), _1766030))))], (48881 ^ _780086) ^ [_1766300, _1766302, _1766304, _1766306] : [48882 ^ _780086 : [(48883 ^ _780086) ^ [] : [_1766302 = _1766306], (48885 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_List_Omember(_1766300), _1766304), _1766306))]], -(hBOOL(hAPP(hAPP(c_List_Omember(_1766300), hAPP(hAPP(c_List_Olist_OCons(_1766300), _1766302), _1766304)), _1766306)))], (48871 ^ _780086) ^ [_1766166, _1766168, _1766170, _1766172] : [hBOOL(hAPP(hAPP(c_List_Omember(_1766166), hAPP(hAPP(c_List_Olist_OCons(_1766166), _1766168), _1766170)), _1766172)), -(_1766168 = _1766172), -(hBOOL(hAPP(hAPP(c_List_Omember(_1766166), _1766170), _1766172)))], (48889 ^ _780086) ^ [_1766465] : [-(c_List_Omember(_1766465) = c_List_Oset(_1766465))], (48891 ^ _780086) ^ [_1766504, _1766506] : [hBOOL(hAPP(hAPP(c_List_Omember(_1766504), c_List_Olist_ONil(_1766504)), _1766506))], (48893 ^ _780086) ^ [_1766556, _1766558, _1766560] : [hBOOL(hAPP(hAPP(c_List_Omember(_1766556), _1766558), _1766560)), -(hBOOL(hAPP(hAPP(c_member(_1766556), _1766560), hAPP(c_List_Oset(_1766556), _1766558))))], (48899 ^ _780086) ^ [_1766669, _1766671, _1766673] : [hBOOL(hAPP(hAPP(c_member(_1766669), _1766673), hAPP(c_List_Oset(_1766669), _1766671))), -(hBOOL(hAPP(hAPP(c_List_Omember(_1766669), _1766671), _1766673)))], (48905 ^ _780086) ^ [_1766788, _1766790, _1766792, _1766794, _1766796, _1766798] : [-(c_Nitpick_Opair__box_Opair__box__size(_1766788, _1766790, _1766792, _1766794, c_Nitpick_Opair__box_OPairBox(_1766788, _1766790, _1766796, _1766798)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1766792, _1766796)), hAPP(_1766794, _1766798))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (48907 ^ _780086) ^ [_1766868, _1766870, _1766872] : [c_List_Olist__ex1(_1766868, _1766870, _1766872), 48911 ^ _780086 : [(48912 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1766868), 48910 ^ [_1766868, _1766870, _1766872]), hAPP(c_List_Oset(_1766868), _1766872))))], (48914 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1766870, 48910 ^ [_1766868, _1766870, _1766872])))], (48916 ^ _780086) ^ [_1767114] : [-(_1767114 = 48910 ^ [_1766868, _1766870, _1766872]), hBOOL(hAPP(hAPP(c_member(_1766868), _1767114), hAPP(c_List_Oset(_1766868), _1766872))), hBOOL(hAPP(_1766870, _1767114))]]], (48926 ^ _780086) ^ [_1767301, _1767303, _1767305] : [-(c_List_Olist__ex1(_1767301, _1767303, _1767305)), 48927 ^ _780086 : [(48928 ^ _780086) ^ [_1767395] : [hBOOL(hAPP(hAPP(c_member(_1767301), _1767395), hAPP(c_List_Oset(_1767301), _1767305))), hBOOL(hAPP(_1767303, _1767395)), 48936 ^ _780086 : [(48937 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1767301), 48935 ^ [_1767301, _1767303, _1767305, _1767395]), hAPP(c_List_Oset(_1767301), _1767305))))], (48939 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1767303, 48935 ^ [_1767301, _1767303, _1767305, _1767395])))], (48941 ^ _780086) ^ [] : [48935 ^ [_1767301, _1767303, _1767305, _1767395] = _1767395]]]]], (48945 ^ _780086) ^ [_1767730, _1767732, _1767734, _1767736] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(_1767730, _1767732)), c_Nitpick_Opair__box_OPairBox(_1767730, _1767732, _1767734, _1767736)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48947 ^ _780086) ^ [_1767799, _1767801, _1767803, _1767805, _1767807, _1767809] : [c_Nitpick_Opair__box_OPairBox(_1767799, _1767801, _1767803, _1767805) = c_Nitpick_Opair__box_OPairBox(_1767799, _1767801, _1767807, _1767809), 48950 ^ _780086 : [(48951 ^ _780086) ^ [] : [-(_1767803 = _1767807)], (48953 ^ _780086) ^ [] : [-(_1767805 = _1767809)]]], (48955 ^ _780086) ^ [_1767926, _1767928, _1767930, _1767932, _1767934, _1767936] : [-(c_Nitpick_Opair__box_OPairBox(_1767926, _1767928, _1767930, _1767932) = c_Nitpick_Opair__box_OPairBox(_1767926, _1767928, _1767934, _1767936)), _1767930 = _1767934, _1767932 = _1767936], (48965 ^ _780086) ^ [_1768093, _1768095, _1768097, _1768099, _1768101, _1768103] : [-(c_Nitpick_Opair__box_Opair__box__case(_1768093, _1768095, _1768097, _1768099, c_Nitpick_Opair__box_OPairBox(_1768093, _1768095, _1768101, _1768103)) = hAPP(hAPP(_1768099, _1768101), _1768103))], (48967 ^ _780086) ^ [_1768143, _1768145, _1768147, _1768149, _1768151, _1768153] : [-(c_Nitpick_Opair__box_Opair__box__rec(_1768143, _1768145, _1768147, _1768149, c_Nitpick_Opair__box_OPairBox(_1768143, _1768145, _1768151, _1768153)) = hAPP(hAPP(_1768149, _1768151), _1768153))], (48969 ^ _780086) ^ [_1768205, _1768207, _1768209] : [-(c_FunDef_OTHE__default(_1768207, _1768209, _1768205) = c_HOL_OThe(_1768207, _1768205)), 48970 ^ _780086 : [(48971 ^ _780086) ^ [_1768269] : [hBOOL(hAPP(_1768205, _1768269)), 48975 ^ _780086 : [(48976 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1768205, 48974 ^ [_1768205, _1768207, _1768209, _1768269])))], (48978 ^ _780086) ^ [] : [48974 ^ [_1768205, _1768207, _1768209, _1768269] = _1768269]]]]], (48982 ^ _780086) ^ [_1768463, _1768465, _1768467] : [-(c_FunDef_OTHE__default(_1768465, _1768467, _1768463) = _1768467), 48984 ^ _780086 : [(48985 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1768463, 48983 ^ [_1768463, _1768465, _1768467])))], (48987 ^ _780086) ^ [_1768585] : [hBOOL(hAPP(_1768463, _1768585)), -(_1768585 = 48983 ^ [_1768463, _1768465, _1768467])]]], (48995 ^ _780086) ^ [_1768724, _1768726, _1768728, _1768730] : [class_Groups_Ocomm__monoid__add(_1768724), hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1768726, tc_HOL_Obool)), _1768728)), 49005 ^ _780086 : [(49006 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1768726, tc_HOL_Obool)), 49004 ^ [_1768724, _1768726, _1768728, _1768730]), _1768728)))], (49008 ^ _780086) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1768726), 49004 ^ [_1768724, _1768726, _1768728, _1768730]))]], 49012 ^ _780086 : [(49013 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1768726, tc_HOL_Obool)), 49011 ^ [_1768724, _1768726, _1768728, _1768730]), _1768728)))], (49016 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1768726, tc_HOL_Obool)), 49014 ^ [_1768724, _1768726, _1768728, _1768730]), _1768728)))], (49018 ^ _780086) ^ [] : [49011 ^ [_1768724, _1768726, _1768728, _1768730] = 49014 ^ [_1768724, _1768726, _1768728, _1768730]], (49021 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1768726), 49019 ^ [_1768724, _1768726, _1768728, _1768730]), 49011 ^ [_1768724, _1768726, _1768728, _1768730])))], (49023 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1768726), 49019 ^ [_1768724, _1768726, _1768728, _1768730]), 49014 ^ [_1768724, _1768726, _1768728, _1768730])))], (49025 ^ _780086) ^ [] : [hAPP(_1768730, 49019 ^ [_1768724, _1768726, _1768728, _1768730]) = c_Groups_Ozero__class_Ozero(_1768724)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1768726, _1768724), _1768730), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1768726, tc_HOL_Obool), _1768728)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(_1768726, tc_HOL_Obool), _1768724), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1768726, _1768724), _1768730)), _1768728))], (49029 ^ _780086) ^ [_1769721, _1769723, _1769725, _1769727, _1769729, _1769731, _1769733] : [49031 ^ _780086 : [(49032 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1769721), 49030 ^ [_1769721, _1769723, _1769725, _1769727, _1769729, _1769731, _1769733]), _1769723)))], (49034 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1769725, 49030 ^ [_1769721, _1769723, _1769725, _1769727, _1769729, _1769731, _1769733]), _1769727), _1769729))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1769721, tc_fun(_1769731, tc_fun(_1769733, tc_HOL_Obool))), _1769723), _1769725), _1769727), _1769729)))], (49038 ^ _780086) ^ [_1769979, _1769981, _1769983, _1769985, _1769987, _1769989, _1769991] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1769979, tc_fun(_1769981, tc_fun(_1769983, tc_HOL_Obool))), _1769985), _1769987), _1769989), _1769991)), 49042 ^ _780086 : [(49043 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1769979), 49041 ^ [_1769979, _1769981, _1769983, _1769985, _1769987, _1769989, _1769991]), _1769985)))], (49045 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1769987, 49041 ^ [_1769979, _1769981, _1769983, _1769985, _1769987, _1769989, _1769991]), _1769989), _1769991)))]]], (49047 ^ _780086) ^ [_1770205, _1770207] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1770205)), _1770207)), 49051 ^ _780086 : [(49052 ^ _780086) ^ [_1770306] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1770205)), _1770306), _1770207)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1770205)), _1770306)), 49050 ^ [_1770205, _1770207])))]]], (49058 ^ _780086) ^ [_1770445] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1770445)), c_Lazy__Sequence_Olazy__sequence_OEmpty(_1770445)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49060 ^ _780086) ^ [_1770492, _1770494, _1770496] : [c_Lazy__Sequence_Olazy__sequence_OEmpty(_1770492) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1770492, _1770494, _1770496)], (49062 ^ _780086) ^ [_1770540, _1770542, _1770544] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1770540, _1770542, _1770544) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1770540)], (49064 ^ _780086) ^ [_1770573, _1770575] : [-(c_Lazy__Sequence_Oappend(_1770573, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1770573), _1770575) = _1770575)], (49066 ^ _780086) ^ [_1770604, _1770606, _1770608, _1770610] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1770604, _1770606, _1770608, _1770610, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1770606)) = _1770608)], (49068 ^ _780086) ^ [_1770641, _1770643] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1770641, _1770643), c_Lazy__Sequence_Olazy__sequence_OEmpty(_1770641)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49070 ^ _780086) ^ [_1770692, _1770694, _1770696] : [c_List_Olist__all(tc_Int_Oint, _1770692, c_List_Oupto(_1770694, _1770696)), -(c_List_Oall__interval__int(_1770692, _1770694, _1770696))], (49076 ^ _780086) ^ [_1770777, _1770779, _1770781] : [c_List_Oall__interval__int(_1770777, _1770779, _1770781), -(c_List_Olist__all(tc_Int_Oint, _1770777, c_List_Oupto(_1770779, _1770781)))], (49082 ^ _780086) ^ [_1770886, _1770888, _1770890] : [c_List_Olist__ex(tc_Int_Oint, _1770886, c_List_Oupto(_1770888, _1770890)), c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint, c_fNot), _1770886), _1770888, _1770890)], (49088 ^ _780086) ^ [_1770976, _1770978, _1770980] : [-(c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint, c_fNot), _1770976), _1770978, _1770980)), -(c_List_Olist__ex(tc_Int_Oint, _1770976, c_List_Oupto(_1770978, _1770980)))], (49104 ^ _780086) ^ [_1771223, _1771225, _1771227] : [49106 ^ _780086 : [(49107 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 49105 ^ [_1771223, _1771225, _1771227]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1771225, _1771227))))], (49109 ^ _780086) ^ [] : [hBOOL(hAPP(_1771223, 49105 ^ [_1771223, _1771225, _1771227]))]], -(c_List_Oall__interval__int(_1771223, _1771225, _1771227))], (49094 ^ _780086) ^ [_1771042, _1771044, _1771046] : [c_List_Oall__interval__int(_1771042, _1771044, _1771046), 49097 ^ _780086 : [(49098 ^ _780086) ^ [_1771120] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1771120), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1771044, _1771046))), -(hBOOL(hAPP(_1771042, _1771120)))]]], (49113 ^ _780086) ^ [_1771399, _1771401, _1771403, _1771405] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1771399, _1771401, _1771403, c_Code__Numeral_OSuc__code__numeral(_1771405)) = hAPP(hAPP(_1771403, _1771405), c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1771399, _1771401, _1771403, _1771405)))], (49115 ^ _780086) ^ [_1771461, _1771463, _1771465, _1771467] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1771461), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))), -(c_Random__Sequence_ORandom(_1771463, _1771465, _1771461, _1771467) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1771463)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1771463)))], (49121 ^ _780086) ^ [_1771592, _1771594, _1771596, _1771598] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1771592), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))), -(c_Random__Sequence_ORandom(_1771594, _1771596, _1771592, _1771598) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1771594, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm)), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1771594)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(_1771596, _1771598)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1771594)))), tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1771594)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)))), tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1771594)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_prod(_1771594, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1771594)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1771594)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random__Sequence_ORandom(_1771594, _1771596, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1771592), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1771598))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1771594)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1771594))))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1771594)))), tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1771594)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)))), tc_prod(_1771594, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1771594)))), tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1771594)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1771594))))), c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1771594)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1771594)))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1771594)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1771594))))), tc_prod(_1771594, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Ounion(_1771594)), hAPP(hAPP(c_COMBB(_1771594, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1771594)))), tc_prod(_1771594, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Osingle(_1771594)), c_Product__Type_Ofst(_1771594, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))))))))], (49127 ^ _780086) ^ [_1771971, _1771973, _1771975] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1771971, _1771973, _1771975, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1771973)], (49129 ^ _780086) ^ [_1772003, _1772005, _1772007] : [-(c_Random__Sequence_Oempty(_1772003, _1772005, _1772007) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1772003)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1772003)))], (49131 ^ _780086) ^ [_1772052, _1772054, _1772056, _1772058] : [-(hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(_1772052), _1772054), _1772056), _1772058) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1772052)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_DSequence_Osingle(_1772052), _1772054)))], (49133 ^ _780086) ^ [_1772113, _1772115, _1772117, _1772119] : [-(c_Random__Sequence_Omap(_1772113, _1772115, _1772117, _1772119) = c_Random__Sequence_Obind(_1772113, _1772115, _1772119, hAPP(c_Fun_Ocomp(_1772115, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1772115)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))))), _1772113, c_Random__Sequence_Osingle(_1772115)), _1772117)))], (49135 ^ _780086) ^ [_1772184, _1772186, _1772188, _1772190, _1772192, _1772194, _1772196] : [hBOOL(hAPP(hAPP(_1772184, hAPP(c_Product__Type_Osnd(_1772186, _1772188), _1772190)), hAPP(c_Product__Type_Ofst(_1772186, _1772188), _1772190))), 49142 ^ _780086 : [(49143 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(_1772184, 49141 ^ [_1772184, _1772186, _1772188, _1772190, _1772192, _1772194, _1772196]), 49140 ^ [_1772184, _1772186, _1772188, _1772190, _1772192, _1772194, _1772196])))], (49145 ^ _780086) ^ [] : [hBOOL(hAPP(_1772192, hAPP(hAPP(_1772194, 49140 ^ [_1772184, _1772186, _1772188, _1772190, _1772192, _1772194, _1772196]), 49141 ^ [_1772184, _1772186, _1772188, _1772190, _1772192, _1772194, _1772196])))]], -(hBOOL(hAPP(_1772192, hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1772186, _1772188, _1772196), _1772194), _1772190))))], (49149 ^ _780086) ^ [_1772581, _1772583, _1772585, _1772587] : [-(hAPP(c_Relation_OImage(_1772581, _1772583, hAPP(c_Set_OCollect(tc_prod(_1772581, _1772583)), hAPP(c_Product__Type_Oprod_Oprod__case(_1772581, _1772583, tc_HOL_Obool), _1772585))), _1772587) = hAPP(c_Set_OCollect(_1772583), hAPP(hAPP(c_COMBB(tc_fun(_1772581, tc_HOL_Obool), tc_HOL_Obool, _1772583), c_HOL_OEx(_1772581)), hAPP(hAPP(c_COMBB(tc_fun(_1772581, tc_HOL_Obool), tc_fun(_1772581, tc_HOL_Obool), _1772583), hAPP(c_COMBS(_1772581, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1772581), c_fconj), hAPP(hAPP(c_COMBC(_1772581, tc_fun(_1772581, tc_HOL_Obool), tc_HOL_Obool), c_member(_1772581)), _1772587)))), hAPP(c_COMBC(_1772581, _1772583, tc_HOL_Obool), _1772585)))))], (49151 ^ _780086) ^ [_1772707, _1772709, _1772711, _1772713, _1772715] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1772707), tc_List_Olist(_1772707))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1772707), tc_List_Olist(_1772707)), _1772709), _1772711)), c_List_Olexord(_1772707, _1772713))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1772707), tc_List_Olist(_1772707))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1772707), tc_List_Olist(_1772707)), _1772711), _1772715)), c_List_Olexord(_1772707, _1772713))), c_Relation_Otrans(_1772707, _1772713), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1772707), tc_List_Olist(_1772707))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1772707), tc_List_Olist(_1772707)), _1772709), _1772715)), c_List_Olexord(_1772707, _1772713))))], (49165 ^ _780086) ^ [] : [-(c_Relation_Otrans(tc_Nat_Onat, c_Wellfounded_Oless__than))], (49167 ^ _780086) ^ [_1773104, _1773106, _1773108, _1773110] : [c_Relation_Otrans(_1773104, _1773106), c_Relation_Otrans(_1773108, _1773110), -(c_Relation_Otrans(tc_prod(_1773104, _1773108), c_Wellfounded_Olex__prod(_1773104, _1773108, _1773106, _1773110)))], (49177 ^ _780086) ^ [_1773257, _1773259, _1773261, _1773263, _1773265] : [c_Relation_Otrans(_1773257, _1773259), hBOOL(hAPP(hAPP(c_member(tc_prod(_1773257, _1773257)), hAPP(hAPP(c_Product__Type_OPair(_1773257, _1773257), _1773261), _1773263)), _1773259)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1773257, _1773257)), hAPP(hAPP(c_Product__Type_OPair(_1773257, _1773257), _1773263), _1773265)), _1773259)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1773257, _1773257)), hAPP(hAPP(c_Product__Type_OPair(_1773257, _1773257), _1773261), _1773265)), _1773259)))], (49205 ^ _780086) ^ [_1774027, _1774029] : [49208 ^ _780086 : [(49209 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1774027, _1774027)), hAPP(hAPP(c_Product__Type_OPair(_1774027, _1774027), 49206 ^ [_1774027, _1774029]), 49207 ^ [_1774027, _1774029])), _1774029)))], (49212 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1774027, _1774027)), hAPP(hAPP(c_Product__Type_OPair(_1774027, _1774027), 49207 ^ [_1774027, _1774029]), 49210 ^ [_1774027, _1774029])), _1774029)))], (49214 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1774027, _1774027)), hAPP(hAPP(c_Product__Type_OPair(_1774027, _1774027), 49206 ^ [_1774027, _1774029]), 49210 ^ [_1774027, _1774029])), _1774029))]], -(c_Relation_Otrans(_1774027, _1774029))], (49191 ^ _780086) ^ [_1773585, _1773587] : [c_Relation_Otrans(_1773585, _1773587), 49194 ^ _780086 : [(49195 ^ _780086) ^ [_1773721, _1773723] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1773585, _1773585)), hAPP(hAPP(c_Product__Type_OPair(_1773585, _1773585), _1773723), _1773721)), _1773587)), 49198 ^ _780086 : [(49199 ^ _780086) ^ [_1773864] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1773585, _1773585)), hAPP(hAPP(c_Product__Type_OPair(_1773585, _1773585), _1773721), _1773864)), _1773587)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1773585, _1773585)), hAPP(hAPP(c_Product__Type_OPair(_1773585, _1773585), _1773723), _1773864)), _1773587)))]]]]], (49218 ^ _780086) ^ [_1774447, _1774449] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1774447, tc_HOL_Obool), _1774449) = hAPP(c_Set_OCollect(_1774447), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1774447, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1774447), c_HOL_OEx(tc_fun(_1774447, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1774447, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1774447, tc_HOL_Obool), tc_HOL_Obool), _1774447), hAPP(c_COMBS(tc_fun(_1774447, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1774447, tc_HOL_Obool)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1774447, tc_HOL_Obool), tc_fun(tc_fun(_1774447, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1774447, tc_HOL_Obool))), _1774449)))), c_member(_1774447)))))], (49220 ^ _780086) ^ [_1774575, _1774577] : [c_Relation_Otrans(_1774575, _1774577), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1774575, _1774575), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1774575, _1774575, _1774575), _1774577), _1774577)), _1774577)))], (49226 ^ _780086) ^ [_1774698, _1774700, _1774702] : [c_Relation_Otrans(_1774698, _1774700), c_Relation_Otrans(_1774698, _1774702), -(c_Relation_Otrans(_1774698, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1774698, _1774698), tc_HOL_Obool)), _1774700), _1774702)))], (49236 ^ _780086) ^ [_1774859, _1774861] : [-(c_Relation_Otrans(_1774859, c_Transitive__Closure_Ortrancl(_1774859, _1774861)))], (49238 ^ _780086) ^ [_1774887] : [-(c_Relation_Otrans(_1774887, c_Relation_OId(_1774887)))], (49240 ^ _780086) ^ [_1774912] : [-(c_Relation_Otrans(tc_fun(_1774912, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1774912)))], (49242 ^ _780086) ^ [_1774940, _1774942] : [c_Relation_Otrans(_1774940, _1774942), -(c_Transitive__Closure_Otrancl(_1774940, _1774942) = _1774942)], (49248 ^ _780086) ^ [_1775023, _1775025] : [-(c_Relation_Otrans(_1775023, c_Transitive__Closure_Otrancl(_1775023, _1775025)))], (49250 ^ _780086) ^ [_1775051, _1775053] : [-(c_Relation_Otrans(_1775051, c_Relation_OId__on(_1775051, _1775053)))], (49252 ^ _780086) ^ [_1775079, _1775081] : [c_Relation_Otrans(_1775079, _1775081), -(c_Relation_Otrans(tc_List_Olist(_1775079), c_List_Olexord(_1775079, _1775081)))], (49258 ^ _780086) ^ [_1775166, _1775168, _1775170] : [hBOOL(hAPP(hAPP(c_member(_1775168), _1775166), c_Orderings_Obot__class_Obot(tc_fun(_1775168, tc_HOL_Obool)))), hBOOL(hAPP(_1775170, _1775166))], (49264 ^ _780086) ^ [_1775272, _1775274] : [c_Relation_Otrans(_1775272, _1775274), -(c_Relation_Otrans(tc_List_Olist(_1775272), c_List_Olistrel(_1775272, _1775274)))], (49270 ^ _780086) ^ [_1775374, _1775376] : [c_Relation_Otrans(_1775374, hAPP(c_Relation_Oconverse(_1775374, _1775374), _1775376)), -(c_Relation_Otrans(_1775374, _1775376))], (49276 ^ _780086) ^ [_1775459, _1775461] : [c_Relation_Otrans(_1775459, _1775461), -(c_Relation_Otrans(_1775459, hAPP(c_Relation_Oconverse(_1775459, _1775459), _1775461)))], (49282 ^ _780086) ^ [_1775550, _1775552, _1775554, _1775556] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1775550), _1775552)), 49285 ^ _780086 : [(49296 ^ _780086) ^ [] : [49298 ^ _780086 : [(49299 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1775550), 49297 ^ [_1775550, _1775552, _1775554, _1775556]), _1775552)))], (49301 ^ _780086) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1775554), hAPP(c_Set_OCollect(_1775554), hAPP(hAPP(c_COMBC(_1775554, _1775550, tc_HOL_Obool), _1775556), 49297 ^ [_1775550, _1775552, _1775554, _1775556]))))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1775554), hAPP(c_Set_OCollect(_1775554), hAPP(hAPP(c_COMBB(tc_fun(_1775550, tc_HOL_Obool), tc_HOL_Obool, _1775554), c_HOL_OEx(_1775550)), hAPP(hAPP(c_COMBB(tc_fun(_1775550, tc_HOL_Obool), tc_fun(_1775550, tc_HOL_Obool), _1775554), hAPP(c_COMBS(_1775550, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1775550), c_fconj), hAPP(hAPP(c_COMBC(_1775550, tc_fun(_1775550, tc_HOL_Obool), tc_HOL_Obool), c_member(_1775550)), _1775552)))), _1775556))))))], (49286 ^ _780086) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1775554), hAPP(c_Set_OCollect(_1775554), hAPP(hAPP(c_COMBB(tc_fun(_1775550, tc_HOL_Obool), tc_HOL_Obool, _1775554), c_HOL_OEx(_1775550)), hAPP(hAPP(c_COMBB(tc_fun(_1775550, tc_HOL_Obool), tc_fun(_1775550, tc_HOL_Obool), _1775554), hAPP(c_COMBS(_1775550, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1775550), c_fconj), hAPP(hAPP(c_COMBC(_1775550, tc_fun(_1775550, tc_HOL_Obool), tc_HOL_Obool), c_member(_1775550)), _1775552)))), _1775556))))), 49289 ^ _780086 : [(49290 ^ _780086) ^ [_1775858] : [hBOOL(hAPP(hAPP(c_member(_1775550), _1775858), _1775552)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1775554), hAPP(c_Set_OCollect(_1775554), hAPP(hAPP(c_COMBC(_1775554, _1775550, tc_HOL_Obool), _1775556), _1775858)))))]]]]], (49316 ^ _780086) ^ [_1776469, _1776471] : [49317 ^ _780086 : [(49318 ^ _780086) ^ [_1776535] : [hBOOL(hAPP(_1776471, _1776535))]], 49320 ^ _780086 : [(49321 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1776469), 49319 ^ [_1776469, _1776471]), c_Orderings_Otop__class_Otop(tc_fun(_1776469, tc_HOL_Obool)))))], (49323 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1776471, 49319 ^ [_1776469, _1776471])))]]], (49305 ^ _780086) ^ [_1776269, _1776271] : [-(hBOOL(hAPP(_1776271, 49312 ^ [_1776269, _1776271]))), 49306 ^ _780086 : [(49307 ^ _780086) ^ [_1776330] : [hBOOL(hAPP(hAPP(c_member(_1776269), _1776330), c_Orderings_Otop__class_Otop(tc_fun(_1776269, tc_HOL_Obool)))), hBOOL(hAPP(_1776271, _1776330))]]], (49325 ^ _780086) ^ [_1776638] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1776638, tc_HOL_Obool) = c_Set_OBex(_1776638))], (49327 ^ _780086) ^ [_1776666, _1776668] : [c_Relation_Otrans(_1776666, _1776668), -(c_Relation_Otrans(_1776666, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1776666, _1776666), tc_HOL_Obool)), _1776668), c_Relation_OId(_1776666))))], (49333 ^ _780086) ^ [_1776775, _1776777, _1776779, _1776781] : [c_Relation_Otrans(_1776775, _1776777), -(c_Relation_Otrans(_1776779, hAPP(hAPP(c_Relation_Oinv__image(_1776775, _1776779), _1776777), _1776781)))], (49349 ^ _780086) ^ [_1777082, _1777084, _1777086] : [c_List_Olist__ex(_1777082, _1777086, _1777084), 49353 ^ _780086 : [(49354 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1777082), 49352 ^ [_1777082, _1777084, _1777086]), hAPP(c_List_Oset(_1777082), _1777084))))], (49356 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1777086, 49352 ^ [_1777082, _1777084, _1777086])))]]], (49339 ^ _780086) ^ [_1776892, _1776894, _1776896] : [-(c_List_Olist__ex(_1776892, _1776896, _1776894)), 49340 ^ _780086 : [(49341 ^ _780086) ^ [_1776949] : [hBOOL(hAPP(hAPP(c_member(_1776892), _1776949), hAPP(c_List_Oset(_1776892), _1776894))), hBOOL(hAPP(_1776896, _1776949))]]], (49358 ^ _780086) ^ [_1777260, _1777262, _1777264] : [c_List_Olist__ex(_1777260, _1777262, _1777264), 49362 ^ _780086 : [(49363 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1777260), 49361 ^ [_1777260, _1777262, _1777264]), hAPP(c_List_Oset(_1777260), _1777264))))], (49365 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1777262, 49361 ^ [_1777260, _1777262, _1777264])))]]], (49367 ^ _780086) ^ [_1777414, _1777416, _1777418] : [-(c_List_Olist__ex(_1777414, _1777416, _1777418)), 49368 ^ _780086 : [(49369 ^ _780086) ^ [_1777471] : [hBOOL(hAPP(hAPP(c_member(_1777414), _1777471), hAPP(c_List_Oset(_1777414), _1777418))), hBOOL(hAPP(_1777416, _1777471))]]], (49377 ^ _780086) ^ [_1777610, _1777612, _1777614, _1777616] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1777610, tc_fun(_1777612, tc_HOL_Obool)), _1777614), _1777616) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1777612, tc_HOL_Obool), hAPP(c_Set_OCollect(tc_fun(_1777612, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1777610, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1777612, tc_HOL_Obool)), c_HOL_OEx(_1777610)), hAPP(hAPP(c_COMBB(tc_fun(_1777610, tc_HOL_Obool), tc_fun(_1777610, tc_HOL_Obool), tc_fun(_1777612, tc_HOL_Obool)), hAPP(c_COMBS(_1777610, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1777610), c_fconj), hAPP(hAPP(c_COMBC(_1777610, tc_fun(_1777610, tc_HOL_Obool), tc_HOL_Obool), c_member(_1777610)), _1777614)))), hAPP(hAPP(c_COMBC(tc_fun(_1777612, tc_HOL_Obool), tc_fun(_1777610, tc_fun(_1777612, tc_HOL_Obool)), tc_fun(_1777610, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1777612, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1777610, tc_fun(_1777612, tc_HOL_Obool)), tc_fun(_1777610, tc_HOL_Obool)), tc_fun(_1777612, tc_HOL_Obool)), c_COMBB(tc_fun(_1777612, tc_HOL_Obool), tc_HOL_Obool, _1777610)), c_fequal)), _1777616))))))], (49379 ^ _780086) ^ [_1777794, _1777796, _1777798, _1777800] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1777794, tc_fun(_1777796, tc_HOL_Obool)), _1777798), _1777800) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1777796, tc_HOL_Obool), hAPP(c_Set_OCollect(tc_fun(_1777796, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1777794, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1777796, tc_HOL_Obool)), c_HOL_OEx(_1777794)), hAPP(hAPP(c_COMBB(tc_fun(_1777794, tc_HOL_Obool), tc_fun(_1777794, tc_HOL_Obool), tc_fun(_1777796, tc_HOL_Obool)), hAPP(c_COMBS(_1777794, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1777794), c_fconj), hAPP(hAPP(c_COMBC(_1777794, tc_fun(_1777794, tc_HOL_Obool), tc_HOL_Obool), c_member(_1777794)), _1777798)))), hAPP(hAPP(c_COMBC(tc_fun(_1777796, tc_HOL_Obool), tc_fun(_1777794, tc_fun(_1777796, tc_HOL_Obool)), tc_fun(_1777794, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1777796, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1777794, tc_fun(_1777796, tc_HOL_Obool)), tc_fun(_1777794, tc_HOL_Obool)), tc_fun(_1777796, tc_HOL_Obool)), c_COMBB(tc_fun(_1777796, tc_HOL_Obool), tc_HOL_Obool, _1777794)), c_fequal)), _1777800))))))], (49381 ^ _780086) ^ [_1777978, _1777980, _1777982, _1777984] : [class_Complete__Lattice_Ocomplete__lattice(_1777978), -(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1777980, _1777978), _1777982), _1777984) = c_Complete__Lattice_OSup__class_OSup(_1777978, hAPP(c_Set_OCollect(_1777978), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1777980, _1777978), tc_HOL_Obool), tc_HOL_Obool, _1777978), c_HOL_OEx(tc_fun(_1777980, _1777978))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1777980, _1777978), tc_HOL_Obool), tc_fun(tc_fun(_1777980, _1777978), tc_HOL_Obool), _1777978), hAPP(c_COMBS(tc_fun(_1777980, _1777978), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1777980, _1777978)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1777980, _1777978), tc_fun(tc_fun(_1777980, _1777978), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1777980, _1777978))), _1777982)))), hAPP(hAPP(c_COMBC(_1777978, tc_fun(tc_fun(_1777980, _1777978), _1777978), tc_fun(tc_fun(_1777980, _1777978), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1777978, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1777980, _1777978), _1777978), tc_fun(tc_fun(_1777980, _1777978), tc_HOL_Obool)), _1777978), c_COMBB(_1777978, tc_HOL_Obool, tc_fun(_1777980, _1777978))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1777980, _1777978), _1777980, _1777978), c_COMBI(tc_fun(_1777980, _1777978))), _1777984)))))))], (49387 ^ _780086) ^ [_1778421, _1778423, _1778425, _1778427] : [class_Complete__Lattice_Ocomplete__lattice(_1778421), -(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1778423, _1778421), _1778425), _1778427) = c_Complete__Lattice_OSup__class_OSup(_1778421, hAPP(c_Set_OCollect(_1778421), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1778423, _1778421), tc_HOL_Obool), tc_HOL_Obool, _1778421), c_HOL_OEx(tc_fun(_1778423, _1778421))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1778423, _1778421), tc_HOL_Obool), tc_fun(tc_fun(_1778423, _1778421), tc_HOL_Obool), _1778421), hAPP(c_COMBS(tc_fun(_1778423, _1778421), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1778423, _1778421)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1778423, _1778421), tc_fun(tc_fun(_1778423, _1778421), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1778423, _1778421))), _1778425)))), hAPP(hAPP(c_COMBC(_1778421, tc_fun(tc_fun(_1778423, _1778421), _1778421), tc_fun(tc_fun(_1778423, _1778421), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1778421, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1778423, _1778421), _1778421), tc_fun(tc_fun(_1778423, _1778421), tc_HOL_Obool)), _1778421), c_COMBB(_1778421, tc_HOL_Obool, tc_fun(_1778423, _1778421))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1778423, _1778421), _1778423, _1778421), c_COMBI(tc_fun(_1778423, _1778421))), _1778427)))))))], (49393 ^ _780086) ^ [_1778864, _1778866, _1778868, _1778870] : [class_Complete__Lattice_Ocomplete__lattice(_1778864), -(hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1778866, _1778864), _1778868), _1778870) = c_Complete__Lattice_OInf__class_OInf(_1778864, hAPP(c_Set_OCollect(_1778864), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1778866, _1778864), tc_HOL_Obool), tc_HOL_Obool, _1778864), c_HOL_OEx(tc_fun(_1778866, _1778864))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1778866, _1778864), tc_HOL_Obool), tc_fun(tc_fun(_1778866, _1778864), tc_HOL_Obool), _1778864), hAPP(c_COMBS(tc_fun(_1778866, _1778864), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1778866, _1778864)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1778866, _1778864), tc_fun(tc_fun(_1778866, _1778864), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1778866, _1778864))), _1778868)))), hAPP(hAPP(c_COMBC(_1778864, tc_fun(tc_fun(_1778866, _1778864), _1778864), tc_fun(tc_fun(_1778866, _1778864), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1778864, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1778866, _1778864), _1778864), tc_fun(tc_fun(_1778866, _1778864), tc_HOL_Obool)), _1778864), c_COMBB(_1778864, tc_HOL_Obool, tc_fun(_1778866, _1778864))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1778866, _1778864), _1778866, _1778864), c_COMBI(tc_fun(_1778866, _1778864))), _1778870)))))))], (49399 ^ _780086) ^ [_1779307, _1779309, _1779311, _1779313] : [class_Complete__Lattice_Ocomplete__lattice(_1779307), -(hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1779309, _1779307), _1779311), _1779313) = c_Complete__Lattice_OInf__class_OInf(_1779307, hAPP(c_Set_OCollect(_1779307), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1779309, _1779307), tc_HOL_Obool), tc_HOL_Obool, _1779307), c_HOL_OEx(tc_fun(_1779309, _1779307))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1779309, _1779307), tc_HOL_Obool), tc_fun(tc_fun(_1779309, _1779307), tc_HOL_Obool), _1779307), hAPP(c_COMBS(tc_fun(_1779309, _1779307), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1779309, _1779307)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1779309, _1779307), tc_fun(tc_fun(_1779309, _1779307), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1779309, _1779307))), _1779311)))), hAPP(hAPP(c_COMBC(_1779307, tc_fun(tc_fun(_1779309, _1779307), _1779307), tc_fun(tc_fun(_1779309, _1779307), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1779307, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1779309, _1779307), _1779307), tc_fun(tc_fun(_1779309, _1779307), tc_HOL_Obool)), _1779307), c_COMBB(_1779307, tc_HOL_Obool, tc_fun(_1779309, _1779307))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1779309, _1779307), _1779309, _1779307), c_COMBI(tc_fun(_1779309, _1779307))), _1779313)))))))], (49405 ^ _780086) ^ [_1779750, _1779752, _1779754, _1779756] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1779750), _1779752)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1779750), _1779754)), -(_1779754 = c_Orderings_Obot__class_Obot(tc_fun(_1779750, tc_HOL_Obool))), -(c_Wellfounded_Omax__extp(_1779750, _1779756, _1779752, _1779754)), 49419 ^ _780086 : [(49420 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1779750), 49418 ^ [_1779750, _1779752, _1779754, _1779756]), _1779752)))], (49422 ^ _780086) ^ [_1780095] : [hBOOL(hAPP(hAPP(c_member(_1779750), _1780095), _1779754)), hBOOL(hAPP(hAPP(_1779756, 49418 ^ [_1779750, _1779752, _1779754, _1779756]), _1780095))]]], (49430 ^ _780086) ^ [_1780276, _1780278] : [c_Predicate_Otransp(_1780276, _1780278), -(c_Relation_Otrans(_1780276, hAPP(c_Set_OCollect(tc_prod(_1780276, _1780276)), hAPP(c_Product__Type_Oprod_Oprod__case(_1780276, _1780276, tc_HOL_Obool), _1780278))))], (49436 ^ _780086) ^ [_1780379, _1780381] : [c_Relation_Otrans(_1780379, hAPP(c_Set_OCollect(tc_prod(_1780379, _1780379)), hAPP(c_Product__Type_Oprod_Oprod__case(_1780379, _1780379, tc_HOL_Obool), _1780381))), -(c_Predicate_Otransp(_1780379, _1780381))], (49442 ^ _780086) ^ [_1780488, _1780490, _1780492, _1780494, _1780496] : [c_Predicate_Otransp(_1780488, _1780490), hBOOL(hAPP(hAPP(_1780490, _1780492), _1780494)), hBOOL(hAPP(hAPP(_1780490, _1780494), _1780496)), -(hBOOL(hAPP(hAPP(_1780490, _1780492), _1780496)))], (49456 ^ _780086) ^ [_1780717, _1780719] : [c_Equiv__Relations_Oequivp(_1780717, _1780719), 49459 ^ _780086 : [(49460 ^ _780086) ^ [] : [-(c_Predicate_Oreflp(_1780717, _1780719))], (49462 ^ _780086) ^ [] : [-(c_Predicate_Osymp(_1780717, _1780719))], (49464 ^ _780086) ^ [] : [-(c_Predicate_Otransp(_1780717, _1780719))]]], (49466 ^ _780086) ^ [_1780848, _1780850] : [c_Predicate_Oreflp(_1780848, _1780850), c_Predicate_Osymp(_1780848, _1780850), c_Predicate_Otransp(_1780848, _1780850), -(c_Equiv__Relations_Oequivp(_1780848, _1780850))], (49480 ^ _780086) ^ [_1781029, _1781031, _1781033, _1781035] : [c_Predicate_Osymp(_1781029, _1781031), hBOOL(hAPP(hAPP(_1781031, _1781033), _1781035)), -(hBOOL(hAPP(hAPP(_1781031, _1781035), _1781033)))], (49490 ^ _780086) ^ [_1781201, _1781203] : [c_Equiv__Relations_Oequivp(_1781201, _1781203), 49493 ^ _780086 : [(49494 ^ _780086) ^ [] : [-(c_Predicate_Oreflp(_1781201, _1781203))], (49496 ^ _780086) ^ [] : [-(c_Predicate_Osymp(_1781201, _1781203))], (49498 ^ _780086) ^ [] : [-(c_Predicate_Otransp(_1781201, _1781203))]]], (49500 ^ _780086) ^ [_1781324, _1781326] : [-(c_Equiv__Relations_Oequivp(_1781324, _1781326)), c_Predicate_Oreflp(_1781324, _1781326), c_Predicate_Osymp(_1781324, _1781326), c_Predicate_Otransp(_1781324, _1781326)], (49514 ^ _780086) ^ [_1781528, _1781530, _1781532, _1781534] : [c_Wellfounded_Omax__extp(_1781528, _1781530, _1781532, _1781534), 49517 ^ _780086 : [(49518 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1781528), _1781532)))], (49520 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1781528), _1781534)))], (49522 ^ _780086) ^ [] : [_1781534 = c_Orderings_Obot__class_Obot(tc_fun(_1781528, tc_HOL_Obool))], (49524 ^ _780086) ^ [_1781744] : [hBOOL(hAPP(hAPP(c_member(_1781528), _1781744), _1781532)), 49528 ^ _780086 : [(49529 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1781528), 49527 ^ [_1781528, _1781530, _1781532, _1781534, _1781744]), _1781534)))], (49531 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(_1781530, _1781744), 49527 ^ [_1781528, _1781530, _1781532, _1781534, _1781744])))]]]]], (49533 ^ _780086) ^ [_1781928, _1781930, _1781932, _1781934] : [-(c_Wellfounded_Omax__extp(_1781928, _1781930, _1781932, _1781934)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1781928), _1781932)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1781928), _1781934)), -(_1781934 = c_Orderings_Obot__class_Obot(tc_fun(_1781928, tc_HOL_Obool))), 49547 ^ _780086 : [(49548 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1781928), 49546 ^ [_1781928, _1781930, _1781932, _1781934]), _1781932)))], (49550 ^ _780086) ^ [_1782273] : [hBOOL(hAPP(hAPP(c_member(_1781928), _1782273), _1781934)), hBOOL(hAPP(hAPP(_1781930, 49546 ^ [_1781928, _1781930, _1781932, _1781934]), _1782273))]]], (49558 ^ _780086) ^ [_1782441, _1782443] : [c_Relation_Otrans(_1782441, _1782443), c_Relation_Oantisym(_1782441, _1782443), -(c_Relation_Otrans(_1782441, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1782441, _1782441), tc_HOL_Obool)), _1782443), c_Relation_OId(_1782441))))], (49568 ^ _780086) ^ [_1782617, _1782619] : [c_Relation_Oantisym(_1782617, hAPP(c_Relation_Oconverse(_1782617, _1782617), _1782619)), -(c_Relation_Oantisym(_1782617, _1782619))], (49574 ^ _780086) ^ [_1782702, _1782704] : [c_Relation_Oantisym(_1782702, _1782704), -(c_Relation_Oantisym(_1782702, hAPP(c_Relation_Oconverse(_1782702, _1782702), _1782704)))], (49580 ^ _780086) ^ [_1782793] : [-(c_Relation_Oantisym(_1782793, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1782793, _1782793), tc_HOL_Obool))))], (49582 ^ _780086) ^ [_1782824] : [-(c_Relation_Oantisym(_1782824, c_Relation_OId(_1782824)))], (49584 ^ _780086) ^ [_1782849, _1782851] : [-(c_Relation_Oantisym(_1782849, c_Relation_OId__on(_1782849, _1782851)))], (49586 ^ _780086) ^ [_1782877, _1782879, _1782881] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1782877, _1782877), tc_HOL_Obool)), _1782879), _1782881)), c_Relation_Oantisym(_1782877, _1782881), -(c_Relation_Oantisym(_1782877, _1782879))], (49610 ^ _780086) ^ [_1783376, _1783378] : [49613 ^ _780086 : [(49614 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1783376, _1783376)), hAPP(hAPP(c_Product__Type_OPair(_1783376, _1783376), 49611 ^ [_1783376, _1783378]), 49612 ^ [_1783376, _1783378])), _1783378)))], (49616 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1783376, _1783376)), hAPP(hAPP(c_Product__Type_OPair(_1783376, _1783376), 49612 ^ [_1783376, _1783378]), 49611 ^ [_1783376, _1783378])), _1783378)))], (49618 ^ _780086) ^ [] : [49611 ^ [_1783376, _1783378] = 49612 ^ [_1783376, _1783378]]], -(c_Relation_Oantisym(_1783376, _1783378))], (49596 ^ _780086) ^ [_1783051, _1783053] : [c_Relation_Oantisym(_1783051, _1783053), 49599 ^ _780086 : [(49600 ^ _780086) ^ [_1783163, _1783165] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1783051, _1783051)), hAPP(hAPP(c_Product__Type_OPair(_1783051, _1783051), _1783165), _1783163)), _1783053)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1783051, _1783051)), hAPP(hAPP(c_Product__Type_OPair(_1783051, _1783051), _1783163), _1783165)), _1783053)), -(_1783165 = _1783163)]]], (49622 ^ _780086) ^ [_1783697, _1783699, _1783701, _1783703] : [c_Relation_Oantisym(_1783697, _1783699), hBOOL(hAPP(hAPP(c_member(tc_prod(_1783697, _1783697)), hAPP(hAPP(c_Product__Type_OPair(_1783697, _1783697), _1783701), _1783703)), _1783699)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1783697, _1783697)), hAPP(hAPP(c_Product__Type_OPair(_1783697, _1783697), _1783703), _1783701)), _1783699)), -(_1783701 = _1783703)], (49636 ^ _780086) ^ [_1783981, _1783983] : [c_Relation_Oantisym(_1783981, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1783981, _1783981), tc_HOL_Obool)), _1783983), c_Relation_OId(_1783981))), -(c_Relation_Oantisym(_1783981, _1783983))], (49642 ^ _780086) ^ [_1784086, _1784088] : [c_Relation_Oantisym(_1784086, _1784088), -(c_Relation_Oantisym(_1784086, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1784086, _1784086), tc_HOL_Obool)), _1784088), c_Relation_OId(_1784086))))], (49648 ^ _780086) ^ [_1784197, _1784199] : [c_Wellfounded_Oacyclic(_1784197, _1784199), -(c_Relation_Oantisym(_1784197, c_Transitive__Closure_Ortrancl(_1784197, _1784199)))], (49654 ^ _780086) ^ [_1784280, _1784282, _1784284, _1784286, _1784288, _1784290] : [-(c_Partial__Function_Ofun__lub(_1784280, _1784282, _1784284, _1784286, _1784288, _1784290) = hAPP(_1784286, hAPP(c_Set_OCollect(_1784280), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1784284, _1784280), tc_HOL_Obool), tc_HOL_Obool, _1784280), c_HOL_OEx(tc_fun(_1784284, _1784280))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1784284, _1784280), tc_HOL_Obool), tc_fun(tc_fun(_1784284, _1784280), tc_HOL_Obool), _1784280), hAPP(c_COMBS(tc_fun(_1784284, _1784280), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1784284, _1784280)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1784284, _1784280), tc_fun(tc_fun(_1784284, _1784280), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1784284, _1784280))), _1784288)))), hAPP(hAPP(c_COMBC(_1784280, tc_fun(tc_fun(_1784284, _1784280), _1784280), tc_fun(tc_fun(_1784284, _1784280), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1784280, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1784284, _1784280), _1784280), tc_fun(tc_fun(_1784284, _1784280), tc_HOL_Obool)), _1784280), c_COMBB(_1784280, tc_HOL_Obool, tc_fun(_1784284, _1784280))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1784284, _1784280), _1784284, _1784280), c_COMBI(tc_fun(_1784284, _1784280))), _1784290)))))))], (49656 ^ _780086) ^ [_1784493, _1784495] : [c_Relation_Osym(_1784493, _1784495), c_Relation_Otrans(_1784493, _1784495), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1784493, _1784493), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1784493, _1784493, _1784493), hAPP(c_Relation_Oconverse(_1784493, _1784493), _1784495)), _1784495)), _1784495)))], (49666 ^ _780086) ^ [_1784680, _1784682, _1784684, _1784686] : [c_Relation_Osym(_1784680, _1784682), hBOOL(hAPP(hAPP(c_member(tc_prod(_1784680, _1784680)), hAPP(hAPP(c_Product__Type_OPair(_1784680, _1784680), _1784684), _1784686)), _1784682)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1784680, _1784680)), hAPP(hAPP(c_Product__Type_OPair(_1784680, _1784680), _1784686), _1784684)), _1784682)))], (49686 ^ _780086) ^ [_1785171, _1785173] : [49689 ^ _780086 : [(49690 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1785171, _1785171)), hAPP(hAPP(c_Product__Type_OPair(_1785171, _1785171), 49687 ^ [_1785171, _1785173]), 49688 ^ [_1785171, _1785173])), _1785173)))], (49692 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1785171, _1785171)), hAPP(hAPP(c_Product__Type_OPair(_1785171, _1785171), 49688 ^ [_1785171, _1785173]), 49687 ^ [_1785171, _1785173])), _1785173))]], -(c_Relation_Osym(_1785171, _1785173))], (49676 ^ _780086) ^ [_1784908, _1784910] : [c_Relation_Osym(_1784908, _1784910), 49679 ^ _780086 : [(49680 ^ _780086) ^ [_1785014, _1785016] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1784908, _1784908)), hAPP(hAPP(c_Product__Type_OPair(_1784908, _1784908), _1785016), _1785014)), _1784910)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1784908, _1784908)), hAPP(hAPP(c_Product__Type_OPair(_1784908, _1784908), _1785014), _1785016)), _1784910)))]]], (49696 ^ _780086) ^ [_1785436, _1785438, _1785440] : [c_Relation_Osym(_1785436, _1785438), c_Relation_Osym(_1785436, _1785440), -(c_Relation_Osym(_1785436, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1785436, _1785436), tc_HOL_Obool)), _1785438), _1785440)))], (49706 ^ _780086) ^ [_1785597, _1785599] : [c_Relation_Osym(_1785597, _1785599), -(c_Relation_Osym(_1785597, c_Transitive__Closure_Ortrancl(_1785597, _1785599)))], (49712 ^ _780086) ^ [_1785680] : [-(c_Relation_Osym(_1785680, c_Relation_OId(_1785680)))], (49714 ^ _780086) ^ [_1785705, _1785707, _1785709] : [c_Relation_Osym(_1785705, _1785707), c_Relation_Osym(_1785705, _1785709), -(c_Relation_Osym(_1785705, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1785705, _1785705), tc_HOL_Obool)), _1785707), _1785709)))], (49724 ^ _780086) ^ [_1785866, _1785868] : [c_Relation_Osym(_1785866, _1785868), -(c_Relation_Osym(_1785866, c_Transitive__Closure_Otrancl(_1785866, _1785868)))], (49730 ^ _780086) ^ [_1785949, _1785951] : [-(c_Relation_Osym(_1785949, c_Relation_OId__on(_1785949, _1785951)))], (49732 ^ _780086) ^ [_1785977, _1785979] : [c_Relation_Osym(_1785977, _1785979), -(c_Relation_Osym(tc_List_Olist(_1785977), c_List_Olistrel(_1785977, _1785979)))], (49738 ^ _780086) ^ [_1786079, _1786081] : [c_Relation_Osym(_1786079, _1786081), -(hAPP(c_Relation_Oconverse(_1786079, _1786079), _1786081) = _1786081)], (49744 ^ _780086) ^ [_1786164, _1786166] : [hAPP(c_Relation_Oconverse(_1786164, _1786164), _1786166) = _1786166, -(c_Relation_Osym(_1786164, _1786166))], (49750 ^ _780086) ^ [_1786270, _1786272] : [c_Relation_Osym(_1786270, hAPP(c_Relation_Oconverse(_1786270, _1786270), _1786272)), -(c_Relation_Osym(_1786270, _1786272))], (49756 ^ _780086) ^ [_1786355, _1786357] : [c_Relation_Osym(_1786355, _1786357), -(c_Relation_Osym(_1786355, hAPP(c_Relation_Oconverse(_1786355, _1786355), _1786357)))], (49762 ^ _780086) ^ [_1786446, _1786448] : [-(c_Relation_Osym(_1786446, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1786446, _1786446), tc_HOL_Obool)), _1786448), hAPP(c_Relation_Oconverse(_1786446, _1786446), _1786448))))], (49764 ^ _780086) ^ [_1786491, _1786493, _1786495, _1786497] : [c_Relation_Osym(_1786491, _1786493), -(c_Relation_Osym(_1786495, hAPP(hAPP(c_Relation_Oinv__image(_1786491, _1786495), _1786493), _1786497)))], (49770 ^ _780086) ^ [_1786590, _1786592] : [-(c_Relation_Osym(_1786590, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1786590, _1786590), tc_HOL_Obool)), _1786592), hAPP(c_Relation_Oconverse(_1786590, _1786590), _1786592))))], (49772 ^ _780086) ^ [_1786653, _1786655, _1786657] : [c_Equiv__Relations_Oequiv(_1786653, _1786655, _1786657), 49775 ^ _780086 : [(49776 ^ _780086) ^ [] : [-(c_Relation_Orefl__on(_1786653, _1786655, _1786657))], (49778 ^ _780086) ^ [] : [-(c_Relation_Osym(_1786653, _1786657))], (49780 ^ _780086) ^ [] : [-(c_Relation_Otrans(_1786653, _1786657))]]], (49782 ^ _780086) ^ [_1786782, _1786784, _1786786] : [-(c_Equiv__Relations_Oequiv(_1786782, _1786784, _1786786)), c_Relation_Orefl__on(_1786782, _1786784, _1786786), c_Relation_Osym(_1786782, _1786786), c_Relation_Otrans(_1786782, _1786786)], (49796 ^ _780086) ^ [_1786975, _1786977, _1786979] : [c_Relation_Orefl__on(_1786975, _1786977, _1786979), c_Relation_Osym(_1786975, _1786979), c_Relation_Otrans(_1786975, _1786979), -(c_Equiv__Relations_Oequiv(_1786975, _1786977, _1786979))], (49810 ^ _780086) ^ [_1787166, _1787168, _1787170] : [c_Equiv__Relations_Oequiv(_1787166, _1787168, _1787170), 49813 ^ _780086 : [(49814 ^ _780086) ^ [] : [-(c_Relation_Orefl__on(_1787166, _1787168, _1787170))], (49816 ^ _780086) ^ [] : [-(c_Relation_Osym(_1787166, _1787170))], (49818 ^ _780086) ^ [] : [-(c_Relation_Otrans(_1787166, _1787170))]]], (49820 ^ _780086) ^ [_1787318, _1787320] : [c_Predicate_Osymp(_1787318, _1787320), -(c_Relation_Osym(_1787318, hAPP(c_Set_OCollect(tc_prod(_1787318, _1787318)), hAPP(c_Product__Type_Oprod_Oprod__case(_1787318, _1787318, tc_HOL_Obool), _1787320))))], (49826 ^ _780086) ^ [_1787421, _1787423] : [c_Relation_Osym(_1787421, hAPP(c_Set_OCollect(tc_prod(_1787421, _1787421)), hAPP(c_Product__Type_Oprod_Oprod__case(_1787421, _1787421, tc_HOL_Obool), _1787423))), -(c_Predicate_Osymp(_1787421, _1787423))], (49832 ^ _780086) ^ [_1787530, _1787532] : [49833 ^ _780086 : [(49834 ^ _780086) ^ [_1787586] : [hBOOL(hAPP(hAPP(_1787530, _1787586), _1787586))]], c_Predicate_Osymp(_1787532, _1787530), c_Predicate_Otransp(_1787532, _1787530), -(c_Equiv__Relations_Opart__equivp(_1787532, _1787530))], (49846 ^ _780086) ^ [_1787749, _1787751] : [c_Equiv__Relations_Opart__equivp(_1787749, _1787751), 49850 ^ _780086 : [(49851 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(_1787751, 49849 ^ [_1787749, _1787751]), 49849 ^ [_1787749, _1787751])))], (49853 ^ _780086) ^ [] : [-(c_Predicate_Osymp(_1787749, _1787751))], (49855 ^ _780086) ^ [] : [-(c_Predicate_Otransp(_1787749, _1787751))]]], (49857 ^ _780086) ^ [_1787901, _1787903] : [-(c_Equiv__Relations_Opart__equivp(_1787901, _1787903)), 49860 ^ _780086 : [(49861 ^ _780086) ^ [_1787978] : [hBOOL(hAPP(hAPP(_1787903, _1787978), _1787978))]], c_Predicate_Osymp(_1787901, _1787903), c_Predicate_Otransp(_1787901, _1787903)], (49871 ^ _780086) ^ [_1788107, _1788109] : [c_Equiv__Relations_Oequivp(_1788107, _1788109), -(c_Equiv__Relations_Opart__equivp(_1788107, _1788109))], (49877 ^ _780086) ^ [_1788184, _1788186, _1788188, _1788190, _1788192] : [c_Equiv__Relations_Opart__equivp(_1788184, _1788186), hBOOL(hAPP(hAPP(_1788186, _1788188), _1788190)), hBOOL(hAPP(hAPP(_1788186, _1788190), _1788192)), -(hBOOL(hAPP(hAPP(_1788186, _1788188), _1788192)))], (49891 ^ _780086) ^ [_1788413, _1788415, _1788417, _1788419] : [c_Equiv__Relations_Opart__equivp(_1788413, _1788415), hBOOL(hAPP(hAPP(_1788415, _1788417), _1788419)), -(hBOOL(hAPP(hAPP(_1788415, _1788419), _1788417)))], (49932 ^ _780086) ^ [_1789166, _1789168] : [-(c_Equiv__Relations_Opart__equivp(_1789166, _1789168)), 49935 ^ _780086 : [(49936 ^ _780086) ^ [_1789286] : [hBOOL(hAPP(hAPP(_1789168, _1789286), _1789286))]], 49953 ^ _780086 : [(49954 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(_1789168, 49937 ^ [_1789166, _1789168]), 49937 ^ [_1789166, _1789168])))], (49956 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(_1789168, 49938 ^ [_1789166, _1789168]), 49938 ^ [_1789166, _1789168])))], (49958 ^ _780086) ^ [] : [-(hAPP(_1789168, 49937 ^ [_1789166, _1789168]) = hAPP(_1789168, 49938 ^ [_1789166, _1789168]))], (49960 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(_1789168, 49937 ^ [_1789166, _1789168]), 49938 ^ [_1789166, _1789168]))]], 49941 ^ _780086 : [(49942 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(_1789168, 49937 ^ [_1789166, _1789168]), 49938 ^ [_1789166, _1789168])))], (49944 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(_1789168, 49937 ^ [_1789166, _1789168]), 49937 ^ [_1789166, _1789168])), hBOOL(hAPP(hAPP(_1789168, 49938 ^ [_1789166, _1789168]), 49938 ^ [_1789166, _1789168])), hAPP(_1789168, 49937 ^ [_1789166, _1789168]) = hAPP(_1789168, 49938 ^ [_1789166, _1789168])]]], (49901 ^ _780086) ^ [_1788585, _1788587] : [c_Equiv__Relations_Opart__equivp(_1788585, _1788587), 49905 ^ _780086 : [(49906 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(_1788587, 49904 ^ [_1788585, _1788587]), 49904 ^ [_1788585, _1788587])))], (49908 ^ _780086) ^ [_1788758, _1788760] : [hBOOL(hAPP(hAPP(_1788587, _1788760), _1788758)), 49911 ^ _780086 : [(49912 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(_1788587, _1788760), _1788760)))], (49914 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(_1788587, _1788758), _1788758)))], (49916 ^ _780086) ^ [] : [-(hAPP(_1788587, _1788760) = hAPP(_1788587, _1788758))]]], (49918 ^ _780086) ^ [_1788927, _1788929] : [-(hBOOL(hAPP(hAPP(_1788587, _1788929), _1788927))), hBOOL(hAPP(hAPP(_1788587, _1788929), _1788929)), hBOOL(hAPP(hAPP(_1788587, _1788927), _1788927)), hAPP(_1788587, _1788929) = hAPP(_1788587, _1788927)]]], (49964 ^ _780086) ^ [_1789834, _1789836] : [c_Equiv__Relations_Opart__equivp(_1789834, _1789836), 49968 ^ _780086 : [(49969 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(_1789836, 49967 ^ [_1789834, _1789836]), 49967 ^ [_1789834, _1789836])))], (49971 ^ _780086) ^ [] : [-(c_Predicate_Osymp(_1789834, _1789836))], (49973 ^ _780086) ^ [] : [-(c_Predicate_Otransp(_1789834, _1789836))]]], (49975 ^ _780086) ^ [_1789994, _1789996] : [c_Equiv__Relations_Opart__equivp(_1789994, _1789996), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1789994, tc_HOL_Obool)), 49978 ^ [_1789994, _1789996]), hAPP(hAPP(c_COMBB(tc_fun(_1789994, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1789994, tc_HOL_Obool)), c_HOL_OEx(_1789994)), hAPP(hAPP(c_COMBB(tc_fun(_1789994, tc_HOL_Obool), tc_fun(_1789994, tc_HOL_Obool), tc_fun(_1789994, tc_HOL_Obool)), hAPP(c_COMBS(_1789994, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1789994), c_fconj), hAPP(hAPP(c_COMBS(_1789994, _1789994, tc_HOL_Obool), _1789996), c_COMBI(_1789994))))), hAPP(hAPP(c_COMBC(tc_fun(_1789994, tc_HOL_Obool), tc_fun(_1789994, tc_fun(_1789994, tc_HOL_Obool)), tc_fun(_1789994, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1789994, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1789994, tc_fun(_1789994, tc_HOL_Obool)), tc_fun(_1789994, tc_HOL_Obool)), tc_fun(_1789994, tc_HOL_Obool)), c_COMBB(tc_fun(_1789994, tc_HOL_Obool), tc_HOL_Obool, _1789994)), c_fequal)), _1789996))))))], (49982 ^ _780086) ^ [_1790373, _1790375, _1790377] : [c_Fun_Oinj__on(_1790373, _1790375, _1790377, c_Orderings_Otop__class_Otop(tc_fun(_1790373, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1790375, _1790373, _1790373, c_Hilbert__Choice_Oinv__into(_1790373, _1790375, c_Orderings_Otop__class_Otop(tc_fun(_1790373, tc_HOL_Obool)), _1790377)), _1790377) = c_Fun_Oid(_1790373))], (49988 ^ _780086) ^ [_1790502, _1790504, _1790506] : [hAPP(c_Fun_Ocomp(_1790504, _1790502, _1790502, c_Hilbert__Choice_Oinv__into(_1790502, _1790504, c_Orderings_Otop__class_Otop(tc_fun(_1790502, tc_HOL_Obool)), _1790506)), _1790506) = c_Fun_Oid(_1790502), -(c_Fun_Oinj__on(_1790502, _1790504, _1790506, c_Orderings_Otop__class_Otop(tc_fun(_1790502, tc_HOL_Obool))))], (49994 ^ _780086) ^ [_1790637, _1790639, _1790641] : [c_Fun_Oinj__on(_1790637, _1790639, _1790641, c_Orderings_Otop__class_Otop(tc_fun(_1790637, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1790639, _1790637, _1790637, c_Hilbert__Choice_Oinv__into(_1790637, _1790639, c_Orderings_Otop__class_Otop(tc_fun(_1790637, tc_HOL_Obool)), _1790641)), _1790641) = c_Fun_Oid(_1790637))], (50000 ^ _780086) ^ [_1790770, _1790772, _1790774, _1790776] : [-(hAPP(c_Hilbert__Choice_Oinv__into(_1790770, _1790772, c_Orderings_Otop__class_Otop(tc_fun(_1790770, tc_HOL_Obool)), _1790774), _1790776) = c_Hilbert__Choice_OEps(_1790770, hAPP(hAPP(c_COMBC(_1790770, _1790772, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1790772, tc_fun(_1790772, tc_HOL_Obool), _1790770), c_fequal), _1790774)), _1790776)))], (50002 ^ _780086) ^ [_1790838] : [-(c_Hilbert__Choice_Oinv__into(_1790838, _1790838, c_Orderings_Otop__class_Otop(tc_fun(_1790838, tc_HOL_Obool)), c_Fun_Oid(_1790838)) = c_Fun_Oid(_1790838))], (50004 ^ _780086) ^ [_1790875, _1790877, _1790879, _1790881, _1790883] : [c_Fun_Oinj__on(_1790875, _1790877, _1790879, c_Orderings_Otop__class_Otop(tc_fun(_1790875, tc_HOL_Obool))), hAPP(_1790879, _1790881) = _1790883, -(hAPP(c_Hilbert__Choice_Oinv__into(_1790875, _1790877, c_Orderings_Otop__class_Otop(tc_fun(_1790875, tc_HOL_Obool)), _1790879), _1790883) = _1790881)], (50014 ^ _780086) ^ [_1791062, _1791064, _1791066, _1791068] : [c_Fun_Oinj__on(_1791062, _1791064, _1791066, c_Orderings_Otop__class_Otop(tc_fun(_1791062, tc_HOL_Obool))), -(hAPP(c_Hilbert__Choice_Oinv__into(_1791062, _1791064, c_Orderings_Otop__class_Otop(tc_fun(_1791062, tc_HOL_Obool)), _1791066), hAPP(_1791066, _1791068)) = _1791068)], (50020 ^ _780086) ^ [_1791189, _1791191, _1791193, _1791195, _1791197, _1791199] : [c_Fun_Oinj__on(_1791189, _1791191, _1791193, _1791195), hBOOL(hAPP(hAPP(c_member(_1791189), _1791197), _1791195)), hAPP(_1791193, _1791197) = _1791199, -(hAPP(c_Hilbert__Choice_Oinv__into(_1791189, _1791191, _1791195, _1791193), _1791199) = _1791197)], (50034 ^ _780086) ^ [_1791434, _1791436, _1791438, _1791440, _1791442] : [c_Fun_Oinj__on(_1791434, _1791436, _1791438, _1791440), hBOOL(hAPP(hAPP(c_member(_1791434), _1791442), _1791440)), -(hAPP(c_Hilbert__Choice_Oinv__into(_1791434, _1791436, _1791440, _1791438), hAPP(_1791438, _1791442)) = _1791442)], (50044 ^ _780086) ^ [_1791615, _1791617, _1791619, _1791621, _1791623] : [hBOOL(hAPP(hAPP(c_member(_1791615), _1791617), hAPP(c_Set_Oimage(_1791619, _1791615, _1791621), _1791623))), -(hAPP(_1791621, hAPP(c_Hilbert__Choice_Oinv__into(_1791619, _1791615, _1791623, _1791621), _1791617)) = _1791617)], (50050 ^ _780086) ^ [_1791748, _1791750, _1791752, _1791754, _1791756] : [hBOOL(hAPP(hAPP(c_member(_1791748), _1791750), hAPP(c_Set_Oimage(_1791752, _1791748, _1791754), _1791756))), -(hBOOL(hAPP(hAPP(c_member(_1791752), hAPP(c_Hilbert__Choice_Oinv__into(_1791752, _1791748, _1791756, _1791754), _1791750)), _1791756)))], (50056 ^ _780086) ^ [_1791889, _1791891, _1791893, _1791895, _1791897, _1791899] : [hAPP(c_Hilbert__Choice_Oinv__into(_1791889, _1791891, _1791893, _1791895), _1791897) = hAPP(c_Hilbert__Choice_Oinv__into(_1791889, _1791891, _1791893, _1791895), _1791899), hBOOL(hAPP(hAPP(c_member(_1791891), _1791897), hAPP(c_Set_Oimage(_1791889, _1791891, _1791895), _1791893))), hBOOL(hAPP(hAPP(c_member(_1791891), _1791899), hAPP(c_Set_Oimage(_1791889, _1791891, _1791895), _1791893))), -(_1791897 = _1791899)], (50070 ^ _780086) ^ [_1792182, _1792184, _1792186, _1792188] : [hAPP(c_Set_Oimage(_1792182, _1792184, _1792186), c_Orderings_Otop__class_Otop(tc_fun(_1792182, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1792184, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1792182, _1792184, _1792186), hAPP(c_Set_Oimage(_1792184, _1792182, c_Hilbert__Choice_Oinv__into(_1792182, _1792184, c_Orderings_Otop__class_Otop(tc_fun(_1792182, tc_HOL_Obool)), _1792186)), _1792188)) = _1792188)], (50076 ^ _780086) ^ [_1792345, _1792347, _1792349, _1792351] : [hAPP(c_Set_Oimage(_1792345, _1792347, _1792349), c_Orderings_Otop__class_Otop(tc_fun(_1792345, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1792347, tc_HOL_Obool)), -(hAPP(_1792349, hAPP(c_Hilbert__Choice_Oinv__into(_1792345, _1792347, c_Orderings_Otop__class_Otop(tc_fun(_1792345, tc_HOL_Obool)), _1792349), _1792351)) = _1792351)], (50082 ^ _780086) ^ [_1792510, _1792512, _1792514] : [hAPP(c_Set_Oimage(_1792510, _1792512, _1792514), c_Orderings_Otop__class_Otop(tc_fun(_1792510, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1792512, tc_HOL_Obool)), 50085 ^ _780086 : [(50086 ^ _780086) ^ [_1792621] : [-(hAPP(_1792514, hAPP(c_Hilbert__Choice_Oinv__into(_1792510, _1792512, c_Orderings_Otop__class_Otop(tc_fun(_1792510, tc_HOL_Obool)), _1792514), _1792621)) = _1792621)]]], (50088 ^ _780086) ^ [_1792660, _1792662, _1792664] : [hAPP(_1792664, hAPP(c_Hilbert__Choice_Oinv__into(_1792660, _1792662, c_Orderings_Otop__class_Otop(tc_fun(_1792660, tc_HOL_Obool)), _1792664), 50089 ^ [_1792660, _1792662, _1792664])) = 50089 ^ [_1792660, _1792662, _1792664], -(hAPP(c_Set_Oimage(_1792660, _1792662, _1792664), c_Orderings_Otop__class_Otop(tc_fun(_1792660, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1792662, tc_HOL_Obool)))], (50095 ^ _780086) ^ [_1792860, _1792862, _1792864, _1792866, _1792868, _1792870] : [hAPP(c_Set_Oimage(_1792860, _1792862, _1792864), _1792866) = _1792868, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1792862, tc_HOL_Obool)), _1792870), _1792868)), -(hAPP(c_Set_Oimage(_1792860, _1792862, _1792864), hAPP(c_Set_Oimage(_1792862, _1792860, c_Hilbert__Choice_Oinv__into(_1792860, _1792862, _1792866, _1792864)), _1792870)) = _1792870)], (50105 ^ _780086) ^ [_1793077, _1793079, _1793081, _1793083, _1793085] : [-(hAPP(c_Hilbert__Choice_Oinv__into(_1793077, _1793079, _1793081, _1793083), _1793085) = c_Hilbert__Choice_OEps(_1793077, hAPP(hAPP(c_COMBS(_1793077, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1793077), c_fconj), hAPP(hAPP(c_COMBC(_1793077, tc_fun(_1793077, tc_HOL_Obool), tc_HOL_Obool), c_member(_1793077)), _1793081))), hAPP(hAPP(c_COMBC(_1793077, _1793079, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1793079, tc_fun(_1793079, tc_HOL_Obool), _1793077), c_fequal), _1793083)), _1793085))))], (50107 ^ _780086) ^ [_1793177, _1793179, _1793181, _1793183, _1793185] : [c_Fun_Oinj__on(_1793177, _1793179, _1793181, c_Orderings_Otop__class_Otop(tc_fun(_1793177, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1793179, _1793183, _1793177, hAPP(c_Fun_Ocomp(_1793177, _1793183, _1793179, _1793185), c_Hilbert__Choice_Oinv__into(_1793177, _1793179, c_Orderings_Otop__class_Otop(tc_fun(_1793177, tc_HOL_Obool)), _1793181))), _1793181) = _1793185)], (50113 ^ _780086) ^ [_1793326, _1793328, _1793330] : [c_Fun_Oinj__on(_1793326, _1793328, _1793330, c_Orderings_Otop__class_Otop(tc_fun(_1793326, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1793328, _1793326, c_Hilbert__Choice_Oinv__into(_1793326, _1793328, c_Orderings_Otop__class_Otop(tc_fun(_1793326, tc_HOL_Obool)), _1793330)), c_Orderings_Otop__class_Otop(tc_fun(_1793328, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1793326, tc_HOL_Obool)))], (50119 ^ _780086) ^ [_1793473, _1793475, _1793477, _1793479] : [c_Fun_Oinj__on(_1793473, _1793475, _1793477, c_Orderings_Otop__class_Otop(tc_fun(_1793473, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1793475, _1793473, c_Hilbert__Choice_Oinv__into(_1793473, _1793475, c_Orderings_Otop__class_Otop(tc_fun(_1793473, tc_HOL_Obool)), _1793477)), hAPP(c_Set_Oimage(_1793473, _1793475, _1793477), _1793479)) = _1793479)], (50125 ^ _780086) ^ [_1793616, _1793618, _1793620, _1793622] : [c_Fun_Oinj__on(_1793616, _1793618, _1793620, c_Orderings_Otop__class_Otop(tc_fun(_1793616, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1793618, _1793616, c_Hilbert__Choice_Oinv__into(_1793616, _1793618, c_Orderings_Otop__class_Otop(tc_fun(_1793616, tc_HOL_Obool)), _1793620)), hAPP(c_Set_Oimage(_1793616, _1793618, _1793620), _1793622)) = _1793622)], (50131 ^ _780086) ^ [_1793759, _1793761, _1793763] : [hAPP(c_Set_Oimage(_1793759, _1793761, _1793763), c_Orderings_Otop__class_Otop(tc_fun(_1793759, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1793761, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1793761, _1793759, c_Hilbert__Choice_Oinv__into(_1793759, _1793761, c_Orderings_Otop__class_Otop(tc_fun(_1793759, tc_HOL_Obool)), _1793763), c_Orderings_Otop__class_Otop(tc_fun(_1793761, tc_HOL_Obool))))], (50137 ^ _780086) ^ [_1793906, _1793908, _1793910, _1793912, _1793914] : [c_Fun_Oinj__on(_1793906, _1793908, _1793910, _1793912), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1793906, tc_HOL_Obool)), _1793914), _1793912)), -(hAPP(c_Set_Oimage(_1793908, _1793906, c_Hilbert__Choice_Oinv__into(_1793906, _1793908, _1793912, _1793910)), hAPP(c_Set_Oimage(_1793906, _1793908, _1793910), _1793914)) = _1793914)], (50147 ^ _780086) ^ [_1794109, _1794111, _1794113, _1794115, _1794117] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1794109, tc_HOL_Obool)), _1794111), hAPP(c_Set_Oimage(_1794113, _1794109, _1794115), _1794117))), -(c_Fun_Oinj__on(_1794109, _1794113, c_Hilbert__Choice_Oinv__into(_1794113, _1794109, _1794117, _1794115), _1794111))], (50153 ^ _780086) ^ [_1794240, _1794242, _1794244, _1794246, _1794248, _1794250, _1794252] : [c_Fun_Oinj__on(_1794240, _1794242, _1794244, hAPP(c_Set_Oimage(_1794246, _1794240, _1794248), _1794250)), c_Fun_Oinj__on(_1794246, _1794240, _1794248, _1794250), hBOOL(hAPP(hAPP(c_member(_1794242), _1794252), hAPP(c_Set_Oimage(_1794240, _1794242, _1794244), hAPP(c_Set_Oimage(_1794246, _1794240, _1794248), _1794250)))), -(hAPP(c_Hilbert__Choice_Oinv__into(_1794246, _1794242, _1794250, hAPP(c_Fun_Ocomp(_1794240, _1794242, _1794246, _1794244), _1794248)), _1794252) = hAPP(hAPP(c_Fun_Ocomp(_1794240, _1794246, _1794242, c_Hilbert__Choice_Oinv__into(_1794246, _1794240, _1794250, _1794248)), c_Hilbert__Choice_Oinv__into(_1794240, _1794242, hAPP(c_Set_Oimage(_1794246, _1794240, _1794248), _1794250), _1794244)), _1794252))], (50167 ^ _780086) ^ [_1794621, _1794623, _1794625] : [hAPP(c_Set_Oimage(_1794621, _1794623, _1794625), c_Orderings_Otop__class_Otop(tc_fun(_1794621, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1794623, tc_HOL_Obool)), -(hAPP(c_Fun_Ocomp(_1794621, _1794623, _1794623, _1794625), c_Hilbert__Choice_Oinv__into(_1794621, _1794623, c_Orderings_Otop__class_Otop(tc_fun(_1794621, tc_HOL_Obool)), _1794625)) = c_Fun_Oid(_1794623))], (50173 ^ _780086) ^ [_1794770, _1794772, _1794774] : [hAPP(c_Fun_Ocomp(_1794770, _1794772, _1794772, _1794774), c_Hilbert__Choice_Oinv__into(_1794770, _1794772, c_Orderings_Otop__class_Otop(tc_fun(_1794770, tc_HOL_Obool)), _1794774)) = c_Fun_Oid(_1794772), -(hAPP(c_Set_Oimage(_1794770, _1794772, _1794774), c_Orderings_Otop__class_Otop(tc_fun(_1794770, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1794772, tc_HOL_Obool)))], (50179 ^ _780086) ^ [_1794925, _1794927, _1794929, _1794931, _1794933] : [c_Fun_Oinj__on(_1794925, _1794927, _1794929, c_Orderings_Otop__class_Otop(tc_fun(_1794925, tc_HOL_Obool))), 50185 ^ _780086 : [(50186 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1794927), 50184 ^ [_1794925, _1794927, _1794929, _1794931, _1794933]), hAPP(c_Set_Oimage(_1794925, _1794927, _1794929), c_Orderings_Otop__class_Otop(tc_fun(_1794925, tc_HOL_Obool))))))], (50188 ^ _780086) ^ [] : [hBOOL(hAPP(_1794931, hAPP(c_Hilbert__Choice_Oinv__into(_1794925, _1794927, c_Orderings_Otop__class_Otop(tc_fun(_1794925, tc_HOL_Obool)), _1794929), 50184 ^ [_1794925, _1794927, _1794929, _1794931, _1794933])))]], -(hBOOL(hAPP(_1794931, _1794933)))], (50192 ^ _780086) ^ [_1795251, _1795253, _1795255, _1795257, _1795259, _1795261] : [class_Groups_Ocomm__monoid__mult(_1795251), hBOOL(hAPP(c_Finite__Set_Ofinite(_1795253), _1795255)), 50202 ^ _780086 : [(50203 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1795253), 50201 ^ [_1795251, _1795253, _1795255, _1795257, _1795259, _1795261]), _1795255)))], (50205 ^ _780086) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1795257), hAPP(_1795259, 50201 ^ [_1795251, _1795253, _1795255, _1795257, _1795259, _1795261])))]], 50209 ^ _780086 : [(50210 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1795253), 50208 ^ [_1795251, _1795253, _1795255, _1795257, _1795259, _1795261]), _1795255)))], (50213 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1795253), 50211 ^ [_1795251, _1795253, _1795255, _1795257, _1795259, _1795261]), _1795255)))], (50215 ^ _780086) ^ [] : [50208 ^ [_1795251, _1795253, _1795255, _1795257, _1795259, _1795261] = 50211 ^ [_1795251, _1795253, _1795255, _1795257, _1795259, _1795261]], (50217 ^ _780086) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1795257, tc_HOL_Obool)), hAPP(_1795259, 50208 ^ [_1795251, _1795253, _1795255, _1795257, _1795259, _1795261])), hAPP(_1795259, 50211 ^ [_1795251, _1795253, _1795255, _1795257, _1795259, _1795261])) = c_Orderings_Obot__class_Obot(tc_fun(_1795257, tc_HOL_Obool))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1795251, _1795257, c_Groups_Otimes__class_Otimes(_1795251)), _1795261), c_Groups_Oone__class_Oone(_1795251)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1795253, tc_fun(_1795257, tc_HOL_Obool)), _1795255), _1795259)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1795251, _1795253, c_Groups_Otimes__class_Otimes(_1795251)), hAPP(hAPP(c_COMBB(tc_fun(_1795257, tc_HOL_Obool), _1795251, _1795253), hAPP(hAPP(c_Finite__Set_Ofold__image(_1795251, _1795257, c_Groups_Otimes__class_Otimes(_1795251)), _1795261), c_Groups_Oone__class_Oone(_1795251))), _1795259)), c_Groups_Oone__class_Oone(_1795251)), _1795255))], (50221 ^ _780086) ^ [_1796211] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1796211), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), -(_1796211 = hAPP(c_Code__Numeral_Onat__of, 50224 ^ [_1796211]))], (50228 ^ _780086) ^ [_1796316, _1796318] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1796316), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(_1796318, hAPP(c_Code__Numeral_Onat__of, 50233 ^ [_1796316, _1796318]))), -(hBOOL(hAPP(_1796318, _1796316)))], (50240 ^ _780086) ^ [_1796496] : [-(_1796496 = hAPP(c_Code__Numeral_Oof__nat, 50238 ^ [_1796496]))], (50242 ^ _780086) ^ [_1796524] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 50238 ^ [_1796524]), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (50244 ^ _780086) ^ [_1796559, _1796561] : [50246 ^ _780086 : [(50247 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 50245 ^ [_1796559, _1796561]), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (50249 ^ _780086) ^ [] : [hBOOL(hAPP(_1796559, hAPP(c_Code__Numeral_Oof__nat, 50245 ^ [_1796559, _1796561])))]], -(hBOOL(hAPP(_1796559, _1796561)))], (50253 ^ _780086) ^ [_1796728, _1796730, _1796732, _1796734] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1796728, _1796730, _1796732, _1796734, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1796730)) = _1796732)], (50255 ^ _780086) ^ [_1796774, _1796776] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1796774), _1796776)), -(c_Quickcheck_Obeyond(_1796774, _1796776) = _1796776)], (50261 ^ _780086) ^ [_1796861, _1796863] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1796861), _1796863))), -(c_Quickcheck_Obeyond(_1796861, _1796863) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (50267 ^ _780086) ^ [_1796907] : [-(c_Quickcheck_Obeyond(_1796907, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (50269 ^ _780086) ^ [_1796933, _1796935, _1796937, _1796939, _1796941, _1796943] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1796933, _1796935, _1796937, _1796939, c_Lazy__Sequence_Olazy__sequence_OInsert(_1796935, _1796941, _1796943)) = hAPP(hAPP(hAPP(_1796939, _1796941), _1796943), c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1796933, _1796935, _1796937, _1796939, _1796943)))], (50271 ^ _780086) ^ [_1796991, _1796993, _1796995, _1796997] : [c_Fun_Obij__betw(_1796991, _1796993, _1796995, c_Orderings_Otop__class_Otop(tc_fun(_1796991, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1796993, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1796991, _1796993, _1796995), hAPP(c_Set_OCollect(_1796991), _1796997)) = hAPP(c_Set_OCollect(_1796993), hAPP(hAPP(c_COMBB(_1796991, tc_HOL_Obool, _1796993), _1796997), c_Hilbert__Choice_Oinv__into(_1796991, _1796993, c_Orderings_Otop__class_Otop(tc_fun(_1796991, tc_HOL_Obool)), _1796995))))], (50277 ^ _780086) ^ [_1797172, _1797174, _1797176, _1797178, _1797180, _1797182] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1797172, _1797174, _1797176, _1797178), _1797180), _1797182) = hAPP(_1797178, hAPP(hAPP(c_Product__Type_OPair(_1797172, _1797174), _1797180), _1797182)))], (50279 ^ _780086) ^ [_1797228, _1797230, _1797232, _1797234, _1797236] : [hBOOL(hAPP(_1797228, hAPP(hAPP(c_Product__Type_OPair(_1797230, _1797232), _1797234), _1797236))), -(hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1797230, _1797232, tc_HOL_Obool, _1797228), _1797234), _1797236)))], (50285 ^ _780086) ^ [_1797353, _1797355] : [-(c_Fun_Obij__betw(_1797353, _1797353, c_Fun_Oid(_1797353), _1797355, _1797355))], (50287 ^ _780086) ^ [_1797383, _1797385, _1797387, _1797389, _1797391] : [c_Fun_Obij__betw(_1797383, _1797385, _1797387, _1797389, _1797391), -(c_Fun_Obij__betw(_1797385, _1797383, c_Hilbert__Choice_Oinv__into(_1797383, _1797385, _1797389, _1797387), _1797391, _1797389))], (50293 ^ _780086) ^ [_1797488, _1797490, _1797492, _1797494, _1797496, _1797498] : [c_Fun_Obij__betw(_1797488, _1797490, _1797492, _1797494, _1797496), hBOOL(hAPP(hAPP(c_member(_1797488), _1797498), _1797494)), -(hAPP(c_Hilbert__Choice_Oinv__into(_1797490, _1797488, _1797496, c_Hilbert__Choice_Oinv__into(_1797488, _1797490, _1797494, _1797492)), _1797498) = hAPP(_1797492, _1797498))], (50303 ^ _780086) ^ [_1797685, _1797687, _1797689] : [c_Fun_Obij__betw(_1797685, _1797687, _1797689, c_Orderings_Otop__class_Otop(tc_fun(_1797685, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1797687, tc_HOL_Obool))), -(c_Hilbert__Choice_Oinv__into(_1797687, _1797685, c_Orderings_Otop__class_Otop(tc_fun(_1797687, tc_HOL_Obool)), c_Hilbert__Choice_Oinv__into(_1797685, _1797687, c_Orderings_Otop__class_Otop(tc_fun(_1797685, tc_HOL_Obool)), _1797689)) = _1797689)], (50309 ^ _780086) ^ [_1797830, _1797832, _1797834] : [c_Fun_Obij__betw(_1797830, _1797832, _1797834, c_Orderings_Otop__class_Otop(tc_fun(_1797830, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1797832, tc_HOL_Obool))), -(c_Fun_Obij__betw(_1797832, _1797830, c_Hilbert__Choice_Oinv__into(_1797830, _1797832, c_Orderings_Otop__class_Otop(tc_fun(_1797830, tc_HOL_Obool)), _1797834), c_Orderings_Otop__class_Otop(tc_fun(_1797832, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1797830, tc_HOL_Obool))))], (50315 ^ _780086) ^ [_1797981, _1797983, _1797985, _1797987, _1797989] : [c_Fun_Obij__betw(_1797981, _1797983, _1797985, c_Orderings_Otop__class_Otop(tc_fun(_1797981, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1797983, tc_HOL_Obool))), c_Fun_Obij__betw(_1797987, _1797981, _1797989, c_Orderings_Otop__class_Otop(tc_fun(_1797987, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1797981, tc_HOL_Obool))), -(c_Hilbert__Choice_Oinv__into(_1797987, _1797983, c_Orderings_Otop__class_Otop(tc_fun(_1797987, tc_HOL_Obool)), hAPP(c_Fun_Ocomp(_1797981, _1797983, _1797987, _1797985), _1797989)) = hAPP(c_Fun_Ocomp(_1797981, _1797987, _1797983, c_Hilbert__Choice_Oinv__into(_1797987, _1797981, c_Orderings_Otop__class_Otop(tc_fun(_1797987, tc_HOL_Obool)), _1797989)), c_Hilbert__Choice_Oinv__into(_1797981, _1797983, c_Orderings_Otop__class_Otop(tc_fun(_1797981, tc_HOL_Obool)), _1797985)))], (50325 ^ _780086) ^ [_1798266, _1798268, _1798270, _1798272, _1798274, _1798276] : [c_Fun_Obij__betw(_1798266, _1798268, _1798270, c_Orderings_Otop__class_Otop(tc_fun(_1798266, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1798268, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1798266, _1798268, _1798270), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1798272, tc_fun(_1798266, tc_HOL_Obool)), _1798274), _1798276)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1798272, tc_fun(_1798268, tc_HOL_Obool)), _1798274), hAPP(hAPP(c_COMBB(tc_fun(_1798266, tc_HOL_Obool), tc_fun(_1798268, tc_HOL_Obool), _1798272), c_Set_Oimage(_1798266, _1798268, _1798270)), _1798276)))], (50331 ^ _780086) ^ [_1798479, _1798481, _1798483, _1798485, _1798487, _1798489, _1798491, _1798493] : [c_Fun_Obij__betw(_1798479, _1798481, _1798483, _1798485, _1798487), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1798479, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1798489, _1798479, _1798491), _1798493)), _1798485)), 50338 ^ _780086 : [(50339 ^ _780086) ^ [] : [c_Fun_Obij__betw(_1798489, _1798479, _1798491, _1798493, _1798485), -(c_Fun_Obij__betw(_1798489, _1798481, hAPP(c_Fun_Ocomp(_1798479, _1798481, _1798489, _1798483), _1798491), _1798493, _1798487))], (50345 ^ _780086) ^ [] : [c_Fun_Obij__betw(_1798489, _1798481, hAPP(c_Fun_Ocomp(_1798479, _1798481, _1798489, _1798483), _1798491), _1798493, _1798487), -(c_Fun_Obij__betw(_1798489, _1798479, _1798491, _1798493, _1798485))]]], (50351 ^ _780086) ^ [_1798868, _1798870, _1798872, _1798874, _1798876, _1798878, _1798880, _1798882] : [c_Fun_Obij__betw(_1798868, _1798870, _1798872, _1798874, _1798876), c_Fun_Obij__betw(_1798870, _1798878, _1798880, _1798876, _1798882), -(c_Fun_Obij__betw(_1798868, _1798878, hAPP(c_Fun_Ocomp(_1798870, _1798878, _1798868, _1798880), _1798872), _1798874, _1798882))], (50361 ^ _780086) ^ [_1799055, _1799057, _1799059, _1799061, _1799063, _1799065, _1799067, _1799069] : [c_Fun_Obij__betw(_1799055, _1799057, _1799059, _1799061, _1799063), 50364 ^ _780086 : [(50365 ^ _780086) ^ [] : [c_Fun_Obij__betw(_1799057, _1799065, _1799067, _1799063, _1799069), -(c_Fun_Obij__betw(_1799055, _1799065, hAPP(c_Fun_Ocomp(_1799057, _1799065, _1799055, _1799067), _1799059), _1799061, _1799069))], (50371 ^ _780086) ^ [] : [c_Fun_Obij__betw(_1799055, _1799065, hAPP(c_Fun_Ocomp(_1799057, _1799065, _1799055, _1799067), _1799059), _1799061, _1799069), -(c_Fun_Obij__betw(_1799057, _1799065, _1799067, _1799063, _1799069))]]], (50377 ^ _780086) ^ [_1799346, _1799348, _1799350, _1799352, _1799354] : [c_Fun_Obij__betw(_1799346, _1799348, _1799350, c_Orderings_Otop__class_Otop(tc_fun(_1799346, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1799348, tc_HOL_Obool))), c_Fun_Obij__betw(_1799348, _1799352, _1799354, c_Orderings_Otop__class_Otop(tc_fun(_1799348, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1799352, tc_HOL_Obool))), -(c_Fun_Obij__betw(_1799346, _1799352, hAPP(c_Fun_Ocomp(_1799348, _1799352, _1799346, _1799354), _1799350), c_Orderings_Otop__class_Otop(tc_fun(_1799346, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1799352, tc_HOL_Obool))))], (50387 ^ _780086) ^ [_1799581, _1799583, _1799585, _1799587, _1799589] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1799581, _1799583, tc_HOL_Obool, _1799585), _1799587), _1799589)), -(hBOOL(hAPP(_1799585, hAPP(hAPP(c_Product__Type_OPair(_1799581, _1799583), _1799587), _1799589))))], (50393 ^ _780086) ^ [_1799706, _1799708, _1799710, _1799712, _1799714] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1799706, _1799708, tc_HOL_Obool, _1799710), _1799712), _1799714)), -(hBOOL(hAPP(_1799710, hAPP(hAPP(c_Product__Type_OPair(_1799706, _1799708), _1799712), _1799714))))], (50399 ^ _780086) ^ [_1799831, _1799833, _1799835, _1799837, _1799839, _1799841] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1799831, _1799833, _1799835, _1799837), _1799839), _1799841) = hAPP(_1799837, hAPP(hAPP(c_Product__Type_OPair(_1799831, _1799833), _1799839), _1799841)))], (50401 ^ _780086) ^ [_1799887, _1799889, _1799891, _1799893] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1799887, _1799889, _1799891), c_Product__Type_Ocurry(_1799887, _1799889, _1799891, _1799893)) = _1799893)], (50403 ^ _780086) ^ [_1799928, _1799930, _1799932, _1799934] : [-(c_Product__Type_Ocurry(_1799928, _1799930, _1799932, hAPP(c_Product__Type_Oprod_Oprod__case(_1799928, _1799930, _1799932), _1799934)) = _1799934)], (50405 ^ _780086) ^ [_1799969, _1799971, _1799973, _1799975] : [c_Fun_Obij__betw(_1799969, _1799971, _1799973, c_Orderings_Otop__class_Otop(tc_fun(_1799969, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1799971, tc_HOL_Obool))), 50408 ^ _780086 : [(50409 ^ _780086) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1799969), hAPP(c_Set_Ovimage(_1799969, _1799971, _1799973), _1799975))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1799971), _1799975)))], (50415 ^ _780086) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1799971), _1799975)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1799969), hAPP(c_Set_Ovimage(_1799969, _1799971, _1799973), _1799975))))]]], (50421 ^ _780086) ^ [_1800259, _1800261, _1800263, _1800265] : [c_Fun_Obij__betw(_1800259, _1800261, _1800263, c_Orderings_Otop__class_Otop(tc_fun(_1800259, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1800261, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1800259, _1800261, _1800263), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1800259, tc_HOL_Obool)), _1800265)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1800261, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1800259, _1800261, _1800263), _1800265)))], (50427 ^ _780086) ^ [_1800426, _1800428, _1800430, _1800432, _1800434, _1800436, _1800438] : [c_Fun_Obij__betw(_1800426, _1800428, _1800430, _1800432, _1800434), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1800426, tc_HOL_Obool)), _1800436), _1800432)), hAPP(c_Set_Oimage(_1800426, _1800428, _1800430), _1800436) = _1800438, -(c_Fun_Obij__betw(_1800426, _1800428, _1800430, _1800436, _1800438))], (50441 ^ _780086) ^ [_1800683, _1800685, _1800687] : [c_Fun_Obij__betw(_1800683, _1800685, _1800687, c_Orderings_Otop__class_Otop(tc_fun(_1800683, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1800685, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1800683, _1800685, _1800687), c_Orderings_Otop__class_Otop(tc_fun(_1800683, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1800685, tc_HOL_Obool)))], (50447 ^ _780086) ^ [_1800822, _1800824, _1800826, _1800828] : [c_Fun_Obij__betw(_1800822, _1800824, _1800826, _1800828, c_Orderings_Otop__class_Otop(tc_fun(_1800824, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1800822, _1800824, _1800826), c_Orderings_Otop__class_Otop(tc_fun(_1800822, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1800824, tc_HOL_Obool)))], (50453 ^ _780086) ^ [_1800977, _1800979, _1800981, _1800983, _1800985] : [c_Fun_Obij__betw(_1800977, _1800979, _1800981, _1800983, _1800985), 50456 ^ _780086 : [(50457 ^ _780086) ^ [] : [-(c_Fun_Oinj__on(_1800977, _1800979, _1800981, _1800983))], (50459 ^ _780086) ^ [] : [-(hAPP(c_Set_Oimage(_1800977, _1800979, _1800981), _1800983) = _1800985)]]], (50461 ^ _780086) ^ [_1801106, _1801108, _1801110, _1801112, _1801114] : [-(c_Fun_Obij__betw(_1801106, _1801108, _1801110, _1801112, _1801114)), c_Fun_Oinj__on(_1801106, _1801108, _1801110, _1801112), hAPP(c_Set_Oimage(_1801106, _1801108, _1801110), _1801112) = _1801114], (50471 ^ _780086) ^ [_1801273, _1801275, _1801277, _1801279] : [c_Fun_Oinj__on(_1801273, _1801275, _1801277, _1801279), -(c_Fun_Obij__betw(_1801273, _1801275, _1801277, _1801279, hAPP(c_Set_Oimage(_1801273, _1801275, _1801277), _1801279)))], (50477 ^ _780086) ^ [_1801378, _1801380, _1801382, _1801384, _1801386] : [c_Fun_Obij__betw(_1801378, _1801380, _1801382, _1801384, _1801386), -(c_Fun_Oinj__on(_1801378, _1801380, _1801382, _1801384))], (50483 ^ _780086) ^ [_1801471, _1801473, _1801475] : [c_Fun_Obij__betw(_1801471, _1801473, _1801475, c_Orderings_Otop__class_Otop(tc_fun(_1801471, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1801473, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1801471, _1801473, _1801475, c_Orderings_Otop__class_Otop(tc_fun(_1801471, tc_HOL_Obool))))], (50489 ^ _780086) ^ [_1801590, _1801592, _1801594, _1801596, _1801598] : [c_Fun_Obij__betw(_1801590, _1801592, _1801594, _1801596, _1801598), -(c_Fun_Obij__betw(_1801592, _1801590, c_Fun_Othe__inv__into(_1801590, _1801592, _1801596, _1801594), _1801598, _1801596))], (50495 ^ _780086) ^ [_1801695, _1801697, _1801699, _1801701, _1801703] : [c_Fun_Obij__betw(_1801695, _1801697, _1801699, _1801701, _1801703), -(hAPP(c_Finite__Set_Ocard(_1801695), _1801701) = hAPP(c_Finite__Set_Ocard(_1801697), _1801703))], (50501 ^ _780086) ^ [_1801804, _1801806, _1801808, _1801810] : [c_Fun_Obij__betw(_1801804, _1801806, _1801808, _1801810, c_Orderings_Obot__class_Obot(tc_fun(_1801806, tc_HOL_Obool))), -(_1801810 = c_Orderings_Obot__class_Obot(tc_fun(_1801804, tc_HOL_Obool)))], (50507 ^ _780086) ^ [_1801911, _1801913, _1801915, _1801917] : [c_Fun_Obij__betw(_1801911, _1801913, _1801915, c_Orderings_Obot__class_Obot(tc_fun(_1801911, tc_HOL_Obool)), _1801917), -(_1801917 = c_Orderings_Obot__class_Obot(tc_fun(_1801913, tc_HOL_Obool)))], (50513 ^ _780086) ^ [_1802018, _1802020, _1802022, _1802024] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1802018), _1802020)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1802022), _1802024)), 50520 ^ _780086 : [(50521 ^ _780086) ^ [] : [50522 ^ _780086 : [(50523 ^ _780086) ^ [_1802207] : [c_Fun_Obij__betw(_1802018, _1802022, _1802207, _1802020, _1802024)]], -(hAPP(c_Finite__Set_Ocard(_1802018), _1802020) = hAPP(c_Finite__Set_Ocard(_1802022), _1802024))], (50527 ^ _780086) ^ [] : [hAPP(c_Finite__Set_Ocard(_1802018), _1802020) = hAPP(c_Finite__Set_Ocard(_1802022), _1802024), -(c_Fun_Obij__betw(_1802018, _1802022, 50530 ^ [_1802018, _1802020, _1802022, _1802024], _1802020, _1802024))]]], (50534 ^ _780086) ^ [_1802372, _1802374, _1802376, _1802378, _1802380] : [c_Fun_Obij__betw(_1802372, _1802374, _1802376, _1802378, _1802380), 50537 ^ _780086 : [(50538 ^ _780086) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1802372), _1802378)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1802374), _1802380)))], (50544 ^ _780086) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1802374), _1802380)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1802372), _1802378)))]]], (50550 ^ _780086) ^ [_1802645, _1802647, _1802649] : [c_Fun_Obij__betw(_1802645, _1802645, c_Fun_Oid(_1802645), _1802647, _1802649), -(_1802647 = _1802649)], (50556 ^ _780086) ^ [_1802730, _1802732, _1802734] : [_1802732 = _1802734, -(c_Fun_Obij__betw(_1802730, _1802730, c_Fun_Oid(_1802730), _1802732, _1802734))], (50562 ^ _780086) ^ [_1802821] : [-(c_Fun_Obij__betw(_1802821, _1802821, c_Fun_Oid(_1802821), c_Orderings_Otop__class_Otop(tc_fun(_1802821, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1802821, tc_HOL_Obool))))], (50564 ^ _780086) ^ [_1802954, _1802956, _1802958, _1802960, _1802962, _1802964, _1802966] : [c_Fun_Obij__betw(_1802954, _1802956, _1802958, _1802960, _1802962), c_Fun_Obij__betw(_1802954, _1802956, _1802958, _1802964, _1802966), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1802956, tc_HOL_Obool)), _1802962), _1802966) = c_Orderings_Obot__class_Obot(tc_fun(_1802956, tc_HOL_Obool)), -(c_Fun_Obij__betw(_1802954, _1802956, _1802958, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1802954, tc_HOL_Obool)), _1802960), _1802964), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1802956, tc_HOL_Obool)), _1802962), _1802966)))], (50578 ^ _780086) ^ [_1803576, _1803578, _1803580, _1803582, _1803584, _1803586, _1803588] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1803576, tc_HOL_Obool)), _1803578), _1803580) = c_Orderings_Obot__class_Obot(tc_fun(_1803576, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1803582, tc_HOL_Obool)), _1803584), _1803586) = c_Orderings_Obot__class_Obot(tc_fun(_1803582, tc_HOL_Obool)), c_Fun_Obij__betw(_1803576, _1803582, _1803588, _1803578, _1803584), c_Fun_Obij__betw(_1803576, _1803582, _1803588, _1803580, _1803586), -(c_Fun_Obij__betw(_1803576, _1803582, _1803588, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1803576, tc_HOL_Obool)), _1803578), _1803580), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1803582, tc_HOL_Obool)), _1803584), _1803586)))], (50596 ^ _780086) ^ [_1804312, _1804314, _1804316] : [c_Fun_Obij__betw(_1804312, _1804314, _1804316, c_Orderings_Otop__class_Otop(tc_fun(_1804312, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1804314, tc_HOL_Obool))), 50599 ^ _780086 : [(50600 ^ _780086) ^ [] : [-(c_Fun_Oinj__on(_1804312, _1804314, _1804316, c_Orderings_Otop__class_Otop(tc_fun(_1804312, tc_HOL_Obool))))], (50602 ^ _780086) ^ [] : [-(hAPP(c_Set_Oimage(_1804312, _1804314, _1804316), c_Orderings_Otop__class_Otop(tc_fun(_1804312, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1804314, tc_HOL_Obool)))]]], (50604 ^ _780086) ^ [_1804631, _1804633, _1804635] : [-(c_Fun_Obij__betw(_1804631, _1804633, _1804635, c_Orderings_Otop__class_Otop(tc_fun(_1804631, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1804633, tc_HOL_Obool)))), c_Fun_Oinj__on(_1804631, _1804633, _1804635, c_Orderings_Otop__class_Otop(tc_fun(_1804631, tc_HOL_Obool))), hAPP(c_Set_Oimage(_1804631, _1804633, _1804635), c_Orderings_Otop__class_Otop(tc_fun(_1804631, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1804633, tc_HOL_Obool))], (50614 ^ _780086) ^ [_1805030, _1805032, _1805034] : [c_Fun_Oinj__on(_1805030, _1805032, _1805034, c_Orderings_Otop__class_Otop(tc_fun(_1805030, tc_HOL_Obool))), hAPP(c_Set_Oimage(_1805030, _1805032, _1805034), c_Orderings_Otop__class_Otop(tc_fun(_1805030, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1805032, tc_HOL_Obool)), -(c_Fun_Obij__betw(_1805030, _1805032, _1805034, c_Orderings_Otop__class_Otop(tc_fun(_1805030, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1805032, tc_HOL_Obool))))], (50624 ^ _780086) ^ [_1805455, _1805457, _1805459, _1805461, _1805463] : [c_Fun_Obij__betw(_1805455, _1805457, _1805459, c_Orderings_Otop__class_Otop(tc_fun(_1805455, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1805457, tc_HOL_Obool))), 50627 ^ _780086 : [(50628 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1805455, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1805455, _1805457, _1805459), _1805461)), _1805463)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1805457, tc_HOL_Obool)), _1805461), hAPP(c_Set_Oimage(_1805455, _1805457, _1805459), _1805463))))], (50634 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1805457, tc_HOL_Obool)), _1805461), hAPP(c_Set_Oimage(_1805455, _1805457, _1805459), _1805463))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1805455, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1805455, _1805457, _1805459), _1805461)), _1805463)))]]], (50640 ^ _780086) ^ [_1806119, _1806121, _1806123, _1806125] : [c_Fun_Obij__betw(_1806119, _1806121, _1806123, c_Orderings_Otop__class_Otop(tc_fun(_1806119, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1806121, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_1806119, _1806121, _1806123), _1806125) = hAPP(c_Set_Oimage(_1806121, _1806119, c_Hilbert__Choice_Oinv__into(_1806119, _1806121, c_Orderings_Otop__class_Otop(tc_fun(_1806119, tc_HOL_Obool)), _1806123)), _1806125))], (50646 ^ _780086) ^ [_1806415, _1806417] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1806415), _1806417)), -(c_Fun_Obij__betw(tc_Nat_Onat, _1806415, 50649 ^ [_1806415, _1806417], c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1806415), _1806417)), _1806417))], (50653 ^ _780086) ^ [_1806782, _1806784, _1806786, _1806788, _1806790, _1806792] : [c_Fun_Oinj__on(_1806782, _1806784, _1806786, _1806788), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1806784, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1806782, _1806784, _1806786), _1806788)), _1806790)), c_Fun_Oinj__on(_1806784, _1806782, _1806792, _1806790), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1806782, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1806784, _1806782, _1806792), _1806790)), _1806788)), -(c_Fun_Obij__betw(_1806782, _1806784, 50668 ^ [_1806782, _1806784, _1806786, _1806788, _1806790, _1806792], _1806788, _1806790))], (50672 ^ _780086) ^ [_1807497, _1807499] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1807497), _1807499)), -(c_Fun_Obij__betw(tc_Nat_Onat, _1807497, 50675 ^ [_1807497, _1807499], hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1807497), _1807499)), _1807499))], (50679 ^ _780086) ^ [_1807805, _1807807] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1807805), _1807807)), -(c_Fun_Obij__betw(_1807805, tc_Nat_Onat, 50682 ^ [_1807805, _1807807], _1807807, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1807805), _1807807))))], (50686 ^ _780086) ^ [_1808155, _1808157, _1808159, _1808161, _1808163] : [50688 ^ _780086 : [(50689 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1808155), 50687 ^ [_1808155, _1808157, _1808159, _1808161, _1808163]), _1808157)))], (50691 ^ _780086) ^ [] : [c_Relation_Orefl__on(_1808159, hAPP(_1808161, 50687 ^ [_1808155, _1808157, _1808159, _1808161, _1808163]), hAPP(_1808163, 50687 ^ [_1808155, _1808157, _1808159, _1808161, _1808163]))]], -(c_Relation_Orefl__on(_1808159, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1808155, tc_fun(_1808159, tc_HOL_Obool)), _1808157), _1808161), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1808155, tc_fun(tc_prod(_1808159, _1808159), tc_HOL_Obool)), _1808157), _1808163)))], (50695 ^ _780086) ^ [_1808683, _1808685, _1808687] : [c_Equiv__Relations_Oequivp(_1808683, _1808685), 50698 ^ _780086 : [(50710 ^ _780086) ^ [] : [50711 ^ _780086 : [(50712 ^ _780086) ^ [_1809266] : [hBOOL(hAPP(_1808687, _1809266))]], 50714 ^ _780086 : [(50715 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1808683), 50713 ^ [_1808683, _1808685, _1808687]), c_Quotient_ORespects(_1808683, _1808685))))], (50717 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1808687, 50713 ^ [_1808683, _1808685, _1808687])))]]], (50699 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1808687, 50706 ^ [_1808683, _1808685, _1808687]))), 50700 ^ _780086 : [(50701 ^ _780086) ^ [_1808914] : [hBOOL(hAPP(hAPP(c_member(_1808683), _1808914), c_Quotient_ORespects(_1808683, _1808685))), hBOOL(hAPP(_1808687, _1808914))]]]]], (50719 ^ _780086) ^ [_1809652, _1809654, _1809656] : [hBOOL(hAPP(hAPP(c_member(_1809652), _1809654), c_Quotient_ORespects(_1809652, _1809656))), -(hBOOL(hAPP(hAPP(_1809656, _1809654), _1809654)))], (50725 ^ _780086) ^ [_1809850, _1809852, _1809854] : [hBOOL(hAPP(hAPP(_1809854, _1809852), _1809852)), -(hBOOL(hAPP(hAPP(c_member(_1809850), _1809852), c_Quotient_ORespects(_1809850, _1809854))))], (50731 ^ _780086) ^ [_1810141, _1810143, _1810145] : [hBOOL(hAPP(c_Quotient_ORespects(_1810141, _1810143), _1810145)), -(hBOOL(hAPP(hAPP(_1810143, _1810145), _1810145)))], (50737 ^ _780086) ^ [_1810329, _1810331, _1810333] : [hBOOL(hAPP(hAPP(_1810331, _1810333), _1810333)), -(hBOOL(hAPP(c_Quotient_ORespects(_1810329, _1810331), _1810333)))], (50743 ^ _780086) ^ [_1810595, _1810597, _1810599, _1810601] : [c_Equiv__Relations_Oequivp(_1810595, _1810597), 50749 ^ _780086 : [(50750 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1810599, 50748 ^ [_1810595, _1810597, _1810599, _1810601])))], (50752 ^ _780086) ^ [] : [hBOOL(hAPP(_1810601, 50748 ^ [_1810595, _1810597, _1810599, _1810601]))]], 50755 ^ _780086 : [(50756 ^ _780086) ^ [_1811056] : [hBOOL(hAPP(_1810599, _1811056))]], 50758 ^ _780086 : [(50759 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1810595), 50757 ^ [_1810595, _1810597, _1810599, _1810601]), c_Quotient_ORespects(_1810595, _1810597))))], (50761 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1810601, 50757 ^ [_1810595, _1810597, _1810599, _1810601])))]]], (50763 ^ _780086) ^ [_1811443, _1811445, _1811447, _1811449] : [c_Equiv__Relations_Oequivp(_1811443, _1811445), -(c_Quotient_OBabs(_1811443, _1811447, c_Quotient_ORespects(_1811443, _1811445), _1811449) = _1811449)], (50769 ^ _780086) ^ [_1811723, _1811725, _1811727, _1811729, _1811731] : [hBOOL(hAPP(hAPP(c_member(_1811723), _1811725), _1811727)), -(hAPP(c_Quotient_OBabs(_1811723, _1811729, _1811727, _1811731), _1811725) = hAPP(_1811731, _1811725))], (50775 ^ _780086) ^ [_1812001, _1812003, _1812005] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1812001, _1812001)), hAPP(hAPP(c_Product__Type_OPair(_1812001, _1812001), hAPP(_1812003, hAPP(c_Nat_OSuc, 50776 ^ [_1812001, _1812003, _1812005]))), hAPP(_1812003, 50776 ^ [_1812001, _1812003, _1812005]))), c_Transitive__Closure_Ortrancl(_1812001, _1812005))), c_Wellfounded_Owf(_1812001, c_Transitive__Closure_Otrancl(_1812001, _1812005)), 50784 ^ _780086 : [(50785 ^ _780086) ^ [_1812464] : [-(hAPP(_1812003, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 50783 ^ [_1812001, _1812003, _1812005]), _1812464)) = hAPP(_1812003, 50783 ^ [_1812001, _1812003, _1812005]))]]], (50787 ^ _780086) ^ [_1812658, _1812660, _1812662, _1812664, _1812666] : [50789 ^ _780086 : [(50790 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1812658), 50788 ^ [_1812658, _1812660, _1812662, _1812664, _1812666]), _1812660)))], (50792 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1812662, tc_HOL_Obool)), _1812664), hAPP(_1812666, 50788 ^ [_1812658, _1812660, _1812662, _1812664, _1812666])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1812662, tc_HOL_Obool)), _1812664), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1812658, tc_fun(_1812662, tc_HOL_Obool)), _1812660), _1812666))))], (50796 ^ _780086) ^ [_1813221, _1813223, _1813225, _1813227, _1813229, _1813231] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1813221, tc_HOL_Obool)), _1813223), _1813225)), 50802 ^ _780086 : [(50803 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1813221), 50801 ^ [_1813221, _1813223, _1813225, _1813227, _1813229, _1813231]), _1813225)))], (50805 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1813227, tc_HOL_Obool)), hAPP(_1813229, 50801 ^ [_1813221, _1813223, _1813225, _1813227, _1813229, _1813231])), hAPP(_1813231, 50801 ^ [_1813221, _1813223, _1813225, _1813227, _1813229, _1813231])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1813227, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1813221, tc_fun(_1813227, tc_HOL_Obool)), _1813225), _1813229)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1813221, tc_fun(_1813227, tc_HOL_Obool)), _1813225), _1813231))))], (50809 ^ _780086) ^ [_1814001, _1814003, _1814005, _1814007, _1814009, _1814011, _1814013, _1814015] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1814001, _1814003), tc_prod(_1814001, _1814003))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1814001, _1814003), tc_prod(_1814001, _1814003)), hAPP(hAPP(c_Product__Type_OPair(_1814001, _1814003), _1814005), _1814007)), hAPP(hAPP(c_Product__Type_OPair(_1814001, _1814003), _1814009), _1814011))), c_Transitive__Closure_Ortrancl(tc_prod(_1814001, _1814003), _1814013))), hBOOL(hAPP(hAPP(_1814015, _1814005), _1814007)), 50820 ^ _780086 : [(50821 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1814001, _1814003), tc_prod(_1814001, _1814003))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1814001, _1814003), tc_prod(_1814001, _1814003)), hAPP(hAPP(c_Product__Type_OPair(_1814001, _1814003), _1814005), _1814007)), hAPP(hAPP(c_Product__Type_OPair(_1814001, _1814003), 50818 ^ [_1814001, _1814003, _1814005, _1814007, _1814009, _1814011, _1814013, _1814015]), 50819 ^ [_1814001, _1814003, _1814005, _1814007, _1814009, _1814011, _1814013, _1814015]))), c_Transitive__Closure_Ortrancl(tc_prod(_1814001, _1814003), _1814013))))], (50825 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1814001, _1814003), tc_prod(_1814001, _1814003))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1814001, _1814003), tc_prod(_1814001, _1814003)), hAPP(hAPP(c_Product__Type_OPair(_1814001, _1814003), 50818 ^ [_1814001, _1814003, _1814005, _1814007, _1814009, _1814011, _1814013, _1814015]), 50819 ^ [_1814001, _1814003, _1814005, _1814007, _1814009, _1814011, _1814013, _1814015])), hAPP(hAPP(c_Product__Type_OPair(_1814001, _1814003), 50822 ^ [_1814001, _1814003, _1814005, _1814007, _1814009, _1814011, _1814013, _1814015]), 50823 ^ [_1814001, _1814003, _1814005, _1814007, _1814009, _1814011, _1814013, _1814015]))), _1814013)))], (50827 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(_1814015, 50818 ^ [_1814001, _1814003, _1814005, _1814007, _1814009, _1814011, _1814013, _1814015]), 50819 ^ [_1814001, _1814003, _1814005, _1814007, _1814009, _1814011, _1814013, _1814015])))], (50829 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(_1814015, 50822 ^ [_1814001, _1814003, _1814005, _1814007, _1814009, _1814011, _1814013, _1814015]), 50823 ^ [_1814001, _1814003, _1814005, _1814007, _1814009, _1814011, _1814013, _1814015]))]], -(hBOOL(hAPP(hAPP(_1814015, _1814009), _1814011)))], (50833 ^ _780086) ^ [_1816329, _1816331, _1816333, _1816335, _1816337, _1816339, _1816341] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1816329, _1816331), tc_prod(_1816329, _1816331))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1816329, _1816331), tc_prod(_1816329, _1816331)), hAPP(hAPP(c_Product__Type_OPair(_1816329, _1816331), _1816333), _1816335)), hAPP(hAPP(c_Product__Type_OPair(_1816329, _1816331), _1816337), _1816339))), c_Transitive__Closure_Ortrancl(tc_prod(_1816329, _1816331), _1816341))), -(hAPP(hAPP(c_Product__Type_OPair(_1816329, _1816331), _1816333), _1816335) = hAPP(hAPP(c_Product__Type_OPair(_1816329, _1816331), _1816337), _1816339)), 50842 ^ _780086 : [(50843 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1816329, _1816331), tc_prod(_1816329, _1816331))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1816329, _1816331), tc_prod(_1816329, _1816331)), hAPP(hAPP(c_Product__Type_OPair(_1816329, _1816331), _1816333), _1816335)), hAPP(hAPP(c_Product__Type_OPair(_1816329, _1816331), 50840 ^ [_1816329, _1816331, _1816333, _1816335, _1816337, _1816339, _1816341]), 50841 ^ [_1816329, _1816331, _1816333, _1816335, _1816337, _1816339, _1816341]))), _1816341)))], (50845 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1816329, _1816331), tc_prod(_1816329, _1816331))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1816329, _1816331), tc_prod(_1816329, _1816331)), hAPP(hAPP(c_Product__Type_OPair(_1816329, _1816331), 50840 ^ [_1816329, _1816331, _1816333, _1816335, _1816337, _1816339, _1816341]), 50841 ^ [_1816329, _1816331, _1816333, _1816335, _1816337, _1816339, _1816341])), hAPP(hAPP(c_Product__Type_OPair(_1816329, _1816331), _1816337), _1816339))), c_Transitive__Closure_Ortrancl(tc_prod(_1816329, _1816331), _1816341))))]]], (50847 ^ _780086) ^ [_1817679, _1817681, _1817683, _1817685, _1817687, _1817689, _1817691, _1817693] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1817679, _1817681), tc_prod(_1817679, _1817681))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1817679, _1817681), tc_prod(_1817679, _1817681)), hAPP(hAPP(c_Product__Type_OPair(_1817679, _1817681), _1817683), _1817685)), hAPP(hAPP(c_Product__Type_OPair(_1817679, _1817681), _1817687), _1817689))), c_Transitive__Closure_Ortrancl(tc_prod(_1817679, _1817681), _1817691))), hBOOL(hAPP(hAPP(_1817693, _1817687), _1817689)), 50860 ^ _780086 : [(50861 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1817679, _1817681), tc_prod(_1817679, _1817681))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1817679, _1817681), tc_prod(_1817679, _1817681)), hAPP(hAPP(c_Product__Type_OPair(_1817679, _1817681), 50856 ^ [_1817679, _1817681, _1817683, _1817685, _1817687, _1817689, _1817691, _1817693]), 50857 ^ [_1817679, _1817681, _1817683, _1817685, _1817687, _1817689, _1817691, _1817693])), hAPP(hAPP(c_Product__Type_OPair(_1817679, _1817681), 50858 ^ [_1817679, _1817681, _1817683, _1817685, _1817687, _1817689, _1817691, _1817693]), 50859 ^ [_1817679, _1817681, _1817683, _1817685, _1817687, _1817689, _1817691, _1817693]))), _1817691)))], (50863 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1817679, _1817681), tc_prod(_1817679, _1817681))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1817679, _1817681), tc_prod(_1817679, _1817681)), hAPP(hAPP(c_Product__Type_OPair(_1817679, _1817681), 50858 ^ [_1817679, _1817681, _1817683, _1817685, _1817687, _1817689, _1817691, _1817693]), 50859 ^ [_1817679, _1817681, _1817683, _1817685, _1817687, _1817689, _1817691, _1817693])), hAPP(hAPP(c_Product__Type_OPair(_1817679, _1817681), _1817687), _1817689))), c_Transitive__Closure_Ortrancl(tc_prod(_1817679, _1817681), _1817691))))], (50865 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(_1817693, 50858 ^ [_1817679, _1817681, _1817683, _1817685, _1817687, _1817689, _1817691, _1817693]), 50859 ^ [_1817679, _1817681, _1817683, _1817685, _1817687, _1817689, _1817691, _1817693])))], (50867 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(_1817693, 50856 ^ [_1817679, _1817681, _1817683, _1817685, _1817687, _1817689, _1817691, _1817693]), 50857 ^ [_1817679, _1817681, _1817683, _1817685, _1817687, _1817689, _1817691, _1817693]))]], -(hBOOL(hAPP(hAPP(_1817693, _1817683), _1817685)))], (50871 ^ _780086) ^ [_1820115, _1820117, _1820119, _1820121, _1820123, _1820125] : [50874 ^ _780086 : [(50875 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1820115, _1820115)), hAPP(hAPP(c_Product__Type_OPair(_1820115, _1820115), 50872 ^ [_1820115, _1820117, _1820119, _1820121, _1820123, _1820125]), 50873 ^ [_1820115, _1820117, _1820119, _1820121, _1820123, _1820125])), _1820117)))], (50879 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1820119, _1820119)), hAPP(hAPP(c_Product__Type_OPair(_1820119, _1820119), 50876 ^ [_1820115, _1820117, _1820119, _1820121, _1820123, _1820125]), 50877 ^ [_1820115, _1820117, _1820119, _1820121, _1820123, _1820125])), _1820121)))], (50881 ^ _780086) ^ [] : [hAPP(hAPP(_1820123, 50872 ^ [_1820115, _1820117, _1820119, _1820121, _1820123, _1820125]), 50876 ^ [_1820115, _1820117, _1820119, _1820121, _1820123, _1820125]) = hAPP(hAPP(_1820123, 50873 ^ [_1820115, _1820117, _1820119, _1820121, _1820123, _1820125]), 50877 ^ [_1820115, _1820117, _1820119, _1820121, _1820123, _1820125])]], -(c_Equiv__Relations_Ocongruent2(_1820115, _1820119, _1820125, _1820117, _1820121, _1820123))], (50885 ^ _780086) ^ [_1821382, _1821384, _1821386, _1821388] : [50888 ^ _780086 : [(50889 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1821382, _1821382)), hAPP(hAPP(c_Product__Type_OPair(_1821382, _1821382), 50886 ^ [_1821382, _1821384, _1821386, _1821388]), 50887 ^ [_1821382, _1821384, _1821386, _1821388])), _1821384)))], (50891 ^ _780086) ^ [] : [hAPP(_1821386, 50886 ^ [_1821382, _1821384, _1821386, _1821388]) = hAPP(_1821386, 50887 ^ [_1821382, _1821384, _1821386, _1821388])]], -(c_Equiv__Relations_Ocongruent(_1821382, _1821388, _1821384, _1821386))], (50895 ^ _780086) ^ [_1821985, _1821987, _1821989] : [-(c_Lazy__Sequence_Oflat(_1821985, c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Lazy__Sequence_Olazy__sequence(_1821985), _1821987, _1821989)) = c_Lazy__Sequence_Oappend(_1821985, _1821987, c_Lazy__Sequence_Oflat(_1821985, _1821989)))], (50907 ^ _780086) ^ [_1822522, _1822524, _1822526] : [50909 ^ _780086 : [(50910 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 50908 ^ [_1822522, _1822524, _1822526]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1822524), _1822526))))], (50912 ^ _780086) ^ [] : [hBOOL(hAPP(_1822522, 50908 ^ [_1822522, _1822524, _1822526]))]], -(c_List_Oall__interval__nat(_1822522, _1822524, _1822526))], (50897 ^ _780086) ^ [_1822155, _1822157, _1822159] : [c_List_Oall__interval__nat(_1822155, _1822157, _1822159), 50900 ^ _780086 : [(50901 ^ _780086) ^ [_1822311] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1822311), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1822157), _1822159))), -(hBOOL(hAPP(_1822155, _1822311)))]]], (50916 ^ _780086) ^ [_1822907] : [-(c_Lazy__Sequence_Oflat(_1822907, c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Lazy__Sequence_Olazy__sequence(_1822907))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1822907))], (50918 ^ _780086) ^ [_1823066, _1823068, _1823070] : [c_List_Olist__all(tc_Nat_Onat, _1823066, c_List_Oupt(_1823068, _1823070)), -(c_List_Oall__interval__nat(_1823066, _1823068, _1823070))], (50924 ^ _780086) ^ [_1823244, _1823246, _1823248] : [c_List_Oall__interval__nat(_1823244, _1823246, _1823248), -(c_List_Olist__all(tc_Nat_Onat, _1823244, c_List_Oupt(_1823246, _1823248)))], (50930 ^ _780086) ^ [_1823515, _1823517, _1823519] : [c_List_Olist__ex(tc_Nat_Onat, _1823515, c_List_Oupt(_1823517, _1823519)), c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat, c_fNot), _1823515), _1823517, _1823519)], (50936 ^ _780086) ^ [_1823700, _1823702, _1823704] : [-(c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat, c_fNot), _1823700), _1823702, _1823704)), -(c_List_Olist__ex(tc_Nat_Onat, _1823700, c_List_Oupt(_1823702, _1823704)))], (50942 ^ _780086) ^ [_1823950, _1823952, _1823954, _1823956] : [-(hAPP(c_Lazy__Sequence_Obind(_1823950, _1823952, _1823954), _1823956) = c_Lazy__Sequence_Oflat(_1823952, c_Lazy__Sequence_Omap(_1823950, tc_Lazy__Sequence_Olazy__sequence(_1823952), _1823956, _1823954)))], (50944 ^ _780086) ^ [_1824164, _1824166, _1824168, _1824170, _1824172, _1824174, _1824176, _1824178] : [c_Finite__Set_Ofolding__image(_1824164, _1824166, _1824168, _1824170, _1824172), hBOOL(hAPP(c_Finite__Set_Ofinite(_1824166), _1824174)), 50954 ^ _780086 : [(50955 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1824166), 50953 ^ [_1824164, _1824166, _1824168, _1824170, _1824172, _1824174, _1824176, _1824178]), _1824174)))], (50957 ^ _780086) ^ [] : [hAPP(_1824176, 50953 ^ [_1824164, _1824166, _1824168, _1824170, _1824172, _1824174, _1824176, _1824178]) = hAPP(_1824178, 50953 ^ [_1824164, _1824166, _1824168, _1824170, _1824172, _1824174, _1824176, _1824178])]], -(hAPP(hAPP(_1824172, _1824176), _1824174) = hAPP(hAPP(_1824172, _1824178), _1824174))], (50961 ^ _780086) ^ [_1824964, _1824966, _1824968, _1824970, _1824972] : [-(c_Lazy__Sequence_Omap(_1824964, _1824966, _1824968, c_Lazy__Sequence_Olazy__sequence_OInsert(_1824964, _1824970, _1824972)) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1824966, hAPP(_1824968, _1824970), c_Lazy__Sequence_Omap(_1824964, _1824966, _1824968, _1824972)))], (50963 ^ _780086) ^ [_1825099, _1825101, _1825103] : [-(c_Lazy__Sequence_Omap(_1825099, _1825101, _1825103, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1825099)) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1825101))], (50965 ^ _780086) ^ [_1825246, _1825248, _1825250, _1825252, _1825254] : [-(c_New__DSequence_Opos__map(_1825246, _1825248, _1825250, _1825252, _1825254) = c_Lazy__Sequence_Omap(_1825246, _1825248, _1825250, hAPP(_1825252, _1825254)))], (50967 ^ _780086) ^ [_1825389, _1825391, _1825393] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1825389), _1825391)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1825389), _1825393))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1825389)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1825391), _1825393)))], (50977 ^ _780086) ^ [_1825717] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1825717), _1825717)))], (50979 ^ _780086) ^ [_1825829, _1825831] : [class_Rings_Ocomm__semiring__1(_1825829), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1825829), _1825831), c_Groups_Ozero__class_Ozero(_1825829))))], (50985 ^ _780086) ^ [_1826026] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1826026)))], (50987 ^ _780086) ^ [_1826135, _1826137] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1826135), _1826137)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1826137)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1826135), _1826137)))], (50997 ^ _780086) ^ [_1826472, _1826474, _1826476] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1826472), _1826474)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1826472), _1826476))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1826472)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1826474), _1826476)))], (51007 ^ _780086) ^ [_1826843, _1826845, _1826847] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1826843)), 51010 ^ _780086 : [(51011 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1826843), _1826845)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1826843), _1826847))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1826845), _1826847)))], (51017 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1826845), _1826847)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1826843), _1826845)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1826843), _1826847))))]]], (51023 ^ _780086) ^ [_1827431, _1827433, _1827435, _1827437, _1827439] : [class_Groups_Ocomm__monoid__mult(_1827431), class_Rings_Odvd(_1827431), hBOOL(hAPP(c_Finite__Set_Ofinite(_1827433), _1827435)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1827433, tc_HOL_Obool)), _1827437), _1827435)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827431), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1827433, _1827431), _1827439), _1827437)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1827433, _1827431), _1827439), _1827435))))], (51041 ^ _780086) ^ [_1828066, _1828068, _1828070, _1828072] : [class_Rings_Ocomm__ring(_1828066), class_Rings_Odvd(_1828066), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828066), _1828068), _1828070)), 51052 ^ _780086 : [(51053 ^ _780086) ^ [_1828505, _1828507] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828066), _1828068), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1828066), _1828507), _1828072))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828066), _1828068), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1828066), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1828066), _1828507), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1828066), _1828505), _1828070))), _1828072))))], (51059 ^ _780086) ^ [_1828791, _1828793] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828066), _1828068), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1828066), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1828066), _1828793), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1828066), _1828791), _1828070))), _1828072))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828066), _1828068), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1828066), _1828793), _1828072))))]]], (51065 ^ _780086) ^ [_1829166, _1829168, _1829170, _1829172] : [class_Rings_Ocomm__ring(_1829166), class_Rings_Odvd(_1829166), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1829166), _1829168), _1829170)), 51076 ^ _780086 : [(51077 ^ _780086) ^ [_1829605, _1829607] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1829166), _1829168), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1829166), _1829607), _1829172))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1829166), _1829168), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1829166), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1829166), _1829607), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1829166), _1829605), _1829170))), _1829172))))], (51083 ^ _780086) ^ [_1829891, _1829893] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1829166), _1829168), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1829166), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1829166), _1829893), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1829166), _1829891), _1829170))), _1829172))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1829166), _1829168), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1829166), _1829893), _1829172))))]]], (51089 ^ _780086) ^ [_1830266, _1830268, _1830270, _1830272] : [class_Divides_Osemiring__div(_1830266), -(_1830268 = c_Groups_Ozero__class_Ozero(_1830266)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1830266), _1830268), _1830270)), 51100 ^ _780086 : [(51101 ^ _780086) ^ [] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1830266), _1830270), _1830268) = _1830272, -(_1830270 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1830266), _1830272), _1830268))], (51107 ^ _780086) ^ [] : [_1830270 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1830266), _1830272), _1830268), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1830266), _1830270), _1830268) = _1830272)]]], (51113 ^ _780086) ^ [_1831061, _1831063, _1831065, _1831067, _1831069] : [class_Divides_Osemiring__div(_1831061), -(_1831063 = c_Groups_Ozero__class_Ozero(_1831061)), -(_1831065 = c_Groups_Ozero__class_Ozero(_1831061)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1831061), _1831063), _1831067)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1831061), _1831065), _1831069)), 51132 ^ _780086 : [(51133 ^ _780086) ^ [] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1831061), _1831067), _1831063) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1831061), _1831069), _1831065), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1831061), _1831067), _1831065) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1831061), _1831063), _1831069))], (51139 ^ _780086) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1831061), _1831067), _1831065) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1831061), _1831063), _1831069), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1831061), _1831067), _1831063) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1831061), _1831069), _1831065))]]], (51145 ^ _780086) ^ [_1832123, _1832125, _1832127] : [class_Divides_Osemiring__div(_1832123), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1832123), _1832125), _1832127)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1832123), _1832125), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1832123), _1832127), _1832125)) = _1832127)], (51155 ^ _780086) ^ [_1832504, _1832506, _1832508, _1832510] : [class_Divides_Osemiring__div(_1832504), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1832504), _1832506), _1832508)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1832504), _1832510), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1832504), _1832508), _1832506)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1832504), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1832504), _1832510), _1832508)), _1832506))], (51165 ^ _780086) ^ [_1832913, _1832915, _1832917] : [class_Divides_Osemiring__div(_1832913), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1832913), _1832915), _1832917)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1832913), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1832913), _1832917), _1832915)), _1832915) = _1832917)], (51175 ^ _780086) ^ [_1833294, _1833296, _1833298, _1833300] : [class_Divides_Osemiring__div(_1833294), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1833294), _1833296), _1833298)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1833294), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1833294), _1833298), _1833296)), _1833300) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1833294), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1833294), _1833298), _1833300)), _1833296))], (51185 ^ _780086) ^ [_1833731, _1833733, _1833735, _1833737, _1833739] : [class_Divides_Osemiring__div(_1833731), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1833731), _1833733), _1833735)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1833731), _1833737), _1833739)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1833731), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1833731), _1833735), _1833733)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1833731), _1833739), _1833737)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1833731), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1833731), _1833735), _1833739)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1833731), _1833733), _1833737)))], (51199 ^ _780086) ^ [_1834297, _1834299, _1834301] : [class_Rings_Ocomm__semiring__1(_1834297), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1834297), _1834299), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1834297), _1834299), _1834301))))], (51205 ^ _780086) ^ [_1834555, _1834557, _1834559] : [class_Rings_Ocomm__semiring__1(_1834555), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1834555), _1834557), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1834555), _1834559), _1834557))))], (51211 ^ _780086) ^ [_1834827, _1834829, _1834831, _1834833] : [class_Rings_Ocomm__semiring__1(_1834827), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1834827), _1834829), _1834831)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1834827), _1834829), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1834827), _1834831), _1834833))))], (51221 ^ _780086) ^ [_1835216, _1835218, _1835220, _1835222] : [class_Rings_Ocomm__semiring__1(_1835216), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1835216), _1835218), _1835220)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1835216), _1835218), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1835216), _1835222), _1835220))))], (51231 ^ _780086) ^ [_1835619, _1835621, _1835623, _1835625, _1835627] : [class_Rings_Ocomm__semiring__1(_1835619), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1835619), _1835621), _1835623)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1835619), _1835625), _1835627)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1835619), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1835619), _1835621), _1835625)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1835619), _1835623), _1835627))))], (51245 ^ _780086) ^ [_1836149, _1836151, _1836153, _1836155] : [class_Rings_Odvd(_1836149), _1836151 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1836149), _1836153), _1836155), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1836149), _1836153), _1836151)))], (51255 ^ _780086) ^ [_1836524, _1836526, _1836528, _1836530] : [class_Rings_Ocomm__semiring__1(_1836524), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1836524), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1836524), _1836526), _1836528)), _1836530)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1836524), _1836526), _1836530)))], (51265 ^ _780086) ^ [_1836913, _1836915, _1836917, _1836919] : [class_Rings_Ocomm__semiring__1(_1836913), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1836913), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1836913), _1836915), _1836917)), _1836919)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1836913), _1836917), _1836919)))], (51275 ^ _780086) ^ [_1837302, _1837304, _1837306, _1837308] : [class_Rings_Oidom(_1837302), 51278 ^ _780086 : [(51289 ^ _780086) ^ [] : [51290 ^ _780086 : [(51291 ^ _780086) ^ [] : [_1837304 = c_Groups_Ozero__class_Ozero(_1837302)], (51293 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1837302), _1837306), _1837308))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1837302), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1837302), _1837304), _1837306)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1837302), _1837304), _1837308))))], (51279 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1837302), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1837302), _1837304), _1837306)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1837302), _1837304), _1837308))), -(_1837304 = c_Groups_Ozero__class_Ozero(_1837302)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1837302), _1837306), _1837308)))]]], (51297 ^ _780086) ^ [_1838086, _1838088, _1838090, _1838092] : [class_Rings_Oidom(_1838086), 51300 ^ _780086 : [(51311 ^ _780086) ^ [] : [51312 ^ _780086 : [(51313 ^ _780086) ^ [] : [_1838090 = c_Groups_Ozero__class_Ozero(_1838086)], (51315 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1838086), _1838088), _1838092))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1838086), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1838086), _1838088), _1838090)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1838086), _1838092), _1838090))))], (51301 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1838086), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1838086), _1838088), _1838090)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1838086), _1838092), _1838090))), -(_1838090 = c_Groups_Ozero__class_Ozero(_1838086)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1838086), _1838088), _1838092)))]]], (51329 ^ _780086) ^ [_1839191, _1839193, _1839195] : [51330 ^ _780086 : [(51331 ^ _780086) ^ [] : [_1839191 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (51333 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1839193), _1839195))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1839191), _1839193)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1839191), _1839195))))], (51319 ^ _780086) ^ [_1838885, _1838887, _1838889] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1838885), _1838887)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1838885), _1838889))), -(_1838885 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1838887), _1838889)))], (51337 ^ _780086) ^ [_1839543, _1839545, _1839547] : [class_Rings_Odvd(_1839543), class_Rings_Osemiring__0(_1839543), 51344 ^ _780086 : [(51345 ^ _780086) ^ [] : [51346 ^ _780086 : [(51347 ^ _780086) ^ [_1839862] : [hBOOL(hAPP(_1839545, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1839543), _1839547), _1839862)))]], 51349 ^ _780086 : [(51350 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1839543), _1839547), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1839543), 51348 ^ [_1839543, _1839545, _1839547]), c_Groups_Ozero__class_Ozero(_1839543)))))], (51352 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1839545, 51348 ^ [_1839543, _1839545, _1839547])))]]], (51354 ^ _780086) ^ [] : [-(hBOOL(hAPP(_1839545, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1839543), _1839547), 51361 ^ [_1839543, _1839545, _1839547])))), 51355 ^ _780086 : [(51356 ^ _780086) ^ [_1840222] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1839543), _1839547), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1839543), _1840222), c_Groups_Ozero__class_Ozero(_1839543)))), hBOOL(hAPP(_1839545, _1840222))]]]]], (51365 ^ _780086) ^ [_1840627, _1840629] : [_1840627 = _1840629, -(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1840627, _1840629) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1840627), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (51371 ^ _780086) ^ [_1840830] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1840830, _1840830) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1840830), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (51373 ^ _780086) ^ [_1840991, _1840993, _1840995] : [c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1840991, _1840993) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1840995), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), 51376 ^ _780086 : [(51377 ^ _780086) ^ [] : [-(_1840991 = _1840993)], (51379 ^ _780086) ^ [] : [-(_1840993 = _1840995)]]], (51381 ^ _780086) ^ [_1841258, _1841260, _1841262] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1841258, _1841260) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1841262), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), _1841258 = _1841260, _1841260 = _1841262], (51401 ^ _780086) ^ [_1841907, _1841909] : [51402 ^ _780086 : [(51403 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1841907), _1841909)))], (51405 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1841909), _1841907))]], -(c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1841907, _1841909))], (51391 ^ _780086) ^ [_1841620, _1841622] : [c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1841620, _1841622), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1841620), _1841622)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1841622), _1841620)))], (51419 ^ _780086) ^ [_1842546, _1842548] : [51420 ^ _780086 : [(51421 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1842546), _1842548)))], (51423 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1842548), _1842546))]], -(c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1842546, _1842548))], (51409 ^ _780086) ^ [_1842259, _1842261] : [c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1842259, _1842261), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1842259), _1842261)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1842261), _1842259)))], (51437 ^ _780086) ^ [_1843185, _1843187] : [51438 ^ _780086 : [(51439 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1843185), _1843187)))], (51441 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1843187), _1843185))]], -(c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1843185, _1843187) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (51427 ^ _780086) ^ [_1842898, _1842900] : [c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1842898, _1842900) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1842898), _1842900)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1842900), _1842898)))], (51455 ^ _780086) ^ [_1843824, _1843826] : [51456 ^ _780086 : [(51457 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1843824), _1843826)))], (51459 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1843826), _1843824))]], -(c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1843824, _1843826) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (51445 ^ _780086) ^ [_1843537, _1843539] : [c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1843537, _1843539) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1843537), _1843539)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1843539), _1843537)))], (51463 ^ _780086) ^ [_1844147, _1844149] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1844147), _1844149)), -(c_SetInterval_Oord_OgreaterThanLessThan(tc_Nat_Onat, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1844149, _1844147) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (51469 ^ _780086) ^ [_1844377, _1844379] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1844377), _1844379)), -(c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1844379, _1844377) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (51475 ^ _780086) ^ [_1844609, _1844611] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1844609), _1844611)), -(c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1844611, _1844609) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (51481 ^ _780086) ^ [_1844870, _1844872] : [c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1844870, _1844872), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1844870), _1844872))], (51487 ^ _780086) ^ [_1845053, _1845055] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1845053), _1845055))), -(c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1845053, _1845055))], (51493 ^ _780086) ^ [_1845317, _1845319] : [c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1845317, _1845319) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1845317), _1845319))], (51499 ^ _780086) ^ [_1845500, _1845502] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1845500), _1845502))), -(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1845500, _1845502) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (51505 ^ _780086) ^ [_1845735, _1845737] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1845737, _1845735) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1845735), _1845737)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1845737), _1845735)))], (51515 ^ _780086) ^ [_1846081, _1846083, _1846085] : [class_Divides_Oring__div(_1846081), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1846081), _1846083), _1846085)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1846081), _1846085), hAPP(c_Groups_Ouminus__class_Ouminus(_1846081), _1846083)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1846081), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1846081), _1846085), _1846083)))], (51525 ^ _780086) ^ [_1846468, _1846470, _1846472] : [class_Divides_Oring__div(_1846468), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1846468), _1846470), _1846472)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1846468), hAPP(c_Groups_Ouminus__class_Ouminus(_1846468), _1846472)), _1846470) = hAPP(c_Groups_Ouminus__class_Ouminus(_1846468), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1846468), _1846472), _1846470)))], (51535 ^ _780086) ^ [_1846855, _1846857, _1846859] : [class_Rings_Ocomm__ring__1(_1846855), 51538 ^ _780086 : [(51539 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1846855), hAPP(c_Groups_Ouminus__class_Ouminus(_1846855), _1846857)), _1846859)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1846855), _1846857), _1846859)))], (51545 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1846855), _1846857), _1846859)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1846855), hAPP(c_Groups_Ouminus__class_Ouminus(_1846855), _1846857)), _1846859)))]]], (51551 ^ _780086) ^ [_1847400, _1847402, _1847404] : [class_Rings_Ocomm__ring__1(_1847400), 51554 ^ _780086 : [(51555 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1847400), _1847402), hAPP(c_Groups_Ouminus__class_Ouminus(_1847400), _1847404))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1847400), _1847402), _1847404)))], (51561 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1847400), _1847402), _1847404)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1847400), _1847402), hAPP(c_Groups_Ouminus__class_Ouminus(_1847400), _1847404))))]]], (51567 ^ _780086) ^ [_1847946] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1847946), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_1847946 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (51573 ^ _780086) ^ [_1848112] : [_1848112 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1848112), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (51579 ^ _780086) ^ [_1848342, _1848344, _1848346] : [class_Divides_Osemiring__div(_1848342), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1848342), _1848344), _1848346)), -(c_Divides_Odiv__class_Omod(_1848342, _1848346, _1848344) = c_Groups_Ozero__class_Ozero(_1848342))], (51589 ^ _780086) ^ [_1848689, _1848691, _1848693] : [class_Divides_Osemiring__div(_1848689), 51592 ^ _780086 : [(51593 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1848689), _1848691), _1848693)), -(c_Divides_Odiv__class_Omod(_1848689, _1848693, _1848691) = c_Groups_Ozero__class_Ozero(_1848689))], (51599 ^ _780086) ^ [] : [c_Divides_Odiv__class_Omod(_1848689, _1848693, _1848691) = c_Groups_Ozero__class_Ozero(_1848689), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1848689), _1848691), _1848693)))]]], (51605 ^ _780086) ^ [_1849230, _1849232, _1849234, _1849236] : [class_Divides_Osemiring__div(_1849230), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1849230), _1849232), _1849234)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1849230), _1849232), _1849236)), 51616 ^ _780086 : [(51617 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1849230), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1849230), _1849234), _1849232)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1849230), _1849236), _1849232))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1849230), _1849234), _1849236)))], (51623 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1849230), _1849234), _1849236)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1849230), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1849230), _1849234), _1849232)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1849230), _1849236), _1849232))))]]], (51629 ^ _780086) ^ [_1850032, _1850034] : [class_Rings_Ocomm__semiring__1(_1850032), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1850032), c_Groups_Ozero__class_Ozero(_1850032)), _1850034)), -(_1850034 = c_Groups_Ozero__class_Ozero(_1850032))], (51639 ^ _780086) ^ [_1850379, _1850381, _1850383, _1850385] : [class_Divides_Osemiring__div(_1850379), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1850379), _1850381), c_Divides_Odiv__class_Omod(_1850379, _1850383, _1850385))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1850379), _1850381), _1850385)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1850379), _1850381), _1850383)))], (51653 ^ _780086) ^ [_1850871, _1850873, _1850875, _1850877] : [class_Divides_Osemiring__div(_1850871), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1850871), _1850873), _1850875)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1850871), _1850873), _1850877)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1850871), _1850873), c_Divides_Odiv__class_Omod(_1850871, _1850875, _1850877))))], (51667 ^ _780086) ^ [_1851363, _1851365, _1851367, _1851369] : [class_Divides_Osemiring__div(_1851363), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1851363), _1851365), _1851367)), -(c_Divides_Odiv__class_Omod(_1851363, c_Divides_Odiv__class_Omod(_1851363, _1851369, _1851367), _1851365) = c_Divides_Odiv__class_Omod(_1851363, _1851369, _1851365))], (51677 ^ _780086) ^ [_1851746, _1851748, _1851750, _1851752] : [class_Divides_Osemiring__div(_1851746), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1851746), _1851748), _1851750)), 51684 ^ _780086 : [(51685 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1851746), _1851748), c_Divides_Odiv__class_Omod(_1851746, _1851752, _1851750))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1851746), _1851748), _1851752)))], (51691 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1851746), _1851748), _1851752)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1851746), _1851748), c_Divides_Odiv__class_Omod(_1851746, _1851752, _1851750))))]]], (51697 ^ _780086) ^ [_1852429, _1852431, _1852433, _1852435] : [class_Rings_Ocomm__semiring__1(_1852429), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1852429), _1852431), _1852433)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1852429), _1852433), _1852435)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1852429), _1852431), _1852435)))], (51711 ^ _780086) ^ [_1852885, _1852887] : [class_Rings_Ocomm__semiring__1(_1852885), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1852885), _1852887), _1852887)))], (51717 ^ _780086) ^ [_1853107, _1853109] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1853107), _1853109)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1853109), _1853107))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1853109), _1853107)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1853107), _1853109)))], (51731 ^ _780086) ^ [_1853558, _1853560, _1853562] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1853558), _1853560)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1853560), _1853558))), 51746 ^ _780086 : [(51747 ^ _780086) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1853558), _1853562)))], (51749 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1853562), _1853558))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1853560), _1853562)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1853562), _1853560)))], (51751 ^ _780086) ^ [] : [-(class_Lattices_Obounded__lattice(tc_HOL_Obool))], (51753 ^ _780086) ^ [_1854252, _1854254] : [class_Lattices_Obounded__lattice(_1854252), -(class_Lattices_Obounded__lattice(tc_fun(_1854254, _1854252)))], (51759 ^ _780086) ^ [_1854464, _1854466] : [class_Complete__Lattice_Ocomplete__lattice(_1854464), -(class_Complete__Lattice_Ocomplete__lattice(tc_fun(_1854466, _1854464)))], (51765 ^ _780086) ^ [_1854676, _1854678] : [class_Lattices_Obounded__lattice(_1854676), -(class_Lattices_Obounded__lattice__top(tc_fun(_1854678, _1854676)))], (51771 ^ _780086) ^ [_1854888, _1854890] : [class_Lattices_Obounded__lattice(_1854888), -(class_Lattices_Obounded__lattice__bot(tc_fun(_1854890, _1854888)))], (51777 ^ _780086) ^ [_1855100, _1855102] : [class_Lattices_Olattice(_1855100), -(class_Lattices_Osemilattice__sup(tc_fun(_1855102, _1855100)))], (51783 ^ _780086) ^ [_1855312, _1855314] : [class_Lattices_Olattice(_1855312), -(class_Lattices_Osemilattice__inf(tc_fun(_1855314, _1855312)))], (51789 ^ _780086) ^ [_1855524, _1855526] : [class_Lattices_Odistrib__lattice(_1855524), -(class_Lattices_Odistrib__lattice(tc_fun(_1855526, _1855524)))], (51795 ^ _780086) ^ [_1855736, _1855738] : [class_Lattices_Oboolean__algebra(_1855736), -(class_Lattices_Oboolean__algebra(tc_fun(_1855738, _1855736)))], (51801 ^ _780086) ^ [_1855948, _1855950] : [class_Orderings_Opreorder(_1855948), -(class_Orderings_Opreorder(tc_fun(_1855950, _1855948)))], (51807 ^ _780086) ^ [_1856160, _1856162] : [-(class_Finite__Set_Ofinite(tc_fun(_1856160, _1856162))), class_Finite__Set_Ofinite(_1856160), class_Finite__Set_Ofinite(_1856162)], (51817 ^ _780086) ^ [_1856459, _1856461] : [class_Lattices_Olattice(_1856459), -(class_Lattices_Olattice(tc_fun(_1856461, _1856459)))], (51823 ^ _780086) ^ [_1856671, _1856673] : [class_Orderings_Oorder(_1856671), -(class_Orderings_Oorder(tc_fun(_1856673, _1856671)))], (51829 ^ _780086) ^ [_1856883, _1856885] : [class_Orderings_Otop(_1856883), -(class_Orderings_Otop(tc_fun(_1856885, _1856883)))], (51835 ^ _780086) ^ [_1857095, _1857097] : [class_Orderings_Oord(_1857095), -(class_Orderings_Oord(tc_fun(_1857097, _1857095)))], (51841 ^ _780086) ^ [_1857307, _1857309] : [class_Orderings_Obot(_1857307), -(class_Orderings_Obot(tc_fun(_1857309, _1857307)))], (51847 ^ _780086) ^ [_1857519, _1857521] : [class_Groups_Ouminus(_1857519), -(class_Groups_Ouminus(tc_fun(_1857521, _1857519)))], (51853 ^ _780086) ^ [_1857731, _1857733] : [class_Groups_Ominus(_1857731), -(class_Groups_Ominus(tc_fun(_1857733, _1857731)))], (51859 ^ _780086) ^ [_1857943, _1857945] : [-(class_Enum_Oenum(tc_fun(_1857943, _1857945))), class_Enum_Oenum(_1857943), class_Enum_Oenum(_1857945)], (51869 ^ _780086) ^ [] : [-(class_Nat_Osize(tc_Com_Ocom))], (51871 ^ _780086) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (51873 ^ _780086) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (51875 ^ _780086) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (51877 ^ _780086) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (51879 ^ _780086) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (51881 ^ _780086) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint))], (51883 ^ _780086) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (51885 ^ _780086) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (51887 ^ _780086) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))], (51889 ^ _780086) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (51891 ^ _780086) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (51893 ^ _780086) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (51895 ^ _780086) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (51897 ^ _780086) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (51899 ^ _780086) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (51901 ^ _780086) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (51903 ^ _780086) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (51905 ^ _780086) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (51907 ^ _780086) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (51909 ^ _780086) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (51911 ^ _780086) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (51913 ^ _780086) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (51915 ^ _780086) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint))], (51917 ^ _780086) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Int_Oint))], (51919 ^ _780086) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Int_Oint))], (51921 ^ _780086) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Int_Oint))], (51923 ^ _780086) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (51925 ^ _780086) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (51927 ^ _780086) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (51929 ^ _780086) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (51931 ^ _780086) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_Int_Oint))], (51933 ^ _780086) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (51935 ^ _780086) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (51937 ^ _780086) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (51939 ^ _780086) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (51941 ^ _780086) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (51943 ^ _780086) ^ [] : [-(class_Groups_Osemigroup__add(tc_Int_Oint))], (51945 ^ _780086) ^ [] : [-(class_Divides_Osemiring__div(tc_Int_Oint))], (51947 ^ _780086) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (51949 ^ _780086) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Int_Oint))], (51951 ^ _780086) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (51953 ^ _780086) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (51955 ^ _780086) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (51957 ^ _780086) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (51959 ^ _780086) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (51961 ^ _780086) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (51963 ^ _780086) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (51965 ^ _780086) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (51967 ^ _780086) ^ [] : [-(class_Rings_Osemiring__1(tc_Int_Oint))], (51969 ^ _780086) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (51971 ^ _780086) ^ [] : [-(class_Lattices_Olattice(tc_Int_Oint))], (51973 ^ _780086) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (51975 ^ _780086) ^ [] : [-(class_Divides_Oring__div(tc_Int_Oint))], (51977 ^ _780086) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (51979 ^ _780086) ^ [] : [-(class_Rings_Ocomm__ring(tc_Int_Oint))], (51981 ^ _780086) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (51983 ^ _780086) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (51985 ^ _780086) ^ [] : [-(class_Int_Onumber__ring(tc_Int_Oint))], (51987 ^ _780086) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (51989 ^ _780086) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (51991 ^ _780086) ^ [] : [-(class_Groups_Ouminus(tc_Int_Oint))], (51993 ^ _780086) ^ [] : [-(class_Groups_Osgn__if(tc_Int_Oint))], (51995 ^ _780086) ^ [] : [-(class_Groups_Oabs__if(tc_Int_Oint))], (51997 ^ _780086) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (51999 ^ _780086) ^ [] : [-(class_Groups_Ominus(tc_Int_Oint))], (52001 ^ _780086) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (52003 ^ _780086) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (52005 ^ _780086) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (52007 ^ _780086) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (52009 ^ _780086) ^ [] : [-(class_Int_Onumber(tc_Int_Oint))], (52011 ^ _780086) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (52013 ^ _780086) ^ [] : [-(class_Rings_Odvd(tc_Int_Oint))], (52015 ^ _780086) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (52017 ^ _780086) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (52019 ^ _780086) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (52021 ^ _780086) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (52023 ^ _780086) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat))], (52025 ^ _780086) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (52027 ^ _780086) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (52029 ^ _780086) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (52031 ^ _780086) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (52033 ^ _780086) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (52035 ^ _780086) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (52037 ^ _780086) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (52039 ^ _780086) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (52041 ^ _780086) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (52043 ^ _780086) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Nat_Onat))], (52045 ^ _780086) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Nat_Onat))], (52047 ^ _780086) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Nat_Onat))], (52049 ^ _780086) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (52051 ^ _780086) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (52053 ^ _780086) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (52055 ^ _780086) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (52057 ^ _780086) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (52059 ^ _780086) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (52061 ^ _780086) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (52063 ^ _780086) ^ [] : [-(class_Groups_Osemigroup__add(tc_Nat_Onat))], (52065 ^ _780086) ^ [] : [-(class_Divides_Osemiring__div(tc_Nat_Onat))], (52067 ^ _780086) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (52069 ^ _780086) ^ [] : [-(class_Orderings_Owellorder(tc_Nat_Onat))], (52071 ^ _780086) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Nat_Onat))], (52073 ^ _780086) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (52075 ^ _780086) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (52077 ^ _780086) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (52079 ^ _780086) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (52081 ^ _780086) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (52083 ^ _780086) ^ [] : [-(class_Rings_Osemiring__1(tc_Nat_Onat))], (52085 ^ _780086) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (52087 ^ _780086) ^ [] : [-(class_Lattices_Olattice(tc_Nat_Onat))], (52089 ^ _780086) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (52091 ^ _780086) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (52093 ^ _780086) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (52095 ^ _780086) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (52097 ^ _780086) ^ [] : [-(class_Orderings_Obot(tc_Nat_Onat))], (52099 ^ _780086) ^ [] : [-(class_Groups_Ominus(tc_Nat_Onat))], (52101 ^ _780086) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (52103 ^ _780086) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (52105 ^ _780086) ^ [] : [-(class_Int_Onumber(tc_Nat_Onat))], (52107 ^ _780086) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (52109 ^ _780086) ^ [] : [-(class_Rings_Odvd(tc_Nat_Onat))], (52111 ^ _780086) ^ [] : [-(class_Nat_Osize(tc_Nat_Onat))], (52113 ^ _780086) ^ [] : [-(class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool))], (52115 ^ _780086) ^ [] : [-(class_Lattices_Obounded__lattice__top(tc_HOL_Obool))], (52117 ^ _780086) ^ [] : [-(class_Lattices_Obounded__lattice__bot(tc_HOL_Obool))], (52119 ^ _780086) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_HOL_Obool))], (52121 ^ _780086) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_HOL_Obool))], (52123 ^ _780086) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_HOL_Obool))], (52125 ^ _780086) ^ [] : [-(class_Lattices_Oboolean__algebra(tc_HOL_Obool))], (52127 ^ _780086) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (52129 ^ _780086) ^ [] : [-(class_Finite__Set_Ofinite(tc_HOL_Obool))], (52131 ^ _780086) ^ [] : [-(class_Lattices_Olattice(tc_HOL_Obool))], (52133 ^ _780086) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (52135 ^ _780086) ^ [] : [-(class_Orderings_Otop(tc_HOL_Obool))], (52137 ^ _780086) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (52139 ^ _780086) ^ [] : [-(class_Orderings_Obot(tc_HOL_Obool))], (52141 ^ _780086) ^ [] : [-(class_Groups_Ouminus(tc_HOL_Obool))], (52143 ^ _780086) ^ [] : [-(class_Groups_Ominus(tc_HOL_Obool))], (52145 ^ _780086) ^ [] : [-(class_Enum_Oenum(tc_HOL_Obool))], (52147 ^ _780086) ^ [] : [-(class_Nat_Osize(tc_HOL_Obool))], (52149 ^ _780086) ^ [] : [-(class_Nat_Osize(tc_Com_Ostate))], (52151 ^ _780086) ^ [_1865701] : [class_Lazy__Sequence_Osmall__lazy(_1865701), -(class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(_1865701)))], (52157 ^ _780086) ^ [_1865876] : [-(class_Nat_Osize(tc_List_Olist(_1865876)))], (52159 ^ _780086) ^ [_1865984, _1865986] : [-(class_Finite__Set_Ofinite(tc_sum(_1865984, _1865986))), class_Finite__Set_Ofinite(_1865984), class_Finite__Set_Ofinite(_1865986)], (52169 ^ _780086) ^ [_1866283, _1866285] : [-(class_Enum_Oenum(tc_sum(_1866283, _1866285))), class_Enum_Oenum(_1866283), class_Enum_Oenum(_1866285)], (52179 ^ _780086) ^ [_1866567, _1866569] : [-(class_Nat_Osize(tc_sum(_1866567, _1866569)))], (52181 ^ _780086) ^ [_1866664] : [class_Finite__Set_Ofinite(_1866664), -(class_Finite__Set_Ofinite(tc_Option_Ooption(_1866664)))], (52187 ^ _780086) ^ [_1866854] : [class_Enum_Oenum(_1866854), -(class_Enum_Oenum(tc_Option_Ooption(_1866854)))], (52193 ^ _780086) ^ [_1867029] : [-(class_Nat_Osize(tc_Option_Ooption(_1867029)))], (52195 ^ _780086) ^ [_1867122, _1867124] : [-(class_Nat_Osize(tc_Nitpick_Opair__box(_1867122, _1867124)))], (52197 ^ _780086) ^ [_1867233, _1867235] : [-(class_Lazy__Sequence_Osmall__lazy(tc_prod(_1867233, _1867235))), class_Lazy__Sequence_Osmall__lazy(_1867233), class_Lazy__Sequence_Osmall__lazy(_1867235)], (52207 ^ _780086) ^ [_1867532, _1867534] : [-(class_Finite__Set_Ofinite(tc_prod(_1867532, _1867534))), class_Finite__Set_Ofinite(_1867532), class_Finite__Set_Ofinite(_1867534)], (52217 ^ _780086) ^ [_1867831, _1867833] : [-(class_Enum_Oenum(tc_prod(_1867831, _1867833))), class_Enum_Oenum(_1867831), class_Enum_Oenum(_1867833)], (52227 ^ _780086) ^ [_1868115, _1868117] : [-(class_Nat_Osize(tc_prod(_1868115, _1868117)))], (52229 ^ _780086) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit))], (52231 ^ _780086) ^ [] : [-(class_Finite__Set_Ofinite(tc_Product__Type_Ounit))], (52233 ^ _780086) ^ [] : [-(class_Enum_Oenum(tc_Product__Type_Ounit))], (52235 ^ _780086) ^ [] : [-(class_Nat_Osize(tc_Product__Type_Ounit))], (52237 ^ _780086) ^ [] : [-(class_Nat_Osize(tc_Code__Evaluation_Oterm))], (52239 ^ _780086) ^ [_1868462] : [-(class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(_1868462)))], (52241 ^ _780086) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52243 ^ _780086) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral))], (52245 ^ _780086) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (52247 ^ _780086) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52249 ^ _780086) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (52251 ^ _780086) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52253 ^ _780086) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (52255 ^ _780086) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52257 ^ _780086) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral))], (52259 ^ _780086) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral))], (52261 ^ _780086) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52263 ^ _780086) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral))], (52265 ^ _780086) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral))], (52267 ^ _780086) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral))], (52269 ^ _780086) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral))], (52271 ^ _780086) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52273 ^ _780086) ^ [] : [-(class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral))], (52275 ^ _780086) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral))], (52277 ^ _780086) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (52279 ^ _780086) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral))], (52281 ^ _780086) ^ [] : [-(class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral))], (52283 ^ _780086) ^ [] : [-(class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral))], (52285 ^ _780086) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral))], (52287 ^ _780086) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral))], (52289 ^ _780086) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral))], (52291 ^ _780086) ^ [] : [-(class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral))], (52293 ^ _780086) ^ [] : [-(class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral))], (52295 ^ _780086) ^ [] : [-(class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral))], (52297 ^ _780086) ^ [] : [-(class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral))], (52299 ^ _780086) ^ [] : [-(class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral))], (52301 ^ _780086) ^ [] : [-(class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral))], (52303 ^ _780086) ^ [] : [-(class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral))], (52305 ^ _780086) ^ [] : [-(class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral))], (52307 ^ _780086) ^ [] : [-(class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral))], (52309 ^ _780086) ^ [] : [-(class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral))], (52311 ^ _780086) ^ [] : [-(class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral))], (52313 ^ _780086) ^ [] : [-(class_Power_Opower(tc_Code__Numeral_Ocode__numeral))], (52315 ^ _780086) ^ [] : [-(class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral))], (52317 ^ _780086) ^ [] : [-(class_Int_Onumber(tc_Code__Numeral_Ocode__numeral))], (52319 ^ _780086) ^ [] : [-(class_Groups_Oone(tc_Code__Numeral_Ocode__numeral))], (52321 ^ _780086) ^ [] : [-(class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral))], (52323 ^ _780086) ^ [] : [-(class_Nat_Osize(tc_Code__Numeral_Ocode__numeral))], (52325 ^ _780086) ^ [_1870767] : [-(class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(_1870767)))], (52327 ^ _780086) ^ [_1870860, _1870862] : [-(hAPP(c_COMBI(_1870860), _1870862) = _1870862)], (52329 ^ _780086) ^ [_1870987, _1870989, _1870991, _1870993] : [-(hAPP(hAPP(c_COMBK(_1870987, _1870989), _1870991), _1870993) = _1870991)], (52331 ^ _780086) ^ [_1871150, _1871152, _1871154, _1871156, _1871158, _1871160] : [-(hAPP(hAPP(hAPP(c_COMBB(_1871150, _1871152, _1871154), _1871156), _1871158), _1871160) = hAPP(_1871156, hAPP(_1871158, _1871160)))], (52333 ^ _780086) ^ [_1871327, _1871329, _1871331, _1871333, _1871335, _1871337] : [-(hAPP(hAPP(hAPP(c_COMBC(_1871327, _1871329, _1871331), _1871333), _1871335), _1871337) = hAPP(hAPP(_1871333, _1871337), _1871335))], (52335 ^ _780086) ^ [_1871504, _1871506, _1871508, _1871510, _1871512, _1871514] : [-(hAPP(hAPP(hAPP(c_COMBS(_1871504, _1871506, _1871508), _1871510), _1871512), _1871514) = hAPP(hAPP(_1871510, _1871514), hAPP(_1871512, _1871514)))], (52337 ^ _780086) ^ [_1871643, _1871645] : [hBOOL(hAPP(hAPP(c_fequal, _1871643), _1871645)), -(_1871643 = _1871645)], (52343 ^ _780086) ^ [_1871865, _1871867] : [_1871865 = _1871867, -(hBOOL(hAPP(hAPP(c_fequal, _1871865), _1871867)))], (52349 ^ _780086) ^ [] : [hBOOL(c_fFalse)], (52351 ^ _780086) ^ [] : [-(hBOOL(c_fTrue))], (52353 ^ _780086) ^ [_1872178] : [hBOOL(hAPP(c_fNot, _1872178)), hBOOL(_1872178)], (52359 ^ _780086) ^ [_1872373] : [-(hBOOL(_1872373)), -(hBOOL(hAPP(c_fNot, _1872373)))], (52365 ^ _780086) ^ [_1872584, _1872586] : [hBOOL(_1872584), hBOOL(_1872586), -(hBOOL(hAPP(hAPP(c_fconj, _1872584), _1872586)))], (52375 ^ _780086) ^ [_1872893, _1872895] : [hBOOL(hAPP(hAPP(c_fconj, _1872893), _1872895)), -(hBOOL(_1872893))], (52381 ^ _780086) ^ [_1873113, _1873115] : [hBOOL(hAPP(hAPP(c_fconj, _1873113), _1873115)), -(hBOOL(_1873115))], (52387 ^ _780086) ^ [_1873333, _1873335] : [hBOOL(_1873333), -(hBOOL(hAPP(hAPP(c_fdisj, _1873333), _1873335)))], (52393 ^ _780086) ^ [_1873553, _1873555] : [hBOOL(_1873553), -(hBOOL(hAPP(hAPP(c_fdisj, _1873555), _1873553)))], (52399 ^ _780086) ^ [_1873773, _1873775] : [hBOOL(hAPP(hAPP(c_fdisj, _1873773), _1873775)), -(hBOOL(_1873773)), -(hBOOL(_1873775))], (52409 ^ _780086) ^ [_1874081, _1874083] : [-(hBOOL(_1874081)), -(hBOOL(hAPP(hAPP(c_fimplies, _1874081), _1874083)))], (52415 ^ _780086) ^ [_1874300, _1874302] : [hBOOL(_1874300), -(hBOOL(hAPP(hAPP(c_fimplies, _1874302), _1874300)))], (52421 ^ _780086) ^ [_1874520, _1874522] : [hBOOL(hAPP(hAPP(c_fimplies, _1874520), _1874522)), hBOOL(_1874520), -(hBOOL(_1874522))], (52431 ^ _780086) ^ [_1874815] : [c_Hoare__Mirabelle_Ohoare__derivs(t_b, v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b), hAPP(v_P_H, _1874815)), hAPP(v_c0, _1874815)), hAPP(v_Q_H, _1874815))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(t_b, v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b), hAPP(v_P, _1874815)), hAPP(v_c0, _1874815)), hAPP(v_Q, _1874815))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b), tc_HOL_Obool)))))], (52437 ^ _780086) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(t_a), v_F)))], (52439 ^ _780086) ^ [] : [hBOOL(hAPP(hAPP(c_member(t_a), v_x), v_F))], (52447 ^ _780086) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(t_b, v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b), hAPP(v_P_H, v_x)), hAPP(v_c0, v_x)), hAPP(v_Q_H, v_x))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b), tc_HOL_Obool)))))], (52449 ^ _780086) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(t_b, v_G, hAPP(c_Set_Oimage(t_a, tc_Hoare__Mirabelle_Otriple(t_b), hAPP(hAPP(c_COMBS(t_a, tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_b)), hAPP(hAPP(c_COMBS(t_a, tc_Com_Ocom, tc_fun(tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_b))), hAPP(hAPP(c_COMBB(tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_b))), t_a), c_Hoare__Mirabelle_Otriple_Otriple(t_b)), v_P_H)), v_c0)), v_Q_H)), v_F)))], (52441 ^ _780086) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(t_b, v_G, hAPP(c_Set_Oimage(t_a, tc_Hoare__Mirabelle_Otriple(t_b), hAPP(hAPP(c_COMBS(t_a, tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_b)), hAPP(hAPP(c_COMBS(t_a, tc_Com_Ocom, tc_fun(tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_b))), hAPP(hAPP(c_COMBB(tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_b))), t_a), c_Hoare__Mirabelle_Otriple_Otriple(t_b)), v_P_H)), v_c0)), v_Q_H)), v_F)), -(c_Hoare__Mirabelle_Ohoare__derivs(t_b, v_G, hAPP(c_Set_Oimage(t_a, tc_Hoare__Mirabelle_Otriple(t_b), hAPP(hAPP(c_COMBS(t_a, tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_b)), hAPP(hAPP(c_COMBS(t_a, tc_Com_Ocom, tc_fun(tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_b))), hAPP(hAPP(c_COMBB(tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_b))), t_a), c_Hoare__Mirabelle_Otriple_Otriple(t_b)), v_P)), v_c0)), v_Q)), v_F)))]], input).
% 1.88/2.50  ncf('1',plain,[c_Hoare__Mirabelle_Ohoare__derivs(t_b, v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b), hAPP(v_P, v_x)), hAPP(v_c0, v_x)), hAPP(v_Q, v_x))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b), tc_HOL_Obool))))],start(52451 ^ 0)).
% 1.88/2.50  ncf('1.1',plain,[-(c_Hoare__Mirabelle_Ohoare__derivs(t_b, v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b), hAPP(v_P, v_x)), hAPP(v_c0, v_x)), hAPP(v_Q, v_x))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b), tc_HOL_Obool))))), c_Hoare__Mirabelle_Ohoare__derivs(t_b, v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b), hAPP(v_P_H, v_x)), hAPP(v_c0, v_x)), hAPP(v_Q_H, v_x))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b), tc_HOL_Obool))))],extension(52431 ^ 1,bind([[_1874815], [v_x]]))).
% 1.88/2.50  ncf('1.1.1',plain,[-(c_Hoare__Mirabelle_Ohoare__derivs(t_b, v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b), hAPP(v_P_H, v_x)), hAPP(v_c0, v_x)), hAPP(v_Q_H, v_x))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b), tc_HOL_Obool)))))],extension(52447 ^ 2)).
% 1.88/2.50  %-----------------------------------------------------
% 1.88/2.50  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------